definition travel through time

Is Time Travel Possible?

We all travel in time! We travel one year in time between birthdays, for example. And we are all traveling in time at approximately the same speed: 1 second per second.

We typically experience time at one second per second. Credit: NASA/JPL-Caltech

NASA's space telescopes also give us a way to look back in time. Telescopes help us see stars and galaxies that are very far away . It takes a long time for the light from faraway galaxies to reach us. So, when we look into the sky with a telescope, we are seeing what those stars and galaxies looked like a very long time ago.

However, when we think of the phrase "time travel," we are usually thinking of traveling faster than 1 second per second. That kind of time travel sounds like something you'd only see in movies or science fiction books. Could it be real? Science says yes!

This image from the Hubble Space Telescope shows galaxies that are very far away as they existed a very long time ago. Credit: NASA, ESA and R. Thompson (Univ. Arizona)

How do we know that time travel is possible?

More than 100 years ago, a famous scientist named Albert Einstein came up with an idea about how time works. He called it relativity. This theory says that time and space are linked together. Einstein also said our universe has a speed limit: nothing can travel faster than the speed of light (186,000 miles per second).

Einstein's theory of relativity says that space and time are linked together. Credit: NASA/JPL-Caltech

What does this mean for time travel? Well, according to this theory, the faster you travel, the slower you experience time. Scientists have done some experiments to show that this is true.

For example, there was an experiment that used two clocks set to the exact same time. One clock stayed on Earth, while the other flew in an airplane (going in the same direction Earth rotates).

After the airplane flew around the world, scientists compared the two clocks. The clock on the fast-moving airplane was slightly behind the clock on the ground. So, the clock on the airplane was traveling slightly slower in time than 1 second per second.

Credit: NASA/JPL-Caltech

Can we use time travel in everyday life?

We can't use a time machine to travel hundreds of years into the past or future. That kind of time travel only happens in books and movies. But the math of time travel does affect the things we use every day.

For example, we use GPS satellites to help us figure out how to get to new places. (Check out our video about how GPS satellites work .) NASA scientists also use a high-accuracy version of GPS to keep track of where satellites are in space. But did you know that GPS relies on time-travel calculations to help you get around town?

GPS satellites orbit around Earth very quickly at about 8,700 miles (14,000 kilometers) per hour. This slows down GPS satellite clocks by a small fraction of a second (similar to the airplane example above).

GPS satellites orbit around Earth at about 8,700 miles (14,000 kilometers) per hour. Credit: GPS.gov

However, the satellites are also orbiting Earth about 12,550 miles (20,200 km) above the surface. This actually speeds up GPS satellite clocks by a slighter larger fraction of a second.

Here's how: Einstein's theory also says that gravity curves space and time, causing the passage of time to slow down. High up where the satellites orbit, Earth's gravity is much weaker. This causes the clocks on GPS satellites to run faster than clocks on the ground.

The combined result is that the clocks on GPS satellites experience time at a rate slightly faster than 1 second per second. Luckily, scientists can use math to correct these differences in time.

If scientists didn't correct the GPS clocks, there would be big problems. GPS satellites wouldn't be able to correctly calculate their position or yours. The errors would add up to a few miles each day, which is a big deal. GPS maps might think your home is nowhere near where it actually is!

In Summary:

Yes, time travel is indeed a real thing. But it's not quite what you've probably seen in the movies. Under certain conditions, it is possible to experience time passing at a different rate than 1 second per second. And there are important reasons why we need to understand this real-world form of time travel.

If you liked this, you may like:

Time travel: Is it possible?

Science says time travel is possible, but probably not in the way you're thinking.

Albert Einstein's theory

• General relativity and GPS
• Wormhole travel
• Alternate theories

Science fiction

Is time travel possible? Short answer: Yes, and you're doing it right now — hurtling into the future at the impressive rate of one second per second. 

You're pretty much always moving through time at the same speed, whether you're watching paint dry or wishing you had more hours to visit with a friend from out of town. 

But this isn't the kind of time travel that's captivated countless science fiction writers, or spurred a genre so extensive that Wikipedia lists over 400 titles in the category "Movies about Time Travel." In franchises like " Doctor Who ," " Star Trek ," and "Back to the Future" characters climb into some wild vehicle to blast into the past or spin into the future. Once the characters have traveled through time, they grapple with what happens if you change the past or present based on information from the future (which is where time travel stories intersect with the idea of parallel universes or alternate timelines). 

Related: The best sci-fi time machines ever

Although many people are fascinated by the idea of changing the past or seeing the future before it's due, no person has ever demonstrated the kind of back-and-forth time travel seen in science fiction or proposed a method of sending a person through significant periods of time that wouldn't destroy them on the way. And, as physicist Stephen Hawking pointed out in his book " Black Holes and Baby Universes" (Bantam, 1994), "The best evidence we have that time travel is not possible, and never will be, is that we have not been invaded by hordes of tourists from the future."

Science does support some amount of time-bending, though. For example, physicist Albert Einstein 's theory of special relativity proposes that time is an illusion that moves relative to an observer. An observer traveling near the speed of light will experience time, with all its aftereffects (boredom, aging, etc.) much more slowly than an observer at rest. That's why astronaut Scott Kelly aged ever so slightly less over the course of a year in orbit than his twin brother who stayed here on Earth. 

Related: Controversially, physicist argues that time is real

There are other scientific theories about time travel, including some weird physics that arise around wormholes , black holes and string theory . For the most part, though, time travel remains the domain of an ever-growing array of science fiction books, movies, television shows, comics, video games and more. 

Einstein developed his theory of special relativity in 1905. Along with his later expansion, the theory of general relativity , it has become one of the foundational tenets of modern physics. Special relativity describes the relationship between space and time for objects moving at constant speeds in a straight line. 

The short version of the theory is deceptively simple. First, all things are measured in relation to something else — that is to say, there is no "absolute" frame of reference. Second, the speed of light is constant. It stays the same no matter what, and no matter where it's measured from. And third, nothing can go faster than the speed of light.

From those simple tenets unfolds actual, real-life time travel. An observer traveling at high velocity will experience time at a slower rate than an observer who isn't speeding through space. 

While we don't accelerate humans to near-light-speed, we do send them swinging around the planet at 17,500 mph (28,160 km/h) aboard the International Space Station . Astronaut Scott Kelly was born after his twin brother, and fellow astronaut, Mark Kelly . Scott Kelly spent 520 days in orbit, while Mark logged 54 days in space. The difference in the speed at which they experienced time over the course of their lifetimes has actually widened the age gap between the two men.

"So, where[as] I used to be just 6 minutes older, now I am 6 minutes and 5 milliseconds older," Mark Kelly said in a panel discussion on July 12, 2020, Space.com previously reported . "Now I've got that over his head."

General relativity and GPS time travel

The difference that low earth orbit makes in an astronaut's life span may be negligible — better suited for jokes among siblings than actual life extension or visiting the distant future — but the dilation in time between people on Earth and GPS satellites flying through space does make a difference. 

Read more: Can we stop time?

The Global Positioning System , or GPS, helps us know exactly where we are by communicating with a network of a few dozen satellites positioned in a high Earth orbit. The satellites circle the planet from 12,500 miles (20,100 kilometers) away, moving at 8,700 mph (14,000 km/h). 

According to special relativity, the faster an object moves relative to another object, the slower that first object experiences time. For GPS satellites with atomic clocks, this effect cuts 7 microseconds, or 7 millionths of a second, off each day, according to the American Physical Society publication Physics Central .  

Read more: Could Star Trek's faster-than-light warp drive actually work?

Then, according to general relativity, clocks closer to the center of a large gravitational mass like Earth tick more slowly than those farther away. So, because the GPS satellites are much farther from the center of Earth compared to clocks on the surface, Physics Central added, that adds another 45 microseconds onto the GPS satellite clocks each day. Combined with the negative 7 microseconds from the special relativity calculation, the net result is an added 38 microseconds. 

This means that in order to maintain the accuracy needed to pinpoint your car or phone — or, since the system is run by the U.S. Department of Defense, a military drone — engineers must account for an extra 38 microseconds in each satellite's day. The atomic clocks onboard don’t tick over to the next day until they have run 38 microseconds longer than comparable clocks on Earth.

Given those numbers, it would take more than seven years for the atomic clock in a GPS satellite to un-sync itself from an Earth clock by more than a blink of an eye. (We did the math: If you estimate a blink to last at least 100,000 microseconds, as the Harvard Database of Useful Biological Numbers does, it would take thousands of days for those 38 microsecond shifts to add up.) 

This kind of time travel may seem as negligible as the Kelly brothers' age gap, but given the hyper-accuracy of modern GPS technology, it actually does matter. If it can communicate with the satellites whizzing overhead, your phone can nail down your location in space and time with incredible accuracy. 

Can wormholes take us back in time?

General relativity might also provide scenarios that could allow travelers to go back in time, according to NASA . But the physical reality of those time-travel methods is no piece of cake. 

Wormholes are theoretical "tunnels" through the fabric of space-time that could connect different moments or locations in reality to others. Also known as Einstein-Rosen bridges or white holes, as opposed to black holes, speculation about wormholes abounds. But despite taking up a lot of space (or space-time) in science fiction, no wormholes of any kind have been identified in real life. 

Related: Best time travel movies

"The whole thing is very hypothetical at this point," Stephen Hsu, a professor of theoretical physics at the University of Oregon, told Space.com sister site Live Science . "No one thinks we're going to find a wormhole anytime soon."

Primordial wormholes are predicted to be just 10^-34 inches (10^-33 centimeters) at the tunnel's "mouth". Previously, they were expected to be too unstable for anything to be able to travel through them. However, a study claims that this is not the case, Live Science reported . 

The theory, which suggests that wormholes could work as viable space-time shortcuts, was described by physicist Pascal Koiran. As part of the study, Koiran used the Eddington-Finkelstein metric, as opposed to the Schwarzschild metric which has been used in the majority of previous analyses.

In the past, the path of a particle could not be traced through a hypothetical wormhole. However, using the Eddington-Finkelstein metric, the physicist was able to achieve just that.

Koiran's paper was described in October 2021, in the preprint database arXiv , before being published in the Journal of Modern Physics D.

Alternate time travel theories

While Einstein's theories appear to make time travel difficult, some researchers have proposed other solutions that could allow jumps back and forth in time. These alternate theories share one major flaw: As far as scientists can tell, there's no way a person could survive the kind of gravitational pulling and pushing that each solution requires.

Infinite cylinder theory

Astronomer Frank Tipler proposed a mechanism (sometimes known as a Tipler Cylinder ) where one could take matter that is 10 times the sun's mass, then roll it into a very long, but very dense cylinder. The Anderson Institute , a time travel research organization, described the cylinder as "a black hole that has passed through a spaghetti factory."

After spinning this black hole spaghetti a few billion revolutions per minute, a spaceship nearby — following a very precise spiral around the cylinder — could travel backward in time on a "closed, time-like curve," according to the Anderson Institute. 

The major problem is that in order for the Tipler Cylinder to become reality, the cylinder would need to be infinitely long or be made of some unknown kind of matter. At least for the foreseeable future, endless interstellar pasta is beyond our reach.

Time donuts

Theoretical physicist Amos Ori at the Technion-Israel Institute of Technology in Haifa, Israel, proposed a model for a time machine made out of curved space-time — a donut-shaped vacuum surrounded by a sphere of normal matter.

"The machine is space-time itself," Ori told Live Science . "If we were to create an area with a warp like this in space that would enable time lines to close on themselves, it might enable future generations to return to visit our time."

Amos Ori is a theoretical physicist at the Technion-Israel Institute of Technology in Haifa, Israel. His research interests and publications span the fields of general relativity, black holes, gravitational waves and closed time lines.

There are a few caveats to Ori's time machine. First, visitors to the past wouldn't be able to travel to times earlier than the invention and construction of the time donut. Second, and more importantly, the invention and construction of this machine would depend on our ability to manipulate gravitational fields at will — a feat that may be theoretically possible but is certainly beyond our immediate reach.

Time travel has long occupied a significant place in fiction. Since as early as the "Mahabharata," an ancient Sanskrit epic poem compiled around 400 B.C., humans have dreamed of warping time, Lisa Yaszek, a professor of science fiction studies at the Georgia Institute of Technology in Atlanta, told Live Science .  

Every work of time-travel fiction creates its own version of space-time, glossing over one or more scientific hurdles and paradoxes to achieve its plot requirements. 

Some make a nod to research and physics, like " Interstellar ," a 2014 film directed by Christopher Nolan. In the movie, a character played by Matthew McConaughey spends a few hours on a planet orbiting a supermassive black hole, but because of time dilation, observers on Earth experience those hours as a matter of decades. 

Others take a more whimsical approach, like the "Doctor Who" television series. The series features the Doctor, an extraterrestrial "Time Lord" who travels in a spaceship resembling a blue British police box. "People assume," the Doctor explained in the show, "that time is a strict progression from cause to effect, but actually from a non-linear, non-subjective viewpoint, it's more like a big ball of wibbly-wobbly, timey-wimey stuff." 

Long-standing franchises like the "Star Trek" movies and television series, as well as comic universes like DC and Marvel Comics, revisit the idea of time travel over and over. 

Related: Marvel movies in order: chronological & release order

Here is an incomplete (and deeply subjective) list of some influential or notable works of time travel fiction:

Books about time travel:

• Rip Van Winkle (Cornelius S. Van Winkle, 1819) by Washington Irving
• A Christmas Carol (Chapman & Hall, 1843) by Charles Dickens
• The Time Machine (William Heinemann, 1895) by H. G. Wells
• A Connecticut Yankee in King Arthur's Court (Charles L. Webster and Co., 1889) by Mark Twain
• The Restaurant at the End of the Universe (Pan Books, 1980) by Douglas Adams
• A Tale of Time City (Methuen, 1987) by Diana Wynn Jones
• The Outlander series (Delacorte Press, 1991-present) by Diana Gabaldon
• Harry Potter and the Prisoner of Azkaban (Bloomsbury/Scholastic, 1999) by J. K. Rowling
• Thief of Time (Doubleday, 2001) by Terry Pratchett
• The Time Traveler's Wife (MacAdam/Cage, 2003) by Audrey Niffenegger
• All You Need is Kill (Shueisha, 2004) by Hiroshi Sakurazaka

Movies about time travel:

• Planet of the Apes (1968)
• Superman (1978)
• Time Bandits (1981)
• The Terminator (1984)
• Back to the Future series (1985, 1989, 1990)
• Star Trek IV: The Voyage Home (1986)
• Bill & Ted's Excellent Adventure (1989)
• Groundhog Day (1993)
• Galaxy Quest (1999)
• The Butterfly Effect (2004)
• 13 Going on 30 (2004)
• The Lake House (2006)
• Meet the Robinsons (2007)
• Hot Tub Time Machine (2010)
• Midnight in Paris (2011)
• Looper (2012)
• X-Men: Days of Future Past (2014)
• Edge of Tomorrow (2014)
• Interstellar (2014)
• Doctor Strange (2016)
• A Wrinkle in Time (2018)
• The Last Sharknado: It's About Time (2018)
• Avengers: Endgame (2019)
• Tenet (2020)
• Palm Springs (2020)
• Zach Snyder's Justice League (2021)
• The Tomorrow War (2021)

Television about time travel:

• Doctor Who (1963-present)
• The Twilight Zone (1959-1964) (multiple episodes)
• Star Trek (multiple series, multiple episodes)
• Samurai Jack (2001-2004)
• Lost (2004-2010)
• Phil of the Future (2004-2006)
• Steins;Gate (2011)
• Outlander (2014-2023)
• Loki (2021-present)

Games about time travel:

• Chrono Trigger (1995)
• TimeSplitters (2000-2005)
• Kingdom Hearts (2002-2019)
• Prince of Persia: Sands of Time (2003)
• God of War II (2007)
• Ratchet and Clank Future: A Crack In Time (2009)
• Sly Cooper: Thieves in Time (2013)
• Dishonored 2 (2016)
• Titanfall 2 (2016)
• Outer Wilds (2019)

Additional resources

Explore physicist Peter Millington's thoughts about Stephen Hawking's time travel theories at The Conversation . Check out a kid-friendly explanation of real-world time travel from NASA's Space Place . For an overview of time travel in fiction and the collective consciousness, read " Time Travel: A History " (Pantheon, 2016) by James Gleik. 

Join our Space Forums to keep talking space on the latest missions, night sky and more! And if you have a news tip, correction or comment, let us know at: [email protected].

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Ailsa is a staff writer for How It Works magazine, where she writes science, technology, space, history and environment features. Based in the U.K., she graduated from the University of Stirling with a BA (Hons) journalism degree. Previously, Ailsa has written for Cardiff Times magazine, Psychology Now and numerous science bookazines. 

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Where Does the Concept of Time Travel Come From?

Time; he's waiting in the wings.

The dream of traveling through time is both ancient and universal. But where did humanity's fascination with time travel begin, and why is the idea so appealing?

The concept of time travel — moving through time the way we move through three-dimensional space — may in fact be hardwired into our perception of time . Linguists have recognized that we are essentially incapable of talking about temporal matters without referencing spatial ones. "In language — any language — no two domains are more intimately linked than space and time," wrote Israeli linguist Guy Deutscher in his 2005 book "The Unfolding of Language." "Even if we are not always aware of it, we invariably speak of time in terms of space, and this reflects the fact that we think of time in terms of space."

Deutscher reminds us that when we plan to meet a friend "around" lunchtime, we are using a metaphor, since lunchtime doesn't have any physical sides. He similarly points out that time can not literally be "long" or "short" like a stick, nor "pass" like a train, or even go "forward" or "backward" any more than it goes sideways, diagonal or down.

Related: Why Does Time Fly When You're Having Fun?

Perhaps because of this connection between space and time, the possibility that time can be experienced in different ways and traveled through has surprisingly early roots. One of the first known examples of time travel appears in the Mahabharata, an ancient Sanskrit epic poem compiled around 400 B.C., Lisa Yaszek, a professor of science fiction studies at the Georgia Institute of Technology in Atlanta, told Live Science 

In the Mahabharata is a story about King Kakudmi, who lived millions of years ago and sought a suitable husband for his beautiful and accomplished daughter, Revati. The two travel to the home of the creator god Brahma to ask for advice. But while in Brahma's plane of existence, they must wait as the god listens to a 20-minute song, after which Brahma explains that time moves differently in the heavens than on Earth. It turned out that "27 chatur-yugas" had passed, or more than 116 million years, according to an online summary , and so everyone Kakudmi and Revati had ever known, including family members and potential suitors, was dead. After this shock, the story closes on a somewhat happy ending in that Revati is betrothed to Balarama, twin brother of the deity Krishna. 

Time is fleeting

To Yaszek, the tale provides an example of what we now call time dilation , in which different observers measure different lengths of time based on their relative frames of reference, a part of Einstein's theory of relativity.

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Such time-slip stories are widespread throughout the world, Yaszek said, citing a Middle Eastern tale from the first century BCE about a Jewish miracle worker who sleeps beneath a newly-planted carob tree and wakes up 70 years later to find it has now matured and borne fruit (carob trees are notorious for how long they take to produce their first harvest). Another instance can be found in an eighth-century Japanese fable about a fisherman named Urashima Tarō who travels to an undersea palace and falls in love with a princess. Tarō finds that, when he returns home, 100 years have passed, according to a translation of the tale published online by the University of South Florida . 

In the early-modern era of the 1700 and 1800s, the sleep-story version of time travel grew more popular, Yaszek said. Examples include the classic tale of Rip Van Winkle, as well as books like Edward Belamy's utopian 1888 novel "Looking Backwards," in which a man wakes up in the year 2000, and the H.G. Wells 1899 novel "The Sleeper Awakes," about a man who slumbers for centuries and wakes to a completely transformed London. 

Related: Science Fiction or Fact: Is Time Travel Possible ?

In other stories from this period, people also start to be able to move backward in time. In Mark Twain’s 1889 satire "A Connecticut Yankee in King Arthur's Court," a blow to the head propels an engineer back to the reign of the legendary British monarch. Objects that can send someone through time begin to appear as well, mainly clocks, such as in Edward Page Mitchell's 1881 story "The Clock that Went Backwards" or Lewis Carrol's 1889 children's fantasy "Sylvie and Bruno," where the characters possess a watch that is a type of time machine . 

The explosion of such stories during this era might come from the fact that people were "beginning to standardize time, and orient themselves to clocks more frequently," Yaszek said. 

Time after time

Wells provided one of the most enduring time-travel plots in his 1895 novella "The Time Machine," which included the innovation of a craft that can move forward and backward through long spans of time. "This is when we’re getting steam engines and trains and the first automobiles," Yaszek said. "I think it’s no surprise that Wells suddenly thinks: 'Hey, maybe we can use a vehicle to travel through time.'"

Because it is such a rich visual icon, many beloved time-travel stories written after this have included a striking time machine, Yaszek said, referencing The Doctor's blue police box — the TARDIS — in the long-running BBC series "Doctor Who," and "Back to the Future"'s silver luxury speedster, the DeLorean . 

More recently, time travel has been used to examine our relationship with the past, Yaszek said, in particular in pieces written by women and people of color. Octavia Butler's 1979 novel "Kindred" about a modern woman who visits her pre-Civil-War ancestors is "a marvelous story that really asks us to rethink black and white relations through history," she said. And a contemporary web series called " Send Me " involves an African-American psychic who can guide people back to antebellum times and witness slavery. 

"I'm really excited about stories like that," Yaszek said. "They help us re-see history from new perspectives."

Time travel has found a home in a wide variety of genres and media, including comedies such as "Groundhog Day" and "Bill and Ted's Excellent Adventure" as well as video games like Nintendo's "The Legend of Zelda: Majora's Mask" and the indie game "Braid." 

Yaszek suggested that this malleability and ubiquity speaks to time travel tales' ability to offer an escape from our normal reality. "They let us imagine that we can break free from the grip of linear time," she said. "And somehow get a new perspective on the human experience, either our own or humanity as a whole, and I think that feels so exciting to us." 

That modern people are often drawn to time-machine stories in particular might reflect the fact that we live in a technological world, she added. Yet time travel's appeal certainly has deeper roots, interwoven into the very fabric of our language and appearing in some of our earliest imaginings. 

"I think it's a way to make sense of the otherwise intangible and inexplicable, because it's hard to grasp time," Yaszek said. "But this is one of the final frontiers, the frontier of time, of life and death. And we're all moving forward, we're all traveling through time."

• If There Were a Time Warp, How Would Physicists Find It?
• Can Animals Tell Time?
• Why Does Time Sometimes Fly When You're NOT Having Fun?

Originally published on Live Science .

Adam Mann is a freelance journalist with over a decade of experience, specializing in astronomy and physics stories. He has a bachelor's degree in astrophysics from UC Berkeley. His work has appeared in the New Yorker, New York Times, National Geographic, Wall Street Journal, Wired, Nature, Science, and many other places. He lives in Oakland, California, where he enjoys riding his bike. 

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March 18, 2024

The Great Debate: Could We Ever Travel through Time?

Our space and physics editors go head-to-head over a classic mind-bending question.

By Clara Moskowitz & Lee Billings

cemagraphics/Getty Images

Clara Moskowitz: Hi, I’m Clara Moskowitz, a space editor here at Scientific American. We’re taking a break this week to look back at some of our favorite podcast episodes. I chose this one about the physics of time travel, because I’m a big sci-fi geek, so I’m fascinated by the topic. But also, it was such a fun debate to have with my colleague and friend, Lee Billings, another space editor here. We each picked a side – I was pro time travel, he was con—and dug our heels in. Check it out!

[Clip: Show theme music]

Moskowitz: We’re here today to talk about time travel. A perennial – dare I say, timeless–topic of science fiction, but is it possible? Is there any chance at all that it could actually happen?

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If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

Lee Billings: No. No, no no no no. (laughs). Well, kinda. Not really. ARGH. I’m Lee Billings.

Moskowitz: I’m Clara Moskowitz, and this is Cosmos, Quickly , the biweekly space podcast from Scientific American . 

Moskowitz: We’re going to have a little friendly debate.

Billings: Really? I came for a throwdown.

Moskowitz: Well, a wrangle. A parley. A confab. Lee, what do you have against time travel?

Billings: So I love the idea of time travel! And in fact I do it all the time—like most everyone else I’m traveling into the future at one second per second. I’m less of a fan, though, of more speculative time travel, which is good fodder for goofy sci-fi stories, but in the real world it’s an implausible distraction.

Moskowitz: But really, we can stay within plausible physics and still see how more extreme versions of time travel are possible. See, Einstein’s special theory of relativity shows that the rate time flows at depends on how fast you’re moving. 

Billings: Einstein strikes again, what a rascal.

Moskowitz: If you’re traveling in a starship at close to the speed of light, you’ll still experience the familiar one-second-per-second ticking of a clock– but an observer back on Earth would see your clock moving glacially slow. To them, you’d be moving through time at a snail’s pace. That means that when you finally got back,  maybe only a year would have passed for you, but a century could have gone by for your friends on Earth. Ergo, you just traveled to the future! 

Billings: Right, right, no one’s disputing any of that! We can even measure this sort of “time dilation” right now on Earth, not with starships, but with subatomic particles. Some of those particles have very short lifetimes, decaying almost instantaneously. But if we drastically speed them up, like in a particle accelerator, we find they endure longer in proportion to how fast they’re going. So riddle me this, though, Clara: How can we travel into the past? That’s something so hard to do–effectively impossible, almost–that it’s scarcely worth thinking about.

[Clip: Back to the Future : “This is what makes time travel possible. The flux capacitor!”]

Moskowitz: I get it—no one has yet conceived of a way to journey to the past. But the crazy thing is it’s not impossible. Time is one of the four dimensions in the universe, along with three dimensions of space. And we move through space in all directions just fine, and according to physics, travel through time should be just as possible.

One way that people have looked into is via a wormhole—a shortcut bridge through spacetime that was predicted by general relativity. Wormholes can connect distant points in spacetime, meaning you could conceivably use one to bridge not just the gap between here and a distant galaxy, but the span between 2023 and 1923. 

[CLIP: Interstellar : “That’s the wormhole.”]

Billings : Ah yes, wormholes—the last refuge of scoundrels and desperate physicists. The trouble with wormholes Clara, is that, unlike a DeLorean, we have no evidence they actually exist—and, even if they did, it seems the only ways to make them traversable and stable involves using negative energy or negative mass  to prop them open. And, guess what, just like wormholes themselves, we have no evidence these weird forms of matter and energy actually exist, either. And let’s just beat this dead horse one more time—even if wormholes exist, as well as the means to make them traversable, to go back in time seems to require anchoring one end in a region of very warped spacetime, like around a black hole, or accelerating it to nearly lightspeed. Are you sensing a theme here, Clara?

Moskowitz: Yeah, yeah. All I can say is that just because there’s no evidence any of these things exist, there’s also no evidence they don’t or can’t exist. Wormholes are real solutions to the equations of general relativity, and even negative energy and mass are concepts that come up in the math and aren’t prohibited.

Billings: Well how about some more practical arguments, then? If time travel were possible, wouldn’t we have met some time travelers by now? Wouldn’t someone have gone back and killed Hitler—or at least prevented me from wearing that ridiculous outfit to my high school prom? You know there’s a famous story about physicist Stephen Hawking, who invited time travelers to come to a party he was holding. The trick was the the party happened in 2009, but the invitation came out in a miniseries that was broadcast in 2010—thus, only time travelers would have been able to attend. 

[CLIP: Stephen Hawking Time Travel Party: “Here is the invitation, giving the exact coordinates in time and space. I am hoping in one form or another it will survive for many thousands of years.”]

Billings: Sadly, the hors d'oeuvres went uneaten and the champagne sat unopened, because, clearly, time travel to the past is impossible! 

Moskowitz: I admit a party with Stephen Hawking should have been pretty alluring to time travelers, if they were out there. But you’re forgetting about the International Clause of Secrecy that all time travelers probably have to swear to, making sure to hide their identities and abilities from those in earlier eras.  

Billings: Hmm, yes the clause of secrecy here. Feels like we’re really veering into science fiction territory special pleading here. And don’t forget all the paradoxes that we have to worry about too. There are lots of good reasons to think time travel might introduce insurmountable paradoxes in physics. The most famous being the grandfather—or grandmother—paradox. If time travel were possible into the past, so the thinking goes, then a person could go back in time and kill their own grandparents, thus making it impossible for them to be born and impossible for them to travel back in time to ever commit the murder, and so on and so on.

Moskowitz: I wonder if it could be like a many-worlds scenario, where each change a time traveler makes to the past spawns a whole new universe that carries on from that point. So if I went back in time and killed one of my forebears, then a new branch universe would begin where that whole line of descendents, including me, never existed. I mean, it sounds crazy, but then again, physics is pretty enamored with multiverses, and they seem to pop up for lots of reasons already. Maybe it’s not impossible? 

Billings: If not impossible, then I’d say, implausible.

Moskowitz: Well, I’m forever an optimist, Lee! Thanks for listening to the Cosmos, Quickly .

Billings: Our show is produced by Jeff DelViscio, Tulika Bose and Kelso Harper.  Our music was composed by Dominic Smith.

Moskowtiz: If you like the show, please consider rating or leaving a review. You can also email feedback, questions, and tips to [email protected] . 

Billings: For more spacetime hijinks and all your science news, head to SciAm.com. This has been Cosmos, Quickly . I’m Lee Billings. 

Moskowitz: I’m Clara Moskowitz. 

Billings: And we’ll see you next time, in the future!

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time travel

• hypothetical transport through time into the past or the future.

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Whatever variant they meet will likely be very interested in time travel through the Quantum Realm, as the title Quantumania suggests.

It feels like every day, we get one step closer to figuring out the science behind time travel.

Considering that Loki will involve lots of time travel, it’s probable that we’ll get a glimpse of the multiverse in this show.

Then we would better understand space and time and perhaps finally decide if time travel is a realistic possibility, and if so, how to achieve it.

Physicists are far from agreeing over whether time travel of this sort is possible.

Underneath its comic-book action and time-travel shenanigans, X-Men: Days of Future Past questions the use of military robots.

The title of his forthcoming book is Rush Revere and the Brave Pilgrims: Time Travel Adventures with Exceptional Americans.

But somehow in the long run, truth and time travel the same road.

As soon as I entered West 100th Street, I understood that this experience was going to involve time travel.

Nine years ago he dazzled audiences with his $7,000 time-travel flick ‘Primer.’

His story is plausible, logical, once you grant the basic premise that time travel is an actuality.

It seems absurd that parts of the same train can at any time travel in opposite directions, but such is the case.

During this journey we recovered something of the conditions of old-time travel.

Even for younger Destinyworkers, time travel at best was an exhausting business.

We may dimly perceive something of the trials and hardships of old-time travel in that expression harbouring.

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Time Travel and Modern Physics

Time travel has been a staple of science fiction. With the advent of general relativity it has been entertained by serious physicists. But, especially in the philosophy literature, there have been arguments that time travel is inherently paradoxical. The most famous paradox is the grandfather paradox: you travel back in time and kill your grandfather, thereby preventing your own existence. To avoid inconsistency some circumstance will have to occur which makes you fail in this attempt to kill your grandfather. Doesn’t this require some implausible constraint on otherwise unrelated circumstances? We examine such worries in the context of modern physics.

1. Paradoxes Lost?

2. topology and constraints, 3. the general possibility of time travel in general relativity, 4. two toy models, 5. slightly more realistic models of time travel, 6. the possibility of time travel redux, 7. even if there are constraints, so what, 8. computational models, 9. quantum mechanics to the rescue, 10. conclusions, other internet resources, related entries.

• Supplement: Remarks and Limitations on the Toy Models

Modern physics strips away many aspects of the manifest image of time. Time as it appears in the equations of classical mechanics has no need for a distinguished present moment, for example. Relativity theory leads to even sharper contrasts. It replaces absolute simultaneity, according to which it is possible to unambiguously determine the time order of distant events, with relative simultaneity: extending an “instant of time” throughout space is not unique, but depends on the state of motion of an observer. More dramatically, in general relativity the mathematical properties of time (or better, of spacetime)—its topology and geometry—depend upon how matter is arranged rather than being fixed once and for all. So physics can be, and indeed has to be, formulated without treating time as a universal, fixed background structure. Since general relativity represents gravity through spacetime geometry, the allowed geometries must be as varied as the ways in which matter can be arranged. Alongside geometrical models used to describe the solar system, black holes, and much else, the scope of variation extends to include some exotic structures unlike anything astrophysicists have observed. In particular, there are spacetime geometries with curves that loop back on themselves: closed timelike curves (CTCs), which describe the possible trajectory of an observer who returns exactly back to their earlier state—without any funny business, such as going faster than the speed of light. These geometries satisfy the relevant physical laws, the equations of general relativity, and in that sense time travel is physically possible.

Yet circular time generates paradoxes, familiar from science fiction stories featuring time travel: [ 1 ]

• Consistency: Kurt plans to murder his own grandfather Adolph, by traveling along a CTC to an appropriate moment in the past. He is an able marksman, and waits until he has a clear shot at grandpa. Normally he would not miss. Yet if he succeeds, there is no way that he will then exist to plan and carry out the mission. Kurt pulls the trigger: what can happen?
• Underdetermination: Suppose that Kurt first travels back in order to give his earlier self a copy of How to Build a Time Machine. This is the same book that allows him to build a time machine, which he then carries with him on his journey to the past. Who wrote the book?
• Easy Knowledge: A fan of classical music enhances their computer with a circuit that exploits a CTC. This machine efficiently solves problems at a higher level of computational complexity than conventional computers, leading (among other things) to finding the smallest circuits that can generate Bach’s oeuvre—and to compose new pieces in the same style. Such easy knowledge is at odds with our understanding of our epistemic predicament. (This third paradox has not drawn as much attention.)

The first two paradoxes were once routinely taken to show that solutions with CTCs should be rejected—with charges varying from violating logic, to being “physically unreasonable”, to undermining the notion of free will. Closer analysis of the paradoxes has largely reversed this consensus. Physicists have discovered many solutions with CTCs and have explored their properties in pursuing foundational questions, such as whether physics is compatible with the idea of objective temporal passage (starting with Gödel 1949). Philosophers have also used time travel scenarios to probe questions about, among other things, causation, modality, free will, and identity (see, e.g., Earman 1972 and Lewis’s seminal 1976 paper).

We begin below with Consistency , turning to the other paradoxes in later sections. A standard, stone-walling response is to insist that the past cannot be changed, as a matter of logic, even by a time traveler (e.g., Gödel 1949, Clarke 1977, Horwich 1987). Adolph cannot both die and survive, as a matter of logic, so any scheme to alter the past must fail. In many of the best time travel fictions, the actions of a time traveler are constrained in novel and unexpected ways. Attempts to change the past fail, and they fail, often tragically, in just such a way that they set the stage for the time traveler’s self-defeating journey. The first question is whether there is an analog of the consistent story when it comes to physics in the presence of CTCs. As we will see, there is a remarkable general argument establishing the existence of consistent solutions. Yet a second question persists: why can’t time-traveling Kurt kill his own grandfather? Doesn’t the necessity of failures to change the past put unusual and unexpected constraints on time travelers, or objects that move along CTCs? The same argument shows that there are in fact no constraints imposed by the existence of CTCs, in some cases. After discussing this line of argument, we will turn to the palatability and further implications of such constraints if they are required, and then turn to the implications of quantum mechanics.

Wheeler and Feynman (1949) were the first to claim that the fact that nature is continuous could be used to argue that causal influences from later events to earlier events, as are made possible by time travel, will not lead to paradox without the need for any constraints. Maudlin (1990) showed how to make their argument precise and more general, and argued that nonetheless it was not completely general.

Imagine the following set-up. We start off having a camera with a black and white film ready to take a picture of whatever comes out of the time machine. An object, in fact a developed film, comes out of the time machine. We photograph it, and develop the film. The developed film is subsequently put in the time machine, and set to come out of the time machine at the time the picture is taken. This surely will create a paradox: the developed film will have the opposite distribution of black, white, and shades of gray, from the object that comes out of the time machine. For developed black and white films (i.e., negatives) have the opposite shades of gray from the objects they are pictures of. But since the object that comes out of the time machine is the developed film itself it we surely have a paradox.

However, it does not take much thought to realize that there is no paradox here. What will happen is that a uniformly gray picture will emerge, which produces a developed film that has exactly the same uniform shade of gray. No matter what the sensitivity of the film is, as long as the dependence of the brightness of the developed film depends in a continuous manner on the brightness of the object being photographed, there will be a shade of gray that, when photographed, will produce exactly the same shade of gray on the developed film. This is the essence of Wheeler and Feynman’s idea. Let us first be a bit more precise and then a bit more general.

For simplicity let us suppose that the film is always a uniform shade of gray (i.e., at any time the shade of gray does not vary by location on the film). The possible shades of gray of the film can then be represented by the (real) numbers from 0, representing pure black, to 1, representing pure white.

Let us now distinguish various stages in the chronological order of the life of the film. In stage \(S_1\) the film is young; it has just been placed in the camera and is ready to be exposed. It is then exposed to the object that comes out of the time machine. (That object in fact is a later stage of the film itself). By the time we come to stage \(S_2\) of the life of the film, it has been developed and is about to enter the time machine. Stage \(S_3\) occurs just after it exits the time machine and just before it is photographed. Stage \(S_4\) occurs after it has been photographed and before it starts fading away. Let us assume that the film starts out in stage \(S_1\) in some uniform shade of gray, and that the only significant change in the shade of gray of the film occurs between stages \(S_1\) and \(S_2\). During that period it acquires a shade of gray that depends on the shade of gray of the object that was photographed. In other words, the shade of gray that the film acquires at stage \(S_2\) depends on the shade of gray it has at stage \(S_3\). The influence of the shade of gray of the film at stage \(S_3\), on the shade of gray of the film at stage \(S_2\), can be represented as a mapping, or function, from the real numbers between 0 and 1 (inclusive), to the real numbers between 0 and 1 (inclusive). Let us suppose that the process of photography is such that if one imagines varying the shade of gray of an object in a smooth, continuous manner then the shade of gray of the developed picture of that object will also vary in a smooth, continuous manner. This implies that the function in question will be a continuous function. Now any continuous function from the real numbers between 0 and 1 (inclusive) to the real numbers between 0 and 1 (inclusive) must map at least one number to itself. One can quickly convince oneself of this by graphing such functions. For one will quickly see that any continuous function \(f\) from \([0,1]\) to \([0,1]\) must intersect the line \(x=y\) somewhere, and thus there must be at least one point \(x\) such that \(f(x)=x\). Such points are called fixed points of the function. Now let us think about what such a fixed point represents. It represents a shade of gray such that, when photographed, it will produce a developed film with exactly that same shade of gray. The existence of such a fixed point implies a solution to the apparent paradox.

Let us now be more general and allow color photography. One can represent each possible color of an object (of uniform color) by the proportions of blue, green and red that make up that color. (This is why television screens can produce all possible colors.) Thus one can represent all possible colors of an object by three points on three orthogonal lines \(x, y\) and \(z\), that is to say, by a point in a three-dimensional cube. This cube is also known as the “Cartesian product” of the three line segments. Now, one can also show that any continuous map from such a cube to itself must have at least one fixed point. So color photography can not be used to create time travel paradoxes either!

Even more generally, consider some system \(P\) which, as in the above example, has the following life. It starts in some state \(S_1\), it interacts with an object that comes out of a time machine (which happens to be its older self), it travels back in time, it interacts with some object (which happens to be its younger self), and finally it grows old and dies. Let us assume that the set of possible states of \(P\) can be represented by a Cartesian product of \(n\) closed intervals of the reals, i.e., let us assume that the topology of the state-space of \(P\) is isomorphic to a finite Cartesian product of closed intervals of the reals. Let us further assume that the development of \(P\) in time, and the dependence of that development on the state of objects that it interacts with, is continuous. Then, by a well-known fixed point theorem in topology (see, e.g., Hocking & Young 1961: 273), no matter what the nature of the interaction is, and no matter what the initial state of the object is, there will be at least one state \(S_3\) of the older system (as it emerges from the time travel machine) that will influence the initial state \(S_1\) of the younger system (when it encounters the older system) so that, as the younger system becomes older, it develops exactly into state \(S_3\). Thus without imposing any constraints on the initial state \(S_1\) of the system \(P\), we have shown that there will always be perfectly ordinary, non-paradoxical, solutions, in which everything that happens, happens according to the usual laws of development. Of course, there is looped causation, hence presumably also looped explanation, but what do you expect if there is looped time?

Unfortunately, for the fan of time travel, a little reflection suggests that there are systems for which the needed fixed point theorem does not hold. Imagine, for instance, that we have a dial that can only rotate in a plane. We are going to put the dial in the time machine. Indeed we have decided that if we see the later stage of the dial come out of the time machine set at angle \(x\), then we will set the dial to \(x+90\), and throw it into the time machine. Now it seems we have a paradox, since the mapping that consists of a rotation of all points in a circular state-space by 90 degrees does not have a fixed point. And why wouldn’t some state-spaces have the topology of a circle?

However, we have so far not used another continuity assumption which is also a reasonable assumption. So far we have only made the following demand: the state the dial is in at stage \(S_2\) must be a continuous function of the state of the dial at stage \(S_3\). But, the state of the dial at stage \(S_2\) is arrived at by taking the state of the dial at stage \(S_1\), and rotating it over some angle. It is not merely the case that the effect of the interaction, namely the state of the dial at stage \(S_2\), should be a continuous function of the cause, namely the state of the dial at stage \(S_3\). It is additionally the case that path taken to get there, the way the dial is rotated between stages \(S_1\) and \(S_2\) must be a continuous function of the state at stage \(S_3\). And, rather surprisingly, it turns out that this can not be done. Let us illustrate what the problem is before going to a more general demonstration that there must be a fixed point solution in the dial case.

Forget time travel for the moment. Suppose that you and I each have a watch with a single dial neither of which is running. My watch is set at 12. You are going to announce what your watch is set at. My task is going to be to adjust my watch to yours no matter what announcement you make. And my actions should have a continuous (single valued) dependence on the time that you announce. Surprisingly, this is not possible! For instance, suppose that if you announce “12”, then I achieve that setting on my watch by doing nothing. Now imagine slowly and continuously increasing the announced times, starting at 12. By continuity, I must achieve each of those settings by rotating my dial to the right. If at some point I switch and achieve the announced goal by a rotation of my dial to the left, I will have introduced a discontinuity in my actions, a discontinuity in the actions that I take as a function of the announced angle. So I will be forced, by continuity, to achieve every announcement by rotating the dial to the right. But, this rotation to the right will have to be abruptly discontinued as the announcements grow larger and I eventually approach 12 again, since I achieved 12 by not rotating the dial at all. So, there will be a discontinuity at 12 at the latest. In general, continuity of my actions as a function of announced times can not be maintained throughout if I am to be able to replicate all possible settings. Another way to see the problem is that one can similarly reason that, as one starts with 12, and imagines continuously making the announced times earlier, one will be forced, by continuity, to achieve the announced times by rotating the dial to the left. But the conclusions drawn from the assumption of continuous increases and the assumption of continuous decreases are inconsistent. So we have an inconsistency following from the assumption of continuity and the assumption that I always manage to set my watch to your watch. So, a dial developing according to a continuous dynamics from a given initial state, can not be set up so as to react to a second dial, with which it interacts, in such a way that it is guaranteed to always end up set at the same angle as the second dial. Similarly, it can not be set up so that it is guaranteed to always end up set at 90 degrees to the setting of the second dial. All of this has nothing to do with time travel. However, the impossibility of such set ups is what prevents us from enacting the rotation by 90 degrees that would create paradox in the time travel setting.

Let us now give the positive result that with such dials there will always be fixed point solutions, as long as the dynamics is continuous. Let us call the state of the dial before it interacts with its older self the initial state of the dial. And let us call the state of the dial after it emerges from the time machine the final state of the dial. There is also an intermediate state of the dial, after it interacts with its older self and before it is put into the time machine. We can represent the initial or intermediate states of the dial, before it goes into the time machine, as an angle \(x\) in the horizontal plane and the final state of the dial, after it comes out of the time machine, as an angle \(y\) in the vertical plane. All possible \(\langle x,y\rangle\) pairs can thus be visualized as a torus with each \(x\) value picking out a vertical circular cross-section and each \(y\) picking out a point on that cross-section. See figure 1 .

Figure 1 [An extended description of figure 1 is in the supplement.]

Suppose that the dial starts at angle \(i\) which picks out vertical circle \(I\) on the torus. The initial angle \(i\) that the dial is at before it encounters its older self, and the set of all possible final angles that the dial can have when it emerges from the time machine is represented by the circle \(I\) on the torus (see figure 1 ). Given any possible angle of the emerging dial, the dial initially at angle \(i\) will develop to some other angle. One can picture this development by rotating each point on \(I\) in the horizontal direction by the relevant amount. Since the rotation has to depend continuously on the angle of the emerging dial, circle \(I\) during this development will deform into some loop \(L\) on the torus. Loop \(L\) thus represents all possible intermediate angles \(x\) that the dial is at when it is thrown into the time machine, given that it started at angle \(i\) and then encountered a dial (its older self) which was at angle \(y\) when it emerged from the time machine. We therefore have consistency if \(x=y\) for some \(x\) and \(y\) on loop \(L\). Now, let loop \(C\) be the loop which consists of all the points on the torus for which \(x=y\). Ring \(I\) intersects \(C\) at point \(\langle i,i\rangle\). Obviously any continuous deformation of \(I\) must still intersect \(C\) somewhere. So \(L\) must intersect \(C\) somewhere, say at \(\langle j,j\rangle\). But that means that no matter how the development of the dial starting at \(I\) depends on the angle of the emerging dial, there will be some angle for the emerging dial such that the dial will develop exactly into that angle (by the time it enters the time machine) under the influence of that emerging dial. This is so no matter what angle one starts with, and no matter how the development depends on the angle of the emerging dial. Thus even for a circular state-space there are no constraints needed other than continuity.

Unfortunately there are state-spaces that escape even this argument. Consider for instance a pointer that can be set to all values between 0 and 1, where 0 and 1 are not possible values. That is, suppose that we have a state-space that is isomorphic to an open set of real numbers. Now suppose that we have a machine that sets the pointer to half the value that the pointer is set at when it emerges from the time machine.

Figure 2 [An extended description of figure 2 is in the supplement.]

Suppose the pointer starts at value \(I\). As before we can represent the combination of this initial position and all possible final positions by the line \(I\). Under the influence of the pointer coming out of the time machine the pointer value will develop to a value that equals half the value of the final value that it encountered. We can represent this development as the continuous deformation of line \(I\) into line \(L\), which is indicated by the arrows in figure 2 . This development is fully continuous. Points \(\langle x,y\rangle\) on line \(I\) represent the initial position \(x=I\) of the (young) pointer, and the position \(y\) of the older pointer as it emerges from the time machine. Points \(\langle x,y\rangle\) on line \(L\) represent the position \(x\) that the younger pointer should develop into, given that it encountered the older pointer emerging from the time machine set at position \(y\). Since the pointer is designed to develop to half the value of the pointer that it encounters, the line \(L\) corresponds to \(x=1/2 y\). We have consistency if there is some point such that it develops into that point, if it encounters that point. Thus, we have consistency if there is some point \(\langle x,y\rangle\) on line \(L\) such that \(x=y\). However, there is no such point: lines \(L\) and \(C\) do not intersect. Thus there is no consistent solution, despite the fact that the dynamics is fully continuous.

Of course if 0 were a possible value, \(L\) and \(C\) would intersect at 0. This is surprising and strange: adding one point to the set of possible values of a quantity here makes the difference between paradox and peace. One might be tempted to just add the extra point to the state-space in order to avoid problems. After all, one might say, surely no measurements could ever tell us whether the set of possible values includes that exact point or not. Unfortunately there can be good theoretical reasons for supposing that some quantity has a state-space that is open: the set of all possible speeds of massive objects in special relativity surely is an open set, since it includes all speeds up to, but not including, the speed of light. Quantities that have possible values that are not bounded also lead to counter examples to the presented fixed point argument. And it is not obvious to us why one should exclude such possibilities. So the argument that no constraints are needed is not fully general.

An interesting question of course is: exactly for which state-spaces must there be such fixed points? The arguments above depend on a well-known fixed point theorem (due to Schauder) that guarantees the existence of a fixed point for compact, convex state spaces. We do not know what subsequent extensions of this result imply regarding fixed points for a wider variety of systems, or whether there are other general results along these lines. (See Kutach 2003 for more on this issue.)

A further interesting question is whether this line of argument is sufficient to resolve Consistency (see also Dowe 2007). When they apply, these results establish the existence of a solution, such as the shade of uniform gray in the first example. But physicists routinely demand more than merely the existence of a solution, namely that solutions to the equations are stable—such that “small” changes of the initial state lead to “small” changes of the resulting trajectory. (Clarifying the two senses of “small” in this statement requires further work, specifying the relevant topology.) Stability in this sense underwrites the possibility of applying equations to real systems given our inability to fix initial states with indefinite precision. (See Fletcher 2020 for further discussion.) The fixed point theorems guarantee that for an initial state \(S_1\) there is a solution, but this solution may not be “close” to the solution for a nearby initial state, \(S'\). We are not aware of any proofs that the solutions guaranteed to exist by the fixed point theorems are also stable in this sense.

Time travel has recently been discussed quite extensively in the context of general relativity. General relativity places few constraints on the global structure of space and time. This flexibility leads to a possibility first described in print by Hermann Weyl:

Every world-point is the origin of the double-cone of the active future and the passive past [i.e., the two lobes of the light cone]. Whereas in the special theory of relativity these two portions are separated by an intervening region, it is certainly possible in the present case [i.e., general relativity] for the cone of the active future to overlap with that of the passive past; so that, in principle, it is possible to experience events now that will in part be an effect of my future resolves and actions. Moreover, it is not impossible for a world-line (in particular, that of my body), although it has a timelike direction at every point, to return to the neighborhood of a point which it has already once passed through. (Weyl 1918/1920 [1952: 274])

A time-like curve is simply a space-time trajectory such that the speed of light is never equaled or exceeded along this trajectory. Time-like curves represent possible trajectories of ordinary objects. In general relativity a curve that is everywhere timelike locally can nonetheless loop back on itself, forming a CTC. Weyl makes the point vividly in terms of the light cones: along such a curve, the future lobe of the light cone (the “active future”) intersects the past lobe of the light cone (the “passive past”). Traveling along such a curve one would never exceed the speed of light, and yet after a certain amount of (proper) time one would return to a point in space-time that one previously visited. Or, by staying close to such a CTC, one could come arbitrarily close to a point in space-time that one previously visited. General relativity, in a straightforward sense, allows time travel: there appear to be many space-times compatible with the fundamental equations of general relativity in which there are CTC’s. Space-time, for instance, could have a Minkowski metric everywhere, and yet have CTC’s everywhere by having the temporal dimension (topologically) rolled up as a circle. Or, one can have wormhole connections between different parts of space-time which allow one to enter “mouth \(A\)” of such a wormhole connection, travel through the wormhole, exit the wormhole at “mouth \(B\)” and re-enter “mouth \(A\)” again. CTCs can even arise when the spacetime is topologically \(\mathbb{R}^4\), due to the “tilting” of light cones produced by rotating matter (as in Gödel 1949’s spacetime).

General relativity thus appears to provide ample opportunity for time travel. Note that just because there are CTC’s in a space-time, this does not mean that one can get from any point in the space-time to any other point by following some future directed timelike curve—there may be insurmountable practical obstacles. In Gödel’s spacetime, it is the case that there are CTCs passing through every point in the spacetime. Yet these CTCs are not geodesics, so traversing them requires acceleration. Calculations of the minimal fuel required to travel along the appropriate curve should discourage any would-be time travelers (Malament 1984, 1985; Manchak 2011). But more generally CTCs may be confined to smaller regions; some parts of space-time can have CTC’s while other parts do not. Let us call the part of a space-time that has CTC’s the “time travel region” of that space-time, while calling the rest of that space-time the “normal region”. More precisely, the “time travel region” consists of all the space-time points \(p\) such that there exists a (non-zero length) timelike curve that starts at \(p\) and returns to \(p\). Now let us turn to examining space-times with CTC’s a bit more closely for potential problems.

In order to get a feeling for the sorts of implications that closed timelike curves can have, it may be useful to consider two simple models. In space-times with closed timelike curves the traditional initial value problem cannot be framed in the usual way. For it presupposes the existence of Cauchy surfaces, and if there are CTCs then no Cauchy surface exists. (A Cauchy surface is a spacelike surface such that every inextendable timelike curve crosses it exactly once. One normally specifies initial conditions by giving the conditions on such a surface.) Nonetheless, if the topological complexities of the manifold are appropriately localized, we can come quite close. Let us call an edgeless spacelike surface \(S\) a quasi-Cauchy surface if it divides the rest of the manifold into two parts such that

• every point in the manifold can be connected by a timelike curve to \(S\), and
• any timelike curve which connects a point in one region to a point in the other region intersects \(S\) exactly once.

It is obvious that a quasi-Cauchy surface must entirely inhabit the normal region of the space-time; if any point \(p\) of \(S\) is in the time travel region, then any timelike curve which intersects \(p\) can be extended to a timelike curve which intersects \(S\) near \(p\) again. In extreme cases of time travel, a model may have no normal region at all (e.g., Minkowski space-time rolled up like a cylinder in a time-like direction), in which case our usual notions of temporal precedence will not apply. But temporal anomalies like wormholes (and time machines) can be sufficiently localized to permit the existence of quasi-Cauchy surfaces.

Given a timelike orientation, a quasi-Cauchy surface unproblematically divides the manifold into its past (i.e., all points that can be reached by past-directed timelike curves from \(S)\) and its future (ditto mutatis mutandis ). If the whole past of \(S\) is in the normal region of the manifold, then \(S\) is a partial Cauchy surface : every inextendable timelike curve which exists to the past of \(S\) intersects \(S\) exactly once, but (if there is time travel in the future) not every inextendable timelike curve which exists to the future of \(S\) intersects \(S\). Now we can ask a particularly clear question: consider a manifold which contains a time travel region, but also has a partial Cauchy surface \(S\), such that all of the temporal funny business is to the future of \(S\). If all you could see were \(S\) and its past, you would not know that the space-time had any time travel at all. The question is: are there any constraints on the sort of data which can be put on \(S\) and continued to a global solution of the dynamics which are different from the constraints (if any) on the data which can be put on a Cauchy surface in a simply connected manifold and continued to a global solution? If there is time travel to our future, might we we able to tell this now, because of some implied oddity in the arrangement of present things?

It is not at all surprising that there might be constraints on the data which can be put on a locally space-like surface which passes through the time travel region: after all, we never think we can freely specify what happens on a space-like surface and on another such surface to its future, but in this case the surface at issue lies to its own future. But if there were particular constraints for data on a partial Cauchy surface then we would apparently need to have to rule out some sorts of otherwise acceptable states on \(S\) if there is to be time travel to the future of \(S\). We then might be able to establish that there will be no time travel in the future by simple inspection of the present state of the universe. As we will see, there is reason to suspect that such constraints on the partial Cauchy surface are non-generic. But we are getting ahead of ourselves: first let’s consider the effect of time travel on a very simple dynamics.

The simplest possible example is the Newtonian theory of perfectly elastic collisions among equally massive particles in one spatial dimension. The space-time is two-dimensional, so we can represent it initially as the Euclidean plane, and the dynamics is completely specified by two conditions. When particles are traveling freely, their world lines are straight lines in the space-time, and when two particles collide, they exchange momenta, so the collision looks like an “\(X\)” in space-time, with each particle changing its momentum at the impact. [ 2 ] The dynamics is purely local, in that one can check that a set of world-lines constitutes a model of the dynamics by checking that the dynamics is obeyed in every arbitrarily small region. It is also trivial to generate solutions from arbitrary initial data if there are no CTCs: given the initial positions and momenta of a set of particles, one simply draws a straight line from each particle in the appropriate direction and continues it indefinitely. Once all the lines are drawn, the worldline of each particle can be traced from collision to collision. The boundary value problem for this dynamics is obviously well-posed: any set of data at an instant yields a unique global solution, constructed by the method sketched above.

What happens if we change the topology of the space-time by hand to produce CTCs? The simplest way to do this is depicted in figure 3 : we cut and paste the space-time so it is no longer simply connected by identifying the line \(L-\) with the line \(L+\). Particles “going in” to \(L+\) from below “emerge” from \(L-\) , and particles “going in” to \(L-\) from below “emerge” from \(L+\).

Figure 3: Inserting CTCs by Cut and Paste. [An extended description of figure 3 is in the supplement.]

How is the boundary-value problem changed by this alteration in the space-time? Before the cut and paste, we can put arbitrary data on the simultaneity slice \(S\) and continue it to a unique solution. After the change in topology, \(S\) is no longer a Cauchy surface, since a CTC will never intersect it, but it is a partial Cauchy surface. So we can ask two questions. First, can arbitrary data on \(S\) always be continued to a global solution? Second, is that solution unique? If the answer to the first question is \(no\), then we have a backward-temporal constraint: the existence of the region with CTCs places constraints on what can happen on \(S\) even though that region lies completely to the future of \(S\). If the answer to the second question is \(no\), then we have an odd sort of indeterminism, analogous to the unwritten book: the complete physical state on \(S\) does not determine the physical state in the future, even though the local dynamics is perfectly deterministic and even though there is no other past edge to the space-time region in \(S\)’s future (i.e., there is nowhere else for boundary values to come from which could influence the state of the region).

In this case the answer to the first question is yes and to the second is no : there are no constraints on the data which can be put on \(S\), but those data are always consistent with an infinitude of different global solutions. The easy way to see that there always is a solution is to construct the minimal solution in the following way. Start drawing straight lines from \(S\) as required by the initial data. If a line hits \(L-\) from the bottom, just continue it coming out of the top of \(L+\) in the appropriate place, and if a line hits \(L+\) from the bottom, continue it emerging from \(L-\) at the appropriate place. Figure 4 represents the minimal solution for a single particle which enters the time-travel region from the left:

Figure 4: The Minimal Solution. [An extended description of figure 4 is in the supplement.]

The particle “travels back in time” three times. It is obvious that this minimal solution is a global solution, since the particle always travels inertially.

But the same initial state on \(S\) is also consistent with other global solutions. The new requirement imposed by the topology is just that the data going into \(L+\) from the bottom match the data coming out of \(L-\) from the top, and the data going into \(L-\) from the bottom match the data coming out of \(L+\) from the top. So we can add any number of vertical lines connecting \(L-\) and \(L+\) to a solution and still have a solution. For example, adding a few such lines to the minimal solution yields:

Figure 5: A Non-Minimal Solution. [An extended description of figure 5 is in the supplement.]

The particle now collides with itself twice: first before it reaches \(L+\) for the first time, and again shortly before it exits the CTC region. From the particle’s point of view, it is traveling to the right at a constant speed until it hits an older version of itself and comes to rest. It remains at rest until it is hit from the right by a younger version of itself, and then continues moving off, and the same process repeats later. It is clear that this is a global model of the dynamics, and that any number of distinct models could be generating by varying the number and placement of vertical lines.

Knowing the data on \(S\), then, gives us only incomplete information about how things will go for the particle. We know that the particle will enter the CTC region, and will reach \(L+\), we know that it will be the only particle in the universe, we know exactly where and with what speed it will exit the CTC region. But we cannot determine how many collisions the particle will undergo (if any), nor how long (in proper time) it will stay in the CTC region. If the particle were a clock, we could not predict what time it would indicate when exiting the region. Furthermore, the dynamics gives us no handle on what to think of the various possibilities: there are no probabilities assigned to the various distinct possible outcomes.

Changing the topology has changed the mathematics of the situation in two ways, which tend to pull in opposite directions. On the one hand, \(S\) is no longer a Cauchy surface, so it is perhaps not surprising that data on \(S\) do not suffice to fix a unique global solution. But on the other hand, there is an added constraint: data “coming out” of \(L-\) must exactly match data “going in” to \(L+\), even though what comes out of \(L-\) helps to determine what goes into \(L+\). This added consistency constraint tends to cut down on solutions, although in this case the additional constraint is more than outweighed by the freedom to consider various sorts of data on \({L+}/{L-}\).

The fact that the extra freedom outweighs the extra constraint also points up one unexpected way that the supposed paradoxes of time travel may be overcome. Let’s try to set up a paradoxical situation using the little closed time loop above. If we send a single particle into the loop from the left and do nothing else, we know exactly where it will exit the right side of the time travel region. Now suppose we station someone at the other side of the region with the following charge: if the particle should come out on the right side, the person is to do something to prevent the particle from going in on the left in the first place. In fact, this is quite easy to do: if we send a particle in from the right, it seems that it can exit on the left and deflect the incoming left-hand particle.

Carrying on our reflection in this way, we further realize that if the particle comes out on the right, we might as well send it back in order to deflect itself from entering in the first place. So all we really need to do is the following: set up a perfectly reflecting particle mirror on the right-hand side of the time travel region, and launch the particle from the left so that— if nothing interferes with it —it will just barely hit \(L+\). Our paradox is now apparently complete. If, on the one hand, nothing interferes with the particle it will enter the time-travel region on the left, exit on the right, be reflected from the mirror, re-enter from the right, and come out on the left to prevent itself from ever entering. So if it enters, it gets deflected and never enters. On the other hand, if it never enters then nothing goes in on the left, so nothing comes out on the right, so nothing is reflected back, and there is nothing to deflect it from entering. So if it doesn’t enter, then there is nothing to deflect it and it enters. If it enters, then it is deflected and doesn’t enter; if it doesn’t enter then there is nothing to deflect it and it enters: paradox complete.

But at least one solution to the supposed paradox is easy to construct: just follow the recipe for constructing the minimal solution, continuing the initial trajectory of the particle (reflecting it the mirror in the obvious way) and then read of the number and trajectories of the particles from the resulting diagram. We get the result of figure 6 :

Figure 6: Resolving the “Paradox”. [An extended description of figure 6 is in the supplement.]

As we can see, the particle approaching from the left never reaches \(L+\): it is deflected first by a particle which emerges from \(L-\). But it is not deflected by itself , as the paradox suggests, it is deflected by another particle. Indeed, there are now four particles in the diagram: the original particle and three particles which are confined to closed time-like curves. It is not the leftmost particle which is reflected by the mirror, nor even the particle which deflects the leftmost particle; it is another particle altogether.

The paradox gets it traction from an incorrect presupposition. If there is only one particle in the world at \(S\) then there is only one particle which could participate in an interaction in the time travel region: the single particle would have to interact with its earlier (or later) self. But there is no telling what might come out of \(L-\): the only requirement is that whatever comes out must match what goes in at \(L+\). So if you go to the trouble of constructing a working time machine, you should be prepared for a different kind of disappointment when you attempt to go back and kill yourself: you may be prevented from entering the machine in the first place by some completely unpredictable entity which emerges from it. And once again a peculiar sort of indeterminism appears: if there are many self-consistent things which could prevent you from entering, there is no telling which is even likely to materialize. This is just like the case of the unwritten book: the book is never written, so nothing determines what fills its pages.

So when the freedom to put data on \(L-\) outweighs the constraint that the same data go into \(L+\), instead of paradox we get an embarrassment of riches: many solution consistent with the data on \(S\), or many possible books. To see a case where the constraint “outweighs” the freedom, we need to construct a very particular, and frankly artificial, dynamics and topology. Consider the space of all linear dynamics for a scalar field on a lattice. (The lattice can be though of as a simple discrete space-time.) We will depict the space-time lattice as a directed graph. There is to be a scalar field defined at every node of the graph, whose value at a given node depends linearly on the values of the field at nodes which have arrows which lead to it. Each edge of the graph can be assigned a weighting factor which determines how much the field at the input node contributes to the field at the output node. If we name the nodes by the letters a , b , c , etc., and the edges by their endpoints in the obvious way, then we can label the weighting factors by the edges they are associated with in an equally obvious way.

Suppose that the graph of the space-time lattice is acyclic , as in figure 7 . (A graph is Acyclic if one can not travel in the direction of the arrows and go in a loop.)

Figure 7: An Acyclic Lattice. [An extended description of figure 7 is in the supplement.]

It is easy to regard a set of nodes as the analog of a Cauchy surface, e.g., the set \(\{a, b, c\}\), and it is obvious if arbitrary data are put on those nodes the data will generate a unique solution in the future. [ 3 ] If the value of the field at node \(a\) is 3 and at node \(b\) is 7, then its value at node \(d\) will be \(3W_{ad}\) and its value at node \(e\) will be \(3W_{ae} + 7W_{be}\). By varying the weighting factors we can adjust the dynamics, but in an acyclic graph the future evolution of the field will always be unique.

Let us now again artificially alter the topology of the lattice to admit CTCs, so that the graph now is cyclic. One of the simplest such graphs is depicted in figure 8 : there are now paths which lead from \(z\) back to itself, e.g., \(z\) to \(y\) to \(z\).

Figure 8: Time Travel on a Lattice. [An extended description of figure 8 is in the supplement.]

Can we now put arbitrary data on \(v\) and \(w\), and continue that data to a global solution? Will the solution be unique?

In the generic case, there will be a solution and the solution will be unique. The equations for the value of the field at \(x, y\), and \(z\) are:

Solving these equations for \(z\) yields

which gives a unique value for \(z\) in the generic case. But looking at the space of all possible dynamics for this lattice (i.e., the space of all possible weighting factors), we find a singularity in the case where \(1-W_{zx}W_{xz} - W_{zy}W_{yz} = 0\). If we choose weighting factors in just this way, then arbitrary data at \(v\) and \(w\) cannot be continued to a global solution. Indeed, if the scalar field is everywhere non-negative, then this particular choice of dynamics puts ironclad constraints on the value of the field at \(v\) and \(w\): the field there must be zero (assuming \(W_{vx}\) and \(W_{wy}\) to be non-zero), and similarly all nodes in their past must have field value zero. If the field can take negative values, then the values at \(v\) and \(w\) must be so chosen that \(vW_{vx}W_{xz} = -wW_{wy}W_{yz}\). In either case, the field values at \(v\) and \(w\) are severely constrained by the existence of the CTC region even though these nodes lie completely to the past of that region. It is this sort of constraint which we find to be unlike anything which appears in standard physics.

Our toy models suggest three things. The first is that it may be impossible to prove in complete generality that arbitrary data on a partial Cauchy surface can always be continued to a global solution: our artificial case provides an example where it cannot. The second is that such odd constraints are not likely to be generic: we had to delicately fine-tune the dynamics to get a problem. The third is that the opposite problem, namely data on a partial Cauchy surface being consistent with many different global solutions, is likely to be generic: we did not have to do any fine-tuning to get this result.

This third point leads to a peculiar sort of indeterminism, illustrated by the case of the unwritten book: the entire state on \(S\) does not determine what will happen in the future even though the local dynamics is deterministic and there are no other “edges” to space-time from which data could influence the result. What happens in the time travel region is constrained but not determined by what happens on \(S\), and the dynamics does not even supply any probabilities for the various possibilities. The example of the photographic negative discussed in section 2, then, seems likely to be unusual, for in that case there is a unique fixed point for the dynamics, and the set-up plus the dynamical laws determine the outcome. In the generic case one would rather expect multiple fixed points, with no room for anything to influence, even probabilistically, which would be realized. (See the supplement on

Remarks and Limitations on the Toy Models .

It is ironic that time travel should lead generically not to contradictions or to constraints (in the normal region) but to underdetermination of what happens in the time travel region by what happens everywhere else (an underdetermination tied neither to a probabilistic dynamics nor to a free edge to space-time). The traditional objection to time travel is that it leads to contradictions: there is no consistent way to complete an arbitrarily constructed story about how the time traveler intends to act. Instead, though, it appears that the more significant problem is underdetermination: the story can be consistently completed in many different ways.

Echeverria, Klinkhammer, and Thorne (1991) considered the case of 3-dimensional single hard spherical ball that can go through a single time travel wormhole so as to collide with its younger self.

Figure 9 [An extended description of figure 9 is in the supplement.]

The threat of paradox in this case arises in the following form. Consider the initial trajectory of a ball as it approaches the time travel region. For some initial trajectories, the ball does not undergo a collision before reaching mouth 1, but upon exiting mouth 2 it will collide with its earlier self. This leads to a contradiction if the collision is strong enough to knock the ball off its trajectory and deflect it from entering mouth 1. Of course, the Wheeler-Feynman strategy is to look for a “glancing blow” solution: a collision which will produce exactly the (small) deviation in trajectory of the earlier ball that produces exactly that collision. Are there always such solutions? [ 4 ]

Echeverria, Klinkhammer & Thorne found a large class of initial trajectories that have consistent “glancing blow” continuations, and found none that do not (but their search was not completely general). They did not produce a rigorous proof that every initial trajectory has a consistent continuation, but suggested that it is very plausible that every initial trajectory has a consistent continuation. That is to say, they have made it very plausible that, in the billiard ball wormhole case, the time travel structure of such a wormhole space-time does not result in constraints on states on spacelike surfaces in the non-time travel region.

In fact, as one might expect from our discussion in the previous section, they found the opposite problem from that of inconsistency: they found underdetermination. For a large class of initial trajectories there are multiple different consistent “glancing blow” continuations of that trajectory (many of which involve multiple wormhole traversals). For example, if one initially has a ball that is traveling on a trajectory aimed straight between the two mouths, then one obvious solution is that the ball passes between the two mouths and never time travels. But another solution is that the younger ball gets knocked into mouth 1 exactly so as to come out of mouth 2 and produce that collision. Echeverria et al. do not note the possibility (which we pointed out in the previous section) of the existence of additional balls in the time travel region. We conjecture (but have no proof) that for every initial trajectory of \(A\) there are some, and generically many, multiple-ball continuations.

Friedman, Morris, et al. (1990) examined the case of source-free non-self-interacting scalar fields traveling through such a time travel wormhole and found that no constraints on initial conditions in the non-time travel region are imposed by the existence of such time travel wormholes. In general there appear to be no known counter examples to the claim that in “somewhat realistic” time-travel space-times with a partial Cauchy surface there are no constraints imposed on the state on such a partial Cauchy surface by the existence of CTC’s. (See, e.g., Friedman & Morris 1991; Thorne 1994; Earman 1995; Earman, Smeenk, & Wüthrich 2009; and Dowe 2007.)

How about the issue of constraints in the time travel region \(T\)? Prima facie , constraints in such a region would not appear to be surprising. But one might still expect that there should be no constraints on states on a spacelike surface, provided one keeps the surface “small enough”. In the physics literature the following question has been asked: for any point \(p\) in \(T\), and any space-like surface \(S\) that includes \(p\) is there a neighborhood \(E\) of \(p\) in \(S\) such that any solution on \(E\) can be extended to a solution on the whole space-time? With respect to this question, there are some simple models in which one has this kind of extendability of local solutions to global ones, and some simple models in which one does not have such extendability, with no clear general pattern. The technical mathematical problems are amplified by the more conceptual problem of what it might mean to say that one could create a situation which forces the creation of closed timelike curves. (See, e.g., Yurtsever 1990; Friedman, Morris, et al. 1990; Novikov 1992; Earman 1995; and Earman, Smeenk, & Wüthrich 2009). What are we to think of all of this?

The toy models above all treat billiard balls, fields, and other objects propagating through a background spacetime with CTCs. Even if we can show that a consistent solution exists, there is a further question: what kind of matter and dynamics could generate CTCs to begin with? There are various solutions of Einstein’s equations with CTCs, but how do these exotic spacetimes relate to the models actually used in describing the world? In other words, what positive reasons might we have to take CTCs seriously as a feature of the actual universe, rather than an exotic possibility of primarily mathematical interest?

We should distinguish two different kinds of “possibility” that we might have in mind in posing such questions (following Stein 1970). First, we can consider a solution as a candidate cosmological model, describing the (large-scale gravitational degrees of freedom of the) entire universe. The case for ruling out spacetimes with CTCs as potential cosmological models strikes us as, surprisingly, fairly weak. Physicists used to simply rule out solutions with CTCs as unreasonable by fiat, due to the threat of paradoxes, which we have dismantled above. But it is also challenging to make an observational case. Observations tell us very little about global features, such as the existence of CTCs, because signals can only reach an observer from a limited region of spacetime, called the past light cone. Our past light cone—and indeed the collection of all the past light cones for possible observers in a given spacetime—can be embedded in spacetimes with quite different global features (Malament 1977, Manchak 2009). This undercuts the possibility of using observations to constrain global topology, including (among other things) ruling out the existence of CTCs.

Yet the case in favor of taking cosmological models with CTCs seriously is also not particularly strong. Some solutions used to describe black holes, which are clearly relevant in a variety of astrophysical contexts, include CTCs. But the question of whether the CTCs themselves play an essential representational role is subtle: the CTCs arise in the maximal extensions of these solutions, and can plausibly be regarded as extraneous to successful applications. Furthermore, many of the known solutions with CTCs have symmetries, raising the possibility that CTCs are not a stable or robust feature. Slight departures from symmetry may lead to a solution without CTCs, suggesting that the CTCs may be an artifact of an idealized model.

The second sense of possibility regards whether “reasonable” initial conditions can be shown to lead to, or not to lead to, the formation of CTCs. As with the toy models above, suppose that we have a partial Cauchy surface \(S\), such that all the temporal funny business lies to the future. Rather than simply assuming that there is a region with CTCs to the future, we can ask instead whether it is possible to create CTCs by manipulating matter in the initial, well-behaved region—that is, whether it is possible to build a time machine. Several physicists have pursued “chronology protection theorems” aiming to show that the dynamics of general relativity (or some other aspects of physics) rules this out, and to clarify why this is the case. The proof of such a theorem would justify neglecting solutions with CTCs as a source of insight into the nature of time in the actual world. But as of yet there are several partial results that do not fully settle the question. One further intriguing possibility is that even if general relativity by itself does protect chronology, it may not be possible to formulate a sensible theory describing matter and fields in solutions with CTCs. (See SEP entry on Time Machines; Smeenk and Wüthrich 2011 for more.)

There is a different question regarding the limitations of these toy models. The toy models and related examples show that there are consistent solutions for simple systems in the presence of CTCs. As usual we have made the analysis tractable by building toy models, selecting only a few dynamical degrees of freedom and tracking their evolution. But there is a large gap between the systems we have described and the time travel stories they evoke, with Kurt traveling along a CTC with murderous intentions. In particular, many features of the manifest image of time are tied to the thermodynamical properties of macroscopic systems. Rovelli (unpublished) considers a extremely simple system to illustrate the problem: can a clock move along a CTC? A clock consists of something in periodic motion, such as a pendulum bob, and something that counts the oscillations, such as an escapement mechanism. The escapement mechanism cannot work without friction; this requires dissipation and increasing entropy. For a clock that counts oscillations as it moves along a time-like trajectory, the entropy must be a monotonically increasing function. But that is obviously incompatible with the clock returning to precisely the same state at some future time as it completes a loop. The point generalizes, obviously, to imply that anything like a human, with memory and agency, cannot move along a CTC.

Since it is not obvious that one can rid oneself of all constraints in realistic models, let us examine the argument that time travel is implausible, and we should think it unlikely to exist in our world, in so far as it implies such constraints. The argument goes something like the following. In order to satisfy such constraints one needs some pre-established divine harmony between the global (time travel) structure of space-time and the distribution of particles and fields on space-like surfaces in it. But it is not plausible that the actual world, or any world even remotely like ours, is constructed with divine harmony as part of the plan. In fact, one might argue, we have empirical evidence that conditions in any spatial region can vary quite arbitrarily. So we have evidence that such constraints, whatever they are, do not in fact exist in our world. So we have evidence that there are no closed time-like lines in our world or one remotely like it. We will now examine this argument in more detail by presenting four possible responses, with counterresponses, to this argument.

Response 1. There is nothing implausible or new about such constraints. For instance, if the universe is spatially closed, there has to be enough matter to produce the needed curvature, and this puts constraints on the matter distribution on a space-like hypersurface. Thus global space-time structure can quite unproblematically constrain matter distributions on space-like hypersurfaces in it. Moreover we have no realistic idea what these constraints look like, so we hardly can be said to have evidence that they do not obtain.

Counterresponse 1. Of course there are constraining relations between the global structure of space-time and the matter in it. The Einstein equations relate curvature of the manifold to the matter distribution in it. But what is so strange and implausible about the constraints imposed by the existence of closed time-like curves is that these constraints in essence have nothing to do with the Einstein equations. When investigating such constraints one typically treats the particles and/or field in question as test particles and/or fields in a given space-time, i.e., they are assumed not to affect the metric of space-time in any way. In typical space-times without closed time-like curves this means that one has, in essence, complete freedom of matter distribution on a space-like hypersurface. (See response 2 for some more discussion of this issue). The constraints imposed by the possibility of time travel have a quite different origin and are implausible. In the ordinary case there is a causal interaction between matter and space-time that results in relations between global structure of space-time and the matter distribution in it. In the time travel case there is no such causal story to be told: there simply has to be some pre-established harmony between the global space-time structure and the matter distribution on some space-like surfaces. This is implausible.

Response 2. Constraints upon matter distributions are nothing new. For instance, Maxwell’s equations constrain electric fields \(\boldsymbol{E}\) on an initial surface to be related to the (simultaneous) charge density distribution \(\varrho\) by the equation \(\varrho = \text{div}(\boldsymbol{E})\). (If we assume that the \(E\) field is generated solely by the charge distribution, this conditions amounts to requiring that the \(E\) field at any point in space simply be the one generated by the charge distribution according to Coulomb’s inverse square law of electrostatics.) This is not implausible divine harmony. Such constraints can hold as a matter of physical law. Moreover, if we had inferred from the apparent free variation of conditions on spatial regions that there could be no such constraints we would have mistakenly inferred that \(\varrho = \text{div}(\boldsymbol{E})\) could not be a law of nature.

Counterresponse 2. The constraints imposed by the existence of closed time-like lines are of quite a different character from the constraint imposed by \(\varrho = \text{div}(\boldsymbol{E})\). The constraints imposed by \(\varrho = \text{div}(\boldsymbol{E})\) on the state on a space-like hypersurface are:

• local constraints (i.e., to check whether the constraint holds in a region you just need to see whether it holds at each point in the region),
• quite independent of the global space-time structure,
• quite independent of how the space-like surface in question is embedded in a given space-time, and
• very simply and generally stateable.

On the other hand, the consistency constraints imposed by the existence of closed time-like curves (i) are not local, (ii) are dependent on the global structure of space-time, (iii) depend on the location of the space-like surface in question in a given space-time, and (iv) appear not to be simply stateable other than as the demand that the state on that space-like surface embedded in such and such a way in a given space-time, do not lead to inconsistency. On some views of laws (e.g., David Lewis’ view) this plausibly implies that such constraints, even if they hold, could not possibly be laws. But even if one does not accept such a view of laws, one could claim that the bizarre features of such constraints imply that it is implausible that such constraints hold in our world or in any world remotely like ours.

Response 3. It would be strange if there are constraints in the non-time travel region. It is not strange if there are constraints in the time travel region. They should be explained in terms of the strange, self-interactive, character of time travel regions. In this region there are time-like trajectories from points to themselves. Thus the state at such a point, in such a region, will, in a sense, interact with itself. It is a well-known fact that systems that interact with themselves will develop into an equilibrium state, if there is such an equilibrium state, or else will develop towards some singularity. Normally, of course, self-interaction isn’t true instantaneous self-interaction, but consists of a feed-back mechanism that takes time. But in time travel regions something like true instantaneous self-interaction occurs. This explains why constraints on states occur in such time travel regions: the states “ ab initio ” have to be “equilibrium states”. Indeed in a way this also provides some picture of why indeterminism occurs in time travel regions: at the onset of self-interaction states can fork into different equi-possible equilibrium states.

Counterresponse 3. This is explanation by woolly analogy. It all goes to show that time travel leads to such bizarre consequences that it is unlikely that it occurs in a world remotely like ours.

Response 4. All of the previous discussion completely misses the point. So far we have been taking the space-time structure as given, and asked the question whether a given time travel space-time structure imposes constraints on states on (parts of) space-like surfaces. However, space-time and matter interact. Suppose that one is in a space-time with closed time-like lines, such that certain counterfactual distributions of matter on some neighborhood of a point \(p\) are ruled out if one holds that space-time structure fixed. One might then ask

Why does the actual state near \(p\) in fact satisfy these constraints? By what divine luck or plan is this local state compatible with the global space-time structure? What if conditions near \(p\) had been slightly different?

And one might take it that the lack of normal answers to these questions indicates that it is very implausible that our world, or any remotely like it, is such a time travel universe. However the proper response to these question is the following. There are no constraints in any significant sense. If they hold they hold as a matter of accidental fact, not of law. There is no more explanation of them possible than there is of any contingent fact. Had conditions in a neighborhood of \(p\) been otherwise, the global structure of space-time would have been different. So what? The only question relevant to the issue of constraints is whether an arbitrary state on an arbitrary spatial surface \(S\) can always be embedded into a space-time such that that state on \(S\) consistently extends to a solution on the entire space-time.

But we know the answer to that question. A well-known theorem in general relativity says the following: any initial data set on a three dimensional manifold \(S\) with positive definite metric has a unique embedding into a maximal space-time in which \(S\) is a Cauchy surface (see, e.g., Geroch & Horowitz 1979: 284 for more detail), i.e., there is a unique largest space-time which has \(S\) as a Cauchy surface and contains a consistent evolution of the initial value data on \(S\). Now since \(S\) is a Cauchy surface this space-time does not have closed time like curves. But it may have extensions (in which \(S\) is not a Cauchy surface) which include closed timelike curves, indeed it may be that any maximal extension of it would include closed timelike curves. (This appears to be the case for extensions of states on certain surfaces of Taub-NUT space-times. See Earman, Smeenk, & Wüthrich 2009). But these extensions, of course, will be consistent. So properly speaking, there are no constraints on states on space-like surfaces. Nonetheless the space-time in which these are embedded may or may not include closed time-like curves.

Counterresponse 4. This, in essence, is the stonewalling answer which we indicated in section 1. However, whether or not you call the constraints imposed by a given space-time on distributions of matter on certain space-like surfaces “genuine constraints”, whether or not they can be considered lawlike, and whether or not they need to be explained, the existence of such constraints can still be used to argue that time travel worlds are so bizarre that it is implausible that our world or any world remotely like ours is a time travel world.

Suppose that one is in a time travel world. Suppose that given the global space-time structure of this world, there are constraints imposed upon, say, the state of motion of a ball on some space-like surface when it is treated as a test particle, i.e., when it is assumed that the ball does not affect the metric properties of the space-time it is in. (There is lots of other matter that, via the Einstein equation, corresponds exactly to the curvature that there is everywhere in this time travel worlds.) Now a real ball of course does have some effect on the metric of the space-time it is in. But let us consider a ball that is so small that its effect on the metric is negligible. Presumably it will still be the case that certain states of this ball on that space-like surface are not compatible with the global time travel structure of this universe.

This means that the actual distribution of matter on such a space-like surface can be extended into a space-time with closed time-like lines, but that certain counterfactual distributions of matter on this space-like surface can not be extended into the same space-time. But note that the changes made in the matter distribution (when going from the actual to the counterfactual distribution) do not in any non-negligible way affect the metric properties of the space-time. (Recall that the changes only effect test particles.) Thus the reason why the global time travel properties of the counterfactual space-time have to be significantly different from the actual space-time is not that there are problems with metric singularities or alterations in the metric that force significant global changes when we go to the counterfactual matter distribution. The reason that the counterfactual space-time has to be different is that in the counterfactual world the ball’s initial state of motion starting on the space-like surface, could not “meet up” in a consistent way with its earlier self (could not be consistently extended) if we were to let the global structure of the counterfactual space-time be the same as that of the actual space-time. Now, it is not bizarre or implausible that there is a counterfactual dependence of manifold structure, even of its topology, on matter distributions on spacelike surfaces. For instance, certain matter distributions may lead to singularities, others may not. We may indeed in some sense have causal power over the topology of the space-time we live in. But this power normally comes via the Einstein equations. But it is bizarre to think that there could be a counterfactual dependence of global space-time structure on the arrangement of certain tiny bits of matter on some space-like surface, where changes in that arrangement by assumption do not affect the metric anywhere in space-time in any significant way . It is implausible that we live in such a world, or that a world even remotely like ours is like that.

Let us illustrate this argument in a different way by assuming that wormhole time travel imposes constraints upon the states of people prior to such time travel, where the people have so little mass/energy that they have negligible effect, via the Einstein equation, on the local metric properties of space-time. Do you think it more plausible that we live in a world where wormhole time travel occurs but it only occurs when people’s states are such that these local states happen to combine with time travel in such a way that nobody ever succeeds in killing their younger self, or do you think it more plausible that we are not in a wormhole time travel world? [ 5 ]

An alternative approach to time travel (initiated by Deutsch 1991) abstracts away from the idealized toy models described above. [ 6 ] This computational approach considers instead the evolution of bits (simple physical systems with two discrete states) through a network of interactions, which can be represented by a circuit diagram with gates corresponding to the interactions. Motivated by the possibility of CTCs, Deutsch proposed adding a new kind of channel that connects the output of a given gate back to its input —in essence, a backwards-time step. More concretely, given a gate that takes \(n\) bits as input, we can imagine taking some number \(i \lt n\) of these bits through a channel that loops back and then do double-duty as inputs. Consistency requires that the state of these \(i\) bits is the same for output and input. (We will consider an illustration of this kind of system in the next section.) Working through examples of circuit diagrams with a CTC channel leads to similar treatments of Consistency and Underdetermination as the discussion above (see, e.g., Wallace 2012: § 10.6). But the approach offers two new insights (both originally due to Deutsch): the Easy Knowledge paradox, and a particularly clear extension to time travel in quantum mechanics.

A computer equipped with a CTC channel can exploit the need to find consistent evolution to solve remarkably hard problems. (This is quite different than the first idea that comes to mind to enhance computational power: namely to just devote more time to a computation, and then send the result back on the CTC to an earlier state.) The gate in a circuit incorporating a CTC implements a function from the input bits to the output bits, under the constraint that the output and input match the i bits going through the CTC channel. This requires, in effect, finding the fixed point of the relevant function. Given the generality of the model, there are few limits on the functions that could be implemented on the CTC circuit. Nature has to solve a hard computational problem just to ensure consistent evolution. This can then be extended to other complex computational problems—leading, more precisely, to solutions of NP -complete problems in polynomial time (see Aaronson 2013: Chapter 20 for an overview and further references). The limits imposed by computational complexity are an essential part of our epistemic situation, and computers with CTCs would radically change this.

We now turn to the application of the computational approach to the quantum physics of time travel (see Deutsch 1991; Deutsch & Lockwood 1994). By contrast with the earlier discussions of constraints in classical systems, they claim to show that time travel never imposes any constraints on the pre-time travel state of quantum systems. The essence of this account is as follows. [ 7 ]

A quantum system starts in state \(S_1\), interacts with its older self, after the interaction is in state \(S_2\), time travels while developing into state \(S_3\), then interacts with its younger self, and ends in state \(S_4\) (see figure 10 ).

Figure 10 [An extended description of figure 10 is in the supplement.]

Deutsch assumes that the set of possible states of this system are the mixed states, i.e., are represented by the density matrices over the Hilbert space of that system. Deutsch then shows that for any initial state \(S_1\), any unitary interaction between the older and younger self, and any unitary development during time travel, there is a consistent solution, i.e., there is at least one pair of states \(S_2\) and \(S_3\) such that when \(S_1\) interacts with \(S_3\) it will change to state \(S_2\) and \(S_2\) will then develop into \(S_3\). The states \(S_2, S_3\) and \(S_4\) will typically be not be pure states, i.e., will be non-trivial mixed states, even if \(S_1\) is pure. In order to understand how this leads to interpretational problems let us give an example. Consider a system that has a two dimensional Hilbert space with as a basis the states \(\vc{+}\) and \(\vc{-}\). Let us suppose that when state \(\vc{+}\) of the young system encounters state \(\vc{+}\) of the older system, they interact and the young system develops into state \(\vc{-}\) and the old system remains in state \(\vc{+}\). In obvious notation:

Similarly, suppose that:

Let us furthermore assume that there is no development of the state of the system during time travel, i.e., that \(\vc{+}_2\) develops into \(\vc{+}_3\), and that \(\vc{-}_2\) develops into \(\vc{-}_3\).

Now, if the only possible states of the system were \(\vc{+}\) and \(\vc{-}\) (i.e., if there were no superpositions or mixtures of these states), then there is a constraint on initial states: initial state \(\vc{+}_1\) is impossible. For if \(\vc{+}_1\) interacts with \(\vc{+}_3\) then it will develop into \(\vc{-}_2\), which, during time travel, will develop into \(\vc{-}_3\), which inconsistent with the assumed state \(\vc{+}_3\). Similarly if \(\vc{+}_1\) interacts with \(\vc{-}_3\) it will develop into \(\vc{+}_2\), which will then develop into \(\vc{+}_3\) which is also inconsistent. Thus the system can not start in state \(\vc{+}_1\).

But, says Deutsch, in quantum mechanics such a system can also be in any mixture of the states \(\vc{+}\) and \(\vc{-}\). Suppose that the older system, prior to the interaction, is in a state \(S_3\) which is an equal mixture of 50% \(\vc{+}_3\) and 50% \(\vc{-}_3\). Then the younger system during the interaction will develop into a mixture of 50% \(\vc{+}_2\) and 50% \(\vc{-}_2\), which will then develop into a mixture of 50% \(\vc{+}_3\) and 50% \(\vc{-}_3\), which is consistent! More generally Deutsch uses a fixed point theorem to show that no matter what the unitary development during interaction is, and no matter what the unitary development during time travel is, for any state \(S_1\) there is always a state \(S_3\) (which typically is not a pure state) which causes \(S_1\) to develop into a state \(S_2\) which develops into that state \(S_3\). Thus quantum mechanics comes to the rescue: it shows in all generality that no constraints on initial states are needed!

One might wonder why Deutsch appeals to mixed states: will superpositions of states \(\vc{+}\) and \(\vc{-}\) not suffice? Unfortunately such an idea does not work. Suppose again that the initial state is \(\vc{+}_1\). One might suggest that that if state \(S_3\) is

one will obtain a consistent development. For one might think that when initial state \(\vc{+}_1\) encounters the superposition

it will develop into superposition

and that this in turn will develop into

as desired. However this is not correct. For initial state \(\vc{+}_1\) when it encounters

will develop into the entangled state

In so far as one can speak of the state of the young system after this interaction, it is in the mixture of 50% \(\vc{+}_2\) and 50% \(\vc{-}_2\), not in the superposition

So Deutsch does need his recourse to mixed states.

This clarification of why Deutsch needs his mixtures does however indicate a serious worry about the simplifications that are part of Deutsch’s account. After the interaction the old and young system will (typically) be in an entangled state. Although for purposes of a measurement on one of the two systems one can say that this system is in a mixed state, one can not represent the full state of the two systems by specifying the mixed state of each separate part, as there are correlations between observables of the two systems that are not represented by these two mixed states, but are represented in the joint entangled state. But if there really is an entangled state of the old and young systems directly after the interaction, how is one to represent the subsequent development of this entangled state? Will the state of the younger system remain entangled with the state of the older system as the younger system time travels and the older system moves on into the future? On what space-like surfaces are we to imagine this total entangled state to be? At this point it becomes clear that there is no obvious and simple way to extend elementary non-relativistic quantum mechanics to space-times with closed time-like curves: we apparently need to characterize not just the entanglement between two systems, but entanglement relative to specific spacetime descriptions.

How does Deutsch avoid these complications? Deutsch assumes a mixed state \(S_3\) of the older system prior to the interaction with the younger system. He lets it interact with an arbitrary pure state \(S_1\) younger system. After this interaction there is an entangled state \(S'\) of the two systems. Deutsch computes the mixed state \(S_2\) of the younger system which is implied by this entangled state \(S'\). His demand for consistency then is just that this mixed state \(S_2\) develops into the mixed state \(S_3\). Now it is not at all clear that this is a legitimate way to simplify the problem of time travel in quantum mechanics. But even if we grant him this simplification there is a problem: how are we to understand these mixtures?

If we take an ignorance interpretation of mixtures we run into trouble. For suppose that we assume that in each individual case each older system is either in state \(\vc{+}_3\) or in state \(\vc{-}_3\) prior to the interaction. Then we regain our paradox. Deutsch instead recommends the following, many worlds, picture of mixtures. Suppose we start with state \(\vc{+}_1\) in all worlds. In some of the many worlds the older system will be in the \(\vc{+}_3\) state, let us call them A -worlds, and in some worlds, B -worlds, it will be in the \(\vc{-}_3\) state. Thus in A -worlds after interaction we will have state \(\vc{-}_2\) , and in B -worlds we will have state \(\vc{+}_2\). During time travel the \(\vc{-}_2\) state will remain the same, i.e., turn into state \(\vc{-}_3\), but the systems in question will travel from A -worlds to B -worlds. Similarly the \(\vc{+}\) \(_2\) states will travel from the B -worlds to the A -worlds, thus preserving consistency.

Now whatever one thinks of the merits of many worlds interpretations, and of this understanding of it applied to mixtures, in the end one does not obtain genuine time travel in Deutsch’s account. The systems in question travel from one time in one world to another time in another world, but no system travels to an earlier time in the same world. (This is so at least in the normal sense of the word “world”, the sense that one means when, for instance, one says “there was, and will be, only one Elvis Presley in this world.”) Thus, even if it were a reasonable view, it is not quite as interesting as it may have initially seemed. (See Wallace 2012 for a more sympathetic treatment, that explores several further implications of accepting time travel in conjunction with the many worlds interpretation.)

We close by acknowledging that Deutsch’s starting point—the claim that this computational model captures the essential features of quantum systems in a spacetime with CTCs—has been the subject of some debate. Several physicists have pursued a quite different treatment of evolution of quantum systems through CTC’s, based on considering the “post-selected” state (see Lloyd et al. 2011). Their motivations for implementing the consistency condition in terms of the post-selected state reflects a different stance towards quantum foundations. A different line of argument aims to determine whether Deutsch’s treatment holds as an appropriate limiting case of a more rigorous treatment, such as quantum field theory in curved spacetimes. For example, Verch (2020) establishes several results challenging the assumption that Deutsch’s treatment is tied to the presence of CTC’s, or that it is compatible with the entanglement structure of quantum fields.

What remains of the grandfather paradox in general relativistic time travel worlds is the fact that in some cases the states on edgeless spacelike surfaces are “overconstrained”, so that one has less than the usual freedom in specifying conditions on such a surface, given the time-travel structure, and in some cases such states are “underconstrained”, so that states on edgeless space-like surfaces do not determine what happens elsewhere in the way that they usually do, given the time travel structure. There can also be mixtures of those two types of cases. The extent to which states are overconstrained and/or underconstrained in realistic models is as yet unclear, though it would be very surprising if neither obtained. The extant literature has primarily focused on the problem of overconstraint, since that, often, either is regarded as a metaphysical obstacle to the possibility time travel, or as an epistemological obstacle to the plausibility of time travel in our world. While it is true that our world would be quite different from the way we normally think it is if states were overconstrained, underconstraint seems at least as bizarre as overconstraint. Nonetheless, neither directly rules out the possibility of time travel.

If time travel entailed contradictions then the issue would be settled. And indeed, most of the stories employing time travel in popular culture are logically incoherent: one cannot “change” the past to be different from what it was, since the past (like the present and the future) only occurs once. But if the only requirement demanded is logical coherence, then it seems all too easy. A clever author can devise a coherent time-travel scenario in which everything happens just once and in a consistent way. This is just too cheap: logical coherence is a very weak condition, and many things we take to be metaphysically impossible are logically coherent. For example, it involves no logical contradiction to suppose that water is not molecular, but if both chemistry and Kripke are right it is a metaphysical impossibility. We have been interested not in logical possibility but in physical possibility. But even so, our conditions have been relatively weak: we have asked only whether time-travel is consistent with the universal validity of certain fundamental physical laws and with the notion that the physical state on a surface prior to the time travel region be unconstrained. It is perfectly possible that the physical laws obey this condition, but still that time travel is not metaphysically possible because of the nature of time itself. Consider an analogy. Aristotle believed that water is homoiomerous and infinitely divisible: any bit of water could be subdivided, in principle, into smaller bits of water. Aristotle’s view contains no logical contradiction. It was certainly consistent with Aristotle’s conception of water that it be homoiomerous, so this was, for him, a conceptual possibility. But if chemistry is right, Aristotle was wrong both about what water is like and what is possible for it. It can’t be infinitely divided, even though no logical or conceptual analysis would reveal that.

Similarly, even if all of our consistency conditions can be met, it does not follow that time travel is physically possible, only that some specific physical considerations cannot rule it out. The only serious proof of the possibility of time travel would be a demonstration of its actuality. For if we agree that there is no actual time travel in our universe, the supposition that there might have been involves postulating a substantial difference from actuality, a difference unlike in kind from anything we could know if firsthand. It is unclear to us exactly what the content of possible would be if one were to either maintain or deny the possibility of time travel in these circumstances, unless one merely meant that the possibility is not ruled out by some delineated set of constraints. As the example of Aristotle’s theory of water shows, conceptual and logical “possibility” do not entail possibility in a full-blooded sense. What exactly such a full-blooded sense would be in case of time travel, and whether one could have reason to believe it to obtain, remain to us obscure.

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How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Adlam, Emily, unpublished, “ Is There Causation in Fundamental Physics? New Insights from Process Matrices and Quantum Causal Modelling ”, 2022, arXiv: 2208.02721. doi:10.48550/ARXIV.2208.02721
• Rovelli, Carlo, unpublished, “ Can We Travel to the Past? Irreversible Physics along Closed Timelike Curves ”, arXiv: 1912.04702. doi:10.48550/ARXIV.1912.04702

causation: backward | determinism: causal | quantum mechanics | quantum mechanics: retrocausality | space and time: being and becoming in modern physics | time machines | time travel

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Time Travel

Arguably, we are always travelling though time, as we move from the past into the future. But time travel usually refers to the possibility of changing the rate at which we travel into the future, or completely reversing it so that we travel into the past. Although a plot device in fiction since the 19 th Century (see the section on Time in Literature ), time travel has never been practically demonstrated or verified, and may still be impossible.

Time travel is not possible in Newtonian absolute time (we move deterministically and linearly forward into the future). Neither is it possible according to special relativity (we are constrained by our light cones). But general relativity does raises the prospect (at least theoretically) of travel through time, i.e. the possibility of movement backwards and/or forwards in time, independently of the normal flow of time we observe on Earth, in much the same way as we can move between different points in space.

Time travel is usually taken to mean that a person’s mind and body remain unchanged, with their memories intact, while their location in time is changed. If the traveller’s body and mind reverted its condition at the destination time, then no time travel would be perceptible.

Time Travel Scenarios

Although, in the main, differing fundamentally from the H.G. Wells concept of a physical machine with levers and dials, many different speculative time travel solutions and scenarios have been put forward over the years. However, the actual physical plausibility of these solutions in the real world remains uncertain.

At its simplest, as we have seen in the section on Relativistic Time , if one were to travel from the Earth at relativistic speeds and then return, then more time would have passed on Earth than for the traveller, so the traveller would, from his perspective, effectively have “travelled into the future”. This is not to say that the traveller suddenly jumped into the Earth’s future, in the way that time travel is often envisioned, but that, as judged by the Earth’s external time, the traveller has experienced less passage of time than his twin who remained on Earth. This is not real time travel, though, but more in the nature of “fast-forwarding” through time: it is a one-way journey forwards with no way back.

There does, however, appear to be some scientific basis within the Theory of Relativity for the possibility of real time travel in certain scenarios. Kurt Gödel showed, back in the early days of relativity, that there are some solutions to the field equations of general relativity that describe space-times so warped that they contain “ closed time-like curves ”, where an individual time-cone twists and closes in on itself, allowing a path from the present to the distant future or the past. Gödel’s solution was the first challenge in centuries to the dominant idea of linear time on which most of physics rests. Although a special case solution, based on an infinite, rotating universe (not the finite, non-rotating universe we actually find ourselves in), other time travel solution have been identified since then that do not require an infinite, rotating universe, but they remain contentious.

In the 1970s, controversial physicist Frank Tipler published his ideas for a “time machine”, using an infinitely long cylinder which spins along its longitudinal axis, which he claimed would allow time travel both forwards and backwards in time without violating the laws of physics, although Stephen Hawking later disproved Tipler’s ideas.

In 1994, Miguel Alcubierre proposed a hypothetical system whereby a spacecraft would contract space in front of it and expand space behind it, resulting in effective faster-than-light travel and therefore (potentially) time travel, but again the practicalities of constructing this kind of a “ warp drive ” remain prohibitive.

Other theoretical physicists like Kip Thorne and Paul Davies have shown how a wormhole in space-time could theoretically provide an instantaneous gateway to different time periods, in much the same way as general relativity allows the theoretical possibility of instantaneous spatial travel through wormholes. Wormholes are tubes or conduits or short-cuts through space-time, where space-time is so warped that it bends back on itself, another science fiction concept made potential reality by the Theory of Relativity. The drawback is that unimaginable amounts of energy would be required to bring about such a wormhole, although experiments looking into the possibility of creating mini-wormholes and mini-black holes are being carried out at the particle accelerator at CERN in Switzerland. It also seems likely that such a wormhole would collapse instantly into a black hole unless some method of holding it open were devised (possibly so-called “negative energy”, which is known to be theoretically possible, but which is not yet practically feasible). Stephen Hawking has suggested that radiation feedback, analogous to feedback in sound, would destroy the wormhole, which would therefore not last long enough to be used as a time machine. Actually controlling where (and when) a wormhole exits is another pitfall.

Another potential time travel possibility, although admittedly something of a long shot, relates to cosmic strings (or quantum strings ), long shreds of energy left over after the Big Bang, thinner than an atom but incredibly dense, that weave through the entire universe. Richard Gott has suggested that if two such cosmic strings were to pass close to each other, or even close to a black hole, the resulting warpage of space-time could well be so severe as to create a closed-time-like curve. However, cosmic strings remain speculative and the chances of finding such a phenomenon are vanishingly small (and, even if it were possible, such a loop may well find itself trapped inside a rotating black hole).

Physicist Ron Mallet has been looking into the possibility of using lasers to control extreme levels of gravity, which could then potentially be used to control time. According to Mallet, circulating beams of laser-controlled light could create similar conditions to a rotating black hole, with its frame-dragging and potential time travel properties.

Others are looking to quantum mechanics for a solution to time travel. In quantum physics, proven concepts such as superposition and entanglement effectively mean that a particle can be in two (or more) places at once. One interpretation of this (see the section on Quantum Time ) is the “ many worlds ” view in which all the different quantum states exist simultaneously in multiple parallel universes within an overall multiverse. If we could gain access to these alternative parallel universes, a form of time travel might then be possible.

At the sub-sub-microscopic level – at the level of so-called quantum foam , tiny bubbles of matter a billion-trillion-trillionths of a centimetre in length, perpetually popping into and out of existence – it is speculated that tiny tunnels or short-cuts through space-time are constantly forming, disappearing and reforming. Some scientists believe that it may be possible to capture such a quantum tunnel and enlarge it many trillions of times to the human scale. However, the idea is still at a very speculative stage,

It should be noted that, with all of these schemes and ideas, it does not look to be possible to travel any further back in time that the time at which the travel technology was devised.

Faster-Than-Light Particles

The equations of relativity imply that faster-than-light ( superluminal ) particles, if they existed, would theoretically travel backwards in time. Therefore, they could, again theoretically, be used to build a kind of “ antitelephone ” to send signals faster than light, and thus communicate backwards in time. Although the Theory of Relativity disallows particles from accelerating from sub-light speed to the speed of light (among other effects, time would slow right down and effectively stop for such a particle, and its mass would increase to infinity), it does not preclude the possibility of particles that ALWAYS travel faster than light. Therefore, the possibility does still exist in theory for faster-than-light travel in the case of a particle with such properties.

There is a rather strange theoretical particle in physics called the tachyon that routinely travels faster than light, with the corollary that such a particle would naturally travel backwards in time as we know it. So, in theory, one could never see such a particle approaching, only leaving, and the particle could even violate the normal order of cause and effect. For a tachyon, the speed of light is the lower speed limit, while the upper speed limit is infinity, and its speed increases as its energy decreases. Even stranger, the mass of a tachyon would technically be an imaginary number (i.e. the number squared is negative), whatever that might actually mean in practice.

It should be stressed that there is no experimental evidence to suggests that tachyons actually exist, and many physicists deny even the possibility. A tachyon has never been observed or recorded (although the search continues, particularly through analysis of cosmic rays and in particle accelerators), and neither has one ever been created, so they remain hypothetical, although theory strongly supports their existence.

Research using MINOS and OPERA detectors has suggested that tiny particles called neutrinos may travel faster than light. Other more recent research from CERN, however, has put the findings into dispute, and the matter remains inconclusive. Neutrinos are not merely hypothetical particles like tachyons, but a well-known part of modern particle physics. But they are tiny, almost-massless, invisible, electrically neutral, weakly-interacting particles that pass right through normal matter, and consequently are very difficult to measure and deal with (even their mass has never been measured accurately).

Time Travel Paradoxes

The possibility of travel backwards in time is generally considered by scientists to be much more unlikely than travel into the future. The idea of time travel to the past is rife with problems, not least the possibility of temporal paradoxes resulting from the violation of causality (i.e. the possibility that an effect could somehow precede its cause). This is most famously exemplified by the grandfather paradox : if a hypothetical time traveller goes back in time and kills his grandfather, the time traveller himself would never be born when he was meant to be; if he is never born, though, he is unable to travel through time and kill his grandfather, which means that he WOULD be born; etc, etc.

Some have sought to justify the possibility of time travel to the past by the very fact that such paradoxes never actually arise in practice. For example, the simple fact that the time traveller DOES exist at the start of his journey is itself proof that he could not kill his grandfather or change the past in any way, either because free will ceases to exist in the past, or because the outcomes of such decisions are predetermined. Or, alternatively, it is argued, any changes made by a hypothetical future time traveller must already have happened in the traveller’s past, resulting in the same reality that the traveller moves from.

Theoretical physicist Stephen Hawking has suggested that the fundamental laws of nature themselves – particularly the idea that causes always precede effects – may prevent time travel in some way. The apparent absence of “tourists from the future” here in our present is another argument, albeit not a rigorous one, that has been put forward against the possibility of time travel, even in a technologically advanced future (the assumption here is that future civilizations, millions of years more technologically advanced than us, should be capable of travel).

Some interpretations of time travel, though, have tried to resolve such potential paradoxes by accepting the possibility of travel between “ branch points ”, parallel realities or parallel universes , so that any new events caused by a time traveller’s visit to the past take place in a different reality and so do not impact on the original time stream. The idea of parallel universes, first put forward by Hugh Everett III in his “ many worlds ” interpretation of quantum theory in the 1950s, is now quite mainstream and accepted by many (although by no means all) physicists.

>> Quantum Time

Physics of Time

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Exploring the Reality of Time Travel: Science Fact vs. Science Fiction

By Adi Foord, University of Maryland, Baltimore County November 16, 2023

Time travel, a longstanding fascination in science fiction, remains a complex and unresolved concept in science. The second law of thermodynamics suggests time can only move forward, while Einstein’s theory of relativity shows time’s relativity to speed. Theoretical ideas like wormholes offer potential methods, but practical challenges and paradoxes, such as the “grandfather paradox,” complicate the feasibility of actual time travel.

Will it ever be possible for time travel to occur?

Have you ever dreamed of traveling through time, like characters do in science fiction movies? For centuries, the concept of time travel has captivated people’s imaginations. Time travel is the concept of moving between different points in time, just like you move between different places. In movies, you might have seen characters using special machines, magical devices or even hopping into a futuristic car to travel backward or forward in time.

But is this just a fun idea for movies, or could it really happen?

The Science Behind Time Travel

The question of whether time is reversible remains one of the biggest unresolved questions in science. If the universe follows the laws of thermodynamics , it may not be possible. The second law of thermodynamics states that things in the universe can either remain the same or become more disordered over time.

It’s a bit like saying you can’t unscramble eggs once they’ve been cooked. According to this law, the universe can never go back exactly to how it was before. Time can only go forward, like a one-way street.

Time Is Relative

However, physicist Albert Einstein’s theory of special relativity suggests that time passes at different rates for different people. Someone speeding along on a spaceship moving close to the speed of light – 671 million miles per hour! – will experience time slower than a person on Earth.

People have yet to build spaceships that can move at speeds anywhere near as fast as light, but astronauts who visit the International Space Station orbit around the Earth at speeds close to 17,500 mph. Astronaut Scott Kelly has spent 520 days at the International Space Station, and as a result has aged a little more slowly than his twin brother – and fellow astronaut – Mark Kelly. Scott used to be 6 minutes younger than his twin brother. Now, because Scott was traveling so much faster than Mark and for so many days, he is 6 minutes and 5 milliseconds younger .

Theoretical Possibilities and Challenges

Some scientists are exploring other ideas that could theoretically allow time travel. One concept involves wormholes, or hypothetical tunnels in space that could create shortcuts for journeys across the universe. If someone could build a wormhole and then figure out a way to move one end at close to the speed of light – like the hypothetical spaceship mentioned above – the moving end would age more slowly than the stationary end. Someone who entered the moving end and exited the wormhole through the stationary end would come out in their past.

However, wormholes remain theoretical: Scientists have yet to spot one. It also looks like it would be incredibly challenging to send humans through a wormhole space tunnel.

Paradoxes and Failed Dinner Parties

There are also paradoxes associated with time travel. The famous “ grandfather paradox ” is a hypothetical problem that could arise if someone traveled back in time and accidentally prevented their grandparents from meeting. This would create a paradox where you were never born, which raises the question: How could you have traveled back in time in the first place? It’s a mind-boggling puzzle that adds to the mystery of time travel.

Famously, physicist Stephen Hawking tested the possibility of time travel by throwing a dinner party where invitations noting the date, time, and coordinates were not sent out until after it had happened. His hope was that his invitation would be read by someone living in the future, who had capabilities to travel back in time. But no one showed up.

As he pointed out : “The best evidence we have that time travel is not possible, and never will be, is that we have not been invaded by hordes of tourists from the future.”

Artist’s rendering of the James Webb Space Telescope. Credit: Northrop Grumman

Telescopes Are Time Machines

Interestingly, astrophysicists armed with powerful telescopes possess a unique form of time travel . As they peer into the vast expanse of the cosmos, they gaze into the past universe. Light from all galaxies and stars takes time to travel, and these beams of light carry information from the distant past. When astrophysicists observe a star or a galaxy through a telescope, they are not seeing it as it is in the present, but as it existed when the light began its journey to Earth millions to billions of years ago.

NASA’s newest space telescope , the James Webb Space Telescope , is peering at galaxies that were formed at the very beginning of the Big Bang , about 13.7 billion years ago.

While we aren’t likely to have time machines like the ones in movies anytime soon, scientists are actively researching and exploring new ideas. But for now, we’ll have to enjoy the idea of time travel in our favorite books, movies, and dreams.

Written by Adi Foord, Assistant Professor of Astronomy and Astrophysics, University of Maryland, Baltimore County.

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8 comments on "exploring the reality of time travel: science fact vs. science fiction".

Until the problem of the second law of thermodynamics(entropy) is solved, the concept of time travel will remain the subject of science fiction. Since this is a basic law of our universe, there is no conceivable way that we know of to do this. The great thing about our knowledge of the universe is that it continues to grow and with that our view of what is possible continues to change. After all, at one time it was believed we could never leave earth!

The 7 planets are soul pollen in the space @ life has been the world has been prepared @ The pollen of the universe is hidden @ Around the axis of the galaxy, the universe is hidden@@ The pollen of the galaxies is a hidden cluster Itis made that we thought about what wisdom is in God’s work and how it is arranged in the form of words.The verse that is made is as follows @@ John, you are in time @ worlds, planets around the axis of the branches of galaxies @@ 8 Prophets, divine prophets, God-aware witnesses @ God’s words of revelation, they are aware @@ 48 What the words of revelation that every prophet has about @ sometimes Sometimes the message of God has become a verbal cliché in the head @@ 62 The message of God was given to every prophet @ The message was made around the power of God @@ 46 The truth of the religions of the cradle of time is said in the world @ Prophets always came for justice in time @@ 62 A warrior became brave in time @ Delaver Ghahrmani Boud Taarani@@ 43 Omar Noah never died, who knows!@ Imransan Is there an unseen world, immortality!?@@ 49 Men’s rights in the sign @ Human rights, the observance of world justice @@ 40 We have God’s love @ A love that is not patched, separation!!!: @@ 39 Take one word from the end of the first and second stanzas to the bottom of these eight verbal verses, and this sentence is made @@ God-aware, the world is born, you know the sign of God @ Agah,the beginning of time, the world, eternity, the world of separation @@ The meaning of this sentence is That God, who before us humans lived on the earth, formed the earth’s crusts with full knowledge, and we humans know the sign of God, which is on the earth, on the continents and countries, and some names have been shown by God for our knowledge since the end of time.In a later video, if I have a lifetime left, I will explain exactly about these poems, God willing @@ The word of the Prophet 17 is the 17th and Muhammad (PBUH) said that the Bedouin Arabs should pray 17 rakats so that theyperform ablution and be clean and not kill and loot.From the caravans, these were all God’s will, and he is good everywhere, in every nation, God does not like evildoers, sinners, and oppressors.Muhammad (PBUH) was God’s last messenger to the Arab people, he was God’s best prophet, and the third verse is because they do not accept Muhammad (PBUH).Some Iranians who were in contact with me, that’s why in the third verse of this surah, he said that his message was given to every prophet, the message is based on divine power, and the word truth, the first two letters of which istruth, is truth, and truth is the 43rd and forty-third word, and the word is time.It is exactly 46, and this song of the Prophets was revealed at the age of 46 ببخشید اگر قبلآ مطالبی فرستادم که به مذاهب مذاهم ارتباط داد شاید به درد شما نمیخورد من در کامنت های بعدی سعی میکنم از نجوم و حیات زمین سخن بگویم این چند بیت را به خارجی انگلیسی که تبدیل کردم معنی آن حیرت انگیز تعغیر کرد گفتم برای شما بفرستم و بداند که این کلام من نبوده کلام خداوند بوده شما نظرتان در مورد خداوند چیست من میگویم خداوند که پدر ومادر انسان بودند قادر به ساختن ما بودند اما آیا آنها قادر به ساختن ستاره ها هم بودند

Your comment has validity to God. But it surely has no place here, it is only fare if the hole comment were in english and has less of a convincing push in a belief a person either believes or not.

It’s too bad physics can’t come to a complete consensus about time, I would like to add some thought about discoveries it has been proven that time travels in only one direction forward, the experiment dealt with light thru glass and how it reacts in the middle and what change happens after light exits the other side, a simple explanation of this experiment. Brings me to theorize and start that time existed before the big bang and is outside of our universes influence, when time is acted on by gravity the ( Form ) of time is changed until the influence no longer has effect, this could go hand in hand with light photons the photon has a influence in the Form that time has. This can not be a observed difference unless we were to see beyond the speed of light. We do agree that physics changes at a subatomic state and also does some strange changing once the speed of light has been exceeded.

The experiment I referred to was posted on IFL in October 2023 headlined ( Solution to complex light problem shows that time can only go Forward ).

One of the problem with travel time is the one people keep forever. And, that is that the earth is always move through space. Matter of fact, the earth is not in the same place that it was 50 years ago. So you will have to move through space as well as time.

Ironically, the only science fiction that seems to handle this is the original story “The Time Machine”.

Time travel is happening now. It has been done since the 1950s. The method satisfies all the requirements. Traveler can’t change the past, but only observe. You can’t go farther back than when the machine was first invented (1950s). There’s one more limitation, you can only observe what the machine was directed. The time machine, the common video camera, and video tape recorder. Now it’s the camera, and file capture computer. Yes, viewing a video tape is effectively going back in time. It’s more than the video, it’s the sound too. There are working versions of smell, and touch which can be recorded too. If you record, and replicate all the senses, you have effectively complete time travel. The most primitive form is the picture. This technology has been around for thousands of years, and is manually intensive. Later many pictures were strung together to make a film. Using a camera to record film was the first example of complete visual time travel (back to when the film was made). Later sound was added, and we have the movies. A way of going back in time that included sight, and sound. Now we have video systems (YouTub) that can play back past events selected by you. Yes, video systems are virtual time travel machines we have now.

How Stellar Cannibalism Illuminates Cosmic Evolution

جزایر فیلیپین دایناسوری که توسط انسان خلق شده در بیش ده ها میلیون سال و بخاطر ریخته شدن دوهزار متر خاک غرق شده بخاطر بالا آمدن آب اقیانوس اما جزایر فیلیپین شبیه دایناسوریست

The address of the above comment on the site about a thief who was trained by a dinosaur bird who was trained by humans tens of millions of years ago and who arrested murderers and robbers.The police were arrested by big birds.don’t the scientists of the world think about this?They were buried in the bed of important cities, they were buried with all the tools and machines, the traces of humans tens of millions of years ago, they had a civilization and a history of hundreds of thousands of years, they built a base underthe earth, from the meteorites that explode from the planets when they hit the sun, and they knew that several thousand meters of soil is poured on the surface of the seas and islands, and they knew that the shapes they made of the islands in thecountry of Papua may go under the ocean, of course, the Philippine islands.The picture is of a baby dinosaur that went under the ocean, but the northern island of Australia, which is Papua, is quite clear.It is a big dinosaur whose tail is towards the east and its mouth is open towards the west.There is the Philippines, but it was more difficult to take the soil to the Philippine islands to create a dinosaur than the island of Papua, that is why the height of the soil in the Philippines is lower, and when the meteorites fell a few kilometerson the surface of the ocean, the image created by humans under the ocean in the shape of a dinosaur is hidden in the American continent The picture is of a bird in the shape of a dinosaur that is flying, and this bird was made to flyby the Indians of the tribe, that bird was talking to people, but its spirit might have heard something from the police because a thief while in the bird’s mouth He was handcuffed by the police and the weapon, which is a machine gun, is fromthe east of the American continent on the coast

The country of Florida is a machine gun.When you continue to New York City, you will reach the mouth of the dinosaur, where a thief is trapped in the mouth of a bird, and the little finger of the police handcuffed the thief’s hand, and a small colt is in the hand ofthe thief, who the police caught in the mouth of the dinosaur.put in the mouth of the bird dinosaur, you can clearly see that the thief fell on the ground and was shot in the head, and it is clear that his forehead was pierced, the bird’s mouth is open in flight, the head of the birdis from the east of the American continent, and a fish is placed in the bird’s mouth in the water of the ocean.The stretched glove of the police, which is in the form of a fist, with a handcuff attached to the left hand of the thief who fell on the ground in the sea and the mouth of the bird, the head of the thief and the killer, is located towards the southwest and west coast of America.All these images were created from the American continent and islands by Humans were created, but they didn’t have enough fuel and time to create more accurate images and meteorites ruined the beauty of the images, but it is clear that all these changes were createdby humans, but you have to consider that two thousand meters of soil from meteorites are fish.And they buried the whales under the beaches, and after a very long time, the bodies of the whales turned into oil under the two thousand meters of soil on the beaches, and on the other hand, the presence of two thousand meters of soil onthe surface of the seas and droughts could not make the created images disappear.

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Is Time Travel Possible?

• Cosmology & Astrophysics
• Physics Laws, Concepts, and Principles
• Quantum Physics
• Important Physicists
• Thermodynamics
• Weather & Climate

• M.S., Mathematics Education, Indiana University
• B.A., Physics, Wabash College

Stories regarding travel into the past and the future have long captured our imagination, but the question of whether time travel is possible is a thorny one that gets right to the heart of understanding what physicists mean when they use the word "time." 

Modern physics teaches us that time is one of the most mysterious aspects of our universe, though it may at first seem straightforward. Einstein revolutionized our understanding of the concept, but even with this revised understanding, some scientists still ponder the question of whether or not ​ time actually exists or whether it is a mere "stubbornly persistent illusion" (as Einstein once called it). Whatever time is, though, physicists (and fiction writers) have found some interesting ways to manipulate it to consider traversing it in unorthodox ways.

Time and Relativity

Though referenced in H.G. Wells' The Time Machine (1895), the actual science of time travel didn't come into being until well into the twentieth century, as a side-effect of Albert Einstein 's theory of general relativity (developed in 1915). Relativity describes the physical fabric of the universe in terms of a 4-dimensional spacetime, which includes three spatial dimensions (up/down, left/right, and front/back) along with one time dimension. Under this theory, which has been proven by numerous experiments over the last century, gravity is a result of the bending of this spacetime in response to the presence of matter. In other words, given a certain configuration of matter, the actual spacetime fabric of the universe can be altered in significant ways.

One of the amazing consequences of relativity is that movement can result in a difference in the way time passes, a process known as time dilation . This is most dramatically manifested in the classic Twin Paradox . In this method of "time travel," you can move into the future faster than normal, but there's not really any way back. (There's a slight exception, but more on that later in the article.)

Early Time Travel

In 1937, Scottish physicist W. J. van Stockum first applied general relativity in a way that opened the door for time travel. By applying the equation of general relativity to a situation with an infinitely long, extremely dense rotating cylinder (kind of like an endless barbershop pole). The rotation of such a massive object actually creates a phenomenon known as "frame dragging," which is that it actually drags spacetime along with it. Van Stockum found that in this situation, you could create a path in 4-dimensional spacetime which began and ended at the same point - something called a closed timelike curve - which is the physical result that allows time travel. You can set off in a space ship and travel a path which brings you back to the exact same moment you started out at.

Though an intriguing result, this was a fairly contrived situation, so there wasn't really much concern about it taking place. A new interpretation was about to come along, however, which was much more controversial.

In 1949, the mathematician Kurt Godel - a friend of Einstein's and a colleague at Princeton University's Institute for Advanced Study - decided to tackle a situation where the whole universe is rotating. In Godel's solutions, time travel was actually allowed by the equations if the universe were rotating. A rotating universe could itself function as a time machine.

Now, if the universe were rotating, there would be ways to detect it (light beams would bend, for example, if the whole universe were rotating), and so far the evidence is overwhelmingly strong that there is no sort of universal rotation. So again, time travel is ruled out by this particular set of results. But the fact is that things in the universe do rotate, and that again opens up the possibility.

Time Travel and Black Holes

In 1963, New Zealand mathematician Roy Kerr used the field equations to analyze a rotating black hole , called a Kerr black hole, and found that the results allowed a path through a wormhole in the black hole, missing the singularity at the center, and make it out the other end. This scenario also allows for closed timelike curves, as theoretical physicist Kip Thorne realized years later.

In the early 1980s, while Carl Sagan worked on his 1985 novel Contact , he approached Kip Thorne with a question about the physics of time travel, which inspired Thorne to examine the concept of using a black hole as a means of time travel. Together with the physicist Sung-Won Kim, Thorne realized that you could (in theory) have a black hole with a wormhole connecting it to another point in space held open by some form of negative energy.

But just because you have a wormhole doesn't mean that you have a time machine. Now, let's assume that you could move one end of the wormhole (the "movable end). You place the movable end on a spaceship, shooting it off into space at nearly the speed of light . Time dilation kicks in, and the time experienced by the movable end is much less than the time experienced by the fixed end. Let's assume that you move the movable end 5,000 years into the future of the Earth, but the movable end only "ages" 5 years. So you leave in 2010 AD, say, and arrive in 7010 AD.

However, if you travel through the movable end, you will actually pop out of the fixed end in 2015 AD (since 5 years have passed back on Earth). What? How does this work?

Well, the fact is that the two ends of the wormhole are connected. No matter how far apart they are, in spacetime, they're still basically "near" each other. Since the movable end is only five years older than when it left, going through it will send you back to the related point on the fixed wormhole. And if someone from 2015 AD Earth steps through the fixed wormhole, they'd come out in 7010 AD from the movable wormhole. (If someone stepped through the wormhole in 2012 AD, they'd end up on the spaceship somewhere in the middle of the trip and so on.)

Though this is the most physically reasonable description of a time machine, there are still problems. No one knows if wormholes or negative energy exist, nor how to put them together in this way if they do exist. But it is (in theory) possible.

• Can We Travel Through Time to the Past?
• Closed Timelike Curve
• Wormholes: What Are They and Can We Use Them?
• What Is the Twin Paradox? Real Time Travel
• Time Travel: Dream or Possible Reality?
• Einstein's Theory of Relativity
• The Science of Star Trek
• What Is Time? A Simple Explanation
• Understanding Time Dilation Effects in Physics
• Is Warp Drive From 'Star Trek' Possible?
• Understanding Cosmology and Its Impact
• An Introduction to Black Holes
• Cosmos Episode 4 Viewing Worksheet
• The History of Gravity
• Spiral Galaxies
• Black Holes and Hawking Radiation

• Red Light, Green Light
• Engineering Healthy Silence: Using Noise-Cancelling Headphones to Block Harmful Sound
• Crushing the Sound Barrier
• The Powers of Melanin
• E-Ink Technology: the Secret Behind Kindle

USC Viterbi School of Engineering

The Science of Time Travel

About the Author: Mark Villanueva

At the time of publication, Mark Villanueva was a student at the University of Southern California in his third year towards his BS in Computer Science. Back to the Future is one of his favorite movies.

Introduction

Definition of time travel.

Traversing in the fourth dimension is vastly different than moving in the previously mentioned three. We simply cannot will ourselves to move forward five minutes or back ten days. In other words, time only moves forward, and we are stuck moving in that direction like corks bobbing helplessly in a river [1]. Thus, the end goal of time travel is to enable us to control where we go in this fourth dimension. Much like moving back and forth, time travel involves moving to either the past or the future. However, our actions in the fourth dimension are cause for concern. What we do now in the present affects our future. In the same manner, our actions in the past should have affected our present lives. Changing the outcomes of past events leads to what physicists and philosophers refer to as the “Grandfather Paradox,” an issue that needs to be addressed in any serious discussion of time travel.

The Grandfather Paradox

“building” a time machine.

Unfortunately​, no black hole has yet been positively identified. Black holes, if they exist, could come in an extreme range of sizes. The English physicist Stephen Hawking has speculated that tiny black holes with masses no larger than that of a large mountain are possible. Such black holes, in the size range of elementary particles, would have been formed only under the extreme conditions that cosmology theories indicate existed in the very first moments of the universe. On the other hand, gigantic black holes may lie at the center of galaxies [7]. Einstein envisioned a situation in which the ends of two different black holes could be connected. This is known as a wormhole.

The wormhole is one basis for time travel into the past. Physicists liken wormholes to quick paths through the universe, much like the hole a worm burrows through an apple [8]. Instead of apples, these wormholes are theoretical tunnel shortcuts through space (Fig. 3).The trick in this case would be flying a spaceship into the one mouth of the wormhole and coming out the other side in a different time and place [9]. This involves moving one end of the wormhole close to the speed light and keeping the other end stationary near earth in outer space. Like the example with the spaceship traveling near the speed of light in space, the moving end of the wormhole in space will “age” slower than the stationary one; the “younger” end is a quick shortcut that connects to an earlier time on the fixed end [1], so the moving end of the wormhole will bring the traveler back to the past. The time travel process will probably involve a team of advanced scientists that can create wormholes and move them while the time traveler goes through the wormhole in outer space via a spaceship.

The Reality of Time Travel

• [1] J. R. Gott. “Will We Travel Back (Or Forward) In Time?”  Time , Apr. 10, 2000: pp. 68.
• [2] M. Kaku.  Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. New York: Anchor Books, 1994.
• [3] P. J. Riggs. “The Principal Paradox of Time Travel.”  Ratio X , Apr. 1, 1997: pp. 49-64.
• [4] S. Mowbray. “Let’s do the time warp again.”  Popular Science]/i], Mar. 2002: pp. 46-51.
• [5] “How to murder your grandfather and still get born.”  The Economist , Jan. 20, 1996: pp. 81.
• [6] J. M. Zavisa. “How Special Relativity Works” Internet: http://www.howstuffw​orks.com, May 2, 2003. [Oct. 18, 2002].
• [7] L. Smarr. “Black Hole”.  The New Grolier Multimedia Encyclopedia . CD-ROM. 1993 Grolier Electronic Publishing, Inc.
• [8] A. Ramirez. “Clockwork: time travel isn’t what it used to be.”  The New York Times  Jul. 28 2002, natl. ed.: pp. WK3.
• [9] S. W. Hawking. “Protecting the Past: Is Time Travel Possible?”  Astronomy , Apr. 2002: pp. 46.
• [10] M. Moyer. “The Physics of Time Travel.”  Popular Science , Mar. 2002: pp. 52-53.
• [11] C. J. Wheeler. “Of wormholes, time machines and paradoxes.”  Astronomy , Feb 1996: pp. 52-58.
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Time travel could be possible, but only with parallel timelines

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Have you ever made a mistake that you wish you could undo? Correcting past mistakes is one of the reasons we find the concept of time travel so fascinating. As often portrayed in science fiction, with a time machine, nothing is permanent anymore — you can always go back and change it. But is time travel really possible in our universe , or is it just science fiction?

Read more: Curious Kids: is time travel possible for humans?

Our modern understanding of time and causality comes from general relativity . Theoretical physicist Albert Einstein’s theory combines space and time into a single entity — “spacetime” — and provides a remarkably intricate explanation of how they both work, at a level unmatched by any other established theory. This theory has existed for more than 100 years, and has been experimentally verified to extremely high precision, so physicists are fairly certain it provides an accurate description of the causal structure of our universe.

For decades, physicists have been trying to use general relativity to figure out if time travel is possible . It turns out that you can write down equations that describe time travel and are fully compatible and consistent with relativity. But physics is not mathematics, and equations are meaningless if they do not correspond to anything in reality.

Arguments against time travel

There are two main issues which make us think these equations may be unrealistic. The first issue is a practical one: building a time machine seems to require exotic matter , which is matter with negative energy. All the matter we see in our daily lives has positive energy — matter with negative energy is not something you can just find lying around. From quantum mechanics, we know that such matter can theoretically be created, but in too small quantities and for too short times .

However, there is no proof that it is impossible to create exotic matter in sufficient quantities. Furthermore, other equations may be discovered that allow time travel without requiring exotic matter. Therefore, this issue may just be a limitation of our current technology or understanding of quantum mechanics.

The other main issue is less practical, but more significant: it is the observation that time travel seems to contradict logic, in the form of time travel paradoxes . There are several types of such paradoxes, but the most problematic are consistency paradoxes .

A popular trope in science fiction, consistency paradoxes happen whenever there is a certain event that leads to changing the past, but the change itself prevents this event from happening in the first place.

For example, consider a scenario where I enter my time machine, use it to go back in time five minutes, and destroy the machine as soon as I get to the past. Now that I destroyed the time machine, it would be impossible for me to use it five minutes later.

But if I cannot use the time machine, then I cannot go back in time and destroy it. Therefore, it is not destroyed, so I can go back in time and destroy it. In other words, the time machine is destroyed if and only if it is not destroyed. Since it cannot be both destroyed and not destroyed simultaneously, this scenario is inconsistent and paradoxical.

Eliminating the paradoxes

There’s a common misconception in science fiction that paradoxes can be “created.” Time travellers are usually warned not to make significant changes to the past and to avoid meeting their past selves for this exact reason. Examples of this may be found in many time travel movies, such as the Back to the Future trilogy.

But in physics, a paradox is not an event that can actually happen — it is a purely theoretical concept that points towards an inconsistency in the theory itself. In other words, consistency paradoxes don’t merely imply time travel is a dangerous endeavour, they imply it simply cannot be possible.

This was one of the motivations for theoretical physicist Stephen Hawking to formulate his chronology protection conjecture , which states that time travel should be impossible. However, this conjecture so far remains unproven. Furthermore, the universe would be a much more interesting place if instead of eliminating time travel due to paradoxes, we could just eliminate the paradoxes themselves.

One attempt at resolving time travel paradoxes is theoretical physicist Igor Dmitriyevich Novikov’s self-consistency conjecture , which essentially states that you can travel to the past, but you cannot change it.

According to Novikov, if I tried to destroy my time machine five minutes in the past, I would find that it is impossible to do so. The laws of physics would somehow conspire to preserve consistency.

Introducing multiple histories

But what’s the point of going back in time if you cannot change the past? My recent work, together with my students Jacob Hauser and Jared Wogan, shows that there are time travel paradoxes that Novikov’s conjecture cannot resolve. This takes us back to square one, since if even just one paradox cannot be eliminated, time travel remains logically impossible.

So, is this the final nail in the coffin of time travel? Not quite. We showed that allowing for multiple histories (or in more familiar terms, parallel timelines) can resolve the paradoxes that Novikov’s conjecture cannot. In fact, it can resolve any paradox you throw at it.

The idea is very simple. When I exit the time machine, I exit into a different timeline. In that timeline, I can do whatever I want, including destroying the time machine, without changing anything in the original timeline I came from. Since I cannot destroy the time machine in the original timeline, which is the one I actually used to travel back in time, there is no paradox.

After working on time travel paradoxes for the last three years , I have become increasingly convinced that time travel could be possible, but only if our universe can allow multiple histories to coexist. So, can it?

Quantum mechanics certainly seems to imply so, at least if you subscribe to Everett’s “many-worlds” interpretation , where one history can “split” into multiple histories, one for each possible measurement outcome – for example, whether Schrödinger’s cat is alive or dead, or whether or not I arrived in the past.

But these are just speculations. My students and I are currently working on finding a concrete theory of time travel with multiple histories that is fully compatible with general relativity. Of course, even if we manage to find such a theory, this would not be sufficient to prove that time travel is possible, but it would at least mean that time travel is not ruled out by consistency paradoxes.

Time travel and parallel timelines almost always go hand-in-hand in science fiction, but now we have proof that they must go hand-in-hand in real science as well. General relativity and quantum mechanics tell us that time travel might be possible, but if it is, then multiple histories must also be possible.

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Time travel: five ways that we could do it

Cathal O’Connell

Cathal O'Connell is a science writer based in Melbourne.

In 2009 the British physicist Stephen Hawking held a party for time travellers – the twist was he sent out the invites a year later (No guests showed up). Time travel is probably impossible. Even if it were possible, Hawking and others have argued that you could never travel back before the moment your time machine was built.

But travel to the future? That’s a different story.

Of course, we are all time travellers as we are swept along in the current of time, from past to future, at a rate of one hour per hour.

But, as with a river, the current flows at different speeds in different places. Science as we know it allows for several methods to take the fast-track into the future. Here’s a rundown.

1. Time travel via speed

This is the easiest and most practical way to time travel into the far future – go really fast.

According to Einstein’s theory of special relativity, when you travel at speeds approaching the speed of light, time slows down for you relative to the outside world.

This is not a just a conjecture or thought experiment – it’s been measured. Using twin atomic clocks (one flown in a jet aircraft, the other stationary on Earth) physicists have shown that a flying clock ticks slower, because of its speed.

In the case of the aircraft, the effect is minuscule. But If you were in a spaceship travelling at 90% of the speed of light, you’d experience time passing about 2.6 times slower than it was back on Earth.

And the closer you get to the speed of light, the more extreme the time-travel.

Computer solves a major time travel problem

The highest speeds achieved through any human technology are probably the protons whizzing around the Large Hadron Collider at 99.9999991% of the speed of light. Using special relativity we can calculate one second for the proton is equivalent to 27,777,778 seconds, or about 11 months , for us.

Amazingly, particle physicists have to take this time dilation into account when they are dealing with particles that decay. In the lab, muon particles typically decay in 2.2 microseconds. But fast moving muons, such as those created when cosmic rays strike the upper atmosphere, take 10 times longer to disintegrate.

2. Time travel via gravity

The next method of time travel is also inspired by Einstein. According to his theory of general relativity, the stronger the gravity you feel, the slower time moves.

As you get closer to the centre of the Earth, for example, the strength of gravity increases. Time runs slower for your feet than your head.

Again, this effect has been measured. In 2010, physicists at the US National Institute of Standards and Technology (NIST) placed two atomic clocks on shelves, one 33 centimetres above the other, and measured the difference in their rate of ticking. The lower one ticked slower because it feels a slightly stronger gravity.

To travel to the far future, all we need is a region of extremely strong gravity, such as a black hole. The closer you get to the event horizon, the slower time moves – but it’s risky business, cross the boundary and you can never escape.

And anyway, the effect is not that strong so it’s probably not worth the trip.

Assuming you had the technology to travel the vast distances to reach a black hole (the nearest is about 3,000 light years away), the time dilation through travelling would be far greater than any time dilation through orbiting the black hole itself.

(The situation described in the movie Interstellar , where one hour on a planet near a black hole is the equivalent of seven years back on Earth, is so extreme as to be impossible in our Universe, according to Kip Thorne, the movie’s scientific advisor.)

The most mindblowing thing, perhaps, is that GPS systems have to account for time dilation effects (due to both the speed of the satellites and gravity they feel) in order to work. Without these corrections, your phones GPS capability wouldn’t be able to pinpoint your location on Earth to within even a few kilometres.

3. Time travel via suspended animation

Another way to time travel to the future may be to slow your perception of time by slowing down, or stopping, your bodily processes and then restarting them later.

Bacterial spores can live for millions of years in a state of suspended animation, until the right conditions of temperature, moisture, food kick start their metabolisms again. Some mammals, such as bears and squirrels, can slow down their metabolism during hibernation, dramatically reducing their cells’ requirement for food and oxygen.

Could humans ever do the same?

Though completely stopping your metabolism is probably far beyond our current technology, some scientists are working towards achieving inducing a short-term hibernation state lasting at least a few hours. This might be just enough time to get a person through a medical emergency, such as a cardiac arrest, before they can reach the hospital.

In 2005, American scientists demonstrated a way to slow the metabolism of mice (which do not hibernate) by exposing them to minute doses of hydrogen sulphide, which binds to the same cell receptors as oxygen. The core body temperature of the mice dropped to 13 °C and metabolism decreased 10-fold. After six hours the mice could be reanimated without ill effects.

Unfortunately, similar experiments on sheep and pigs were not successful, suggesting the method might not work for larger animals.

Another method, which induces a hypothermic hibernation by replacing the blood with a cold saline solution, has worked on pigs and is currently undergoing human clinical trials in Pittsburgh.

4. Time travel via wormholes

General relativity also allows for the possibility for shortcuts through spacetime, known as wormholes, which might be able to bridge distances of a billion light years or more, or different points in time.

Many physicists, including Stephen Hawking, believe wormholes are constantly popping in and out of existence at the quantum scale, far smaller than atoms. The trick would be to capture one, and inflate it to human scales – a feat that would require a huge amount of energy, but which might just be possible, in theory.

Attempts to prove this either way have failed, ultimately because of the incompatibility between general relativity and quantum mechanics.

5. Time travel using light

Another time travel idea, put forward by the American physicist Ron Mallet, is to use a rotating cylinder of light to twist spacetime. Anything dropped inside the swirling cylinder could theoretically be dragged around in space and in time, in a similar way to how a bubble runs around on top your coffee after you swirl it with a spoon.

According to Mallet, the right geometry could lead to time travel into either the past and the future.

Since publishing his theory in 2000, Mallet has been trying to raise the funds to pay for a proof of concept experiment, which involves dropping neutrons through a circular arrangement of spinning lasers.

His ideas have not grabbed the rest of the physics community however, with others arguing that one of the assumptions of his basic model is plagued by a singularity, which is physics-speak for “it’s impossible”.

The Royal Institution of Australia has an Education resource based on this article. You can access it here .

Related Reading: Computer solves a major time travel problem

Originally published by Cosmos as Time travel: five ways that we could do it

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The Science of Mental Time Travel and Why Our Ability to Imagine the Future Is Essential to Our Humanity

By maria popova.

Lewis Carroll’s Alice in Wonderland remains one of my all-time favorite books , largely because Carroll taps his training as a logician to imbue the whimsical story with an allegorical dimension that blends the poetic with the philosophical. To wit: The Red Queen remembers the future instead of the past — an absurd proposition so long as we think of time as linear and memory as beholden to the past, and yet a prescient one given how quantum physics (coincidentally, a perfect allegorical exploration of Wonderland ) conceives of time and what modern cognitive science tells us about how elastic our experience of time is . As it turns out, the Red Queen is far more representative of how human memory actually works than we dare believe.

“To be human,” writes Dan Falk in In Search of Time: The History, Physics, and Philosophy of Time ( public library ), “is to be aware of the passage of time; no concept lies closer to the core of our consciousness” — something evidenced by our millennia-old quest to map this invisible dimension . One of the most remarkable and evolutionarily essential elements of experiencing time through human consciousness is something psychologists and cognitive scientists call mental time travel — a potent bi-directional projection that combines episodic memory , which allows us to draw on our autobiographical experience and call up events, experiences, and emotions that occurred in the past, with the ability to imagine and anticipate future events. Falk puts it unambiguously:

Without it, there would be no planning, no building, no culture; without an imagined picture of the future, our civilization would not exist.

As it turns out, episodic memory — a term coined in the early 1970s by Canadian neuroscientist Endel Tulving, author of the seminal book Elements of Episodic Memory — is central to our capacity for mental time travel and, according to many scientists, fairly unique to humans. Unlike other facets of memory, such as the acquisition of new skills, which are rooted in the here-and-now, Falk points out that episodic memory allows us “to peer back across time, using our imagination to revisit just about any event that we choose.” This mental reliving of the past may be the root of some distinct human maladies — take the wistful reminiscence over a lost love, for instance — but it is also central to our evolutionary survival, allowing us to anticipate future outcomes based on past ones and thus to plan better and be more prepared for what tomorrow may bring. (The dark side of this evolutionarily beneficial faculty is that our over-planning often ends up shortchanging our happiness .)

And yet the benefits outweigh the costs, in evolutionary terms. Falk explains:

The capacity for mental time travel gave our ancestors an invaluable edge in the struggle for survival. They believe there is a profound link between remembering the past and imagining the future. The very act of remembering, they argue, gives one the “raw material” needed to construct plausible scenarios of future events and act accordingly. Mental time travel “provides increased behavioral flexibility to act in the present to increase future survival chances.” If this argument is correct, then mental time travel into the past — remembering — “is subsidiary to our ability to imagine future scenarios.” Tulving agrees: “What is the benefit of knowing what has happened in the past? Why do you care? The importance is that you’ve learned a lesson,” he says. “Perhaps the evolutionary advantage has to do with the future rather than the past.” Modern neuroscience appears to confirm that line of reasoning: as far as your brain is concerned, the act of remembering is indeed very similar to the act of imagining the future.

Though we might not be able to “remember” the future, as the Red Queen does, we do envision it in ways strikingly similar to how we picture events from the past — Falk notes that fMRI studies indicate we use similar regions in the brain’s frontal and temporal lobes when thinking about events in either direction of time. What’s more, psychologists have found that much like it’s harder for us to remember an event in the distant past than a recent one, it’s harder for us to imagine an event in the distant future than one expected to take place soon. This hints at the massively misguided way in which we think of and evaluate memory, which we falsely depict as a recording device , versus foresight. Falk writes:

When we imagine the future, we know what we picture is really just an educated guess; we may be right in the broad brushstrokes, but we are almost certainly wrong in the details. We hold memory to a higher standard. We feel — most of the time — that our memories are more than guesses, that they reflect what really happened. When confronted with a conflicting account of how last week’s party unfolded, we cling to our beliefs: He must be mistaken; I know what I saw.

Falk cites the Harvard psychologist Daniel Schacter:

[The brain is] a fundamentally prospective organ that is designed to use information from the past and the present to generate predictions about the future. Memory can be thought of as a tool used by the prospective brain to generate simulations of possible future events… We tend to think of memory as having primarily to do with the past… And maybe one reason we have it is so that we can have a warm feeling when we reminisce, and so on. But I think the thing that has been neglected is its role in allowing us to predict and simulate the future.

In order to mentally time-travel into the future, the brain has to accomplish a couple of things at once — we activate our “semantic memory,” which encompasses our basic knowledge of facts about the world and thus helps paint a backdrop for the imagined scene, and we call on our episodic memory, which pulls on our autobiographical library of remembered experiences to fill in specific details for this general scene. Curiously, episodic memory tends to be rather flawed but, according to two scientists Falk quotes, that’s okay since its core purpose is to provide “a more general toolbox that allowed us to escape from the present and develop foresight, and perhaps create a sense of personal identity.”

To be sure, just like elsewhere in cognitive science , human exceptionalism may be misplaced here — scientists have found that other species are also capable of varying degrees of mental time travel. Falk cites one of the most intriguing experiments, involving scrub jays. He writes:

Psychologist Nicola Clayton and her colleagues housed the birds on alternate days in two different compartments — one in which the jays always received “breakfast,” and one in which they did not. Then the birds were unexpectedly given extra food in the evening, at a location where they could access either compartment. The jays promptly cached their surplus — and they preferentially cached it in the “no breakfast” compartment. Because the birds were not hungry at the time of the caching, the researchers claim that the birds truly anticipated the hunger they would experience the next morning.

Still, the fact that humans are capable of remarkably elaborate and detailed mental time travel reveals something unique about our evolution and the development of such hallmarks of humanity as language and theory of mind. Falk writes:

In all likelihood, the capacity for mental time travel did not develop in isolation but rather alongside other crucial cognitive abilities. “To entertain a future event one needs some kind of imagination,” [the prominent psychologists Thomas] Suddendorf and [Michael] Corballis write, “some kind of representational space in our mind for the imaginary performance.” Language could also play an important role. Our language skills embrace mental time travel by the use of tenses and recursive thinking; when we say “A year from now, he will have retired,” we’re imagining a future time in which some event — which has not yet happened — will lie in the past… Mental time travel may have been “a pre-requisite to the evolution of language itself.” If mental time travel is indeed unique to humans, it may help us understand why complex language is also, apparently, unique.

In fact, the development of mental time travel may even be how the concept of time itself came into existence — according to Suddendorf and Corballis, our species emerged victorious in “an extraordinary evolutionary arms race” largely due to our growing capacity for foresight and sophisticated language, which not only gave us culture and “coordinated aggression” but also, for the first time in evolutionary history, enabled us to understand the concepts of “past” and “future.” The mental reconstruction of what has been and the imagining of what could be, they argue, created the concept of time and enabled us to understand the continuity between the past and the future. Falk, once again, puts it succinctly:

Mental time travel may indeed be the cognitive rudder that allows our brains to navigate the river of time.

In Search of Time is a fantastic read in its entirety, covering such facets of life’s most intricate dimension as how the calendar was born, why illusion and reality aren’t always so discernible from one another, and what the ultimate fate of the universe might be. Complement it with these seven excellent books on time and a fascinating read on how our memory works .

— Published July 1, 2014 — https://www.themarginalian.org/2014/07/01/mental-time-travel-dan-falk/ —

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These are the three alternatives Loveland officials hope could alleviate the city's traffic issues

LOVELAND, Ohio — Renderings and possible designs for traffic flow alternatives through Loveland were shown to community members at an open house meeting as city officials seek feedback on where residents' and travelers' priorities lie.

The meeting was held Tuesday evening at New Hope Baptist Church on Loveland Madeira Road.

During the meeting, the project team gave a presentation showcasing three alternatives intended to reduce traffic congestion at the bridge and improve travel time through downtown Loveland.

In 2022, Loveland city officials announced they hoped to work with the Ohio Department of Transportation to perform a traffic study. The city conducted a public survey for the traffic project over the summer of 2023; during that period, Loveland officials said they received more than 1,700 responses.

At that time, discussed options to relieve the bridge's congestion included addressing the need for cross-river connectivity and other regional network improvements that could reduce downtown congestion. The high traffic volumes are likely from commuters from Clermont and Warren counties, city officials said.

The West Loveland Avenue bridge is the only access point in the city that allows drivers to pass over the Little Miami River from Clermont County into Hamilton County; The closest other crossings are three miles south in Miamiville, Ohio, or four miles north in Foster, which sits in Warren County.

As part of the solution, city officials said they plan to add a traffic light to the bike and pedestrian crossings along the bike trail, along with finishing up a new parking lot.

City Manager Dave Kennedy said the city is also working with neighboring municipalities and ODOT on a traffic study that could lead to a second bridge spanning the Little Miami River. But where that bridge could go is still in question.

One spot could be on Fields Ertel Road, Kennedy said, but there's still plenty to decide.

"Will it attract more the Hamilton Township traffic, or will it attract more the Miami Township traffic and give them a better alternative than going through downtown?" said Kennedy.

The city said data received from ODOT in June showed that around 10,000 drivers travel West Loveland Avenue daily through the center of Loveland's downtown.

City officials said in 2022 that, since Loveland's city limits spans three different counties and neighbors multiple townships, there were unique challenges in finding which solutions to the traffic issues would be best for the region.

"Public involvement is a critical component of the project development process for proposed roadway improvements," said Kennedy. "Input from the public will be used to inform decision-making as we move forward."

Changes won't necessarily come right away, though; the city said the project is not currently funded and no timeframe has been established for when any construction would begin. Still, the city is hoping feedback on the alternative options will help identify which steps to take when carrying the project forward into further studies, like engineering and environmental demands.

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The newer, the better: How wheelchair users can travel smoothly

Chris Ricci can walk only short distances at a time, but he has traveled the world on his scooter.

The 57-year-old U.S. Army veteran has limited mobility stemming from a foot injury he sustained in the 1980s and related complications has found cruises an accessible way to explore destinations like Alaska or the Caribbean. Just this month, he, his wife and friends took a week-long Royal Caribbean International cruise to Belize, Honduras and Mexico.

Ricci, who is based in Lakeland, Florida, simply had to drive to Tampa to board the Enchantment of the Seas. “I think it’s pretty easy,” he told USA TODAY. They booked an accessible stateroom for the first time, too.

“It was really big,” said Ricci, who chronicles his cruises and other travels on his YouTube channel, Scootin Around the World.  “I had no problem getting the scooter into the room.”

Cruise ships can offer guests who use mobility devices an accessible, streamlined way to travel. But some extra planning can go a long way toward ensuring the trip goes smoothly. Here’s what to know.

How this adult-only cruise line integrated accessibility into its experiences

Do cruise ships have accessible staterooms for mobility devices?

Cruise lines do offer accessible staterooms, but they’re not all the same. “Make sure that you have the accessible room that's best for you,” said Joy Burns, organization and PR manager at accessible travel booking platform Wheel the World .

For instance, some staterooms may be better suited to motorized wheelchair users, but the setup may not be conducive for passengers who use other kinds of devices, according to her husband, Bert, who has been paralyzed since 1982 and has taken more than 20 cruises.

“If I got a wheelchair-accessible room that's made for a power wheelchair with a Hoyer lift, the bed’s up real high,” he said. “I can’t transfer with a high bed. I use a manual wheelchair, so I’m down low.”

Standard staterooms may also be able to accommodate mobility devices, but guests should familiarize themselves with cruise lines’ requirements.

Passengers booking a standard cabin on Carnival Cruise Line ships must have devices that can fit through a 22-inch-wide doorway, according to its website . The devices must also fold and collapse to allow for safe exit from the room (passengers cannot store mobility devices in corridors or public spaces).

“Guests who bring scooters that are larger than 21" (53.34 cm) wide, or travel with multiple scooters in the same stateroom, must purchase a fully accessible stateroom with a wider doorway (32”, 81.3 cm), or rent a smaller scooter appropriately suited for their stateroom,” the line said on its website. “Guests may be required to have their scooters sized at the time of check-in to ensure it fits in the stateroom.”

Major cruise lines typically have accessibility departments that can help guests navigate the process, according to Sylvia Longmire, an accessible travel writer who runs the blog and travel brand Spin the Globe .

“Talk to the accessibility department to ask the questions and let them know what kind of equipment you're bringing if you're bringing your own stuff,” said Longmire, who has multiple sclerosis and has taken over 30 cruises, most of which have been with a scooter or wheelchair. “Let them know what your ability or disability is, what your level is, what your accessibility requirements are. And that way, they can tell you what kind of cabin you might need, what location, (information) about the ship, and everything before you even call to make the reservation.”

For those booking through a travel agent, she said she “highly” recommends working with someone who has a disability or is an expert in accessible travel.

What cruises are best for guests with mobility devices?

Some destinations may also be better suited to guests with mobility devices than others. 

Once, during a New Zealand cruise, the Burnses’ ship hit some rough water, causing Bert to roll out of the casino and crash into the bar (though no one was hurt). Joy recommended researching the conditions of the seas. ( Click here for USA TODAY’S guide to the best times to cruise by region.)

She added that expedition cruises , which often feature activities that require guests to get on and off Zodiac boats, may not be as accessible.

What cruise ship is best for guests with mobility devices?

New ships tend to have more features that can make a trip easier for guests with mobility devices, said the Burnses and Longmire. Those include automatic sliding doors in public spaces, stateroom locks that allow passengers to wave their key to open the door and pool lifts.

“The newer the ship, the better the accessibility,” said Longmire.

Can I get a mobility device through a cruise line?

Guests can arrange to rent mobility devices through vendors like Scootaround or Special Needs at Sea (Longmire is a contract employee for Scootaround).

Rentals may also be available at the cruise terminal, and some lines have a limited number of scooters and wheelchairs available on the ship, according to Longmire. She estimated rentals can run from roughly $80 to $250 depending on the type of equipment, the length of time guests need it and other factors.

Do cruise lines have accessible excursions?

Yes, but options may be limited. Joy said accessible shore excursions available through cruise lines are “few and far between,” and she and Bert have taken cruises where there were none available through the cruise line at all.

Longmire noted that “cruise lines are entirely dependent on the availability of excursions with whoever they're contracting with.” If a given destination doesn’t have wheelchair taxis, for example, that limits cruise lines’ offerings.

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When they are available through the line, Longmire said many of them are what she calls windshield tours – bus tours with a group of other passengers that might include one or two 15-minute stops to take photos. “And the rest of it is just seeing everything out the window,” she said.

However, she added that cruise lines “get a little bit better” each year about offering those.

Joy said passengers can also book accessible shore excursions through companies like Wheel the World. Longmire has had luck booking shuttles and tours directly through providers in various ports as well, though guests should take care to be back in time before the ship leaves.

Are tender ports accessible?

When it comes to accessibility at tender ports – where guests have to take a small vessel from the ship to shore – Longmire said it’s “not very black and white.” Cruise ships may let guests board tenders and some have technology to help passengers with wheelchairs do so, but the port’s capabilities may be different.

“Just because you're able to get from the ship to the tender doesn't mean that you'll be able to get from the tender to the dock,” said Longmire.

Rules may differ as well, with some lines allowing guests in manual wheelchairs to use tenders but prohibiting motorized devices. She recommended checking with the accessibility department about those policies.

The Burnses, for their part, have generally found tender ports to be inaccessible, and Joy suggested travelers review itineraries to see how many they include. 

Overall, Longmire said her experience on cruises has been “really good,” both for their accessibility and convenience (you can visit multiple places but unpack once, for instance). “I always recommend to wheelchair users for their first travel experience, like, if you don't get seasick and you’re okay with cruises, a cruise is the way to go.”

Nathan Diller is a consumer travel reporter for USA TODAY based in Nashville. You can reach him at [email protected].

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What the New Overtime Rule Means for Workers

One of the basic principles of the American workplace is that a hard day’s work deserves a fair day’s pay. Simply put, every worker’s time has value. A cornerstone of that promise is the  Fair Labor Standards Act ’s (FLSA) requirement that when most workers work more than 40 hours in a week, they get paid more. The  Department of Labor ’s new overtime regulation is restoring and extending this promise for millions more lower-paid salaried workers in the U.S.

Overtime protections have been a critical part of the FLSA since 1938 and were established to protect workers from exploitation and to benefit workers, their families and our communities. Strong overtime protections help build America’s middle class and ensure that workers are not overworked and underpaid.

Some workers are specifically exempt from the FLSA’s minimum wage and overtime protections, including bona fide executive, administrative or professional employees. This exemption, typically referred to as the “EAP” exemption, applies when: 

1. An employee is paid a salary,  

2. The salary is not less than a minimum salary threshold amount, and 

3. The employee primarily performs executive, administrative or professional duties.

While the department increased the minimum salary required for the EAP exemption from overtime pay every 5 to 9 years between 1938 and 1975, long periods between increases to the salary requirement after 1975 have caused an erosion of the real value of the salary threshold, lessening its effectiveness in helping to identify exempt EAP employees.

The department’s new overtime rule was developed based on almost 30 listening sessions across the country and the final rule was issued after reviewing over 33,000 written comments. We heard from a wide variety of members of the public who shared valuable insights to help us develop this Administration’s overtime rule, including from workers who told us: “I would love the opportunity to...be compensated for time worked beyond 40 hours, or alternately be given a raise,” and “I make around $40,000 a year and most week[s] work well over 40 hours (likely in the 45-50 range). This rule change would benefit me greatly and ensure that my time is paid for!” and “Please, I would love to be paid for the extra hours I work!”

The department’s final rule, which will go into effect on July 1, 2024, will increase the standard salary level that helps define and delimit which salaried workers are entitled to overtime pay protections under the FLSA. 

Starting July 1, most salaried workers who earn less than $844 per week will become eligible for overtime pay under the final rule. And on Jan. 1, 2025, most salaried workers who make less than $1,128 per week will become eligible for overtime pay. As these changes occur, job duties will continue to determine overtime exemption status for most salaried employees.

The rule will also increase the total annual compensation requirement for highly compensated employees (who are not entitled to overtime pay under the FLSA if certain requirements are met) from $107,432 per year to $132,964 per year on July 1, 2024, and then set it equal to $151,164 per year on Jan. 1, 2025.

Starting July 1, 2027, these earnings thresholds will be updated every three years so they keep pace with changes in worker salaries, ensuring that employers can adapt more easily because they’ll know when salary updates will happen and how they’ll be calculated.

The final rule will restore and extend the right to overtime pay to many salaried workers, including workers who historically were entitled to overtime pay under the FLSA because of their lower pay or the type of work they performed. 

We urge workers and employers to visit  our website to learn more about the final rule.

Jessica Looman is the administrator for the U.S. Department of Labor’s Wage and Hour Division. Follow the Wage and Hour Division on Twitter at  @WHD_DOL  and  LinkedIn .  Editor's note: This blog was edited to correct a typo (changing "administrator" to "administrative.")

• Wage and Hour Division (WHD)
• Fair Labor Standards Act
• overtime rule

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Midwest tornadoes cause severe damage in Omaha suburbs

The Associated Press

Gopala Penmetsa walks past his house after it was leveled by a tornado near Omaha, Neb., on Friday. Chris Machian/Omaha World-Herald via AP hide caption

Gopala Penmetsa walks past his house after it was leveled by a tornado near Omaha, Neb., on Friday.

OMAHA, Neb. — A tornado plowed through suburban Omaha, Nebraska, on Friday afternoon, damaging hundreds of homes and other structures as the twister tore for miles along farmland and into subdivisions. Injuries were reported but it wasn't yet clear if anyone was killed in the storm.

Multiple tornadoes were reported in Nebraska but the most destructive storm moved from a largely rural area into suburbs northwest of Omaha, a city of 485,000 people.

Photos on social media showed heavily damaged homes and shredded trees. Video showed homes with roofs stripped of shingles, in a rural area near Omaha. Law enforcement were blocking off roads in the area.

Hundreds of houses sustained damage in Omaha, mostly in the Elkhorn area in the western part of the city, police Lt. Neal Bonacci said.

Police and firefighters are now going door-to-door helping people who are trapped.

Omaha Fire Chief Kathy Bossman said crews had gone to the "hardest hit area" and had a plan to search anywhere someone could be trapped.

"They're going to be putting together a strategic plan for a detailed search of the area, starting with the properties with most damage," Bossman said. "We'll be looking throughout properties in debris piles, we'll be looking in basements, trying to find any victims and make sure everybody is rescued who needs assistance."

Damaged houses are seen after a tornado passed through the area near Omaha, Neb., on Friday. Chris Machian/Omaha World-Herald via AP hide caption

Damaged houses are seen after a tornado passed through the area near Omaha, Neb., on Friday.

Omaha police Lt. Neal Bonacci said many homes were destroyed or severely damaged.

"You definitely see the path of the tornado," Bonacci said.

In one area of Elkhorn, dozens of newly built, large homes were damaged. At least six were destroyed, including one that was leveled, while others had the top half ripped off.

There were dozens of emergency vehicles in the area.

"We watched it touch down like 200 yards over there and then we took shelter," said Pat Woods, who lives in Elkhorn. "We could hear it coming through. When we came up our fence was gone and we looked to the northwest and the whole neighborhood's gone."

His wife, Kim Woods added, "The whole neighborhood just to the north of us is pretty flattened."

Dhaval Naik, who said he works with the man whose house was demolished, said three people, including a child, were in the basement when the tornado hit. They got out safely.

KETV-TV video showed one woman being removed from a demolished home on a stretcher in Blair, a city just north of Omaha.

Omaha Police Chief Todd Schmaderer said there appeared to be few serious injuries, in part because people had plenty of warning that storms were likely.

The exact link between tornadoes and climate change is hard to draw. Here's why

"We not upon by a sudden storm," Schmaderer said. "People had warnings of this and that saved lives."

The tornado warning was issued in the Omaha area on Friday afternoon just as children were due to be released from school. Many schools had students shelter in place until the storm passed. Hours later, buses were still transporting students home.

Another tornado hit an area on the eastern edge of Omaha, passing directly through parts of Eppley Airfield, the city's airport. Officials closed the airport to aircraft operations to access damage but then reopened the facility, Omaha Airport Authority Chief Strategy Officer Steve McCoy said.

Severe weather damage to Eppley Airfield in Omaha, Neb., can be seen from the Lewis and Clark Monument in Council Bluffs, Iowa on Friday Anna Reed/Omaha World-Herald via AP hide caption

Severe weather damage to Eppley Airfield in Omaha, Neb., can be seen from the Lewis and Clark Monument in Council Bluffs, Iowa on Friday

The passenger terminal wasn't hit by the tornado but people rushed to storm shelters until the twister passed, McCoy said.

Flight delays are expected Friday evening.

After passing through the airport, the tornado crossed the Missouri River and into Iowa, north of Council Bluffs.

Nebraska Emergency Management Agency spokesperson Katrina Sperl said damage is just now being reported. Taylor Wilson, a spokesperson for the University of Nebraska Medical Center, said they hadn't seen any injuries yet.

Before the tornado hit the Omaha area, three workers in an industrial plant were injured Friday afternoon when a tornado struck an industrial plant in Lancaster County, sheriff's officials said in an update on the damage.

The building just northeast of the state capital of Lincoln had collapsed with about 70 employees inside and several people trapped, sheriff's officials said. Everyone was evacuated, and three people had injuries that were considered not life-threatening, authorities said.

Sheriff's officials say they also had reports of a tipped-over train near Waverly, also in Lancaster County.

Two people who were injured when the tornado passed through Lancaster County were being treated at the trauma center at Bryan Medical Center West Campus in Lincoln, the facility said in a news release. It said the patients were in triage and no details were released on their condition.

The Omaha Public Power District reported that nearly 10,000 customers were without power in the Omaha area.

Daniel Fienhold, manager of the Pink Poodle Steakhouse in Crescent, Iowa, said he was outside watching the weather with his daughter and restaurant employees. He said "it looked like a pretty big tornado was forming" northeast of town.

"It started raining, and then it started hailing, and then all the clouds started to kind of swirl and come together, and as soon as the wind started to pick up, that's when I headed for the basement, but we never saw it," Fienhold said.

The Weather Service also issued tornado watches across parts of Iowa, Kansas, Missouri, Oklahoma and Texas. And forecasters warned that large hail and damaging wind gusts were possible.