clock time travel

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.

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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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Vicky Stein is a science writer based in California. She has a bachelor's degree in ecology and evolutionary biology from Dartmouth College and a graduate certificate in science writing from the University of California, Santa Cruz (2018). Afterwards, she worked as a news assistant for PBS NewsHour, and now works as a freelancer covering anything from asteroids to zebras. Follow her most recent work (and most recent pictures of nudibranchs) on Twitter. 

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Time is of your own making; its clock ticks in your head. The moment you stop thought time too stops dead.

Is time travel possible? Why one scientist says we 'cannot ignore the possibility.'

A common theme in science-fiction media , time travel is captivating. It’s defined by the late philosopher David Lewis in his essay “The Paradoxes of Time Travel” as “[involving] a discrepancy between time and space time. Any traveler departs and then arrives at his destination; the time elapsed from departure to arrival … is the duration of the journey.”

Time travel is usually understood by most as going back to a bygone era or jumping forward to a point far in the future . But how much of the idea is based in reality? Is it possible to travel through time? 

Is time travel possible?

According to NASA, time travel is possible , just not in the way you might expect. Albert Einstein’s theory of relativity says time and motion are relative to each other, and nothing can go faster than the speed of light , which is 186,000 miles per second. Time travel happens through what’s called “time dilation.”

Time dilation , according to Live Science, is how one’s perception of time is different to another's, depending on their motion or where they are. Hence, time being relative. 

Learn more: Best travel insurance

Dr. Ana Alonso-Serrano, a postdoctoral researcher at the Max Planck Institute for Gravitational Physics in Germany, explained the possibility of time travel and how researchers test theories. 

Space and time are not absolute values, Alonso-Serrano said. And what makes this all more complex is that you are able to carve space-time .

“In the moment that you carve the space-time, you can play with that curvature to make the time come in a circle and make a time machine,” Alonso-Serrano told USA TODAY. 

She explained how, theoretically, time travel is possible. The mathematics behind creating curvature of space-time are solid, but trying to re-create the strict physical conditions needed to prove these theories can be challenging. 

“The tricky point of that is if you can find a physical, realistic, way to do it,” she said. 

Alonso-Serrano said wormholes and warp drives are tools that are used to create this curvature. The matter needed to achieve curving space-time via a wormhole is exotic matter , which hasn’t been done successfully. Researchers don’t even know if this type of matter exists, she said.

“It's something that we work on because it's theoretically possible, and because it's a very nice way to test our theory, to look for possible paradoxes,” Alonso-Serrano added.

“I could not say that nothing is possible, but I cannot ignore the possibility,” she said. 

She also mentioned the anecdote of  Stephen Hawking’s Champagne party for time travelers . Hawking had a GPS-specific location for the party. He didn’t send out invites until the party had already happened, so only people who could travel to the past would be able to attend. No one showed up, and Hawking referred to this event as "experimental evidence" that time travel wasn't possible.

What did Albert Einstein invent?: Discoveries that changed the world

Just Curious for more? We've got you covered

USA TODAY is exploring the questions you and others ask every day. From "How to watch the Marvel movies in order" to "Why is Pluto not a planet?" to "What to do if your dog eats weed?" – we're striving to find answers to the most common questions you ask every day. Head to our Just Curious section to see what else we can answer for you. 

A beginner's guide to time travel

Learn exactly how Einstein's theory of relativity works, and discover how there's nothing in science that says time travel is impossible.

Everyone can travel in time . You do it whether you want to or not, at a steady rate of one second per second. You may think there's no similarity to traveling in one of the three spatial dimensions at, say, one foot per second. But according to Einstein 's theory of relativity , we live in a four-dimensional continuum — space-time — in which space and time are interchangeable.

Einstein found that the faster you move through space, the slower you move through time — you age more slowly, in other words. One of the key ideas in relativity is that nothing can travel faster than the speed of light — about 186,000 miles per second (300,000 kilometers per second), or one light-year per year). But you can get very close to it. If a spaceship were to fly at 99% of the speed of light, you'd see it travel a light-year of distance in just over a year of time. 

That's obvious enough, but now comes the weird part. For astronauts onboard that spaceship, the journey would take a mere seven weeks. It's a consequence of relativity called time dilation , and in effect, it means the astronauts have jumped about 10 months into the future. 

Traveling at high speed isn't the only way to produce time dilation. Einstein showed that gravitational fields produce a similar effect — even the relatively weak field here on the surface of Earth . We don't notice it, because we spend all our lives here, but more than 12,400 miles (20,000 kilometers) higher up gravity is measurably weaker— and time passes more quickly, by about 45 microseconds per day. That's more significant than you might think, because it's the altitude at which GPS satellites orbit Earth, and their clocks need to be precisely synchronized with ground-based ones for the system to work properly. 

The satellites have to compensate for time dilation effects due both to their higher altitude and their faster speed. So whenever you use the GPS feature on your smartphone or your car's satnav, there's a tiny element of time travel involved. You and the satellites are traveling into the future at very slightly different rates.

But for more dramatic effects, we need to look at much stronger gravitational fields, such as those around black holes , which can distort space-time so much that it folds back on itself. The result is a so-called wormhole, a concept that's familiar from sci-fi movies, but actually originates in Einstein's theory of relativity. In effect, a wormhole is a shortcut from one point in space-time to another. You enter one black hole, and emerge from another one somewhere else. Unfortunately, it's not as practical a means of transport as Hollywood makes it look. That's because the black hole's gravity would tear you to pieces as you approached it, but it really is possible in theory. And because we're talking about space-time, not just space, the wormhole's exit could be at an earlier time than its entrance; that means you would end up in the past rather than the future.

Trajectories in space-time that loop back into the past are given the technical name "closed timelike curves." If you search through serious academic journals, you'll find plenty of references to them — far more than you'll find to "time travel." But in effect, that's exactly what closed timelike curves are all about — time travel

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There's another way to produce a closed timelike curve that doesn't involve anything quite so exotic as a black hole or wormhole: You just need a simple rotating cylinder made of super-dense material. This so-called Tipler cylinder is the closest that real-world physics can get to an actual, genuine time machine. But it will likely never be built in the real world, so like a wormhole, it's more of an academic curiosity than a viable engineering design.

Yet as far-fetched as these things are in practical terms, there's no fundamental scientific reason — that we currently know of — that says they are impossible. That's a thought-provoking situation, because as the physicist Michio Kaku is fond of saying, "Everything not forbidden is compulsory" (borrowed from T.H. White's novel, "The Once And Future King"). He doesn't mean time travel has to happen everywhere all the time, but Kaku is suggesting that the universe is so vast it ought to happen somewhere at least occasionally. Maybe some super-advanced civilization in another galaxy knows how to build a working time machine, or perhaps closed timelike curves can even occur naturally under certain rare conditions.

This raises problems of a different kind — not in science or engineering, but in basic logic. If time travel is allowed by the laws of physics, then it's possible to envision a whole range of paradoxical scenarios . Some of these appear so illogical that it's difficult to imagine that they could ever occur. But if they can't, what's stopping them? 

Thoughts like these prompted Stephen Hawking , who was always skeptical about the idea of time travel into the past, to come up with his "chronology protection conjecture" — the notion that some as-yet-unknown law of physics prevents closed timelike curves from happening. But that conjecture is only an educated guess, and until it is supported by hard evidence, we can come to only one conclusion: Time travel is possible.

A party for time travelers 

Hawking was skeptical about the feasibility of time travel into the past, not because he had disproved it, but because he was bothered by the logical paradoxes it created. In his chronology protection conjecture, he surmised that physicists would eventually discover a flaw in the theory of closed timelike curves that made them impossible. 

In 2009, he came up with an amusing way to test this conjecture. Hawking held a champagne party (shown in his Discovery Channel program), but he only advertised it after it had happened. His reasoning was that, if time machines eventually become practical, someone in the future might read about the party and travel back to attend it. But no one did — Hawking sat through the whole evening on his own. This doesn't prove time travel is impossible, but it does suggest that it never becomes a commonplace occurrence here on Earth.

The arrow of time 

One of the distinctive things about time is that it has a direction — from past to future. A cup of hot coffee left at room temperature always cools down; it never heats up. Your cellphone loses battery charge when you use it; it never gains charge. These are examples of entropy , essentially a measure of the amount of "useless" as opposed to "useful" energy. The entropy of a closed system always increases, and it's the key factor determining the arrow of time.

It turns out that entropy is the only thing that makes a distinction between past and future. In other branches of physics, like relativity or quantum theory, time doesn't have a preferred direction. No one knows where time's arrow comes from. It may be that it only applies to large, complex systems, in which case subatomic particles may not experience the arrow of time.

Time travel paradox 

If it's possible to travel back into the past — even theoretically — it raises a number of brain-twisting paradoxes — such as the grandfather paradox — that even scientists and philosophers find extremely perplexing.

Killing Hitler

A time traveler might decide to go back and kill him in his infancy. If they succeeded, future history books wouldn't even mention Hitler — so what motivation would the time traveler have for going back in time and killing him?

Killing your grandfather

Instead of killing a young Hitler, you might, by accident, kill one of your own ancestors when they were very young. But then you would never be born, so you couldn't travel back in time to kill them, so you would be born after all, and so on … 

A closed loop

Suppose the plans for a time machine suddenly appear from thin air on your desk. You spend a few days building it, then use it to send the plans back to your earlier self. But where did those plans originate? Nowhere — they are just looping round and round in time.

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Andrew May holds a Ph.D. in astrophysics from Manchester University, U.K. For 30 years, he worked in the academic, government and private sectors, before becoming a science writer where he has written for Fortean Times, How It Works, All About Space, BBC Science Focus, among others. He has also written a selection of books including Cosmic Impact and Astrobiology: The Search for Life Elsewhere in the Universe, published by Icon Books.

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April 26, 2023

Is Time Travel Possible?

The laws of physics allow time travel. So why haven’t people become chronological hoppers?

By Sarah Scoles

yuanyuan yan/Getty Images

In the movies, time travelers typically step inside a machine and—poof—disappear. They then reappear instantaneously among cowboys, knights or dinosaurs. What these films show is basically time teleportation .

Scientists don’t think this conception is likely in the real world, but they also don’t relegate time travel to the crackpot realm. In fact, the laws of physics might allow chronological hopping, but the devil is in the details.

Time traveling to the near future is easy: you’re doing it right now at a rate of one second per second, and physicists say that rate can change. According to Einstein’s special theory of relativity, time’s flow depends on how fast you’re moving. The quicker you travel, the slower seconds pass. And according to Einstein’s general theory of relativity , gravity also affects clocks: the more forceful the gravity nearby, the slower time goes.

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“Near massive bodies—near the surface of neutron stars or even at the surface of the Earth, although it’s a tiny effect—time runs slower than it does far away,” says Dave Goldberg, a cosmologist at Drexel University.

If a person were to hang out near the edge of a black hole , where gravity is prodigious, Goldberg says, only a few hours might pass for them while 1,000 years went by for someone on Earth. If the person who was near the black hole returned to this planet, they would have effectively traveled to the future. “That is a real effect,” he says. “That is completely uncontroversial.”

Going backward in time gets thorny, though (thornier than getting ripped to shreds inside a black hole). Scientists have come up with a few ways it might be possible, and they have been aware of time travel paradoxes in general relativity for decades. Fabio Costa, a physicist at the Nordic Institute for Theoretical Physics, notes that an early solution with time travel began with a scenario written in the 1920s. That idea involved massive long cylinder that spun fast in the manner of straw rolled between your palms and that twisted spacetime along with it. The understanding that this object could act as a time machine allowing one to travel to the past only happened in the 1970s, a few decades after scientists had discovered a phenomenon called “closed timelike curves.”

“A closed timelike curve describes the trajectory of a hypothetical observer that, while always traveling forward in time from their own perspective, at some point finds themselves at the same place and time where they started, creating a loop,” Costa says. “This is possible in a region of spacetime that, warped by gravity, loops into itself.”

“Einstein read [about closed timelike curves] and was very disturbed by this idea,” he adds. The phenomenon nevertheless spurred later research.

Science began to take time travel seriously in the 1980s. In 1990, for instance, Russian physicist Igor Novikov and American physicist Kip Thorne collaborated on a research paper about closed time-like curves. “They started to study not only how one could try to build a time machine but also how it would work,” Costa says.

Just as importantly, though, they investigated the problems with time travel. What if, for instance, you tossed a billiard ball into a time machine, and it traveled to the past and then collided with its past self in a way that meant its present self could never enter the time machine? “That looks like a paradox,” Costa says.

Since the 1990s, he says, there’s been on-and-off interest in the topic yet no big breakthrough. The field isn’t very active today, in part because every proposed model of a time machine has problems. “It has some attractive features, possibly some potential, but then when one starts to sort of unravel the details, there ends up being some kind of a roadblock,” says Gaurav Khanna of the University of Rhode Island.

For instance, most time travel models require negative mass —and hence negative energy because, as Albert Einstein revealed when he discovered E = mc 2 , mass and energy are one and the same. In theory, at least, just as an electric charge can be positive or negative, so can mass—though no one’s ever found an example of negative mass. Why does time travel depend on such exotic matter? In many cases, it is needed to hold open a wormhole—a tunnel in spacetime predicted by general relativity that connects one point in the cosmos to another.

Without negative mass, gravity would cause this tunnel to collapse. “You can think of it as counteracting the positive mass or energy that wants to traverse the wormhole,” Goldberg says.

Khanna and Goldberg concur that it’s unlikely matter with negative mass even exists, although Khanna notes that some quantum phenomena show promise, for instance, for negative energy on very small scales. But that would be “nowhere close to the scale that would be needed” for a realistic time machine, he says.

These challenges explain why Khanna initially discouraged Caroline Mallary, then his graduate student at the University of Massachusetts Dartmouth, from doing a time travel project. Mallary and Khanna went forward anyway and came up with a theoretical time machine that didn’t require negative mass. In its simplistic form, Mallary’s idea involves two parallel cars, each made of regular matter. If you leave one parked and zoom the other with extreme acceleration, a closed timelike curve will form between them.

Easy, right? But while Mallary’s model gets rid of the need for negative matter, it adds another hurdle: it requires infinite density inside the cars for them to affect spacetime in a way that would be useful for time travel. Infinite density can be found inside a black hole, where gravity is so intense that it squishes matter into a mind-bogglingly small space called a singularity. In the model, each of the cars needs to contain such a singularity. “One of the reasons that there's not a lot of active research on this sort of thing is because of these constraints,” Mallary says.

Other researchers have created models of time travel that involve a wormhole, or a tunnel in spacetime from one point in the cosmos to another. “It's sort of a shortcut through the universe,” Goldberg says. Imagine accelerating one end of the wormhole to near the speed of light and then sending it back to where it came from. “Those two sides are no longer synced,” he says. “One is in the past; one is in the future.” Walk between them, and you’re time traveling.

You could accomplish something similar by moving one end of the wormhole near a big gravitational field—such as a black hole—while keeping the other end near a smaller gravitational force. In that way, time would slow down on the big gravity side, essentially allowing a particle or some other chunk of mass to reside in the past relative to the other side of the wormhole.

Making a wormhole requires pesky negative mass and energy, however. A wormhole created from normal mass would collapse because of gravity. “Most designs tend to have some similar sorts of issues,” Goldberg says. They’re theoretically possible, but there’s currently no feasible way to make them, kind of like a good-tasting pizza with no calories.

And maybe the problem is not just that we don’t know how to make time travel machines but also that it’s not possible to do so except on microscopic scales—a belief held by the late physicist Stephen Hawking. He proposed the chronology protection conjecture: The universe doesn’t allow time travel because it doesn’t allow alterations to the past. “It seems there is a chronology protection agency, which prevents the appearance of closed timelike curves and so makes the universe safe for historians,” Hawking wrote in a 1992 paper in Physical Review D .

Part of his reasoning involved the paradoxes time travel would create such as the aforementioned situation with a billiard ball and its more famous counterpart, the grandfather paradox : If you go back in time and kill your grandfather before he has children, you can’t be born, and therefore you can’t time travel, and therefore you couldn’t have killed your grandfather. And yet there you are.

Those complications are what interests Massachusetts Institute of Technology philosopher Agustin Rayo, however, because the paradoxes don’t just call causality and chronology into question. They also make free will seem suspect. If physics says you can go back in time, then why can’t you kill your grandfather? “What stops you?” he says. Are you not free?

Rayo suspects that time travel is consistent with free will, though. “What’s past is past,” he says. “So if, in fact, my grandfather survived long enough to have children, traveling back in time isn’t going to change that. Why will I fail if I try? I don’t know because I don’t have enough information about the past. What I do know is that I’ll fail somehow.”

If you went to kill your grandfather, in other words, you’d perhaps slip on a banana en route or miss the bus. “It's not like you would find some special force compelling you not to do it,” Costa says. “You would fail to do it for perfectly mundane reasons.”

In 2020 Costa worked with Germain Tobar, then his undergraduate student at the University of Queensland in Australia, on the math that would underlie a similar idea: that time travel is possible without paradoxes and with freedom of choice.

Goldberg agrees with them in a way. “I definitely fall into the category of [thinking that] if there is time travel, it will be constructed in such a way that it produces one self-consistent view of history,” he says. “Because that seems to be the way that all the rest of our physical laws are constructed.”

No one knows what the future of time travel to the past will hold. And so far, no time travelers have come to tell us about it.

A history of time travel: the how, the why and the when of turning back the clock

Pop on Aqua's 'Turn Back Time' and settle in

For most of human history, the world didn’t change very quickly. Until the 1700s, kids could largely expect their lives to be similar to their parents, and that their children would have an experience very similar to their own, too. There were obviously changes in how humans lived over longer stretches of time, but nothing that even different generations could easily observe.

My first introduction to science fiction was Valérian and Laureline. I was ten years old. Every Wednesday there was a magazine called Pilote in France, and there was two pages of Valerian every week. It was the first time I’d seen a girl and a guy in space, agents travelling in time and space. That was amazing.

The past is written. The present? We have to deal with it. But the future is a white page. So I don’t understand why people on this white page are putting all this darkness.

God! Let’s have some color! Let’s have some fun! Let’s at least imagine a better world. Maybe we won’t be able to do it, but we have to try.

The industrial revolution changed all of this. For the first time in human history, the pace of technological change was visible within a human lifespan. 

It is not a coincidence that it was only after science and technological change became a normal part of the human experience, that time travel became something we dreamed of.

Time travel is actually somewhat unique in science fiction. Many core concepts have their origins earlier in history. 

The historical roots of the concept of a 'robot' can be seen in Jewish folklore for example: Golems were anthropomorphic beings sculpted from clay. In Greek mythology, characters would travel to other worlds, and it's no coincidence that The Matrix features a character called Persephone. But time travel is different.

The first real work to envisage travelling in time was The Time Machine by HG Wells, which was published in 1895. 

The book tells the story of a scientist who builds a machine that will take him to the year 802,701 - a world in which ape-like Morlocks are evolutionary descendants of humanity, and have regressed to a primitive lifestyle. 

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The book was a product of its time - both in terms of the science played upon (Charles Darwin had only published Origin of the Species 35 years earlier), and the racist attitudes: it is speculated that the Morlocks were inspired by the Morlachs, a real ethnic group in the Balkans who were often characterised as “primitive”.

Real science

But of course, this was science fiction - what about science fact? The two have always been closely linked, and during the early days it was no different. In 1907, the physicist Hermann Minkowski first argued that Einstein’s Special Relativity could be expressed in geometric terms as a fourth dimension (to add to our known three) - which is exactly how Wells visualised time travel in his work of fiction.

The development of Special and then General Relativity was significant as it provided the theoretical backbone for how time travel could be conceived in scientific terms. In 1949 Kurt Gödel took Einstein’s work and came up with a solution which as a mathematical necessity included what he called “closed timelike curves” - the idea that if you travel far enough, time will loop back around (like how if you keep flying East, you’ll eventually end up back where you started).

In other words, using what became known as the Gödel Metric, it is theoretically possible to travel between any one point in time and space and any other. 

There was just one problem: for Gödel’s theory to be right, the universe would have to be spinning - and scientists don’t believe that it is. So while the maths might make sense, Gödel’s universe does not appear to be the one we’re actually living in. Though he never gave up hope that he might be right: Apparently even on this deathbed, he would ask if anyone has found evidence of a spinning universe. And if he does ever turn out to be right, it means that time travel can happen, and is actually fairly straightforward (well, as far as physics goes anyway).

Since Gödel, scientists have continued to hypothesise about time travel, with perhaps the best known example being tachyons - or particles that move faster than the speed of light (therefore, effectively travelling in time). So far, despite one false alarm at CERN in 2011, there is no evidence that they actually exist.

Chancers and hoaxes

Of course, the lack of real science when it comes to time travel has not stopped some people from claiming to have done it. With the likes of Marty McFly and Doctor Who on the brain, chancers and hoaxers have realised that time travel is immediately a compelling prospect. Here’s a couple of amusing examples.

At the turn of the millennium, when the internet was still in its infancy, forums were captivated by the story of John Titor. Titor claimed he was from the year 2036, and had been sent back in time by the government to obtain an IBM 5100 computer. The thinking appeared to be that by obtaining the computer, the government could find a solution to the UNIX 2038 bug - in which clocks could be reset, Millennium Bug-style, leading to chaos everywhere.

Posting on the 'Time Travel Institute' forums, Titor went into details on how his time machine worked:  It was powered by “two top-spin, dual positive singularities”, and used an X-ray venting system. He also gave a potted history of what humanity could expect: A new American civil war in 2004, and World War III in 2015. He also claimed the “many worlds” interpretation of quantum physics was true, hence why he wasn’t violating the so-called “grandfather paradox”.

Titor claimed he was from the year 2036, and had been sent back in time by the government to obtain an IBM 5100 computer.

Okay, so he probably wasn’t a real time traveller, but in the early days of the internet, when anonymity was more commonplace, he truly captured the imaginations of nerdy early adopters who perhaps, just a little bit, hoped that he might be the real thing.

More recently, in 2013, an Iranian scientist named Ali Razeghi claimed to have invented a time machine of sorts. It was supposedly capable of predicting the next 5-8 years for an individual, with up to 98% accuracy. According to The Telegraph , Razeghi said the invention fits into the size of a standard PC case and “It will not take you into the future, it will bring the future to you”. The idea is that the Iranian government could use it to predict future security threats and military confrontations. So perhaps it is time to check in and see if he managed to predict Donald Trump?

So is this the best we can do? Will we ever manage to crack time travel? Some scientists are still sceptical that it could ever be possible. This includes Stephen Hawking, who proposed the 'Chronology Protection Conjecture' – which is what it sounds like. Essentially, he argues that the laws of physics are as they are to specifically make time travel impossible – on all but “submicroscopic” scales. Essentially, this is to protect how causality works, as if we are suddenly allowed to travel back and kill our grandfathers, it would create massive time paradoxes.

Hawking revealed to Ars Technica in 2012 how he had held a party for time travellers, but only sent out invitations after the date it was held. So did the party support his argument that time travel is impossible? Or did he end up spending the evening in the company of John Titor and Doctor Who?

“I sat there a long time, but no one came”, he said, much to our disappointment.

Huge thanks to Stephen Jorgenson-Murray for walking us through some of the more brain-mangling science for this article.

To celebrate the release of Valerian and the City of a Thousand Planets , Luc Besson is today behind the lens at TechRadar. Here’s what we’ve got in store for you:

• Luc Besson presents TechRadar
• From Verne to Valerian: how France became the home of sci-fi
• Luc Besson talks streaming, viral videos and cinema tech
• Star spangled glamour: making space travel cooler than ever before
• A history of time travel: the how, the why and the when
• 20 best sci-fi films on Netflix and Amazon Prime
• Amazing future tech from sci-fi films that totally exist now

Valerian and the City of a Thousand Planets is released in UK cinemas August 2nd, and is out now in the US.

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From millennium-skipping Victorians to phone booth-hopping time traveler teenagers, the term time travel often summons our most fantastic visions of what it means to move through the fourth dimension. But of course you don't need a time machine or a fancy wormhole to jaunt through the years.

As you've probably noticed, we're all constantly engaged in the act of time travel. At its most basic level, time is the rate of change in the universe -- and like it or not, we are constantly undergoing change. We age, the planets move around the sun, and things fall apart.

We measure the passage of time in seconds, minutes, hours and years, but this doesn't mean time flows at a constant rate. In fact Einstein's theory of relativity determines that time is not universal. Just as the water in a river rushes or slows depending on the size of the channel, time flows at different rates in different places. In other words, time is relative.

But what causes this fluctuation along our one-way trek from the cradle to the grave? It all comes down to the relationship between time and space. Human beings frolic about in the three spatial dimensions of length, width and depth. Time joins the party as that most crucial fourth dimension . Time can't exist without space, and space can't exist without time. The two exist as one: the space time continuum . Any event that occurs in the universe has to involve both space and time.

In this article, we'll look at the real-life, everyday methods of time travel in our universe, as well as some of the more far-fetched methods of dancing through the fourth dimension.

Did you know your GPS devices rely on time-travel calculations to help you navigate around town? It's true! GPS satellite clocks are about 3 8 seconds longer per day than a clock closer to earth due to the gravitational frequency shift. They make up for this discrepancy by using time travel calculations or they could be way off from your current location and time.

Please copy/paste the following text to properly cite this HowStuffWorks.com article:

Internet Encyclopedia of Philosophy

Time travel.

Before the twentieth century, scientists and philosophers rarely investigated time travel, but now it is an exciting and deeply studied topic. There are investigations into travel to the future and travel to the past, although travel to the past is more problematical and receives more attention.   There are also investigations of the logical possibility of time travel, the physical possibility of time travel, and the technological practicality of time travel. The most attention is paid to time travel that is consistent with current physical theory such as Einstein’s general theory of relativity. In science, different models of the cosmos and the laws of nature governing the universe imply different possibilities for time travel. So, theories about time travel have changed radically as the dominant cosmological theories have evolved from classical, Newtonian conceptions to modern, relativistic and quantum mechanical conceptions. Philosophers were quick to note some of the implications of the new physics for venerable issues in metaphysics: the nature of time, causation and personal identity, to name just a few. The subject continues to produce a fruitful cross-fertilization of ideas between scientists and philosophers as theorists in both fields struggle to resolve confounding paradoxes that emerge when time travel is pondered seriously. This article discusses both the scientific and philosophical issues relevant to time travel.

Table of Contents

• Introduction
• Time in Philosophy
• Newtonian Cosmology
• Special Relativity
• General Relativity
• Quantum Interpretations
• The Grandfather Paradox
• Causal Loops
• Personal Identity
• References and Further Reading

1. Introduction

Time travel stories have been a staple of the science fiction genre for the past century. Good science fiction stories often pay homage to the fundamentals of scientific knowledge of the time. Thus, we see time travel stories of the variety typified by H. G. Wells as set within the context of a Newtonian universe: a three-dimensional Euclidean spatial manifold that changes along an inexorable arrow of time. By the early to mid-twentieth century, time travel stories evolved to take into account the features of an Einsteinian universe: a four-dimensional spacetime continuum that curves and in which time has the character of a spatial dimension (that is, there can be local variations or “warps”). More recently, time travel stories have incorporated features of quantum theory: phenomena such as superposition and entanglement suggest the possibility of parallel or many universes, many minds, or many histories. Indeed, the sometimes counter-intuitive principles and effects of quantum theory have invigorated time travel stories. Bizarre phenomena like negative energy density (the Casimir effect) lend their strangeness to the already odd character of time travel stories.

In this article, we make a distinction between time travel stories that might be possible within the canon of known physical laws and those stories that contravene or go beyond known laws. The former type of stories, which we shall call natural time travel, exploit the features or natural topology of spacetime regions. Natural time travel tends to severely constrain the activities of a time traveler and entails immense technological challenges. The latter type of stories, which we shall call Wellsian time travel, enable the time traveler more freedom and simplify the technological challenges, but at the expense of the physics. For example, in H. G. Wells’ story, the narrator is a time traveler who constructs a machine that transports him through time. The time traveler’s journey, as he experiences it, occurs over some nonzero duration of time. Also, the journey is through some different nonzero duration of time in the world. It is the latter condition that distinguishes the natural time travel story from the Wellsian time travel story. Our laws of physics do not allow travel through a nonzero duration of time in the world (in a sense that will be made clearer below). Wellsian time travel stories are mortgaged on our hope or presumption that more fundamental laws of nature are yet to be discovered beyond the current horizon of scientific knowledge. Natural time travel stories can be analyzed for consistency with known physics while Wellsian time travel stories can be analyzed for consistency with logic. Finally, time travel stories implicate themselves in a constellation of common philosophical problems. Among these philosophically related issues we will address in this article are the metaphysics of time, causality, and personal identity.

2. Definition

What is time travel? One standard definition is that of David Lewis’s: an object time travels iff the difference between its departure and arrival times in the surrounding world does not equal the duration of the journey undergone by the object. This definition applies to both natural and Wellsian time travel. For example, Jane might be a time traveler if she travels for one hour but arrives two hours later in the future (or two hours earlier in the past). In both types of time travel, the times experienced by a time traveler are different from the time undergone by their surrounding world.

But what do we mean by the “time” in time travel? And what do we mean by “travel” in time travel? As the definition for time travel presently stands, we need to clarify what we mean by the word “time” (see the next section). While philosophical analysis of time travel has attended mostly to the difficult issue of time, might there also be vagueness in the word “travel”? Our use of the word “travel” implies two places: an origin and a destination. “I’m going to Morocco,” means “I’m departing from my origination point here and I plan to arrive eventually in Morocco.” But when we are speaking of time travel, where exactly does a time traveler go? The time of origin is plain enough: the time of the time traveler and the time traveler’s surrounding world coincide at the beginning of the journey. But “where” does the time traveler arrive? Are we equivocating in our use of the word ‘travel’ by simply substituting a when for a where? In truth, how do we conceive of a “when”—as a place, a locale, or a region? Different scientific ontologies result in different ideas of what travel through time might be like. Also, different metaphysical concepts of time result in different ideas of what kinds of time travel are possible. It is to the issue of time in philosophy that we now turn.

3. Time in Philosophy

How is time related to existence? Philosophy offers three primary answers to this metaphysical question: eternalism, possibilism, and presentism. The names of these views indicate the ontological status given to time. The eternalist thinks that time, correctly understood, is a fourth dimension essentially constitutive of reality together with space. All times, past, present and future, are actual times just like all points distributed in space are actual points in space. One cannot privilege any one moment in the dimension of time as “more” real than any other moment just like one cannot privilege any point in space as “more” real than any other point. The universe is thus a spacetime “block,” a view that has philosophical roots at least as far back as Parmenides . Everything is one; the appearance of things coming to be and ceasing to be, of time passing or flowing, is simply phenomenal, not real. Objects from the past and future have equal ontological status with present objects. Thus, a presently extinct individual dodo bird exists as equably as a presently existing individual house finch, and the dodo bird and the house finch exist as equably as an individual baby sparrow hatched next Saturday. Whether or not the dodo bird and the baby sparrow are present is irrelevant ontologically; they simply aren’t in our spacetime region right now. The physicist typically views the relation of time to existence in the way that the eternalist does. The life of an object in the universe can be properly shown as:

This diagram shows the spatial movement (in one dimension) of an object through time. The standard depiction of an object’s spacetime “worldline” in Special Relativity, the Minkowski diagram (see below), privileges this block view of the universe. Many Wellsian time travel stories assume the standpoint of eternalism. For example, in Wells’ The Time Machine, the narrator (the time traveler) explains: “There is no difference between Time and any of the three dimensions of Space except that our consciousness moves along it.” Eternalism fits easily into the metaphysics of time travel.

The second view is possibilism, also known as the “growing block” or “growing universe” view. The possibilist thinks that the eternalist’s picture of the universe is correct except for the status of the future. The past and the present are fixed and actual; the future is only possible. Or more precisely, the future of an object holds the possibility of many different worldlines, only one of which will become actual for the object. If eternalism seems overly deterministic, eliminating indeterminacies and human free choice, then possibilism seems to retain some indeterminacy and free choice, at least as far as the future is concerned. For the possibilist, the present takes on a special significance that it does not have for the eternalist. The life of an object according to possibilism might be shown as:

This diagram shows that the object’s worldline is not yet fixed or complete. (It should be pointed out that the necessity of illustrating the time axis with a beginning and end should not be construed as an implicit claim that time itself has a beginning and end.) Some Wellsian time travel stories make use of possibilism. Stories like Back to the Future and Terminator suggest that we can change the outcome of historical events in our world, including our own personal future, through time travel. The many different possible histories of an object introduce other philosophical problems of causation and personal identity, issues that we will consider in greater depth in later sections of the article.

The third view is presentism. The presentist thinks that only temporally present objects are real. Whatever is, exists now. The past was, but exists no longer; the future will be, but does not exist yet. Objects are scattered throughout space but they are not scattered throughout time. Presentists do not think that time is a dimension in the same sense as the three spatial dimensions; they say the block universe view of the eternalists (and the intermediate view of the possibilists) gets the metaphysics of time wrong. If eternalism has its philosophical roots in Parmenides, then presentism can be understood as having its philosophical roots in Heraclitus. Presently existing things are the only actuality and only what is now is real. Each “now” is unique: “You cannot step twice into the same river; for fresh waters are ever flowing in upon you.” The life of an object according to presentism might be shown as:

Many presentists account for the continuity of time, the timelike connection of one moment to the next moment, by appealing to the present intrinsic properties of the world (Bigelow). To fully describe some of these present intrinsic properties of the world, you need past- and future-tensed truths to supervene on those properties. For example, in ordinary language we might make the claim that “George Washington camped at Valley Forge.” This sentence has an implicit claim to a timeless truth, that is, it was true 500 years ago, it was true when it was happening, it is true now, and it will be true next month. But, according to presentism, only presently existing things are real. Thus, the proper way to understand the truth of this sentence is to translate it into a more primitive form, where the tense is captured by an operator. So in our example, the truth of the sentence supervenes on the present according to the formulation “WAS(George Washington camps at Valley Forge).” In this way, presentists can describe events in the past and future as truths that supervene on the present. It is the basis for their account of persistence through time in issues like causality and personal identity.

4. Time in Physics

Since the use of the term ‘time’ in our definition of time travel remains ambiguous, we may further distinguish external, or physical time from personal, or inner time (again, following Lewis). In the ordinary world, external time and one’s personal time coincide with one another. In the world of the time traveler, they do not. So, with these two senses of time, we may further clarify time travel to occur when the duration of the journey according to the personal time of the time traveler does not equal the duration of the journey in external time. Most (but not all) philosophy of time concerns external time (see the encyclopedia entry Time ). For the purpose of natural time travel, we need to examine the scientific understanding of external time and how it has changed.

a. Newtonian Cosmology

Newton argued that space, time and motion were absolute, that is, that the entire universe was a single, uniform inertial frame and that time passed equably throughout it according to an eternally fixed, immutable and inexorable rate, without relation to anything external. Natural time travel in the Newtonian universe is impossible; there are no attributes or topography of space or time that can be exploited for natural time travel stories. Only time travel stories that exceed the bounds of Newtonian physics are possible and scenarios described by some Wellsian time travel stories (most notably like the one Wells himself wrote) are examples of such unscientific time travel.

Several philosophers and scientists objected to the notion of absolute space, time and motion, most notably Leibniz, Berkeley and Mach. Mach rejected Newton’s implication that there was anything substantive about time: “It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction, at which we arrive by means of the changes of things” (The Science of Mechanics, 1883). For Mach, change was more fundamental than the concept of time. We talk about time “passing” but what we’re really noticing is that things move and change around us. We find it convenient to talk as if there were some underlying flowing substance like the water of a river that carries these changes along with it. We abstract time to have a standard measuring tool by which we can quantify change. These views of Mach’s were influential for the young Albert Einstein. In 1905, Einstein published his famous paper on Special Relativity. This theory began the transformation of our understanding of space, time and motion.

b. Special Relativity

The theory of Special Relativity has two defining principles: the principle of relativity and the invariance of the speed of light. Briefly, the principle of relativity states that the laws of physics are the same for any inertial observer. An observer is an inertial observer if the observer’s trajectory has a constant velocity and therefore is not under the influence of any force. The second principle is the invariance of the speed of light. All inertial observers measure the speed c of light in a vacuum as 3 x 10 8 m/s, regardless of their velocities relative to one another. This principle was implied in Maxwell’s equations of electromagnetism (1873) and the constancy of c was verified by the Michelson-Morley interferometer experiment (1887).

This second principle profoundly affected the model of the cosmos: the constancy of c was inconsistent with Newtonian physics. The invariance of the speed of light according to Special Relativity replaces the invariance of time and distance in the Newtonian universe. Intervals of space, like length, and intervals of time (and hence, motion) are no longer absolute quantities. Instead of speaking of an object in a particular position independently of a particular time, we now speak of an event in which position and time are inseparable. We can relate two events with a new quantity, the spacetime interval. For any pair of events, the spacetime interval is an absolute quantity (that is, has the same value) for all inertial observers. To visualize this new quantity, one constructs spacetime diagrams (Minkowski diagrams) in which an event is defined by its spatial position (usually restricted to one dimension, x) and its time (ct). Thus, a spacetime interval might be null (parallel to the trajectory of light, which, because of the y-axis units, is shown at a 45° angle), spacelike (little or no variation in time), or timelike (little or no variation in spatial position). The following figure shows a Minkowski diagram depicting the flat spacetime of Special Relativity and three different spacetime intervals, or worldlines .

What are the consequences of Special Relativity for time travel? First, we lose the common sense meaning of simultaneity. For example, the same event happens at two different times if one observer’s inertial frame is stationary relative to another observer’s inertial frame moving at some velocity. Furthermore, an observer in the stationary inertial frame may determine two events to have happened simultaneously, but an observer in the second moving inertial frame would see the same two events happening at different times. Thus, there is no universal or absolute external time; we can only speak of external time within one’s own frame of reference. The lack of simultaneity across frames of reference means that we might experience the phenomenon of time dilation. If your frame of reference is moving at some fraction of the speed of light, your external time passes more slowly than the external time in a frame of reference that is stationary relative to yours. If we imagine that someone in the stationary frame of reference could peek at a clock in your frame of reference, they would see your clock run very slowly. So in Special Relativity, we can find a kind of natural time travel. An example of Special Relativity time travel is of an astronaut who travels some distance in the universe at a velocity near the speed of light. The astronaut’s personal time elapses at the same rate it always has. He travels to his destination and then returns home to find that external time has passed there quite differently. Everyone he knew has aged more than he, or perhaps has even been dead for hundreds or thousands of years.

Such stories are physically consistent with the Einsteinian universe of Special Relativity, but of course they remain technologically beyond our present capability. Nevertheless, they are an example of a natural time travel story—adhering to the known laws of physics—which do not require exceptions to fundamental scientific principles (for example, the invariant and inviolable speed of light). But as a time travel story, they require that the time traveler also be an ordinary traveler, too, that is, that he travel some distance through space at extraordinary speeds. Furthermore, this sort of natural time traveler can only time travel into the future. (Conversely, from the perspective of those in the originating frame of reference, when the astronaut returns, they witness the effects of time travel to the past perhaps because they have a person present among them who was alive in their distant past.) So natural time travel according to Special Relativity is perhaps too limited for what we normally mean by time travel since it requires (considerable) spatial travel in order to work.

In addition, there are other limitations, not least of which is mass-energy equivalence. This principle was published by Einstein in his second paper of 1905, entitled “Does the Inertia of a Body Depend Upon Its Energy Content?” Mass-energy equivalence was implied by certain consequences of Special Relativity (other theorists later discovered that it was suggested by Maxwell’s electromagnetism theory). Mass-energy equivalence is expressed by the famous formula, E = mc 2 . It means that there is an energy equivalent to the mass of a particle at rest. When we harmonize mass-energy equivalence with the conservation law of energy, we find that if a mass ceases to exist, its equivalent amount of energy must appear in some form. Mass is interchangeable with energy. Now only mass-less objects, like photons, can actually move at the speed of light. They have kinetic energy but no mass energy. Indeed, all objects with mass at rest, like people and spaceships cannot, in principle, attain the speed of light. They would require an infinite amount of energy.

c. General Relativity

In Special Relativity, all inertial frames are equivalent, and while this is a useful approximation, it does not yet suggest how inertial frames are to be explained. Mach had stated that the distribution of matter determines space and time. But how? This was the question answered by Einstein in his theory of General Relativity (1916). Special Relativity is actually a subset of General Relativity. General Relativity takes into account accelerating frames of reference (that is, non-inertial frames) and thus, the phenomenon of gravity. The topography of spacetime is created by the distribution of mass. Spacetime is dynamic, it curves, and matter “tells” a region of spacetime how to curve. Likewise, the resultant geometry of a spacetime region determines the motion of matter in it.

The fundamental principle in General Relativity is the equivalence principle, which states that gravity and acceleration are two names designating the same phenomenon. If you are accelerating upwards at a rate g in an elevator located in a region of spacetime without a gravitational field, the force you would feel and the motion of objects in the elevator with you would be indistinguishable from an elevator that is stationary within a downward uniform gravitational field of magnitude g. To be more precise, there is no “force” of gravity. When we observe astronauts who are in orbit over the Earth, it is not true to say that they are in an environment with no gravity. Rather, they are in free fall within the Earth’s gravitational field. They are in a local inertial frame and thus do not feel the weight of their own mass.

One curious effect of General Relativity is that light bends when it travels near objects. This may seem strange when we remember that light has no mass. How can light be affected by gravity? Light always travels in straight lines. Light bends because the geometry of spacetime is non-Euclidean in the vicinity of any mass. The curved path of light around a massive body is only apparent; it is simply traveling a geodesic straight line. If we draw the path of an airplane traveling the shortest international route in only two dimensions (like on a flat map), the path appears curved; however, because the earth itself is curved and not flat, the shortest distance, a straight line, must always follow a geodesic path. Light travels along the straight path through the various contours of spacetime. Another curious effect of General Relativity is that gravity affects time. Imagine a uniformly accelerating frame, like a rocket during an engine burn. General Relativity predicts that, depending on one’s location in the rocket, one will measure time differently. To an observer at the bottom or back of the rocket (depending on how you want to visualize its motion), a clock at the top or front of the rocket will appear to run faster. According to the principle of equivalence, then, a clock at sea level on the Earth runs a little slower than a clock at the top of Mount Everest because the strength of the field is weaker the further you are from the center of mass.

Are natural time travel stories possible in General Relativity? Yes, they are, and some of them are quite curious. While most of spacetime seems to be flat or gently rolling contours, physicists are aware of spacetime regions with unusual and severe topologies such as rotating black holes. Black holes are entities that remain from the complete collapse of stars. Black holes are the triumph of gravity over all other forces and are predicted by a solution to Einstein’s General Relativity equations (Kerr, 1963). When they rotate, the singularity of the black hole creates a ring or torus, which might be traversable (unlike the static black hole, whose singularity would be an impenetrable point). If an intrepid astronaut were to position herself near the horizon of the rapidly spinning center of a black hole (without falling into its center and possibly being annihilated), she would be treated to a most remarkable form of time travel. In a brief period of her personal time she would witness an immensely long time span in the universe beyond the black hole horizon; her spacetime region would be so far removed from the external time of the surrounding cosmos that she conceivably could witness thousands, millions, or billions of years elapse. This is a kind of natural time travel; however, it severely restricts the activity of the astronaut/time traveler and she is limited to “travel” into the future. Are there solutions to General Relativity that allow natural time travel into the past? Yes, but unlike rotating black holes, they remain only theoretical possibilities.

Einstein’s neighbor in Princeton, Kurt Gödel, developed one such solution. In 1949, Gödel discovered that some worldlines in closed spacetime could curve so severely that they curved back onto themselves, forming a loop in spacetime. These loops are known as closed timelike curves (CTCs). If you were an object on a CTC worldline, you would eventually arrive at the same spacetime position from which you started, that is, your older self would appear at one of its own earlier spacetime points. Gödel’s CTC spacetime describes a rotating universe; thus, it is an extreme case for a CTC because it is globally intrinsic to the structure of the universe. It is not considered a realistic solution since current cosmological theory states that the universe is expanding, not rotating.

One type of spacetime region that a natural time traveler might exploit is a wormhole : two black holes whose throats are linked by a tunnel. Wormholes would connect two regions of space and two regions of time as well. Physicist Kip Thorne speculated that if one could trap one of the black holes that comprise the mouths of the wormhole it would be conceivable to transport it, preferably at speeds near the speed of light. The moving black hole would age more slowly than the stationary black hole at the other end of the wormhole because of time dilation. Eventually, the two black holes would become unsynchronized and exist in different external times. The natural time traveler could then enter the stationary black hole and emerge from the wormhole some years earlier than when he departed. Unfortunately for our time traveler, if wormholes exist naturally many scientists think that they are probably quite unstable (particularly if quantum effects are taken into account). So, any natural wormhole would require augmentation from exotic phenomena like negative energy in order to be useful as a time machine.

Another type of CTC suggested by Gott (1991) employs two infinitely long and very fast moving cosmic “strings” of extremely dense material. The atom-width strings would have to travel parallel to one another in opposite directions. As they rush past one another, they would create severely curved spacetime such that spacetime curved back on itself. The natural time traveler would be prepared to exploit these conditions at just the right moment and fly her spaceship around the two strings. If executed properly, she would return to her starting point in space but at an earlier time.

One common feature of all CTCs, whether it is the global Gödelian rotating universe or the local regions of rolled-up spacetime around a wormhole or cosmic strings, is that they are solutions to General Relativity that would describe CTCs as already built into the universe. The natural time traveler would have to seek out these structures through ordinary travel and then exploit them. So far, we are not aware of any solution to General Relativity that describes the evolution of a CTC in a spacetime region where time travel had not been possible previously; however, it is usually assumed that there are such solutions to the equations. These solutions would entail particular physical constraints. One constraint would be the creation of a singularity in a finite region of spacetime. To enter the region where time travel might be possible, one would have to cross the Cauchy horizon, the hourglass-shaped (for two crossing cosmic strings) boundary of the singularity in which the laws of physics are unknown. Were such a CTC constructed, a second constraint would limit the external time that would be accessible to the time traveler. You could not travel to a time prior to the inception date of the CTC. (For more on this sort of time travel, see Earman, Smeenk, and Wüthrich, 2002.)

Natural time travel according to General Relativity faces daunting technological challenges especially if you want to have some control over the trajectory of your worldline. One problem already mentioned is that of stability. But equally imposing is the problem of energy. Fantastic amounts of exotic matter (or structures and conditions similar to the early moments of the Big Bang, like membranes with negative tension boundary layers, or gravitational vacuum polarization) would be needed to construct and manage a usable wormhole; infinitely long tubes of hyperdense matter would be needed for cosmic strings. Despite these technological challenges, it should be pointed out that the possibility of natural time travel into the past is consistent with General Relativity. But Hawking and other physicists recognize another problem with actual time travel into the past along CTCs: maintaining a physically consistent history within causal loops (see Causation below). One advantage of some interpretations of relativistic quantum theory is that the logical requirement for a consistent history in a time travel story is seemingly avoided by postulating alternative histories (or worlds) instead of one history of the universe.

d. Quantum Interpretations

Certain aspects of quantum theory are relevant to time travel, in particular the field of quantum gravity. The fundamental forces of nature (strong nuclear force, electromagnetic force, weak nuclear force, and gravitation) have relativistic quantum descriptions; however, attempts to incorporate gravity in quantum theory have been unsuccessful to date. On the current standard model of the atom, all forces are carried by “virtual” particles called gauge bosons (corresponding to the order given above for the forces: mesons and gluons, photons, massive W and Z particles, and the hypothetical graviton). A physicist might say that the photon “carries” electromagnetic force between “real” particles. The graviton, which has eluded attempts to detect it, “carries” gravity. This particle-characterization of gravity in quantum theory is very different from Einstein’s geometrical characterization in General Relativity. Reconciling these two descriptions is a robust area of research and many hope that gravity can be understood in the same way as the other fundamental forces. This might eventually lead to the formulation of a “theory of everything.”

Scientists have proposed several interpretations of quantum theory. The central issue in interpretations of quantum theory is entanglement. When two quantum systems enter into temporary physical interaction, mutually influencing one another through known forces, and then separate, the two systems cannot be described again in the same way as when they were first brought together. Microstate and macrostate entanglement occurs when an observer measures some physical property, like spin, with some instrumentation. The rule, according to the orthodox (or Copenhagen) interpretation, is that when observed the state vector (the equation describing the entangled system) reduces or jumps from a state of superposition to one of the actually observed states. But what happens when an entangled state “collapses?” The orthodox interpretation states that we don’t know; all we can say about it is to describe the observed effects, which is what the wave equation or state vector does.

Other interpretations claim that that the state vector does not “collapse” at all. Instead, some no-collapse interpretations claim that all possible outcomes of the superposition of states become real outcomes in one way or another. In the many-worlds version of this interpretation (Everett, 1957), at each such event the universe that involves the entangled state exfoliates into identical copies of the universe, save for the values of the properties included in the formerly entangled state vector. Thus, at any given moment of “collapse” there exist two or more nearly identical universes, mutually unobservable yet equally real, that then each divide further as more and more entangled events evolve. On this view, it is conceivable that you were both born and not born, depending on which world we’re referring to; indeed, the meaning of ‘world’ becomes problematic. The many universes are collectively designated as the multiverse. There are other variations on the many-worlds interpretation, including the many minds version (Albert and Loewer, 1988) and the many histories version (Gell-Mann and Hartle, 1989); however, they all share the central claim that the state vector does not “collapse.”

Many natural time travel stories make use of these many-worlds conceptions. Some scientists and storytellers speculate that if we were able to travel through a wormhole that we would not be traversing a spacetime interval in our own universe, but instead we would be hopping from “our” universe to an alternative universe. A natural time traveler in a many-worlds universe would, upon their return trip, enter a different world history. This possibility has become quite common in Wellsian time travel stories, for example, in Back to the Future and Terminator. These types of stories suggest that through time travel we can change the outcome of historical events in our world. The idea that the history of the universe can be changed is why many of the inconsistencies with causation and personal identity arise. We now turn to these topics to examine the philosophical implications of time travel stories.

5. Causation

Inconsistencies and incoherence in time travel stories often result from spurious applications of causation. Causation describes the connected continuity of events that change. The nature of this relation between events, for example, whether it is objective or subjective, is a subject of debate in philosophy. But for our purposes, we need only notice that events generally appear to have causes. The distinction made between external and personal time is crucial now for the difficulties of causation in some time travel stories.

Imagine Heloise is a time traveler who travels 80 years in the past to visit Harold. They have a fight and Heloise knocks out one of Harold’s teeth. If we follow the progression of Heloise’s personal time (or of Harold’s), the story is consistent; indeed, time travel seems to have little effect upon the events described. The difficulty arises when we test the consistency of the story in external time, because it involves an earlier event being affected by a later event. The ordinary forward progress of events related to Harold 80 years ago requires a schism in the connectivity and continuity of those events to allow the entry of a later event, namely, Heloise’s time travel journey. The activity of Heloise is causally continuous with respect to her personal time but not with respect to external time (assuming that the continuity of her personal identity is not in question, as we shall discuss in the next section). With respect to external time, this story describes reversed causation, for later events produce changes in earlier events. How does the story change if Heloise is homicidal and encounters her own grandfather 80 years ago? This is a scenario many think show that time travel into the past is inconsistent and thus impossible.

a. The Grandfather Paradox

Heloise despises her paternal grandfather. Heloise is homicidal and has been trained in various lethal combat techniques. Despite her relish at the thought of murdering her grandfather, time has conspired against her, for her grandfather has been dead for 30 years. As a crime investigator might say, she has motive and means, but lacks the opportunity; that is, until she fortuitously comes into the possession of a time machine. Now Heloise has the opportunity to fulfill her desire. She makes the necessary settings on the machine and plunges back into time 80 years. She emerges from the machine and begins to stalk her grandfather. He suspects nothing. She waits for the perfect moment and place to strike so that she can enjoy the full satisfaction of her hatred. At this point, we might pause to observe: “If Heloise murders her grandfather, she will have prevented him from fathering any children. That means that Heloise’s own father will not be born. And that means that Heloise will not be born. But if she never comes into existence, then how is she able to return…?” And so we have the infamous grandfather paradox. Before we examine what happens next, let’s consider the possible outcomes of her impending action.

First, let’s assume that the many-worlds hypothesis correctly describes the universe. If so, then we avoid the paradox. If Heloise succeeds in killing her grandfather before her father is conceived, then the state of the world includes quantum entanglement of the events involved in Heloise’s mind, body, surrounding objects, etc., such that when she succeeds in killing her grandfather (or willing his death just prior to the physical accomplishment of it), the universe at that moment divides into one universe in which she succeeded and a second universe in which she did not. So the paradox of causal continuity in external time does not arise; causation presumably connects events in the different universes without any inconsistency. But as we shall see in the next section this quantum interpretation trades-off a causation paradox for a personal identity paradox.

Next, let’s assume that we do not have the many-worlds quantum interpretation available to us, nor for that matter, any theory of different worlds. Can Heloise murder her grandfather? As David Lewis famously remarked, in one sense she can, and in another sense she can’t. The sense in which she can murder her grandfather refers to her ability, her willingness, and her opportunity to do so. But the sense in which she cannot murder her grandfather trumps the sense in which she can. In fact, she does not murder her grandfather because the moments of external time that have already passed are no longer separable. Assuming that events 80 years ago did not include Heloise murdering her grandfather, she cannot create another moment 80 years ago that does. A set of facts is arranged such that it is perfectly appropriate to say that, in one sense, Heloise can murder her grandfather. However, this set of facts is enclosed by the larger set of facts that include the survival of her grandfather. Were Heloise to actually succeed in carrying out her murderous desire, this larger set of facts would contain a contradiction (that her grandfather both is murdered and is not murdered 80 years ago), which is impossible. History remains consistent.

This is also related to Stephen Hawking’s view (1992). According to his so-called Chronology Protection Conjecture, he claims that the laws of physics conspire to prevent macroscopic inconsistencies like the grandfather paradox. A “Chronology Protection Agency” works through events like vacuum fluctuations or virtual particles to prevent closed trajectories of spacetime curvature in the negative direction (CTCs). If Hawking is right and many-worlds quantum interpretations are not available, then is time travel to the past still possible? Hawking’s view about consistent history then takes us to the special case of causation paradoxes: the causal loop.

b. Causal Loops

A causal loop is a chain of causes that closes back on itself. A causes B, which causes C,…which causes X, which causes A, which causes B…and so on ad infinitum. This sequence of events is exploited in some natural and Wellsian time travel stories. It is a point of debate whether all time travel stories involving travel to the past include causal loops. As we have seen, causal loops can occur when extraordinary cosmic structures curve spacetime in a negative direction. Wellsian time travel stories with causal loops describe scenarios like the following one by Keller and Nelson (2001).

Jennifer, a young teenager, is visited by an old woman who materializes in her bedroom. The old woman describes intimate details that only Jennifer would know and thus convinces Jennifer to pursue a professional tennis career. Jennifer does exactly as the old woman suggested and eventually retires, successful and happy. One day she comes into the possession of a time machine and decides to use it to travel back in time so that she might try to make her teenage years happier. Jennifer travels back into the past and stands before a person she recognizes as her younger self. Jennifer begins to talk to the teenager about her hidden talents and the bright future before her as a tennis professional. At the end of their conversation, Jennifer activates the time machine and returns to her original time. We can describe the causal loop in Keller and Nelson’s story as follows. The story contained within in the causal loop is presented on the left side. At event C, the story splits, with the causal loop continuing along C1, and the exit from the loop beginning at C2. At C2, the worldline of Jennifer continues outside the causal loop events. Thus:

The events of Jennifer’s life include a causal loop: some of those events have no beginning and no end. What is the problem with the story? Each moment of the causal sequence is explicable in terms of the prior events. But where (or when) did the crucial information that Jennifer would have a successful tennis career come from originally? While each part of the causal sequence makes sense, the causal loop as a whole is surprising because it includes information ex nihilo . It is controversial whether such uncaused causes are possible. Some philosophers (for example, Mellor, 1998) think that causal loop time travel stories are impossible because causal loops are themselves impossible. They argue that time and causality must progress in the same direction. Other philosophers (for example, Horwich, 1987) argue that while causal loops are not impossible, they are highly implausible, and thus spacetime does not permit time travel into the “local” past (like one’s own life) because fantastic amounts of energy would be required. Still other philosophers (for example, Lewis) think that causal loops are possible because at least some events, like the Big Bang, appear to be events without causes, introducing information ex nihilo .

According to Hawking, causal loop stories that employ CTCs are like grandfather paradox stories. While backwards causation might be logically possible, it is not physically possible. The “Chronology Protection Agency” actively prevents them from occurring. The laws of physics conspire such that natural time travel into the past thwarts backwards or reverse causation. In closed spacetime, the Cauchy horizon of a CTC acts as an impenetrable barrier to a timelike worldline for objects. If a time traveler could travel to the past, whether or not that past included their younger self, they are prevented from interacting with the events of the past.

If causal loops are possible, then the objects may interact with the events of the past, but only in a consistent way, that is, only in a way that preserves the already established events of the past. Perhaps we could call it the CTC prime directive (see Ray Bradbury’s short story “A Sound of Thunder”). Causal loops, like any other aporia of uncaused causes, occupy the inexplicable perimeter of philosophical thought about causation. Nevertheless, causal loop stories like that of Jennifer raise another issue: personal identity .

6. Personal Identity

The old Jennifer travels back in time to talk with her younger self. Are there two Jennifers or just one Jennifer at event A? At the same moment in external time, a young Jennifer and an old Jennifer are separated by a distance of a few feet. At that moment, is there one person or two? Identity theory involves the relationships between the mind and the body that attempts to show the connection between mental states and physical states (see the entry Personal Identity ). It tries, for example, to describe and explain the connection (if any) between mind and the brain. For Lewis, the mental/physical distinction is crucial for explaining how a time traveler like Jennifer is one person, even when she travels back to talk with her younger self. Our cognitions change according to the requirement of causal continuity. These mental states occur in personal time. For everyday purposes, we can ignore the distinction between personal time and external time; personal time and external time coincide. But for a time traveler like Jennifer, identity is maintained only by virtue of the traveler’s personal time; their mental states continue like anyone else’s and at any given point in personal time, later mental states do not cause earlier ones.

In the case of Jennifer, it is therefore proper to say that at event A in her life, there is only one person, even though it is also true to say from an external perspective, that she has two different bodies present at event A. Lewis’s distinction between the sense in which you can and the sense in which you can’t has its coda in the subject of personal identity. In the sense of personal time, Jennifer is one person who is perceiving another person (from either Jennifer’s perspective). The older Jennifer’s materialization into the presence of the younger Jennifer is strange, to be sure, but in a time travel story, it is explicable. Regardless, in her personal time, the causal continuity of her perception (and thus mental states) is consistent. In the sense of external time, from the perspective of their surrounding world, there are two Jennifers at event A. The mental state of the younger Jennifer is not identical to the mental state of the older Jennifer. But these mental states, these stages of Jennifer’s life are not duplicates of the same stage; rather, two moments of personal time overlap at one moment of external time. So is it still proper to say that there are two of her? Lewis argues no, it is not. In the strange case of a time traveler like Jennifer, her stages are scattered in such a way that they do not connect in a continuously forward direction through external time, but they do connect continuously forward through her personal time. The time traveler who meets up with her younger self gives the appearance to an outside observer that she is two different people, but in reality, there is only one person.

The question of how objects persist through time is the subject of the endurance and perdurance debate in philosophy. An endurantist is someone who thinks that objects are wholly present at each moment of an interval of time. A perdurantist is someone who thinks that objects only have a temporal part present at each moment of an interval of time. The perdurantist claims that the identity of the whole object is identified as the sum of these temporal parts over the lifetime of the object. It seems that it is impossible for an endurantist to believe the story about Jennifer because she would have to be wholly present in two different spatial locations at the same time. The endurantist can avoid this problem by appealing to the distinction between personal time and external time. If Jennifer is wholly present at different locations “at the same time,” which kind of time do we mean? We mean external time. The endurantist can claim that two different temporal stages in her personal time just so happen to coincide because she is a time traveler at different locations at a single moment of external time. For those of us who are not time travelers, our different temporal stages are also distinct moments in external time. But in either case, whether time traveler or not, a person is wholly present at any moment of their personal time.

The perdurantist seems to have an easier way with the problem of personal identity in time travel stories. Since a person is only partially present at each moment of external time, it is readily conceivable that different temporal parts might coincide, but we still need to appeal to the distinction between personal time and external time. The two temporal parts of Jennifer’s life that occur when the young and old Jennifer meet and have a conversation are each elements among many others that in toto form the whole person.

Personal identity is especially problematic in a many-worlds hypothesis. Consider the case of Heloise and her desire to murder her grandfather. According to the many-worlds hypothesis, she travels back in time but by doing so also skips into another universe. Heloise is free to kill her grandfather because she would not be killing “her” grandfather, that is, the same grandfather that she knew about before her time travel journey. Indeed, Heloise herself may have split into two different persons. Whatever she does after she travels into the past would be consistent with the history of the alternative universe. But the question of who exactly Heloise or her grandfather is becomes problematic, especially if we assume that her actions in the different universes are physically distinct. Is Heloise the sum of her appearances in the many worlds? Or is each appearance of Heloise a unique person?

Also, see the related article Time in this Encyclopedia.

7. References and Further Reading

• Albert, David and Barry Loewer. 1988. Interpreting the many worlds interpretation. Synthese 77:195-213.
• Bigelow, John. Time travel fiction. In Gerhard Preyer and Frank Siebelt, eds., Reality and Humean Supervenience. Lanham, MD: Rowan & Littlefield, 2001. 58-91.
• Bigelow, John. Presentism and properties. In James E. Tomberlin, ed., Philosophical Perspectives 10. Cambridge, MA: Blackwell Publishers, 1996. 35-52.
• Bradbury, Ray. 1952. A Sound of Thunder. In R is for Rocket. New York: Doubleday.
• Earman, John. 1995. Outlawing Time Machines: chronology protection theorems. Erkenntnis 42(2):125-139.
• Earman, John, Smeenk, Christopher and Wüthrich, Christian. 2002. Take a ride on a time machine. In R. Jones and P. Ehrlich, eds., Reverberations of the Shaky Game: Festschrift for Arthur Fine. Oxford: Oxford University Press.
• Everett, Hugh. 1957. Relative state formulation of quantum mechanics. Review of Modern Physics 29:454-62.
• Gell-Mann, Murray and James B. Hartle. 1989. Quantum mechanics in the light of quantum cosmology. In Proceedings of the 3rd International Symposium on the Foundations of Quantum Mechanics. Tokyo, Japan. 321-43.
• Gott, J. Richard. Time Travel in Einstein’s Universe: The Physical Possibilities of Travel Through Time. Boston: Houghton Mifflin, 2001.
• Hawking, S. W. 1992. Chronology protection conjecture. Physical Review D 46(2):603-11.
• Horwich, Paul. 1987. Asymmetries in Time: Problems in the Philosophy of Science. Cambridge, MA: MIT Press.
• Keller, Simon and Michael Nelson. 2001. Presentists should believe in time-travel. Australasian Journal of Philosophy 79:333-45.
• Lewis, David. 1976. The paradoxes of time travel. American Philosophical Quarterly 13:145-52.
• Mellor, D. H. Real Time II. London: Routledge, 1998.
• Monton, Bradley. 2003. Presentists can believe in closed timelike curves. Analysis 63(3).
• Smith, Nicholas J. J. 1997. Bananas enough for time travel? British Journal of Philosophy 48:363-389.

Author Information

Joel Hunter Email: [email protected] Truckee Meadows Community College U. S. A.

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What’s the time in China right now? The time in Dubai? Time in London? Time in Japan? What’s the time in all those places at once?! The World Time Travel Clock displays the time at multiple locations around the world simultaneously on a single clock face. With its time travel feature you can easily visualize how times change together moving into the future or backwards in the past. Just swipe your finger around the circle to move time forwards or backwards. Align a location’s time arrow to a future time to see the times in the other locations. Also shows which day it is in the different locations. Great for planning long distance meetings, plane trips, viewing sports events or just knowing if it's Tuesday or Wednesday in Bora Bora.

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User's Guide

The World Time Travel Clock is a global time zone clock that shows the time at multiple locations around the world. Each location is displayed as a yellow banner with the location's name and an arrow pointing to the current time at that location. The clock also shows the dividing lines between days. One line pointing to midnight divides the globe into two days, which are labeled on either side of the line. The other line - that rotates with the clock face as it moves - is the international date line.

Above the clock is a label showing a location's name and its current time and date. Tap on the label to cycle through the custom locations you have selected. The label underneath the clock shows the timezone associated with the current location.

Time Machine

Customize locations, view times and set notifications, notifications, troubleshooting notifications.

• The mute switch is on, or the ringer volume is set all the way down.
• Do not disturb is on (change in Settings app -> Do Not Disturb)
• The app is not allowed to get notifications (change in Settings app -> Notifications -> Travel Clock)
• You have an Apple Watch and it is set to mirror alerts from iPhone app. Sometimes it will send the alert to the watch, but sometimes it won't, and either way you won't hear any sound on the phone. (Change in Watch app -> Notifications -> scroll down to the "Mirror iPhone Alerts From:" section and find "Travel Clock").

Clock Style

Perspective.

Why does time change when traveling close to the speed of light? A physicist explains

Assistant Professor of Physics and Astronomy, Rochester Institute of Technology

Disclosure statement

Michael Lam does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

Rochester Institute of Technology provides funding as a member of The Conversation US.

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Curious Kids is a series for children of all ages. If you have a question you’d like an expert to answer, send it to [email protected] .

Why does time change when traveling close to the speed of light? – Timothy, age 11, Shoreview, Minnesota

Imagine you’re in a car driving across the country watching the landscape. A tree in the distance gets closer to your car, passes right by you, then moves off again in the distance behind you.

Of course, you know that tree isn’t actually getting up and walking toward or away from you. It’s you in the car who’s moving toward the tree. The tree is moving only in comparison, or relative, to you – that’s what we physicists call relativity . If you had a friend standing by the tree, they would see you moving toward them at the same speed that you see them moving toward you.

In his 1632 book “ Dialogue Concerning the Two Chief World Systems ,” the astronomer Galileo Galilei first described the principle of relativity – the idea that the universe should behave the same way at all times, even if two people experience an event differently because one is moving in respect to the other.

If you are in a car and toss a ball up in the air, the physical laws acting on it, such as the force of gravity, should be the same as the ones acting on an observer watching from the side of the road. However, while you see the ball as moving up and back down, someone on the side of the road will see it moving toward or away from them as well as up and down.

Special relativity and the speed of light

Albert Einstein much later proposed the idea of what’s now known as special relativity to explain some confusing observations that didn’t have an intuitive explanation at the time. Einstein used the work of many physicists and astronomers in the late 1800s to put together his theory in 1905, starting with two key ingredients: the principle of relativity and the strange observation that the speed of light is the same for every observer and nothing can move faster. Everyone measuring the speed of light will get the same result, no matter where they are or how fast they are moving.

Let’s say you’re in the car driving at 60 miles per hour and your friend is standing by the tree. When they throw a ball toward you at a speed of what they perceive to be 60 miles per hour, you might logically think that you would observe your friend and the tree moving toward you at 60 miles per hour and the ball moving toward you at 120 miles per hour. While that’s really close to the correct value, it’s actually slightly wrong.

This discrepancy between what you might expect by adding the two numbers and the true answer grows as one or both of you move closer to the speed of light. If you were traveling in a rocket moving at 75% of the speed of light and your friend throws the ball at the same speed, you would not see the ball moving toward you at 150% of the speed of light. This is because nothing can move faster than light – the ball would still appear to be moving toward you at less than the speed of light. While this all may seem very strange, there is lots of experimental evidence to back up these observations.

Time dilation and the twin paradox

Speed is not the only factor that changes relative to who is making the observation. Another consequence of relativity is the concept of time dilation , whereby people measure different amounts of time passing depending on how fast they move relative to one another.

Each person experiences time normally relative to themselves. But the person moving faster experiences less time passing for them than the person moving slower. It’s only when they reconnect and compare their watches that they realize that one watch says less time has passed while the other says more.

This leads to one of the strangest results of relativity – the twin paradox , which says that if one of a pair of twins makes a trip into space on a high-speed rocket, they will return to Earth to find their twin has aged faster than they have. It’s important to note that time behaves “normally” as perceived by each twin (exactly as you are experiencing time now), even if their measurements disagree.

You might be wondering: If each twin sees themselves as stationary and the other as moving toward them, wouldn’t they each measure the other as aging faster? The answer is no, because they can’t both be older relative to the other twin.

The twin on the spaceship is not only moving at a particular speed where the frame of references stay the same but also accelerating compared with the twin on Earth. Unlike speeds that are relative to the observer, accelerations are absolute. If you step on a scale, the weight you are measuring is actually your acceleration due to gravity. This measurement stays the same regardless of the speed at which the Earth is moving through the solar system, or the solar system is moving through the galaxy or the galaxy through the universe.

Neither twin experiences any strangeness with their watches as one moves closer to the speed of light – they both experience time as normally as you or I do. It’s only when they meet up and compare their observations that they will see a difference – one that is perfectly defined by the mathematics of relativity.

Hello, curious kids! Do you have a question you’d like an expert to answer? Ask an adult to send your question to [email protected] . Please tell us your name, age and the city where you live.

And since curiosity has no age limit – adults, let us know what you’re wondering, too. We won’t be able to answer every question, but we will do our best.

• General Relativity
• Special Relativity
• Time dilation
• Speed of light
• Albert Einstein
• Curious Kids
• Theory of relativity
• Curious Kids US

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World Time Travel Clock, with Backlight Display Lightweight Multi Time Zone Pocket Sized Digital Travel Alarm Clock, Portable 3 Bright Led'S for Traveling

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• ⏲️World Time Travel Clock---Travel Alarm Clock. The alarm clock is lightweight and pocket sized flashlight with world time clock with 18 time zones. Flashlight contains 3 bright LED's, can help you light up in the dark night. This travel alarm clock is ideal for traveling. Very lightweight to put in your pocket.
• ⏲️Multifunction---Portable Alarm Clock for Travel. Lightweight and pocket sized flashlight with world time clock with 18 time zones. Flashlight contains 3 bright LED's, can help you light up in the dark night. Temperature display function: Can switch between ℃ and ℉. Alarm with 16 wake up melodies, you will never boring of the same music. Perpetual calendar with full month view and date.
• ⏲️Clear Digital Display---Multi Functional Clock. This travel alarm clock has a large LCD screen, and the time, date, full month date and temperature can be easily read. You can give it as a gift to your friends, family. It will be a particularly practical gift.
• ⏲️Pocket Size---This travel alarm clock is very lightweight and compact, only pocket size. Just store it in your pocket and carry it. Easy to carry and storage. This travel alarm clock is perfect for travel and camping. Smart clock alarm clock.
• ⏲️Long Lasting---Travel Alarm Clock Flashlight. This travel alarm clock is made of ABS material and is of good quality and durable. It can be used for a long time even if it is used outdoors for a long time.

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The alarm clock is lightweight and pocket sized flashlight with world time clock with 18 time zones. Flashlight contains 3 bright LED's, can help you light up in the dark night. This travel alarm clock is ideal for traveling. Very lightweight to put in your pocket.

Material: ABS Display Type: LCD Voltage: 4.5V Power: 2 AAA batteries (not included)

Size: 13 x 3.8 x 4 cm / 5.12 x 1.50 x 1.57 in (appr.)

Package Included:

1 x World Time Travel Clock (Not include the battery)

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Unraveling the Mystery of Jet Lag: Expert Strategies for Managing Jet Lag from Airplane Travel

• Jet lag is a universal travel woe affecting approximately 93% of travelers.
• Jet lag is notably worse when flying eastward due to our bodies' difficulty adapting to shorter days.
• Adopting specific strategies can help manage and even prevent jet lag symptoms.
• Follow Dr. Charles Czeisler’s advice: understand that jet lag is about aligning internal and external time.
• Personal tips and tricks from seasoned travel journalist Kevin Erickson .

Jet Lag: The Sleep-Thief of the Skies

According to the American Sleep Association, an alarming 93% of travelers will experience jet lag at some point. This statistic emphasizes the scale of the problem and its ubiquitous nature. It's a travel issue that's almost as certain as a passport check at the airport.

Jet lag , by definition, is a temporary disorder resulting from a rapid change in time zones, leading to sleep disturbances, fatigue, disorientation, and even digestive issues. As Dr. Charles Czeisler , Director of Sleep Medicine at Harvard Medical School, puts it, " Jet lag is not just about changing time zones. It's about changing internal time to external time. The more time zones we cross rapidly, the more severe jet lag symptoms tend to be. "

Understanding the Eastward Dilemma

While all travel can cause jet lag, not all travel is created equal. It's a well-established fact that jet lag is worse when traveling eastward. The culprit? Our bodies' innate circadian rhythms prefer longer days (as experienced when traveling westward) over shorter ones (eastward travel). It's a bit like being a time-traveling vampire – disoriented, grumpy, and avoiding sunlight!

Defeating Jet Lag: Your Game Plan

Embrace Strategic Sunlight Exposure: Sunlight is a key influencer of our internal body clock. Seek morning light when traveling eastward, and afternoon light when heading westward to help recalibrate your internal clock.

Hydrate and Eat Smart: Dehydration can worsen jet lag symptoms, so guzzle water on the flight. And, mimic the meal times of your destination to give your body a headstart on adjusting.

Time Your Sleep: Adjust your sleep schedule before you travel, if possible. For eastward journeys, try going to bed slightly earlier each night for a few days before departure.

Consider Short Naps: If you're feeling crushed by fatigue upon arrival, take a short nap-just don't let it exceed 20 minutes to avoid slipping into deep sleep and further disrupting your sleep schedule.

Stay Active: Exercise aids in resetting your biological clock. A brisk walk or quick workout can help stimulate alertness and adapt to the new time zone.

Light Therapy: If sunlight is scarce, light therapy glasses can help stimulate the dawn or dusk light needed to reset your internal clock.

A Glimpse from a Frequent Flier's Diary

Kevin Erickson , a seasoned travel journalist, shares some of his golden nuggets for managing jet lag. "I swear by noise-canceling headphones and an eye mask for a peaceful sleep on the plane," Erickson shares. "Upon reaching, I avoid succumbing to sleep until the local bedtime, even if it means splashing cold water on my face or a quick jog around the block!"

Decoding Jet Lag: It’s Not Only About Time Zones

Jet lag is more than just a shift in time zones. It's an internal battle between our internal clocks and external time. The human body operates on a roughly 24-hour cycle known as the circadian rhythm. This rhythm regulates sleep, wakefulness, hunger, and other physiological functions. When you travel across multiple time zones, this internal clock gets thrown out of sync with local time, resulting in the constellation of symptoms we know as jet lag.

Melatonin: The Jet Lag Alleviator

Melatonin, a hormone produced by the body, plays a crucial role in regulating sleep-wake cycles. Its production increases with darkness and decreases with light. Travelers have found melatonin supplements to be an effective jet lag remedy. However, they should be used with caution and preferably under a doctor's guidance.

Technology to the Rescue

Several apps can help manage jet lag. For instance, Timeshifter uses algorithms developed based on sleep and circadian neuroscience to provide personalized jet lag plans. By inputting travel dates, times, and sleeping patterns , you can receive a customized schedule for sleeping, exposure to light, caffeine intake, and optional melatonin use.

Post-flight Rituals: Your Key to Adjustment

Kevin Erickson also emphasizes the importance of post-flight rituals. "Once I'm at the destination, I take a shower immediately. It's not just about freshness, but the warm water can ease any muscle stiffness from the flight. Afterward, a light meal – not room service hamburgers! – and a walk around the new locale are my ways to reset the body clock ," he shares.

Why is jet lag worse when traveling eastward?

Our bodies find it harder to adjust to a shorter day (as experienced when traveling eastward) than to a longer day (traveling westward). This makes jet lag symptoms more pronounced when flying east.

Can hydration levels affect jet lag?

Yes. Dehydration can worsen jet lag symptoms. It's important to drink plenty of water before, during, and after your flight.

Can meal timings affect jet lag?

Indeed. Eating according to your destination's local time can help your body adjust to its new schedule.

What is the role of sunlight in managing jet lag?

Sunlight is a major regulator of our body's internal clock. Proper exposure to sunlight at appropriate times can help reset our body clock, aiding in managing jet lag.

How can I adjust my sleep schedule to combat jet lag?

Depending on your direction of travel, you could try going to bed slightly earlier (for eastward flights) or later (for westward flights) in the days leading up to your journey.

Does melatonin help with jet lag?

Yes, melatonin, which is a hormone that regulates sleep-wake cycles, can help manage jet lag symptoms. However, it should be used with caution and under a doctor's guidance.

Are there any technological tools to combat jet lag?

Yes, several apps, such as Timeshifter, offer personalized jet lag management plans based on your travel schedule and sleeping patterns.

What are some post-flight rituals to help adjust to a new time zone?

Kevin Erickson , a travel journalist, recommends a post-flight shower, a light meal, and a walk around the local area to help reset the body clock.

In Conclusion

Jet lag doesn't have to be your constant travel companion . With a little understanding and a few strategic moves, you can outwit this pesky byproduct of flying. Remember, it's all about aligning your internal time with the external. 

Managing jet lag from airplane travel is part art, part science. It's about understanding your body, preparing in advance, and leveraging tips and tricks along the way. With these strategies under your belt, you're now ready to kick jet lag to the curb. Make the most of your journeys without losing precious time to jet lag! Happy travels!

• American Sleep Association
• Harvard Medical School: Sleep Medicine
• Scientific study on Eastward vs. Westward travel
• The National Sleep Foundation: Jet Lag
• Timeshifter - The Jet Lag App
• Interview with Kevin Erickson

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Trump Has Been Convicted. Here’s What Happens Next.

Donald J. Trump has promised to appeal, but he may face limits on his ability to travel and to vote as he campaigns for the White House.

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By Jesse McKinley and Maggie Astor

• May 30, 2024

The conviction of former President Donald J. Trump on Thursday is just the latest step in his legal odyssey in New York’s court system. The judge, Juan M. Merchan, set Mr. Trump’s sentencing for July 11, at which point he could be sentenced to as much as four years behind bars, or to probation.

It won’t stop him from running for president, though: There is no legal prohibition on felons doing that . No constitutional provision would stop him even from serving as president from a prison cell, though in practice that would trigger a crisis that courts would almost certainly have to resolve.

His ability to vote — for himself, presumably — depends on whether he is sentenced to prison. Florida, where he is registered, requires felons convicted there to complete their full sentence, including parole or probation, before regaining voting rights. But when Floridians are convicted in another state, Florida defers to the laws of that state, and New York disenfranchises felons only while they are in prison.

The Trump Manhattan Criminal Verdict, Count By Count

Former President Donald J. Trump faced 34 felony charges of falsifying business records, related to the reimbursement of hush money paid to the porn star Stormy Daniels in order to cover up a sex scandal around the 2016 presidential election.

“Because Florida recognizes voting rights restoration in the state of conviction, and because New York’s law states that those with a felony conviction do not lose their right to vote unless they are incarcerated during the election, then Trump will not lose his right to vote in this case unless he is in prison on Election Day,” said Blair Bowie, a lawyer at the Campaign Legal Center, a nonprofit watchdog group.

Mr. Trump will almost certainly appeal his conviction, after months of criticizing the case and attacking the Manhattan district attorney, who brought it, and Justice Merchan, who presided over his trial.

Long before that appeal is heard, however, Mr. Trump will be enmeshed in the gears of the criminal justice system.

A pre-sentencing report makes recommendations based on the defendant’s criminal record — Mr. Trump had none before this case — as well as his personal history and the crime itself. The former president was found guilty of falsifying business records in relation to a $130,000 payment to Stormy Daniels, a porn star who says she had a brief sexual tryst with Mr. Trump in 2006, in order to buy her silence.

At the pre-sentence interview, a psychologist or social worker working for the probation department may also talk to Mr. Trump, during which time the defendant can “try to make a good impression and explain why he or she deserves a lighter punishment,” according to the New York State Unified Court System.

The pre-sentencing report can also include submissions from the defense, and may describe whether “the defendant is in a counseling program or has a steady job.”

In Mr. Trump’s case, of course, he is applying — as it were — for a steady job as president of the United States, a campaign that may be complicated by his new status as a felon. Mr. Trump will likely be required to regularly report to a probation officer, and rules on travel could be imposed.

Mr. Trump was convicted of 34 Class E felonies, New York’s lowest level , each of which carry a potential penalty of up to four years in prison. Probation or home confinement are other possibilities that Justice Merchan can consider.

That said, Justice Merchan has indicated in the past that he takes white-collar crime seriously . If he did impose prison time, he would likely impose the punishment concurrently, meaning that Mr. Trump would serve time on each of the counts he was convicted of simultaneously.

If Mr. Trump were instead sentenced to probation, he could still be jailed if he were later found to have committed additional crimes. Mr. Trump, 77, currently faces three other criminal cases: two federal, dealing with his handling of classified documents and his efforts to overturn the 2020 election , and a state case in Georgia that concerns election interference.

Mr. Trump’s lawyers can file a notice of appeal after sentencing, scheduled for July 11 at 10 a.m. And the judge could stay any punishment during an appeal, something that could delay punishment beyond Election Day.

The proceedings will continue even if he wins: Because it’s a state case, not federal, Mr. Trump would have no power as president to pardon himself .

Jesse McKinley is a Times reporter covering upstate New York, courts and politics. More about Jesse McKinley

Maggie Astor covers politics for The New York Times, focusing on breaking news, policies, campaigns and how underrepresented or marginalized groups are affected by political systems. More about Maggie Astor

Our Coverage of the Trump Hush-Money Trial

Guilty Verdict : Donald Trump was convicted on all 34 counts  of falsifying records to cover up a sex scandal that threatened his bid for the White House in 2016, making him the first American president to be declared a felon .

What Happens Next: Trump’s sentencing hearing on July 11 will trigger a long and winding appeals process , though he has few ways to overturn the decision .

Reactions: Trump’s conviction reverberated quickly across the country  and around the world . Here’s what voters , New Yorkers , Republicans , Trump supporters  and President Biden  had to say.

The Presidential Race : The political fallout of Trump’s conviction is far from certain , but the verdict will test America’s traditions, legal institutions and ability to hold an election under historic partisan tension .

Making the Case: Over six weeks and the testimony of 20 witnesses, the Manhattan district attorney’s office wove a sprawling story  of election interference and falsified business records.

Legal Luck Runs Out: The four criminal cases that threatened Trump’s freedom had been stumbling along, pleasing his advisers. Then his good fortune expired .