Time and Again: The Science Fiction of Time Travel

By: Dr. John Millam¹

What is Time?
On the Nature of Time
Arrow of Time
Causality
The Science of Time Travel
Time Travel Paradoxes
Are These Paradoxes Resolvable?
Time Travel in Literature and Movies
Closing Thoughts
Back Matter

Have you ever wondered if time travel was possible? Whether you could go back and meet a younger version of yourself? Whether you could visit any time in history, past and future? Those are exciting questions that many people ask. Currently, time travel only exists in science fiction, but could it ever cross into science fact? Fire up the flux capacitor in your time-traveling DeLorean and join me as we explore this provocative topic.

What is Time?

Before pondering the possibility of time travel, we need to start with a much more basic question, “What is time?”²

Time is intangible. We cannot see it, hear it, or touch it. So, if you were asked to draw a picture of time, what would you draw? Perhaps you would sketch a clock or a watch ticking every second. Alternatively, you might draw a calendar with X’s over each day to represent the passing of time. But clocks only measure the passage of time and calendars serve to organize time. We carry watches and smartphones so that we always know the date and time. We scurry about trying to be “on time” for meetings and appointments. We are obsessed with time yet even the wisest struggle to define what it is.

Understanding the true nature of time is difficult because we are trapped within time. We cannot step out of time and view it objectively from the outside. This situation is like a fish trying to understand water having always lived in water. Our overfamiliarity with time leads to many common misunderstandings about the nature of time. These include that time is real and objective, time continually ticks away at an even rate and is the same for everyone everywhere, time flows linearly from the past to the present to the future, and that only the experienced present ‘now’ is real with the past and future being unreal. Closer examination, however, brings many of these ideas into question.

In studying the nature of time, we must carefully distinguish it from our subject perception of time. As we all know, time seems to pass at different rates depending on circumstances. If we are at a party having fun, time sseems to fly by but when we are bored, time seems to crawl by. The effect is an aspect of how our brain processes events rather than fluctuations in the passage of time.

On the Nature of Time

Circling back to the central question, “What is time?” Even from very early history, great thinkers pondered over the nature of time, finding it to be paradoxically both simple and completely mysterious. The Greek philosopher Aristotle (384-322 BC) is said to have concluded: ‘”[Time is] the most unknown of unknown things.” In another example, the great church theologian, Augustine (354-430 AD), who wrestled with the nature of time concluded: “What, then, is time? If no one ask of me, I know; if I wish to explain to him who asks, I know not.” (Confessions 11.14(17)). Even with all our current knowledge, it is still difficult to properly define time. Perhaps the simplest definition of physical time is that it is the realm of cause and effect. More precisely, time can be defined as the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, and into the future.

Arrow of Time

Scientists frequently describe time as a dimension very much like our familiar three dimensions of space. For this reason, time has been colloquially called the “fourth dimension.” Albert Einstein’s theory of relativity went so far as to join space and time together into a single composite entity called spacetime. Despite the many similarities between space and time, there is one glaring difference: time flows in only one direction, forward. There is currently no way to go backward in time or even stay fixed in time, effectively dividing time into past, present, and future. This behavior is a sharp contrast to space where we can travel in any direction we desire

Imagine watching a short video clip of a coffee cup falling off the edge of the table and smashing on the floor (see Figure 1). Now, imagine watching the same video but in reverse—the coffee cup fragments leap toward each other and reassemble the cup which then flies up and lands on the table. People can instantly recognize that this second scenario is never observed in real life.

**Figure 1: Coffee cup falling and smashing on the floor.**
Credit: VideoHive

In most cases, people can readily distinguish whether a video is being played forward or backward in time. You can scramble eggs with a whisk but not unscramble them. Similarly, we may observe a wood log burning down to ashes, but we never see ashes spontaneously reassembling into a log. In our universe, time appears to have an intrinsic direction pointing toward the future. In 1927, Sir Arthur Eddington called this property the arrow of time.

While the unidirectionality of time may seem obvious to us at the human level, this was difficult for physicists to explain because there is no law of physics demanding that time must only go forward. The equations governing the motion of fundamental particles are indifferent to the direction of time. Let us consider the collision of two fundamental particles as predicted by physics. If you exactly reverse the velocity of each particle, the system will behave as if time was reversed (see Figure 2). This is a sharp contrast to the falling coffee cup.

Why does time have an obvious direction at the macroscopic (i.e., human) level but not at the microscopic (i.e., particle) level? The answer to this enigma came from the development of thermodynamics in the 19th century. The second law of thermodynamics states that the entropy of
the universe must always increase with time. Entropy can be loosely thought of as the measure of disorder in a system. The coffee cup falling off the table and shattering increases the entropy of the system and therefore represents forward time. In contrast, the coffee cup reassembling itself decreases entropy, so it is never spontaneously observed in nature. Increasing entropy serves as the arrow of time because it distinguishes between the forward flow of time and the reverse.

Causality

The unidirectional nature of time is tied to another important concept: causality. We are all familiar with this concept yet rarely think deeply about it

Causality simply affirms that effects occur after their causes. If a light bulb in a
room suddenly lights up, it is reasonable to assume that someone flicked the switch
a minute fraction of a second earlier. It is absurd to suppose that the light bulb
could light up because someone ten years in the future flicks a switch. The idea
that effects could occur before their causes is denied by the rational mind. – William
Kaufman, The Cosmic Frontiers of General Relativity³

As long as time can only progress in the forward direction, we can guarantee that causality will be respected. But what if we could travel into the past and influence events? This would allow an effect to take place prior to its cause. Violating causality leads to seemingly contradictory situations known as temporal paradoxes. These paradoxes and their implications will be covered in detail later.

Time’s arrow and causality have many important consequences that we are all familiar with. One is that we can remember the past, but not the future. Claude Shannon, the father of information theory, stated it this way:

Thus we may have knowledge of the past but cannot control it; we may control the
future but have no knowledge of it – Claude Elwood Shannon

A second major consequence of time’s arrow is that we are prisoners of time. We cannot change the past. It remains forever unreachable.

Time, not necessarily as it is, for who knows that, but as thought has constituted
it—monomaniacally forbids second chances. – Ian McEwan

But what if we could travel into the past? Even better, what if we could change the past? These are the profound questions that we will explore next. For more about time, see Appendix: On the Nature of Time.

The Science of Time Travel

When Isaac Newton published the world’s first fully mathematical framework for physics, known as Newtonian mechanics, in 1687, he treated both space and time as simple, self-existent properties of the universe. He defined them as:

Absolute, true and mathematical time, flowing without relation to anything
external. … Absolute space, in its own nature, without relation to anything external,
remains always similar and immovable. – Isaac Newton⁴

These definitions represent absolute space and time where time is fixed and unchanging and is the same for all observers. Newton’s perspective is very intuitive because it matches our everyday experience.

Einstein and the Theory of Relativity

Newton’s concept of time was shattered when Albert Einstein published his theory of special relativity in 1905. According to his theory, the speed of light in a vacuum was the same for all observers. Consequently, measurements of distance and time must vary depending on the person’s reference frame. Space and time are therefore relative. Contrary to Newton, identical clocks will not record the same time for everyone.

According to special relativity, if two people are moving at a constant velocity with respect to each other, then their clocks will differ in their elapsed time. An observer will measure the moving clock as ticking more slowly than a clock at rest in his own reference frame. This is known as time dilation. Under normal earthbound conditions, this effect is negligible⁵, but if a spaceship could travel at speeds close to that of light, time dilation would be very significant. At such speeds, even the apparent ordering of events may differ.

Ten years after publishing special relativity, Einstein introduced general relativity describing accelerating reference frames and explaining gravity by revealing how mass bends spacetime. One consequence of this theory is that residing next to a strong gravitational field also results in time dilation.

Time dilation due to Earth’s gravity is extremely feeble⁶. Only by using ultra-precise atomic clocks have scientists been able to demonstrate that time passes faster the farther one is located from the center of the Earth. For example, clocks on GPS satellites experience 38 microseconds less time per day than ones on Earth’s surface⁷. It is even possible to demonstrate that time passes faster at the top of a building compared to its basement, and similarly time passes faster at your head than your feet, although such effects are negligibly small. To get a truly significant time dilation, one would need to orbit close to a massive compact object, such as a neutron star (the collapsed remnant of a massive star) or a black hole (a region of spacetime where gravity is so strong that nothing, not even light, can escape it).

The Twin Paradox

One simple illustration of time dilation is the twin paradox thought experiment⁸. Consider a pair of identical twins. One twin becomes an astronaut traveling to the Alpha Centauri star system 4 light years away in a spaceship traveling at 80% the speed of light and then immediately returning to Earth at the same speed. The traveling astronaut would record an elapsed time of only about 6 years due to time dilation while his earth-bound twin would have aged 10 years. Even though the twins were initially the same age, the non-traveling twin would now be 4 years older. If we consider speeds even closer to the speed of light, then the disparity between the ages for the twins would be even greater. While we do not have spacecraft capable of reaching such extreme speeds, we can directly observe the lengthening of the lifetimes of particles in particle accelerators due to time dilation⁹.

To further illustrate the twin paradox, let us consider traveling to a more distant star, Rigel, located 860 light years away. Table 1 shows how the difference in age between twins for a round trip with the spacecraft traveling at different speeds. For the twin staying behind, the increase in speed from 60% the speed of light to nearly 100% only modestly reduces the elapsed trip time. For the traveling twin, however, the impact of time dilation is enormous with the trip time being reduced from thousands of years to a modest 2.4 years.

Table 1: Twin Paradox for Spacecraft Traveling Round Trip to the Star Rigel¹⁰

Spacecraft Speed (% speed light)	Earth Years	Starship Years	Difference Years
60% 80% 90% 99% 99.9% 99.99% 99.999% 99.9999%	2866.7 2150.0 1911.1 1737.4 1721.7 1720.2 1720.0 1720.0	2293.3 1290.0 833.0 245.1 77.0 24.3 7.7 2.4	573.4 860.0 1078.2 1492.3 1644.7 1695.9 1712.3 1717.6

For a more detailed examination of the theory of relativity, time dialation, and black holes in a way that is understandable by a general audience, read Martin Gardner, Relativity Simply Explained.

Closed Timelike Curves

While time dilation is demonstrably real, it is not the same as time travel because it can only take us to the future and not to the past. However, by pushing general relativity to the extreme, physicists began to discover curious mathematical solutions known as closed timelike curves, or put more simply, time travel. These paths through spacetime return to their starting point (same time and same location) forming a closed loop. Because the path returns to the same time, it must involve traveling backward in time for part of the journey. This prospect alarmed physicists because backward time travel potentially leads to troubling temporal paradoxes, such as the grandfather paradox, as will be discussed a little later.

The first example of a closed timelike curve came in 1937 when Willem Jacob van Stockum was studying solutions to Einstein’s equations for an observer orbiting an infinitely-long rapidly-rotating cylinder. He showed in his paper that if the cylinder was rotating fast enough then the observer could return to his starting point before he left, thus forming a closed timelike curve. Although this was little more than a mathematical curiosity, it set the stage for additional examples:

Kurt Gödel (1948) showed that in a rotating universe it would be possible to find orbits that led back into the past. This model was based on some artificial assumptions and experimental evidence demonstrates that the universe is not rotating.
John Wheeler (1957) conjectured the existence of wormholes, a hypothetical shortcut through spacetime. Representing space in two-dimensions, Figure 3 shows the shortest route (a) through normal space (magenta line). Route (b) shows the shorter path through the wormhole (yellow-green line). Kip Thorne (1989) proposed that traversable wormholes could be used for time travel.
Roy Kerr (1963) discovered that rotating black holes could contain time loops. If an astronaut could somehow survive the journey, they could pass through a rotating black hole and exit in a different part of the universe at a differen time11. It is expected that astronomical black holes will rotate due to their formation via the collapose of rotating stellar objects.
Frank Tipler (1974), working along the lines of Stockum, showed that a Tipler cylinder, an infinitely-long superdense cylinder rotating at half the speed of light, could generate closed timelike curves.
J. Richard Gott III (1991) proposed a cosmic-string machine. Cosmic strings are hypothetical entities left over from the big bang consisting of astronomically long threads containing vast amounts of mass; each kilometerof cosmic string would weigh about the same as planet Earth. For a pair of infinitely long cosmic strings moving apart at close to the speed of light, there will exist a region in which an astronaut could travel back in time by executing a loop around the strings¹².

Unfortunately, most of these scenarios are entirely implausible and all are currently well beyond our ability to test.

Of these solutions, only traversable wormholes merit special consideration. For details on how one might construct one, see Appendix: How to Build a Wormhole Time Machine. One important detail to consider here is that a traversable wormhole time machine would only allow you to travel back to when the wormhole was opened. It would not allow you to travel arbitrarily far back in time.

Tachyons

Relativity allows for yet another curious possibility—sending messages backward in time via tachyons. The particles that make up the stuff that we see around us possess mass and therefore must travel slower than the speed of light. Physicists classify them as bradyons based on the Greek word for “slow.” The one exception is massless photons of light (classified as luxons) that always travel at exactly the speed of light. Tachyons (from the Greek word for “swift”) are hypothetical particles that would have mass but always travel faster than the speed of light.

Prior to relativity, Newtonian mechanics allowed particles to travel at any speed without any special considerations. Under relativity, the energy required to accelerate any object with mass will drastically increase as the object’s speed approaches the speed of light. As a result, it would require an infinite amount of energy to accelerate even a single electron up to the speed of light. Therefore, it is impossible to accelerate an object (composed of bradyons) to a speed faster than light to become a tachyon. Similarly, tachyons would always travel faster than light and could never be slowed below that speed limit.

In 1907, Albert Einstein showed that according to relativity, tachyons (or any object) traveling faster than light naturally travel backward in time. In a thought experiment, he showed that tachyonic signals could arrive before they were sent. This scenario led to a paradox of causality with the effect preceding the cause and was dubbed the “tachyon telephone paradox.” Three years later, Einstein and Arnold Summerfield described this scenario as a means “to telegraph to the past.” Later, this concept was generalized so that any device capable of sending signals to the past was called a “tachyonic antiphone.”

An example of the tachyon telephone paradox would be to send a message back in time telling yourself not to send the message. This leads to a paradoxical situation where the message is both sent and not sent. One person described this scenario as a “logically pernicious selfinhibitor.” (This scenario is a version of the grandfather paradox that will be discussed later.)

Although tachyons are a staple of science fiction there is currently no evidence that they exist anywhere in our universe. We cannot make tachyons by accelerating normal matter particles until they move faster than light, but they might exist naturally. Recent work demonstrates that mathematically, there is nothing that forbids them from existing; however, it remains to be seen if physicists will ever discover these hypothetical particles.

Warp Drive

The newest and most exciting time machine candidate is the Alcubierre warp drive. Proposed in 1994 by theoretical physicist Miguel Alcubierre, it would potentially allow people to travel faster than the speed of light without violating the principles of general relativity. Reminiscent of Star Trek’s warp drive, it would operate by contracting the fabric of space ahead of the spacecraft and having the space behind it expand (see Figure 4). Like a surfer riding a wave, the ship would be carried along by the contraction and expansion of spacetime. This motion can exceed the speed of light because spacetime, unlike matter, is not limited by the speed of light.

The spacecraft itself would reside inside a region of flat space, known as a warp bubble, that would be carried along due to the actions of the drive (see Figure 4). Inside the warp bubble, objects would behave normally, that is, move slower than the speed of light as required by relativity.

This technology would allow us to reach nearby stars in a reasonable time frame but would also allow for time travel. Physicists, however, are divided over whether Alcubierre’s warp drive is even possible. First, it requires a large negative energy density to expand space behind it. The proposed way to generate that requires exotic matter possessing negative mass but it is unknown whether such exotic matter exists. It might be possible to substitute negative energy, which exists but has its own limitations. (For a more complete discussion of negative energy, see Appendix: How to Build a Wormhole Time Machine). Second, Alcubierre’s model is based on pure general relativity and including quantum mechanical effects may invalidate it. In addition, current models require unfeasibly large energy densities nearly equivalent to a black hole.

Time-Reversed Antimatter?

The strangest idea for time travel comes was proposed by John Wheeler in the 1940s and popularized by his graduate student Richard Feynman. He proposed that antimatter particles are just matter particles moving backward in time. We know that all fundamental particles have an antimatter twin with the same properties but opposite charge. When a matter particle encounters its antimatter partner, they annihilate each other releasing two photons. Since we know that antimatter exists, does this mean that we have a viable means for time travel in our grasp?

For simplicity, let us restrict our discussion to the electron and its antimatter partner, the positron. Imagine an electron and a positron annihilating each other and emitting two photons. According to Wheeler, we could view this event as the electron (moving forward in time) being converted into a positron (moving backward in time). Similarly, the generation of an electronpositron pair could be viewed as the time-reversed positron reconverting into a forward moving electron. Following this logic, one would conclude that the entire universe contained a single electron that is constantly bouncing forward and backward in time! This would neatly explain why all electrons have identical properties (because they would all be manifestations of the same particle). The same would be true for all other fundamental particles. But is this model true?

The main challenge to Wheeler’s proposition is that it predicts that there should be equal amounts of matter and antimatter in the universe, yet current evidence shows far disportionaly more matter than antimatter. Regardless of its validity, his theory does not allow any information to be sent to the past. So, even if antiparticles are regular particles moving backward in time, they cannot be utilized for time travel.

Viability of Time Travel Mechanisms

So, when do I get my time machine? Unfortunately, none of these time travel possibilities are realistically testable in the foreseeable future and many have features that could render them impossible to construct. Stockum’s solution and the Tipler cylinder both require an infinitely long rotating cylinder and are therefore not physically realizable. We have no evidence for the existence of the cosmic strings needed for Gott’s solution. Rotating black holes exist but we have no way to access them much less to safely travel through one. Warp drive requires copious amounts of hypothetical exotic matter that may not exist. Until (and if) tachyons are found, tachyon-based communication is not possible.

Beyond these individual challenges, there is a more general problem. Early work on closed timelike curves was based on pure general relativity. We know, however, that relativity alone is not sufficient to describe the universe. Quantum mechanics, developed in the 1920s and 30s, is needed to describe how things behave at the sub-atomic level. Black holes and wormholes both involve enormous spacetime curvature (requiring relativity) with matter compressed down to microscopic dimensions (requiring quantum mechanics). It is possible that the inclusion of quantum effects could render all time travel scenarios impossible.

Unfortunately, no one has been able to model wormholes, warp drives, and closed timelike curves in a way that fully includes both general relativity and quantum mechanics because there is no generally accepted theory of quantum general relativity. The central problem is that general relativity and quantum mechanics are incompatible. What we need is a super-theory, the so called “theory of everything,” that reconciles these two pillars of modern physics. Currently, string theory is our best candidate for the theory of everything and loop quantum gravity is another contender. Unfortunately, string theory does not make any predictions that can be experimentally tested, so currently there is no way to validate it.

In the absence of an ultimate theory, there is an approximate method for modeling quantum fields in the curved spacetime of general relativity, known as semiclassical gravity. This theory has allowed physicists to analyze aspects of closed timelike curves, although any conclusions drawn are not definitive.

The Case Against Backward Time Travel

During his life, Stephen Hawking strongly opposed the possibility of backward time travel. In support of his position, he proposed his chronology protection conjecture in 1992. The central idea is that any scenario leading to closed timelike curves would always be thwarted by the laws of physics. Proposed solutions that are permitted under general relativity would be prevented by quantum effects.

To understand its implications, let us consider the three closed timelike curves proposed by Stockum, Tipler, and Gott. Each requires an infinitely long structure, making them physically unrealizable. These infinities were introduced to make the math easier, so could finite versions of these mechanisms work? As one part of his conjecture, Hawking proved that according to general relativity, closed timelike curves cannot be created in a finite region of space unless there is negative mass exotic matter present. That makes the three closed timelike curves unrealizable unless the required exotic matter exists. For the case of traversable wormholes, Hawking theorized that quantum feedback between the ends would cause the wormhole to collapse before anything could pass through. The other proposed time travel methods might be impossible for various other reasons.

In summary, if Hawking’s chronological protection conjecture is true, then backward time travel is fundamentally impossible. Consequently, it would be impossible for anyone to change the past. Personifying nature as a human agency, he wittily summarized the key consequence of his work:

It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the universe safe for historians. – Stephen Hawking

While this conjecture may be good news for historians (because history could not be changed), it is bad news for aspiring time travelers.

Scientists are divided over the validity of Hawking’s conjecture. Currently, there is no final theory of quantum gravity, so Hawking is basing his work on semiclassical gravity that is our best approximation. And even within that approximation, it is not entirely clear that it would prevent time travel in all circumstances. For now, we must leave Hawking’s conjecture as a tantalizing but unproven claim. Perhaps future work will be able to settle this debate once and for all.

Ever the skeptic, Stephen Hawking found a more direct way to experimentally test the idea of time travel. In 2009, Hawking organized a time traveler party. He arranged balloons, champagne, and nibbles for his guests but waited until the very next day to send out invitations to all interested time travelers. On the day of the party, he waited several hours, and no one came. He regarded the event as “experimental evidence that time travel is not possible.”

A potentially stronger argument against time travel is the lack of evidence for travelers having visited from the future. If time travel becomes a viable possibility in the future, then we should have evidence of their visits. People might want to visit the past in the same way people today visit iconic locations, such as the Statue of Liberty, the Eifel Tower, and the Pyramids of Giza. Although there are occasional claims of temporal visitors there has never been any real evidence.

Of course, neither Hawking’s party nor the apparent absence of time travelers serve as decisive arguments against time travel. The current lack of evidence for time travelers does not prove that they have not visited. More importantly, some time travel mechanisms may limit how far back in time a person might travel. Science fiction generally permits unrestricted travel to the past, but the traversable wormhole mechanism would not allow you to go back to a time before the wormhole was created

Now let us consider the central problem with backward time travel—temporal paradoxes.

Time Travel Paradoxes

The biggest objection to the possibility of time travel is that it naturally leads to effects preceding their cause violating causality and resulting in seemingly unresolvable temporal paradoxes. If someone travels backward in time and interacts in any way, then the resulting changes will ripple forward in time resulting in an altered timeline. This modified version of history experienced by the time traveler will not match events from when he began his foray back in time. So, which version of history represents what is experienced? Is it the original version? Or does the altered version become the new reality? Or perhaps, both versions can be reconciled in some manner?

If backward time travel is impossible, then there are no difficulties to unravel. Others, however, have struggled to find ways to tackle these apparent paradoxes. Our current understanding of physics is unable to provide a definitive resolution to this mystery, so we turn instead to science fiction to help fill in this gap in our thinking. These stories do an incredible job of illustrating these paradoxes and highlighting potential unforeseen consequences of time travel.

Although many different time travel paradoxes have been identified, they can be roughly divided into two broad categories:

Consistency Paradoxes, such as the Grandfather Paradox and other similar variants such as the Hitler Paradox and Polchinski’s Paradox, which generate a number of timeline inconsistencies related to the possibility of altering the past.
Closed Casual Loops, such as the Predestination Paradox and the Bootstrap Paradox, which involve a self-existing time loop in which cause and effect run in a repeating circle but is also internally consistent with the timeline’s history.

Consistency paradoxes focus on the contradictions between the two divergent timelines while closed causal loops attempt to merge the two timelines into a single timeline.

Now let us examine the most well-known paradoxes in detail and illustrate them using books and movies. Our discussion here is loosely derived from James Miller, Astronomy Trek, “5 Bizarre Paradoxes Of Time Travel Explained.”

Grandfather paradox

The best-known example of a time travel paradox is the grandfather paradox. In the December 1929 issue of Science Wonder Stories, there appeared a short story, “The Time Oscillator” by Henry F. Kirkham involving time travel into the distant past. This story prompted the magazine editor, Hugo Gernsback, to consider the implications of the story’s premise. Could the time traveler interact with people and objects in the past rather than simply watching passively? If so, what would be the consequences? In a special editor’s note, he summed up what he considered to be a potential problem:

Suppose I can travel back in time, let me say 200 years; and I visit the homestead of my great great great great grandfather… I am thus enabled to shoot him, while he is still a young man and as yet unmarried. From this it will be noted that I could have prevented my own birth; because the time of propagation would have ceased right there. – Hugo Gernsback¹³

This is a consistency paradox. By killing his ancestor (whether intentionally or accidentally) in the past prevents the time traveler from being born, thus preventing him from going back in time to commit the deed. How can the time traveler be both alive (in the original timeline) and unborn (in the altered timeline)? Both cannot be true. The very act of time travel seems to render itself impossible.

Of course, this type of paradox is far more general than the specific scenario described here. Any alteration in the past that prevents or substantially alters the time traveler’s birth would lead to the same paradoxical situation. Consider the movie Back to the Future (1985). Marty McFly (Michael J. Fox) travels to the past where he meets his parents. His mother falling in love with him would prevent her from marrying his father, thus preventing him from being born. By altering events in the past, he is changing his future. A picture of him and his two siblings shows them fading from existence as the new timeline takes hold. This disaster is averted when he successfully ensures that his parents fall in love with each other thus restoring his original timeline

Examples: Examples of the Grandfather Paradox in movies include Back to the Future (1985), Back to the Future Part II (1989), and Back to the Future Part III (1990). Example of the Grandfather Paradox in books include Dr. Quantum in the Grandfather Paradox by Fred Alan Wolf, The Grandfather Paradox by Steven Burgauer, and Future Times Three (1944) by René Barjavel, the very first treatment of a grandfather paradox in a novel.

The Hitler Paradox

Another consistency paradox involves the situation where someone travels into the past to kill Adolf Hitler in hopes of preventing the horrors of World War II. The problem is that if the time traveler is successful, then in the modified timeline he would have eliminated the motivation for traveling into the past. Unlike in the grandfather paradox, the time traveler is still capable of traveling to the past to complete the time loop but no longer has reason to do so. Any failure to go back in time and kill Hitler leads to the paradox. Of course, this paradox is not limited to killing Hitler and can be generalized to a wide range of scenarios in which going back in time eliminates the reason for going back in time.

Examples: By far the best treatment for this notion occurred in a Twilight Zone episode called Cradle of Darkness which sums up the difficulties involved in trying to change history, with another being an episode of Doctor Who called “Let’s Kill Hitler.” Examples of the Let’s Kill Hitler Paradox in books include How to Kill Hitler: A Guide For Time Travelers by Andrew Stanek, and the graphic novel I Killed Adolf Hitler by Jason (pen name for John Arne Sæterøy).

Polchinski’s Paradox

This paradox was originally proposed by American theoretical physicist Joeseph Polchinski in 1990. For this scenario, imagine a billiard ball table where the pockets represent entrances and exits of a time machine (Figure 5a). Starting with a billiard ball in corner A, it is launched toward the pocket in the opposite corner, B (Figure 5b). Entering the pocket, the ball is taken back a moment in time emerging out a side pocket, C. If everything is aligned correctly, the ball will collide with its younger self, thus preventing itself from entering the time pocket (Figure 5c).

Polchinski’s paradox provides a succinct representation of the grandfather paradox that is ideally suited for scientific analysis. Moreover, the use of billiard balls instead of people completely avoids the issue of human free will.

One additional aspect of this setup is that it highlights the possibility that a time traveler could overlap in time with a younger or older version of himself. Having two (or more) versions of oneself at a given time poses numerous challenges. First, there is the metaphysical question of having more than one version of yourself present. Which one is the real you? Second, this situation seems to violate conservation of energy with the universe seemingly having increased in mass-energy by the mass of the time traveler.

Examples: Paradoxes of Time Travel by Ryan Wasserman is a wide-ranging exploration of time and time travel, including Polchinski’s Paradox

Predestination Paradox

Time travel to the past naturally creates an alternate timeline that conflicts with the original timeline. One potential way of avoiding this conflict is to insist that the two timelines are, in fact, identical. The time travel has already taken place and thus the time traveler starts in the altered timeline. This avoids the timeline inconsistency but replaces it with a different paradox—the time traveler must go back in time to complete causal loop. The time traveler is therefore predestined to act in a specific way independent of choice or desire.

A good example of this paradox is the movie 12 Monkeys (1995). The film starts in 2035 in a post-apocalyptic world where humanity has been nearly wiped out by a deadly virus. The leaders believe that the virus was released in 1996 by a group known as the Army of 12 Monkeys. A criminal, James Cole (Bruce Willis), is sent back in time to pinpoint who was responsible for spreading the virus in return for a reduced sentence. At the end of the movie, he is shot and killed, thus preventing him from stopping the release of the virus—the past cannot be changed. Even worse, his talking about the viral outbreak in the past may have inspired the person who released the virus, thus causing the very action he was trying to prevent.

As a second predestination paradox, James, as a young boy, has memories of seeing a man being gunned down. When he is killed at the end, it is his own death that he witnessed in the past and remembers as a bad dream. He was predestined to go back in time to fulfill the event that he already had a memory of.

Examples: Examples of predestination paradoxes in the movies include 12 Monkeys (1995), Time Crimes (2007), The Time Traveler’s Wife (2009), and Predestination (2014). An example of a predestination paradox in a book is Phoebe Fortune and the Pre-destination Paradox by M.S. Crook.

Bootstrap Paradox

The bootstrap paradox is a situation involving a self-caused cause. That is, a cause that leads to an effect that leads back to the original cause. Cause and effect follow each other in a perpetual loop without an external cause. This situation involves people, objects, or information that seems to give rise to itself without ever being created. The paradox gets its name because the object is pulling itself into existence by its own bootstraps

A simple example of the bootstrap paradox is sending the schematics for your time machine to your past self, from which you create a time machine that then serves as the design that is sent back in time. Both your younger and older selves received it from the other, so who actually developed it? Similarly, in the movie Star Trek IV: The Voyage Home (1986), the Enterprise crew from the 23rd century travels back in time to the 20th century to save Earth. During their visit, chief engineer, Montgomery Scott, gives the formula for transparent aluminum to the person who supposedly invented it. So, where did the knowledge for transparent aluminum actually come from?

To help visualize this, recall Polchinski’s pool table time machine. For this variant, the pool ball at A travels to time pocket B. Traveling back in time, it exits from time pocket C. From there, it encounters an object at A that deflects it toward time pocket B. It will continue its circuit of A to B to C and back to A cycling over and over again like a broken record (see Figure 6). The paradox lies in how this cycle could start

Examples: Examples of bootstrap paradoxes in the movies include Somewhere in Time (1980), Bill and Ted’s Excellent Adventure (1989), the Terminator movies, and Time Lapse (2014). The Netflix series Dark (2017-19) also features a book called A Journey Through Time which presents another classic example of a bootstrap paradox. Examples of bootstrap paradoxes in books include Michael Moorcock’s Behold The Man, Tim Powers’ The Anubis Gates, and Heinlein’s By His Bootstraps.

The Butterfly Effect

Although the butterfly effect is not a paradox, it deserves to be considered here because it has important implications for time travel. The butterfly effect is a manifestation of chaos theory where even miniscule changes in some systems can result in large scale alterations to the system making the system’s long-term behavior unpredictable. A simple example is flipping a coin. Even though the dynamics of the flip are governed by deterministic equations, the outcome is random and unpredictable.

Early work on the butterfly effect came from mathematician and meteorologist Edward Norton Lorenz. In running weather simulations on a computer, he noticed in 1960 that when he had to restart a simulation midway through, it produced a dramatically different outcome compared to a previous unrestarted calculation. After checking many possibilities, he realized the difference in outcomes was the result of a seemingly insignificant rounding of variables during the restart process. (This extreme sensitivity to even small variations in detail is a major reason why weather is so difficult to accurately predict.) The term “butterfly effect” came from a 1972 talk where Lorentz famously stated that “a butterfly flapping its wings in Brazil can produce a tornado in Texas.”

The important implication of the butterfly effect for time travel is that even the smallest action can have massive, unexpected consequences. While we expect something as dramatic as killing Adolf Hitler in the past would have significant ramifications for history in the present, what about something trivial like sending a letter to yourself in the past? The butterfly effect informs us that even a seemingly innocuous action will eventually result in significant and unpredictable deviations to the timeline

This principle is well illustrated in the movie, The Butterfly Effect (2004). The main character, Evan Treborn (Ashton Kutcher), learns that he can briefly travel back in time to inhabit the body of his younger self while retaining his adult memories. This gives him a chance to go back in time, make changes, and then observe the consequences in the present. The problem is that every time he goes back to fix one issue, he inadvertently creates a different problem.

A second example is A Sound of Thunder (2005), a movie based on the 1952 short story of the same name by Ray Bradbury. In it, a company called Time Safari, Inc. offers rich people the opportunity to travel into the past to hunt dinosaurs. To prevent accidentally altering the past, only dinosaurs that were going to die anyways are killed and guests must stay on the designated path. During one outing, someone strays from the path and steps on a butterfly. After returning to the present, the city is hit by “time waves” that progressively transform the city to match the altered timeline. Ultimately, they must go back in time again to prevent the butterfly from being killed thus restoring the world back to its original state

Perhaps the favorite example of the butterfly effect is The City on the Edge of Forever (Star Trek: The Original Series, season 1, episode 28). In an accident, Leonard McCoy accidentally injects himself with a drug that renders him temporarily extremely paranoid. Escaping from the others, he flees through the Guardian of Forever, a sentient time portal. This action changes one event in the past whose effects ripple forward cause the Enterprise and the rest of the Federation of Planets to no longer exist in the present. To undo this change, James T. Kirk and Spock go through the time portal to Depression-era New York City to prevent McCoy from changing the timeline by preventing Edith Keller (Joan Collins) from being killed in a car accident. Kirk and Spock must allow her to die to restore the timeline.

Are These Paradoxes Resolvable?

For Stephen Hawking and many others, the existence of temporal paradoxes is a strong argument that time travel to the past must be impossible. Others, however, are not convinced. There does appear to be several physically realizable time travel mechanisms, and it is not clear if Hawking’s chronology protection conjecture can block each of these possibilities. Perhaps, we should examine potential ways to prevent or resolve paradoxes.

Multiverse

The simplest and most general way to avoid paradoxes is for the act of traveling back in time to create a new and independent timeline. Subsequent events happen in the new universe leaving the original universe unchanged. This leaves the time traveler free to act without fear of creating paradoxes. For example, you could kill your grandfather without endangering your own existence because your actual grandfather and father would remain safe and untouched in the original universe.

Surprisingly, there is a possible scientific basis for this idea. In the many-worlds interpretation of quantum mechanics, every quantum event causes the universe to branch with each possible outcome occurring in a different universe. This interpretation is very controversial but if true it lends support for the notion of a multiverse consisting of all possible universes. Every possible choice you could make would be played out in one of these alternate timelines.

While the multiverse concept resolves temporal paradoxes, it has its share of problems. One of the biggest objections is that currently we have no evidence that these other universes exist. Nor are we likely to ever prove their existence, making the multiverse idea untestable. Second, invoking an infinite number of universes beyond our known universe without sufficient evidence goes against Occam’s razor (the principle of simplicity). Third, having an infinite number of versions of yourself scattered across different universes provokes enormous philosophical questions about the nature of self and of free will.

Timeline Protection Hypothesis

A less drastic solution is the science fiction notion of built-in cosmic safeguards that allow time travel while conspiring to prevent any actions that result in paradoxes. One version of this idea are stories involving a predestination paradox in which going back in time and trying to change something, ultimately ends up causing events to happen exactly as they did before, creating a closed loop. Another approach involves attempts to change the past that prove self-defeating. For example, if you try to kill Hitler with a gun, then perhaps your gun jams, your shot misses, or you simply cannot pull the trigger. This plot device has been humorously dubbed the “banana peel mechanism” based on the notion that perhaps a banana peel appears at just the right moment to trip someone up thus preventing them from changing history. The timeline protection hypothesis is speculative and lacks a coherent mechanism.

A related idea found in science fiction is “self-healing” time. According to this model, small changes in the past would only have an effect on the immediate timeline. Subsequent events would adjust themselves so that there would be no long-term effects. Only certain critical changes will trigger lasting repercussions. This is great for science fiction, but this runs completely contrary to the butterfly effect where even small changes will amplify over time, rather than decrease. Yet another variation is the notion of “fixable” changes to history. In stories, someone introduces a change to the past forcing someone else to go back and restore the original timeline. Again, the butterfly effect renders these scenarios unlikely because it would be impossible to perfectly undo the previous change.

Novikov Self-consistency Principle

In the mid-1980s, Igor Novikov proposed a science-based version of the timeline protection hypothesis. Using Polchinski’s paradox as the model case, he argued that any portion of the object’s quantum wavefunction that would lead to the paradox would automatically be zero. Called the Novikov self-consistency principle, this meant that the billiard ball going back in time would necessarily be deflected in such a way that it does not prevent its younger self from entering the time pocket

Novikov’s solution has a lot of merit, yet it is not without challenges. There are several theoretical and mathematical issues that are too complex to summarize here. And although it potentially avoids paradoxes, it fails to eliminate other inconsistencies in the timeline.

No Free Will?

One other proposed way to get around some thorny temporal paradoxes is to deny human free agency. Within this model, people would be constrained to make choices that guarantee the consistency of the timeline. For example, a person going back in time to kill Hitler might unconsciously be forced into decisions that ultimately prevent him from carrying out the act. Lack of free will would be a consequence of both the past and future being determined.

Although this idea is useful in science fiction stories, it fundamentally fails to resolve temporal paradoxes. For example, Polchinski’s paradox does not involve human choice and therefore holds independently of the question of freewill.

Time Travel in Literature and Movies

Time travel to the past can lead to paradoxical situations that defy easy resolution. Our understanding of physics is not sufficient to give us a definite answer as to whether time travel to the past is possible and how to resolve these paradoxes if it is. For this section, we turn to science fiction. Many of our greatest writers have wrestled with this challenge and provided us with many interesting possibilities. Here we will explore these ideas with an eye on what best aligns with our understanding of science.

The Time Machine by H. G. Wells is the first true science fiction story involving time travel and remains a classic on the subject. Written before Einstein’s work on general relativity, his work is remarkably prescient. A full list of the many wonderfully creative book, movies, and television shows incorporating time travel is too long to present here. Instead, a timeline with only a few representative examples is shown for chronological perspective (see Table 2).

Table 2: Influential Books and Movies on Time Travel

Year	Book or Movie
1895 1963 1985 1985 1999	The Time Machine published Doctor Who begins on BBC Television The movie Back to the Future released Carl Sagan writes Contact Michael Crichton’s book Timeline published

Science fiction books, comics, movies, and TV shows frequently use time travel as either a major plot element or incorporate it at key moments in the story. Over the years, eight major types of time travel logic have emerged. For our discussion here, we will follow the analysis of Almost An Author, “The Eight Types of Time Travel.” That work is summary of Eric Voss and Héctor Navarro’s youtube video, “Time Travel Possible? Avengers Endgame vs Tenet (8 Types Explained).”

Type 1: Anything Goes

In these stories, the time traveler can move about freely in time with no consequences. This is not consistent with our current scientific understanding but is popular because it allows the story to focus on exploring different time periods without being bogged down with paradoxes. Doctor Who is an excellent example, with the Doctor flitting backward and forward in time without any problems or paradoxes

Examples: Back to the Future, Bill and Ted’s Excellent Adventure, Hot Tube Time Machine, Frequency, Austin Powers, Men In Black 3, Deadpool 2, The Simpsons, Galaxy Quest, Star Trek TOS, Doctor Who, and 11/22/63 by Stephen King.

Type 2: Branch Reality

Traditionally, people think that history consists of a single timeline. What if the act of traveling to the past spawns a new and independent timeline? This possibility avoids all the standard temporal paradoxes because you are no longer constrained to reconcile events within a single timeline. If each timeline occupies its own parallel universe, then the collection of all these possible universes is the multiverse. The multiverse concept has recently exploded in popularity because it grants great creative flexibility to science fiction writers

Both Marvel Comics and DC Comics have each strongly embraced the multiverse idea because it allows them to unite a wide variety of story lines into a single common framework. Even better, it allows crossovers, where a character from one story line can join a different one.

The branching reality aspect of the multiverse was useful in allowing the Star Trek franchise to reboot itself. Star Trek (2009) reintroduces the well-loved characters from the original series but with entirely new actors. The movie starts with a Romulan ship coming from the future for revenge and in the process spawning a new timeline. This event leaves the characters free to develop in new ways rather than being constrained to follow the established canon of the previous series.

Examples: The Disney Plus series, Loki, used this extensively. See also: Back to the Future Part II, Avenger’s Endgame, the DC Comics multiverse, the Marvel Comics multiverse, Rick and Morty, Star Trek (2009), and A Wrinkle in Time by Madeleine L’Engle.

Type 3: Time Dilation

For someone moving very close to the speed of light or in the presence of a massive gravitational field (e.g., a black hole), time for them would pass at a much slower rate than for the rest of the universe. Known as time dilation, this would effectively allow them to travel into the future (relative to everyone else). This is a known and proven aspect of general relativity, however; creating a non-trivial time dilation effect for people is well beyond our current abilities. It should be emphasized that this only allows us access to the future, not the past, and therefore this is not true time travel.

Various forms of suspended animation can accomplish the same task of allowing us to leap into the future. This type of technology is entirely plausible and will likely to be available in the near future.

A classic example of time dilation in a movie is the original Planet of the Apes (1968). In it, a group of astronauts traveling at close to the speed of light awake and realize that several thousand years have passed on Earth while they have only experienced a few years. Landing on a nearby planet, they discover a race of intelligent speaking apes and tribes of primitive mute humans. In the iconic ending, George Taylor (Charlton Heston) escapes only to discover the remains of the Statue of Liberty. From this, he learns that he is on Earth of the future, not a remote planet

Examples: Planet of the Apes, Ender’s Game, Flight of the Navigator, Interstellar, and Buck Rodgers.

Type 4: This Always Happened

As humans, we naturally believe that we can shape the future with the choices we make, but some ideas about time travel reject that. Perhaps the past and future are fixed, and free will is just an illusion. In the case of time travel to the past, this would mean that certain events must occur (they are predestined) to maintain consistency in the timeline. This is the basis of the predestination paradox that was discussed earlier.

We’ve already discussed 12 Monkeys as an example of the predestination paradox, so let us consider another classic example, The Terminator. In the future, the AI defense network known as Skynet starts a global nuclear war to eliminate humanity. The remaining humans led by John Conner fight back in a daring attempt to destroy Skynet. To avoid this fate, Skynet sends a Terminator robot (Arnold Schwarzenegger) back in time to kill John’s mother, Sarah Conner, thus stopping the resistance before it could ever start. John sends his friend Kyle Reese back in time to prevent the Terminator from killing her. During the course of events, Kyle impregnates Sarah thus becoming John’s father. This action was predestined because otherwise John wouldn’t be around to send Kyle back in time.

Examples: Terminator, Terminator 2, Harry Potter and the Prisoner of Azkaban, Game of Thrones-Season 6, 12 Monkeys, Interstellar, Kate and Leopold, The Butterfly Effect, Predestination, Ricky and Morty-Season 5, and Looper.

Type 5: Seeing the Future

If we cannot physically travel to the future, then perhaps we can see into the future. In ancient times, a prophecy could provide a revelation about the future. The recipient must make choices knowing that their fate may be unavoidable. Modern technology allows a new twist on this idea, technology might somehow allow us to gain certain knowledge of the future

A fun example of this is the movie, Paycheck (2003). In it, Michael Jennings (Ben Affleck) is hired for a secret three-year engineering project. For his work, he will be rewarded with millions of dollars, but afterwards his memories from that time will be wiped to protect the company’s intellectual property. After completing the work, he is surprised to learn that he turned down his financial reward in exchange for an envelope full of seemly random junk with no memory of why he chose them. As he tries to unravel this mystery, he discovers that each item is exactly what he needs at a particular critical moment. We learn at the end that all of this was enabled by his work on a device that allowed him to look into the future

A newer take on this idea is explored in the TV series, The Peripheral (2022). In it, a virtual reality (VR) gamer, Flynne Fisher (Chloë Grace Moretz), is allowed to test a prototype for an advanced headset. Instead participating in an ultra-realistic simulation game, she is really piloting a robot (known as a peripheral) via quantum tunnelling in a version of London set 70 years in the future. Even though she cannot travel there, she has a two-way interaction with the future.

Future bending (receiving information from the future), however, leads to the same paradoxes as those resulting from time travel. For a creative exploration of this idea, watch Action Lab, “Is Future Bending Actually Possible?”

Examples: Oedipus Rex, A Christmas Carol, Minority Report, Arrival, Next (Nicolas Cage), Rick and Morty-Season Four, Star Trek: Discovery-Season 2, and Avenger’s Endgame with Dr. Strange and the Mind Stone.

Type 6: Time Loop/Groundhog Day

A time loop refers to a situation whereby characters re-experience a span of time which is repeated. At the end of the time span, they are returned to the beginning to start the cycle again. This represents a closed timelike curve from the perspective of individuals caught inside it. For a true closed timelike curve, this cycle should repeat itself exactly without end. In fiction, this concept is modified to allow the characters to retain memories from a previous loop. Also, when certain conditions are met, the cycle is broken, and the normal flow of time is restored.

To help picture this type of scenario, consider an old-fashioned vinyl record. In some cases, a record will get scratched such that when played to a certain point the stylus will skip back one groove. The record will continue to progress forward until it hits the defect and again jumps back. This one segment of the record will be played repeatedly until action is taken to resolve the situation.

A classic example of a time loop movie is the romantic comedy, Groundhog Day (1993). In it, weatherman Phil Connors (Bill Murray) is assigned to cover Groundhog Day festivities in Punxsutawney, despite his disdain for the event. To his horror, he discovers that he is caught in a loop always waking up on Groundhog Day at the same time and in the same circumstances while retaining his memories from previous cycles. No matter what he does, not even killing himself, allows him to escape the loop. Only when he changes his character and falls in love is he finally able to move on.

Another brilliant example of a time loop is Cause and Effect (Star Trek: The Next Generation, season 5, episode 18). The episode starts with four of the bridge officers playing poker while the rest of the crew go about their normal routine. Later, the Enterprise encounters the USS Boseman exiting a temporal anomaly resulting in a collision that destroys both ships. This sequence of events continues to repeat with only small variations as people experience déjà vu caused by echoes from previous loops. The cycle is finally broken when information from one cycle is sent to the next providing a way to avoid the collision.

Examples: Obviously, Groundhog Day with Bill Murray, Edge of Tomorrow, Doctor Strange in the ending battle with Dormammu, Russian Dolls (Netflix), Palm Springs, and Star Trek TNG.

Type 7: Unstuck Mind

This class of stories involves the character’s consciousness, rather than their body, moving through time. The character inhabits his/her own body but at different ages. This can involve traveling to either the person’s past or future. There is no scientific basis for this, but it serves as a dramatic non-linear way to tell a story.

Examples: Slaughterhouse 5 by Kurt Vonnegut, X-Men: Days of Future Past, and Desmond in the series Lost.

Type 8: Unstuck Body

Our final type involves a character’s body or object becoming physically detached from the flow of time within the surrounding universe. The person or object can age faster or slower than everyone else or even age in reverse. This latter case is the basis for the story The Curious Case of Benjamin Button, where the main character starts as an old man and reverse ages into a baby. The science fiction thriller, Tenet, uses “inverted entropy” to describe objects that act opposite of the normal flow of time. This allows bullets to reassemble and bombs to unexplode. In the movie’s main battle, they attack the enemy using a “temporal pincer movement,” where regular troops moving forward in time are aided by future troops moving backward in time.

Examples: Dr. Strange (the Hong Kong battle), Tenet, briefly in Endgame with Scott Lang and Bruce, and Primer.

Closing Thoughts

What should we conclude from this quick exploration of the nature of time and the possibility of time travel? On the fundamental question of whether traveling to the past is possible, we must conclude that we simply do not know. We currently lack a comprehensive theory of quantum gravity (a theory that correctly unites quantum mechanics and general relativity) without which we cannot provide a definitive answer to the question of time travel. That leaves genuine time travel a tantalizing possibility even if it is currently unachievable.

This is good news for those who enjoy the thought of traveling back and forth in time. What famous individuals would you want to meet if you could? Or what important historical events would you wish to observe? Another exciting possibility would be the chance to go back in time to “fix” mistakes in the past. You might try to impart wisdom to your younger self. Or you might try to alter world events to undo historical injustices. Alternatively, one might wish to go to the future to bring back certain knowledge of events. Perhaps you might bring back scientific or medical breakthroughs to share with the world. Or be tempted to grab the winning lottery ticket numbers for some quick cash.

Yet, the possibility of genuine time travel extending arbitrarily far in the past leads to some ominous possibilities. I shudder at the thought that even small actions in the past would have a dramatic impact on future events (via the butterfly effect). And if that is true for even the most cautious time traveler, then imagine the impact of someone deliberately changing past events for nefarious purposes. Time travel could be used as a weapon of unimaginable consequences with wholesale changes being made to our timeline. Individuals and even whole people groups could be wiped out of existence while others might be strengthened. In this fashion, time travel could become the ultimate doomsday weapon that would make the threat of nuclear annihilation seem tame by comparison.

For now, viable time travel—whether for good or ill—remains safely out of reach. Until scientists can give us a definite answer to this possibility, we can enjoy our science fiction with peace of mind.

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Footnotes

¹Ph.D. in Theoretical Chemistry from Rice University.

²For a fun short 4-minute video answering “what is time?” targeted for 11-year-olds, see Science Isn’t Scary, Episode 6: “What is Time?”

³Quotation cited from John W. Macvey, Time Travel, p. 141

⁴Newton’s Scholium on Time, Space, Place and Motion. Scholium to the Definitions in Philosophiae Naturalis Principia Mathematica, Bk. 1 (1689); trans. Andrew Motte (1729), rev. Florian Cajori, Berkeley: University of California Press, 1934. pp. 6-12.

⁵After 6 months on the International Space Station (ISS), orbiting Earth at a speed of about 7,700 m/s, an astronaut would have aged about 0.005 seconds less than he would have on Earth

⁶The gravitational time dilation due to Earth’s gravity is about 0.00000007%.

⁷If time dilation was not properly taken into account, your estimated location based on GPS satelites would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers (or 6 miles) each day! The whole system would be utterly worthless for navigation in a very short time.

⁸For a fun take on the twin paradox, watch Action Lab, “I Built a Time Machine—The Real Life Twin Paradox.”

⁹Muons (a type of fundamental particle) decay with a lifetime 2.197 microseconds. However, when muons are held in the muon storage ring at CERN traveling close to the speed of light, their lifetime is increased to 64.378 microseconds. This factor of nearly 30 increase in lifetime is in agreement with the predictions of special relativity

¹⁰Values calculated using Time Dilation Calculator

¹¹John W. Macvey, Time Travel, p. 123-126

¹²J. Richard Gott, Time Travel in Einstein’s Universe, p. 92-110

¹³James Gleick, Time Travel: A History, 2016, p. 71.

Back Matter

This is a collection of all supporting documentation.

Source Material

James Gleick, Time Travel: A History, Pantheon Books, New York, NY 2016

Paul Davies, How to Build a Time Machine, Penguin Group, New York, NY 2001.

John W. Macvey, Time Travel, Scarborough House/Publishers, Chelsea, MI 1990.

J. Richard Gott, Time Travel in Einstein’s Universe: The Physical Properties of Travel Through Time, Houghton Mifflin Company, New York, NY 2001.

Ryan Wasserman, Paradoxes of Time Travel, Oxford University Press, Oxford, UK 2020.

David Deutsch and Michael Lockwood, “The Quantum Physics of Time Travel Common Sense May Rule Out Such Excursions—but the Laws of Physics Do Not,” Scientific American, March 1994, p. 68-74

Martin Gardner, Relativity Simply Explained, Dover Publications, Inc., Mineola, NY 1997.

David Cycleback, “What Is Time?” 2021.

Binge Bytes, “What is Time?” 2024

James Miller, Astronomy Trek, “5 Bizarre Paradoxes Of Time Travel Explained,” 2014.

Sarah Scoles, “Is Time Travel Possible?” Scientific American, April 26, 2023.

Andrew May, How It Works Magazine, “A Beginner’s Guide to Time Travel,” 2022.

B. K. Bass, Campfire, “Past, Present, Paradox: Writing About Time Travel.”

Almost an Author, “The Eight Types of Time Travel,” 2021

Minute Physics, “3 Simple Ways to Time Travel (and 3 Complicated Ones),” 2014.

Minute Physics, “Time Travel in Fiction Rundown,” 2017.

Action Lab, “I Built a Time Machine—The Real Life Twin Paradox,” 2019.

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Appendix: On the Nature of Time

A. Conceptions of Time

There are three major cultural and historical conceptions of time: linear time, cyclical time and timelessness. These conventions appear in theology, philosophy, science, psychology and art.

Linear Time. Linear time follows an inexorable line from the past to the future. Most people today imagine and mark time as linear, and our watches and clocks mark time by this convention. Linear time is the standard convention used in science. Abrahamic religions chose a linear conception of time because it allows for the creation of the universe and a final judgment.
Cyclical Time. Many early cultures had a cyclical conception of time, sometimes called the wheel of time. These cultures include Incan, Mayan, Hinduism, Buddhism and Jainism. They perceived time as consisting of repeating ages and time periods. This helps explain the idea of reincarnation. Circular or repeating conceptions of time are still used today by some cultures, including in India. The observance of repeating seasons is an example of circular time. Early agricultural and other societies were centered around the seasons, the regular apparent rising and falling of the sun, and the regular changing of star formations.
Timelessness. A timeless view of time was common to many early peoples and mystical cultures such as some American Indians tribes, Australian aboriginals and Jewish Kabbalists. In this view of time, the past and present are intimately connected. History and spirits of the dead exist in the present.

The linear view of time is very familiar to us today because we are surrounded by watches, clocks, and calendars that measure our progress through time.

How a civilization views time has many important consequences. One significant example is the linear view of time was vital for the development of science because it allowed for progress¹⁴. In contrast, a cyclic view of history holds that everything moves in cycles like a wheel with everything always coming back to the beginning. As such, a cyclical view of history hindered progress, promoted complacency, and gave no basis for cause-and-effect relationships.

B. Beginning to Time?

Does time have a beginning? Scientific evidence demonstrates that yes, time does have a beginning having come into existence approximately 13.8 billion years ago in what is known as the “big bang.”¹⁵ Given the current scientific consensus, the notion of time having a beginning of time may not seem very controversial today yet this scientific understanding is barely a hundred years old.

How can time have a beginning in time? Indeed, this discontinuity (i.e., transition from non-existence to existence) was so unimaginable that it was nearly unthinkable all the way up to the 20^th century (with one important exception to be discussed later). Looking back in history, time was nearly always viewed as eternal with people generally holding to either eternal time (within in linear view of time) or eternal cycles (within a cyclical view of time). The first scientific cosmology was Immanuel Kant’s infinite static universe model (1755) that held that the universe was infinite in both space and time in agreement with ancient thinking. This model held sway until Edwin Hubble’s measurements (1929) demonstrated an expanding universe. Even with this evidence, many astronomers tried to avoid a beginning of time and matter until the case became overwhelming¹⁶. Why was the idea of a beginning to time so difficult to accept?

Taking the Greeks as an example, they widely believed in creation ex materia (literally, creation “out of [pre-existing] matter”). The absolute certainty that matter existed eternally and could not have been created is reflected in Parmenides’ (c. fifth century BC) famous dictum that “nothing comes from nothing.” Stated more fully, he said:

Yet why would it be created later rather than sooner, if it came from nothing; so, it must either be created altogether or not [created at all]. – Paramenides, Fragment 8

It was against reason that matter could come into existence and must therefore be eternal. The eternality of matter necessitates the eternality of time.

According to creation ex materia, matter existed initially in an unformed state, like a shapeless cloud of atoms, that was later shaped into worldly structures that we observe (e.g., the sun, moon, plants, animals, and people). This involves the formation of objects (i.e., fashioning out of existing materials like a potter with clay) rather than their creation. The gods of polytheism appeared within a pre-existing universe. They could not create space and time but were instead prisoners of it just like mortals.

Only the ancient Hebrews taught a true beginning of both matter and time as did the Christians who followed after them. What set the Hebrews apart from everyone else? It was their belief in a transcendent God leading to a belief in creation (an ultimate beginning for everything) and a final judgement (an ultimate end). The almighty God, without beginning or end, exists entirely independently of the material realm. In modern parlance, we would say that God transcends space and time and was responsible for bringing them into existence.

This view is known as creation ex nihilo (literally, creation “out of nothing”)¹⁷. It is taught in multiple Bible passages with the most well-known being Genesis 1:1 (c. 1500 BC)¹⁸.

In the beginning God created the heavens and the earth. – Genesis 1:1 NIV

Outside of Scripture, we find creation ex nihilo taught in Jewish writings as early as the second century BC and subsequently in Christian writings¹⁹. This teaching was considered vital doctrine and was affirmed in major Christian creedal statements²⁰.

Although less frequently stated, time’s origin was a direct consequence of creation ex nihilo. For example, the New Testament twice speaks of God operating “before the beginning of time” (2 Timothy 1:9 NIV and Titus 1:2 NIV) as well as frequent references to God acting “before the creation of the world.”

The clearest early discussion of the beginning of time comes from the early church father, Augustine (354-430 AD)²¹. In his discourse on time, he addressed the common objection, “what was God doing before he made heaven and earth?” Confessions 11.10 (12). He counters by arguing that God created time, thus rendering the objection meaningless.

For that very time Thou madest, nor could times pass by before Thou madest times. But if before heaven and earth there was no time, why is it asked, What didst Thou then? For there was no “then” when time was not. – Augustine, Confessions 11.13(15).

Augustine’s concept of time being a part of the created order (hence having a beginning) is one of his most profound. This view is amazingly consistent with today’s most advanced scientific understanding of time²².

C. Ontology of Time

In 1908, John McTaggart published “The Unreality of Time,” provoking controversy by suggesting that time was not real. In it he discussed two different models for ordering temporal events that he referred as A series and B series. While McTaggart’s thesis was largely rejected, later philosophers adopted his nomenclature. Known today as the A and B theories of time, these ideas are now commonly used by contemporary philosophers of time to discuss the ontological implications regarding time²³.

Given that we live in the eternal “now,” what is the relationship between the past, present, and future? Let us consider how the two theories answer that question:

A theory (presentism) views time as a constantly flowing stream where the future continuously transforms into the present, and then into the past. In this view, only the present (what is in front of you now) is real, and the past is unreal, and the unknown future is unreal. Time is viewed as “tensed” (in the sense of English verb tenses) with events described as past, present, or future relative to the current moment. Presentism matches the way most people perceive time. Growing block universe is the same as presentism except that it considers both past and present to be real
B theory (eternalism) treats the past, present and future as equally real, and that our perception of only the experienced “now” being real is merely a matter of our brain’s consciousness and our arbitrary place in time. In this view, time is “tenseless” with temporal events located on a fixed timeline, so that the time ordering does not depend upon the current moment.

Presentism and eternalism are not in conflict. They represent different perspectives of the same timeline. Presentism is the up close and personal experience of time, while eternalism is a look at time from afar. It’s akin to driving along a road versus looking at the road on a map.

D. Other Arrows of Time

Time is known to only move forward, not backward. This concept is known as the arrow of time. In the main article, we discussed the law of increasing entropy as the primary arrow of time, preventing us from returning to the past.

Entropic Arrow of Time: according to the second law of thermodynamics an isolated system evolves toward a larger disorder rather than orders spontaneously.

This case can be potentially supplemented with four additional arrows of time:

Radiative Arrow of Time, manifested in waves (e.g. light and sound) travelling only expanding (rather than focusing) in time.
Quantum Arrow of Time, which is related to irreversibility of measurement in quantum mechanics according to the Copenhagen interpretation of quantum mechanics.
Weak Arrow of Time: preference for a certain time direction of weak force in particle physics (see violation of CP symmetry).
Cosmological Arrow of Time, which follows the accelerated expansion of the Universe after the Big Bang

The relationship between these different arrows of time is a hotly debated topic in theoretical physics.

¹⁴Kenneth Richard Samples, Without a Doubt: Answering the 20 Toughest Faith Questions, Baker Books, Grand Rapids, MI, 2004, p. 188-189

¹⁵ Hugh Ross, The Creator and the Cosmos, 3rd Expanded Edition, NavPress, Colorado Springs, CO, 2001.

¹⁶ Hugh Ross, The Fingerprint of God, Second Edition, Promise Publishing Co., Orange, CA 1991. Jeff Zweerink, Escaping the Beginning? Confronting Challenges to the Universe’s Origin, RTB Press, Covina, CA, 2019. Robert Jastrow, God and the Astronomers, W.W. Norton & Company, Inc., New York, NY, 1992.

¹⁷Kenneth Richard Samples, 7 Truths That Changed the World: Discovering Christianity’s Most Dangerous Ideas, Baker Books, Grand Rapids, MI 2012, p. 77-89

¹⁸Paul Copan and William Lane Craig, Creation Out of Nothing, Baker Academic, Grand Rapids, MI 2004.

¹⁹John Millam, “Historic Age Debate: Creation Ex Nihilo,” part 1, part 2, part 3, part 4.

²⁰ John Millam, “Do Christian Creeds Support a Calendar-Day View of Creation?“

²¹ John Millam, “Historic Age Debate: Beginning of Time.”

²² Kenneth Richard Samples, Classic Christian Thinkers: An Introduction, RTB PRess, Covina, CA, 2019, p. 64.

²³ For a fuller discussion of A and B theories of time and their implications for time travel, read Ryan Wasserman, Paradoxes of Time Travel.

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Appendix: How to Build a Wormhole Time Machine

In his book, How to Build a Time Machine, Paul Davies not only states that he believes that time travel is possible, but he also outlines how one might actually build a wormhole time machine. According to his recipe, constructing one only requires four components: a collider, an imploder, an inflator, and a differentiator (see Figure 7). Sounds too easy to be true. Provided here is a brief summary based on Davies’ book. Warning, this section is more technically complex than the other parts of this paper.

Davies’ time machine involves constructing a traversable wormhole. This approach has the advantage that it can theoretically be built based on our current understanding of physics. No infinitely long rotating cylinders, nor exotic matter required.

Constructing a usable wormhole is a tall order given we do not have the tools for cutting and splicing spacetime required to make one. Some naturally occurring wormholes might already exist in the universe being left over from the big bang; however, they would be hard to find and likely located far away. Turning a black hole singularity into a wormhole is too dangerous to be a meaningful solution. So, we must construct our own. The best way to do that is to use naturally occurring wormholes that exist at the Planck scale and expand them to usable dimensions.

According to current thinking, the Planck scale represents the smallest possible divisions of space and
time possible. Planck time is 10 million-trillion-trillion-trillionth of a second (or 10^-43 sec). Planck length is a billion-trillion-trillionth of a cm (or 10^-35 m). To put this in perspective, one Planck length would roughly be smaller than an atom to the extent that an atom is smaller than the solar system.

While ordinary space seems smooth and calm, at extremely small distances there in an unimaginable frenzy of activity with pairs of particles constantly popping into and out of existence. This chaotic frenzy is known as the quantum foam because it resembles the foamy froth of bubbles emerging from surface of boiling water. The Heisenberg uncertainty principle tells us that for shorter and shorter durations, ever more energetic processes will occur. That means that Planckscale virtual wormholes will be constantly popping into and out of existence. So, instead of creating a wormhole from scratch, we can instead try to pluck one from the quantum foam, give it enough energy to convert from virtual to real, and then inflate it to a usable size.

Collider

The first step in building our time machine is to concentrate enormous energies into a single point in space. We can partially accomplish that using existing particle colliders. The best example for our purpose here is the relativistic heavy-ion collider at Brookhaven National Lab. This collider accelerates the nuclei of heavy elements (e.g. gold or uranium) to colossal speeds and then smashes them together. With current technology, we can recreate conditions that existed in the early universe corresponding to temperatures of ten trillion degrees. This is hot enough to create a quark-gluon plasma where quarks are allowed to roam freely. (This plasma formation is sometimes dramatically described as “melting the quantum vacuum.”)

Imploder

This quark-gluon plasma represents one of the highest temperatures achievable using current technology. Unfortunately, this is still 19 orders of magnitude too low for our work. Instead of adding more energy, we can compress the quark-gluon plasma by a factor of a billion billion. That is the job of the imploder.

One potential way to do this is by using explosive magnetic pinching. This type of strategy was investigated initially in the 1950s as part of efforts to develop controlled nuclear fusion. Sandia National Labs is the current leader in applying this strategy. For example, they can concentrate electrical pulses containing 50 trillion watts of energy onto ultrathin tungsten wires.

The total energy required for our imploder is not large, but the challenge is to concentrate it into such a confined space. This is well beyond current technology, but if we found a solution it would enable us to compress the quark-gluon plasma to create densities of 10 trillion trillion trillion trillion trillion trillion trillion trillion (or 1097) kg/m3. Putting it more simply, this is about 1080 times more dense than nuclear matter! Such conditions would rival the energy fluctuations at the Planck scale. If successful, this might create a miniature wormhole that would serve as the seed for our time machine.

Inflator

After completing these two stages, we would have a Planck-scale wormhole. A tremendous accomplishment but not yet very useful. To use it in our time machine, it must be stabilized and inflated large enough to be able to send something through.

To prop the wormhole open, we need something that will counteract the gravitational forces causing it to contract inward. One solution would be to use negative mass exotic matter to provide a force to counteract gravity within the wormhole to stabilize and expand it. But such exotic matter is entirely theoretical, and it is unclear if it exists in reality. Exotic matter is a requirement for many time travel machines but for traversable wormholes we might be able to substitute negative energy that is known to exist (This trick is possible because mass and energy are two sides of the same coin being interrelated by Einstein’s famous equation, E = mc².)

The best-known example of negative energy is the Casimir effect that was proposed in 1948 and first measured in 1958. When two uncharged plates in a vacuum are placed a few nanometers apart, there is a small force of attraction between them because the vacuum energy is lower between the plates than elsewhere. The moving mirror effect and squeezed light are two additional means of generating negative energy. Unfortunately, all three methods produce miniscule quantities. Even worse, there appears to be physical rules limiting how much negative energy can be generated²⁴.This is a major problem because to make even a one-meter diameter wormhole would require a truly enormous amount of negative energy, an amount equal to the mass of Jupiter!

Large gravitational bodies also generate negative energy. Earth produces a small amount while black holes generate considerably more. For example, Hawking radiation (positive energy) emitted by black holes is counterbalanced by negative energy that falls into the black hole. Because wormholes strongly resemble black holes, they too would generate negative energy that might prove useful. It is possible that tiny wormholes could generate enough negative energy to inflate themselves! That would solve a major problem although it is much too early to know if this will work.

Differentiator

At this point in the process, our wormhole would be useful as a bridge for transporting us between two different locations in space but not in time. For that, we need the differentiator. The role of the differentiator is to use time dilation to slow the passage of time at one end but not at the other. This is the twin paradox applied to the two ends. For example, if we perfectly slowed down time at one end for 10 years, then that end would be 10 years younger than the other. That would allow you to jump between these two times either going forward or backward 10 years depending on your direction of travel.

The time dilation of the wormhole can potentially be handled in two ways. First, you can move one end at near light speed. This could be done when the ends of the wormhole are the size of particles. Give one side a slight charge and spin it in a particle accelerator at close to the speed of light. Second, you could place one end close to a neutron star or a black hole. The intense gravity would slow down the passage of time at that end.

Conclusion

One important caveat is that you can only go between the two times corresponding to the two ends of the wormhole. This means that you could never travel farther back in time than when the wormhole was created.

In studying the requirements for each step in constructing a traversable wormhole, we should not be expecting to build one any time soon. Yet it might just be possible in the far future.

²⁴ Lawrence H. Ford and Thomas A. Roman, “Negative Energy, Wormholes, and Warp Drive,” Scientific American, January 2000, p. 46-53.

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Appendix: Quotations About Time

(Organized by Subject)

Nature of Time

[Time is] the most unknown of unknown things. – Aristotle

What then is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not. – Augustine, Confessions 11.14 (17).

Why is it so difficult – so degradingly difficult – to bring the notion of Time into mental focus and keep it there for inspection? What an effort, without fumbling, what irritating fatigue! – Vladamir Nabokov

Time Is…

Time is what keeps everything from happening at once. – Ray Cummings, The Girl in the Golden Atom.

Time exists in order that everything doesn’t happen all at once…and space exists so that it doesn’t all happen to you. – Susan Sontag

Time is an illusion. Lunchtime doubly so. – Douglas Adams, The Hitchhiker’s Guide to the Galaxy.

Time is money.

Time is the landscape of experience. – Daniel Boorstin

Time is but a memory in the making – Vladamir Nabokov

Time is what happens when nothing else does. – Richard Feynmann

[ Time is ] a moving image into eternity. – Plato

Time and space are modes by which we think and not conditions in which we live – Albert Einstein

The Arrow of Time

Time is the fire in which we burn. Yesterday’s the past, tomorrow’s the future, but today is a gift. That’s why it’s called the present. All the world’s a stage, and all the men and women merely players: they have their exits and their entrances; and one man in his time plays many parts, his acts being seven ages. – Gene Roddenberry

The past could always be annihilated. Regret, denial, or forgetfulness could do that. But the future was inevitable. – Oscar Wilde, The Picture of Dorian Gray (1890)

For us believing physicists, the separation between past, present and future has only the meaning of an illusion, albeit a tenacious one. – Albert Einstein

Time, not necessarily as it is, for who knows that, but as thought has constituted it—monomaniacally forbids second chances. – Ian McEwan

No man ever steps in the same river twice, for it’s not the same river and he’s not the same man. –Heraclitus

Thus we may have knowledge of the past but cannot control it; we may control the future but have no knowledge of it. – Claude Elwood Shannon

Who can undo what time hath done?
Who can win back the wind?
Beckon lost music from a broken lute?
Renew the redness of a last year’s rose?
Or dig the sunken sunset from the deep? – Edward Bulwer-Lytton

Causality

Causality simply affirms that effects occur after their causes. If a light bulb in a room suddenly lights up, it is reasonable to assume that someone flicked the switch a minute fraction of a second earlier. It is absurd to suppose that the light bulb could light up because someone ten years in the future flicks a switch. The idea that effects could occur before their causes is denied by the rational mind. – William Kaufman, The Cosmic Frontiers of General Relativity

Is Time Travel Possible?

Time travel will never be impossible forever. – Toba Beta

Originally, the burden of proof was on physicists to prove that time travel was possible. Now the burden of proof is on physicists to prove there must be a law forbidding time travel. – Michio Kaku

In Einstein’s equation, time is a river. It speeds up, meanders, and slows down. The new wrinkle is that it can have whirlpools and fork into two rivers. So, if the river of time can be bent into a pretzel, create whirlpools and fork into two rivers, then time travel cannot be ruled out. – Michio Kaku

Time travel, by its very nature, was invented in all periods of history simultaneously. – Douglas Adams

The best evidence that time travel is impossible is the fact that we haven’t been invaded by hordes of tourists from the future. – Guillaume Musso

Even if it turns out that time travel is impossible, it is important that we understand why it is impossible. – Stephen Hawking

If Time travel were possible, the future would have already taught the present to teach the past how to do it. – Atom Tate

Time and Wisdom

A pipe gives a wise man time to think and a fool something to stick in his mouth. – C. S. Lewis.

Time is free, but it’s priceless. You can’t own it, but you can use it. You can’t keep it, but you can spend it. Once you’ve lost it you can never get it back. – Harvey Mackay.

Someone once told me that time was a predator that stalked us all our lives. I rather believe that time is a companion who goes with us on the journey and reminds us to cherish every moment, because it will never come again. What we leave behind is not as important as how we’ve lived. After all Number One, we’re only mortal. – Jean-Luc Picard

How did it get so late so soon? It’s night before it’s afternoon. December is here before it’s June. My goodness how the time has flewn. How did it get so late so soon? – Dr. Seuss.

Who controls the past controls the future. Who controls the present controls the past. – George Orwell

Life’s biggest tragedy is that we get old too soon and wise too late. – Benjamin Franklin

Humor

There was a young lady named Bright
Whose speed was faster than light;
She set out one day
In a relative way
And returned on the previous night. – A. H. R. Buller

Bartender asks, “What’ll you have?” A tachyon walks in the bar.

A tachyon flies into a bar. The bartender says, “We don’t serve tachyons here.”
“Why not? You did tomorrow.”

Time flies like an arrow and fruit flies like a banana. – Groucho Marx

Life is uncertain, so eat dessert first.

It’s difficult to make predictions, especially about the future. – Yogi Berra

The future ain’t what it used to be. – Yogi Berra

Other

The major problem is simply one of grammar, and the main work to consult in this matter is Dr. Dan Streetmentioner’s Time Traveler’s Handbook of 1001 Tense Formations. It will tell you, for instance, how to describe something that was about to happen to you in the past before you avoided it by time-jumping forward two days in order to avoid it. The event will be described differently according to whether you are talking about it from the standpoint of your own natural time, from a time in the further future, or a time in the further past and is further complicated by the possibility of conducting conversations while you are actually traveling from one time to another with the intention of becoming your own mother or father. Most readers get as far as the Future Semiconditionally Modified Subinverted Plagal Past Subjunctive Intentional before giving up… – Douglas Adams, The Restaurant at the End of the Universe, Chapter 15.

The speed of light: not just a good idea. It’s the law.

Everything not forbidden is compulsory. – T.H. White, The Once And Future King

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Time and Again: The Science Fiction of Time Travel

Table 1: Twin Paradox for Spacecraft Traveling Round Trip to the Star Rigel10

Table 2: Influential Books and Movies on Time Travel

Footnotes

Table 1: Twin Paradox for Spacecraft Traveling Round Trip to the Star Rigel¹⁰