Time Travel

 

INTRODUCTION

 

While we all have an instinctive sense of time, scientific descriptions are less intuitive.   In the simplest sense, time is only a measure of change.  It allows us to quantify such things as the speed of a train moving past a station.  Thus time is not a physical entity in its own right but rather is an observed quality of matter describing how fast things spontaneously change their configurations.  In this sense, like our ideas of velocity or acceleration or temperature, time is only an idealized concept lacking an independent physical existence.  Or we could say that time is merely an independent variable or a mathematical artifact used to attach a necessary accuracy to our measurements of physical change.

 

This is unfortunate for many comforting but fuzzy minded romantic notions.  For if time is ethereal and does not strictly exist in its own right, then, contrary to the poetic notions of some popular ballads, it could never be put in a bottle.  Another wiseass, but perversely wise, witticism is that “Time is nature’s way of keeping everything from happening all at once” [1].

 

In any event, popular literature is replete with fictional travelers from the future travelling to a time past and thus appearing almost by magic in the time present [2].  Such dramatic license stems from the mathematical underpinnings of the classical laws of physics, which states that everything should progress equally well in either direction of time.  That is to say, if the velocities of every particle everywhere were to be instantly reversed, then everything should, at least in principle, regress precisely to an earlier state or configuration or time.

 

REVERSIBILITY OF TIME

 

If an advanced technology could reverse time by reversing the motion of all constituent parts of things, broken eggs would again become whole, melting ice cubes would re-freeze, machines we previously built would disassemble themselves, aging of every sort would be reversed, and people would get younger.   But also our memories of events now in the receding future would progressively erase themselves.   On arriving at the selected date in the past, the flow of time would have to be somehow reversed to the normal forward direction.  Entropy would again begin to increase and we could again form new memories.  Everything would be exactly the same as it was before with no one the wiser.  But on going forward, the putative time traveler, along with everyone else in the universe, would likely make exactly the same decisions based on exactly the same stimuli and rationale.  The net effect could be a universe forever ping-ponging between the selected date in the past and the future instant when the traveler switched on his time reversal apparatus.

 

Of course, we could encase the traveler in a bubble of normal time along with his machinery as he went backwards in time.  This bubble whose atoms had not been reversed in direction could contain a clock that ran forward during the trip to an earlier time while everything else in the universe, including all other clocks, ran backwards.  This would solve the problem of knowing how far to travel into the past before resuming the normal flow.   It would also permit our hero to retain his knowledge of future events, at least into the near future before his new activity changed things and altered his destiny.

 

Time in this protected bubble of normal time would advance in a sort of reverse lockstep with the rate of change in the outside universe.   That is to say, the time traveler would age one year for each year his time machine took him back in time.  Attempts to make the outside universe regress at a faster rate would effectively raise its temperature irreversibly altering the accuracy of the reversal with predictably catastrophic results.  Of course the time traveler might be able to accelerate to relativistic speeds within his local bubble; thus slowing his sense of time and effectively shortening the apparent duration of his journey.

 

But practical difficulties abound.  Since the earth along with the solar system is whizzing around the galaxy at hundreds of miles a second, the reversal of velocities would have to extend at least out to these distances [3].   This would obviously require a lot of energy, perhaps more than the local galaxy or even the universe itself contained.

 

Also the time machine would have to be extremely well isolated during its backward journey in time.  Even the slightest external influence on the reverse evolution of the universe could be catastrophic.  The result might very well be a vastly different past world and might even so jumble the chemistry of living things as to be fatal.

 

But the greatest problem is that by removing the traveler, the reverse evolution of the universe would of necessity diverge.  Any interactions the traveler had with anyone or anything during his lifetime would be entirely absent because he wouldn’t be there evolving backwards in time with everyone else.  The entropy associated with his absence would not reverse itself but rather would exponentially and chaotically increase.  This alone would make it impossible to return precisely to an earlier state of the cosmos.  The same consideration would also apply to any atoms required to construct the time machine itself.

 

Aside from these practical considerations, the above discussion has rather glibly omitted the theoretical difficulties posed by modern physics.  What is required is an almost infinitely precise knowledge of current positions and velocities.  Unfortunately, any measurements would unalterably change one or the other of these values in theoretically unpredictable ways.  This is Heisenberg’s Uncertainty Principle which as a foundation of quantum mechanics has been experimentally verified to great precision.

 

Other considerations of quantum mechanics, as currently understood, raise additional and insurmountable roadblocks to reversibility.   In quantum mechanics, particles are described by wave functions whose evolution are deterministic and exactly predictable using Schrödinger’s equation or Heisenberg’s matrix formulation.   Reversing the time direction of the wave function exactly reverses its evolution.   But the wave function does not strictly describe the physical state of a particle, e.g. its position or velocity, but rather only the probability of it having any particular value.   And experimental tests of Bell’s function indicate that quantum particles exist in a superposition of states.  That is to say, small bits of matter merrily buzz around in a probabilistic array of positions and velocities whose values only become fixed after they are measured.   Since only the probability of a value is deterministic, and not the value itself, it is not currently thought possible for the universe to exactly retrace its former steps if the flow of time were reversed [4].

 

An even more fundamental objection is the occasional observation in extreme circumstances of violations of “CPT invariance.”  This is the fundamental theory of quantum field theory which provides the fundamental underpinning for our belief that the a time reversed universe would exactly retrace it steps.   In detail it says that if we could reverse the charge, the parity (by switching to a mirror image), and the direction of time, then the equations of motion retain exactly the same mathematical form.  But since reversing only the charge and parity is seen in practice to change a particles physical properties, then reversing time cannot be an invariant either.  All other considerations aside, this alone means the universe, contrary to theory, can not exactly retrace its earlier steps if time was reversed.

 

THE TWIN PARADOX

 

As previously mentioned, in everyday terms time is manifest and simply understood.  But with the more refined considerations of Einstein’s General Theory of Relativity, the nature of time is logically more complex and obfuscated.   The space-time vector with four dimensions, three spatial (width, height, and length) along with time multiplied by the speed of light, is of constant length.  Or as one’s velocity approaches the speed of light the length of this vector is rotated into the “time dimension” generally interpreted as a local slowing of time (i.e. the speed at which the gears of a clock move) relative to the rest of the universe.

 

According to Einstein’s Special and General Theories of Relativity, time slows down as one approaches the speed of light making faster than light signaling or travel impossible.  Thus if one twin were to remain on Earth, while the other accelerated to high velocities in a spaceship and then returned, the twin who travelled would not have aged anywhere near as much as his stationary sibling.   In some sense, this would be equivalent to time travel but only into the future.  [This is equivalent in Science Fiction novels to imagined “stasis fields” in which time somehow slows down relative to everything else.]

 

There have been suggestions that if we were able to travel faster than light, we might be able to go backward to an earlier time.  But since our best theories also predict the impossibility of faster than light travel, it is again not certain how to accomplish this much less what would happen if it could be done.

 

CLOSED TIME-LIKE CURVES (CTC)

 

Some solutions to Einstein’s Theory of General Relativity provide paths through space which at first glance take one backwards in time [5-8].  The idea is that one could simply move on a path through a warped space-time in a spaceship without affecting the rest of the universe and magically appear in the past.  Superficially this would eliminate the need to reverse the velocities of everything else in the universe.  There would then be two copies of an individual and one could meet one’s earlier self intact.  Of course this would violate the conservation of mass-energy [9]. 

 

Typically these paths spiral around extraordinarily dense cylinders of infinite length spinning at nearly the speed of light.  Theoretically if a spaceship could traverse such a path, again at nearly the speed of light, the occupants are calculated to travel backwards in time.   Unfortunately, ordinary matter cannot be made sufficiently dense to provide the required gravity gradients.  Also when the spinning cylinders are shortened to any finite length, the mathematical consequences of the boundary conditions seem to eliminate the time traveling effects as well as the paradox of violating the conservation of mass-energy.

 

Time travel enthusiasts are forced to postulate super dense “cosmic strings” circling the entire universe or to assume the existence of “exotic matter” with negative mass.  Since neither of these phenomena has been observed and since their mathematical descriptions are incomplete at best, they are not generally considered a practical solution.

 

But since General Relativity predicts the counter-intuitive slowing of time in a gravitational field and the bending of light around massive objects, both of which are well tested and to great precision, this conjecture has more credence than might otherwise be the case.   In daily life our car’s global positioning system (GPR), which is a boon to the directionally challenged everywhere, must take into account these effects to get us safely from one spot to another.   And the observed bending of light around the sun during an eclipse, in a tribute to German science by an Englishman in the aftermath of WWI, skyrocketed the theory to fame and fortune in the first place.

 

But the greatest problem is that while General Relativity provides only small corrections in the relatively miniscule gravity of the earth or even our sun, it is stretched to the limit of the barely theoretically possible around super-dense rotating cylinders.   At these extremes one might expect quantum mechanical effects to become important or even to dominate.  Since we have not yet been able to combine quantum mechanics with the classical equations of General Relativity, one cannot but suspect that the effect is an artifact of sloppy thinking and illusionary at best.  Nor have we made any allowance for entropic considerations.

 

WORMHOLES

 

Another possibility for constructing a time machine is to use an Einstein-Rosen bridge.  The conjecture is that space might consist of more dimensions than the three, i.e. right-left, up-down, and forward-back, that we normally experience.   Indeed modern string theory at the simplest level requires a total of 11 dimensions.  And while strings are currently fashionable for their mathematical elegance, there has yet to be any demonstrable evidence for their existence.

 

Nevertheless the thought is that we don’t see these extra dimensions because they are curled up somehow.  That is if one were to try to move in the direction of the 7th, or the 8th, or perhaps the 9th dimension, you would circle back to your starting point after a barely measurable microscopic distance.

 

This is analogous to the idea of an ant on very thin rope.  The surface of the rope is two dimensional.   But if we had a vanishingly thin rope and when viewed from a great distance, only one number, i.e. the distance along the length of the rope, might appear to be sufficient to specify one’s location.   The tiny ant on the other hand would experience the full two dimensional surface of the rope.   Like many things, it’s all a matter of perspective.

 

If somehow we could expand and reconnect a few of these extra dimensions, we might fashion a doorway between different locations in our normal three dimensional world.  This is generally called a “wormhole” and would be something like a short tunnel connecting distant parts of our galaxy or even further without limit.  The higher dimensions would still be invisible to us and everything in the doorway would seem to be three dimensional.

 

To create a time machine, we might place one mouth of the wormhole in our living room and the other in the family spaceship parked in the back yard.   We could look through the wormhole from our spaceship and see our living room.   This would not change as the spaceship took off and accelerated close to the speed of light.   Time would slow down on our spaceship but we could still see and perhaps converse normally with our family in the living room.  After returning and landing in our backyard, many years might have passed on earth.   But we could then step from the spaceship, now many years in the future, back into our living room in the present day.  The wormhole would remain and function as a two-way time machine [10].  Of course both ends would then continue to age normally.

 

This would again obviate the need to reverse the direction of every particle in the universe.   Unfortunately, there is no direct evidence for wormholes and not enough energy to create one in the entire universe based on our best current scientific understandings.

 

ANTI-PARTICLES

 

In a fanciful exercise of imagination, Richard Feynman [11-12] expanded on earlier work by Steuckelberg and noted that the equations of anti-particle motion, such as that of a positron, contained a negative sign that could be equally well be applied to the time variable instead of the inverted electrical charge.  In this sense, the positron could be thought of as an ordinary electron moving backwards in time. 

 

Unfortunately this violates so many well verified laws of science, that it is not considered likely.  One problem is that even small quantities of antimatter are observed to become more disordered as normal time moves forward.   This well tested prediction of the Second Law of Thermodynamics for normal matter totally invalidates the basic assumption of time reversal.   This alone removes the possibility of meeting an alien made entirely of anti-matter moving backward in time who would know our future but not our past.  This is unfortunate because it would have made for interesting conversations indeed.   In later years even Feynman abandoned the speculation.

 

CYCLICAL UNIVERSES

 

At one point, Stephen Hawking thought that the universe might repeatedly expand and collapse and that perhaps entropy would reverse during the collapse.  But his mathematics was flawed as he later admitted and he abandoned the futile attempt to deny the necessity of a creation event by postulating a universe infinite in time.

 

CONCLUSIONS

 

There are two closely related and superficial paradoxes.  The first is the reversal of cause and effect as in the “Grandfather Paradox” where one travels back in time to shoot his grandfather before he marries his grandmother.   The other is the “Information Paradox” in which one’s future self travels back in time to gift the instructions on how to build a time machine to one’s earlier self.

 

But if travel to a time past could be accomplished, all the external matter in the universe would still have a continuous unbroken timeline from the perspective of the time traveler.  That is to say if the time traveler could journey years into the past, it would be the second time in his own experience that approximate state of the world existed.  It would be different however because of knowledge acquired on his travels.  And further these two states would be separated in his mind by the time required for his journey.   So it would not be a way to escape moral culpability for prior sins.  In principle we could trace the movement of every atom bouncing around even while reversing and re-reversing its trajectories without creating any closed time loops.  This would effectively remove any superficially apparent paradoxes.

 

In general, the insurmountable difficulties of time travel are mostly entropic as well as violations of the conservation of matter in trying to construct an identical copy of oneself.  And please note these difficulties are theoretical and do not even begin to address the technological challenges.  So fortunately for our current best scientific assumptions and especially our current understanding of the logical nature of cause and effect, it does not now seem to ever be possible to travel backwards in time.

 

But since one might argue that science, by its own methods, proves we can never be absolutely certain of any scientific theory, perhaps we might eventually discover things of which we cannot presently imagine.   The best argument against this however is the question, “If in the far future, time machines are invented, why don’t we see them now?”

 

So apparently we have only one chance to get it right and wasteful speculations on our lost opportunities, other than as object lessons for future improvement, are best disregarded.

 

REFERENCES

 

1.      Wheeler, John A., “Complexity, Entropy, and the Physics of Information”, Proceedings of the Santa Fe Institute Studies in the Sciences of Complexity Workshop, May 29 to June 10, 1989, edited by Wojciech H. Zurek, (1990), page 10 Westview Press.

[Although the quote is whimsically attributed to graffiti culled from the men’s room of the Pecan Street Café in Austin, Texas, earlier references are found in Ray Cumming’s novels “The Girl in the Golden Atom” (1922) and “The Man who Mastered Time” (1929).   Who says physicists don’t have a sense of humor?]

2.      https://en.wikipedia.org/wiki/List_of_time_travel_science_fiction

3.      Henbest and Couper, “Guide to the Galaxy”, Cambridge University Press (1994).

4.      Rothman, T. and Sudarshan, G., “Doubt and Certainty” (1998), Perseus Books Inc.

5.      Lanczos, Kornel, “On a Stationary Cosmology in the Sense of Einstein’s Theory of Gravitation”, General Relativity and Gravatition, Springland 29 (3), pages 363-399 (1924).

6.      Van Stockum, Willem Jacob, “The Gravitational Field of a Distribution of Particles Rotating about an Axis of Symmetry”, Proc. Royal Soc. of Edinburgh (1936)

7.       Tipler, Frank, "Rotating Cylinders and the Possibility of Global Causality Violation", Physical Review D 9 (8), page 2203 (1974).

8.      Thorne, Kip, "Black Holes and Time Warps" (1994), W.W. Norton & Co.

9.      This might be a useful analogy to the creation of matter in the Big Bang.

10.   Greene, Brian, “The Fabric of the Cosmos (Space, Time, and the Texture of Reality)”, Alfred Knopf (2004), page 461.

11.  E.C.G. Stueckelberg, Helv. Phys. Acta. 15, 23 (1942) and R.P. Feynman, "QED", (Princeton, 1985), p.98.

12.  https://arxiv.org/html/physics/9812021