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Wormholes:  Getting from Here to There in No Time


Copyright 1997, 1998 by Andrew Trapp



 

Table of Contents:

  1. Introduction
  2. History
  3. Keeping a Wormhole Open
  4. Having Fun with Wormholes
  5. Manipulating Time with Wormholes
  6. The Here & There of Time Travel
  7. Many-Worlds:  The Best Possibility?
  8. Conclusion
  9. Bibliography

Introduction

   [Author's note:  This paper was originally written for a "Philosophy of Physics" course.  As such, this is not intended to be strictly a technical paper.  Please keep this in mind while reading it.  Enjoy!]

   Of all the various subjects related to astrophysics, the concept of wormholes is among the most fascinating.  With a little creativity one can conceive of amazing things to do with wormholes, from quick galactic jumps to viewing tomorrow’s closing stock market reports.  It should be noted from the start that there is no evidence that wormholes can exist.  However, neither is there proof that they cannot.

   In this paper I will explore some of the many implications, and a few of the uses of wormholes, from a philosophical vantage.  While the possibility and ramifications of using wormholes for time travel will certainly be a major point of focus in this paper, I do not intend on this being merely a paper on time travel.  Wormholes have a number of significant other properties in their own right which merit examination from a philosophical point of view.  After a brief history of wormholes, I will detail some of the myriad effects that wormhole technology could have for an advanced civilization, including traveling.  I’ll then expand on the possibility of using wormholes for time travel, including some novel applications and concluding with a possible explanation of time travel using a many-worlds interpretation.  In this paper I will assume that the reader has a basic understanding of the twin paradox and has heard of the potential use of wormholes as time machines.

History

   In 1935, Albert Einstein and Nathan Rosen developed what is essentially the modern model of a wormhole, called an Einstein-Rosen bridge.  This bridge connects two arbitrarily distant regions of our universe with a space-time tunnel through hyperspace (a theoretical construct), with an opening or mouth at each end.  In a matter of speaking, a wormhole is a topological shortcut between two points in space.  Its common name is in fact a reference to a shortcut from one side of an apple to the other created by a worm tunneling through it.  Unfortunately with no means of internal support, the tunnel gravitationally pinches shut almost instantly, leaving a singularity in each mouth.

   Like their cousins the black holes, wormholes were in fact conjectured long before they became a subject of formal study or even before acquiring their common names.  Just months after Einstein formulated his field equations, in 1916 Ludwig Flamm discovered that an empty, spherical wormhole could be described by the Schwartzchild solution of the field equation by selecting a particular type of topology.

   In recent years, the wormhole has blessed the science-fiction genre with a remarkable device.  With its roots in real theoretical science, the wormhole provides a plausible method of faster-than-light (FTL) travel.  Ships could believably travel among the stars without those who are left planetside aging decades between trips.  Wormholes also make for great special effects on TV and the silver screen.

   The men ultimately responsible for the popularization of wormholes are Carl Sagan and Kip Thorne.  Sagan was writing his first fictional novel and needed some way of transporting the heroine quickly yet safely to the Vega star system, some 26 light-years away.  His original idea was to use some form of black hole as an entryway into hyperspace.  Always the stickler for scientific accuracy, he called upon his friend Kip Thorne for advice.  That got the ball rolling for what would eventually become an in-depth study of the properties of wormholes, first by Thorne and eventually dozens of others.

Keeping a Wormhole Open

   Ordinary matter (mass) has a positive amount of energy, given by the famous equation E=mc2.  This positive amount also means that matter warps space in a positive curvature.  In order to keep a wormhole open, we need to be able to give space a negative curvature.  Thorne’s proposal was to cram the throat of the wormhole with something called exotic matter, having negative mass and energy (as seen by light moving through it) and exerting a gravitational push.  Unfortunately we have seen no evidence whatsoever for the existence of exotic matter, although the theory of inflation predicts that massive amounts of it existed in the first tiny moments after the Big Bang.

   Steven Hawking hints at another possible source for negatively-curved space, through the Casimir effect.  In this variant of Heisenberg’s uncertainty principle, two conducting metal plates spaced very close together will feel an attraction.  Outside the plates, quantum fluctuations produce a uniform pressure on the plates.  Inside, however, only certain modes of waves can exist between the plates, resulting in an area of lower quantum pressure.  Hawking believes that such an area is in fact an area of negative spatial curvature.  Whether such a region is in fact negative or simply less positive, and whether the space in this area could be harnessed in the construction of a stable wormhole, remains to be seen.

   Thorne briefly mentions in his book that it is in fact possible to make a wormhole using entirely classical (i.e. non-quantum) methods, with one caveat:  part of the construction process moves backward in time.  Of course, this might be manageable if one had a worm hole to use as a time machine...a catch-22.  Perhaps it may be possible by manipulating anti-matter somehow, since anti-matter can be regarded as regular matter moving backward in time.

Having Fun with Wormholes

   When (and if) a civilization advances to a level of technology where they can feasibly make a macroscopic, stable wormhole, what uses could they put it to?  Perhaps one of the most controversial is time travel, and I will explore that a bit later.

   The most obvious use, of course, is as an interstellar shortcut.  A wormhole 10 inches long could connect two star systems 10 light-years apart.  Of course you still have to send one mouth to the other star system.  But it has been shown that it should be possible to construct a wormhole mouth with negligible mass and charge.  Thus one could envision using a particle accelerator as a rail gun to boost one mouth to near-light speed and if it is well-aimed, have it enter into a stable orbit of another star system.

   Because time for the traveling mouth would be warped relativistically, a trip of many light-years could seem to take only minutes or hours at near-light speed.  Looking at that mouth from Earth, it would appear to take many years to travel interstellar distances.  But looking at it through the non-accelerated local mouth, the view is as if the observer were travelling with the accelerated mouth, and the journey is drastically faster.  This is the property of wormholes which allows the potential for time travel--using the difference in the rate of the passage of time at each mouth.

   A civilization which had no trouble generating wormholes, and with a big enough armada of space probes, could explore a significant portion of the galaxy in a matter of days or weeks.  Of course this would be in their time frame; the wormholes would still take many years to make their journeys.  Still, the possibilities for space exploration are intriguing.

   Wormholes may allow us to do something presently forbidden:  safely look at a black hole from inside its horizon.  Assuming we could collapse a wormhole at will, we could plunge one mouth down the event horizon and observe through the other.  Since there’s no reason gravity waves couldn’t travel through a wormhole the same as light or matter, you’d have to limit your observations to a few seconds, then collapse the wormhole before the tidal forces overwhelmed everything at your end.  This research is probably far too risky to conduct within our solar system.  Even though the extreme tidal forces would likely collapse the wormhole, catastrophic damage could be done before that happened.

   For intergalactic-scale exploration, shooting a wormhole out of an accelerator would not be efficient.  Even with a beta (v/c) = 0.9999999999995, (no small amount of work for the accelerator,) it would still take 2.25 years to reach the Andromeda galaxy and 36 years to reach the Virgo cluster.  An alternative would be to send a conventional rocket, which would receive a steady supply of fuel from Earth through an on-board wormhole.  Accelerating at just a constant 1 g in its reference frame for half the trip, then turning around and decelerating for the second half, it would reach Andromeda in 28.4 years--considerably longer--but Virgo in just 33.76 years.  The edge of the universe could be reached in about half a century.  (Of course it will have expanded a bit in the intervening 15 billion years.)

   As such a rocket approached the speed of light, it would become increasingly difficult to avoid objects:  rocks at first, then stars, then entire galaxies.  To make matters worse, the Doppler-shifted forward view would shrink to a tiny point.  A 100-ton rocket accelerating at a constant 1 g would have an effective mass of over half a quadrillion tons by the time it reached the Andromeda galaxy, assuming it made it there.  One possible remedy might be to affix the mouth of another wormhole in front of the ship, to safely "dislocate" any matter it may run in to.  It is not clear that this would work if the ship ran into a star, however.

   In addition to exploration, wormholes could be used for colonization, and later for trade.  Colonies connected by wormholes could trade with relative ease, not having to wait years or decades for a transaction to complete.  Indeed, it might be possible to establish a network of wormhole-connected colonies in such a way that they could all go by nearly the same calendar.  (Allowing for local variations in day and year length.)  Such an empire could establish a kind of "stellar absolute time."  If each colony had a wormhole nearby, one need not take relativistic travel into account when doing commerce--it would be more akin to trading among continents.  The only catch is that you’d have to string the colonies together in the order they were created, otherwise going from A to C could set you years apart from going A to B to C.  (Assuming they were created from A to C.)

Manipulating Time with Wormholes

   Then of course there’s the whole matter of time travel.  Many people who write about wormholes and time machines are fond of reciting some variant of the grandfather paradox--what happens if I go back in time and kill my grandfather, thus preventing my future existence?  How morbid.  All this talk of killing one’s grandfather, tossing hapless astronauts into black holes, and playing Russian roulette with cats belonging to Schroedinger makes me wonder what’s behind our greatest scientific minds.  I’ve never understood the need to include death in explaining the laws and effects of physics.

   In fact there are a number of benefits to be derived from time travel for the creatively-minded.  (This is all on the assumption that time travel is both possible and reasonably safe.)  Computers could be constructed which would loop the output back to just after the input was entered, thus creating computers of near infinite power and speed.  Using a variation on the twin paradox, you could relativistically accelerate a wormhole away from then back to Earth, and know how tomorrow’s stock market is going to do.

   A society starved for resources could even travel to the future to cut lumber, collect money left in an account, or mine uranium.  This may not be economically prudent, though; these resources are in effect being "borrowed," and will be gone at the point in the future when the present reaches through and takes them.  That may depend, however, on what the nature of time is really like.

The Here & There of Time Travel

   We’re still a little confused when it comes to time travel.  Although the physicists are making progress on defining the nature of time, the philosophers still have broad reign.  The two most contested questions are, Is time travel possible?  And if so, are causality violations possible?

   I believe these questions to be more a matter of science and technology than of philosophy.  I see no reason why we can not eventually solve them.  There are two main arguments against time travel.  The first, proposed by and ardently subscribed to by Steven Hawking, is called the chronology protection conjecture.  It conspiratorially states that the laws of physics will somehow prevent macroscopic-scale time travel.  For wormholes, he predicts that an infinite feedback of virtual particles will overload and destroy them.  The second is more precise, although lacking in a name.  In a nutshell, it states that there are an infinite variety of scenarios, each with some probability of occurring, that will prevent causality violations from occurring.  For instance, a billiard ball angled through 2 wormholes so that it deflects itself before entering the first, would actually just glance and knock itself onto an alternate trajectory into the wormhole.

   I have a hard time coming to terms with either of these.  The first scenario seems like a technological problem; there may be some way to deflect, dissipate, or absorb the radiation feedback.  Also it is not completely clear that such feedback would in fact be sufficient to destroy the wormhole.  As for the second argument, that seems to be a bad version of the many-worlds hypothesis below; it implies a purposeful "Invisible Hand," and still does not completely outlaw causality violations.  For instance, one could replace the billiard ball with a shock-sensitive grenade.

   So far the most consistent explanation appears to be the many-worlds hypothesis.  Quantum mechanics says that a particle, because of Heisenberg uncertainty, has some particular probability of being at a certain location, and another probability of being at a different location, etc.  The many-worlds interpretation states that a particle actually is at every non-zero-probability location, and that travelling between two points it takes every conceivable path.  When we make an observation, the measurement of the particle we end up with is, in a sense, dependent on which universe we’re in.  If a particle has, say, an 80% chance of being in a particular space, then in 80% of the alternate universes, we would measure it as being there.  This explains time travel by saying that you’re not really going into your own past or future, but that of a parallel universe or timeline.

   A more visual way to describe this might be to imagine that the timeline is like a tree.  Every time an event is going to occur, the timeline branches, with each branch representing a different outcome.  When you travel back through time, you are moving backward down the timeline.  When you arrive at your past destination, your actions which will change the future in any way will send you forward along an alternate branch than the path your timeline originally took.  So you could use time travel to change the past, it just wouldn’t be your past.

   Thus, a homicidal man who wanted to kill his grandfather before he was born, would indeed prevent his own birth--in a "parallel" or alternate universe.  He would continue to exist, and if he returned through the wormhole (or should I say looking glass?), he would find his present-day grandfather the same as when he had left.  In the other universe however, the other him would not have been born, thus could not have traveled to the first man’s universe (or any other) to snuff him.  It’s all logically consistent, and causality violations are handled by saying that an event both did happen (in one universe or reality) and also didn’t happen (in another).

   So how would this affect some of the applications I’ve suggested previously?  In the case of travelling to a future time (let’s say a century, from 2000 to 2100) to harvest resources, from 2000 to 2100 we would reap the benefits of these additional resources.  But in an alternate universe, for one of an infinite number of reasons we are unwilling or unable to make the trip.  Not only that, but when 2100 rolls around, a vast majority of the universes may get a visit from harvesters claiming to be their ancestors from 2000.  We can change our own future (we don’t even need time travel to do that), but the only past we can change is, in effect, someone else’s.

   In that example, the people of 2000 are fairly confident that they can get resources from 2100, or at least that there will be resources in 2100.  But what about when we want to bring information back from the future?  Say we wanted to know tomorrow’s stock prices.  We accelerate one mouth of a wormhole away from then back to Earth.  We on Earth won’t see the other wormhole mouth arrive for years to come, but peering through the one that remained here, from its point of view it arrives in a day, and we can glimpse tomorrow’s stock prices.  Based on this information, we buy a stock that will go up and sell one that will decline.  But won’t this action send us along a different branch than the one that produced the information we’re gleaming?  Yes, because the future we’re looking at is one that branched off from a point in our (immediate) past when we were still ignorant of the information and thus couldn’t have used it.

   So how reliable is information from a future that hasn’t yet happened?  It depends on how big an effect your actions have on the future.  If you see that a stock will decline tomorrow, and you’re a small investor, your actions are unlikely to change the outcome regardless.  You can consider the information reliable (albeit not 100%…maybe 99.9996%) because in a very large majority of possible futures, the stock will decline.  If you’re an institutional investor or other influential figure however, your actions may well have a significant effect on the stock.  The information is then not so reliable, because your actions have a smaller chance of producing the type of future (note I didn’t say exact future) that would have happened if you had done nothing.  Thus, the probability of the information from the future coming to pass is a statistical probability dependent on your actions in the present.

Many-Worlds:  The Best Possibility?

   Let’s try to create a paradox.  Say I arrange two wormhole mouths, with one being located one meter and temporally displaced by two seconds away from the other.  I toss a ball through one mouth on a trajectory that should send it into the past and will deflect "itself" before it has a chance to enter the wormhole.  Steven Hawking would claim that this is a moot experiment, since the laws of physics wouldn’t allow me to create a time machine in the first place.  By the other, unnamed criticism of causality violation, there are an infinite number of ways that the ball could collide with itself and still enter the wormhole, as long as that ball wasn’t a shock-sensitive grenade.

   If we allow a many-worlds interpretation with branching timelines, then there are no causality violations.  Figure 1. shows how this could work.  At point 1, there are (in this example) three possibilities.  Path A, I decide not to do the experiment.  Path B, I do the experiment.  Path C, I am unable to do the experiment because of some outside event.  Just before point 2 I send the ball through, and peering through the same wormhole it entered (travelling along path E), at point 3 in time I can see it collide with and deflect itself before it has the chance to enter the wormhole.  (The branches after point 3 represent different trajectories the balls take after colliding.)  This even though I am certain that in my past, no such ball came through and deflected mine.  However, if I want my ball back, I’m going to have to go through the wormhole into the past and retrieve it.

   The other possibility is that I send the ball through the first wormhole, but before it gets there an identical ball comes out of the other wormhole at point 2 and knocks it off course.  But that other ball couldn’t be mine, because mine never entered the wormhole.  This time I’m travelling down path D.  Looking through the wormhole that the rogue ball came out of, I can see a future version of myself watching the collision, and I realize that it was he who sent the ball.  So in the first reality, going down path E, I successfully change the future but the past remains the same as I remember it, but in the other, path D, my future is altered--takes a different branch--by an external force which I have no causal link to, because it’s on a diverging timeline.  The two wormhole mouths are taking different and diverging paths, starting as soon as they became separated in spacetime.

   Our past is fixed and unchangeable, but we know it for certain; our memories allow us to retrace our path back toward the bottom of the timeline tree.  Our future is constantly changing and branching based on every little thing we (and even our molecules) do, and is not certain beyond our ability to predict.  When I use wormholes to create a time machine, I am creating a causality link from my future self to a point in my past.  By effecting changes to my past, I am creating new branches in my past timeline.  (Or possibly travelling down previously unlikely branches.)  What I observe happening in the past from my vantage point in the future are events which are on a different branch of the timeline than those events I remember happening in my past.  Space and time are united in relativity, and this means that two people or objects separated in time are just as different as two that are separated by space.  Changing my past self won’t change my present self because my past self is essentially a carbon-copy but a different person nonetheless, separated by time instead of just distance.

   This many-worlds interpretation has an interesting consequence.  In a sense, it redefines conservation of energy.  Using wormholes, we can send matter & energy from one timeline to another, then close them off.  Thus in one universe, energy has been destroyed, and in another it has been created.  However over all timelines, energy is still conserved.  This would seem to imply that universes joined by a common timeline have something intrinsically in common after all.  The same observation can be made for entropy.  The amount of entropy is greater in systems with more degrees of freedom, and when wormholes are used in a timelike manner to alter the past, they are creating more degrees of freedom.  Entropy, like matter, can be transferred from one timeline universe to another, but over all timelines, it still obeys the second law of thermodynamics.  A net reduction of entropy in one universe will be met and exceeded by a net increase in another.

Conclusion

   Wormholes are a fascinating subject to study, not just as another vehicle for time travel but also for the great potentials they could endow.  Their travel aspects alone make them valuable for exploration and, eventually, commerce.  If they could be taken advantage of temporally, that would add still more benefits.  Strictly speaking, wormholes may not be possible, but neither have we definitively ruled them out yet.  In any event it will likely be a very long time before humans are ready to either fully dismiss them, or take the next shuttle for a weekend stay at Proxima.


Bibliography

Thorne, Kip S., "Black Holes & Time Warps:  Einstein’s Outrageous Legacy," W. W. Norton & Co., New York, 1994.

Chown, Marcus, "How to Pull a Fast One," New Scientist, Sept. 6 1997, p. 49.

Lagoute, C., and Davoust, E., "The Interstellar Traveler," American Journal of Physics, vol. 63, March 1995, pp. 221-7.

Hawking, Steven, "The Illustrated A Brief History of Time," Bantam Books, New York, 1996, pp. 196-211.

Price, Michael Clive, "Traversable Wormholes:  Some Implications," Extropy #11, vol.5 no.1 (2nd half 1993); and Extropians email list, extropians@maxwell.lucifer.com.

Cover illustration by Joe Bergeron, from a web page.
 



Figure 1.  A greatly pared-down timeline tree.  At each point, a number of alternate timelines equal to the total number of degrees of freedom of everything in the system branches off.  In this drawing the points are arbitrarily far apart, but in reality can be separated by as little as a Planck-second.  See the text for explanations of events (numbers) and outcome branches (letters).  Return to previous text.
Figure 1.

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