The subject of this column brings to mind an old physics-based limerick (one of the clean ones) that I learned many years ago in graduate school . It goes something like this:
There was a young lady named Bright,
who could travel much faster than light.
She set out one day,
in a relative way,
and returned on the previous night.
The physics behind the limerick is that within Einstein’s special theory of relativity there is a subtle connection between faster-than-light and backwards-in-time travel. If you could do one, then in principle you could also do the other. But relativity is carefully contrived to prevent superluminal and back-in-time travel and communication.
To physicists, these prohibitions are something of a comfort, because they evade problems with mind-bending consequences that we don’t know how to solve. Even sending messages backwards-in-time has mind-bending consequences and has become a standard theme in science fiction (examples: Isaac Asimov’s “thiotimoline” pseudo-science-fact articles in Astounding, Greg Benford’s Timescape, Jim Hogan’s Thrice in Time, etc.).
In the real world, we seem to be prevented from sending back-in-time messages by that least-understood law of physics, the Law of Causality, which is the requirement that a cause must precede its effects in all reference frames. However, new cracks may be appearing in the iron wall of causality. In this column, I want to discuss some recent work at the boundaries of string theory and general relativity that seems to offer a way to circumvent the back-in-time barrier.
Some of the modern variants of string theory describe our universe as a 3+1-dimensional space-time “brane,” essentially a thin 4-dimensional membrane embedded in a higher-dimensional space (for further reading, see my AV column in the May 2003 Analog). Almost all of the known particles (electrons, quarks, photons) are restricted to this 4-brane and can move only within it. Further, the three strongest forces (strong, weak, and electromagnetic) are allowed to act only within the brane. Therefore, for most purposes the 3+1 dimensional brane is the only relevant universe, since almost nothing can go outside it.
However, according to some models, the force of gravity gets special treatment in extra dimensions. It is free to leave the brane and spread out into the large extra dimensions in which the brane is embedded. This provides an explanation of why the force of gravity is so weak compared to the other forces: the lines of force for gravity can spread out into the other dimensions, leaving fewer force lines and a much reduced force strength on the brane itself.
Building on this basic scenario, theoretical physicists H. Päs and S. Pakvasa of the University of Hawaii, and T. J. Weiler of Vanderbilt University (I’ll call them PPW) have constructed a scheme for back-in-time communication. The starting point of their scheme is to examine the relativistic “enforcement rules” that normally prevent back-in-time communication. These rules are the Lorentz transformations, devised by Albert Einstein to describe how space and time behave when the observer or the object observed is moving near the speed of light. Within these rules, there is no possibility of superluminal or back-in-time communication.
PPW demonstrate that it is relatively easy to describe an extended universe in which the Lorentz transformations are strictly observed on the brane, but not in the outside “bulk” occupied by the extra dimensions. In particular, within the bulk volume of the extra dimensions the limiting speed (i.e., the speed of light) may be different from its value on the brane. They construct a plausible space-time metric in which the off-brane limiting speed is superluminal and grows quadratically with distance from the brane. This “asymmetrically warped brane universe” is rather like an onion, with each “onion layer” in the bulk having its own limiting speed and its own Lorentz transformations. In such a universe, trajectories that cut across such onion layers are not “Lorentz invariant,” i.e., they can break the local speed limits.
Having found a space-time metric to describe a plausible brane universe, PPW consider a path that leaves the brane, travels some distance in the extra-dimensional bulk outside, and then re-enters the brane. They show that such a path, while it may facilitate moving from one point in space to another at the equivalent of a faster-than-light speed, would not in itself represent backwards-in-time signaling (which they refer to as a “closed timelike curve”). For example, if you could make an extra-dimensional jump from here to Alpha-Centauri in six months, that would be a remarkable feat, but it would not in itself produce any problems for the Law of Causality.
However, PPW go on to consider a more elaborate scenario in which a signal passes out along one such trajectory and then returns to its 3-space starting point along another trajectory in extra-dimensional bulk, with the two trajectories threading through bulk regions with differing limiting speeds. They show that if the extra-dimensional speeds have the right relationship, one can construct a situation in which a signal following this path arrives before it is sent. This constitutes a “timelike loop,” and therefore, it produces a violation of the Law of Causality.
Is this a valid calculation, or did they do something illegal in their use of general relativity? Fortunately, the general relativists have devised several ways of evaluating the merit of calculations of this kind. Such evaluations are based on how well a calculation satisfies various energy conditions that have been suggested as possible “rules of the game” for what our universe will allow. (See the discussion of such rules in my AV column “‘Outlawing’ Wormholes and Warp Drives” in the May 2005 Analog). The PPW scheme for producing a timelike loop does well with these energy conditions, satisfying the null, weak, and dominant energy conditions on the brane and violating only the strong energy condition. We note that the strong energy condition is also violated by some well-known quantum processes.
This all sounds very nice, of course, but it raises the crucial question of just how one might manage to send a signal along a trajectory through the extra dimensions outside this brane we call home. PPW suggest a way of doing this. According to the version of string theory that they use, there are two particle-types that are not constrained to stay within the brane of our universe. These particles are gravitons and sterile neutrinos. These can be considered as possible carriers of the PPW signal.
As signal carriers, gravitons (quantum gravity waves) can probably be ruled out, at least for the near future. LIGO, the biggest and most sensitive detector of gravity waves that our best earth-bound technology can produce (See my AV column on LIGO in the April 1998 Analog), has been in operation for several years and so far has reported no detection of gravity waves from any sources, including super-intense sources like merging neutron-star or black-hole binary systems. If it’s hard to detect a strong gravity wave, it should be even harder to use them for signaling. There have been some recent ideas about the generation and detection of high-frequency gravity waves, which may make the signal transfer problem easier, but presently there is no technology for doing this.
That leaves sterile neutrinos, which will require some explanation. According to the standard model, there are three “flavors” of neutrinos: e, mu, and tau. These are the neutral “twins” of the electron, the mu lepton, and the tau lepton. From recent measurements with the SNO and Super-K neutrino detectors, we now know that a neutrino of a given flavor can “oscillate” into other flavors as it travels some distance. For example, SNO measurements tell us that about 2/3 of the e-type neutrinos produced in the Sun have oscillated into mu neutrinos before arriving at the SNO detector buried deep in a mine in Sudbury, Canada. The Super-K neutrino detector in Japan has provided evidence that the mu neutrinos from cosmic rays oscillate into tau neutrinos on their way to the detector.
Overall, there have been a number of large neutrino detector experiments studying neutrino oscillations in one way or another, and all but one of them give a consistent picture. The wild-card experiment is the LSND measurement at Los Alamos, which measured neutrinos made with the very intense 800 MeV proton beam from the LANSE (formerly LAMPF) accelerator and ran from 1993 to 1998. The neutrino detection measurements from LSND do not fit with the other measurement results. The possibilities are (a) LSND has some fundamental error, or (b) it is observing the oscillation of muon neutrinos into a hypothetical fourth flavor of neutrino called “sterile neutrinos.” Possibility (a) is now being checked by the miniBOONE experiment at Fermi Lab.
If LSND did observe the oscillation of mu neutrinos into sterile neutrinos, that’s a very interesting result, in the context of the present discussion. Sterile neutrinos do not participate in the weak interaction, and are allowed to leave our brane in the same way as gravitons and to have trajectories involving the extra dimensions. Therefore, if sterile neutrinos exist, there is a possible experimental test of the PPW ideas.
One could imagine an experiment in which a modulated beam of mu neutrinos produced by collisions and decays at a large accelerator are beamed down into the Earth, where they oscillate into sterile neutrinos, go on an excursion in other dimensions, oscillate back to mu neutrinos, and are detected by a large detector located at some large distance around on another side of the Earth. According to PPW, if that trajectory was just right, the signal just might arrive before it was sent.
The SF implications of back in time signaling are fairly obvious, but let’s consider them. If you receive a signal from the future, you can either (a) take actions that are consistent with the message, or (b) take actions that are inconsistent with it. Under scenario (a) you might receive tomorrow’s winning Power-Ball Lotto number, buy a ticket for that number, win the lottery, and then send your past self a message containing the winning number to complete the loop. Under scenario (b) you might receive a message warning that tomorrow you will be killed in a car accident, so you carefully stay home, avoid the accident, and change the future.
How, exactly, the universe deals with such positive (a) or negative (b) timelike loops depends on your model of how to resolve time-travel paradoxes. The deterministic scenario is that the future is fixed and cannot be changed, so only scenario (a) events are possible. In some scenarios, usually not well defined in their implications, a scenario (b) event causes the old future to fade away and be replaced by a new future. The novels Timescape, Thrice in Time, and many other SF works implicitly use this model. A third model, based loosely on the many-worlds interpretation of quantum mechanics, is that a scenario (b) event produces a branch universe in which history follows a different path. In my novel, Einstein’s Bridge, I used yet another model in which the creation of a timelike loop “unravels” the universe back to the beginning of the loop, so that it can proceed on a different path.
There are probably even more ways of dealing with time-travel paradoxes. If PPW are correct, we may have to start thinking seriously about them.
AV Columns Online: Electronic reprints of over 120 “The Alternate View” columns by John G. Cramer, previously published in Analog, are available online at: http://www.npl.washington.edu/av. The preprint referenced below can be obtained at: http://www.arxiv.org.
Closed Timelike Curves:
“Closed timelike curves in asymmetrically warped brane universes,” Heinrich Päs, Sandip Pakvasa, and Thomas J. Weiler, ArXiv preprint gr-qc/0603045 (March 13, 2006).