subject of this column brings to mind an old physics-based limerick that I
learned many years ago in graduate school (one of the few clean ones).
It goes something like this:
was a young lady named Bright,
could travel much faster than light.
She set out one day,
in a relative way,
returned on the previous night.
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.
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.
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.
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.
on this basic scenario, theoretical physicists H. Pas 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
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.
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.
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-05 Analog). The PPW scheme for producing a timelike loop does so well within 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.
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.
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-98
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.
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
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
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
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.
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.
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
are probably even more ways of dealing with time-travel paradoxes.
If PPW are correct, we may have to start thinking seriously about them.
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).
SF Novels by John Cramer: my two hard SF novels, Twistor and Einstein's Bridge, are newly released as eBooks by Book View Cafe and are available at : http://bookviewcafe.com/bookstore/?s=Cramer .
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