A Quantum Threat to Special Relativity
By
David Z. Albert and Rivka Galchen
Scientific American, March 2009
Edited by Andy Ross
Our intuition is that things can only directly affect other things that are
right next to them. We term this intuition locality.
Before quantum
mechanics, we believed that a complete description of the physical world
could be expressed as the sum of the stories of its smallest and most
elementary physical constituents. Quantum mechanics violates this belief.
Real, measurable, physical features of collections of particles can
exceed or elude or have nothing to do with the sum of the features of the
individual particles. Particles related in this fashion are quantum
mechanically entangled with one another. Entanglement may connect particles
irrespective of where they are and what they are. Entanglement appears to
entail nonlocality. And nonlocality threatens special relativity.
In
1935, Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen
presented what is now known as the EPR argument. Suppose that we measure the
position of a particle that is entangled with a second particle so that
neither individually has a precise position. When we learn the outcome of
the measurement, we change our description of the first particle.
Entanglement allows us to alter our description of the second particle,
instantaneously, no matter how far away it may be or what may lie between
the two particles.
Einstein, Podolsky and Rosen took it for granted
that the apparent nonlocality of quantum mechanics must be some kind of
anomaly or infelicity. They argued that if locality prevails in the world
and if the experimental predictions of quantum mechanics are correct, then
quantum mechanics must leave aspects of the world out of its account.
In 1964, John S. Bell reasoned that if any local algorithm existed that
made the same predictions for the outcomes of experiments as the quantum
mechanical algorithm does, then the EPR argument would justify dismissing
the nonlocalities in quantum mechanics as mere artifacts of the formalism.
Conversely, if no algorithm could avoid nonlocalities, then they must be
genuine physical phenomena. Bell analyzed a specific entanglement scenario
and concluded that no such local algorithm was mathematically possible. The
world is nonlocal.
Bell had shown that locality was incompatible not
merely with the abstract theoretical apparatus of quantum mechanics but with
certain of its empirical predictions as well. Since then, experimenters have
left no doubt that those predictions are indeed correct. The bad news is not
for quantum mechanics but for the principle of locality — and for special
relativity, which appears to rely on a presumption of locality.
Special relativity is bound up with the impossibility of transmitting
messages faster than the speed of light. If special relativity is true, no
material carrier of a message can be accelerated from rest to speeds greater
than that of light. A message transmitted faster than light would, according
to some clocks, be a message that arrived before it was sent, potentially
unleashing all the paradoxes of time travel.
In 1932, John von
Neumann proved that the nonlocality of quantum mechanics can never be used
to transmit messages instantaneously. The proof seemed to affirm that
quantum-mechanical nonlocality and special relativity can coexist.
In
1994, Tim Maudlin published a rigorous discussion of quantum nonlocality and
relativity. By then, a number of specific proposals existed to account for
apparent nonlocality. These proposals included the Bohmian mechanics of
David Bohm and the GRW model of GianCarlo Ghirardi, Alberto Rimini and
Tullio Weber.
Maudlin pointed out that the special theory of
relativity is a claim about the geometric structure of space and time. The
impossibility of transmitting mass or energy or information or causal
influences faster than light do not show that quantum mechanical nonlocality
and special relativity can coexist. Indeed special relativity is compatible
with a variety of hypothetical mechanisms for faster-than-light transmission
of mass and energy and information and causal influence.
However, the
nonlocal interaction between particles in quantum mechanics depends only on
whether the particles are entangled with each other. This seems to call for
absolute simultaneity, which would pose a threat to special relativity.
In 2006, Roderich Tumulka showed how all the empirical predictions of
quantum mechanics for entangled pairs of particles can be reproduced by a
modification of the GRW theory. The modification is nonlocal, and yet it is
compatible with the spacetime geometry of special relativity.
Tumulka's theory introduces a new variety of nonlocality into the laws of
nature — nonlocality in time. To use his theory to determine the
probabilities of what happens next, one must plug in not only the world's
current complete physical state but also certain facts about the past. In
this way, nonlocality can coexist with special relativity.
So it
turns out that the combination of quantum mechanics and special relativity
contradicts a primordial intuition. We believe that everything there is to
say about the world can in principle be put into the form of a narrative
sequence of propositions about spatial configurations of the world at
specific times. But entanglement and special relativity together imply that
the physical history of the world is far too rich for that.
Special
relativity mixes up space and time to transform entanglements between
systems that are spatially separated into entanglements between their states
at different times. Entanglement and nonlocality are implied by the wave
function that Erwin Schrödinger introduced to define quantum states.
Quantum mechanical wave functions are represented mathematically in a vast
configuration space. If the quantum mechanical waves wave are real physical
objects, then perhaps the history of the world unfolds not in the 3D space
of our everyday experience or in the 4D spacetime of special relativity but
rather in the infinite-dimensional configuration space. Our 3D world and the
idea of locality would need to be understood as emergent.
If temporal
nonlocality is a problem, the status of special relativity is open to
question.
A Relativistic Version of the Ghirardi-Rimini-Weber Model
Carrying out a research program outlined by John S. Bell in 1987, we arrive
at a relativistic version of the Ghirardi-Rimini-Weber (GRW) model of
spontaneous wavefunction collapse. The GRW model was proposed as a solution
of the measurement problem of quantum mechanics and involves a stochastic
and nonlinear modification of the Schrödinger equation. It deviates very
little from the Schrödinger equation for microscopic systems but efficiently
suppresses, for macroscopic systems, superpositions of macroscopically
different states.
As suggested by Bell, we take the primitive
ontology, or local beables, of our model to be a discrete set of space-time
points, at which the collapses are centered. This set is random with
distribution determined by the initial wavefunction. Our model is nonlocal
and violates Bell's inequality though it does not make use of a preferred
slicing of space-time or any other sort of synchronization of spacelike
separated points. Like the GRW model, it reproduces the quantum
probabilities in all cases presently testable, though it entails deviations
from the quantum formalism that are in principle testable. Our model works
in Minkowski space-time as well as in (well-behaved) curved background
space-times.
AR I know David Albert. I read his two books
years ago and watched him lecture at T2K and T2K2. His support for David
Bohm's version of quantum mechanics (where particles are like little
spaceships guided by pilot waves defined by the Schrödinger wavefunction)
always struck me as unfortunate — which ruined his first book for me (quite
apart from its studied avoidance of complex numbers where we all agree they
help).
Now I see that Roderich Tumulka also supports Bohmian
mechanics (BM) too (as shown by his slides for the Perimeter Institute
meeting on time in quantum mechanics held in September 2008), so I guess we
should not dismiss BM yet. My problem with it, for the record, is the deeply
mysterious nature of the instantaneous guidance provided by information in
the pilot waves. Bohm's "implicate order" seems as bad as Bohr's mysticism
to me.
Some years ago I was enamored of the GRW approach to solving
Schrödinger's cat problem, despite the fact that it seemed somewhat
"unromantic" (in John Bell's sense). Still, I was disturbed by its
unrelativistic aspect. Now Tumulka has rescued GRW from that problem and
made it a serious — and potentialy testable — candidate theory.
As
for nonlocality, I fear we're stuck with it. Down at the quantum level
everything is entangled with everything else in a nasty knot that we can
only approach statistically — this seems likely to be a fundamental
limitation on human knowledge. Temporal nonlocality adds no new problem of
principle. I think Albert may be exaggerating the threat here.
Temporal locality is an issue I have reflected upon for twenty years,
following a fine essay by Michael Dummett on the problem it seems to raise
of retroactive causation. This problem was both brilliantly visualized and
neatly resolved in Steven Spielberg's Back to the Future movies, in effect
by taking the Everett-Deutsch approach
of invoking multiple parallel worlds (see my
Mindworlds slides).
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