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).
Michael Dummett
Sir Michael Anthony Eardley Dummett FBA D.Litt (born 1925) is a leading British
philosopher. He has both written on the history of analytic philosophy, and made
original contributions to the subject, particularly in the areas of philosophy
of mathematics, philosophy of logic, philosophy of language and metaphysics. It
is now common to speak of a post-Dummettian generation of English philosophers,
including such figures as John McDowell, Christopher Peacocke, and Crispin
Wright.
Wikipedia
AR I was among that post-Dummettian generation. I knew most of them. I had dealings with Dummett thirty years ago — he in effect directed me to Germany by suggesting that becoming fluent in German could advance my philosophical career. Back then, Crispin Wright supervised my research and helped with his fastidious nonintervention to launch me on my nevertheless stoically nonacademic career path.
