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

Roderich Tumulka, 2006

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).