Two weeks ago, I blogged about David Bohm’s interpretation of quantum mechanics. Like Einstein and Louis de Broglie before him, Bohm argued that quantum randomness is not intrinsic to nature, but reflects our ignorance of a deeper level of reality. One physicist who has developed the idea further is Antony Valentini of Clemson University. Last week, he and a colleague published a paper suggesting an observational test–a rarity in this subject. I’ve invited him to write a guest blog post. I also recommend his lecture on YouTube and an article he wrote for Physics World magazine. For a slightly different take on de Broglie and Bohm’s theory, see this paper.–George Musser



By Antony Valentini

In the late 19th century, some physicists were concerned about the far future of the universe. Eventually the stars would burn out and everything in the universe would reach the same temperature. The new principles of thermodynamics showed that, in such a universal state of thermal equilibrium, it would be impossible to convert heat into work. It would also be impossible to escape the equilibrium state, and all significant change would come to an end. This rather depressing picture came to be known as the thermodynamic “heat death” of the universe.

Needless to say, the feared thermodynamic heat death has not yet occurred. The stars will continue to burn for a very long time to come. But is it possible that there is a deeper level on which something like a heat death has in fact already happened? For more than 20 years I have been arguing that this is indeed the case. Recent cosmological data from the Planck satellite may provide a hint of support–just a hint, but an intriguing one.

The suspicion that we are victims of a kind of heat death arises from an apparent conspiracy in the laws of physics. On the one hand, quantum physics seems to contain what Einstein called a “spooky action at a distance,” with superluminal influences between remote entangled systems. On the other hand, quantum physics also makes it impossible to send faster-than-light signals. It is as if something is going on behind the scenes which we are not allowed to control. Why is our world fine-tuned in this way? One answer is that a quantum analogue of classical heat death has already occurred in our universe–at the deeper level of so-called hidden variables.

Hidden variables are hypothetical features of the world (what physicists call “degrees of freedom”) that can explain the apparently random outcomes of quantum measurements. The best-known example of a hidden-variables theory is the pilot-wave theory proposed by Louis de Broglie in 1927 and further developed by David Bohm in 1952. There the hidden variables are simply trajectories for whatever particles or fields a system may contain. Normally quantum mechanics says that there are no well-defined trajectories.

A hidden-variables theory will agree with quantum mechanics only if the variables have a special quantum equilibrium distribution, analogous to thermal equilibrium. It is because of quantum equilibrium that superluminal influences cannot be used for superluminal signaling. When hidden variables have the equilibrium distribution, the signals average out to zero. If the hidden variables instead had a nonequilibrium distribution, the underlying superluminal signals would become observable and controllable. Relativity theory would be violated; time would be absolute rather than relative to each observer. The Heisenberg uncertainty principle would also be violated.

By this reasoning, there is no real conspiracy. We cannot use entangled systems to send superluminal signals simply because we happen to be stuck in a state of quantum equilibrium, just as hypothetical beings in a classical heat death would not be able to convert heat into work.

But why exactly are we stuck in quantum equilibrium? Pilot-wave theory itself suggests an answer. Theoretical studies and computer simulations have shown that, if a system begins with a nonequilibrium distribution, then, because of the complex motions, it settles very rapidly into equilibrium. This process is analogous to thermal relaxation–the way, for example, gas molecules rapidly spread out uniformly inside a container (figure at left).

Now, all the matter that we see has a long and violent astrophysical history that ultimately traces back to the big bang. If the universe began in a state of quantum nonequilibrium, relaxation may have taken place very rapidly in the earliest moments of the hot big bang. Today, everywhere we look we should expect to find quantum equilibrium, as indeed we do. The feared heat death of the universe has in fact already occurred! To be sure, it takes a rather different form than could have been anticipated in the 19th century.

Even granting that all this could be true, one might conclude that no evidence for hidden variables will ever be found, since there would be little prospect of finding nonequilibrium today, nearly 14 billion years after the big bang. There may, however, be a way. Using the relic radiation known as the cosmic microwave background (CMB), it is possible to test quantum mechanics in the very early universe, potentially probing a time before the quantum heat death took place.

The CMB provides a snapshot of the universe as it was about 400,000 years after the big bang (figure at top). At that time, the universe was almost but not quite homogeneous. As a result, the CMB contains a pattern of hot and cold spots–small ripples in temperature. According to the leading model of the very early universe, known as inflationary cosmology, these ripples were seeded by fluctuations in a quantum field that existed at much earlier times during a period of accelerating expansion. If this early quantum field was in a state of quantum nonequilibrium, anomalies would appear in the pattern of ripples in the CMB.

What kind of anomalies should we expect? There are many possibilities, but one stands out as particularly simple and natural. A rapid expansion of space in the very early universe can suppress or retard the relaxation process over sufficiently long distances. We would then expect anomalies in the CMB at the longest wavelengths. Specifically, at such wavelengths we would expect to see a quantum noise deficit, because complete relaxation would not have taken place at these wavelengths.

Recently, Samuel Colin of Clemson University and I have developed a detailed computer simulation that illustrates this. The figure at left shows the time evolution when space is not expanding. The right column is the (changing) probability distribution predicted by quantum mechanics; the left shows a nonequilibrium distribution that evolves in time according to pilot-wave theory. (Time runs downwards.) The two distributions quickly become virtually identical: the system relaxes.

The figure at right shows the comparable time evolution when space is expanding. Now, the system does not fully relax. In particular, at the final time the width of the nonequilibrium distribution is smaller than the width of the quantum distribution. This translates into fewer fluctuations in the CMB on large scales.

Intriguingly, the Planck satellite has observed just such a lack of large-scale fluctuations. Our model provides a natural mechanism that can explain it. There could, of course, be other explanations. The deficit might even be just a chance fluctuation. Further analysis is required to settle its true nature.

Has new physics been observed in the CMB? We do not yet know. But one thing is certain: inflationary cosmology provides us with a fascinating new laboratory in which to test the foundations of quantum mechanics.

Antony Valentini is professor of physics at Clemson University. He is co-author, with Guido Bacciagaluppi, of Quantum Theory at the Crossroads

CMB image courtesy of ESA and the Planck Collaboration; diagrams by Antony Valentini