Relativity’s time dilation may limit the quantum world

A new theoretical paper has tackled the phenomenon of quantum decoherence, the process by which objects slip out of the quantum world and start behaving classically. The paper approaches this in a new way by applying an effect of general relativity to decoherence. The paper claims that gravity is the key to the disparity between the weird quantum world and the everyday, familiar world of human-sized objects in which we live.

Schrödinger's cat is an example of a quantum system which might decohere due to time dilation - and myriad other interactions.

Decoherence is a concept central to quantum mechanics. Essentially, a quantum particle, unlike a macroscopic object, can exist in a superposition of different states. This means that in a real, physical way, it exists in all those different states at the same time (with varying probabilities; the stronger the probability of a state, the more strongly the particle inhabits that state).

These quantum states include things like the particle’s spin, charge, energy, and location. So in effect, when a particle is in a super-position, it can be in multiple places at once—like when photons or particles interfere with themselves. This marks the obvious difference with our macroscopic world, where we can never see an object inhabiting two places at the same time. (Or spinning in two directions at the same time for that matter and so on.)

Big vs. small

But coherence is fragile. Any interactions with the particle’s environment can make the particle decohere. When it does, all those simultaneous states collapse to a single state, and things start behaving in a more intuitive, classical manner. The more a particle interacts with its environment, the further it decoheres and the fewer states it occupies.

That may be why we observe larger objects acting like they have just one location. Large objects are more complex and interact with their environments in a myriad of ways, so they're always acting classically. The larger the system, in other words, the less likely it is that it would ever occupy a superposition of states. But it’s not clear exactly where the cutoff line is. Researchers have been able to observe larger and larger objects (including microscopic ones) exhibiting quantum behavior, but they’ve no hope of ever observing this in large objects like soccer balls, much less in humans. So what’s the biggest thing that can be observed to exist in a superposition? And why?

To answer this question, the researchers examined decoherence in the presence of gravitational time dilation, which is a consequence of general relativity. Time dilation is a well established, if perhaps counterintuitive, phenomenon. Basically, the closer a clock is to a gravitational field (like the Earth), the less time it will measure compared to a clock further away.

And this isn’t just an illusion—the two clocks will actually experience different passages of time. If instead of clocks, they were people born on the same day at the same time, one would gradually become older than the other. This is a noticeable enough effect that GPS satellites have to compensate for it, lest they get out of sync with the ground and give wrong directions.

The effects of gravity on quantum systems are often not studied, because it’s generally thought to become relevant only in the most extreme situations. Aside from special cases like black holes, gravity generally has a very weak influence on quantum particles, and is negligible compared to the other forces such particles experience.

But the researchers reasoned that time dilation might have a significant effect on a quantum system that changes with time. The researchers calculated the effect of time dilation on a quantum system that’s composed of multiple particles, like a molecule. The individual particles comprising these systems are vibrating constantly. But vibration occurs over time, so if there’s a difference in the rate time passes in the system, the researchers reasoned, it would cause the particles’ frequencies to get out of sync with each other.

The vibrating particles’ frequencies are entangled with the center of mass, so the center of mass decoheres when they get out of sync.

The results

The authors found that time dilation does cause decoherence in the system, at least to a degree. Under Earth’s gravity, according to their calculations, the system’s center of mass does decohere and essentially acts like a classical object. But it’s worth noting that the system as a whole does not. The individual particles moving around that center of mass can still exist in superpositions.

This would make a difference in two-slit experiments, since the center of mass would have to go through one of the slits, acting like a classical object rather than a quantum particle, which would change the outcome. But for other kinds of measurements, it might not.

“Alas, the effect is exceedingly tiny,” notes physicist Sabine Hossenfelder in her blog, “smaller even than the decoherence induced by the cosmic microwave background.”

Because their calculation didn’t include any other environmental effects that might cause decoherence, they claim the effect should happen even in a isolated system, with only gravity causing it to decohere. This has led to other sources reporting that quantum systems will decohere into just one state without any interaction with the environment besides gravity. This doesn’t seem to be the case; according to Hossenfelder, the effect would decohere the system slightly. In other words it would reduce the number of states the system can occupy, but it wouldn’t necessarily reduce that number to one. The system would still exist in a superposition.

To look into this further, the authors also calculate the time it would take a system to decohere completely (to a single state). This depends on the size and complexity of the system, so for an object the size of a human, it would take a thousandth of a second to decohere. But the decoherence time for smaller particles, like the ones commonly involved in quantum physics experiments, is much greater: about a year for a system made up of 100 or so particles.


So time dilation doesn’t seem to be the reason that systems decohere, though it’s probably one of many reasons. It could be a drop in a sea of effects causing decoherence.

This still could be an important discovery. Even if it doesn’t account for the full difference between the quantum world and the macroscopic one, it does contribute to it—and if scientists are to build a more detailed picture of the transition, they’ll need to take many different effects into account. The effect of time dilation may be a less prominent one, but it’s a piece of the puzzle nonetheless, and certainly a fascinating one.

"I am overjoyed to see any new ideas on the influence of gravity in quantum objects," said experimental physicist Holger Müller of the University of California at Berkeley, not part of the study’s team.

As with any theoretical work, the real test comes when it can... well, be tested. The authors use the final section of their paper to discuss possible tests. The key is to eliminate other sources of decoherence, which means the system being tested needs to be rather complex, and conditions have to be perfect. Experimenters would have to supercool the particles or introduce them to an ultrahigh vacuum to have any hope of observing the effect. Hossenfelder is skeptical that it can realistically be tested, but the authors remain optimistic. Only time, relativistically dilated or otherwise, will tell.

Nature Physics, 2015. DOI: 10.1038/NPHYS3366 (About DOIs)

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