Does action at a distance violate any conservation principles?

[syed]

TL;DR

action at a distance

In some interpretations of quantum mechanics, such as Bohmian mechanics, there is the possibility of “action at a distance,” where the behavior of one particle can instantaneously affect another, regardless of spatial separation. I am wondering if such nonlocal influences might violate fundamental conservation principles, such as conservation of energy or momentum.

In particular, since each measurement outcome is ultimately localized in space and time, one would expect each outcome to have a corresponding local cause within its immediate vicinity. If no such local cause exists, and the cause is ultimately the other measurement outcome without a contiguous physical process connecting each outcome through space, then does the result not effectively emerge “from nowhere" locally? Does this not potentially conflict with our usual understanding of conservation laws?

Note that by nonlocal influence, I do not mean a contiguous influence that is faster than light, but rather a truly instantaneous influence of one object upon another without anything propagating through space or time.

 

[PeterDonis]

In some interpretations of quantum mechanics, such as Bohmian mechanics, there is the possibility of “action at a distance,” where the behavior of one particle can instantaneously affect another, regardless of spatial separation.

But such influences are not directly observable. All directly observable results are in accordance with standard QM.

I am wondering if such nonlocal influences might violate fundamental conservation principles, such as conservation of energy or momentum.

Standard QM obeys conservation laws. So any interpretation of standard QM also obeys them, since any interpretation of QM gives the same observable results as standard QM.

since each measurement outcome is ultimately localized in space and time, one would expect each outcome to have a corresponding local cause within its immediate vicinity

"One would expect" doesn't really count here. Scientific models make predictions that can be tested against experiment. So far all of the predictions of QM that have been tested against experiment have been confirmed.

That in itself is of course not satisfying to people who want a story they can tell themselves about "what's really happening", which standard QM does not provide--standard QM is just the mechanism for making predictions, and makes no claims about "what's really happening". Which is why there are various interpretations of QM that attempt to fill in more--each interpretation doing so in a way that's often incompatible and inconsistent with others. Some interpretations try to tell a "local" story, others don't. But since they all make the same experimental predictions, there's no way to rule any of them out. And that includes the experimental predictions of QM that relate to conservation laws.

When you say Bohmian mechanics has what you call "nonlocal influences", all you're really saying is that you don't like the story it's telling you. That's fine--plenty of people share your dislike of the story Bohmian mechanics tells. But there's no way to parlay that into an argument that Bohmian mechanics violates conservation laws--because if there were, the argument would apply to all interpretations of QM, because it would involve actual experimental predictions of QM, and those are the same for all interpretations.

 

[Nugatory]

one would expect each outcome to have a corresponding local cause within its immediate vicinity.

Indeed we might - our mental model of reality, trained by a lifetime of experience with classical phenomena, demands exactly that.

But that's not an iron truth the way that (for example) the irrationality of $\pi$ is. It's an assumption that experience in one domain can be applied in another, and if that assumption gets in the way of understanding the physics we might reasonably drop it.

 

[Demystifier]

I am wondering if such nonlocal influences might violate fundamental conservation principles, such as conservation of energy or momentum.

For intuition, compare it with Newtonian gravity. It also involves nonlocal instantaneous action at a distance. Does it violate conservation of energy or momentum?

You may also think about it this way. Consider two entangled (quantum) particles far away from each other. Experiments show that they are correlated with each other, for example if one of them turns out to have bigger momentum than the other must have smaller momentum, so that the total momentum is fixed, because it must be conserved. But if there is no action at a distance, then how does the other particle knows the momentum of the first particle (which itself is supposed to be random), so that the total momentum can be conserved? It looks a bit mysterious, doesn't it? But action at a distance comes at the rescue, it is precisely the action at a distance that explains how separated particles can conserve the total momentum.

This, of course, is not a proof that action at a distance is necessary for conservation, but it gives a simple intuitive picture of how action at a distance helps in conservation.

 

[PeroK]

Does this not potentially conflict with our usual understanding of conservation laws?

Naively, instantaneous action at a distance ensures conservation. Newton's theory of gravity being a prime example. In particular, Newton's third law (whether acting at a distance or locally) guarantees conservation of momentum.

Whereas, in classical EM we lose Newton's third law - which implies that the momentum of two interacting charged particles is no longer conserved. To correct this, the EM field itself must carry momentum.

In answer to your question, I would say quite the opposite: action at a distance is the simplest way to guarantee conservation laws.

 

[Demystifier]

But on the other hand, the quantum potential in Bohmian mechanics is neither time-translation nor space-translation invariant, so one would expect, by Noether theorem, that neither energy nor momentum is conserved. And that is true in some sense, naively classically defined "energy" and "momentum" in Bohmian mechanics are not conserved during the evolution of the system. However, those "energy" and "momentum" are not what we measure, and Bohmian mechanics should not be viewed as classical mechanics so those naive "energy" and "momentum" do not have much sense even in theory. The measurement theory in Bohmian mechanics provides that the measurable notions of energy and momentum are the same as in standard QM, which are conserved.