Reality, locality, and universality in the EPR paradox

Question

Apologies if this has been asked before. I did some searching but didn't see it anywhere asked quite like this. Thanks in advance for any insights.

Caveat: I am an organic chemist and thus appreciate qualitative descriptions of the behavior of matter more than quantitative ones and tend to struggle when I can't envision a physical correlate for mathematical descriptions. I have found simple and intuitive analogies that readily explain away many of the supposed "paradoxes" of quantum mechanics, but I am stuck on this one.

It's my understanding that locality can be a problem for various interpretations of QM since entangled particles at infinite separation appear to instantaneously determine each other's behavior. The argument goes something along the lines of:

"No information can be transferred from one particle to another faster than the speed of light, so the instantaneous exchange of information between entangled particles separated by some infinite distance must be a violation of the principle of realism or locality."

My question is this: A) why is it assumed that information must be exchanged between entangled particles when one is disturbed/measured and B) why must some intermediary of this information that is constrained by the speed of light be invoked in the sharing of this information?

If I tie a 1.5 mile long length of rope between two trees and then cut the rope at a point 1/3 of its distance between the trees, how long does it take for the far end of the rope to know that it is now only one mile long? It seems the answer is that there is no lag and no need for the invocation of the speed of light - the rope is instantaneously shorter along its entire length in the instant of its cutting. In other words, the system is instantaneously and universally redefined as soon as I interfere with it at any point and there is no need to complain about "locallity" (i.e. arguments that "the cut was made a mile away, therefore it can't instantaneously affect the far end of the rope" are absurd - one instant the rope was universally 1.5 miles long, the next instant it was 1.0 miles long).

If we are going to then consider two entangled particles, the various wavefunctions describing the various behaviors of the particles are not only descriptive of the individual particles but in fact define the entire system universally, do they not? This being the case, if we interfere with either of the particles, thereby introducing a change to a component wavefunction, aren't we necessarily and by definition redefining the entire system? And isn't the entire system redefined universally in the very instant of the interaction, thereby resulting in any dependent change occurring instantaneously (like a spin-flip in the other particle, for instance)? Why is there an expectation of some time lag that is limited by the speed of light any more than in the instance of cutting our rope above?

Answer 1

Short answer:

A) Because if no information was exchanged between the particles, QM would be an incomplete theory (in the sense explained below).

B) Because if locality is assumed, information cannot travel faster than the speed of light, and thus any such intermediary would have to abide by that constraint.

Long answer:

I suppose that the first thing that should be noted is that any solution to the EPR paradox (the one you describe) depends on the adoption of a particular physical interpretation of QM, and I guess it's fair to say that there's still no consensus in the physics community regarding which choice is the correct one (more on that at the end).

Now, to answer your questions more concretely, one must be careful to separate two key concepts: locality and what Einstein called completeness. The first simply means that an event can only directly influence its "close neighbourhood", where "neighbourhood" should here be taken in a spacetime sense and the "close" part indeed refers to the propagation of information at or below the speed of light. Completeness, on the other hand, alludes to the idea that "every element of the physical reality must have a counterpart in the physical theory" - in other words, the theory must describe Nature in its totality if it is to be deemed complete.

The problem with the EPR paradox is that, in QM, the spins of the entangled particles are assumed to be genuinely random before any measurement takes place. In other words, QM claims that Nature is, by itself, probabilistic, and thus the fact that QM calculations are also probabilistic merely reflects the true nature of Nature. In practice, what this means is that the particles themselves do not know beforehand (i.e., before the measurement takes place) if they'll have spin up or down. That addresses your question A: if you assume that no information is exchanged between the particles when they're measured, then you must also assume that the particles' spins were already determined before the measurement (otherwise, how could it be that one always turned out to be up and the other down, i.e., that the measurement of the two spins are always perfectly correlated?). However, doing so is tantamount to admitting that QM is an incomplete description of Nature, as the theory is ostensibly claiming it cannot predict exactly the spins of the particles because Nature itself does not pick the spins before the measurement takes place.

Now, of course a possible solution to the problem raised in the previous paragraph is to say "Fine, the particles do exchange information.". However, that will quickly put you at odds with the principle of locality, because then you must assume that somehow the particles communicate with each other instantaneously (again, otherwise how could it be that the two measurements are always perfectly correlated?).

So, as things stand, one has that either QM is incomplete, or locality doesn't hold. The real conundrum is that physicists have very good theoretical and experimental reasons to believe that both of those statements are false, i.e., that QM is complete and locality is an exact principle of Nature. Thus, accepting the EPR paradox forces one into a very uncomfortable situation.

I hope this long soliloquy managed to explain a bit better what are the issues with the described physical situation. You can find a lot more about this discussion here.

As a final note, I should say that at the root of many (if not all) of the paradoxes that "plague" quantum mechanics is the fact that, to this day, nobody really has a very convincing answer to the question "What's the physical meaning of the mathematical formalism that we use to describe quantum phenomena?". Steven Weinberg made this point as recently as 2017, the key assertion being his statement that

Today there are two widely followed approaches to quantum mechanics, the “realist” and “instrumentalist” approaches, which view the origin of probability in measurement in two very different ways. For reasons I will explain, neither approach seems to me quite satisfactory.

Answer 2

It seems the answer is that there is no lag and no need for the invocation of the speed of light - the rope is instantaneously shorter along its entire length in the instant of its cutting. In other words, the system is instantaneously and universally redefined as soon as I interfere with it at any point, and there is no need to complain about "locality" (i.e. arguments that "the cut was made a mile away; therefore, > it can't instantaneously affect the far end of the rope" are absurd - one instant, the rope was universally 1.5 miles long; the next instant it was 1.0 miles long).

If the rope was relaxed, you are right that its length would instantly become $1$ mile long, and this would make no difference to the tree it was attached to because there is no tension in the string. If the rope was initially under tension, such that the trees are bent towards each other by the tension, then when the rope is cut, the trees do not instantly return to straight and vertical. It takes time for the change in tension in the rope to travel along the rope to the attached tree when the rope is cut. It is about the finite speed at which force can be transmitted and not about the speed at that perceived length is transmitted, although it would still take time in the relaxed state for someone to transmit the information to you that the rope has been cut, because otherwise how would you know?

Consider this analogy. Imagine a weight lifter's barbell having circular weights welded to the ends of the bar so that they cannot rotate independently. If you were to paint vertical radial pointers on both weights, then if you rotated one pointer to horizontal, then the other would 'instantly' change to horizontal as well. Well, it appears instantaneous if the bar is only a metre long, but if it is several kilometres long, it takes non-zero time for the torque to be transmitted along the length of the bar. If we have two entangled photons with the same polarisation, then if one has its polarisation changed, the other instantly rotates to the same polarisation. The entangled photons behave as if they are connected by a rigid bar with infinite speed of torque transmission. They behave as if they are parts of a single particle in a single location. It is as if they are connected by their own personal micro wormhole that allows the connection to take a shortcut through spacetime (although I am not claiming that is what is actually happening.) There are various interpretations of what is 'actually happening' in quantum physics, and until someone comes up with an experiment to distinguish between the various interpretations, we cannot say for sure what exactly is physically happening.