# Reality, locality, and universality in the EPR paradox

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?

• Just a remark about your 1.5 mile long rope: the information that the rope was cut can certainly not arrive at the two ends faster than with the speed of light (probably even much slower, i.e. by the speed of sound in the rope). The speed of light limit is not absurd, but a consequence of special relativity, which is experimentally verified and generally accepted in physics. The speed of sound limit is a consequence of the chemical bonds in the material, which limit the propagation speed of local perturbations like the cut. Commented Feb 18, 2019 at 21:25
• But that seems to suggest that the rate at which sound travels down the rope determines how long the rope is. I'm not challenging the speed of light as a fundamental limit, I'm wondering why changes to the system are dependent on the speed of light. If the particles are entangled, then their states are dependent on the system mutually defined by each - why should there be a lag in changing behavior when a change is made to the system that defines those behaviors? Sort of like pressing on a bubble to induce curvature - I change the diameter, volume, and density of gas within instantaneously.
– user223099
Commented Feb 18, 2019 at 21:43
• physics.stackexchange.com/questions/203831/… Commented Sep 20, 2022 at 6:55

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.

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.

• Thanks for the response, it was very clear. It also follows most of the arguments that I have read on the matter and doesn't really get to the heart of my question, which is almost certainly a function of a lack of clarity on my part. In part A of my question, I'm wondering why we consider the particles at some large separation transferring data across that distance. If the spin of each particle is a defining attribute of the total system, why cannot a change in spin be expected to instantly redefine the entire system and thus the spin of the other particle? Why should distance matter?
– user223099
Commented Feb 18, 2019 at 22:00
• I'd also suggest that many of the "paradoxes" of QM, such as superposed states allowing for a particle to be in two places at once, are only paradoxes if we constrain ourselves to envisioning the superposed wavefunctions as separate entities. If you accept that linear combination of two wavefunctions leads to a unique and novel third wavefunction that retains all of the information of its component states, both of which can be independently modulated to dynamically and instantly redefine the new composite wavefunction, you no longer have a paradox. Can we do the same with entangled particles?
– user223099
Commented Feb 18, 2019 at 22:16
• I guess that your doubts fall within the realm of the Copenhagen interpretation of QM, where it is assumed that the two spins are part of a single system, which simply "collapses" instantaneously to one of its possible states when the measurement occurs, and this is not viewed as a problem. EPR thought the contrary: for them, it constituted a violation of the principle of locality, on the grounds that once the spin of the first particle is measured, the second particle behaves as if it "knows" about it, which suggests that somehow the information propagated between the two particles. Commented Feb 18, 2019 at 23:13
• I suppose what I'm suggesting would work to augment the CI by making the non-locality concern disappear. Instead of wondering how information is passed from one particle to the other over a distance, any local change to one particle would be considered a universal change to the system and this would necessarily cause a change in the behavior of the other entangled particle without any lag. I appreciate that what I'm describing as the "system" is pretty vague. It seems that pilot wave theory suggests something similar but invokes the equivalent of the "ether" as the substance of pilot waves.
– user223099
Commented Feb 19, 2019 at 1:10