Albert Einstein and his colleagues Podolsky and Rosen proposed a simple way to rid quantum mechanics of its most disturbing feature--called non-locality--in which an action undertaken here can affect the result of a measurement undertaken there, even if here and there are far apart. John Bell came up with a way to test Einstein's vision of reality, ultimately showing that Einstein's vision was wrong.That text is correct, but if you listen to the video, Greene says that the world was proved to be nonlocal. He says measuring the spin of a particle can have an effect on a distant particle.

Greene sees the big issue as to whether a spin measurement is a random event at the time of the measurement, or it is predetermined in advance.

Briefly, quantum mechanics is somewhat strange because electrons act like waves, and you cannot measure their position and momentum at the same time. Einstein and others had an idea for replacing quantum mechanics with a classical theory of hidden local variables, because that would be more compatible with his determinism prejudices. Bell and subsequent experiment proved that all those classical theories do not work. The world is quantum.

Bell did not show any nonlocality. He only helped show that the classical theories don't work. Almost everyone was convinced of that in 1930 anyway.

Watching this video will just get you confused. There is no action-at-a-distance.

Greene is very good at explaining a lot of physics, but he really goes off the rails when he talks about Bell's theorem, many-worlds, or string theory.

Dear Roger,

ReplyDelete0. Somewhat unrelated, but let me note it anyway.

1. A few weeks ago, we discussed IAD (instantaneous action a distance) following your post: https://blog.darkbuzz.com/2020/03/trying-to-prove-many-worlds-from-first.html .

In a comment to that post, you had pointed out:

"...if you can suddenly change V everywhere, then you can have instantaneous action-at-a-distance. Relativity and quantum field theory are designed to explain how a field can get from one place to another."

Now, here are my thoughts (which I didn't mention at that time).

1. In the context of QM, the established position is that \Psi is a function of *all* potentials, not just the electrostatic ones. Thus, \Psi is a function of the magnetic field too, if one is present. (Ditto for gravitational and any other fields.)

Now, EM fields don't show IAD; disturbances propagate locally as EM pulse-profiles i.e. waves. Therefore, changes in \Psi, too, cannot propagate instantaneously.

I have little trouble accepting it all.

2. However, I was also just wondering [and this is the "somewhat unrelated" part], what happens if we regard the magnetic field as an *effect* of quantum-mechanical processes, the latter being regarded as more basic?

I mean to say, suppose that the \Psi field does change instantaneously, because the electrostatic field (the "V" in the Schrodinger equation) itself also changes instantaneously. Suppose further that the magnetic field only is an emergent field; it is just another name for some aspects (notably spin-related aspects) of how the combined \Psi corresponding to a *large* number of elementary particles changes with space and time. Suppose that the *emergent* field (which we call magnetism) does show locality (the Maxwellian waves).

In such a case, the EM field turns out to be local, but only at a higher level of abstraction. At a more basic level, everything is governed by just "electrostatic" (inverse-square) V field between charges, and the non-relativistic Schrodinger equation. So, all changes occur instantaneously everywhere.

*In short, what if we regard the magnetic field as a quantum mechanical effect of elementary charges, rather than as a relativistic effect (as Feynman explains in his text-book) of gross bodies?*

3. The above idea isn't as arbitrary as it might seem on the face of it.

Realize, all EM phenomena have been established only in reference to gross bodies, containing a very large number of elementary particles (10^23, to indicate the order). Special relativity is a consequence of Maxwell's equations. If magnetism lies at a higher level to QM, then so does EM. And, therefore, so does relativity. And, therefore, the ideas of locality inspired in the fold of any relativistic theory have no relevance at all at the QM level, because QM now is *twice* basic to relativity: Rel -> Electrodynamics -> QM -> "Electrostatics" i.e inverse-square potential (changing instantaneously, but only between elementary particles)

Just a thought.

But one thing is for certain. Relativity has been validated only in those situations where both multi-scaling effects (from sub-nano-meter scale to meter-scale) and large ensembles (Avogadro) are absolutely relevant ideas. On the other hand, in principle, QM applies to even just two elementary particles separated by a very small distance (small fractions of angstrom or 0.1 nm). So, there.

Best,

--Ajit