Wednesday, June 12, 2019

Constructing Bell paradoxes

An economics professor and puzzle author posted this variant of a Bell Theorem paradox:
The Brain Teaser: Today we both chose Tails and both saw green. What colors were on our Heads sides? ...

Possible Resolution I. There are no such coins. You’re right. There are no such coins. But there are subatomic particles that behave exactly like these coins. ...

Possible Resolution II: The coins are very very sneaky and they like to screw around with our minds, so they change their own colors depending on the choices we make, just to fool us. .. .

Possible Resolution III: Neither side of either coin has a color until we decide to examine it, so that on a day when I examine my tails side, it makes no sense to ask about the color of the heads side in the first place.

Therefore I am not allowed to pose this brain teaser in the first place. ...

So where does this leave us?

It leaves us with quantum mechanics, which correctly predicts the result of this experiment, among kajillions of others, and which is incompatible with classical intuitions (as the puzzle in the post is intended to illustrate), but is perfectly consistent with different intuitions which take a while to cultivate, but are not impossible to get used to.
I do not think that these Bell puzzles are helpful in understanding quantum mechanics.

Quantum mechanics was created to deal with a fundamental observed fact: Electricity and light are sometimes seen as waves, and sometimes particles.

If you model them as waves, then the discrete energy values are puzzling. If you model them as particles, then the interference patterns are puzzling.

Heisenberg got around this difficulty by saying that you could think of an electron as a particle, but one where you cannot measure the position and momentum at the same time, as you could if it were really a particle.

All these Bell paradoxes are based on pretending that the election is a particle where conflicting measurements can be made at the same time.

If you think that an electron or photon is a particle, and you want to see something puzzling, just look at the double-slit experiment.

Subatomic particles are not like coins in the above puzzle. Coins have properties like position and momentum that are independent of observation. Subatomic particles have wave-like properties, and the particle-like properties depend on how they are observed. These are simple facts of nature that have been understood since the 1920s.

I often hear of physicists who hope that someone will find a new interpretation of quantum mechanics that will make these wave-particle puzzles go away. Forget it. They are just refusing to accept facts of nature.

2 comments:

  1. ``If you model them as waves, then the discrete energy values are puzzling.''

    There, there, there, Roger! You forgot the role being played by the potential energy function which is a sum of the functions that are singularly anchored into the positions of nuclei (as also in the electronic positions, for the He atom onwards).

    ``Subatomic particles are not like coins in the above puzzle. Coins have properties like position and momentum that are independent of observation.''

    Well said.

    ``Forget it. They are just refusing to accept facts of nature.''

    Ummm... We are being a bit too dismissive here, aren't we? Especially if we also are forgetful of the singularities that impart some indirect measure of locality to everything in QM? ... After all, arbitrary potentials are an impossibility in actual nature, aren't they?

    Anyway, will check out the puzzle later. (Not in a mood to do any new intellectual task for today. Would rather listen to some good old and new songs...)

    Best,

    --Ajit

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