Bell's inequality and experiment

[leonid.ge]

TL;DR

Is Bell theorem needed if an experiment alone can prove spooky action on distance?

Why need in Bell inequality theorem, when you can just do the experiment with entangled and not entangled particles. If the correlation for entangled particles is notably higher, you deduce there is spooky action in distance.

 

[.Scott]

A simple correlation could be explained by a "hidden variable" shared by each of the entangled particles.
In other words, the Bell Inequality demonstrates that the final measurement results had not been determined all along.

The central issue is called "local reality" - and the challenge on one side (the "non-spooky" side) is to model the measurement results with a system that does not violate "local reality" - that is, by showing that the observed measurement results can be explained with a model where the information needed to determine those results is available without exceeding the speed of light. The challenge on the other (spooky) side is to describe a measurement where no such explanation is possible.

So, if you only measure each of the entangled particles along two pre-set orientations, then model the particles as having predetermined "spin angles" that are opposite of each other, and finally model the measurement as a function of that "spin angle" relative to the orientation of the measurement device, then you're model can explain everything without resorting to spooky action at a distance. Basically, you are saying that the particles coordinated the measurement results by creating and sharing a random angle value that they carried with them from their shared starting point to their two different targets. And there's nothing "spooky" about that.

But Bell (champion of the "spooky side) created an experiment where the measured results of those particles (or, specifically, how those measurements correlate) depended on the orientation of the measuring device. When I explain the Bell experiment, I make a small adjustment to make the arithmetic easier to follow. These two entangled particles are heading for two targets that will measure the spin of the particle along one of three axis. In Bell's description, the "home" position for each of these measurements is where the particles are being measured on the same axis and therefore the results for the two particles will always be opposite. In my experiment, the home position is rotated such that when that home position is chosen by both targets, the results are the same. For each target, there is a home position and two side rotations. Each measurement is made at either A) Home-15 degrees, or B) Home, or C) Home+15 degrees. When both targets happen to pick the same measurement setting (A, B, or C), the results are always the same. But when they are different (off by 15 or 30 degrees), they will agree only a percentage of the time.

Here's the spooky part: When they are off by 30 degrees, the measurements disagree by more than double the amount that when they are off by 15 degrees. It's like saying that the distance between A and C is more than the sum of the distances between A to B plus B to C. It's like the universe is cheating. There is no way to set the entangled particles up ahead of time (with a hidden variable) to create this result. The agreement correlations are necessarily a function of the two measurement orientations - but even when the measurement events are made "simultaneous" (ie "spacelike") , and therefore the needed information is presumable not available to the measuring devices, the AC>(AB+BC) correlations is still observed.

 

[PeroK]

TL;DR Summary: Is Bell theorem needed if an experiment alone can prove spooky action on distance?

Why need in Bell inequality theorem, when you can just do the experiment with entangled and not entangled particles. If the correlation for entangled particles is notably higher, you deduce there is spooky action in distance.

"Spooky action at a distance" was a pejorative term used by Einstein, who was skeptical of QM.

 

[PeterDonis]

Why need in Bell inequality theorem, when you can just do the experiment

The purpose of Bell's theorem is not to prove what happens in experiments. It is to rule out certain possible underlying models of what happens in experiments.

 

[.Scott]

"Spooky action at a distance" was a pejorative term used by Einstein, who was skeptical of QM.

It was pejorative. But I like it because it calls attention to the very non-intuitive results you can get from QM. If you don't see what is "spooky", you are missing something really big and really central from QM.

 

[Nugatory]

If the correlation for entangled particles is notably higher, you deduce there is spooky action in distance.

Not necessarily, although exploring that possibility will take us into an interpretational discussion - many good threads in the interpretation section.

“Action at a distance” is generally understood to imply an asymmetric causal relationship: the action causes some effect on the remote particle; and the action has been set in motion by the measurement of the near particle. But as the discussion in your earlier thread shows, the “action” in spacelike separated entanglement measurements behaves differently: cause and effect cannot be usefully distinguished and the relationship is symmetrical. This is not how a superluminal influence would propagate.

If we reject one or more of the assumptions (both stated and implicit) in Bell’s proof we find possibilities other than action at a distance. One possibility is superdeterminsm. Another goes under the broad umbrella of “non-realism”, and involves accepting contextualism or rejecting counterfactual definiteness.

Of course none of these possibilities are especially satisfying - but then again neither is a superluminal causal influence.

 

[javisot]

TL;DR Summary: Is Bell theorem needed if an experiment alone can prove spooky action on distance?

Why need in Bell inequality theorem, when you can just do the experiment with entangled and not entangled particles. If the correlation for entangled particles is notably higher, you deduce there is spooky action in distance.

It's been many years since they simply called it "spooky action on distance"

https://t.co/y4Xn3qw2P1
https://t.co/CBau5AxMzD

 

[FactChecker]

A good experiment is very tricky and would probably never have been done unless Bell's Theorem showed that entangled particles could give results different from simple random behavior. The trick is to get results from entangled particles with no possibility of a "hidden variable" biasing the results. Fairly recently, random inputs to an experiment were derived from greatly separated sources in the Milky Way galaxy in order to remove the possibility of any "hidden variable" that could spoil the results. Even that might not satisfy the most die-hard skeptics.

 

[.Scott]

A good experiment is very tricky and would probably never have been done unless Bell's Theorem showed that entangled particles could give results different from simple random behavior. The trick is to get results from entangled particles with no possibility of a "hidden variable" biasing the results. Fairly recently, random inputs to an experiment were derived from greatly separated sources in the Milky Way galaxy in order to remove the possibility of any "hidden variable" that could spoil the results. Even that might not satisfy the most die-hard skeptics.

Most commonly, the term "hidden variable" referred to information carried independently by each of the two "entangled" particles that could be used to get the particle measurements to line up with QM expectations. It would also include any information transmitted to each measuring device that could affect the results of the measurement, given the chosen measurement orientation.

When Bell's article was published, the term "hidden variable" was not applied to contrivances of the universe that kept any measurement orientations from being made that could result in contradictions to the QM expectations.

When scientists arrange to have the two measurement decisions based on starlight from opposite corners of the galaxy, they are hedging against much more than the "hidden variable" problem. Their purpose is to make sure that any information used to determine the orientation of one target is not available to the other target. So, they are addressing the "spacelike" aspect of the experiment.

I certainly thank them for doing this, but it is a check that only the deliberately paranoid would find necessary. Just to be clear: having a person at each detector picking the next measurement angle at his own whim would not be sufficiently random - because they want to hedge against the possibility that basic Physics could prevent those two people from making truly independent decisions.

On a much lower level of paranoia, I did have misgivings about some of the claims make in that original Bell article. At the time, the percentage of particles measured at each device was tiny - generally less that a percent or two. With such a low hit rate, a model could readily be made where the hidden variables affected the likelihood of a particle being detected at certain measurement orientations.

So, for a while, improvements in the experiments were really critical. But that is history. Today, the experiments have high enough efficiencies to completely close the door on that kind of hidden variable explanation.