# Bell's inequality

1. Dec 8, 2015

### thinkandmull

I was wondering if someone could explain to me how John Bell and Anton Zeilinger have attempted to prove there is no definite reality in the sub-atomic world. How could it ever be proven there are no hidden variables that humans just don't or can't know about? If I am not mistaken, Einstein for example did not prove there is no ether, just that we can't detect it.

THANKS

2. Dec 8, 2015

### Heinera

Last edited: Dec 8, 2015
3. Dec 8, 2015

### Staff: Mentor

You will also find some good stuff, including a link to Bell's original paper and some simpler but analogous arguments at http://www.drchinese.com/Bells_Theorem.htm, maintained by our own @DrChinese . Read what you find there, follow Heinara's references, and if you still have questions, search this forum for some of the 93 megabazillion previous threads on the subject - chances are that any objections/questions you have have been discovered before. And this book by Louisa Gilder is a good layman-friendly historical summary.

And then if it's still not clear.... Ask away.

Bell's theorem is surprisingly subtle for something so simple in hindsight. The problem was starkly posed by Einstein in 1935, and it was nearly three decades after that before Bell noticed the implications of the correlations between three different observables, as opposed to two.

4. Dec 8, 2015

5. Dec 8, 2015

### thinkandmull

What general argument can I give to lay people who say "there is no way to know if there are hidden forces at work"?

6. Dec 8, 2015

### Weddgyr

Assumming they mean local hidden forces/variables, you can say that any such forces, when measured, produce data which must satisfy certain constraints. Quantum mechanics produces data which violates these constraints, and so cannot be the result of such hidden forces. You can add that the constraints themselves are given by Bell's Theorem and are accessible to even the modestly mathematically inclined.

7. Dec 9, 2015

### RUTA

I think the easiest way to see how QM can imply no counterfactual definiteness is Mermin's explanation of the Hardy experiment. I give an overview here: https://www.physicsforums.com/insig...elayed-choice-no-counterfactual-definiteness/

Mermin also argued against the existence of "instruction sets" aka "counterfactual definiteness" in his paper: Bringing home the atomic world: Quantum mysteries for anybody. American Journal of Physics 49, 940-943 (1981). I give an overview of that paper and its quantum liar implication here: https://www.physicsforums.com/insights/quantum-liar-experiment-instantiation-mermin-device/

Mermin also wrote a simple explanation of how the GHZ experiment implies no instruction sets in his paper: Quantum mysteries refined. American Journal of Physics 62 (10), 880-887 (1994). I give an overview of that paper and its Many Histories implication here:
https://www.physicsforums.com/insights/greenberger-horne-zeilinger-experiment/

8. Dec 9, 2015

### phyzguy

The link given by Nugatory in post #4 is quite accessible to the lay person, and doesn't require any advanced mathematics, just logical thinking. It is old, and since that time there have been many more experimental tests that show that the universe obeys quantum mechanics and violates the Bell inequalities, and hence cannot be locally realistic.

9. Dec 9, 2015

### thinkandmull

Is this getting into philosophical questions though? A theist could still believe that God is the unknown factor, or an Indian mystic an impersonal force he calls Brahman. Is QM really able to refute these claims? I think that was what Einstein was trying to say.

10. Dec 9, 2015

### thinkandmull

Or maybe Einstein however believed the unknown laws could be found apart from God. He did like to read Spinoza though, who thought the world was God in a sense

11. Dec 9, 2015

### RUTA

The philosophical issue here is one of ontology, not epistemology, so no one is questioning the method of physics. Physicists have a working ontological model whenever we employ our equations, usually they're tacit and widely agreed upon. In the "weird" QM experiments of interest here, ontology is exactly what's being discussed. Such discussions are germane to progress in physics, e.g., phlogiston, ether, atoms, etc., so physicists of the highest order have engaged this topic. The goal of such discussions from a physicist's perspective is to generate new theories, not to create despair or advocate for religious belief.

12. Dec 9, 2015

### .Scott

Imagine writing three sets of 1's and zeros each 1000 bits long, sets A, B, and C. Then you compare the sets - matching up the first bit with the first bit, the second with the second, as so on. When you compare A with B, you get a 10% difference. When you compare B with C, you also get a 10% difference. But when you compare A with C, you get a 30% difference. The problem is how can A be 30% different from C when it's only 10% different from B and B is only 10% different than C. There should be a core 80% to 90% of the bits that are common with each other - so A should be no more than 20% different from C.

In very general terms, that is the problem present when the Bell Inequality is violated. You are measuring the differences among three groups of particles, and the result is "unreal".

13. Dec 9, 2015

### thinkandmull

Oh now I get what the argument is. It's similar to Schrodinger's cat. In the world of classical physics though, does quantum mechanics apply? I don't see that atomic phenomena alone can prove that my spouse's body does not exist unless someone is seeing it.

14. Dec 9, 2015

### Staff: Mentor

Quantum mechanics applies to macroscopic and classical systems just fine. If you calculate the quantum mechanical behavior of a large number of individual particles assembled into a classical object, you'll come up with the classical result. It has to turn out that way, because classical physics provides an accurate description of the behavior of objects composed of a large number of particles. Therefore any correct theory of the behavior of particles has to predict that they behave classically when assembled into the large collections we call classical objects - otherwise it wouldn't be a correct theory of the behavior of particles. (This was understood in a heuristic sort of way from the beginning, but it took a lot longer before the non-trivial math was worked out in the middle of last century - google for "quantum decoherence").

In particular, quantum mechanics does not say that your spouse doesn't exist, or that the moon isn't there when no one is looking, or especially that Schrodinger's cat is both alive and dead (or neither dead nor alive, or in any other weird state). Either there's a classical dead cat in the box or there's a classical live cat.

15. Dec 10, 2015

### RUTA

I would add there is no cut between the classical and the quantum, you can get a cat or your spouse into a superposition state if its screened off. It's been done with molecules of over 100 atoms (http://arstechnica.com/science/2012...ith-big-molecules-approaches-the-macroscopic/). And if you do that, the cat or spouse can exhibit no counterfactual definiteness, which is what I assume you mean by "doesn't exist."

16. Dec 10, 2015

### .Scott

Not that I have a cat or spouse that I would like to "screen off", but how long would you need to screen them off before there would be noticeable affects of superpositioning?
----edit----
Actually, that article you cited is based on the double slit experiment. So... If I was tossing 5Kg cats at two slits, I would want the wavelength to be wider that the cats - say 50cm. With λ = h/p, p = h/λ, the momentum would be Planck's constant divided by that 50cm = 6.62607004 × 10-34 m2 kg / s / 0.5m = 1.325 × 10-33m kg / s.
Dividing by 5Kg to get velocity: 1.325 × 10-33m kg / s / 5Kg = 2.65 × 10-34m/s.
Okay, to get a good interference pattern, the feline trajectory should be roughly 20λ or more. That's 10 meters. So the transit time for the cats would be 10m / (2.65 × 10-34m/s) = 3.77 × 1034 seconds = 12.0 × 1026 years. Or about a hundred million billion times the age of the universe.

Last edited: Dec 10, 2015
17. Dec 10, 2015

### Staff: Mentor

That's not quite what I meant - I was responding to the original poster's use of the term "doesn't exist" and his misunderstanding of Schrodinger's cat.

However, you are making a point that I agree with - quantum mechanics does not say that these weird macroscopic states cannot exist, it says that they won't happen (except when we make extraordinary efforts to temporarily suppress decoherence in what are still very small, barely macroscopic systems). There's an analogy with classical statistical mechanics here: statistical mechanics doesn't say that a volume of gas at equilibrium cannot violate $PV=nRT$ (it can - at any moment every particle has a 50% probability of moving towards the edge of the container so we might get lucky and find a large majority of them are doing so), it says that the probability of this happening is so low that for all practical purposes it never happens.

18. Dec 10, 2015

### Staff: Mentor

Not that I dare to claim having understood both statements in their most inner essence, but it seems to me worth debating it:
http://phys.org/news/2015-12-quantum-physics-problem-unsolvable-godel.html

19. Dec 10, 2015

### RUTA

The numbers are correct, but far more problematic for actually making quantum cats is keeping them from interacting with the environment during the incredibly long time it takes them to get from Source to detector. It's certainly not technologically feasible to screen off a cat. My point is that QM says there is no classical-quantum boundary in principle, even if such boundaries exist in practice.

20. Dec 10, 2015

### .Scott

I think we both make the point that it's not practically feasible. Personally, I was more impressed with the problem of keeping the cats (and the investigators) alive for that long. But certainly keeping the cats isolated in a weightless environment is a stretch as well.