Discussion in 'Physics & Math' started by arfa brane, Apr 18, 2017.
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Ok I didn't phrase that like I should have. But you do compare the objects pairwise, or two at a time.
Which does seem to validate what you say: Bell's theorem is about measurements, not probabilities. But measurement is statistical.
You posted this:
It says "collection of countable things" some number of which (a statistic, surely), possess A but not B.
But you say "nothing to do with probability", I can't see it.
I think we can come out of this if we do not apply wave function description to such scenarios. Rather I would say wave function description is not true in all cases.
Not when testing Bell's Inequality.
I can't tell what that means.
The word probability does not appear. Measurements are what they are, with probability one. They are counted, not guessed.
If we don't use quantum theory, we have none of these problems, true.
We also have no theory capable of handling some measured aspects of the physical world. Violations of Bell's Inequality would be one of the measured and counted outcomes of experiments we would have absolutely no way of explaining.
The problem is that you are making a statement based on available text about violation of inequality.
I urge you, if you are aware, to post here concrete example of inequality violation. Not qualitative but with figures, like the value of Bell's expression should have been x but it is y and y > x so inequality is violated.
Already posted two links to actual papers. Here's a third. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.81.5039
Like most papers technical enough to post the math, it's behind a paywall.
A fourth link, with many references: https://physics.aps.org/articles/v8/123
Google is your friend also.
All are statements, you seem to be accepting these statements at face value. Why not give one example with figures like x,y as stated in previous post.
All the papers, including that claim of 16 order push back on local hidden variable with star light, are statements. Where are two values of x and y, such that y > x. Is it too much of asking?
I'm going to have to start over, I see that now.
Can you state what a valid test of Bell's Inequality would be?
Then, can you explain the difference between the test and a derivation?
http://www.johnboccio.com/research/quantum/notes/paper.pdf This article uses a different statement of the Inequality than I prefer (I'm wary of the use of "probabilities" in the language), but it contains an example of actual calculation - how one might derive the predictions of Bell's Inequality violations in quantum theory.
Any test, of course, involves measuring dozens of particles and counting the outcomes, then comparing these counts with the predictions.
The comparison, the data etc, is normally in the bodies of the papers, not the abstracts.
It's also the same article I linked to in post #471. In response to your "not about probabilities" post # 470.
We aren't going in circles I hope.
Can you explain the difference between a test and a derivation of Bell's inequality? Please.
In my universe, there isn't any difference, you see.
There isn't any difference if by a test you mean an actual physical experiment, and by a derivation you mean a thought experiment, because you have to accept the existence of physical things in either case. If that is, you also accept measurement exists and is physical.
I refer you to a good dictionary of the English language - my preference is the American Heritage Third, but the Oxford and some others work.
I see your dictionary and raise you nLab's "derivation" of Bell's theorem:
Come on, that's proof of Bell's inequality, none is questioning that? Can you give figures for an example where it gets violated? It seems that you are avoiding this.
You could try looking at any experiment in which the inequality is violated, that is, try googling "violations of bell's inequality", you should get lots of results.
So what are you asking for?
1) We formulate and prove Bell's Inequality, derive predictions of measurement outcomes from it. This is a "derivation".
2) We derive predictions of measurement outcomes from quantum theory. This is a "derivation".
3) They disagree, in certain circumstances.
4) We create the circumstances in which they disagree, and perform the measurements, and record the measurement outcomes. This is a "test".
-> They match the predictions of quantum theory, and violate Bell's Inequality.
Conclusion: our world is not classical, at quantum scale.
There is a third possibility: that our bi-valued logic, our theory of reasoning we used in the formulation and proof of Bell's Inequality, does not work for quantum phenomena. And the entire universe rests on a base of quantum phenomena.
The situation might be analogous to the discovery of a need for "imaginary" numbers - and then quaternions - in the calculation of physical forces and quantities.
No paper has any explicit violation figures, all are qualitative statements..
And, we can do this with any countable collection, so let's make it a box full of old coins in say, a container you win at auction. The collection also must have distinct properties for each object (a local bit of information, if you like).
A collection of coins can have all kinds of distinct properties, but it turns out you need at least three that all the coins can have. If that's not true you find a subset that does and say it's large enough (make the box bigger). This is essentially how the author at the link we double-posted, does it.
But also note that Bell himself derived his inequality from Stern-Gerlach spin-measurements, as nLab does. I think that indicates at least, the "1)" is redundant.
If it is, so are the "2)", "3)", and "4)".
I say that because Bell derived his inequality by testing his inequality.
None of the coins need to have any of the properties.
You can't derive Bell"s Inequality from quantum theory or quantum properties, because it
->does not hold in quantum world.<- It would be like deriving the formula "angle A + angle B + angle C = 180 degrees" from triangles drawn on a sphere.
That's not a derivation of the inequality. That's a formulation of the Inequality, a translation of it into the language of the specific situation that is going to be tested.
It's a classical inequality, that has nothing to do with quantum theory at all. There is no evidence that Bell tested that Inequality itself, ever, or any reason for him to have done so (it's pretty clear how it works, by inspection or Venn diagram or the like).
Then how do you tell a coin is a coin?
I know. He derived the inequality after considering the results of a quantum experiment and by making the same two assumptions Einstein, Podolsky and Rosen did. So he must have realised the experiment was a violation. I doubt he felt the need to test the inequality itself because it's obviously true by inspection as you say.
Anyway, despite how it was arrived at, why is it considered to be so important? If you want to design a quantum algorithm, say, will Bell's theorem apply necessarily?
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