Hidden Variables
Bell's theorem - for or against Hidden Variables? - Printable Version

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RE: Bell's theorem - for or against Hidden Variables? - Thomas Ray - 09-12-2016

secur wrote:  "'Buridan's principle' is worthwhile; Lamport's point is non-trivial."

Indeed.  You've got good counterarguments; forgive me for ignoring them, and going to your case for free will: " ... with a conscious being like a donkey or human, it's circumvented by free will - the ability to make an (objectively) random choice."

Time flows in reverse.  We can’t experience time flow in reverse, however, because our brains process data digitally.

Or at least, we think that brains process data digitally; after all, we can convert wavelike information into digital data, and make sense of it.  Sense seems always well ordered, so obviously so that we construct an axiom – the axiom of choice – to guarantee it.  

The axiom of choice is equivalent to free will.

What if choice is not an axiom?  What if randomness is built into the system, such that nature makes random choices continuously in a way that makes our own choices only seem random or non-random?  It boils down to what makes nature comprehensible -- in that same 2006 conference paper, I wrote:

5.6 What is the center point of a space that has no center? Or, what is the median prime number? Because we know that the primes are infinite (Euclid), we know that the question has no answer. On the other hand, an arbitrary choice of endpoints in an ordered prime sequence, or in a finite set of primes, allows us to answer from Zorn’s Lemma, or the Axiom of Choice (which are equivalent). [Mathworld, “Zorn’s Lemma”] Suppose we do not wish to appeal to this axiom. One would ask, is nature well ordered in principle? We know that it is not. Quantum events are discrete and random. 


RE: Bell's theorem - for or against Hidden Variables? - Thomas Ray - 09-14-2016

Now I'll deal with the counter-arguments:

Leslie Lamport wrote: Random vibrations make it impossible to balance the ball on the knife edge, but if the ball is positioned randomly, random vibrations are as likely to keep it from falling as to cause it to fall.

secur wrote:  Wrong, he's ignoring the behavior of unstable equilibria.

There are stable equilibria, too.  They are just less numerous than unstable states.

Leslie Lamport wrote: In classical physics, randomness is a manifestation of a lack of knowledge. If we knew the positions and velocities of all atoms in the universe, then even the tiniest vibration could be predicted.

secur wrote:  Even in classical physics that's not true. But it's irrelevant, because QM makes nonsense of Laplace's "Clockwork Universe".

Lamport is saying that perfect information -- such as the numbers imprinted on the sides of a die -- leads to perfect knowledge.  Yes, it's irrelevant to QM, because we don't have access to perfect information.

In QM as well as classical physics, however, absence of evidence is not evidence of absence.


RE: Bell's theorem - for or against Hidden Variables? - secur - 09-14-2016

TR wrote: I rejoice that it is not so hard to understand!

Note, I said physics is easy for a competent physicist. Not, in general, me! IOW physics is easy for those for whom physics is easy ;-)

Anyway I see what you're getting at. It's basically Christian's point. Since motions in space, in particular rotations, are reversible, it makes sense that we should use a simply connected model. Christian might say, colorfully, that if nature used SO(3) we'd all experience gimbal lock. Since we don't nature must use SU(2). That's plausible, and (as I said long ago when I first glanced at the paper) it's worth pursuing. However the problem comes when, willy-nilly, we assume SU(2) and thus prove that classical experiments can violate Bell-type inequalities. That's not true, as far as I can tell.

TR wrote: Time flows in reverse.  We can’t experience time flow in reverse, however, because our brains process data digitally. Or at least, we think that brains process data digitally; after all, we can convert wavelike information into digital data, and make sense of it.

no question there is a digital aspect to the brain. But it's not simply a bunch of digital neurons which either fire or don't (binary 1 / 0) depending on the firing status of their inputs (other neurons connected along the dendritic network). Today we know it's a lot more complex, and includes analog operations as well. So you can't explain the psychological arrow of time that easily.

TR wrote: Sense seems always well ordered, so obviously so that we construct an axiom – the axiom of choice – to guarantee it. The axiom of choice is equivalent to free will.

Yes, sense seems well-ordered in time; Zorn may be relevant, I suppose. Axiom of choice (AC) is not necessarily related to free will. AC is required only for choosing an element from an infinite set. On the face of it the "free choice" involved in (hypothetical) free will is among a finite set of alternatives, so AC is not needed.

TR wrote: What if randomness is built into the system, such that nature makes random choices continuously in a way that makes our own choices only seem random or non-random?

Nature does make random choices - if you want to put it that way - in QM (not, of course, in classical physics). Free will can be defined as the ability to make a truly random choice, unpredictable no matter how much information we have regarding brain state. Note, I'm not claiming such free will exists; I really don't know. But if it does evidently it must involve QM. No other part of physics implements essential unpredictability.

TR wrote: ... an arbitrary choice of endpoints in an ordered prime sequence, or in a finite set of primes, allows us to answer from Zorn’s Lemma, or the Axiom of Choice (which are equivalent).

No, AC is not required to choose from a finite set.

TR wrote: ... is nature well ordered in principle? We know that it is not.

Right. But our senses seem to be.

TR wrote: Now I'll deal with the counter-arguments:

These weren't counter-arguments, per se, against Lamport's essential idea: that Buridan's Principle is valid and interesting. I agree with that. Rather I was just pointing out a couple minor mistakes in his presentation.

TR wrote: There are stable equilibria, too. They are just less numerous than unstable states.

When balancing on a knife edge there's only one equilibrium point and it's unstable.

TR wrote: Lamport is saying that perfect information -- such as the numbers imprinted on the sides of a die -- leads to perfect knowledge.

True but he's also saying (well, implying) that such perfect info is possible - theoretically if not practically - for "the positions and velocities of all atoms in the universe". But that contradicts Uncertainty Principle.


RE: Bell's theorem - for or against Hidden Variables? - Thomas Ray - 09-17-2016

I just finished a four day stay in hospital. Going to resume this dialogue later.


RE: Bell's theorem - for or against Hidden Variables? - secur - 09-18-2016

Well, take care of yourself! Hope you're back in the saddle soon.


RE: Bell's theorem - for or against Hidden Variables? - Thomas Ray - 09-21-2016

Hi secur,

I'm not up to a discussion of specifics, but the attached 2002 paper summarizes my world view, and my attitude toward statistical theories.  You can stop reading at page 5.


RE: Bell's theorem - for or against Hidden Variables? - secur - 09-22-2016

This is a different tangent, a whole 'nother ball of wax, or can of worms :-) The appropriate place for it would be the Personal Theories forum. Many more details would be needed to evaluate it. For one thing the Reimannian conjecture is not equivalent to the fact that sqrt(N/4) = sqrt(N)/2. Optimistically I'm hoping more details would clarify the connection.

If this paper is of more interest to you, the current discussion has come to an end. Well, it's been fun!


RE: Bell's theorem - for or against Hidden Variables? - Thomas Ray - 09-22-2016

Sure, I understand. You don't get my point.


RE: Bell's theorem - for or against Hidden Variables? - secur - 09-24-2016

That's true, I didn't get your point. But my point was, I didn't see any relevance to what had gone before. Therefore it seems to discuss this paper it's time to start a new thread in "Personal Theories".

Re. hospital, hope you're feeling better!


RE: Bell's theorem - for or against Hidden Variables? - Thomas Ray - 09-24-2016

I have good days and bad days. :-)

Anyway, no, this is not a personal theory -- it's a way to get at an objective theory, and in so doing show that Bell's theorem lacks any  criteria for objective knowledge.  This has been the problem from the beginning, in marginalizing Popper's framework for scientific objectivity.  

Ignore the point where the paper diverges into personal theory.  In fact, ignore the paper altogether.  

Consider the demarcation problem.  Do you agree that it is a problem for science, and for Bell's theorem?  Why or why not?

As far as I remember, my original assertion for this thread is that Bell's theorem belongs to philosophy, not science.