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Bell's theorem - for or against Hidden Variables?
Well, I don't think you know enough of Popper's philosophy to know whether or not you are a Popperian.  As you said, you figured out the main premise on your own -- inductivism is not the preferred method of science.  

Now, to that point, please explain what it means for an inequality to be "satisfied".
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For an inequality to be satisfied: consider Christian's paper cited above, equation C15, which is the CHSH inequality, but with Tsirel'son's bound, 2*sqrt(2). He derived it in this appendix for SU(2), not SO(3). He says:

"... the above inequality can be reduced to the form [C15] exhibiting the upper bound on all possible correlations."

Now, for this inequality to be satisfied would mean the following. Do the computations he specifies. If the result is, in fact, less than about 2.828, the inequality has been satisfied. Otherwise, not. That's not philosophy, just math. Philosophy comes in when we ask what this implies, in the real world.

I feel I'm getting a better idea of your complaint against Bell. Consider this quote from him,

"In a theory in which parameters are added to QM to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remotely. Moreover, the signal involved must propagate instantaneously ..."

IOW if a theory violates his inequality, it must be nonlocal. It's not unreasonable to label this "philosophy". The statement's not science because it really can't be falsified. To do so you'd have to demonstrate a violation, and then prove there's no FTL signal. Apparently that's impossible. Bell can always claim there is such a signal, you just haven't detected it yet.

The typical "Bellist" conclusion is similar but not so specific about "nonlocality". If a situation violates the inequality, then it must be - nonreal, nonlocal, noncausal, nonclassical - or something like that. Again, how can that be falsified? It's too vague; there's no prediction here. If a certain result happens we will assign a philosophical label to it. So what?

Perhaps this is what you mean by saying Bell is "founded on philosophy"?
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(09-07-2016, 04:14 PM)secur Wrote: For an inequality to be satisfied: consider Christian's paper cited above, equation C15, which is the CHSH inequality, but with Tsirel'son's bound, 2*sqrt(2). He derived it in this appendix for SU(2), not SO(3). He says:

"... the above inequality can be reduced to the form [C15] exhibiting the upper bound on all possible correlations."

Now, for this inequality to be satisfied would mean the following. Do the computations he specifies. If the result is, in fact, less than about 2.828, the inequality has been satisfied. Otherwise, not. That's not philosophy, just math. Philosophy comes in when we ask what this implies, in the real world.

I feel I'm getting a better idea of your complaint against Bell. Consider this quote from him,

"In a theory in which parameters are added to QM to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remotely. Moreover, the signal involved must propagate instantaneously ..."

IOW if a theory violates his inequality, it must be nonlocal. It's not unreasonable to label this "philosophy". The statement's not science because it really can't be falsified. To do so you'd have to demonstrate a violation, and then prove there's no FTL signal. Apparently that's impossible. Bell can always claim there is such a signal, you just haven't detected it yet.

The typical "Bellist" conclusion is similar but not so specific about "nonlocality". If a situation violates the inequality, then it must be - nonreal, nonlocal, noncausal, nonclassical - or something like that. Again, how can that be falsified? It's too vague; there's no prediction here. If a certain result happens we will assign a philosophical label to it. So what?

Perhaps this is what you mean by saying Bell is "founded on philosophy"?

Excellent reply, secur!

Inequality is a fundamental tool of analysis.  Taking the simple example of the am-gm inequality (the arithmetic mean of two nonnegative real numbers is at least as big the geometric mean), we find that boundary conditions drive the result.  Tsirelson's bound being the most general bound on correlations (any correlations, not just quantum mechanical) at the upper limit, zero assumed at the lower, begs an initial condition within the scope of the real numbers (Lebesgue measure).

What boundary conditions satisfy Bell's inequality?

secur wrote, "I feel I'm getting a better idea of your complaint against Bell. Consider this quote from him, 

"'In a theory in which parameters are added to QM to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remotely. Moreover, the signal involved must propagate instantaneously ...'"

Yes, indeed.  Which is why I don't fault Bell, the accomplished physicist, for the shortcomings of Bell-Aspect, and the conclusions of later acolytes.  In the course of this debate, I will show a clear path pf induction from physical observation to experiment to conclusion.

See what's meant by the importance of falsification? 

secur: "prove there's no FTL signal."

Yes, you do. Smile

It follows that nonlocality is a prior assumption of Bell's theorem.
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First, a theorem is a theorem. So, its character is mathematical. It starts with assumptions and derives conclusions.

The assumptions as well as the conclusions may be philosophical as well as physical (there is anyway no certain boundary between them). Once in the case of Bell's theorem the conclusions - the inequality - can be tested empirically, the conclusions have physical character. Thus, given the mathematical character of the proof, the assumptions, taken together, have physical character too.

On the other hand, this holds only for their combination. Each of the assumptions, taken alone, may be (and with high probability really is) insufficient to derive any falsifiable conclusion. Thus, taken separately, they have metaphysical character.

Secur, your "given the observations, anyone who's competent can figure out the theory" is completely wrong. The observations of stars have been there for thousands of years, but nobody has figured out the Copernican revolution before Copernicus. Out of incompetence? The atomic system as well as the spectral properties of various elements were essentially all the observational evidence sufficient to establish quantum theory. But it was known many years before quantum theory was found. Out of incompetence?

Then I think you underestimate Popper. Popper is good in explaining things, so what he claims seems quite obvious and self-evident if one follows him. But, sorry, to defeat logical positivists was not simple at all. At least nobody has succeeded before him. And whenever I read criticism of Popper, be it Feyerabend, Lakatos, Kuhn or Habermas, I'm frustrated by the strawman they criticize - some strange mixture of Popper with positivism instead of Popper himself.

Of course, Popper is not always right, his political philosophy contains some interesting arguments but is otherwise weak, and his probability interpretation one can forget (Jaynes is much better).
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Schmelzer wrote: First, a theorem is a theorem. So, its character is mathematical. It starts with assumptions and derives conclusions.

That's right. The word "theorem" implies mathematics. We use the phrase "Bell's theorem" somewhat loosely - he never stated it as such. My post above was an attempt to separate the theorem of Bell from the theory of Bell - specifically, the representation. We agree, the theorem is just math. It becomes controversial when we apply it to the physical world.

Schmelzer wrote: The assumptions as well as the conclusions may be philosophical as well as physical (there is anyway no certain boundary between them).

True. Still one can discuss that boundary and delineate the physics from the philosophy, somewhat.

Schmelzer wrote: Once in the case of Bell's theorem the conclusions - the inequality - can be tested empirically, the conclusions have physical character. Thus, given the mathematical character of the proof, the assumptions, taken together, have physical character too.

Yes but there's "philosophy" in there along with the physical character.

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Schmelzer wrote: The observations of stars have been there for thousands of years, but nobody has figured out the Copernican revolution before Copernicus.

Incorrect. Aristarchus of Samos realized the heliocentric fact in the 3rd century BC. (No doubt someone guessed it 50,000 years ago.) Back then many people agreed it might be that way, including Aristotle. Unfortunately he preferred geocentricism, and his view dominated for 1500 years. Throughout all those years, many individuals said "wait a minute, it actually might make more sense if the planets revolve around the sun!" - and were ignored. Copernicus came at the right time, knew the right people, and (with difficulty) was heard. Finally with better data, such as Tycho Brahe's, the facts became indisputable. Within a year of accessing that data, Kepler figured out the key: elliptical orbits. Any other competent thinker would have gotten the same result - in a month, or a decade, it doesn't matter. Once the data is there all it takes is a normal genius to come up with the theory.

Schmelzer wrote: The atomic system as well as the spectral properties of various elements were essentially all the observational evidence sufficient to establish quantum theory. But it was known many years before quantum theory was found.

It started with the observational evidence of Black Body Radiation Curve, in fact, which led Planck to his constant. Rutherford's experiments were necessary to enable Bohr to create his early Quantum atomic theory. The photoelectric effect was important; and other data. Still you're right: atomic spectra were the really vital clue. Note, even that data also improved greatly during the critical years of the early 1900's. If you examine QM history you'll find that the competent geniuses who developed it weren't too far behind experiments - maybe a couple decades. (Of course, in a couple famous cases - positron, neutrino - they were ahead of the data.) Perhaps greater (or, luckier) minds could have gotten to the fundamental ideas faster. But even if it took longer, a few decades, so what? Some competent thinker(s) would have figured it out before too long - I claim.

Schmelzer wrote: Secur, your "given the observations, anyone who's competent can figure out the theory" is completely wrong.

Obviously it depends what we mean by "competent". Very roughly, "competent" might mean "genius" IQ (160) or better. Note, that's supposed to be Einstein's and Stephen Hawking's level. Statistically it's about one out of 3500 people. So in the world today, there would be about 2 million competent people. Admittedly they have to realize their potential by a lot of study.

Another way to look at it: consider Newton. Perhaps he was the greatest physicist ever. But his reputation was very inflated by English patriotism in the 18th and 19th centuries. (Don't believe the propaganda!) He was most likely just an ordinary greatest genius. How many of those are there? Well he came from a population of about 5 million. At that rate there are 1400 like him today.

Generally speaking the rarity and genius of physicists has been extremely over-rated. This stuff is easy if you have the ability. For instance quarks: it's easy to see there ought to be 3 of them in a nucleon, with their charges of one and two thirds, once you get enough data. Even a computer could probably figure it out. Or consider the Higgs mechanism, spontaneous symmetry breaking and associated concepts. I think it's one of the most brilliant ideas in physics. Nevertheless, about ten people came up with it almost simultaneously! It's well known that Anderson, Guralnik and others might have gotten the Nobel instead (as Higgs himself said, often). In one case, if they had just sent the paper off, instead of waiting for a couple minor corrections, they would have beat him to publication (IIRC). So - even this brilliant breakthrough was obvious to competent people working in the field. Also, note that it was decades before much was really done with the idea. So what difference if it had been discovered a few years later?

General Relativity might be the most impressive of all theories, genius-wise. If Einstein hadn't come up with it in 1915, I bet another ten, even twenty, years would have gone by before someone else did. But again, so what? It really didn't make hardly any difference, practically, until about the 1960's. In fact it's precisely because it was so useless that no one else thought of it. Furthermore - as we all know, it's actually not entirely right, in the light of QM. And it allows stuff like wormholes which are probably pure fantasy. So a good case could be made that it's wasted many decades of progress, by causing people to study dead-ends! That's what happens when theoretical genius gets too far ahead of experimental data.

I could go on and on like this. My statement is not just a casual aside, but based on historical knowledge. Of course I could be wrong, it's a matter of opinion. But I seriously think you guys are victims of an age-old propaganda campaign. Any idiot with an IQ over 160 or so, who starts as a teenager and works hard, is capable of more or less any brilliant theory in physics. That's what I'm referring to as "competent".

Consider what's been happening in cosmology and also particle physics. Data comes in sporadically. When a new telescope is launched, or a new particle accelerator, or whatever, new data becomes available, once every few years. Whenever the data arrives dozens of theoreticians immediately figure out whatever there is to figure out. Then they go back to waiting for the next batch of data. There are many more theorists than you need, that's why most of them can't get work. Much worse, the ones who have jobs come up with useless vaporware theories because they have so little data to go on. Just spinning their wheels.

A question might come up. If there are 1000 Newtons in the world today, and 2 million competent people - why aren't they physicists? Only a few percent of today's theoretical physicists are at such a level; none of them are Newtons, except maybe Ed Witten. Well - let's face it, most smart people go into fields where you can make real money, and do something useful. Not theoretical physics. Also, by far the most genius-like quality they need is the ability to ignore dogma, think for themselves - as we do on this web site. But those are exactly the guys who get thrown out of grad school for heresy!

Competent people are readily available. But, especially these days experimental or observational data is much more important. It's a matter of opinion. If you don't agree, that's fine. Maybe you're right.

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Schmelzer wrote: Then I think you underestimate Popper. ... sorry, to defeat logical positivists was not simple at all. At least nobody has succeeded before him.

Of course no one had to defeat them before 1920 or so, since their peculiar mistake hadn't yet been committed. Popper was pretty good. No doubt if I studied him I'd learn a few things I hadn't thought of before. But that's true of any good thinker - they all have something interesting to say.

Philosophy after about 1900, in my humble opinion, took a wrong turn: they mistook science for truth. (There are of course exceptions, Heidegger for one.) Many of them aren't even philosophers, but mathematicians / scientists. You mention Jaynes' treatment of probability - yes, it's fine. But it's math. Same is true of Carnap, Russell etc's symbolic logic. But it's all just a matter of opinion.

Thomas Ray wrote: What boundary conditions satisfy Bell's inequality?

If I understand the q. correctly: SO(3) space.
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Hi secur,

You wrote, "Within a year of accessing that data, Kepler figured out the key: elliptical orbits. Any other competent thinker would have gotten the same result - in a month, or a decade, it doesn't matter. Once the data is there all it takes is a normal genius to come up with the theory."

I don't agree.  However, the reason that I don't agree is the last piece of convincing I needed to fully embrace Popper's philosophy.  

In 2011, I realized the deep implications of Buridan's Principle http://research.microsoft.com/en-us/um/p...ml#buridan while reading Leslie Lamport's 1984 paper which was published in 2012.  Lamport wrote:


"To understand the meaning of Buridan’s Principle as a scientific law, consider the analogous problem with classical mechanics. Kepler’s first law states that the orbit of a planet is an ellipse. This is not experimentally verifiable because any finite-precision measurement of the orbit is consistent with an infinite number of mathematical curves. In practice, what we can deduce from Kepler’s law is that measurement of the orbit will, to a good approximation, be consistent with the predicted ellipse."

So Kepler could not have deduced the law from any amount of observation.  This 'bold conjecture' led to his counterintuitive second law -- that the orbit sweeps "equal areas in equal times".

You seem to be saying competence = intelligence.  I don't buy it; however, I admit my bias -- I agree with Stephen Jay Gould on the 'mismeasure of man'.

"Thomas Ray wrote: What boundary conditions satisfy Bell's inequality?

If I understand the q. correctly: SO(3) space."

Precisely.  How can a connected space (vice the simply connected space S^3) accommodate the time reversibility demanded by Einstein's theories of relativity?

I should add, re intelligence: that there is no general theory of intelligence. So we see the result of reasoning by induction, rampant in the social sciences.
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At least one Bell loyalist, Richard Gill, defers to philosophy over physics.  In a PubPeer debate of his paper "Statistics, Causality and Bell's Theorem" https://pubpeer.com/publications/D985B47...22#fb27706 he wrote to "Peer 1":

"By the way, who is talking about spooky passion or spooky action? I do not think that what is going on here is 'spooky'. What is going on is physics, quantum physics. Quantum physics is different from classical physics. In some respects it makes more things possible, in other respects it allows less. There is certainly nothing spooky about quantum entanglement and all that. There is absolutely no violation of causality and locality principles. Quantum mechanics is compatible with the concept of 'information causality' which is itself a strengthening of 'no action at a distance'."

(Despite that information causality can't 'breathe in empty space'; one more degree of freedom is demanded -- time -- which subsumes QM in a classical framework.)
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Thanks for response, Thomas,

Thomas Ray wrote: You seem to be saying competence = intelligence.  I don't buy it ...

You're right. Yes, I do seem to be saying that; but I don't buy it either!

I wrote 'Very roughly, "competent" might mean "genius" IQ (160) or better.' No question: correlation between IQ and physics competence is less than 1 (.85?). Einstein's IQ is (estimated at) only 160, yet he was at the top of the heap. OTOH Voltaire's is (estimated at) 195, yet he was lousy at math. I used IQ - a well-known concept, close to the right one - just to develop my theme.

The presentation can be cleaned up easily. For IQ substitute something like "Physics Competence Quotient". I want to say that roughly 1 out of 3500 people has the mental qualities required for a "competent" physicist. One out of 5 million, roughly, is "super-competent": you can't get any better. The competent physicist is capable of figuring out any physics theory, given the requisite data; the super-competent just do it faster.

Note, I'm talking about [i]theoretical/i] physics, not experimental. There's no "recipe" for experiments, it's "limited only by your imagination". The greatest experimental conceptions are beyond a merely competent experimenter.

For examples, Schroedinger, de Broglie, Fitzgerald, Carnot, (etc) were merely competent, nevertheless responsible for key theoretical advances.

BTW Schopenhauer felt exactly this way about mathematicians. "No mathematician is a genius" - I don't agree with that, but know what he meant. I forget if he included physicists as well.

This attitude justifies all of us non-mainstream wannabe's. It's not all that hard to learn this stuff, especially with the internet. We haven't been indoctrinated, so it's easy to come up with the next great breakthrough. Just look for the dogma they're most certain of: it's bound to be wrong. Unfortunately it's impossible to sell it to the establishment. If we live long enough we'll see an establishment physicist, some day, achieve "immortality" for obvious ideas we knew decades ago. Not sure how satisfying that will be.

Of course, I could be wrong.

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"Thomas Ray wrote: I should add, re intelligence: that there is no general theory of intelligence.

To create a "general theory of intelligence" you must limit definition of intelligence. A promising avenue: re-define it to apply to a computer.

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Leslie Lamport is interesting. In computer science Buridan's principle can manifest as "deadlock". Another example is gimbal lock? But with a conscious being like a donkey or human, it's circumvented by free will - the ability to make an (objectively) random choice. He's right: an animal will hesitate confronted with two choices. If it's not critical he might hesitate for a long time. But a starving donkey will very quickly go to one or the other pile of hay.

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.

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

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.

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

Leslie Lamport wrote: To understand the meaning of Buridan's Principle as a scientific law, consider the analogous problem with classical mechanics. Kepler's first law states that the orbit of a planet is an ellipse. This is not experimentally verifiable because any finite-precision measurement of the orbit is consistent with an infinite number of mathematical curves. In practice, what we can deduce from Kepler's law is that measurement of the orbit will, to a good approximation, be consistent with the predicted ellipse.

I claim any competent physicist performs this sort of approximation as a matter of course. Sensing what's negligible and what isn't is a core competence in physics. Don't forget the natural philosophers of that day were very familiar with conic sections.

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

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"Thomas Ray wrote: How can a connected space [SO(3)] (vice the simply connected space S^3) accommodate the time reversibility demanded by Einstein's theories of relativity?

At the moment I'm stumped!
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Ok, maybe I figured it out. First, consider a simply connected space, such as S^3. Suppose there's a path through it, point A to point B. Now traverse it in reverse, point B back to point A. That's a closed loop. Since the space is simply connected, it can be shrunk to a point - in particular, the identity of the space. So in this sense traversing the closed loop from A, to B, back to A, is equivalent to the identity. Therefore any path (A and B were of course arbitrarily chosen) is reversible.

But you can't do that with a connected space which is not simple, such as SO(3).

Is that what you're getting at?
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(09-11-2016, 11:34 PM)secur Wrote: Ok, maybe I figured it out. First, consider a simply connected space, such as S^3. Suppose there's a path through it, point A to point B. Now traverse it in reverse, point B back to point A. That's a closed loop. Since the space is simply connected, it can be shrunk to a point - in particular, the identity of the space. So in this sense traversing the closed loop from A, to B, back to A, is equivalent to the identity. Therefore any path (A and B were of course arbitrarily chosen) is reversible.

But you can't do that with a connected space which is not simple, such as SO(3).

Is that what you're getting at?


It's absolutely what I'm getting at, secur.  I rejoice that it is not so hard to understand!

Reversibility is the key property.  As I wrote in a 2006 conference paper:

5.3.1 A move in time, i.e. a real continuous function – on the surface of a closed manifold (S^2 ) – makes no differentiation between a closed loop and a continuous line, but accommodates both. E.g. the Euler Network Formula for a flat plane, V – E + F = 1, becomesV – E + F =  2, for a closed (compact) manifold. If we were to speak of “hypertime,” we would find that what Brouwer took as a fundamental analytical fact of mathematical “twoity” [Brouwer, 1981] is in hyperspace a “fourity” of terms. (Indeed, the “hyper” classifications of numbers – quaternions, octonions and their extensions – due to W.R. Hamilton, Cayley et al – follow. We shall not need these.) 

Bell loyalists can take refuge in formulating the shape of space as toroidal -- Euler characteristic 0, in which case no account is taken of time reversibility, and all events are independent.  With an Euler characteristic of 2, spacetime is properly represented, and we have no worries about "attempting to breathe in empty space."
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