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Bell's theorem - for or against Hidden Variables?
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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RE: Bell's theorem - for or against Hidden Variables? - by secur - 09-08-2016, 11:57 PM

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