The second proof is by the internal consistency of mathematics.
First let me put aside a myth that it was proved by Gödel or others that mathematics is inconsistent. This certainly is not the case. What was proven is what you might describe thus: that a computer programming language cannot prove itself mathematically consistent. But this does not mean the language is inconsistent! It merely means that you cannot write a proof of that consistency in the language itself.
This is what was proven.
There is this ‘Gödel-Escher-Bach’ book, which I have read, and a whole lot of stuff, and a big deal is made of it all, but in fact the matter is so plain obvious as to be pathetic. We realize that now. One feels sorry for the mathematicians and logicians of Gödel’s time, that they were so naïve.
You see, suppose a programming language were mathematically inconsistent. Say it let you say ‘0=1’ and have that be ‘true’. It is known that in such a language you could prove ANYTHING...
THEREFORE YOU COULD PROVE THAT THE LANGUAGE WAS CONSISTENT!
But it isn’t, it is inconsistent. So any proof of its consistency from within a programming language itself is worthless. It was never worth even considering the possibility that one could exist.
So, then, mathematics may or may not be consistent. But we will assume it is. Why?
BECAUSE, WERE IT NOT, IT WOULD BE USELESS. Were mathematics inconsistent, what use would it be for designing bridges? For electric power systems? Etc.
In particular, no matter what mathematical method I use to solve a given word problem, I MUST arrive at THE SAME EXACT ANSWER. This is an example of what is meant by the internal consistency of mathematics.
But what physicists are claiming is precisely this: that, if you solve, say, the Aspect experiment, also called the two-channel optical Bell test (look it up on Wikipedia), by a method called ‘quantum mechanics’, you will get a different answer than if you use, say, probability theory.
This is impossible if mathematics were consistent, so what physicists are claiming is that mathematics is inconsistent and therefore useless.
(Which they will deny, of course, but that is because they do not understand what they are doing. If they did, they would not do it.)
They are wrong.
So the proof here is that ANY mathematical method can be used to solve ANY supposedly ‘quantum’ word problem. Therefore there is nothing ‘quantum’ about the problem. It is an ordinary physics problem.
With regard to the Aspect experiment, physicists both solve the problem incorrectly when they attempt to use probability theory (Bell and Clauser inequalities, all of which are botched mathematics), and run their experiments without actually checking them against the predictions of quantum mechanics. The results obtained by Aspect are impossible, according to quantum mechanics, but no one bothers to check. The experiments are fake.
Quantum physicists are the sloppiest ‘scientists’ in the world.▪
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Footnote: The experiments are fake but probably by extremely strong experimenter bias rather than deliberate fraud.
I think I shall both demonstrate converting the Aspect experiment to an equivalent one, AND show that mathematics actually IS consistent. I will do the latter by deriving the same correlation function as quantum mechanics does, even though physicists claim this can be derived only if you use quantum mechanics.
Which would mean using quantum mechanics gives a different answer than the rest of math, so math is internally inconsistent. Physicists claim nothing less.
Let’s to it
#physics #science
Barry Schwartz 🫖