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An Ada program that simulates a two-channel Bell test polarized photon
experiment, both classically and with ‘entanglement’.

You can compile it with gcc like so:

   gnatmake -f -O3 bell_test_classical_vs_entangled.adb

You can run it for instance, like so:

   ./bell_test_classical_vs_entangled 45 67.5 1000000

Statistical data is printed out and, of course, the results are
similar for both simulations, because there is actually

    NO SUCH THING AS ‘ENTANGLEMENT’

except as a psycho-neurological phenomenon.

For the above example run, the output is:

   φ1 =    45.00000°
   φ2 =    67.50000°

   number of events = 1000000

                          nominal      classical    entangled
   ⇕ ⇔ ⊕ ⊕ frequency      0.03661      0.03655      0.03687
   ⇕ ⇔ ⊕ ⊖ frequency      0.21339      0.21419      0.21264
   ⇕ ⇔ ⊖ ⊕ frequency      0.03661      0.03662      0.03626
   ⇕ ⇔ ⊖ ⊖ frequency      0.21339      0.21332      0.21318
   ⇔ ⇕ ⊕ ⊕ frequency      0.21339      0.21246      0.21378
   ⇔ ⇕ ⊕ ⊖ frequency      0.03661      0.03672      0.03683
   ⇔ ⇕ ⊖ ⊕ frequency      0.21339      0.21319      0.21352
   ⇔ ⇕ ⊖ ⊖ frequency      0.03661      0.03694      0.03692
   correlation coef.     -0.70711     -0.70933     -0.70647

This program, and any like it that YOU write and run, are experimental
evidence of that hypothesis about ‘entanglement’: that it is not a
‘thing’ that happens in the physical world.

That physicists have not written and run such experiments is a
dereliction of their duty, as scientists, to follow scientific
method. They have not performed observations, even simple ones such as
this (or experiments you can do with nothing but sheets of paper, a
ruler, and a protractor), before forming THEIR hypotheses.

Contrary to THEIR hypotheses, which they hypothesized without first
making observations, there is no such thing as ‘entanglement’.

OR, RATHER, ‘entanglement’ is an illusion, in the cerebral cortex of a
person suffering from an education in quantum mechanics, that the
probabilities of different events in experiments (or rather the
corresponding ‘amplitudes’ in a linear state space) are PHYSICAL
THINGS that travel through space.

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This nonsense about ‘entanglement’ actually arose from the 1935 paper
by Einstein, Podolsky, and Rosen (EPR), which argued correctly that
quantum mechanics problems must be soluble by other means. The quantum
physics community has ever since, at least by majority consensus,
tried to hold a monopoly on its problems by insisting EPR were
wrong. ‘Entanglement’ and ‘non-locality’ arose as supposed properties
of ‘quantum’ physics that distinguish it from classical physics.

Let us call this monopoly grip on ‘quantum’ problems ‘irreducibility
of quantum mechanics’. It is the assertion that only quantum mechanics
(QM) can solve ‘quantum’ physics problems.

However, there are two points I can make that will, without
difficulty, demolish ‘irreducibility’, at least for those of us who
retain any respect at all for mathematics and logic.

The first is something that, to me, seems odd to have been overlooked,
which is that the assertion of ‘irreducibility’ is not about physics,
but about mathematics. It is the assertion that a WORD PROBLEM in
‘quantum’ physics can be solved only by the methods of QM. This is
ABSURD. For one thing, the problem will have logical equivalents. A
two-channel Bell test is logically equivalent to, for example, an
experiment with little balls and baffles with wedge-shaped holes in
them! The fact is any method may be used to solve a ‘quantum’ problem,
and that method will, by logical necessity, reach exactly the same
result as the methods invented by Pauli, Dirac, von Neumann, et
al. This is true of ANY problem in ‘quantum’ physics: the entire field
of ‘quantum’ physics is ‘reducible’. There is, in fact, no such field!
‘Quantum’ physics is just physics mistakenly thought to require QM for
its solution.

Whenever ‘quantum’ theorists (Bell, Clauser, etc.) have started
classical calculations and reached results DIFFERENT from those of
quantum mechanics, it is simply because they did not know what they
were doing.

Which brings me to the second point, which concerns John S. Bell’s
perverse version of probability theory, upon which ‘entanglement’ is
based. In actual probability theory, the definition of a conditional
probability is

   P(a|b) = P(a∧b) / P(b)

where a and b are propositions and a∧b is their logical conjunction.
In Bell’s probability theory, by contrast, the definition of a
conditional probability is

   P(a|b) = P(a∧b) / P(b), but, if b has no causal influence on a,
   then P(a|b) = P(a∧b) / P(b) = P(a)

Advocates of this definition will give you longwinded justifications
for it, but you and I retain respect for mathematics and logic and so
understand there is no possible justification for it. But let us try
it out, anyway, and see what we can prove. Suppose I put a red ball
and a white ball into a hat and mix them up. I remove one of the balls
and set it aside. Now I look in the hat and see the red ball
there. Let a = ‘the ball set aside is red’, b = ‘the ball in the hat
is red’. According to Bell’s definition of the conditional
probability,

   P(a|b) = P(a∧b) / P(b) = 0/(1/2) = 0
   P(a|b) = P(a) = 1/2

Therefore all real numbers are both equal and unequal to each
other. Also, division by zero is both valid and invalid. Etc.

But watch for physicists to refer to this conundrum by some such name
as ‘The Mathematical Inconsistency Loophole’. They will dismiss it as
‘a known bug’. This is the sort of thing they do when presented with
such evidence that they are committing scientific fraud. Whether it is
legally fraud is a question for courts to decide. I think that in some
cases it may be: that there are swindlers consciously taking advantage
of the monopoly. I suspect, however, that in most cases the cause is a
university-induced dysfunction of the cerebral cortex. In each
individual case we may or may not be able to repair the damage by
remedial education, although I fear severe cases may require
psychiatry. The damage in those cases may be similar to ‘cult
programming’.

Such is the state of our society in 2023, or whatever year it has
become now, as we face unprecedented physical crises and need capable
mathematical scientists as never before.

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