[ExI] Demonstration of Bell's Inequality

John Clark johnkclark at gmail.com
Thu Nov 24 22:43:08 UTC 2016

```>
>
> ​> ​
> "The spin of particles A and B is W and X" and "the spin of particles A
> and B is Y and Z" are obviously not independent.  You are measuring the
> same thing and trying to declare them separate properties, and then amazed
> when it doesn't work out.

​With existing technology I can make a real physical machine that ​
​behaves in a way that​
Quantum Mechanics can explain
​but​
classical physics or even classical logic can not.
​ And I can do it using nothing but the fact that ​w
hen a photon of undetermined polarization hits a polarizing filter
​set at ANY angle ​
there is
​ALWAYS ​
a 50% chance it will make it through. For many years physicists who
disliked the idea that God played dice with the universe figured there must
be a hidden variable inside the photon that told it what to do. By "hidden
variable" they meant something different about that particular photon that
we just don't know about. They meant something equivalent to a lookup table
inside the photon that for one reason or another we are unable to access
but the photon can when it wants to know if it should go through a filter
or be stopped by one. We now understand that is impossible. In 1964 (but
not published until 1967) John Bell showed that correlations that work by
hidden variables must be less than or equal to a certain value, this is
called Bell's inequality. In experiment it was found that some correlations
are actually greater than that value.

Even if Quantum Mechanics is someday proven to be untrue Bell's argument is
still valid, in fact his original paper had no Quantum Mechanics in it; his
point was that any successful theory about how the world works must explain
why his inequality is violated, and today we know for a fact from
experiments that it is indeed violated. Nature just refuses to be sensible
and doesn't work the way you'd think it should.

OK on to making my machine. I have a black box, it has a red light and a
blue light on it, it also has a rotary switch with 6 connections at the 12,
​ ​
2,
​ ​
4,
​ ​
6,
​ ​
8 and 10 o'clock positions. The red and blue light blink in a manner that
passes all known tests for being completely random, this is true regardless
of what position the rotary switch is in. Such a box could be made and
still be completely deterministic by just pre-computing 6 different random
sequences and recording them as a lookup table in the box. Now the box
would know which light to flash.

I have another black box. When both boxes have the same setting on their
rotary switch they both produce the same random sequence of light flashes.
This would also be easy to reproduce in a classical physics world, just
record the same 6 random sequences in both boxes.

The set of boxes has another property, if the switches on the 2 boxes are
set to opposite positions, 12 and 6 o'clock for example, there is a total
negative correlation; when one flashes red the other box flashes blue and
when one box flashes blue the other flashes red. This just makes it all the
easier to make the boxes because now you only need to pre-calculate 3
random sequences, then just change every 1 to 0 and every 0 to 1 to get the
other 3 sequences and record all 6 in both boxes.

The boxes have one more feature that makes things very interesting, if the
rotary switch on a box is one notch different from the setting on the other
box then the sequence of light flashes will on average be different 1 time
in 4. How on Earth could I make the boxes behave like that? Well, I could
change on average one entry in 4 of the 12 o'clock look-up table (hidden
variable) sequence and make that the 2 o'clock table. Then change 1 in 4 of
the 2 o'clock and make that the 4 o'clock, and change 1 in 4 of the 4
o'clock and make that the 6 o'clock. So now the light flashes on the box
set at 2 o'clock is different from the box set at 12 o'clock on average by
1 flash in 4. The box set at 4 o'clock differs from the one set at 12 by 2
flashes in 4, and the one set at 6 differs from the one set at 12 by 3
flashes in 4.

But I said before that boxes with opposite settings should have a 100%
anti-correlation, the flashes on the box set at 12 o'clock should differ
from the box set at 6 o'clock by 4 flashes in 4 NOT 3 flashes in 4. Thus if
the boxes work by hidden variables then when one is set to 12 o'clock and
the other to 2 there MUST be a 2/3 correlation, at 4 a 1/3 correlation, and
of course at 6 no correlation at all.  A correlation greater than 2/3, such
as 3/4, for adjacent settings produces paradoxes, at least it would if you
expected everything to work mechanistically because of some
​ local​
hidden variable involved.

Does this mean it's impossible to make two boxes that have those
specifications? Nope, but it does mean hidden variables can not be involved
and that means something very weird is going on. Actually it would be quite
easy to make a couple of boxes that behave like that
​;​

​easy to make and easy to demonstrate that they work, but not easy to
understand ​why they work.

Photons behave in just this spooky manner, so to make the boxes all you
need it 4 things:

1) A glorified light bulb, something that will make two photons of
unspecified but identical polarization moving in opposite directions so you
can send one to each box. An excited calcium atom would do the trick, or
you could turn a green photon into two identical lower energy red photons
with a crystal of potassium dihydrogen phosphate.

2) A light detector sensitive enough to observe just one photon.
Incidentally the human eye is not quite good enough to do that but frogs
can, for frogs when light gets very weak it must stop getting dimmer and
appear to flash.

3) A polarizing filter,
​a good pair of sunglasses would do.​

4) Some gears and pulleys so that each time the rotary switch is advanced
one position the filter is
​rotated​
by 30 degrees. This is because it's been known for many years that the
amount of light polarized at 0 degrees that will make it through a
polarizing filter set at X degrees is [COS (x)]^2;
​ for example
if x = 30 DEGREES then the value is .75
​ so
the probability any individual
​0 degree ​
photon will make it through
that​​
filter is 75%.

The bottom line of all this is that there can not be something special
about a specific photon, some internal difference, some hidden variable
that determines if it makes it through a filter or not. Thus the universe
is either non-deterministic or one of two things must be true:

1)
​It's​
not realistic, that is, nothing really exists until it is observed.

2) It's  non-local, that is, everything influences everything else and does
so without regard for the distances involved or amount of time involved or
even if the events happen in the past or the future; the future could
influence the past.

Einstein would have liked the above two possibilities even less than
non-determinism. One thing is certain, whatever the truth is it's weird.

>
>
>> ​>​
>>  That's 2 chances in 8
>
>
> ​>
> No.  If the other ball is blue then there are 4, not 8, cases it could be
>

​ ​
you are certain about one thing

there is 1 chance in 1 the other ball is blue, but there is only 2 chances
in 8 the other ball is blue AND heavy. The 2 balls were picked at random
from a pile of 8 balls and put into sealed packages. You are allowed to
perform one and only one
​test ​
out of a possible 3 to determine a property inside your package
​,​
and you randomly pick X-ray. Perhaps you're confusing this with the Monty
Hall puzzle where Monty knew where the car was so showing you that it
wasn't behind door #3 gave you some new information that Monty had about
where the car was. In this case nobody knew anything about
​ ​
what's
​ ​
in those packages until you X-rayed yours and found it was red.  That told
you that the other ball can't be red, and you know the other ball can't be
​ ​
​ ​
or
​ ​
blue
​ ​
​ ​
because of the question you want answered "is the other ball heavy?".

​Or suppose ​after you X rayed it you suddenly decided you didn't care if
the other ball was heavy but instead wanted to know if it was radioactive;
again classical physics would say 1 chance in 4 and again you would find
through experiment that the true answer is 1 chance in 3. And if instead of
X-raying it you weighed it or used a geiger counter on it you'd get similar
puzzling results.

​>
> Seriously, I don't get why you keep insisting on easily
> provable falsehoods.

​Do
you
​seriously ​
think you are the first to see something clearly that all physicists since
1964 have