Bell's Inequality

From: John Clark (
Date: Fri Jun 02 2000 - 22:59:34 MDT

Jonathan Reeves Wrote:

>Bell's Inequality ? I have not heard of this, brief explaination ?

When a photon of undetermined polarization hits a polarizing filter there is 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. Quantum Mechanics can
explain this, classical physics or even classical logic can not.

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 the world must explain why his inequality is violated.
I'll try to show how to find the inequality, show why it is perfectly logical, and
demonstrate that nature refuses to be sensible and just doesn't work the way you'd
think it should.

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 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 lookup 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 the boxes at opposite settings should have a 100% anti-correlation,
the flashes on the box set at 12 o'clock should differ from the box set 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 that 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 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, it's just not easy to understand how that could be.

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, we've had these for a century or more.

4) Some gears and pulleys so that each time the rotary switch is advanced one position the
    filter is advanced 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; and if x = 30 DEGREES then the value is .75 If light is made
    photons that translates to the probability any individual photon will make it through the 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 non-local, that is, everything influences
everything else and does so without regard for time or space. One thing is certain,
whatever the truth is it's weird.

                         John K Clark jonkc@att.

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