*
*
*The hidden variable concept was Einstein's idea, he
thought there was a local reason all events happened,
even quantum mechanical events, but we just can't see
what they are. It was a reasonable guess at the time
but today experiments have shown that Einstein was
wrong, to do that I'm gonna illustrate some of the
details of Bell's inequality with an example.*
*Do you understand how to derive Bell's Inequality, and
exactly what, and why, its violation means? Wouldn't this
be a better place to start your argument? AG *
*
When a photon of undetermined polarization hits a
polarizing filter there is a 50% chance it will make
it through. For many years physicists like Einstein
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 look-up 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 and can
be derived with high school algebra; 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.
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 look-up 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, 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
polarizations 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 instead.
3) A polarizing filter, we've had these for well over
a century.
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 is [COS (x)]^2; and if X =
30 DEGREES (π/6 radians) then the value is .75; if
the light is so dim that only one photon is sent at a
time then that translates to the probability that 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 local variable that
determines if it makes it through a filter or not.
Thus if we ignore a superdeterministic conspiracy, as
we should, then one of two things MUST be true:
1) The universe is not realistic, that is, things do
NOT exist in one and only one state both before and
after they are observed. In the case of Many Worlds
it means the very look up table as described in the
above cannot be printed in indelible ink but, because
Many Worlds assumes that Schrodinger's Equation means
what it says, the look up table itself not only can
but must exist in many different versions both before
and after a measurement is made.
*
*
2) The universe is 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.
But because Many Worlds is non-realistic, and thus
doesn't have a static lookup table, it has no need to
resort to any of these non-local influences to
explain experimental results.*
*
*
*Einstein liked non-locality even less than
nondeterminism, I'm not sure how he'd feel about
non-realistic theories like Many Worlds, the idea
wasn't discovered until about 10 years after his death.*
*
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*John K Clark See what's on my new list at
Extropolis <https://groups.google.com/g/extropolis>*
