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Introduction:
Einstein and Bell
Einstein
never liked Quantum Mechanics. Even though he virtually invented
the quantum theory of light, the more he rolled the ideas of quantum
mechanics around in his mind, the more he rejected the idea that
it was complete--or even worked at all.
He didn't
like the idea that the momentum of a particle, if it's position
was known, was completely unknowable--random. He said, "God
does not play at dice with the universe." Neils Bohr, one of
the greatest physicists working with quantum mechanics, wittily
replied, "Quit telling God what to do!" (Harrison)
But Einstein
wasn't the only one who didn't like the theory. In 1935 he got together
with two other like-minded physicists, Boris Podolsky and Nathan
Rosen, and wrote a famous paper entitled Can Quantum-Mechanical
Description of Physical Reality be Considered Complete? We now
refer to it as simply the EPR Paradox (no wonder, since the other
title flows off the tongue so well). (Harrison)
It wasn't
until 1964, 29 years after the EPR Paradox was published, that serious
proof was established that Einstein and friends had good reason
to be worried. That was the year John S. Bell published his mathematical
proof, a theorem that elegantly proved that if momentum and position
were absolute values (that is, they exists whether they were measured
or not) then an inequality, now called Bell's Inequality, would
be satisfied (Pool). Einstein's position
was clear: "I think that a particle must have a separate reality
independent of the measurements. That is an electron has spin, location
and so forth even when it is not being measured. I like to think
that the moon is there even if I am not looking at it.(Quotes)
" More on this later.
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What
Exactly is the Problem?
In the EPR
paradox, Einstein and friends imagined a scenario that would let
you measure, say, both the position and momentum (as an example)
of a particle with absolute certainty, a big no-no in quantum mechanics.
A perfect
example is the case of the neutral pion. A pion is a subatomic particle
(very small, see Quantum Physics Is. . .) that decays into two photons,
each with opposite spins. These are difficult concepts to understand,
but all you really need to know is this:
- The pion has no spin.
Imagine a baseball just sitting there, not spinning. Pretty simple.
- When the pion decays
(a common occurrence in the subatomic world) it no longer is a
pion. It splits into two photons that shoot away from each other
in opposite directions.
- Photons have spin,
but these two photons came from a pion with no spin. So, since
you know the spin of one photon, you can find out the spin of
the other photon because their spins have to add up to no spin
at all. Imagine our baseball that was not spinning all of the
sudden flies apart into two golf balls, each spinning in opposite
directions.
Because the photons came
from a single pion, it is said that they are entangled. You'll see
what I mean.
One of the photons flies
to the right. You first measure it's spin along the x-axis with
absolute certainty (quite possible). But, alas, quantum mechanics
won't let you measure the y-axis spin, since you already know the
x-axis spin. So you go to the second photon that flew to the left.
You already know its x-axis spin without even measuring it: it is
the exact opposite of the other photon. The paradox is this: Can
you measure the y-axis spin of the second photon with absolute certainty
even though you already know it's x-axis spin without measuring
it?(Blanton)
Duh, of course you can,
says Einstein. How would the second photon "know" you
measured the first photon? But quantum mechanics says you can't
measure the y-axis spin with absolute certainty. It doesn't matter
if the two photons were separated by an inch or 10 miles, the very
instant you measure the first photon's x-axis spin, the y-axis spin
of the second photon is impossible to measure. Relativity says that
the "knowledge" of the measurement of the first photon
can only travel the speed of light. But quantum mechanics requires
the "knowledge" of the measurement to be instantaneous,
because they have been entangled. Einstein called it "spooky
action at a distance". (Harrison)
If you understood all
that, the rest of this is a piece of cake. If you didn't, don't
worry, the rest is still interesting (you could always ask
a question).
So who's right? Ah, how
the plot thickens when Bell comes on the scene.
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Bell's
Inequality in Detail
To explain away this
quirky paradox, some scientists said that there were "hidden
variables" that exist in the photons that allow them to behave
this way. Hidden variables are variables that we have yet to discover.
They would be aspects of each of the photons that are the same,
since they were entangled, but that did not depend on the other
photon.
Bell proved mathematically
that this was impossible with this inequality:
Number(A,
not B) + Number(B, not C) >= Number(A, not C)
David M. Harrison, a
physicist at the University of Toronto, explains it this way:
In class I often
make the students the collection of objects and choose the parameters
to be:
A: male
B: height over 5'8"
C: blue eyes
Then the inequality becomes that the number of men students
who do not have a height over 5'8" plus the number of students,
male and female, with height over 5'8" but who do not have
blue eyes is greater than or equal to the number of men students
who do not have blue eyes. I absolutely guarantee that for any
collection of people this will turn out to be true.
(Harrison)
What does this have to
do with quantum mechanics? Here goes: you can shoot photons at a
detector that detects the arrival time of the photon, and the photon's
energy. If energy and arrival time were absolute values, that is,
if the energy and arrival time of the photon exists whether it is
measured or not, then the values would have to satisfy Bell's inequality,
regardless of hidden variables. (Pool)
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The
Punch Line: Does Quantum Mechanics Violate the Inequality?
In experiment after experiment
Bell's Inequality is not violated, but instantaneous communication,
or "spooky at a distance", seems to occur. If you rule
out instantaneous communication, Bell's Inequality is violated.
The most interesting
experiment was carried out by a physicist at the University of Geneva,
Switzerland, Nicolas Gisin in 1997. He split a single photon into
two "smaller" photons (which meant they were entangled)
and sent them down fiber optic cable in opposite directions. When
the photons where about 10 kilometers apart they ran into a detector.
Gisin found that even though a large distance separate the photons,
something done to one photon at one end very much affected the photon
at the other end. . . instantaneously. (Strieber)
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What
does this mean?
Let's take a look at
assumptions. Here we invent two assumptions:
All birds have wings.
Everything that has wings flies.
We can conclude from
these two assumptions that all birds fly. If we find a bird
that has wings but doesn't fly, we know that at least one of our
assumptions was wrong. In this case, it's obviously the last assumption
(all the birds I know have wings).
It's interesting to know
that Bell's Theorem has assumptions, too. They are:
Logic is valid.
There is a reality separate from its observation.
No information can travel faster than light.
The last assumption is
called locality. Locality says that everything that is bound by
relativity, everything that can't go faster than light, is local.
If something is non-local it is thought to be part of a larger reality.
More on this later. (Harrison)
So which assumption is
wrong in Bell's Theorem? Nobody knows.
Logic could be wrong.
In 1930, Kurt Gödel proved that any theory proposed for the foundation
of mathematics will be either insufficient for mathematics, incomplete,
or inconsistent. This was a wild and crazy thing for a logician
to do, as it essentially proved that logic was incomplete.
There may be no reality
separate from its observation. This is where physics melds with
philosophy and religion. Could it be that the universe only exists
because we are conscious of it? Perhaps we only exist because someone
or something is conscious of us? The EPR paradox isn't the only
paradox that raises this possibility. Erwin Schrödinger proposed
a way to link the classical world that humanity knows to the quantum
world of electrons and protons. He proposed that in a closed box
one could put a live cat, a vial of poison gas, a geiger counter
that smashes the vial if it detects radiation, and a radioactive
atom. In an hour, the atom's likelihood of having decayed is 50%.
In quantum mechanics, before you measure whether of not the atom
decayed, it actually exists in a superstate of both decayed and
not decayed. It's not that you just don't know, it's that it actually
exists in both states at the same time. Thus, after an hour's time,
before you peer into the box to see if the kitty is alive or dead,
it must exist in a superstate of both dead and alive. If a tree
falls in the forest and no one is around, did it actually exist
at all?
Information might be
able to travel faster than light. Consider a one-dimensional creature,
we shall call him a 1d, that exists on a line. Everything the 1d
creature knows is in terms of length and nothing else. Then along
comes a two dimensional creature, call him 2d. The 1d can measure
the length of the 2d, but isn't aware of anything else. In fact,
it's possible for the 1d to measure two lengths for a single
2d, making the 1d think that the 2d exists in two places at once,
and in his universe he does! The same could be true for our universe.
The popular
press likes to claim that quantum physics allows for faster than
light communication of information. So far, physicists have not
come to this conclusion. Dr. Ken Caviness, chair of the Physics
Department at Southern Adventist University in Tennessee, says this:
I don't know of anyone
in the field who seriously proposes instantaneous communication.
On the contrary it seems that despite quantum entanglement information
cannot be extracted from the system without some (at most) light-speed
exchange of information. (Caviness)
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