So far, I've been telling you about the theory
of QM and how it answers questions about reality.
Today we're going to do something different,
and actually question quantum mechanics itself.
I've been looking forward to this.
Today we're going to understand a paradox
Einstein helped create to disprove Quantum
mechanics.
But first, we need to look at an essential
ingredient in Quantum mechanics, entanglement.
Entanglement isn't something limited to quantum.
Consider this example.
You have two objects, one red, one white.
You put them into boxes and shuffle them around.
Now if you open one of the boxes, and see
it's red, then you know with out having to
check that the other box has the white object
in it.
So we say that these two objects are entangled,
which mean knowing something about one causes
you to know something about the other, with
ever having to see look at it.
However, quantum entanglement is much more
interesting than this garden variety.
Of course the culprit, as it always is in
quantum mechanics, is superposition.
Let's go back to our example.
While the boxes are closed, we don't know
which state the object in each box is in,
red or white.
If it were truly impossible to know which
one is which -which isn't actually the case
in everyday life, but let's say it was this
time, then quantum mechanics tells us, that
each object must be both red and white at
the same time.
But its even weirder than that.
There are only two possibilities, ever, the
A is red, and B is white, or the other way
around.
But superposition tells us, that all possible
things happen at once, so the state of the
two objects is both A is red, B is white and
A is white, B is red.
This is a bizarre superposition.
What happens if Alice checks her box?
She collapses the state of A, which is weird
but as usual, but she also collapses the state
of B, which she didn't even touch.
I'm sure a lot of you are skeptical at this
point.
Why should we accept the quantum picture,
when its' obvious that the classical version
has the same results but by a way less convoluted
method?
Couldn't it be the case that objects aren't
actually in super positions at all?
This is a very good concern, and one we'll
be taking seriously.
We're going to try build a test.
First let's notice something.
In quantum mechanics, these particles are
not independent of each other in a deep sense.
You could argue that the classical particles
aren't either, but here's the difference.
In the classical case, measuring one of the
particles, say finding out that its red, doesn't
actually turn the other one white.
In fact it does nothing to the other one.
The objects already had a colour all along.
On the other hand, according to quantum mechanics,
the objects have to affect each other.
Otherwise, each object is in a superposition
of red and white, and Alice could measure
hers and find it's white, but this doesn't
do anything to B's superposition, so Bob could
measure his, and might find its white as well!
But this never happens.
The EPR paradox is a brilliant and simple
argument that exploits this difference between
the classical case and the quantum one.
They wanted to show that quantum mechanics
can't explain these results.
It's a proof by contradiction, which means
you assume something, in this case, quantum
mechanics, and then show that that would lead
to something happening which is impossible.
Actually we don't need to assume all of the
quantum mechanics is true- just one little
fact.
We just need to assume that if we have an
entangled pair A and B, then measuring A really
does affect B.
We saw that QM has this quality, but we don't
need to worry about superposition etc, for
this argument.
Just this fact alone.
Ok, so now, say that our boxes get shipped
to the other sides of the universe to Alice
and Bob.
Alice opens hers a split second before Bob
opens his Alice finds her object is red, so
bob must find that his is white.
But let's think about what must happen in
that split second between Alice unbox her
object and Bob doing the same.
A must tell B that its been measured and what
result it decided to be or else B won't know
what to do.
But that message has to go an awful long way
in a very short time.
In fact even light couldn't go that.
This is a big problem.
If you've heard of Einstein's theory of relativity,
you might know that the fact that 'nothing
can go faster than the speed of light' is
the foundation of that whole theory.
Therefore accepting our assumption that A
and B can really influence each other is equivalent
to pulling the rug from underneath relativity.
To Einstein, this was impossible so he concluded
that the assumption must be wrong.
What does it mean if the assumption is wrong?
Well, that definitely means quantum mechanics
is wrong.
But actually its even stronger than that.
It says that no theory were measuring one
object changes another object can ever be
true.
But then how can we explain that A and B always
have opposite colours?
We must do it the way classical mechanics
did.
I.e., none of that quantum weirdness, no superposition,
no randomness, no uncertainty principle.
This is big.
The conclusion is basically; either we must
believe that 'nothing can go faster than the
speed of light' and accept that quantum mechanics
is completely false, OR we accept Quantum
but brake the theory of Relativity.
We can't have both.
