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Locality means that to get from one point to another you somehow have to make a connection
in space between these points. You cannot suddenly disappear and reappear elsewhere.
At least that was Einstein’s idea. In quantum mechanics it’s more difficult. Just exactly
how quantum mechanics is and is not local, that’s what we will talk about today.
To illustrate why it’s complicated, let me remind you of an experiment we already
talked about in a previous video. Suppose you have a particle with total spin zero.
The spin is conserved and the particle decays in two new particles. One goes left, one goes
right. But you know that the two new particles cannot each have spin zero. Each can only
have a spin with an absolute value of 1. The easiest way to think of this spin is as a
little arrow. Since the total spin is zero, these two spin-arrows of the particles have
to point in opposite directions. You do not know just which direction either of the arrows
points, but you do know that they have to add to zero. Physicists then say that the
two particles are “entangled”.
The question is now what happens if you measure one of the particles’ spins. This experiment
was originally proposed as a thought experiment by Einstein, Podolsky, and Rosen, and is therefore
also known as the EPR experiment. Well, actually the original idea was somewhat more complicated,
and this is a simpler version that was later proposed by Bohm, but the distinction really
doesn’t matter for us. The EPR experiment has meanwhile actually been done, many times,
so we know what the outcome is. The outcome is… that if you measure the spin on the
particle on one side, then the spin of the particle on the other side has the opposite
value. Ok, I see you are not surprised. Because, eh, we knew this already, right? So what is
the big deal?
Indeed, at first sight entanglement does not appear particularly remarkable because it
seems you can do the same thing without quantum anything. Suppose you take a pair of shoes
and put them in separate boxes. You don’t know which box contains the left shoe and
which the right shoe. You send one box to your friend overseas. The moment the friend
opens their box, she will instantaneously know what’s in your box. That seems to be
very similar to the two particles with total spin zero.
But it is not, and here’s why. Shoes do not have quantum properties, so the question
which box contained the left shoe and which the right shoe was decided already when you
packed them. The one box travels entirely locally to your friend, while the other one
stays with you. When she opens the box, nothing happens with your box, except that now she
knows what’s in it. That’s indeed rather unsurprising.
The surprising bit is that in quantum mechanics this explanation does not work. If you assume
that the spin of the particle that goes left was already decided when the original particle
decayed, then this does not fit with the observations.
The way that you can show this is to not measure the spin in the same direction on both sides,
but to measure them in two different directions. In quantum mechanics, the spin in two orthogonal
directions has the same type of mutual uncertainty as the position and momentum. So if you measure
the spin in one direction, then you don’t know what’s with the other direction. This
means if you on the left side measure the spin in up-down direction and on the right
side measure in a horizontal direction, then there is no correlation between the measurements.
If you measure them in the same direction, then the measurements are maximally correlated.
Where quantum mechanics becomes important is for what happens in between, if you dial
the difference in directions of the measurements from orthogonal to parallel. For this case
you can calculate how strongly correlated the measurement outcomes are if the spins
had been determined already at the time the original particle decayed. This correlation
has an upper bound, which is known as Bell’s inequality. But, and here is the important
point: Many experiments have shown that this bound can be violated.
And *this creates the key conundrum of quantum mechanics. If the outcome of the measurement
had been determined at the time that the entangled state was created, then you cannot explain
the observed correlations. So it cannot work the same way as the boxes with shoes. But
if the spins were not already determined before the measurement, then they suddenly become
determined on both sides the moment you measure at least one of them. And that appears to
be non-local.
So this is why quantum mechanics is said to be non-local. Because you have these correlations
between separated particles that are stronger than they could possibly be if the state had
been determined before measurement. Quantum mechanics, it seems, forces you to give up
on determinism and locality. It is fundamentally unpredictable and non-local.
Ok, you may say, cool, then let us build a transmitter, forget our frequent flyer cards
and travel non-locally from here on. Unfortunately, that does not work. Because while quantum
mechanics somehow seems to be non-local with these strong correlations, there is nothing
that actually observably travels non-locally. You cannot use these correlations to send
information of any kind from one side of the experiment to the other side. That’s because
on neither side do you actually know what the outcome of these measurements will be
if you chose a particular setting. You only know the probability distribution. The only
way you can send information is from the place where the particle decayed to the detectors.
And that is local in the normal way.
So, oddly enough, quantum mechanics is entirely local in the common meaning of the word. When
physicists say that it is non-local, they mean that particles which have a common origin
but then were separated can be stronger correlated than particles without quantum properties
could ever be. I know this sounds somewhat lame, but that’s what quantum non-locality
really means.
Having said this, let me add a word of caution. The conclusion that it is not possible to
explain the observations by assuming the spins were already determined at the moment the
original particle decays requires the assumption that this decay is independent of the settings
of the detectors. This assumption is known as “statistical independence”. If is violated,
it is very well possible to explain the observations locally and deterministically. This option
is known as “superdeterminism” and I will tell you more about this some other time.
That’s it for today, thanks for watching, see you next week.