Spooky action at distance explained.
Introducing spin.
Before we go into what spooky action at a distance entails, let’s chat about spin.
Particles have a property called spin and when the spin of a particle is measured it
will be either spin up or spin down in the axis that it is measured.
Let’s take an example.
Say we take a Particle and we know that it is spin up in Axis 1.
What happens if it is measured in Axis 3?
You might expect it to indicate no spin at all as this axis is perpendicular to axis 1,
but it will. It will be either spin up or spin down but across a number of measurements
the particle will indicate spin up and spin down equally across Axis 3 cancelling the
results out.
So what happens in Axis 2 which is a 60 degree angle from Axis 1?
As Axis 2 is closer to Axis 1 the particle will indicate it is spin up 3/4ths of the
time and spin down 1/4th of the time.
Entangled particles.
Entangled particles describes the phenomena when two particles become connected in such
a way that when the property of one particle is changed an instantaneous change in the
property of the other particle occurs.
Entangled particles have the opposite properties, so when one particle is spin up in one axis
the other particle will be spin down in that same axis.
A pair of entangled particles could be separated by an entire universe and when one is measured
to be spin up in Axis 1 the other will be spin down in that same axis.
Einstein called this phenomena spooky action at a distance.
Two explanations for entanglement.
Quantum mechanics explains the behaviour of entangled particles by saying there seems
to be some sort of instantaneous communication that happens when one particle’s spin is
measured which causes the other particle to take on the opposite spin.
Einstein offered up an alternative explanation. He said that during the entanglement process
it was decided by the particles what spin they would have in all axis to ensure that
they always had the opposite spins to each other.
Einstein’s explanation gives us two scenarios:
One where Particle A could decide that it would show spin up in all axis and Particle
B would show spin down in all axis or
another scenario where Particle A decided to indicate spin up in Axis 1, spin down in
Axis 2 and spin up in Axis 3 while Particle B decided to indicate spin down in Axis 1,
spin up in Axis 2 and spin down in Axis 3.
There could be different combinations.
Let’s call the combination we have just described as combination 1 and we’ll work
our way through another combination where Particle A could decide to indicate spin down
in Axis 1, spin up in Axis 2 and spin down in Axis 3 while Particle B decided to indicate
spin up in Axis 1, spin down in Axis 2 and spin up in Axis 3.
But notice something, the combination is just the same as before but only the particle name
is different.
We won’t go through each combination here but suffice to say that all possible combinations
can be achieved in scenario 2 by changing either the particle name or the axis number.
Bell’s theorem
British professor John Bell then came up with a way of testing which explanation worked
for the behaviour exhibited by entangled particles.
Two entangled particles are separated and placed in detectors that can measure their
spin in three different axis; Axis 1, Axis 2 and Axis 3.
Over a period of time different axis will be chosen and the spins of the particles measured.
This is what happens if Quantum mechanics is correct:
When Particle A is spin up in Axis 1 and Particle B is measured in Axis 1 it will be shown to
be spin down.
Now imagine an imaginary Axis 4 in the Particle B detector.
As the particle is spin down in Axis 1, it follows that it will be spin up in the direction
of Axis 4.
As Axis 2 and 3 are both at 60° angles from Axis 4, the spin of Particle B will indicate
that it is spin up in those two axis 3/4ths of the time as explained earlier in the video
when we first discussed spin.
So in the experiment when Particle A is measured as spin up in Axis 1,
Particle B will be measured in Axis 2 or 3 two thirds of the time - as they are two out
of the three axis that we are measuring - and as the particle will be spin up 3/4ths of the
time in those axis, the probability of Particle B being measured as spin up is:
⅔ x ¾ = ½
Mathematically it was calculated that if quantum mechanics is correct about how spooky action
at a distance works both Particle A and B will indicate the same spins 50% of the time
and different spins 50% of the time.
So now let’s discuss what would happen if Einstein’s alternative explanation is correct?
Well, Einstein’s explanation gave us two scenarios, one where the spin of Particle
A was spin up in all axis and the spin of Particle B was spin down in all axis and another
where Particle A was spin up in Axis 1, spin down in Axis 2 and spin up in Axis 3 while
Particle B decided to indicate spin down in Axis 1, spin up in Axis 2 and spin down in
Axis 3.
In scenario 1 as different axis are chosen and the spins measured both particles would
indicate different spin 100% of the time.
In scenario 2 as spins are measured across different axis there are actually 9 possibilities
that could emerge.
If Axis 1 is picked for both Particle A and B, the measurements show they have different
spins. If Axis 1 is picked for Particle A and Axis
2 is picked for Particle B the measurements show they have the same spins.
If Axis 1 is picked for Particle A and Axis 3 is picked for Particle B the measurements
show they have the different spins.
Let’s take a moment and tally up all the other possibilities.
It’s seen that if Einstein’s alternative explanation is correct, the particles would
show different spins at 5/9ths of the time in scenario 2.
So no matter what scenario, if Einstein's explanation was correct the particles would
indicate different spins somewhere between 5/9ths of the time to all of the time.
So what were the results?
Well, the spins were different 50% of the time and the prediction of quantum mechanics
held true whereas Einstein's alternative explanation didn’t work.
And that is spooky action at a distance summarised and explained.
As always this is a simplified explanation of complex ideas and I hope you found this
video informative and enjoyable and can use it as a springboard for further reading. Remember
to subscribe to LondonCityGirl for more interesting videos and I’ll see you next time.