Hey Crazies.
Back in August of 1959, two physicists published a paper in The Physical Review.
They suggested that, maybe, we’ve been imagining the electromagnetic field all wrong.
They even outlined an experiment to prove it.
An experiment that almost broke locality.
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OK, first order of business:
What the heck is locality?
It’s easily one of the most important principles in all of physics.
It states that the behavior of an object or particle should only be influenced by events or phenomena
at the location of said object or particle.
The universe is inherently local.
In other words, for two things to affect each other
they have to be at the same place.
It’s kind of a big deal.
And not like Big Deal Clone,like an actual big deal.
Hey!
Anyway, most forces require physical contact to work.
Things have to touch each other.
But, even before quantum mechanics came along,
we knew this locality principle had a few notable exceptions.
Gravity being the most obvious.
It seems to be able to reach out over unimaginable distances.
It makes this squirrel fall near the surface of the Earth.
But it also keeps the Moon in orbit around the Earth
and the planets around the Sun,
and the stars inside the galaxy.
Which, you know, seems a little strange.
But, rather than give up on locality, we considered the possibility that, maybe,
that affect isn’t direct.
Instead of the Earth affecting this rock, maybe the Earth does something to space
and it’s the space that actually affects the rock.
It’s something we call a field: a number or set of numbers assigned to points in space.
In classical or Newtonian physics, that field is made up of arrows called vectors.
In general relativity, it’s made up of curvature tensors, but it’s still a field.
It’s a number or set of numbers assigned to points in space.
Isn’t that a little mathematical?
Yes, but so is everything else in physics.
Lots of mathematical things represent something real.
For example, we represent motion with a velocity arrow.
The motion is real. The velocity arrow is not.
It’s just the math that represents the real thing.
The same is true for this gravitational field.
I mean, it’s not like my hand is hitting a bunch of arrows right now.
But locality says the Earth can’t affect this rock directly,
so the force must be due to something located where the rock is.
We call that a gravitational field and represent it with a bunch of arrows.
It’s not a substance or a fluid or anything, but it’s something.
Something is there.
And, whatever it is, it preserves the principle of locality.
The Earth creates a field and it’s that field that affects the rock.
We can very easily extend this concept to electricity and magnetism.
Charges don’t affect each other over a distance.
One charge creates an electric field and that field affects the second charge.
Magnets don’t affect each other over a distance either.
One magnet creates a magnetic field and that field affects the second magnet.
Locality is preserved.
Or is it?!
In this video, we learned the behavior of a particle is described by a wave.
Something we call a quantum wave function.
I also mentioned that wave was unobservable
and that’s true. It is.
But, if we have two particles, we might be able to see a difference.
This wave could have started here
or here
or even here.
As time plays out, you can see these waves are out of sync.
We say they’re out of phase in time.
But all three of those waves describe the same particle.
It’s something we call global phase invariance.
You want the wave to start here instead of here.
Quantum particle don’t care!
The probabilities you calculate from that wave function
will be exactly the same regardless.
But,
back in 1959, two physicists proposed an experiment that calls everything into question.
Say we’ve got a device that emits electrons that are all in-phase.
That means their waves are all synced.
If we separate two of those electrons and then bring them back together,
they should still be in-phase.
And that’s exactly what happens when we do the experiment.
We get a pattern on a detector screen that is consistent with two waves in-phase.
Wait, what’s that screen made of? What kind of electron device? How are you separating the electrons?
None of that matters!
Don’t get hung up on unimportant details.
All that matters here is that they’re in-phase at the end.
How we got there is completely irrelevant.
OK, so we get a pattern on a detector screen that is consistent with two waves in-phase.
Everything is fine so far. No problems at all.
Now let’s consider a second device called a solenoid.
That’s just a long densely-packed coil of wire, nothing too fancy.
If we run an electric current through that wire, we’ll get a magnetic field,
but only inside the coil.
Outside the coil, the field is so weak, you might as well just say it’s zero.
Things start to get weird when we use this coil in our experiment.
Say we place the coil in the middle, so the two electrons go around the outside.
There’s no field out there,
so the principle of locality says they shouldn’t be affected.
Things should only be affected by other things at their location.
Except those electrons are affected.
We get a different pattern on the detector screen.
The electron waves are out-of-phase.
What? What? What?!
I know, right?!
Somehow the magnetic field here is affecting the electrons all the way out here.
That shouldn’t be possible.
So do we finally give up on locality then?
Eh, not so fast.
This phase effect is called the Aharonov-Bohm Effect
after the two physicists who proposed the experiment.
Thankfully, those same two physicists
phys physicist?
phys phys physicist?
Thankfully, those same two physicists also proposed a solution.
What if there is something in the space the electrons are passing through?
We know there’s no magnetic field,
but maybe the magnetic field isn’t the best way to look at this.
In basic mechanics, you normally use forces and Newton’s second law.
That’s where electric and magnetic fields are the most useful.
An electric field is a force per unit charge.
It tells you how much force could be exerted on a charge at that point.
The magnetic field does the same thing for magnets and moving charges.
The two of them together allow us to find an electromagnetic force.
But forces are not the only way to look at a situation.
Sometimes, energy and momentum can give you a deeper insight.
Take this battery for example.
It has a voltage of 1.5 volts
and a volt is just a joule per coulomb, an energy per unit charge.
What that means is the energy at the positive end of the battery is 1.5 volts higher
than the energy at the negative end of the battery.
That number isn’t just limited to those two locations though.
This battery assigns a number like that to every point in space.
It’s something we call the electric potential.
And, since that number is assigned to every point in space, it’s a field.
A scalar field.
This number tells us the energy that one coulomb of charge would receive
from the battery at each location in space.
However, the solenoid in our experiment doesn’t have an electric potential around it.
It has a magnetic potential!
Which fulfills a similar purpose, but for momentum instead of energy.
Since momentum is a vector, so is the magnetic potential,
which is why we call it a vector potential.
We have one of these magnetic potential fields outside our solenoid.
And it solves our locality problem.
The electrons in our experiment pass right through that magnetic potential
and it predicts the phase difference we see on the detection screen.
So, locality, it’s kind of a big deal.
Things should only be affected by other things at their location.
It’s a principle we see obeyed over and over and over again.
If you want to affect something over a distance,
You’ve got to send something between you and that thing.
Maybe that exchange happens because of a physical object.
Ugh! Ouch!
Maybe it happens because there’s some kind of field.
But, no matter what, even in weird quantum experiments like this one,
there is something local.
Locality must be preserved at all costs.
So, do you have any questions?
Please ask in the comments.
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And until next time, remember, it’s OK to be a little crazy.
Wait, what about quantum entanglement?
Aww, sh....
The featured comment comes from Feynstein 100.
who pointed out how amazing the quantum wave function is.
I admit, it is amazing, but that doesn’t make it real.
It’s more like a coded message.
In order to make sense of it, you have to decode it first.
It’s the decoded information that’s real.
Anyway, thanks for watching.