Quantum Entanglement Fully explained

(skipping time-wasting intros. Let's get straight INTO it...)

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Quantum Entanglement Fully explained

( or the incredible weirdness of quantum 'spin ')

There is a seeming disconnect between our common sense view of the world and the seeming 'weirdness' of experimentally verifiable facts!

Quantum mechanics, while 100% successful in predicting experimental results, is notoriously lacking in providing any rationale for its own success!

However actually understanding quantum entanglement has less to do with understanding quantum mechanics, and more to do with looking closely at your common sense view of things.

It is not something that the 'mere mathematics' of quantum mechanics can, by itself, ever give you.

Because quantum mechanics is not where the problem is;

our normal classical view is where the problem is.

And there are basically only two approaches:

(1) accept the postulates of quantum mechanics on faith, because they give the correct results as verified by experiment
(2) clarify your normal common sense view until the postulates of quantum mechanics become self-evident.

The first of these does not lead to understanding, the second does.
So it is the second approach which is pursued here.
Just as you might as well understand why Pythagoras' Theorem is true, as well as merely using it

As presented here then, in order to properly understand entanglement, spin, non-locality, Bell inequality violation etc, it is necessary to understand the chapter titled "falling off a log".

And in order to properly understand the chapter titled "falling off a log", is it necessary to read the chapters preceding it... in sequence.
From the beginning.
They're very simple, non-technical,
but necessary.
So, starting from scrtach...

An electrical current flowing along a wire causes a magnetic field around the wire.

You can see this yourself: just get a battery, a bit of wire, a compass-needle and a bit of string.

If you bend this current-carrying wire into a loop, and attach each end to each end of the battery, one side of this loop will be a north pole and the other side will be a south pole.  Dangle the whole thing from the piece of string and one side will always face magnetic north.

And voila! you have just made an electromagnet.
Its that easy!

That's what "scientists" thought about electrons back in the day.

Electrons have electric charge and since they were thought of as little tiny balls it seemed only reasonable to suppose that if they were to "spin" they would be like little magnets too.
"spin" is represented as a vector.

Positive spin points in the forward direction if the rotation is clockwise.

So spinning charged particles were thought of as little magnets, like this:

If you put a bar-magnet in a uniform magnetic field its north pointing to the South and its south pointing to the North. It won't really get moved either way because the south pole is pulling it south with the same force as the North pole is pulling it north....
(you'd have to get them all exactly half way between the two poles though, which is pretty impossible in practice. But this is just getting an idea accross.)



perhaps a little bit counterintuitively, if the north pole of the apparatus is weaker than the south pole of the apparatus, the bar-magnet will move toward the North pole of the apparatus if the bar-magnet's north pole is pointing toward the North pole of the apparatus and away from the north pole of the apparatus if its south pole is pointing toward the north pole of the apparatus. (assuming all the magnets were all perfectly vertical aligned along the field) .

Classical magnets can have any orientation to the field and you'd never be able to get them to behave like this; they 'd be at all sorts of angles and hence would rotate in the field etc. but again, this is just by way of introducung an idea.


If you fire a bunch of electrons through such an asymetric magnetic field, you might well be baffled about what happens.

Here's what happens:
When you fire a bunch of electrons through, all of who's magnetic vectors / spins are supposedly pointing in random higgledy-piggledy directions, some straight up, some not quite straight up, some nearly 'flat' barrelling through, some slightly pointing down, some pointing straight down, you might expect to see a spread of where these electrons would hit a screen, because each would therefore be deflected differently by the asymetric magnetic field, right?

shock horror! not a bit of it!

What you get is two distinct spots on the screen!

50% of the electrons are spin-up and 50% of them are spin-down, not only that, but they are spin-up or spin-down by EXACTLY the same amount !


Turn the apparatuses sideways and... The dots move. Rotate the apparatus around 360 degrees, and always its the same result: always just two beams: one aligned fully spin-up along the apparatus's magnetic field, and the other aligned fully spin-down.
How could the little magnets behave this way?

But this is only the tip of the iceberg!
It gets even crazier!

Get a whole bunch of those "Stern-Gerlach apparatuses" (sga's) (that's what those asymetric magnetic field things are called. Stern and Gerlach were the guys who discovered this )
Split the beam vertically into two as you did before, and pass the "vertically spin-up" beam into a second SGA, also aligned vertically and this second SGA won't split the spin-up beam; it goes in spin-up and comes out spin-up.

So that's good news, at least there is some sanity in the universe. Every time you measure the spin-up beam in any of your vertically aligned SGAs, it is found to be still vertically spin-up.

ok so all the SGAs are working properly.


But now take a look at how many of these seemingly fully spin-up electrons are spin-up... and a bit left; and how many of them are spin-up and a bit right. 

To do this, set up another SGA on its side and pass the beam of vertically spin-up electrons through it.


You'll discover that exactly 50% of those spin UP electrons are spin-left and 50% of them are spin-right.

So you might think that that just means that half of them have their magnetic vectors oriented up-and-to-the-left and the other half have their magnetic vectors oriented up-and-to-the-right. Sounds reasonable right?

But take say, the beam that is spin-up-and-to-the-right, and check it's vertical spin again, you know, just to make sure, using another vertically aligned SGA, guess what you find.....

50% of them will now be vertically spin-DOWN!

"wtf?" you might say.

Remeasure the horizontal spin of THIS "spin UP and a bit right" beam again and ... 50% of THESE are now NOT spin-right at all; they are spin-LEFT !!!

When you fire a bunch of random electrons through your SGA oriented at an angle, θ, half the electrons come out spin-up in the direction of θ and half come out spin-down in the direction of θ.


when you fire a bunch of spin-up-along-vertical electrons, through your SGA oriented at an angle θ however.....

they don't  come out half and half, up and down along the θ direction!

Not even close !

You find that a beam of electrons, known to be spin-up along some direction R1, if it is later measured along some other direction R2,
the probability that it will be spin-up along R2 depends on the size of the angle θ between R1 and R2.

And it doesn't even have the decency to be proportional to cosine of θ as you might have expected (that is if you dare  to expect anything anymore) but instead it comes out as the square of the cosine of half  the angle θ!

Say "hello" to one of the most mysterious phenomena of modern physics.

It was first discovered back in the 1920's.

And just when you thought it couldn't get any weirder...

Put a bunch of electrons, 100% who's spins are known to be spin UP along the horizontal,
through a vertical SGA,
if you measure the horizontal spin of the upper beam,
such horizontal spin measurements will, as already said, give 50% of them spin UP along horizontal and 50% of them down along horizontal.

Similarly for the lower beam.

But ...

if you join the two beams, without making any measurements, and then make a horizontal spin measurement,

the two paths...
each of which individually result in 50% spin up and 50% spin down along horizontal,...
now combine to give.....
wait for it....

no spin  down along horizontal particles at all!

100% of them come out spin up!


In other words the same way that they went in!
It's as if the splitting and joining of the paths never happened!

...and it gets even WIERDER!

It wasn't long before physicists realized the phenomenon had nothing to DO with "spin" in the usual sense of that word, there WASN'T anything "spinning" at all ! The little magnetic bit was just sort of ...well... there! all non-composite particles seemed to have it.

They had no explanation for it then or now, it is as much a mystery to physicists today as it was back then.

But they said: "well hey, look, if we can't explain it, or account for it, can we at least organize facts about it, maybe tabulate the results in some neat orderly way?
The fact that (1) it is completely random whether a particular electron will come out spin-up or spin-down or spin-right or spin-left etc, and
the fact that (2) it is always fully the one or fully the other, and nothing in between and
the fact that (3) if you measure the spin in one direction, you lose all definite information about the component of spin in any other direction,
attracted the attention particularly of a certain group of physicists: the ones who were into this new fashionable theory "quantum mechanics".

If ever there was a phenomenon screaming out for a probabilistic formulation this was it!

They might not be able to explain it, but they were darned well going to:
organize it,
model it

and give it the full QM spit and polish,
and at least make the darned thing presentable if nothing else!

So they called it "intrinsic", and out of sheer pig-headed stubbornness, "spin". And to this day that's what its called: "intrinsic spin".

Well that's a bit unfair, it wasn't out of pig-headed stubbornness that they called it "intrinsic spin", but rather because, at the time they were still thinking of it as at least a KIND of 'spin'... or 'spin-ISH'... or something somehow RELATED to the notion of spin... and so they looked to their equations of angular momentum for some sort of "guide" or clue as to how to maybe build some SIMILAR equations that might account for THIS weird phenomenon. And they found some. And the equations turned out to be so similar to those of angular momentum that, even though there is nothing actually spinning, they just called it "intrinsic spin".

They have still no clue as to its origin or what it is, but they can measure it accurately, predict precisely the probabilities of its values, work with it, produce it in the lab etc etc.

So they did in fact:
organize it,
model it

and give it the full QM spit and polish,
and at least made the darned thing presentable
"just like it says on the tin".

Since these "quantum" guys were big time into probability and had much less sentimental attachment to classical deterministic physics than their predecessors, it didn't bother these guys in the least that it didn't manage to actually "explain" the phenomenon.

They were.... the new kids on the 'Bloch'.

But first a little armchair philosophy..

a little armchair philosophy

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