(skipping time-wasting intros. Let's get straight INTO it...)
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Quantum Entanglement Fully explained
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,
So, starting from scrtach...
An electrical current flowing along a
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
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
perhaps a little bit counterintuitively,
if the north pole of the apparatus is weaker than the south pole of the
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
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) .
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
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
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
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 avertical SGA, if you
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
Similarly for the lower beam.
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
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!
as if the splitting and joining of the paths never happened!
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
the fact that (3) if you measure the spin in one direction,
you lose all definite information about the component of spin in any
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
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.