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- In the 1930s, Albert Einstein was upset with quantum mechanics. He proposed a thought
experiment where, according to the theory, an event at one point in the universe could
instantaneously affect another event arbitrarily far away. He called this "spooky action at
a distance" because he thought it was absurd. It seemed to imply faster than light communication,
something his theory of relativity ruled out. But nowadays, we can do this experiment, and
what we find is, indeed, spooky. But in order to understand it, we must first understand
spin. All fundamental particles have a property called spin. No, they're not actually spinning,
but the analogy is appropriate. They have angular momentum, and they have an orientation
in space. Now, we can measure the spin of a particle, but we have to choose the direction
in which to measure it, and this measurement can have only one of two outcomes. Either
the particle’s spin is aligned with the direction of measurement, which we'll call
spin up, or, it is opposite the measurement, which we'll call spin down. Now, what happens
if the particle spin is vertical, but we measure it's spin horizontally? Well then, it has
a 50% chance of being spin up, and a 50% chance of being spin down, and after the measurement,
the particle maintains this spin, so measuring its spin actually changes the spin of the
particle. What if we measure spin at an angle 60 degrees from the vertical? Well now, since
the spin of the particle is more aligned to this measurement, it will be spin up 3/4 of
the time, and spin down 1/4 of the time. The probability depends on the square of the cosine
of half the angle. Now, an experiment like the one Einstein proposed can be performed
using two of these particles, but they must be prepared in a particular way. For example,
formed spontaneously out of energy. Now, since the total angular momentum of the universe
must stay constant, you know that if one particle is measured to have spin up, the other, measured
in the same direction, must have spin down. I should point out, it's only if the two particles
are measured in the same direction that their spins must be opposite. Now here's where things
start to get a little weird. You might imagine that each particle is created with a definite
well-defined spin, but that won't work, and here's why. Imagine their spins were vertical
and opposite. Now, if they're both measured in a horizontal direction, each one has a
50/50 chance of being spin up. So, there's actually a 50% chance that both measurements
will yield the same spin outcome, and this would violate the law of conservation of angular
momentum. According to quantum mechanics, these particles don't have a well-defined
spin at all. They are entangled, which means their spin is simply opposite that of the
other particle. So, when one particle is measured, and its spin determined, you immediately know
what the same measurement of the other particle will be. This has been rigorously and repeatedly
tested experimentally. It doesn't matter at which angle the detectors are set, or how
far apart they are, they always measure opposite spins. Now just stop for a minute, and think
about how crazy this is. Both particles have undefined spins, and then you measure one,
and immediately you know the spin of the other particle, which could be light-years away.
It's as though the choice of the first measurement has influenced the result of the second faster
than the speed of light, which is, indeed, how some theorists interpret the result. But
not Einstein. Einstein was really bothered by this. He preferred an alternate explanation,
that all along the particles contained hidden information about which spin they would have
if measured in any direction. It's just that we didn't know this information until we measured
them. Now, since that information was within the particles from the moment they formed
at the same point in space, no signal would ever have to travel between the two particles
faster than light. Now, for a time, scientists accepted this view that there were just some
things about the particles we couldn't know before we measured them. But then along came
John Bell with a way to test this idea. This experiment can determine whether the particles
contain hidden information all along, or not, and this is how it works. There are two spin
detectors, each capable of measuring spin in one of three directions. These measurement
directions will be selected randomly, and independent of each other. Now, pairs of entangled
particles will be sent to the two detectors, and we record whether the measured spins are
the same, both up, or both down, or different. We'll repeat this procedure over and over,
randomly varying those measurement directions, to find the percentage of the time the two
detectors give different results, and this is the key, because that percentage depends
on whether the particles contain hidden information all along, or if they don't. Now, to see why
this is the case, let's calculate the expected frequency of different readings if the particles
do contain hidden information. Now, you can think of this hidden information like a secret
plan the particles agree to, and the only criterion that plan must satisfy is that if
the particles are ever measured in the same direction, they must give opposite spins.
So, for example, one plan could be that one particle will give spin up for every measurement
direction, and its pair would give spin down for every measurement direction. Or another
plan, plan two, could be that one particle could give spin up for the first direction,
spin down for the second direction, and spin up for the third direction, whereas its partner
would give spin down for the first direction, spin up for the second direction, and spin
down for the third direction. All other plans are mathematically equivalent, so we can work
out the expected frequency of different results using these two plans. Here, I'm visually
representing the particles by their plans, their hidden information. With plan one, the
results will obviously be different 100% of the time. It doesn't matter which measurement
directions are selected, but it does for particles using the second plan. For example, if both
detectors measure in the first direction, particle A gives spin up, while particle B
gives spin down. The results are different. But if instead, detector B measured in the
second direction, the result would be spin up, so the spins are the same. We can continue
doing this for all the possible measurement combinations, and what we find, is the results
are different five out of nine times. So, using the second plan, the results should
be different 5/9 of the time, and using the first plan, the results should be different
100% of the time, so overall, if the particles contain hidden information, you should see
different results more than 5/9 of the time. So what do we actually see in experiment?
Well, the results are different only 50% of the time. It doesn't work, so the experiment
rules out the idea that all along, these particles contain hidden information about which spin
they will give in the different directions. So, how does quantum mechanics account for
this result? Well, let's imagine detector A measures spin in the first direction, and
the result is spin up. Now, immediately you know that the other particle is spin down
if measured in the first direction, which would happen randomly 1/3 of the time. However,
if particle B is measured in one of the other two directions, it makes an angle of 60 degrees
with these measurement directions, and recall, from the beginning of this video, the resulting
measurement should be spin up 3/4 of the time. Since these measurement directions will be
randomly selected 2/3 of the time, particle B will give spin up 2/3 times 3/4 equals half
of the time. So both detectors should give the same results half of the time, and different
results half of the time, which is exactly what we see in the experiment. So quantum
mechanics works. But there is debate over how to interpret these results. Some physicists
see them as evidence that there is no hidden information in quantum particles, and it only
makes sense to talk about spins once they've been measured, whereas other physicists believe
that entangled particles can signal each other faster than light to update their hidden information
when one is measured. So, does this mean that we can use entangled particles to communicate
faster than light? Well, everyone agrees that we can't. And that is because the results
that you find at either detector are random. It doesn't matter which measurement direction
you select, or what's happening at the other detector, there's a 50/50 probability of obtaining
spin up or spin down. Only if these observers later met up and compared notebooks, would
they realize that when they selected the same direction, they always got opposite spins.
Both sets of data would be random, just the opposite random from the other observer. That
is, indeed, spooky, but it doesn't allow for the communication, the sending of information
from one point to another, faster than light, so it doesn't violate the theory of relativity.
And that, at the very least, would make Einstein happy.
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Quantum Entanglement & Spooky Action at a Distance

11 分類 收藏
林宜悉 發佈於 2020 年 3 月 29 日
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