Quantum mechanics sometimes looks like an assorted mix of weird stuff. There’s wave-particle duality,
where quantum objects sometimes look like little compact particles and sometimes like
spread-out waves. There’s superposition, where the objects seem to be two things at once.
There’s the uncertainty principle, which says the universe seems to conspire to stop us from knowing
every detail of a quantum object. And then there’s entanglement.
Albert Einstein famously described this as “spooky action at a distance,” where
doing something to one of a pair of entangled particles seems to instantly affect the properties
of the other, no matter how far away it is. Now, the truth is that none of these descriptions
of quantum phenomena is quite right. They’re all really just efforts to use our everyday language
to talk about things that can’t quite be described by it. That’s especially true of entanglement,
which is not spooky action at a distance, at all. It’s something that is difficult
to describe with our everyday intuitions. But its worth trying to understand it because
as Erwin Schrodinger said, it is, “…the characteristic trait of quantum mechanics
that enforces its entire departure from classical lines of thought”
In addition, entanglement is the key ingredient of the newfangled technologies we keep hearing
more and more about: super-powerful quantum computers and uncrackable data
encoding using quantum cryptography. It’s about to become very real for everyone.
So what the heck is entanglement? I think that with a few illustrations and animations,
we may yet be able to understand it a little bit better. And that’s coming up right now…
Entanglement sounds sort of like entangled pairs of people. If Alice and Bob get married – they
literally become entangled by tying the knot. Suppose then that Bob tragically
dies. Alice goes from being a wife to a widow. What happens to Bob changes Alice’s status too.
But what entanglement means for quantum particles is a lot stranger than this. Here’s why:
Imagine the particles are electrons, which have a quantum property called spin that makes them
act like little magnets. If we measure this spin for an electron, we’ll always find it pointing
in just one direction or the opposite: up or down, say. Now, we can imagine entangling two
electrons so that their spins are always pointing in opposite directions. If electron 1 has spin up,
electron 2 must have spin down, and vice versa. The two spins are said to be correlated.
They are like a pair of gloves – if one is right-handed, the other must be left-handed.
So now let’s say we entangle the two electrons in this way, and fire them in opposite directions.
We don’t know which of the pair is up and which one is down until we make a measurement.
If we find that electron 1 is spin up. We know the spin of electron 2 must be down.
This is not remarkable because we could do the same thing with the gloves.
We could put one in a package and send it to Alice, and the other to Bob. The moment Alice
opens her package and finds the right-hand glove, she knows Bob must have the left-hand glove.
The handedness of the gloves, like the spins of the electrons, is correlated.
But there is a crucial difference in this analogy. The handedness of the gloves in the package
was the same from the start. It never changed. It was always the right-hand glove that got sent
to Alice. If someone had intercepted the parcel before Alice got it, that person would have seen
that it was the right handed glove. With entangled particles
that’s not the case. Remember, all we did at the outset was ensure that the entanglement
made them correlated so that their spins point in opposite directions. We didn’t specify whether the
spin-up electron is number 1 or number 2. You might think, well OK, but it’s obviously one
or the other – it’s just that we didn’t know which was which until we measured one of them.
Well, that’s not quite so. Say we set up an electron
so that it could have either spin up or spin down when we measure it. That’s called a superposition.
Then, the electron’s spin orientation simply isn’t determined until the measurement is made.
It’s not just that we don’t know it yet – there is no definite answer one way or the other.
How do we know superposition is real and not just an illusion due to our ignorance? Well, one
experimental clue comes from the double slit experiment. This experiment shows
that a particle is indeed spread out like a wave that can be in many locations,
prior to measurement. But after measurement, the particle becomes distinct and localized.
This phenomenon is weird enough just for a single particle. But with entangled particles
it’s even weirder, because it then seems that a measurement on one particle determines the
outcome not just for that particle, but for both of them. When we only measured electron 1,
the measurement not only forced the universe to choose between spin up and spin down for that
particle – it also forced the opposite choice for electron 2, because of their correlation.
Albert Einstein thought up an experiment like this in 1935, in collaboration with two younger
scientists, Boris Podolsky and Nathan Rosen. They are referred to as EPR for short by combining the
first letters of their last names. They didn’t do it to show how weird quantum mechanics is.
They did it to show that quantum mechanics could be incomplete.
In this experiment it looks as though, by making a measurement on particle 1, we’re
triggering some effect that influences the spin of particle 2. And according to quantum mechanics,
this happens instantaneously: it takes no time for the effect to be felt by the other particle.
But that’s impossible because Einstein’s theory of special relativity, devised 20
years earlier, said that no influence can be transmitted faster than the speed of light.
It was as if, as Einstein said, there was some
impossible spooky action at a distance that passed instantly between particle 1 and particle 2.
Because of this, EPR reasoned that the whole idea of properties of quantum objects
remaining undetermined until one measures them, didn’t make sense. They figured that there must be
something – what Einstein called hidden variables – that fixes the orientations
of the spins all along. And that we couldn't actually measure these variables to find out the
orientations of the spins. That’s why they are hidden. But they must exist, according to EPR.
So the phenomenon they had discovered, which became known as entanglement,
seemed to blow a hole in the logic of quantum mechanics. But others, like Danish physicist
Niels Bohr, said that Einstein was just wrong. Bohr said there were no hidden variables,
and the fact that entanglement seemed to create these weird correlations between particles was
just something we had to accept as reality. There was no obvious way to tell who was right.
Scientists remained divided. It was no good just doing the experiment that EPR had proposed
because simply measuring the spins wouldn't tell you if those spins had been fixed all along,
like EPR thought, or whether they snapped into place after measurement, as Bohr thought.
It wasn’t until almost 30 years later, in 1964, that Irish physicist John Bell figured out how to
set up a clever experiment to determine who was right. It involved running the experiment again
and again on pairs of entangled particles while the experimenters themselves – Alice
and Bob – change exactly how they made those measurement each time. Then you look at how
strong the correlation is between the outcomes of measurement as those changes are being made.
Bell proved that quantum mechanics predicted stronger statistical correlations in the
outcomes of these measurements than any hidden variable theory possibly could.
I made a video about how Bell’s inequality works if you want to learn more about this.
Suffice it to say that when Bell’s experiment was first done in a lab in the 1970s by
physicists John Clauser and Stuart Freedman at the University of California Berkeley,
it showed that there was no sign of hidden variables, and that indeed, outcomes are
determined only by the act of measurement itself. And in the ensuing years, this aspect of quantum
mechanics has proven to be correct over and over again. Bohr was right, and EPR were wrong.
Now you might be thinking how exactly do you entangle two quantum objects to begin with?
The simplest way to make these is to entangle them from birth – like twins you could say.
Typically, researchers make the pair of photons in a single quantum jump,
for example when an atom that has been given some extra energy sheds it by emitting two photons at
once. There are clever ways of doing this with lasers, which is how Freedman and Clauser did it.
But there are other ways of creating entanglement, between objects like atoms or electrons. The
simplest way is to simply bring the particles together and let them interact. If you arrange for one
particle to affect the final state of a second particle, then, when you put the first particle
in a quantum superposition, the pair of particles can end up in a joint superposition – an entangled
pair. That’s really what entanglement is: a quantum superposition of more than one object.
So do Bell tests mean that Einstein’s spooky action at a distance is real?
You might hear that claim, but it's not right. EPR were thinking about entanglement the wrong way.
That’s not surprising, because what they were assuming was just common sense – so much so that
they didn’t even realize it was an assumption. They were thinking of the two particles as
separate objects. And why wouldn’t they? After all, they are sent flying in opposite directions
in space. And in principle you can wait until they are many light years apart before measuring them.
But once objects are entangled, they’re not separate. They are, in a sense,
two parts of a single object. Here’s what that means. In quantum mechanics,
objects are described by wave functions: mathematical expressions that encapsulate
all that can be said about the object. This wave function can be spread out in space. This
is why particles can act as if they are waves. Yet if we entangle two particles, they are then
described by a single wave function. And since two entangled objects are being
described by the same wave function, they are mathematically speaking the same object.
That’s really what entanglement means, and it’s why the particles’ properties
are then interdependent. If you do something to one of the particles, such as measure it,
you change the wave function and so you alter the other particle too, since it
is also described by the same wave function. Now, the question you might ask is: How can two
initially separate particles, by interacting, somehow combine their two wave functions into one?
It really comes down to the math. Before the particles interact, we can separate
the wave function of the whole system of both particles into a part that describes particle 1
and a part that describes particle 2. But after they’ve interacted, that’s no longer true.
We can’t point to any part of the total wave function and say, that bit is particle 1,
and the other bit is particle 2. This mixing up happens for almost any kind of interaction between them.
So once two particles are entangled, we can’t say anything about one of them without considering
the whole wave function. It’s as if their properties are now spread out over both.
This is why it doesn’t matter how far apart entangled particles are located – they’re still
interwoven by their joint wave function.
That’s the really strange thing. We are used to the properties of an object being in
or on that object. If my t-shirt is blue, the blueness is on the tshirt – it’s localized there.
If I have a coffee mug that’s blue, that’s the coffee mug’s blueness,
not the tshirt’s. But for entangled quantum objects, their properties can be nonlocal – spread
between both objects. Some of the tshirt’s blueness can be in the coffee mug's, and vice versa.
This brings us to why entanglement is at the heart of quantum mechanics, because
what it tells us is that the quantum world has a feature called nonlocality.
Things at one place don’t depend just on what happens in the neighborhood of that place,
as they do in the classical world. There seems to be an instantaneous connection between
different regions and particles, regardless of how far apart they are.
Why isn’t this “spooky action at a distance” then? That’s because Einstein’s picture
was of something at one place somehow transmitting its effect to another place – faster than light.
But quantum nonlocality is an alternative to that picture. What it really says is that we
can’t think of those two places as being distinct: quantum mechanics collapses them into a single
thing. In this sense, quantum mechanics seems to make nonsense of our normal sense of space.
In fact, some researchers suspect that quantum entanglement is more fundamental than space
itself, and that our notion of space actually emerges from the quantum entanglements that
connect objects in a vast web of interaction. What about using quantum entanglement for
communication? It’s tempting to imagine that entanglement will let us communicate faster
than light. Let’s say we make a pair of entangled particles and separate them by thousands of miles,
so that Alice has particle 1 in China, and Bob has particle 2 the US. If Bob takes a measurement
in the US, doesn’t that mean Alice’s particle in China is instantly affected? Well, yes it
seems so. But when Alice measures her particle it will seem like a random collapse to her. There’s
nothing meaningful about a measurement Alice makes until she finds out how much it correlates with
what Bob measured. And the only way to do that is by exchanging information about their measurements,
by sending an ordinary message. Email, snail mail, carrier pigeon – however they choose to do it.
They’ll never do it faster than light. This is why it’s impossible
to use the correlation between entangled particles to send any information instantaneously.
Now, there is at least one advantage to using entangled particles to send messages:
you can encrypt the message in a way that it can never be intercepted and decrypted
without that decryption being detected.
And they’ll know their message wasn’t secure.
That’s why quantum-entangled photons sent along optical fibers or by satellite signals are now
being used to encrypt sensitive messages, such as financial data, in a tamper-proof quantum
internet that’s still under construction. Entanglement is also the key to quantum
computing. Quantum computers with just a few dozen entangled quantum bits
have been shown to do calculations in seconds that would take conventional
supercomputers centuries. It’s probably going to play a big role in all our lives.
If you want to learn more about this fascinating world of quantum computing,
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