From time to time, I give public lectures
and my very favorite part is the question and answer session that inevitably follows. The audience often comes up with interesting
questions, but one of them sticks out in my mind. A young woman once asked me “what is the
weirdest physics phenomenon you’ve ever learned about?” Now I don’t remember how I answered her,
but it got me to thinking and I realized that I should have told her about a thing called
quantum entanglement. It still blows my mind. Let’s see if you agree with me. Broadly speaking, quantum mechanics is a physics
theory that describes the behavior of atoms and even smaller particles. But quantum entanglement allows for weird
quantum behaviors to be seen on sizes as big as people or even larger. So just what is quantum entanglement? In an earlier video, I talked about how the
behavior of a subatomic particle, like a photon or an electron, is described by what is called
a wave function. Brushing over many details, the wave function
governs the probability that you will find the particle in a particular configuration. Before you make a measurement, you can’t
know- even in principle- what configuration the particle is in. To give a concrete example of what I mean
by the word configuration, let’s use the direction of the spin of a particle. Now there is a quantum weirdness in that when
you measure the direction of the spin of a particle, you first have to pick a direction
and then the outcome will always be either in the direction you picked or exactly opposite. It can’t be anywhere in between. So, if you picked a measurement direction
to be horizontal, the measurement of the spin direction could be left or right. It couldn’t be up or down, forward or back,
or any direction except for right or left. On the other hand, if you decided to measure
in the vertical direction, the only outcomes of your measurement would be up and down. Left and right would be forbidden. It’s certainly counterintuitive, but it’s
just a weird fact of life in the quantum world. Now, prior to the measurement, the wave function
might say that the spin axis of the particle could be in any direction- indeed, the most
popular understanding of quantum mechanics says that the spin direction actually is in
all directions allowed by the wave function. It’s only when you make a measurement that
the wave function collapses, and the outcome becomes real. If you’d like some more information on wave
functions and how they collapse, that other video might help. Now, what would happen if you had two subatomic
particles? If you’re like me, you’d think that they’d
both be governed by an individual probabilistic wave function and they’d be totally independent,
with the spin direction of one particle having nothing to do with the spin direction of the
other and both of them being in all directions until a measurement is made. And that happens, with four possible outcomes. Two wave functions and two probabilities,
with all combinations of up and down. However, it’s possible to prepare two subatomic
particles so they both are described by a single wave function. That’s what we mean by entangled. Two particles and a single wave function. You’d do this by taking a parent particle
which, in our example, has zero spin, and let it decay into two particles. Spin is a conserved quantity, which means
that it can never change. So, if the parent particle has zero spin,
then the two daughter particles have to have opposite spin. If one has a spin pointing left, the other
is right. If one is up, the other is down, and so on. When you add the two, you get the zero that
you started with. So that’s the simplest example of a pair
of entangled particles, which is to say two particles with opposite spin and a single
wave function that governs both of them. Okay, so now we’re getting somewhere. The entanglement doesn’t depend on the two
particles being close to one another. As long as the two particles don’t interact
with anything, you can separate them by feet, miles, or even huge distances, and the two
particles are connected by a single wave function and the two particles will have opposite spin. Now, remember that one of the key facets of
quantum mechanics is that the quantum world is intrinsically probabilistic. We can’t know- even in principle- the outcome
of a measurement before we make it. So, suppose we select one of the two particles
and pick a direction to measure the spin. Say we pick horizontal. The measured spin will be either right or
left, each 50% of the time. We could have selected the other particle
to do the measurement, with the same result- 50% right and 50% left. The real weirdness arises when we measure
the spin direction of both of the entangled particles. Say we measure the horizontal spin direction
of this particle over here on the left and the measurement says it’s to the right. Then we know the outcome of the other measurement. It will be- 100% of the time- left. A hundred percent of the time. That means that the information that one of
the two particles had a measurement made on it was transported to the other particle. And here’s the spooky thing. We can measure the spin direction of the two
particles in quick succession– so quickly that we measure the second one before any
conceivable information from the first measurement could have arrived. Let’s be super concrete on this by remembering
that the fastest thing in the universe is light. It travels a foot in a billionth of a second. Now let’s take two entangled particles and
separate them by ten feet. It will take light ten billionths of a second
to travel from one to the other. So now let’s get tricky. We’ll measure the horizontal spin of one
of the two particles and see that it’s to the right. Then, five billionths of a second later, we
measure the horizontal spin of the other particle. We find, 100% of the time, that it’s to
the left. And remember that we did it so fast that not
even light could have told the second particle the outcome of the measurement of the first
particle. That means that quantum information can travel
faster than light. You heard me right. Faster than light. That blew Einstein’s mind too. In fact, he coauthored a paper in 1935 with
Boris Podolsky and Nathan Rosen that highlighted this problem. He also called this transfer of quantum information
“spooky action at a distance.” This was one of many reasons why Einstein
didn’t like quantum mechanics. So, what do we think about this phenomenon
today? Does quantum information move at speeds faster
than light? Yeah- it seems to. But it doesn’t invalidate Einstein’s theory
of relativity because we can’t control it. We can make both measurements and the outcome
will seem random and we’ll only know that the two were opposite when we compare the
measurements and that information can be transferred no faster than the speed of light. So that saves Einstein’s theory, which is
a relief. Otherwise, I’d have to learn a whole new
bunch of physics. But it’s still perplexing. How is it that quantum mechanics can travel
so fast? Well there were some people, including Einstein,
who thought that this wasn’t so mysterious at all. Suppose you had a red and blue ball, but you
couldn’t look at them. You grab both of them and put them in boxes
and separate the boxes. Later, you look in one of the boxes and see
that it contains a blue ball. It will surprise nobody that the other ball
is red. The answer was determined at the moment the
balls were put in the boxes, not when the first ball was observed. And, I admit, when I first heard about this,
that was pretty much my reaction. The technical name for this more ordinary
connection is called “hidden variables.” So, the question is “How do we know that
there is something new and different about quantum mechanics?” How can we test the idea of quantum entanglement
and compare it to the more intuitive idea of hidden variables? There is a long history of this, with a prediction
in 1964 by theorist John Bell and a test in 1981 by Alain Aspect, as well as contributions
by many others. I’m going to forgo the history and the details
of the mathematics of the predictions and just explain the measurement. We know that if we measure the spin direction
of one particle, that the other one will be in the opposite direction, but let’s change
it up. Suppose that we measure the spin of the second
particle in a totally different direction. How does that change things? Let’s measure the direction of the first
particle in the vertical direction, but the second one in the horizontal direction. That means that when you measure the spin
of the second particle, it will be either right or left. That’s weird, but remember that's how this
works for quantum spin measurements. Now, I’m going to simplify the discussion
by only talking about the situation when the spin direction measured for the first particle
is just up. We could be more general and include both
up and down cases, but it’s more confusing and the answer is absolutely identical. If you want to do the general case, let me
invoke the phrase that physics professors love and students hate, which is “the exercise
is left to the student.” Okay, now let’s get into both the quantum
and hidden variable predictions. The first measurement is in the vertical direction
and it finds the particle has spin up. When you measure the spin of the second, you
measure it in the horizontal direction, and you get right and left with equal probability. The first measurement gives you zero predictive
information about the second measurement. It turns out that both quantum mechanics and
hidden variables make the same prediction for this scenario. This is very different from if you made the
second measurement in the vertical direction, because, if you did, you’d get a second
measurement in the downward direction 100% of the time. Again, this is the same for both quantum mechanics
and hidden variables. So now we’re ready for the final bit, which
is to look at all possible measurement directions for the second particle and see if the predictions
are different for quantum mechanics and hidden variables. We will still assume that the spin direction
measurement for the first particle is upward and then measure the spin direction for the
second particle, starting upward and then slowly spinning the measurement through 360
degrees. This graph shows the predictions of how often
the second measurement will be in the direction the second arrow is pointing. If the second arrow is pointing upward, we
know that the second measurement is always downward, so that means the second measurement
agrees zero percent of the time. If the second arrow is pointing at 90 degrees
to the right, the second measurement can be right or left with equal probability, so it
will be to the right only 50% of the time. If the second arrow is pointing downward,
we know that the second measurement always is downward, so it is in that direction 100%
of the time. And, as we go to 360 degrees, the pattern
is reversed. It’s very important that we see that the
predictions from hidden variables and quantum mechanics are different. This is key. So those are predictions. What does a measurement say? Well these black dots show the measurement
and they are quite definitive. Quantum mechanics is correct and the whole
idea of hidden variables is completely ruled out. So, what does this mean? It means that the idea that the final measurement
is already determined at the moment the two particles is entangled is false. It means that when you measure one of the
two particles, the quantum information is transferred to the other particle at a speed
faster than light. Now with such a provocative statement, you
can imagine that there is a lot of discussion. So first the biggie– no, this does not mean
that you can use this to transfer actual information. The collapse of the wave function is still
statistical, and it cannot transmit a message. So sorry, we’re still stuck with light-speed
communication for practical matters. Another feature of this measurement is that
scientists have thought very carefully about exactly what it means. There are some ideas, but all are weirder
than quantum mechanics. And, of course, nobody knows if those ideas
are right or not. The bottom line is that, at a minimum, classical
physics and hidden variables just don’t apply in the quantum world. It’s quantum mechanics all the way. The good news is that this new quantum interconnectivity
can be useful in such things as quantum computing and quantum teleportation. Hmmm... did I just come up with the topic
for a future video? Alright- this video was long, but there is
a lot of counter-intuitive stuff in the quantum world. And there is a lot more to learn, which is
great, because this is a thriving research field these days. If you liked learning that we can definitively
rule out classical intuition, please like the video and share it with your friends. And be sure to subscribe to the channel, because
this channel is a place where you can come and hear about the most fascinating fields
of science there is- which is physics of course, because, well- physics is everything.
