I recently gave a talk here at the Ri
on quantum mechanics, which I was very pleased to see
got a big response.
However, some people, some viewers of that talk,
expressed some bafflement or worse about an analogy
that I used during it.
And so I wanted here to go through that analogy
in a little more detail, hopefully, a little more
clearly, and explain what it's really about
and what it's really trying to show.
It's an analogy to try to understand the quantum
phenomenon called entanglement.
And I want first of all to point out
that the analogy isn't mine.
It's not something that I've invented.
It's adapted from an analogy that
was devised in the late 1990s by two physicists, Sandu
Popescu and Daniel Rohrlich.
And they were trying to understand
the implications of this quantum property of entanglement.
And I'll come back at the end to what it
was that they were exploring.
Now I think some people had the impression
that this was just a very complicated way of talking
about entanglement.
It's not doing that.
This analogy is actually doing something a little more
than that.
But I'll talk first of all about what entanglement is.
It's what happens when any two quantum particles interact.
It has to happen.
And what results from that is that those
particles, once they've interacted, they are entangled.
And it means that their quantum states are interdependent.
There's a correlation between them,
so that if one is in one particular state,
then the other one has to have some other particular state,
depending on the kind of entanglement that they have.
So the classic example would involve, say, two electrons.
And electrons have a quantum property
called spin, which you don't need to know anything about,
other than that the spin of an electron can have two values.
It's a bit like a sort of quantum heads or tails.
An electron can be spin up or spin down.
And if the electrons become entangled,
then this may create a situation where those two spins are
correlated such that if one of the electrons has a spin up,
then the other one must have a spin down.
Now this is a prediction of quantum mechanics.
And it was pointed out that this phenomenon of entanglement
can happen.
It was pointed out by Albert Einstein in 1935.
And he figured that there was something wrong about it.
I explained in the talk how we can think about entanglement.
In some ways, this correlation between the two
states of electrons, in some ways,
it's a bit like having two gloves, a left-handed
and a right-handed glove.
Now if you imagine that you have those two gloves,
and you send them out to two people on different sides
of the world, maybe.
And these two people-- we're going to meet them again
shortly-- are called Alice and Bob.
And they know that these gloves are a pair.
And so as soon as Alice receives her glove and opens the package
and finds she has the left-handed glove,
then she knows right away that Bob
must have the right-handed glove, because there is
this correlation between them.
There's nothing magical about how she gets that information.
It's just simple logic.
However, here's the complication in quantum mechanics.
Because Niels Bohr, the Danish physicist who pioneered early
quantum mechanics, suggested that,
in the case of quantum particles,
it's not the fact that they have this property, whatever it is,
spin or whatever,
all the time.
They only have that property with a fixed value
when we observe it.
So for these two entangled photons,
if we think of sending those out to Alice and Bob,
Bohr said, while they're going outwards,
they don't have a fixed orientation of their spin.
All we can say is that those spins are correlated.
So if Alice then measures her electron
and finds it has spin up, then Bob's will have spin down.
But that spin wasn't determined until Alice measured it.
And this is where Einstein felt there
was a problem with entanglement, because it seemed
to indicate that the act of Alice measuring her electron
spin somehow affected Bob's spin.
So that once Alice had found the spin had to be spin up,
somehow, magically-- or "spookily," as Einstein said--
that seemed to sort of transmit some kind of influence
to Bob's spin to make sure that it was spin down.
Alice could equally have measured her electron
and found that it had spin down, in which case,
Bob's would be spin up.
So there seemed to be this, what Einstein called,
"a spooky action at a distance" implied by Bohr's
idea of quantum mechanics.
Einstein and two colleagues, Podolsky and Rosen,
suggested in 1935 that, actually, there
has to be some alternative to this,
because spooky action at a distance
shouldn't be allowed in physics.
Einstein had showed that it is impossible for any signal,
any information to be transmitted faster than light.
And so you can't have this instantaneous action
at a distance.
There has to be some time for a signal to span the distance.
And so Einstein suggested that what must be going on instead
is that, all along, these two electrons had
some property that somehow fixed their spins already.
It's just that it was a property that we couldn't measure.
He called them hidden variables.
So you couldn't find out in any experiment which
of the two possible spins Alice's electron had
as it was going towards her.
But nevertheless, it was fixed.
And so that then reduces the situation
to being like the left-handed and the right-handed glove,
which were left-handed and right-handed
all along in transit.
So there were these two possibilities
for what entanglement was about, Bohr's view and Einstein's
view.
The trouble was, there was no obvious way of distinguishing
between them, because they both predicted the same outcome,
which was that we would measure--
or Alice and Bob would measure--
that there are these correlations
that exist between the spins of these two entangled electrons.
How do we know if that's due to hidden variables
or due to something else that Bohr was suggesting?
That changed in 1964, when the Irish physicist John
Bell suggested an experiment.
In that case, at that stage, it was just a thought experiment
that he said would allow us to distinguish between these two
possibilities.
And it's John Bell's experiment that these boxes, these quantum
boxes, are mimicking.
Personally, I've never seen an explanation
of John Bell's experiment that is at all easy to follow.
So instead of trying to explain John Bell's experiment,
that's what these boxes are for.
So here's how this box analogy works.
There are these two boxes.
They are machines, slot machines,
into which you can put a coin and get out a toy.
So you can put it in either-- they
will take either one-pound coins or two-pound coins.
And out will come one of two types of toy,
either a rabbit or a dog.
And there are particular rules for each kind of machine
that will tell you, if you put in a certain coin, then
you will get out a certain animal, OK?
And we have to figure out combinations
of which coins give which kind of animals in order
to satisfy three rules.
And I'm just going to postulate these rules.
But of course, they've actually been carefully chosen
so that they replicate the kind of situation
that quantum mechanics imposes in John Bell's experiment.
And the rules go as follow.
The first rule is very simple, that if Alice
puts in a 1-pound coin into her box, it will spit out a rabbit.
The second rule is that if both Bob and Alice put
in 2-pound coins into their boxes,
then the boxes will produce one rabbit and one dog.
And it doesn't matter which way 'round that is,
but they will have that combination.
The third rule is that any other combination
of coins other than two 2-pound coins
will produce either two rabbits or two dogs.
So we have to find inputs and outputs that
satisfy these three rules.
So what can they be?
Well, let's work through them.
We know already what the output of Alice's box
has to be if she puts in a 1-pound coin.
It has to be a rabbit.
That's the first rule.
Now when we think about it, this means that no matter which
coin-- whether a 1-pound or 2-pound--
Bob puts into his box, it has to produce also a rabbit.
That's because if Alice has produced a rabbit with 1 pound,
then the only way we can get a dog is that if they both put
in 2 pounds.
So Alice already put in 1 pound.
So Bob's box has to produce a rabbit in both of those cases,
with a 1-pound or a 2-pound.
So we've almost already figured out what our rules have to be.
So all we need to figure out now is
what a 2-pound coin in Alice's box will produce.
Well, let's think about it.
If she puts into a 2-pound, Bob puts in a 2-pound, too.
We've also got the second rule, which
says that two 2-pound coins have to produce
a rabbit and the dog.
So that must mean that a 2-pound in Alice's box produces a dog.
And then we've satisfied the second rule.
The trouble with that is that those inputs and outputs
violate the rules in another case.
Because for a 1-pound and a 2-pound,
we've got this combination of rabbit and dog.
But we're only meant to get that if they both put in 2 pounds.
So in one time out of the four possible permutations,
the rules are violated.
And no matter how you try and do this,
no matter how you try and think of different combinations,
you will find that you can never do better than three times out
of four.
Now if you think that you have found a solution that satisfies
these three rules all the time in all four cases,
it's probable that you've come up
with a solution like this one, a solution in which, let's say,
Alice's box alters its output depending
on which coin Bob put in.
There is no physical way--
if these boxes are unconnected, there
is nothing that passes between them--
there is no physical way in which
we can build a machine that does that, that somehow magically
or telepathically knows what the other person has
put in into their box.
So that's not going to work.
However, there is a way that we can allow that to happen,
which is that we produce a physical connection
between the boxes that sends a signal between them
so that Bob's box, for example, receives a signal telling it
what Alice has put into her box.
And then it might alter its output accordingly.
It's perfectly possible to produce a mechanism like that.
The trouble with that is that Bob
has to wait until the signal is received from Alice's box,
or until she's put in her coin and the signal has been sent.
He has to wait until that's happened
before he puts in his coin so that his box knows what to do.
That takes some finite amount of time.
Even if the signal is travelling at the speed of light,
it's still going to take some time to get there.
So that's not going to work if we're
trying to make boxes that satisfy
these rules instantaneously, when Bob and Alice put
in their coins at exactly the same moment.
We want an instantaneous solution to this problem.
So that's never going to happen.
At least, it's never going to happen for classical boxes.
If these are quantum boxes--
if we allow them this property of quantum entanglement
so that their inputs and outputs can be correlated in some way--
then we can do better.
And in fact, we know exactly how much better
we can do, because the laws of quantum mechanics-- the rules,
the mathematical equations-- allow
us to calculate exactly how much more often
we can satisfy the four rules compared to the classical case.
So in the classical case, we can only
get it three times out of four, 75% success rate.
Quantum mechanics tells you that you can get roughly 85%
success rate.
And why 85?
Well, that is just a number that the equations give you.
It's actually, more precisely, it's
a number that involves the square root of two.
We don't need to worry about that.
It's just approximately 85%.
But I will come back to why 85% later.
So quantum mechanics allows you to do better if these two
boxes are entangled.
And this is really what Bell's experiment
was allowing you to do.
You did the equivalent measurement
with two particles that were entangled.
And Bob and Alice were making measurements, making choices
about how they make those measurements,
and seeing how strong the correlation was between them.
According to classical physics, you could only
get a 75% correlation.
But the same was true, John Bell showed,
of Einstein's hidden variables.
It was only if quantum mechanics went beyond that,
as Bohr suggested it did, that you
could do better and get 85%.
Well, as I say this was just a thought experiment
for John Bell.
But very soon, physicists realised that you could do it
for real.
You could create two entangled particles
and make the measurements.
And this was done.
It was first done in the 1970s and then more
definitively in the 1980s.
And since then, it's been done many, many times
in many, many different ways.
Every single time, the result has been very clear.
The classical limit or the hidden variables limit
of 75% correlation between the particles is always exceeded.
You get this 85% success.
And so this suggests that Einstein's idea
that there are these things called hidden variables, which
fix the properties of quantum particles
before they're measured, this doesn't apply.
It seems that Bohr was right.
Now this doesn't imply, as you might sometimes hear,
that there really is some spooky action at a distance.
Many times, when experiments like this have been done,
the newspaper headlines have proclaimed
that Einstein is proven wrong and that spooky action
at a distance is real.
Spooky action at a distance was what Einstein's interpretation
of entanglement involved.
But actually, it is a better way to think about entanglement
to say something a little different.
And one way to think about it is to say that once the two
boxes become entangled, they are no longer separate objects, so
that what happens over here is completely independent of what
happens over here.
They are, in some quantum sense, the same object.
And that remains the case no matter how far apart they are.
Even if the particles that you measure were separated,
were on the opposite sides of a galaxy,
they remain, in some sense, a single quantum entity.
Another way of thinking about that
is to say that there is some kind of sharing
of information between them.
And this is really what Popescu and Rohrlich's quantum boxes
were about.
It was expressing this situation in terms of a kind of sharing
of information.
Physicists call this quantum nonlocality.
And it's distinct from this notion
that somehow making a measurement on this particle
is transmitting information--
is transmitting a signal--
to the other particle to fix what the value of its property
is.
That doesn't happen.
If it did happen, it would violate special relativity,
as Einstein suggested.
But quantum mechanics tells you something else.
It tells you that there is this property called
quantum nonlocality, which is very hard to find words for,
but that is a real property of the world.
So if you see headlines saying spooky action at a distance
is real, don't believe them.
Now I want to come back, finally,
to what Popescu and Rohrlich were
trying to do with their boxes.
Because one physicist, Yakir Aharonov,
suggested that perhaps what we're seeing here with this
quantum nonlocality is kind of a stretching of the normal laws
of cause and effect, as far as special relativity will allow,
so that somehow, quantum mechanics is sort of almost
violating the spirit of special relativity without violating it
actually in practise, without actually allowing you
to transmit information faster than light.
Perhaps quantum mechanics is doing
this right up to the limit of what is physically possible.
Well, Popescu and Rohrlich thought, let's see about that.
Can we imagine a case in which there
is some kind of entanglement that
does better than quantum mechanics, that
does better than 85%?
And they thought about it.
And they came up with this idea of these two boxes
that they showed could have a set of rules that,
without violating special relativity,
allows you 100% correlation.
It's physically breaking no laws, let's say,
that we know of to have a situation like this--
if you like, a kind of super-quantum correlation.
And so the question becomes, why isn't the world like this?
You see, we often think about quantum mechanics
as something sort of added on or something
different from classical mechanics.
Classical mechanics give you this sort of 75% success
rate in this case.
Quantum mechanics does something more.
So we kind of think, where does that come from?
Why does quantum mechanics allow you to do these things
that you can't do classically?
Popescu and Rohrlich approached it from another angle.
Because they show that, actually, things
could be even, if you like, more quantum than they are.
And so why aren't they?
And so that raises a new question.
If we could understand why quantum mechanics is
limited in what quantum nonlocality can do--
limited to this 85% figure instead of 100%--
if we could understand that, then maybe
we would understand a little more
about why it is that the world has these quantum properties
that it seems to have at the level of fundamental particles.
If you still find this analogy a little bit
confusing, then probably what you need to do
is to look it up in my book, Beyond Weird,
which talks about this and more and goes
into more detail about what quantum entanglement does
and doesn't mean, and also about how we're starting to make use
of it in quantum technologies, like quantum computing
and quantum cryptography.
And let me remind you, if you haven't already
subscribed to the Ri YouTube channel,
then you should do that.