Henry: If you have polarized sunglasses,
you have a quantum measurement device. Grant: Each of these pieces of glass is what's
called a "polarizing filter", which means when a photon of light reaches the glass,
it either passes through, or it doesn’t. And whether or not it passes through is effectively
a measurement of whether that photon is polarized in a given direction. Henry: Try this: Find yourself several sets
of polarized sunglasses. Look through one set of sunglasses at some
light source, like a lamp, then hold a second polarizing filter, between you and the light.
As you rotate that second filter, the lamp
will look lighter and darker. It should look darkest when the second filter
is oriented 90 degrees off from the first. What you're observing is that the photons
with polarization that allows them to pass through a filter along one axis have a much
lower probability of passing through a second filter along a perpendicular axis – in principle
0%. Grant: Here's where things get quantum-ly
bizarre. All these filters do is remove light – they
“filter” it out. But if you take a third filter, orient it
45 degrees off from the first filter, and put it between the two, the lamp will actually
look brighter. This is not the middle filter generating more
light – somehow introducing another filter actually lets more light through. With perfect filters, if you keep adding
more and more in between at in-between angles, this trend continues – more light! Henry: This feels super weird. But it’s not just weird that more light
comes through; when you dig in quantitatively to exactly how much more comes through, the
numbers don’t just seem too high, they seem impossibly high.
And when we tug at this thread, it leads to
an experiment a little more sophisticated than this sunglasses demo that forces us to
question some very basic assumptions we have about the way the universe works – like,
that the results of experiments describe properties of the thing you’re experimenting on, and
that cause and effect don’t travel faster than the speed of light. Grant: Where we're headed is Bell’s theorem:
one of the most thought-provoking discoveries in modern physics. To appreciate it, it’s worth understanding
a little of the math used to represent quantum states, like the polarization of a photon. We actually made a second video showing
more of the details for how this works, which you can find on 3blue1brown, but for now let’s
just hit the main points. First, photons are waves in a thing called
the electromagnetic field, and polarization just means the direction in which that wave
is wiggling. Grant: Polarizing filters absorb this wiggling
energy in one direction, so the wave coming out the other side is wiggling purely in the
direction perpendicular to the one where energy absorption is happening.
But unlike a water or sound wave, photons
are quantum objects, and as such they either pass through a polarizer completely, or not
at all, and this is apparently probabilistic, like how we don’t know whether or not Schrodinger’s
Cat will be alive or dead until we look in the box. Henry: For anyone uncomfortable with the nondeterminism
of quantum mechanics, it’s tempting to imagine that a probabilistic event like this might
have some deeper cause that we just don’t know yet. That there is some “hidden variable”
describing the photon’s state that would tell us with certainty whether it should pass
through a given filter or not, and maybe that variable is just too subtle for us to probe
without deeper theories and better measuring devices. Or maybe it’s somehow fundamentally unknowable,
but still there. Henry: The possibility of such a hidden
variable seems beyond the scope of experiment. I mean, what measurements could possibly
probe at a deeper explanation that might or might not exist? And yet, we can do just that. Grant:…With sunglasses and polarization
of light. Grant: Let’s lay down some numbers here. When light passes through a polarizing filter
oriented vertically, then comes to another polarizing filter oriented the same way, experiments
show that it’s essentially guaranteed to make it through the second filter.
If that second filter is tilted 90 degrees
from the first, then each photon has a 0% chance of passing through. And at 45 degrees, there’s a 50/50 chance. Henry: What’s more, these probabilities
seem to only depend on the angle between the two filters in question, and nothing else
that happened to the photon before, including potentially having passed through a different
filter. Grant: But the real numerical weirdness happens
with filters oriented less than 45° apart. For example, at 22.5 degrees, any photon which
passes through the first filter has an 85% chance of passing through the second filter. To see where all these numbers come from,
by the way, check out the second video. Henry: What’s strange about that last number
is that you might expect it to be more like halfway between 50% and 100% since 22.5°
is halfway between 0° and 45° – but it’s significantly higher. Henry: To see concretely how strange this
is, let’s look at a particular arrangement of our three filters: A, oriented vertically,
B, oriented 22.5 degrees from vertical, and C, oriented 45 degrees from vertical. We’re going to compare just how many photons
get blocked when B isn’t there with how many get blocked when B is there.
When B is not there, half of those passing
through A get blocked at C. That is, filter C makes the lamp look half as bright as it
would with just filter A. Henry: But once you insert B, like we said,
85% of those passing through A pass through B, which means 15% are blocked at B. And
15% of those that pass through B are blocked at C. But how on earth does blocking 15% twice
add up to the 50% blocked if B isn’t there? Well, it doesn’t, which is why the lamp
looks brighter when you insert filter B, but it really makes you wonder how the universe
is deciding which photons to let through and which ones to block. Grant: In fact, these numbers suggest that
it’s impossible for there to be some hidden variable determining each photon’s state
with respect to each filter.
That is, if each one has some definite answers
to the three questions “Would it pass through A”, “Would it pass through B” and “Would
it pass through C”, even before those measurements are made. Grant: We’ll do a proof by contradiction,
where we imagine 100 photons who do have some hidden variable which, through whatever crazy
underlying mechanism you might imagine, determines their answers to these questions. And let’s say all of these will definitely
pass through A, which I’ll show by putting all 100 inside this circle representing photons
that pass through A. Grant: To produce the results we see in experiments,
about 85 of these photons would have to have a hidden variable determining that they pass
through B, so let’s put 85 of these guys in the intersection of A and B, leaving 15
in this crescent moon section representing photons that pass A but not B.
Similarly,
among those 85 that would pass through B, about 15% would get blocked by C, which is
represented in this little section inside the A and B circles, but outside the C circle. So the actual number whose hidden variable
has them passing through both A and B but not C is certainly no more than 15. Grant: But think of what Henry was just saying,
what was weird was that when you remove filter B, never asking the photons what they think
about 22.5 degree angles, the number that get blocked at C seems much too high. So look back at our Venn diagram, what does
it mean if a photon has some hidden variable determining that it passes A but is blocked
at C? It means it’s somewhere in this crescent
moon region inside circle A and outside circle C. Grant: Now, experiments show that a full 50
of these 100 photons that pass through A should get blocked at C, but if we take into account
how these photons would behave with B there, that seems impossible.
Either those photons would have passed through
B, meaning they’re somewhere in this region we talked about of passing both A and B but
getting blocked at C, which includes fewer than 15 photons. Or they would have been blocked by B, which
puts them in a subset of this other crescent moon region representing those passing A and
getting blocked at B, which has 15 photons. So the number passing A and getting blocked
at C should be strictly smaller than 15 + 15…but at the same time it’s supposed
to be 50? How does that work? Grant: Remember, that number 50 is coming
from the case where the photon is never measured at B, and all we’re doing is asking what
would have happened if it was measured at B, assuming that it has some definite state
even when we don’t make the measurement, and that gives this numerical contradiction.
Grant: For comparison, think of any other,
non-quantum questions you might ask. Like, take a hundred people, and ask them
if they like minutephysics, if they have a beard, and if they wear glasses. Well, obviously everyone likes minutephysics. Then among those, take the number that don’t
have beards, plus the number who do have a beard but not glasses. That should greater than or equal to the
number who don’t have glasses. I mean, one is a superset of the other. But as absurdly reasonable as that is, some
questions about quantum states seem to violate this inequality, which contradicts the premise
that these questions could have definite answers, right? Henry: Well…Unfortunately, there’s a
hole in that argument. Drawing those Venn diagrams assumes that
the answer to each question is static and unchanging. But what if the act of passing through one
filter changes how the photon will later interact with other filters? Then you could easily explain the results
of the experiment, so we haven’t proved hidden variable theories are impossible; just
that any hidden variable theory would have to have the interaction of the particle with
one filter affect the interaction of the particle with other filters.
Henry: We can, however, rig up an experiment
where the interactions cannot affect each other without faster than light communication,
but where the same impossible numerical weirdness persists. The key is to make photons pass not through
filters at different points in time, but at different points in space at the same time. And for this, you need entanglement. Henry: For this video, what we'll mean when
we say two photons are "entangled" is that if you were to pass each one of them through
filters oriented the same way, either both pass through, or both get blocked. That is, they behave the same way when measured
along the same axis. And this correlated behavior persists no matter
how far away the photons and filters are from each other, even if there's no way for one
photon to influence the other. Unless, somehow, it did so faster than the
speed of light. But that would be crazy. Grant: So now here’s what you do for the
entangled version of our photon-filter experiment.
Instead of sending one photon through multiple
polarizing filters, you’ll send entangled pairs of photons to two far away locations,
and simultaneously at each location, randomly choose one filter to put in the path of that
photon. Doing this many times, you’ll collect a
lot of data about how often both photons in an entangled pair pass through the different
combinations of filters. Henry: But the thing is, you still see all
the same numbers as before. When you use filter A at one site and filter
B at the other, among all those that pass through filter A, about 15% have an entangled
partner that gets blocked at B.
Likewise, if they’re set to B and C, about 15% of
those that do pass through B have an entangled partner that gets blocked by C. And with
settings A and C, half of those that through A get blocked at C. Grant: Again, if you think carefully about
these numbers, they seem to contradict the idea that there can be some hidden variable
determining the photon’s states. Here, draw the same Venn Diagram as before,
which assumes that each photon actually does have some definite answers to the questions
“Would it pass through A”, “Would it pass through B” and “Would it pass through
C”. Grant: If, as Henry said, 15% of those that
pass through A get blocked at B, we should nudge these circles a bit so that only 15%
of the area of circle A is outside circle B.
Likewise, based on the data from entangled
pairs measured at B and C, only 15% of the photons which pass through B would get blocked
at C, so this region here inside B and outside C needs to be sufficiently small. Grant: But that really limits the number of
photons that would pass through A and get blocked by C. Why? Well the region representing photons passing
A and blocked at C is entirely contained inside the previous two. And yet, what quantum mechanics predicts,
and what these entanglement experiments verify, is that a full 50% of those measured to pass
through A should have an entangled partner getting blocked at C. Grant: If you assume that all these circles
have the same size, which means any previously unmeasured photon has no preference for one
of these filters over the others, there is literally no way to accurately represent all
three of these proportions in a diagram like this, so it’s not looking good for hidden
variable theories.
Henry: Again, for a hidden variable theory
to survive, this can only be explained if the photons are able to influence each other
based on which filters they passed through. But now we have a much stronger result,
because in the case of entangled photons, this influence would have to be faster than
light. Henry: The assumption that there is some deeper
underlying state to a particle even if it’s not being probed is called “realism”. And the assumption that faster than light
influence is not possible is called “locality”. What this experiment shows is that either
realism is not how the universe works, or locality is not how the universe works, or
some combination (whatever that means). Henry: Specifically, it’s not that quantum
entanglement appears to violate realism or the speed of light while actually being locally
real at some underlying level – it the contradictions in this experiment show it CANNOT be locally
real, period. Grant: What we’ve described here is one
example of what's called a Bell inequality. It's a simple counting relationship that
must be obeyed by a set of questions with definite answers, but which quantum states
seem to disobey.
Grant: In fact, the mathematics of quantum
theory predicts that entangled quantum states should violate Bell inequalities in exactly
this way. John Bell originally put out the inequalities
and the observation that quantum mechanics would violate them in 1964. Henry: Since then, numerous experiments have
put it into practice, but it turns out it’s quite difficult to get all your entangled
particles and detectors to behave just right, which can mean observed violations of this
inequality might end with certain “loopholes” that might leave room for locality and realism
to both be true. The first loophole-free test happened only
in 2015. Grant: There have also been numerous theoretical
developments in the intervening years, strengthening Bell’s and other similar results (that is,
strengthening the case against local realism). Henry: In the end, here’s what I find crazy:
Bell’s Theorem is an incredibly deep result upending what we know about how our universe
works that humanity has only just recently come to know, and yet the math at its heart
is a simple counting argument, and the underlying physical principles can be seen in action
with a cheap home demo! It’s frankly surprising more people don’t know about it
