Name: Bell's Theorem: The Quantum Venn Diagram Paradox
Uploaded: 2021-08-18T19:45:07.000Z
Duration: 17 min 35 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

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

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

With perfect filters, if you keep adding more and more in between at in-between angles,

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

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

Grant:  Where we're headed is Bell's theorem: one of the most thought-provoking discoveries

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

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

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

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

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

Grant:...With sunglasses and polarization of light.

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

If that second filter is tilted 90 degrees from the first, then each photon has a 0%

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

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

We're going to compare just how many photons get blocked when B isn't there with how

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

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

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

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

Subtitles ListPlay Video

Bell's Theorem: The Quantum Venn Diagram Paradox

weird

assume

determine

experiment