What am I getting wrong about polarizing filters & quantum mechanics?

I saw a video where they used polarizing filters. At first they took two and put them so that one is perpendicular to the other. They shone light through them and nothing passed. They then inserted a third filter in between, at 45 degree angle, and some light passed through. They claimed this shows how weird quantum mechanics is since there is no classic explanation as to how a filter increases light.

Now, I understand the explanation of quantum mechanics. But why can't it be explained classically (without collapsing and probabilities)? If I understand correctly, we can think of a filter as projecting the light wave onto its axis. So the horizontal filter will take the y portion of the wave, and the vertical filter will take the x portion. If placed on on top the other, then after the wave passes the first, it has no component of the axis of the second filter, so nothing passes through. But, if we insert a 45 angle filter in between, then it'll project the wave to its axis and then the wave has a portion that can be projected to the third filter's axis. It's thinking of filters as slits that cause the wave to align as it passes through them.

The amount of light that passes will be different in the two theories (I think 1/8 in quantum and ~1/2 in my classic explanation (if it is correct)), but the fact that inserting a filter causes light to pass through can be explained in both cases, no?

• First of all, if you're going to refer to a video, please post a link! Second, you're completely correct to question that video's ridiculous statement that quantum mechanics is needed to explain the observations. That is totally wrong. You're reasoning is correct, and in fact both classical and quantum approaches give the same result about what fraction of the light gets through. – DanielSank Nov 1 '18 at 7:48
• @DanielSank, added link to the video at the bottom – user46265 Nov 1 '18 at 16:51

It does work as well, the sentence "there is no classical explanation" is just wrong... Of course you can explain what is going on using quantum mechanics, but why would you?

A photon is a VERY complicated thing, and I think that trying to explain classical phenomena using photons is just pedagogically wrong but that is my opinion . Some people don't think that way... Anyway, you're correct.

They claimed this shows how weird quantum mechanics is since there is no classic explanation as to how a filter increases light.

They claimed, but it is absolutely false.

If I understand correctly, we can think of a filter as projecting the light wave onto its axis.

Yes, if you correctly interpret "projecting".

I think 1/8 in quantum and ~1/2 in my classic explanation

How do you arrive at your ~1/2? The right answer is 1/8, exactly like the quantum answer. Let's see why.

First, we have to know something about the light we are using. In most situations light we have around, coming from sun or from artificial sources, is non-polarized (in a moment I'll explain). There are important exceptions, however.

One is light diffused from clear sky: this is polarized more or less markedly. You can verify it very easily, with polarizing sunglasses, if you close one eye and rotate one lens kept in front of the open eye. (The best effect will obtain if you gaze high sky, at 90° from sun.)

Another exception is light reflected by glass or water, and even by a paved road. (Actually, this is a major reason why polarizing sunglasses are useful when driving: they are built to suppress the polarized light reflected by road, so reducing glare when driving against the light.)

Coming back to unpolarized light, in it electric field (always orthogonal to propagation direction) varies randomly its direction in time. A polarizer "projects" field in its preferred direction, thus transmitting a field reduced by a factor $$\cos\theta$$. As intensity is proportional to the field squared, it is reduced by $$\cos^2\theta$$. It varies from 0 to 1 according to $$\theta$$ and since in unpolarized light $$\theta$$ varies randomly, its average value is 1/2.

Assume unpolarized light is propagating along $$z$$ and your polarizer transmits light whose electric field is directed $$x$$. After this filter light intensity is cut in half. A second polarizer at 45° will effect a second projection, reducing field by $$\cos45^\circ=1/\sqrt2$$. Intensity will be halved again, i.e. at 1/4 of incoming light.

The rest is obvious. If a third filter is inserted, directed as $$y$$ (but also an $$x$$-filter would work the same way), it forms an angle of 45° with the electric field of light exiting the second filter. So it will effect a further halving of intensity. And you see we have arrived at an 1/8 reduction, just like the quantum prediction.

A final note. It is true that photons are complicated. To think of them as tiny particles, as most layman talking of photons surely do, is dangerous. It can work sometimes, but blatantly fails in other cases.

I think QM plays an important role. QM would say that a photon hitting the first filter at 45 deg has a 50/50 chance of going thru vs being absorbed. (almost 100% and 0% probability at 0 and 90). The exiting wave is polarized but when incident on a another filter at 45 again 50% gets thru. The last filter at 45 is another 50% so net 1/8 passes the 3 filters. So the filters are not really doing projections they are making probabilistic interactions with photos and electrons.

• As I wrote, I understand the QM explanation, which I didn't elaborate about because my question was whether the classical explanation works as well – user46265 Nov 1 '18 at 16:40