You guys know Henry from MinutePhysics, right? Well, he and I just made a video on a certain quantum mechanical topic – “Bell’s inequalities”. It’s a really mind-warping topic that not enough people know about, and even though it’s a quantum thing, it’s based on some surprisingly simple math, and you should definitely check it out. For this video, we have in mind those viewers who actually want to learn some quantum mechanics more deeply. And obviously, it’s a huge topic, nowhere near the scope of a single video. But the question we asked was what topic could we present that’s not meant to be some eye-catching piece of quantum weirdness, but which actually lays down some useful foundations for anyone who, you know, wants to learn this field. What topic would set the right intuitions for someone before they dove into, say, the Feynman lectures. Well, a natural place to start, where quantum mechanics itself started, is light. Specifically, if you want to learn quantum, you have to have an understanding of waves, and how they’re described mathematically. And what we’d like to build to here is the relationship between the energy in a purely classical wave and the probabilities that govern quantum behavior. In fact, we’ll actually spend most of the time talking through the pre-quantum understanding of light, since that sets up a lot of the relevant wave mechanics. The thing is, a lot of ideas from quantum mechanics, like describing states as superpositions with various amplitudes and phases, come up in the context of classical waves in a way that doesn’t involve any of the quantum weirdness people might be familiar with. This also helps to appreciate what’s actually different in quantum mechanics, namely, certain restrictions on how much energy these waves can have, how they behave when measured, and quantum entanglement, though we won’t cover entanglement in this video. So, we’ll start with the late 1800s understanding of light as waves in the electromagnetic field. Here, let’s break that down a bit. The electric field is a vector field, and that means every point in space has some arrow attached to it, indicating the direction and strength of the field. Now, the physical meaning of those arrows is that if you have some charged particle in space, there’s going to be a force on that particle in the direction of the arrow, and it’s proportional to the length of the arrow and the specific charge of the particle. Likewise, the magnetic field is another vector field, where now the physical meaning of each arrow is that when a charged particle is moving through that space, there’s going to be a force perpendicular to both its direction of motion and to the direction of the magnetic field, and the strength of that force is proportional to the charge of the particle, its velocity, and the length of the magnetic field arrow. For example, a wire with a current of moving charges next to a magnet is either pushed or pulled by that magnetic field. A kind of culmination of the 19th century physics understanding of how these two fields work are Maxwell’s equations, which among other things describe how each of these fields can cause a change to the other. Specifically, what Maxwell’s equations tell us is that when the electric field arrows seem to be forming a loop around some region, the magnetic field will be increasing inside that region, perpendicular to the plane of the loop. And symmetrically, such a loop in the magnetic field corresponds to a change in the electric field within it, perpendicular to the plane of the loop. Now the specifics for how exactly these equations work is really beautiful, and worth a full video on its own. But all you need to know for now is that one natural consequence of this mutual interplay and how changes to one field cause changes to the other in its neighboring regions is that you get these propagating waves, where the electric field and magnetic fields are oscillating perpendicular to each other, and perpendicular to the direction of propagation. When you hear the term “electromagnetic radiation”, which refers to things like radio waves and visible light, this is what is talking about: propagating waves in both the electric and magnetic fields. Of course, it’s now almost mainstreamed to know of light as electromagnetic radiation, but it’s neat to think about just how surprising this was in Maxwell’s time, that these fields that have to do with forces on charged particles and magnets, not only have something to do with light, but that what light is is a propagating wave as these two fields dance with each other, causing this mutual oscillation of increasing and decreasing field strength. With this as a visual, let’s take a moment to lay down the math used to describe waves. It’ll still be purely classical, but ideas that are core to quantum mechanics, like superposition, amplitudes, phases, all of these come up in this context, and I would argue with a clearer motivation for what they actually mean. Take this wave and think of it as directed straight out of the screen towards your face. And let’s go ahead and ignore the magnetic field right now, just looking at how the electric field oscillates. And also, we’re only going to focus on one of these vectors oscillating in the plane of the screen, which we’ll think of as the xy plane. If it oscillates horizontally like this, we say that the light is “horizontally polarized”, so the y component of this electric field is zero at all times. And we might write the x component as something like cos(2πft), where f represents some frequency, and t is time. So, if f was 1, for example, that means it takes exactly 1 second for this cosine function to go through a full cycle. For a lower frequency, that would mean it takes more time for the cosine to go through its full cycle. As the value t increases, the inside of this cosine function increases more slowly. Also, we’re going to include another term in here – φ, called the “phase shift”, which tells us where this vector is in its cycle at time t=0. You’ll see why that matters in just a moment. Now by default, cosine only oscillates between -1 and 1, so let’s put another term in front – A that gives us the amplitude of this wave. One more thing, just to make things look a little more like they often do in quantum mechanics, instead of writing it as a column vector like this, I’m going to separate it out into two different components using these symbols called “kets”. This ket here indicates a unit vector in the horizontal direction, and this ket over here represents a unit vector in the vertical direction. If the light is vertically polarized, meaning the electric field is wiggling purely in the up-and-down direction, its equation might look like this, where the horizontal component is now zero, and the vertical component is a cosine with some frequency, amplitude, and a phase shift. Now if you have two distinct waves, two ways of wiggling through space over time that solve Maxwell’s equations, then adding both of these together gives another valid wave, at least in a vacuum. That is, at each point in time, add these two vectors tip-to-tail to get a new vector. Doing this at all points in space and all points in time gives a new valid solution to Maxwell’s equations, at least this is all true in a vacuum. This is because Maxwell’s equations in a vacuum are what’s called “linear equations”. They’re essentially a combination of derivatives acting on the electric and magnetic fields to give zero. So if one field F_1 satisfies this equation and another field F_2 satisfies it, then their sum F_1 plus F_2 also satisfies it, since derivatives are linear. So the sum of two or more solutions to Maxwell’s equations is also a solution to Maxwell’s equations. This new wave is called a “superposition” of the first two. And here, superposition essentially just means sum, or, in some context, weighted sum, since if you include some kind of amplitude and phase shift in each of these components, it can still be called a superposition of the two original vectors. Now, right now the resulting superposition is a wave wiggling in the diagonal direction. But if the horizontal and vertical components were out of phase with each other, which might happen if you increase the phase shift in one of them, their sum might instead trace out some sort of ellipse. And in the case where the phases are exactly 90° out of sync with each other, and the amplitudes are both equal, this is what we call “circularly polarized light”. This, by the way, is why it’s important to keep track not just of the amplitude in each direction, but also of the phase – it affects the way that two waves add together. That’s also an important idea that carries over to quantum, and underlies some of the things that look confusing at first. And here’s another important idea. We’re describing waves by adding together the horizontal and vertical components, but we could also choose to describe everything with respect to different directions. I mean, you could describe waves as some superposition of the diagonal and the anti-diagonal directions. In that case, vertically polarized light would actually be a superposition of these two diagonal wiggling directions, at least when both are in phase with each other, and they have the same magnitude. Now, the choice of which directions you write things in terms of is called a “basis”. And which basis is nicest to work with? Well, that typically depends on what you’re actually doing with the light. For example, if you have a polarizing filter, like that from a set of polarized sunglasses, the way these work is by absorbing the energy from electromagnetic oscillations in some particular direction. A vertically oriented polarizer, for example, would absorb all of the energy from these waves along the horizontal directions, at least classically that’s how you might think about it. So, if you’re analyzing light and it’s passing through a filter like this, it’s nice to describe it with respect to the horizontal and vertical directions. That way, what you can say is that whatever light passes through the filter is just the vertical component of the original wave. But if you had a filter oriented, say diagonally, well, then it would be convenient to describe things as a superposition of that diagonal direction and it’s perpendicular anti-diagonal direction. These ideas will carry over almost word-for-word to the quantum case. Quantum states, much like this wiggling direction of our wave, are described as a superposition of multiple base states, where you have many choices for what base states to use. And just like with classical waves, the components of such a superposition will have both an amplitude and a phase of some kind. And by the way, for those of you who do read more into quantum mechanics, you’ll find that these components are actually given using a single complex number rather than a cosine expression like this one. One way to think of this is that complex numbers are just a very convenient and natural mathematical way to encode an amplitude and a phase with a single value. That can make things a little confusing, because it’s hard to visualize a pair of complex numbers, which is what would describe a superposition of two base states. But you can think about the use of complex numbers throughout quantum mechanics as a result of its underlying wavy nature and its need to encapsulate the amplitude and the phase for each direction. Okay, just one quick point before getting into the quantum. Look at one of these waves, and focus just on the electric field portion like we were before. Classically, we think about the energy of a wave like this as being proportional to the square of its amplitude. And I want you to notice how well this lines up with the Pythagorean theorem. If you were to describe this wave as a superposition of a horizontal component with amplitude A_x and a vertical component with amplitude A_y, then its energy density is proportional to (A_x)^2 plus (A_y)^2. And you can think of this in two different ways: either it’s because you’re adding up the energies of each component in the superposition, or it’s just that you’re figuring out the new amplitude using the Pythagorean theorem, and taking the square. Isn’t that nice? In the classical understanding of light, you should be able to dial this energy up and down continuously however you want by changing the amplitude of the wave. But what physicists started to notice in the late 19th and early 20th centuries was that this energy actually seems to come in discrete amounts. Specifically, the energy of one of these electromagnetic waves always seems to come as an integer multiple of a specific constant times the frequency of that wave. We now call this constant “Planck’s constant”, commonly denoting it with the letter h. Physically, what this means is that whenever this wave trades its energy with something else, like an electron, the amount of energy it trades off is always an integer multiple of h times its frequency. Importantly, this means there is some minimal non-zero energy level for waves of a given frequency – hf. If you have an electromagnetic wave with this frequency and energy, you cannot make it smaller without eliminating it entirely. That feels weird when the conception of a wave is a nice continuously oscillating vector field, but that’s not how the universe works as late 19th and early 20th century experiments started to expose. In fact, I’ve done a video about this, called “the origin of quantum mechanics”. However, it’s worth noting that this phenomenon is actually common in waves when they’re constrained in certain ways, like in pipes or instrument strings, and it’s called “harmonics”. What’s weird is that electromagnetic waves do this in free space, even when they’re not constrained. And what do we call an electromagnetic wave with this minimal possible energy? A photon! But like I said, the math used to describe classical electromagnetic waves carries over to describing a photon. It might have, say, a 45° diagonal polarization, which can be described as a superposition of a purely horizontal state and a purely vertical state, where each one of these components has some amplitude and phase. And with a different choice of basis, that same state might be described as a superposition of two other directions. All of this is stuff that you would see if you started reading more into quantum mechanics, but this superposition has a different interpretation than before, and it has to. Let’s say you were thinking of this diagonally polarized photon kind of classically, and you said it has an amplitude of 1 unit for some appropriate unit system. Well, that would make the hypothetical amplitudes of its horizontal and vertical components each √(1/2). and like Henry said, the energy of a photon is this special constant h times its frequency. And because in a classical setting, energy is proportional to the square of the amplitude of this wave, it’s tempting to think of half of the energy as being in the horizontal component, and half of it as being in the vertical component. But waves of this frequency cannot have half the energy of a photon. I mean, the whole novelty of quantum here is that energy comes in these discrete indivisible chunks. So these components with an imagined amplitude of 1/√2 could not exist in isolation, and you might wonder what exactly they mean. Well, let’s get experimental about it. If you were to take a vertically oriented polarizing filter, and shoot this diagonally polarized photon right at it, what do you think would happen? Classically, the way you’d interpret the superposition is that the half of its energy in the horizontal direction would be absorbed, but because energy comes in these discrete photon packets, it either has to pass through with all of its energy, or get absorbed entirely. And if you actually did this experiment, about half the time the photon goes through entirely, and about half the time it gets absorbed entirely, and it appears to be random whether a given photon passes through or not. If it does pass through, forcing it to make a decision like this actually changes it so that it’s polarization is oriented along the filter’s direction. This is analogous to the classic Schrodinger’s cat setup: you have something that’s in a superposition of two states, but once you make a measurement of that superposition, forcing it to interact with an observer, in a way where each of those two states would behave differently. From the perspective of that observer, this superposition collapses to be entirely in one state, or entirely in another: dead or alive, horizontal or vertical. One pretty neat way to see this in action, which Henry and I talked about in the other video, is to take several polarized sunglasses or some other form of polarizing filters and start by holding two of them between you and some light source. If you rotate them to be 90° off from each other, the light source is blacked out completely. (or at least with perfect filters it would be) Because all of the photons passing through that first one are polarized vertically, so they actually have a 0% chance of passing a filter oriented horizontally. But if you insert a third filter oriented at a 45° angle between the two, it actually lets more light through! And what’s going on here is that 50% of the photons passing that vertical filter will also pass through the diagonal filter. And once they do, they’re going to be changed to have a purely diagonal polarization. And then once they’re in that state, they have a 50/50 chance of passing through the filter oriented at 90°. So even though 0% of the photons passing through the first would pass through that last if nothing was in between, by introducing another filter, 25% of them now passed through all three. Now that’s something that you could not explain unless that middle filter forces the photons to change their states. And that experiment, by the way, becomes all the weirder when you dig into the specific probabilities for angles between 0 and 45°, and that’s actually what we talked about in the other video. For example, one specific value we focus on there is the probability that a photon whose polarization is 22.5° off the direction of a filter is going to end up passing through that filter. Again, it’s helpful to think of this wave as having an amplitude of 1, and then you think of the horizontal component as having amplitude sin(22.5°), which is around 0.38; and the vertical component would have an amplitude cos(22.5°), which is around 0.92. Classically, you might think of its horizontal component as having energy proportional to 0.38^2, which is around 0.15. Likewise, you might think of the vertical component as having an energy proportional to 0.92^2, which comes out to be around 0.85. And like we said before, classically, this would mean, if you pass it through a vertical filter, 15% of its energy is absorbed in the horizontal direction, but because the energy of light comes in these discrete quanta that cannot be subdivided, instead, what you observe is that 85% of the time the photon passes through entirely, and 15% of the time it gets completely blocked. Now I want to emphasize that the wave equations don’t change. The photon is still described as a superposition of two oscillating components, each with some phase and amplitude, and these are often encoded using a single complex number. The difference is that classically the squares of the amplitudes of each component tells you the amount of that wave’s energy in each direction; but with quantized light, at this minimal non-zero energy level, the squares of those amplitudes tell you the probabilities that a given photon is going to be found to have all of its energy in one direction or not. Also, these components could still have some kind of phase difference. Just like with classical waves, photons can be circularly polarized, and there exists polarizing filters that only let through photons that are polarized circularly, say in the clockwise direction. Or rather, they let through all photons probabilistically, where the probabilities are determined by describing each one of those photons as a superposition of the clockwise and counterclockwise states, and then the square of the amplitude of the clockwise component gives you the desired probability. Photons are, of course, just one quantum phenomenon, one where we initially understood it as a wave thanks to Maxwell’s equations, and then as individual particles or quanta – hence, the name “quantum mechanics”. But as many of you well know, there’s a flipside to this, where are many things that were understood to come in discrete little packets, like electrons, were discovered to be governed by similar wavy quantum mechanics. In cases way more general than this one photon polarization example, quantum mechanical states are described as some superposition of multiple base states, and the superposition depends on what basis you choose. Each component in this superposition is given with an amplitude and a phase often encoded as a single complex number. And the need for this phase arises from the wave nature of these objects. As with the photon example, the choice of how to measure these objects can determine a set of base states, where the probability of measuring a particle to be in one of these base states is proportional to the squares of the amplitudes of these numbers. It’s funny to think, though, that if the wavy nature of electrons and other particles was discovered first, we might instead refer to the whole subject as “harmonic mechanics”, or something like that, since the weirdness there is not that waves come in discrete units, but that particles are governed by wave equations. This video was supported in part by Brilliant. And as viewers of this channel know, what I like about Brilliant is that they’re a great compliment to passively watching educational videos. All of you here want to learn more math, or physics, or the math that prepares you for physics. And the only way to actually learn this stuff is to actively grapple with puzzles and problem solving. Brilliant offers many really well curated sequences of problems that help you to master all sorts of technical subjects. You all like physics clearly, so I think that you would enjoy their courses on “Classical Mechanics” and “Gravitational Physics”. And honestly, “Group Theory” would give you a really good foundation. But there are many other great courses too, especially in math. If you go to brilliant.org/3b1b, that one lets them know that you came from here, and also the first 200 people that go to that link are going to get 20% off the annual Brilliant premium subscription. That’s the subscription I’ve been using, and it’s actually really fun to have a bank of these puzzles and problems. But of course, for those of you who want some more passive viewing, don’t forget that Henry and I just put out a video on Bell’s inequalities over on MinutePhysics. If for some reason you haven’t been following MinutePhysics these days, (and I don’t know why you wouldn’t have been) the videos there have been really top-notch. So definitely take a moment to poke around the rest of his channel.

Can we figure out if 0^0 approximates 0 or 1 by measuring if particles pass through or not?

Please make a video on maxwell's Equations and how electric fields and electric fields interact mathematically.

He said "If you want to learn this field"….LOLOLOLOL

There is no weirdness in Quantum Mechanics, for it is reality. The weirdness is in your intuitions that fail to match up to reality. There are no surprising facts, only models that are surprised by facts.

You've probably got this comment before and might not check comments on older videos, but maybe next time you guys do a collaboration you should consider sticking to one background color. Constantly swapping between black backgrounds and white backgrounds while in a dark room was very taxing.

Visual criticism aside, I love the video and as I browse youtube tonight I'm quickly becoming a fan of the channel. Hopefully I remember to stop watching videos about physics and do my physics hw at some point tonight.

The problem with this explanation of polarising light filters is that the description of what the "filter" does is incomplete, and that is yielding incorrect assumptions about the light that comes through it. The quantum equations aren't accounting for what actually happens to the "absorbed" light, it's treating it as if it simply goes away, but we know this cannot be true – filters cannot destroy energy as energy cannot be destroyed. What actually happens it the absorption of the light by one of the long crystals adds the energy to the crystal, which then will re-emit the energy, in the polarised direction, which can constructively interfere with the part of the light that gets through, as the new light will be a superposition of the light that passes through and the newly emitted light. This happens because the experiment fires photons at the filters quickly enough that each component of a photon that gets through is being affected by the re-emission of the component of an earlier photon that got absorbed. So while each photon is being treated as a separate experiment, with a separate result, it simply isn't behaving that way, each experiment is contaminated by the previous experiment… the filter does not "observe", it temporally shifts. If it didn't add absorbed light to passed light, then adding the 45 degree filter in between wouldn't increase the overall light that gets through… it's not "quantum is just weird", it is completely intuitive once you account for everything that actually happens, and people MAKE it weird when they do not.

4:31 trying to hypnotize us are you?

At 12:20 …Yes! But think about what it then actually means! https://www.researchgate.net/publication/331314978_Planck_constant_Light_length_Heisenberg's_uncertainty_principle_Josephson_constant_Klitzing_constant_Quantization_revisited

…and thanks for the great video.

I think that in the future it will be illegal to collapse a wave function without a licence.

Also I confidently predict the emergence of a superhero who can assume several superpositions at once.

Why introduce coordinates?

where can you learn more about why the energy Levels are integer multiplied? without going full way

YouTube comment experts much appreciated

I need more! reverse deduction

Sorry. I can't say I like physics…

I LOVE PHYSICS!

At 9:47 shouldn´t it be -0.71*cos(2*pi*f*t) |↖⟩ + 0.71*cos(2*pi*f*t) |↗⟩? Because if you have 0.71*cos(2*pi*f*t) |↖⟩ + 0.71*cos(2*pi*f*t) |↖⟩ and change the basis to |→⟩ and |↑⟩ it would be a vertikal wave…

The explanation of the Venn Diagram Paradox presented so beautifully in your other video is actually clearer for me in the brief description given here, starting around 16:10 (and based on understanding the couple of minutes shown just before). Anyone whose head is still aching after watching the Venn Diagram video should definitely watch this one. The realization that ALL of the photon's quantized energy must change its polarization to the diagonal state after interacting with filter B – and will therefore have a different interaction with filter C than we would predict from a purely classical perspective, is the key. I wish you would add this conclusion just as succinctly to the other video. That said, these video are fantastic and I'm yet another deeply appreciative admirer.

One big electromagnetic soup…

what languages and or programs do you use for your simulations?

I thought you only had a couple videos now I see these full series including some physics so now I have to go to your channel and watch every video from beginning to end.

Also, I worked in a computational neurolinguistics lab and I never full understood why the time signal data processed in the EEG had these dot product sums that I was programming with Fourier and Hamiltonian transforms and now I finally realize that the whole phase shift thing which I made a theory using some code to test the some event related potentials as they relate to processing language as an in or out of phase state of the individual’s latent brain waves with the frequency of the language at the instant it’s being processed in the brain up until the known point of the event related potential signaling it had been processed that hypothesized in phase states would help the individual understand the language minutely faster and out of phase would be minutely slower. I only processed the data for a single electrode in the most important area because I was and am limited in my programming skills. But I finally know what the hell I was talking about, books really can’t do this justice like these videos can. Thanks, now I can think about it a bit deeper and maybe figure out what was wrong even though I’m not in that lab anymore and didn’t even go into that field :/? Lol

I finally understand what polarization pattern is 🙂

But your whole model is based upon the assumption of fixed space, while we are perceiving expanding space.

What if light is just lagging energy of various degrees, not expanding as fast as the energy around it, but faster or slower ?

That difference in expansion we perceive as light, colors, radio waves, the full spectrum.

One thing that fascinates me, if the space in the universe is constantly expanding, are we now massively larger than we were 10 years ago ?

But so is everything and everyone else, so we do not notice we have all grown larger than mountains from 10 years back in time ?

Will this expansion of space go on forever until it evaporates into nothingness?

Does the expansion make time travel impossible, because you would be shredding to nothingness if your now-you physically travels into the past, or crushed into a singularity if you attempt to travel into the expanded larger future ?

Which gets into this 'time' stuff – what is time ? Are their particles or waves of time ? Which gets into the whole quantum mechanics of space-time….and how long until we can bend the rules of quantum mechanics and travel Different Than Light DTL Drive Engine ?

(not FTL faster than light, because that is a misconception – Baryonic matter moving in different dimensions than light so it seems faster).

16:30 This phenomenon has stumped me for years! Finally, someone explains it clearly!

These visualizations are great! I took an Electromagnetics course and we went over polarization, the visualizations you have in this video make it really clear what's going on… Perhaps you could do a video on antennas! I think that would be really cool to do those visuals, although probably not the most "popular" subject for casual youtube viewers I think it would be really helpful.

I find it easier to understand this if you don’t try to equate it to anything you know

Just accept that they do things that way

My head hurts. I tried to keep up with the math, but got lost at some point.

Nothing wrong with you. Your teaching is fine. The limitation is in me 🙁

Wish I had stumbled across this particular video yesterday, before turning in my lab on polarization of light today and learning about polarization of light in class probably next week or something…

THANK YOU!!! I highly recommend this video to anyone trying to approach quantum mechanics. But, then again, who am I?😉

Did you just made something simpler… By making it more complicaded!?

YESSS! The ultimate cross-over!!!!

They work so well together!!!!

It's like combining quantum mechanics with general relatively!

Actually wait . . . No, nvm.

It's not like that at all.

15:04

My head exploded

Cool !!!!!

Quantum computing

finally a QM video that doesnt keep saying in QM you cant have this you cant have that

Thank you for your videos. You are truly doing a service to humanity. Your videos are helping me with my scientific endeavors. Don’t stop sharing your love and truth with the world.

Great video, but

pleaseget rid of the background music. It isverydistracting.Why does energy of photon depend on the frequency

you have stared that photons are quantized and they can have only discrete frequencies

Does that mean all the photons have same amplitude irrespective of frequency ??

Why would anyone dislikes such videos?!

Wow!

Very good!

Shrodinger's cat at 9:57, nice.

I believe this is a real-world application to the video that was done by 3Blue1Brown on calculating Pythagorean Triples. The only way a wave can be split into its respective x and y components is if the triangle's sides are all comprised of multiples of Planck's Constant. When Planck's Constant is divided out from all three sides, you are left with the Pythagorean Triple.

Aaaargh video not good for late night watching…..

10:20 Complex numbers are just a very convenient and natural way of……??? Complex number are THE NATURAL way.

One of the equations at the third minute is not correct. It should be “curl E = – dB/dt”.

Light is made of only three kinds of photons. Red, Green and Blue.

Please help solve Navier-Stokes Equation with info in Chapter 3 of this book using Logarithms – log b where b=9 (9X9=81) 0=81=1 or 1/81= 0.0123456789, Pi=3, Diameter (D) =1 (Actual measured Diameter (AD) is the scaling factor or AD x 1=AD. https://youtu.be/A9BC2nh1MPU

I want to learn Blender to design 3D systems. What software are you using in this video?

Why can't Classical Physics explain the resultant energy of light when it passes through the 0 – 45 – 90 deg polarised filter arrangement?

When light passes through the 0-deg filter, it will have a component only in the vertical direction. However, with respect to 45-deg filter, the light can be assumed to have both diagonal and anti-diagonal components. So when it passes through the 45-deg filter, only the diagonal component remains. Now, again, this diagonally polarised light (after getting filtered through 45-deg filter) can be assumed to have both vertical and horizontal components (though reduced in Amplitude). When it passes through the 90-deg filter, the vertical component will remain and the horizontal component will vanish.

Isn't this explanation in line with classical physics concepts? If yes, then how can we say that classical physics doesn't explain 0-45-90 deg filter results?

@3:19

U got Maxwell's equation wrong

CurlE=-dB/dt

And

CurlB=1/c^2xdE/dt

Polar glass is great tool to demonstrate this probability behaviors of quantum mechanic. I first learnt this from traditional physics video. And it is never better than this instrument applied to interpret the concepts!

At many times in this video you talk of the electric field and magnetic field as if they are two separate field interacting with eachother.

I thought it was one field, the electromagnetic field, with two ways of looking at it. With them both directly implying the other's state by being directly related to eachother's derivative or how they're moving or something.

If they are two separate fields which interact, is there a delay between something changing in one field and the other field being affected?

Beautiful graphics

Fine, I'll go check out brilliant .org.

For a new video on the subject of the EM field, you might consider my new paper in Physica Scripta, https://doi.org/10.1088/1402-4896/ab0c53 (the preprint, https://arxiv.org/abs/1709.06711, is slightly different: I can send a copy of the accepted version on request, or else the differences can be seen described in a blog post, https://quantumclassical.blogspot.com/2019/03/to-appear-in-physica-scripta-classical.html). Specifically, your discussion of the EM field is deterministic, but there is a

random fieldversion of the EM field that is "probabilistic" and that is isomorphic to the quantized EM field in a well-established sense that is different from quantization, for a helpful understanding of quantum fields. No worries if you're not interested: I'm trying many places to find someone willing and able to bring this approach to a wider audience.9:59 LMAO That's a cat at the upper left. 😀 The graphics on this video are simply sublime.

What if a circularly poarised photon identify as a male neutron with a backspin orientated to the black-mass-matters-movement is trying to pass the filter? Will it be forced to go back wherever it came from and would this turn the filter poli-racism?

Please do a deticated video on Maxwell's Equations(3:13)

Best channel on youtube!!!!

Can you make a video about how quantization solves the ultraviolet catastrophe?

cool vid

I think I finally understand a little bit how the math I was doing in Pchem actually relates to the physical reality of the quantum world, thank you!

Pls make a video on classical electrodynamics

Strangely enough I'm starting to have some sort of idea about this

I watched the both videos..i was fascinated by bells theorem and so i am here

Wow.

This explanation actually enables one to ask: Why does this even work???

And then saying something like… "Waves seem to be more than just the parts of a sum."

https://youtu.be/MzRCDLre1b4?t=1138 and that's where things get weird for me..

2:27 I guess the force is in downward direction to the plane

everything explained beautifully except a small mistake, the zero point energy of photon is (1/2hf) not (0hf)

Stunning!

thank you

Starting at 2:50 those Maxwell equations are wrong. The changing electric field introduced by the curl of an electric field does not depend on the speed of light at all. If you just check the units you will see that there is no constatnt between those two.

Strangely that five seconds earlier the equation used is correct.

Ok. So I don’t know much about quantum physics, but I’ve thought too much about this tonight and I still don’t quite get the problem. In the first video you explain that the polarization of photons through filters is unexplainable in the way that 85% are allowed through the 22.5 degree filter, because you’d expect it to be 25% as that’s the percentage of rotation from 90%. Yet in this video you explicitly state that the probability of the quantum particle (photon) getting through the 22.5 degree filter is the square of the cos(22.5) which is .85. The photons that pass through both filters are the sum of both filters probabilities of passage, not the probability of passage through the sum of both filter’s angles. Exactly what the experiments show actually get through. How is that so mysterious? Does the vertical amplitude of the electric field directly dictate the number/percentage of photons that pass through the filter? Or is it that, classically, the presumption is that the frame of reference does not change from a through c? Again, from what little I understand of quantum physics, the trouble you seem to be describing is that you are incapable of measuring a quantum particle in two separate frames of reference. A frame of reference does not consider acceleration of the particle. Does the direction of the photon’s acceleration not change once it passes through the filter, as it’s a “minimal unit” and must amount to 1 or nothing? Passing through a filter would inherently change the frame of reference and thusly requires a “new calculation” to be performed on the subsequent filtering. It seems to be an issue of operationalizing the order of calculations, rather than a mathematical inconsistency. For a simple example:

10 + 10 * 10 = ??

200 or 110?

Quantum wierdness…

I'm new!

HELLO FANS OF THIS CHANNEL!

OK, but how does one discreet package know that it has to be blocked, since the other before passed. Or does this work with only 2 photons? One will pass, one will stop? Or just with a bazillion the probability seems like a sentient decision-making? Basically, is this like a coinflip?

I thought the physics was going to be light.

I saw the video about the 4th dimension right before this one… and it feels like the waves move in a 4 dimension space, don't they? I mean, just like when you rotated the 4d sphere and we observed this really weird patterns in 3d, waves have a perception of moving in a weird way in 3d, but it might totally natural in 4d, WDYT?

How is light a transverse wave if the electric field is not bounded?..

Psicologia e' tecnologia nell'elettromagnetismo c'e' idealismo

I love this collab

This… This video is amazing. Thanks man?

I appreciate you guys fueling my insomnia, but could you not abruptly switch between black and white

Bes channel ever, no doubts

i feel like this video actually explains bell's inequality better than the bell's inequality video

Recently finished two semesters of quantum…gotta say, wish I saw this first!

I love physics quantic. That was the easiest chapter at my physic exams..

I guess it's because it's kinda new and they study very basic things at a new level just because it's new

https://youtu.be/o2SevH886Rc

Thankss it cleared to me the picture of photon but i have one question photon is actually an oscilating E and B feild therefore there should be some time in photo electric effect but why is does not happen??

Thank you. Beautifully explained, clear examples, a good pace. So many HS math classes would motivate people to pursue STEM careers if they taught as you do. Sadly, they don't.

great work.

keep it up, thankyou.

what happens to the blocked photon? are they absorbed by the polarizers? Are the polarizers warming or lightening? Are the blocked photon reflected or transformed into IR photon?

This is incredible, exactly what I was looking for to explain the deeper meaning of quantum mechanics

I love the thumbnail

30secondphysics and 1.5blue0.5brown

@7:13 Can positions be added to superpositions in order to produce more solutions to Maxwell's Equations?

You're the best!! This collaboration between 3Blue1Brown and minutephysics almost made me cry.

Please, I’d like to know what software does those 2D / 3D graphics.

Many thanks.

Very well done video. One of my favorites!

This is the third time that I've watched the bit about polarising filters, and it's starting to make sense to me. Either that or it's some weird form of Stockholm Syndrome, in which my brain has been held hostage for so long that it's starting to agree with its kidnappers.

12:40 No that's about the frequency, that's different