- Part 1 of this story: th-cam.com/video/yP1kKN3ghOU/w-d-xo.html In that one I explained why the common explanations are incorrect or incomplete. I also measured whether light really does slow down using my phone. - 3Blue1Brown's explanation of Feynman's proof is so great: th-cam.com/video/KTzGBJPuJwM/w-d-xo.html - If you'd like more detail on the physics that went into the simulation, I'm writing it up here: colab.research.google.com/drive/1L9X_tq-Kjt-foEhcnSXpvNujbbJEedBz?usp=sharing The 3D simulation lives on my github. I would love to update it though, so if you have ideas or time to work on it, I'd love to hear about it : github.com/mithuna-y/speed_of_light_in_a_medium/tree/main/multiple_layers
From Wikipedia's page on Ewald-Oseen extinction theorem (as pointed to by another commenter Danyel). 'The characteristic "extinction length" of a medium is the distance after which the original wave can be said to have been completely replaced. For visible light, traveling in air at sea level, this distance is approximately 1 mm. In interstellar space, the extinction length for light is 2 light years. At very high frequencies, the electrons in the medium can't "follow" the original wave into oscillation, which lets that wave travel much further: for 0.5 MeV gamma rays, the length is 19 cm of air and 0.3 mm of Lucite, and for 4.4 GeV, 1.7 m in air, and 1.4 mm in carbon.' The way I read this (in the context of your video [loved it!]) was that yes, light does just travel at its own speed but parts moving faster than the "group velocity"(? I have to admit I didn't get what that really is) just get damped down at a different rate that is very quick. This is similar to what another comment Samuel Owens has commented.
Mithuna, I and my father Prof. Dr. Tolga Yarman (Ph.D. in Nuclear Engineering from MIT) think we have the answer to your quandary. Please search "Quantal Yarman Annals of Physics" in Google to read our recent article (Quantal Theory of Gravity: Essential points and implications, July 2023 -- C. Marchal, T. Yarman, A.L. Kholmetskii, M Arik, O. Yarman) that we published on the idea of what you call "disjoint pulses" which "lag behind". Our paper deals with the splitting of a gravitating test particle like a photon into two constituents just like you describe in your simulation. The hf constituent is conjectured to speed up to reach the utmost theoretical c while the kernel constituent slows down and the object eventually gets torn apart. We thus believe a similar thing happens for light traversing mediums with differing refractive indexes. We would hence like to discuss more on this topic with you and incorporate your contributions. Please contact us in the e-mail provided in the said article. We congratulate you for your progress and findings! Cordially, Prof. Dr. Ozan Yarman, Istanbul University.
Thanks for this interesting pair of videos. What left me wondering, is that you didn't seem to explicitly mention optical dispersion (unless I missed it). At 14:20 of the Part 1 video you dismissed the explanation of group velocity because 'that phenomenon is only relevant if you already have waves going at different speeds'. But that's exactly the case due to dispersion: water has different refractive indices at different wavelengths, so those waves with different wavelengths indeed have different phase velocities. At 17:03 of the current video it seems you have incorporated dispersion in your model. That is evidenced by the fact that the pulse travels more slowly, and that it broadens during propagation. In Feynman's analysis, the refractive index is a function of the angular frequency omega, so indeed it takes dispersion into account (by assuming the Lorentz oscillator model). As for the question of how the electrons conspire such that the light pulse must always travel more slowly than c: the dispersion relation (i.e. how the refractive index depends on wavelength) satisfies the Kramers-Kronig relations, which are derived from the assumption that the electron's response to incident light must be causal. Therefore, causality is built into the physics. If you want to avoid the use of Fourier transforms (where unphysical 'infinite waves' are added), you'd probably have to infer the frequency-domain response of the water from its dispersion curve, infer the time-domain impulse response (which should be 0 for time
I'm not a physicist so I can't weigh in on the technical side, but this was a really great video. A lot of educational content is so fixated on portraying the aesthetic of expertise that it misses out on the _process_ of expertise, and this is a great example of what that looks like, even if you don't wind up with a nice, clean answer to wrap things up.
Alpha Phoenix has recently posted similar content with a similar process. You really understand all the trouble he's gone to in gaining this knowledge. LookingGlassUniverse and AlphaPhoenix need to team up to muddle their way through the next physics problem!
A lot of educational content also tends to assume that the viewer is either completely new to the subject and can only digest gross simplifications, or has all the prerequisites for a university-level course. There's seldom much content for viewers that have a good phenomenological understanding of the subject but are missing the math. 12tone, since you're showing up on a physics video, is there any chance you could do a series on music theory for STEM majors? People who understand small integer frequency ratios and twelfth roots of 2, but stare blankly when you say "this resolves to that". (Fun fact, there is actually an intriguing bit of orbital mechanics that locks the orbital period of Pluto to be exactly a perfect fifth away from that of Neptune).
@@LookingGlassUniverse while your simulations are good, you can see that your first simulation clips show the 3 circle dots lagging behind but they start lagging more as time passes. This is not what we see when we see light slowing down because otherwise that would imply that given a larger volume of water, we would see light slowing down more (basically additively slowing) and at some point light will be absorbed by the water and we would see water being opaque. That does not happen. I am not sure if anyone has actually figured out why light slows down in different mediums. But I think it's because of gravity or space-time. From a photon's perspective, it does not experience time at all. The beginning and the end of the universe for the photon happens instantaneously as if time did not exist. For a photon, it always travels in a straight line too. Everything around it curves. So why then do we see light bending around a black hole? It's the same principle. For a photon it travels in a straight line and will never curve, but it has to maintain its speed, and because of the space-time curvature around a black hole it travels with the same speed but will have to do so in a curve, and thus we see it being curved. Well the important point is this space-time curvature is actually density. You can replace a black hole with something else, and add gas instead of just pure vacuum instead while maintaining the space-time effects that photon was experiencing, and it will behave the same way. This is the same as satellites experiencing slower time than people on Earth. This rate of flow of time changes depending on the density. In the case of light going through water, the difference will be compounded because photons are small enough for quantum effects of atoms to be affecting it (maybe my theory is implying that gravitons exist and there's graviton interaction happening between atoms and photons). That's why people won't experience slow rate of time if they are submerged in water (because we and any mass particle is too big), but for something which is massless, this is as good as traveling near a black hole where you see it curving. If you consider light directly aimed at a center of a black hole, it's going to slow down and down till it reaches the event horizon at which point time stops and light also stops traveling. Now imagine light being incident perpendicular to the surface of water. It's the same exact thing (the angle of refraction is a different concept and not relevant to the scope of this). If we had different type of water with varying refractive indices, we could simulate what light must experience if it is aimed at a black hole. It all has to do with density and how time interacts inside dense material. Changing wavelengths or even phases doesn't help at all here, since it will completely break down if you consider the position of a single photon and track it from vacuum to water or from air to water, and then measure the speed.
Fantastic video! It's already been three weeks, so I'm not sure if anyone is still reading the comments, but I have three happy remarks to share: 1. Regarding the Ewald-Oseen Extinction Theorem, if we delve into the mathematics, it's not about the initial pulse being magically and continuously canceled. Instead, the initial pulse is canceled right at the outset, and the negation wave (already generated by the first layer of electrons) travels automatically alongside the initial pulse wave at the speed of light. Consequently, the rest of the electrons don't even "feel" any field traveling at the speed of light. I hope this explanation makes the whole intuition much more acceptable. 2. You demonstrated how significant results are actually achieved. By delving a bit more into simulation and discussing the results with a mathematician, you could have independently discovered the Ewald-Oseen Extinction Theorem. This showcases that great results stem from a physicist's intuition and the meticulous pursuit of an idea. 3. I understand your reluctance to use plane waves, considering they exist indefinitely everywhere. However, under Maxwell's equations, questioning the physical possibility of the superposition of plane waves is not valid since they are mathematically equivalent. Philosophically speaking, when two physical events are equivalent, they indeed, should be described by the same mathematics. However, when the same mathematics can be interpreted as representing two different physical events, it doesn't necessarily imply that both must be real. I hope this perspective offers some solace. :)
Adding a bit to point 1: under the framework of Maxwell's equations, we might not even need to delve into atoms or electrons. This is because the negation wave is a purely mathematical consequence of the "smoothed" electric/magnetic permeability of the medium. The use of a group of "electrons" in simulations is essentially an approximation of the Microscopic Maxwell equations (even though more "real" ).
Doesn't the Ewald-Oseen Extinction Theorem also show that the binary star argument for the independence of the speed of light from the speed of the source does not hold if the light hits an intervening gas cloud?
Ewald-Oseen treats the medium as a continuum of dipoles, which implies a uniform continuum of positive & negative charge, which can't for a in the body of the medium, as the charges will cancel except at the boundaries, and there would be speed-of-light delay for the effects of excess charge at the boundaries. A real medium is made of of rather discrete atoms, with gaps in between. There is no accounting for the leading edge of a light pulse light slowing down in these gaps. We can even align our light pulse's path through a crystal structure so that it has an unobstructed path between layers of atoms. The oscillating electrons can never _completely_ cancel the leading edge of an electromagnetic pulse. But they can diminish the leading "tail" (or "nose") of the pulse to so near zero as to be undetectable. As it turns out, in the strictest sense, information is _always_ transmitted at vacuum _c,_ the speed of causality in relativistic QFT, and you will always have a nonzero probability of detecting a photon after a delay of L/c from the time the photon enters the medium, to a detect at distance L on the other side of the medium.
I've heard that negative results get published much rarely than positive ones. This makes this video even greater! We need more like this one. After all, stating difficult questions without straight answers is what gets us to advance.
Sadly, that is more the rule than the exception. It would help a lot if research funding terms either required publication regardless the outcome, or after some period of time, the funder would publish that the study was commissioned, and what the hypothesis was. So if the researchers didn't publish, others would know to ask questions.
We def need a Journal of Negative Results. Especially since we don't need to use dead trees for that any more. There are a lot of negative results, but that's partly because there's no Journal of Negative Results! Also that needs to be moderated ...
As an AMO prof I’ve always taken the Feynman explanation at face value and I loved to see you tackle it head on. Thank you. These videos do a wonderful job of how to think like a physicist but more importantly, that it is ok to be wrong bi intend to share this with students the next time I teach from Matter and Interactions.
Thank you so much for the lovely comment. Matter and Interactions is still one of my absolute favourites- but you're right, we can't take things written in textbooks for granted
Great analysis! I've been thinking about this same problem (off and on) since 2017, but have had almost no time to actually work on it. This video might inspire me to spend the time (and also give me a bit of a head start).
I have the impression from these two videos (I am not a scientist) that each electron blunts the front of the pulse a tiny bit, which would explain the "coincidence" of why the cancellation effect should be so exact - I think I get that. The "coincidence" I don't get is that the sum of the wave interference from the wake of the original pusle, from the surrounding electrons, reproduces the original pulse to the extent that it looks like it's the "same" light but slower, hence a slower information speed. But why is the information preserved at all? The reason I'm posting this as a reply to Nick's comment is because it reminds me of his video about mirrors: light from the angle of incidence hits the silver atoms, which in response radiate in ALL directions, and the sum of their waves at the angle of reflection just happens to exactly reproduce the light from the angle of incidence. I didn't really get the WHY of that, either. Is it a similar effect here, or am I just embarrassing myself?
I love this. Lots of others in the comment are saying this, but I have to agree - I love that you're going into how you go about doing science (idea -> hypothesis -> experiment -> analysis - and also lots of false leads and false starts and looking up other references, and the fact that, no matter what the math says, if the experiments show something different then that's what's ultimately real), and then despite all that you only end up with a partial result. But not only is it the try-fail cycles that I like, but also your explanations are in-depth enough that it's very easy to follow your thought processes (and I was totally convinced by your explanation and was just as mystified as you were at the end of Part 1). It feels like we're not only being told about the process, but shown it and taken through every major step of the way. I would love to poke around to see if I can get any further with the intuition of where that funny double peak is coming from, but I don't know if I'll find the time... I hope someone else can get to something!
Thank you so much! I'm weirdly very happy to hear that you were also confused at the end of part 1. I wanted to take people on the journey and the emotions so I'm glad it worked :)
I didn't want you to be right, I wanted you to teach me something. You excelled. These two videos were exceedingly worthwhile. Imagine what else we don't know because someone thought it might be embarrassing to share.
The Ewald-Oseen extinction theorem seems to exactly about this topic. The electrons produce a second wave that (somehow, I don't know how) cancels out the original wave, while also producing a new wave that appears to travel at a slower speed. The wikipedia page also mentions "extinction length", i.e. how far into the medium the original light has to travel until you can consider it negated.
However, note that the mere existence of a nonzero "extinction length" means that the leading edge of the pule is never _completely_ extinguish in the strictest sense, as at any point along the way we can treat that as the starting point of a pulse and extend that for the give extinction length. So the extinction length simply tells us a distance at which for all practical purposes the leading edge will be undetectable. Ewald-Oseen treats the medium as a continuum of dipoles, which implies a uniform continuum of positive & negative charge, which can't for a in the body of the medium, as the charges will cancel except at the boundaries, and there would be speed-of-light delay for the effects of excess charge at the boundaries. A real medium is made of of rather discrete atoms, with gaps in between. There is no accounting for the leading edge of a light pulse light slowing down in these gaps. We can even align our light pulse's path through a crystal structure so that it has an unobstructed path between layers of atoms. The oscillating electrons can never _completely_ cancel the leading edge of an electromagnetic pulse. But they can diminish the leading "tail" (or "nose") of the pulse to so near zero as to be undetectable. As it turns out, in the strictest sense, information is _always_ transmitted at vacuum _c,_ the speed of causality in relativistic QFT, and you will always have a nonzero probability of detecting a photon after a delay of L/c from the time the photon enters the medium, to a detect at distance L on the other side of the medium.
I think an important thing to remember is that if the light is doing work on the electrons by moving them, then it must be transferring energy to them, at least temporarily. Thus, the original wave should lose energy as it travels, and if the energy loss just some % per length, then you would get an exponential suppression of the original wave. Jackson probably has an explanation of this somewhere -- sections 7.8 and 7.9 look promising, but I'm sick right now, and understanding Jackson is too much work for me to do right now \:D. There's also a QFT-style explanation involving the difference between "real" photons (which correspond to the vacuum solutions of Maxwell's equations) and "virtual" photons (corresponding to propagators/the Green's functions of Maxwell's equations) that I could try to type up if people want.
Not even energy loss necessarily. Elastic scattering as per light in water doesn't lose energy, but it excites electrons, because the preservation of kinetic energy is maintained by directional change. Thing is, aren't we then back to the idea she put down at the beginning of last video that light doesn't slow because its taking a longer path..because that sounds like a longer path to me, if photons repeatedlychange directuib even if there is a lot to do with phase cancellation we must add to this.
@@jorgepeterbarton I would say that the process of scattering is equivalent to absorption-emission for this specific ondulatory model. Even if this experiment is a case of elastic scattering and the hole system doesn’t lose energy, the analythical vacuum pulse does, it is just reemited by the medium by the exact same amount. If I am right, the scattering explanation (for a wave model) was right since the beginning. It is just that the phase superposition is preferent in one direction (which doesn’t have to be the same as vacuum's since there is refraction). I don't know about QFT but I guess the mechanics are similar to photonics. Is that correct?
A little late to the party but: If it's still an open question, why c is smaller in a medium than in vaccuum I would be glad to provide an explanation (I'm a physicist working in kinda this area). All the puzzle pieces are already given in this and 3blue1browns video. The key is the harmonic oszillator. However a satisfying explanation would take some time (maths, physics, simulation). But if you're interested I would get back to you some time before christmas.
I'm also late to the party - but here are my two cents: from the theoretical end of things, I think a crucial ingredient are the so-called 'macroscopic' Maxwell equations, which I find surprising never getting mentioned in videos on this topic. There's also the matter of, if light 'slows' down in a medium, that's akin to say its quantum is a _massive_ photon, so that we need something like Proca's equations to properly explain it - which, IMHO, has something or the other to do with symmetry breaking (i.e., the medium is responsible for breaking the _conformal_ invariance of light in a vacuum).
It's not so hard to accept that the original wave is rapidly (exponentially) extinguished in the medium, and you're only left with the slower radiated light field. But I agree that to then say that "light travels slower in the medium" seems a bit misleading as it's more like a synthesized light, rather than an unmolested light wave.
Yes, the electron interaction somehow converts the original light energy into re-radiated and thus delayed light. There is no need for the electrons to send out a signal at the speed of c to cancel the original light wave.
I’m an electronics and RF person so I was fascinated by your journey, knowing that using a 100m length of coaxial cable, a switch and a battery plus an oscilloscope you can easily measure the ‘slowing of c’ - known in my field as the velocity factor - typical value being 0.535 for RG58 coaxial cable. We also use on a daily basis antennas that form their beams by delaying the signal passing to different elements - using electronics for antennas that need to change their beam direction rapidly, or just pieces of coaxial cable for fixed delay lines. The variable we’d look at is the permittivity of the medium, and as far as light as an EM wave propagating in a vacuum, air or water this is the critical parameter.
You might like the fact that we can do the same thing with light in what is aptly named optical phased arrays. Of course RF and light are just the same thing.
I don't think that a pulse moving along a wire counts as a photon. Isn't the pulse in a piece of coax an alternating magnetic and electric field with the energy exchanging between the two. It wouldn't work if there was not the copper conductor? And since there is resistance there is a time constant for the energy to go from the electric field (capacitance) and magnetic field (inductance). It's not the same thing as light until it leaves the wave guide?
@@Richardincancale If you connect a capacitor and an inductor in parallel and inject some electrical energy then the energy cycles between being stored in the magnetic field of the inductor and the electric field of the capacitor. That occilation is not a photon. A coax cable is like a string of LC circuits connected in series.
@@petewright4640 Yes a coaxial cable can be approximately modelled as a series of LC and R, but it’s a model. The actual propagation mode of RF is as a TEM (transverse electric magnetic) wave. Check out some references from a Google search for “wave propagation in coaxial cable”
This is really awesome, thank you! It's so wonderful to see the uncertainty and tenacity at play, combined with the willingness to concede when you've got it wrong. I actually also really appreciate how you can dare to challenge whether 'definitive' sources have it right at all, then go about trying to convince yourself rather than taking the word of some text or video at face value. I am a game developer who's been learning physics over the last few years, and often go through these moments where I can go from being so convinced I've nailed something, to thinking I know nothing, then oscillating between these two while developing a deeper understanding of things. Keep up the great work, really enjoy your content!
There's a few things I can recommend that could help. Now you've written your own code you might consider downloading a PIC (particle in cell) code that'll model the incident field and particle response for you. For your own code you might also be able to use the huygens-fresnel principle (calculates the vector E field from a series of points at a new point) to speed it up. I've written something similar previously and nearly everything was a vector or matrix operation so pretty fast. Well, faster than I expected. Thirdly, is it right to model a pulse as a sum of plane waves in this case? Isn't it more accurate (and conceptually easier) to model the pulse as the product of a single cosine and a gaussian envelope? Then you should see the envelope travel at dw/dk but the phase at w/k? In fact you might even be coming afoul of violating the slowly varying envelope approximation (SVEA) and having an envelope function would let you easily test pulses of different number of wavelengths per envelope.
Wouldn't the pulses differ fundamentally from a continuous beam anyway? The electron light that is emitted keeps up with the original pulse, there is nothing to lag, or to continually produce other waves.
i feel like you did get the answer with the simulation. And it's the same thing as was with the veritasium vs electroboom argument about the lightbulb puzzle (i'm assuming you know it and have seen all Mehdi's videos). So, the electromagnetic field travels with c, but the amplitude that arrives "immediately" with c isn't big enough to detect. What any equipment is able to detect is the peak of the wave in the pulse which arrives later - with the speed 3/4 c.
That...sounds really plausible to a layperson like me. I did see all the lightbulb videos, so I understand what you mean. If you are right...then she's also right that the light 'hits' the other side of the water tank at the same time as light through a vacuum. And then it's also right that the actual detection (at a big enough amplitude) is indeed the phase speed of the combined wave. But...is that consistent with refraction?
so, the distinction I am seeing is that she had a problem with electrons conspiring to 'perfectly' cancel out the c wave. But rather, you are suggesting that perfect cancellation is like an unobtainable limit it tends toward but never reaches, so dependant on the material and size of material, its reduced to a miniscule but varying amount?
@@jorgepeterbarton I'm saying that the front part of the pulse wave that looks like /\_ gets stretched to a shallower and shallower form the further in the material the pulse travels - with the peak travelling at 3/4 c and the needle "front" is travelling at c. it gets so shallow, it's basically undetectable - it's amplitude is going to be below the natural noise level (which in reality will never be a pure mathematical zero).
I think you're right. The graphic at 18:46 seems to show exactly this. The front peak moves at the speed of light in a vacuum, but peters out to undetectable fairly quickly. Nevertheless, it seems that this tiny peak would arrive at the other side of the water at c, but just be undetectable.
I've had the same question after watching 3b1b's video and he recommend viewers to come here. I love your video! And I think your video answers your own question more than you've given yourself credit. Basically after watching your video, I've now understood that 1) the front of the original light travels at c, as you've assumed 2) the front leaves some of its energy behind at each layer of electrons 3) which will emit the energy back (hence water is transparent) 4) but will emit to all directions hence the emitted light will be slower and slower, 5) and lastly, the original front of the light would lose energy quickly until it is undetectable.
for 5), looks like you worked really hard to try to show the effect with either math or computer simulation - but I think we could attack the math from a different angle. As long as each layer of electron reduces energy of the front of the light, it will become indetectable or effectively 'cancelled out'.
Thank you for this high quality content! After watching it, I think I finally got what happens: I believe the answer may already be in the video: my hypothesis is that, just as the incident wave influences the electrons in water, eliciting a secondary wave in response, the electrons themselves affect the electromagnetic wave (after all, what we are analyzing is the oscillation of the electric field), acting as a damping mechanism for the primary wave, which "decays" after a few layers of electrons. Thus, the primary wave reaches the end but becomes undetectable, and what is detectable is the resulting wave from the interaction. Therefore, the simulation should also incorporate the effect of electrons on the electric field in the space through which the wave passes.
These videos were a fascinating rollercoaster and gave me an intuitive sense of what we mean when we say "light slows down in a medium". My take away is that "c" is a constant in any medium if we think about it only as the "wave velocity of the EM field". But the "apparent" velocity of the "speed of information" slows down in a medium simply because the group velocity resulting from the original wave, and subsequent waves induced by charges in the medium, add to create an apparent new clean slow wave. But it is not really a new single clean wave, it is just the group wave. And this "speed of information" in a medium is confirmed be to slower by your LIDAR measurements, which rely on the group pulse to determine distance. So "c" is constant, and the "maximum" speed of information is "c". Even for the single pulse example at the end, you have to pick a point on the pulse to represent the wave front in order to ask the question "when does the light reach the end?". Your simulation shows the apparent resulting peak lags the non-medium peak, again showing the "speed of information" is slower in the medium. I think the semantics you pointed out in the beginning are key.
The constant "c" has nothing to do with light. It's the max. speed at which causality between two systems can occur. I would avoid the term "information". It has no use in physics and it's actually rather counterintuitive even in information theory (random sequences aka noise contain the most information, constant sequences have almost none with exception of their length). The actual speed of light in a medium, OTOH, is strongly variable.
Thanks a lot for the videos. It is so rare to see how a physicist thinks since we usually see the completed results only. I am so happy to join your journey of the light speed in a media. And I hope we can see the follow up of your journey to understanding the world. Thanks again! 😃
I LOVE how you're doing all these videos about light, and your backgrounds and backdrops all have interesting lighting. Like the light coming out of that clear cylindrical thing, the lights on the wall in the background, etc. it's all so interesting and very fitting
You totally nerd-sniped me for the weekend, congratulations! Tonight I was apparently talking in my dream about fourier and light pulses in a medium. The closest intuitive explanation I could come up with is an analogy to a bunch of coupled series LC circuits. Driving them below resonance (where circuit acts capacitively) will cause the voltage to lag behind the current and slow down the propagation of the signal similar to what happens in media with n > 1. Driving them above resonance (where circuit acts inductively) will cause the voltage to precede the current and apparently speed up the propagation, but only apparently because we find that the circuit acts as a transmission line when we try to transmit information and modulate the signal. Thinking about light in terms of voltage and current may seem like a stretch, but I can convince myself (and no one else) that it's equivalent to thinking about electric and magnetic fields and their interaction described by Maxwells equations.
I agree actually. I think your analogy holds up very well. After all, the free-space propagation of a signal is actually the same thing as a transmission line (yeah, it spreads out more in free space, and therefore dissipates more quickly at a receiving point, but the transmission is very similar). After all, free space does have a characteristic impedance - 377 ohms. Just like a transmission line does. Now, compare how signals are affected by a more capacitive transmission line and how light is affected by a material with a higher dielectric permittivity than air/vacuum - the maths are identical.
I like your LC analogy and how it imulates Maxwells equations. It also demonstrates the phase velocity of infinite signals can lead or lag the input signal but an impulse is always delayed by the network.
You just flew to the very top of my favorite TH-cam channels list, and didn't even break a sweat. I know this is about physics and stuff, and really important. But seeing that you care so much that your voice starts to break down at the end really makes me want to give you a hug. These kind of questions have been boggling us for a long time, and will continue to do so for even longer still. You did a great job, weather it is conclusive or not.
Honestly the coding journey felt like a microcosm of this whole process… like trying to find an intuitive answer for these questions was its own kind of personal growth! I loved seeing the whole process of testing different hypotheses and every step was more satisfying; the simulation was so cool to see working. The stopwatch reminded me of the early videos with the white rabbit and reminded me how much this channel has grown too, and this video really reminded me of how lucky we are to see people like Mithuna confiding honestly about the uncertainty at each step. I’m inspired again to do something with science, and I hope to see someone get to the homework at the end 😸 PS: The 3b1b video also tries not to give a false sense of understanding, as some math TH-camrs give warnings about. Still, I wasn’t going to chase down the derivation for the 90° phase shift until this video showed how hard it is; it's been fun to see all the other people in the comments who HAD to peruse the Feynman lectures, even experts with ideas about chapter 30!
Thank you so so much for this really sweet comment, it reminded me how much has changed with these videos and how much I learnt along the way, but also made me nostalgic. I hope people realise I am assigning them homework with this video!
I love your bravery of doing a public experiment and publishing the results even when the results do not match your hypothesis. I wish more people would be more concerned with exploring reality and trying to understand it like you, and less concerned with being right all the time.
Thanks for this! I had this same question/hypothesis after watching grants video but it’s clear the answer now. The medium produces destructive interference for the original light. When new a combination of light is created in the next layer, the destructive interference also applies to that and hence it that slowly propagates the light backwards. Even though the original light still exists it’s almost completely cancelled by light from the electrons.
As mentioned in Grants original video, When a photon passes an electron, it immediately induces it to generate its own photon at 90degree phase shift to the original. Because it’s the light that induces it and it’s not independent, it’s always 90° to whatever resultant light is going through the medium, and even though it’s small, it slowly deconstructs the original wave until it no longer exists, replaced by light that’s always phase shifted 90 back
@@MrChinleungyau Woudln't that suggest that light traveling through a short amount of transparent material would be slowed less (per distance) than through a thicker piece of material, since there have been fewer interactions and less time for the destructive interfererence to result in a phase shift ?
Wow, these two videos and the one by 3Blue1Brown taught me to understand something really deep which I thought I had down, but... understood as little as apparently almost everybody else. What I find most awesome about them is how you included all the wrong turns and frustrations on the way to figuring this out instead of just presenting the result. That is not just only a great way to teach, but also gave the videos an emotional depth that had me absolutely gripped while watching them... or maybe the emotional depth is just the thing that makes your teaching style so great.
This is a great exploration of a very cool problem! I'm a phd student in computational electromagnetics and am very familiar with this kind of scientific computing. I'd be happy to help work on that code of yours to make it more efficient if you'd like another set of eyes on it!
wow, that was mind blowing. i have the feeling that you explained in an intuitive way why light slows down in a medium. even if you weren't able to explain in detail the results of the last simulation about the light pulse. thanks for all that work, i feel less ignorant.
Long time fan of your work! Really enjoyed your approach of challenging what we take for granted. Perhaps this was mentioned in a previous comment, but for high frequency/wavenumber, you should recover the speed of light in vacuum for both the phase and group velocity. This assumes you are using something like Sellmeier’s equation or the harmonic oscillator response in the FLP, both of which are essentially lowpass filters. Perhaps the frequency of the wave packet was too low in your simulation. This suggests that the impulse response should travel at the speed of light (in vacuum), as the frequency tail will play an important role. This works in a continuous medium which simplifies computation (pen and paper or simulation). Also, the effect is already visible in 1D, so I was not fully convinced by the argument of different electrons transverse to the beam contributing to delay. If you’re looking for inputs/bibliography, did you try forums like Physics SE? It would be easier to share equations. Anyway, can’t wait to see your next video!
Hi! I would love to hear more about this- is there any resources you recommend? Feel free to email me at looking dot glass dot universe at gmail Thank you!
Your videos are engaging mini movie rollercoasters of narrative; perfect little wave packets of photonic physics. I really love your channel, because; a) I’m equally as fascinated by the physics of light and energy, and b) you are transparent about the challenging and laborious processes involved in driving your own understanding, AND c) you bring the viewer on an emotional journey through that process.
The surprising side effect of these two videos, for me, is the somewhat calming realisation that it ok to wonder about what many would consider the most basic things, not understand them, be wrong and slowly figure it out even after studying this stuff for years and getting a PhD ...
Now I want to know the answer so much! I have been watching your videos for a while now and you explain things very nicely and in a manner that is simple to understand, without sacrificing nuance! If anything new comes up on this topic please make a new video about it!!!
Doesn't the speed of light in a medium depend on the wavelength? From googling the refractive index should increase with smaller wavelength, so maybe simulate with higher frequencies to get a more pronounced effect? Also it looks like you are doing your simulation in real-time? If so, just do it off-line and dump the simulation steps to a file, maybe just every 100th and then visualize that, as a suggestion.
No, it's not really the "complexity," it's the size of the code. Large software projects are written by multiple programmers, which naturally include some whose skill is mediocre.
Honest reporting of results with methods is the heart of science. You feel badly because you know someone has figured this out but you have not yet. But that's nothing to feel badly about. Not accepting what others tell you as an answer is the (ok maybe "a") key to keeping science alive. This kind of video is as at least as important as explanatory videos which follow accepted science.
In the "linear restoring force" model each electron, at least initially, experiences 0 restoring force, so it can be thought of as a free electron if we're talking about very low time scales (small fraction of a light wave period). A free electron tends to (partially) cancel out any field passing through it (because it accelerates with the electric field, and thus emits an opposing electric field). In fact we know (I think?) an electron gas is completely opaque. Maybe that's enough to explain the complete suppression of the "fast" component of the light? It takes time for the electron to move away from its initial position sufficiently to start "feeling" the effect of the lattice, and thus transitioning into mode of pi/2 phase shift (after initially starting at 0 phase shift) relative to the electric field of the light that "drives" it.
That's a really good point. The restoring force is proportional to the distance away, while (in the steady state plane wave case) the light's force is strongest when the displacement is zero. I will have a think about this!
@@LookingGlassUniverse wait are you sure? I think the opposite is true: in the steady state we expect the net force to be 0 at displacement 0 (because double derivative of sin is -sin). My point was to consider what happens when we're *out* of steady state, when the initial pulse arrives.
I'm an AMO physicist and this reminds me of a time I was co-running a course on special relativity with a professor. He wasn't satisfied with the explanation of the twin "paradox" in the course material and that we should come up with another one . After weeks of us both researching, we concluded that neither of us really understood it and just admitted that to the students. A very humbling but valuable experience. Great video!
From what I recall from a university course I took on modern physics, the twin paradox works because each twin has a different reference frame from which it appears the other twin is aging slower. Let's say in this world where we've developed rockets that can instantly accelerate to a fraction of the speed of light, Adam goes off to space at 0.4c relative to Earth, while his twin Bill stays on Earth. While they are moving relative to each other, each reference frame says the other twin is younger, because they disagree on which points are "simultaneous". Neither one is actually correct. It's only because of acceleration, and changing reference frames, that we can find that one twin is definitively younger. We want to compare Adam and Bill's ages, so the twins have to reunite on the same reference frame. (a) We could say that five Earth-years from now, Adam decides to head back to Earth at the speed of 0.4c. Once he reenters Earth's reference frame, he will be younger and it will appear that his time has slowed down for the ten Earth-years they've been apart. (b) But you could also say that, Earth has managed to double the speed of their instantly-accelerating rockets in the five years since Adam left Earth, and now Bill decides to catch up to him in the latest-technology 0.8c rocket. Five years later, Bill slows his rocket to half-speed and docks on Adam's rocket. Now Bill is the one who's younger, as his reference frame has always been 0.4c relative to Adam's. [I suppose the "years" in this scenario would be relative to Adam's perspective, if we want this scenario to be symmetrical to (a).] (c) Or perhaps Adam and Bill both decide after five years to meet each other in rockets going 0.4c toward each other, whereupon they land on the planet Causality, which is traveling 0.2c from Earth in the same direction that Adam left! Now they're both the same age after all, since they were both traveling at 0.2c the whole time, relative to Causality's reference frame.
The bit that's always confused *me* is why the speed of light was ever suspected to be the maximum speed of causality anyway. Weren't the thought experiments leading up to it something like "You shouldn't be able to tell your speed in an inertial reference frame, and you wouldn't be able to see the light in your rocket if you're going faster than light"? Surely this can't be about light produced inside the rocket, because if light speed weren't a universal constant, the light coming from the light bulbs in your vehicle would be sped up along with the rocket, and there'd be no problem seeing anything from turning on a light (just like you wouldn't stop hearing things while riding in a supersonic vehicle). But if it's external light, then what's the problem with not being able to see light that's coming from a star that's moving faster than light speed away from you? It feels as though there was some other reason that Einstein intuited light speed would be the same as the speed limit of the universe, and that particular kind of thought experiment is just some question-begging justification for that.
@@michaels4340 It was an experimentally observed fact, due to the Michelson-Morley experiment. It was also hinted at by Maxwell's equations, which predict a speed for light but don't say what it's relative to. Einstein's thought experiments weren't a proof of the constancy of c; they were him taking it as an axiom and exploring the consequences of it.
I think your original explanation for the reason the light doesn't slow down has the right spirit. Only that, the only light that keeps in lockstep, as you say, is the forward scattered one (electron in line). You can show that this one has to always be opposite in phase to the drive (optical theorem), so this light will be reduced while it travels and disappears eventually. The light that is left comes from the other electrons, arriving slightly later. But this process repeats as the combined field drives further electrons, so gradually the front edge of the light gets eaten out, slowing down the pulse. The Feynman explanation is taylored to the long time steady state, but what you want to describe is the first transient. The intuition you get out of it doesn't always apply.
Thank you for this! This is what I thought originally, but the issue seemed to be that the phase of the electrons in the centre line is the same as the phase of the original light is the refractive index is greater than 1. Do you know how to deal with that case?
@@LookingGlassUniverse sure, that's what I meant in the end of the comment. The scattered field is in phase in steady state, but for you what matters is the short time response
@@LookingGlassUniverseyou could show it by repeating the forced oscillator calculation in the Feynman notes, but with a force that is a delta function in time for example. The restoring force doesn't have time to respond. Personally, I think the best argument for this is just energy conservation. If the scattering is in phase, the drive would get amplified indefinitely and there are no other fields fast enough to catch up to it.. it must be out of phase
@@LookingGlassUniverse here is another argument. The value of the index of refraction depends on the frequency of the light. When the light first hits the electron, how does it know what the frequency (and the index of refraction) is? It's going to take at least a period for the electron to realise this and start responding with the expected phase. This shows you that the concept of index of refraction is not relevant for what the scattered field looks like immediately when the field hits.
This and the other video are just fantastic. The real nitty gritty of understanding a concept in physics through theory, experiment and finally computation. I've always just taken the slow-down of light in water at face value...now I'll have to think about why!
Yes! But as long as some of the light going on the shortest path is still there (and hasn't been cancelled out) then some of the information will still travel the shortest path. But as long as the short path's light is cancelled then yes, the light's gone a longer way
Is there really some light going the shortest path? In a lecture Feynman taught that electrons going from A to B always travel through the whole universe and the observed result is the sum of all probabilities. Isn't it the same with light? I think to answer this question there must be some quantum mechanics involved. The problem is that nobody really understands quantum mechanics. Maybe GPT 8 will give us an answer
Wonderful video! Pharmacist/Programmer here. I think there might be a decent intuitive mechanical analogy in SEC. Size exclusion chromatography (SEC) separates molecules[colors] based on their size by filtration through a gel[glass] in a column under e.g. water pressure. Separation occurs when molecules of different sizes are included or excluded from the pores within the gel matrix. A given size molecule may travel directly through the gel material, but with smaller size it is very unlikely and undetectable. The average molecule will zig-zag through lots and bring down the measurable group velocity. The smaller molecules find more pores to travel through. SEC is used to separate the molecules by size, by measuring their time to traverse the gel.
I have watched both yours and 3Blue1Brown’s videos, and spent several hours thinking about it, and I have arrived at what I believe to be a satisfying explanation as to why the information speed of the pulse light slows down. As per 10:30 in your original video: th-cam.com/video/yP1kKN3ghOU/w-d-xo.html the light created by an electron responding to light would be the equal and opposite wave. This would cancel out, but as 3Blue1Brown says in this section of his video: th-cam.com/video/KTzGBJPuJwM/w-d-xo.html the restoring force on the electron from the medium causes the resultant wave to be weaker (typically) and out of phase. However when the electron is at equilibrium (i.e.: before the pulse reaches it) the restoring force would be zero, and for the first instant that the pulse reaches it the reaction wave would exactly cancel out the arriving wave, as that repeats in the many layers of material, it eats away at the front of the wave.
Thanks for an almost satisfying answer. It may well be holes in my understanding stopping it from being completely satiating. Maybe you can help? What exactly the phase of the electron light is and why, is something I am still a little unsure of. Can you elaborate at all? Perhaps for an idealised case with no restoring force and a more realistic case. In 3b1b's video, he said the phase was retarded by 90 degrees, whereas here it was said to be out of phase. Is there something about negative charges that I should be thinking about? Perhaps producing inverted waves? It also surprised me to hear that there was no delay in the arrival of the wave and the production of the secondary wave. I thought this would involve infinitely fast acceleration of an object with mass. But I suppose if it is the acceleration of the charge (not it achieving some speed) that produces the wave there is no reason there has to be a delay between the arrival of a force and the production of the wave. Your input would be appreciated, thanks!
Your nerdiness is contagious, and I am really struggling to keep myself from exploring your code and trying to see what I can do to speed it up hahah Coming from Computer Science and having worked as a Software Engineer for 8 years now, I do sometimes miss these nerdy assignments we did in CS classes like Algorithms 2 and 3, where you approach the limits of physical hardware and you have to start thinking hard to make shortcuts!
Here is a question though: in Maxwell's equations, the speed of light is just 1 over the sqrt of the product of the electric permittivity and the magnetic permeability. Maxwell calculated the speed of light based on the measured permittivity and permeabililty of the vacuum, features that were already understood from experiments with electricity and magnetism. But you can calculate permeability and permittivity for any material, and indeed we routinely do In electric engineering and other scientific fields, although it seems like those numbers are usually calculated for very different freqencies than the visible light range. But the refractive index of a material is actaully calculated based on the permittivity and permeability values. Permittivity "is a measure of how well the molecules of substance align, aka polarize, under an electric field. The better the molecules polarize, the more that substance resists the electric field." According to one googled source. So from that perspective, it seems like we understand why C slows down in transparent materials quite well, without needing to resort to addional EM waves, quantum effects, or anything else. So what is going on here? Is this just a classical representation that doesn't get at the underlying complex physics? Is it just a restatement of the same problem from a different perspective? Or is it really as simple as: materials have intrnal polarity and thus internal electric fields, and the stronger the electric field is, the slower an EM wave (aka a light wave) will propogate through it? This seems so much like it could be the right answer, and it's so simple. Yet if true, why doesn't it show up in these physics explanations?
Yes, you got it right. its ε0 & μ0 that determine the speed of light. In transparent materials the Permeability & Permittivtity is different from vacuum which decrease the speed of light. People like to make physics unnecessarily complicated.
I would think that this is an oversimplified classical explanation, considering this is part of the same model that produced the ultraviolet catastrophe. It works for predicting the result quite well but only if you don't poke at the details.
The classical result should have been enough to convince her that the effect is readily observable. But, to me, it has no explanatory power. It just says materials have these properties that were determined empirically, and using these properties we can predict the propagation speed of electromagnetic waves through the medium.
I think your argument is correct. When it comes to most materials, I think the front speed is going to be c as you originally expected. But if that front gets worn down as you suggest, it won't be detectable. It could be fun to redo your experiment with different amounts of water to see if you can demonstrate that the detectable front goes discontinuously from v < c to v = c. I suspect the lidar won't be sensitive enough to capture this though.
The best textbook that I think explains what is happening is "Absorption and Scattering of Light by Small Particles" by Bohren and Huffman. It was the first source that taught me about the Ewald-Oseen theorem---when I learned about it it did feel like learning about a conspiracy related to the scattering of light. I have tried myself an experiment with single photons, the HOM interferometer. Then you put a piece of glass in once of the arms and the dip shifts by the amount the single photons get delayed in the glass. I can try it with a bit of water in the way and see how much it changes.
Thank you so much for this great recommendation! It sounds like it probably has the answer in it! That's incredible that you have a HOM interferometer, I'd love to hear about the result. My email is on my about page!
That the open questions in today's physics, like the nature of gravity, the lack of a unified theory, the crisis in cosmology, and the nature of dark matter without viable alternatives, must be considered parts of that physics, is self evident. That all the attempts on answering them remain unsuccessful, makes every new question all the more important! I think your openness and willingness to ask every question, is precisely the approach that is needed!
I love your honesty. The way I think about it is via the actual derivation of the vacuum speed of light from Maxwell's equations. There, c is found to depend on the permittivity and permeability of free space. In other words, the strength of the electric and magnetic fields in response to charges and currents are just natural constants. Now, when we introduce a medium, the response changes. You can see this with dielectrics where the induced polarisation reduces the magnitude of the field. These medium responses change the permittivity and permeability constants, and hence the speed of light. I think that reducing this medium response via the superposition principle has caused the problems here. If you imagine a medium as being composed of a continuum of springs, the response of the medium will depend on the spring constants. These spring constants are always less that those of the vacuum due to screening. This is all covered in gorey detail in Panofsky and Phillips, Classical Electricity and Magnetism, although I doubt that this will aid your intuition. I think that considering disturbance propagation in an elastic medium is much easier to grasp.
That's just how massless particles work in this universe. They all move at c, they cannot do otherwise. And all massive particles are slower than c. Now c is 1/sqrt(ε0μ0), with the electric constant ε0 and the magnetic constant μ0, but I think c is likely the more fundamental one.
@@KaiHenningsen You could say the same exact thing about the speed of light in water... I think we're all looking for an explanation rather than an equation.
She touches on briefly in the previous video. c is the speed of causality, and it makes sense for it to also be the speed of light in a vacuum. Why causality has a speed? We don't really have an explanation, that's how the universe is, but that simple idea explains a lot of things. Attempts to model light as a wave travelling an a medium has been done before. It was, in fact, the leading theory (luminiferous aether) before special relativity turned out to work much better. Nowadays, explaining why some things go slower than c is the hard part, that's how we got the Higgs field and all that stuff.
@@gubx42It just seems unlikely to understand why the speed changes when you don't understand why there's even a speed to begin with. And I think it's funny that the aether has been dismissed only to be replaced with "free space" which has properties. Isn't it just a different name for the same thing? So I think that thinking in terms of electrons is a far cry short of what's needed to understand the speeds of light. There is necessarily something far more extraordinary happening. The very nature of spacetime and light and their relationship must be revealed. Light appears to transcend spacetime and in some way also be entangled with it.
@@FaithLikeAMustardSeed The problem is that the speed of light (c) is the same everywhere, including on things that move. This is hard to reconcile with the idea of light being a wave traveling through a medium since the relative motion of the medium itself would have to be taken into account.
Its great to see your journey through what i have thought is one of the hardest concepts in physics. The interaction of light and matter. During my PhD i was given a great book on light and matter called QED by you guessed it Richard Feynman. You might enjoy it.
Maybe the light isn't _really_ slowing down from its perspective but actually traveling farther. Consider Kelvin's Knot Vortex Theory of atoms. Of course the frequency dependence would have to be accounted for (perhaps a short-circuiting of certain crossings or something like that).
Yes Naomie, I think you are on the right track. Regarding frequency dependence, could it be that wavelengths larger than the distortions in space (that are the atoms) do not have to traverse those distortions. Consider this 1D string, with distortions representing the matter: ___________/\_____/\_____/\_____/\_____/\___________ Wiggle the string with a wavelength shorter than the distortions like ---^^^^^--- and those waves will traverse the distortions. But wiggle the string with a wavelength longer than the distortions like ___/‾‾‾‾‾\___/‾‾‾‾‾\___ and those waves will not need to traverse the distortions. See my other comment.
Thanks so much for making this video. It takes courage to present one’s struggles rather than a neat and tidy solution all completely figured out. It is fun to watch a ten minute TH-cam video where someone achieves something wonderful with little apparent effort, but it leaves the viewer with a distorted view of reality and frustration when they themselves face adversity. I’m speaking from experience. To me, it seems that your ultimate question was, “If the speed of propagation through the field is always constant, what can make the ACTUAL propagation (the delivery of information from point A to point B) slow down?” This line of inquiry fascinates me, making me wonder if it might have wider implications. Could this be related to the phenomena whereby the quantum electromagnetic field permeates the universe, with a constant maximum speed of information propagation, and yet for different frames of reference the propagation (the speed of light) differs relative to the global frame of the field? I.e. the speed of light measured in all different frames in motion is the same. To make this work, there would also have to be something that makes clocks run slower or faster in each reference frame. But since clocks are nothing but mater elements propagating through their own respective quantum fields, perhaps the same principles would apply. It probably is not related, but it is interesting to me to consider. Thanks for making this video!
Feel free to correct me if I'm wrong: The original pulse should fall off exponentially. As it's the first to interact with each layer of electrons, they'll cancel out a percentage of the original wave (through their secondary wave). As each layer does that, the pulses amplitude should fall off exponentially. This fall off happens at the same time the slower wavefront is created from constructive interferance behind the dwindling first pulse. This would mean *some* light does travel at c, but it drops off very quickly. That's at least my intuition, but again, please feel free to correct me.
That's my intuition as well! The secondary wave produced by the jiggling electrons is in the opposite direction of the original wave, and so will create almost perfect destructive interference with the original wave (as more and more layers cancel off more and more of the original wave). The end result is that the front edge of the pulse still moves at speed c, but with such a tiny amount of energy that it's undetectable; the main energy of the pulse will only arrive much later. The mystery that still needs to be explained is why the cancellation happens in such a perfectly predictable way every time - I don't have a good intuitive reason for why the bulk of the energy should arrive after a very predictable delay. Water and glass aren't crystals, so a good explanation can't depend in any way on the symmetry or perfect spacing of the "layers" of electrons.
This was what I thought too, till I realised that if the refractive index is great than 1 (which is most of the time) the electron wave actually reenforces the light- which is mind bending. I don't understand it at all
@@LookingGlassUniverse that's really interesting - could that be explained as a "layer effect" coming from the many electrons in the layer that are farther away? My hypothesis is that the very front edge of the light pulse will only be affected by the closest electrons in the layer it passes (since the waves from the other electrons in the layer don't have time to reach it), and the secondary wave from these close electron will cause destructive interference, flatting the front of the pulse. But the contributions from the further away electrons take longer to reach the same spot, and they combine in a way that interferes constructively with the original pulse. So the combined electron wave has the effect of surpressing the front edge of the pulse and boosting the back edge of the pulse, with the apparent result that (1) the pulse is delayed, and (2) for the section of the pulse that "remains," the phase agrees with both the original wave and the electron wave, so it looks like the electron wave is reinforcing the light. Does this explanation run into issues somewhere?
@@LookingGlassUniverse Re the simulation. Remember energy conversation. The EM energy in the delayed wave comes from the initial wave. The exact details don't matter - the first wave must die out as the delayed wave is created.
Such a great video! It brought me weeks of joy appreciating the wonders of the world. As a beginner in physics, I recently came across the concept of "Quantum Decoherence" (en.wikipedia.org/wiki/Quantum_decoherence) which seems to partially explain the slowing down phenomenon in your video. On one hand, under the influence of the environment (such as water or other media), the degradation of quantum characteristics and the enhancement of classical particle behavior can account for the decrease in speed. On the other hand, I got some feeling of the transition from infinite wave plane to a pulse: when the mathematical expression on an infinite time axis (perfect "coherence") undergoes "decoherence" due to the method of laser generation, interference from the propagation medium, or even observation behavior, lead to a degradation in wave characteristics. Recently, I have been trying to use this naive understanding to understand classical phenomena like the double-slit interference without bothering the complex partial differential equation calculations 🙂
21:56 how to fix the bad framerate of your simulation: If you, instead of recording your simulation with a screen recorder, save all the different slices after rendering each iteration, as screenshots, and then later stitch them together, you can get a really smooth animation, especially if you select a small enough dt.
It wasreally interesting to follow through your struggle with those experiments and simulation. I certainly undestood more than in other videos, which are also great, but I'm easily getting lost with all the sinus formulas and angular/vector graph comparisons. Your rather visual and "slo-mo" way of explanation is much more intuitive for me. Also I must admit I got distracted by your beauty quite a few times :) Anyway, subscribed.
He commented on the part 1 video actually. He said he thinks the range finder with the red laser actually just used triangulation. Edit: And now it looks like he's seen this one too.
I'm sure there are many fans of your channel who can help out with programming, me included. I often spend midnight hours watching videos like yours and 3blue1brown, I'd be more than happy to help out.
Thank you so so much- I would love that! I have it on my github but I'm going to write up a doc on what factors need to go into the simulation so that people can write their own (probably much much better) version. github.com/mithuna-y/speed_of_light_in_a_medium/tree/main/multiple_layers
Love the video! =D In astronomical observations, particularly of pulsars, we observe a phenomenon known as dispersion. This is characterized by a time delay in the observed light, which is dependent on the frequency of the light. This dispersion serves as observational evidence for delay in information speed. As a side note, from the photon's frame of reference, the time experienced is always effectively zero, due to the relativistic effects at the speed of light.
Is the dispersion caused by intervening matter? I am under the impression that in a theoretical perfect vacuum, there would be no dispersion. Dispersion happens in transmission lines also (like coaxial cable, for example).
This is a great project and some great work! This is really a question that's been bugging me for a long time, and while it's a bit disappointing (and understandably frustrating for you) that you did not manage to find a definitive answer, you should be super proud of all the work you've done and the insights they brought to you (and everyone who watched your videos). Hopefully, someone will take on the challenge and deliver a final explanation for all the curious mind around here :)
Great effort and honesty. Keep it up. The process of light slowing down in materials is ultimately explained in quantum field theory which describes the interactions of the fields involved in the process(photon, electron, quark up and quark down), but it would be too computationally expensive to predict the refractive behavior of a material with those equations, that's why they further abstracted it with density functional theory, which still doesn't do quite a good job.
I think what your simulation is missing is the phase/frequency dispersion of a medium, AKA it's complex-valued index of refraction. The refractive index of gamma rays through anything is basically "1", but the limit of refractive index as frequency --> 0 is basically infinite.
Thanks! In the simulation about midway you can see the dispersion happening- or ‘chirping’ as it’s also called. The previously peaked red wave becomes a much wider wave. I didn’t include complex refractive indexes because the video was too long, but they account for absorption
Fantastic videos ! Thanks to you i realized I didn't really understand the slowdown of light in matter. I'm quite sure that there are many other examples of physics phenomenon that everybody takes at face value but if we really digged down we'd find out that we don't really. understand. Congratulations for your great work and honesty !
I love that the answer in the end is just "I don't know". The journey matters just as much as the destination, if not more. This video and the previous one are both excellent.
An explanation to why light slows down in material medium: The electrical permittivity and magnetic permeability, which basically means how easily electromagnetic (EM) force is propagated through the EM field, is different from the vacuum. This happens due to the presence of charges in the medium, hence Feynman's explanation comes in handy and is correct. Also, you can use plane waves in your explanation, since mathematically every wave is equivalent to a sum of plain waves. DO note that I said MATHEMATICALLY, meaning we can describe the real phenomena more easily, even though plane wave are not real. You correctly explained the problem when you got the answer for plane waves, just needing to use Fourier SERIES to then get the real signal. Why series instead of transform you may ask. Fourier transform, as the name implies, transform a function to it's correspondent in the dual space. The Fourier series is the expansion of a function into sines and cosines, similarly to how a Taylor series expands a function into a polynomial.
Cool video! This is my favorite kind of science vid, the intersection of physics, research and programming. I'm glad you made the video despite things not panning out like you wanted, very neat watch even to someone like myself who's not much of a physics knower.
From a simulation perspective, something that might be worth looking into are "Finite Difference Time Domain" and "Finite Difference Frequency Domain". As a computer science researcher that works with waves a lot I can say those methods impressed me a lot. Though they're a bit too optimised to be particularly comprehensible for understanding in my opinion. If looking into those methods proves too confusing, I generally recommend trying to code up a lattice simulation of electrodynamics. That is to say, breaking space into a discrete grid and looking at the physics from the perspective of space instead of the perspective of the waves / particles. You can create a full wave simulation using just convolutions. That is to say, each pixel in your grid can only see the pixels surrounding it and moves in respect to them.
I found this video strangely moving. You put so much time and effort into your research. But it seems like you learned many valuable things along the way. Thank you for sharing the journey.
Amazing! Thank you and 3blue1brown so much! Your series' have improved my understanding of light 10-fold. I think you came soooooo close to the final answer right at the end. Your simulation showed that while the speed of light doesn't change, the speed of the resulting *interference pattern* does. That is to say: yes: the resonant responses interfere to perfectly cancel the original light wave. In terms of the original explanations you discussed - this is closest in analogy to "the light gets absorbed then re-emitted" because for the electrons to resonate, they have to absorb energy from the original light source. As for why the light doesn't scatter... yes it does! Sort of. You can see the laser inside the water from all directions, meaning some light must radiate in all directions from every point. However most of the light is parallel to the original light source because at the microscope scale the laser approximates an infinite plane (think of how many trillions of atoms wide that laser is).
Right... This is an approach I wasn't quite thinking about. So if it weren't for the re-admitting of light then the medium would be opaque due to the loss of energy in the original wave?
@@PulseCodeMusic Well I know for certain the light has to conserve energy. If the matter had no charge there would be no interaction with the light (assuming no direct collision, though IDK what that even means at this scale). Anything with a charge is going to vibrate in response to the light. For the charged particle to vibrate it has absorbed some energy. The charged particle can either re-emit that or absorb it as heat. But this getting beyond my level of knowledge of physics because at this scale what is heat but vibration? Perhaps "heat" in this context means converting the energy to a different frequency? Of course the magnitude of the effect comes into play. There can be energy absorption and transmission (think of shining a light through a piece of paper) - it depends on the rate of absorption and thickness of material.
@@003Jetfire it definitely doesn't give all the energy in back to the wave that continues through the material as half of that wave goes in the opposite direction. The question is, how much energy is lost. I would love to see this simulation but minus the secondary light to see how far the original light got. If it decays quickly then that's your answer.
"I don't know the answer" should be the most exciting thing in the world for a scientist, its sad that our society has made you feel badly about something that needn't be bad at all. I was thrilled watching this and inspired to learn more about it myself now, thank you
Love your honesty and scientific process in this video. Shows clearly how much work, deep understanding and perseverance goes into your physics work. Light is enigmatic, but even Einstein was stumped at how mysterious it is, and remains so to this day!
About a quarter of the way through this video I was thinking, wow what a phenomenal representation of the experience of being a working scientist. Still though, it's missing the part where you try to make a computer model and at first it seems great but it ultimately doesn't work and your sanity erodes until you eventually give up and question whether you even deserve to probe into the secrets of the universe. Whether this whole enterprise has been arrogant and your human mind can never dream of brushing up against the roots of existence. So you give up for a while and have a huge crisis over it but then you look at your code with fresh eyes and realize that while you should not be allowed within ten feet of a computer (not that this will stop you) you absolutely deserve to probe the secrets of the universe and you fix it and it's one of the best feelings you've ever had in your life. You know, science. Anyways, well played. One of the best videos I've seen on this site btw. I'll be showing my students.
Honestly, you gave so much more information on why light slows down in a medium than Dr. Don from Fermilab. Absolutely incredible video and it pairs so well with 3b1b's recent upload!
which of your simulation files is proving to be the bottleneck? Maybe one of us programmers can make a PR to enhance your simulations. Stellar video and really appreciated how candid it is
The one that's just a pile of for loops is this one: github.com/mithuna-y/speed_of_light_in_a_medium/tree/main/multiple_layers I would absolutely love if you're interested in improving it! I'm going to write up a proper explanation of what I did so others can take the idea and simulate it in a better way
Really loved your videos on the speed of light through water. I think that you have come to the same conclusion I have: Incumbent physics does not understand how light propagates in general, and that the inability to apply the incumbent models to transmission through transparent media is the red flag exposing this inconvenient truth. If you try to simplify things by assuming the propagation of a single photon, then things become even more obvious. The whole idea that the light "jiggles" the electrons means that it must be imparting energy to those electrons. That can only happen if the photon loses energy. According to the E = hf equation, this means that this "primary photon" must experience a reduction in frequency as it traverses the water. Also, any wave emitted by the jiggled electrons can only be as photons. Again, their frequencies must be different from that of the original photon. It is not credible that these "secondary photons" would be angled in exactly the right direction to now again interact with the primary photon. Regardless, if this mechanism was at play, the photons emerging on the far side of the water would have a different frequency to that of the primary photon. The Fourier transform is a very useful mathematical way for engineers to calculate the measured effects of wave-like phenomena, but we should be weary of believing it is telling us something about fundamental physics. It would also be instructive to take into account effects like the change of light speed in still and flowing water. I believe that the honest answer to your question is that incumbent physics does not understand the phenomenon either.
Wow, very interesting. It's a much more difficult question to really answer for certain than expected. I would hope you keep at the problem, as a definitive result, especially with a good simulation, would certainly be very valuable scientific research for everyone. Great job!
As the pulse travels, the layer that it has reached emits a secondary wave not only in the forward direction, canceling the incoming light, but also backwards towards the other layers that the pulse had passed. This back and forth emission causes the same slowing down as in the infintie-duration case.
I'm not sure if there's any mistakes in this explanation but here I go. I think the whole original wave is destroyed and a slower one is created is the correct explanation. First, let us consider a wave of light travelling through a straight line of electrons, but first we will only consider the response waves that the electrons generate in the same direction of the original wave. This response wave is some multiple of the original wave, say 10%. So the second electron would see 90% of the original wave, the next would see 89%, etc. Eventually the wave will be completely annihilated. For any wave, this means that it will cancel out with the response waves that are travelling in the same direction. This doesn't quite explain how the slower wave is generated, but i guess an argument would be that the remaining waves which don't travel in the same direction in the original wave can be added together to create another wave in the original direction at speed c, however it will be pushed back by a phase shift because it took an indirect path. And then the same argument applies Hopefully that makes sense??
Sorry if it was mentioned already, but the conspiratorial cancellation of the incoming wave by the electron induced waves was mathematically proven by Ewald-Oseen. See, for example, section 2.4.2 in Born & Wolf's Principles of Optics.
I really appreciate your painstaking search of a convincing truth on this argument!!! that me think the best for you and for your Phisics Theory career. These videos let me literally jawdropping seeing all 3 in just one shot!. I really hope you can come up to an acceptable solution, that, for your behavior, could only mean to finally explain the phenomena. Thanks for sharing! Hope my best wishes to you!
2:41 The plane waive represents the timeless quality of a photon. Because of the very nature of its speed, it has no time component. Because of that, any experiment you do with light has to take into account that from the moment that photon was emitted, it is no longer in your reference frame in regards to time. All things are experienced by the photon in the same instant it is created. Hence why it both does and does not slow down when passing through a medium. You increase the distance traveled so from our reference point outside that solid medium, it slows down. Have a look at Cherenkov radiation. Excited particles basically blasting through a medium without regards to the refractive index of that material... creating a blue light. I'm very much enjoying your videos as you look at these things experimentally rather than theoretically. Great stuff. 16:24 Send him a bottle of his favorite adult beverage. Best advice anyone could have possibly given you. When faced with adversity, always try and turn your failures into success... either yours or someone else's. Only way to do this is to let colleagues (or the internet) in on your failures or confusion. You are Waaayyyy smarter than I am. Mathematically you have such a gift and such a firm grasp on this that it has me subscribing to see what else you are on about. The only thing you lack is what you are embarking on now... experimentation. I was blessed to have worked for nearly two decades in an incredibly well funded industrial lab environment where for a period of about 5 years I was working on the EXACT thing you are wrestling with now. That's what actually had me click on this pair of videos... and I'm glad I did. 26:09 A brilliant and humble admission. I hope you continue to revisit this from time to time as I too would LOVE to know the exact reason(s) for what we have both seen experimentally.
So cool, just watched both videos and I really want to congratulate with you for all these efforts. I was like "no way she is getting into coding to simulate it", but you actually did, and with great results (even though you didn't vectorize the code haha). Btw, I agree with you, the answers is still not satisfactory and it still would look like it wouldn't actually slow down...Damn. But maybe is as you said, the first front might be chipped away but many subsequent "layers" of electrons. This is actually very interesting and your model really makes sense. I always supposed that there actually was a "correct" physical answers to this question, but that, given its complexity, everyone was just working its way around it; you really make it look as if we really don't know what's going on. I think that's crazy for such an important thing in physics.
- Part 1 of this story: th-cam.com/video/yP1kKN3ghOU/w-d-xo.html In that one I explained why the common explanations are incorrect or incomplete. I also measured whether light really does slow down using my phone.
- 3Blue1Brown's explanation of Feynman's proof is so great: th-cam.com/video/KTzGBJPuJwM/w-d-xo.html
- If you'd like more detail on the physics that went into the simulation, I'm writing it up here: colab.research.google.com/drive/1L9X_tq-Kjt-foEhcnSXpvNujbbJEedBz?usp=sharing
The 3D simulation lives on my github. I would love to update it though, so if you have ideas or time to work on it, I'd love to hear about it : github.com/mithuna-y/speed_of_light_in_a_medium/tree/main/multiple_layers
From Wikipedia's page on Ewald-Oseen extinction theorem (as pointed to by another commenter Danyel).
'The characteristic "extinction length" of a medium is the distance after which the original wave can be said to have been completely replaced. For visible light, traveling in air at sea level, this distance is approximately 1 mm. In interstellar space, the extinction length for light is 2 light years. At very high frequencies, the electrons in the medium can't "follow" the original wave into oscillation, which lets that wave travel much further: for 0.5 MeV gamma rays, the length is 19 cm of air and 0.3 mm of Lucite, and for 4.4 GeV, 1.7 m in air, and 1.4 mm in carbon.'
The way I read this (in the context of your video [loved it!]) was that yes, light does just travel at its own speed but parts moving faster than the "group velocity"(? I have to admit I didn't get what that really is) just get damped down at a different rate that is very quick. This is similar to what another comment Samuel Owens has commented.
Mithuna, I and my father Prof. Dr. Tolga Yarman (Ph.D. in Nuclear Engineering from MIT) think we have the answer to your quandary. Please search "Quantal Yarman Annals of Physics" in Google to read our recent article (Quantal Theory of Gravity: Essential points and implications, July 2023 -- C. Marchal, T. Yarman, A.L. Kholmetskii, M Arik, O. Yarman) that we published on the idea of what you call "disjoint pulses" which "lag behind". Our paper deals with the splitting of a gravitating test particle like a photon into two constituents just like you describe in your simulation. The hf constituent is conjectured to speed up to reach the utmost theoretical c while the kernel constituent slows down and the object eventually gets torn apart. We thus believe a similar thing happens for light traversing mediums with differing refractive indexes. We would hence like to discuss more on this topic with you and incorporate your contributions. Please contact us in the e-mail provided in the said article. We congratulate you for your progress and findings! Cordially, Prof. Dr. Ozan Yarman, Istanbul University.
@@armandaneshjoo USE TAYLOR SERIES
when you get a chance see my reply below. and let me know when it dawns on you lol. i thought about it for 30 years off and on.
Thanks for this interesting pair of videos. What left me wondering, is that you didn't seem to explicitly mention optical dispersion (unless I missed it). At 14:20 of the Part 1 video you dismissed the explanation of group velocity because 'that phenomenon is only relevant if you already have waves going at different speeds'. But that's exactly the case due to dispersion: water has different refractive indices at different wavelengths, so those waves with different wavelengths indeed have different phase velocities.
At 17:03 of the current video it seems you have incorporated dispersion in your model. That is evidenced by the fact that the pulse travels more slowly, and that it broadens during propagation. In Feynman's analysis, the refractive index is a function of the angular frequency omega, so indeed it takes dispersion into account (by assuming the Lorentz oscillator model).
As for the question of how the electrons conspire such that the light pulse must always travel more slowly than c: the dispersion relation (i.e. how the refractive index depends on wavelength) satisfies the Kramers-Kronig relations, which are derived from the assumption that the electron's response to incident light must be causal. Therefore, causality is built into the physics. If you want to avoid the use of Fourier transforms (where unphysical 'infinite waves' are added), you'd probably have to infer the frequency-domain response of the water from its dispersion curve, infer the time-domain impulse response (which should be 0 for time
So glad this is finally out! I always appreciate the combined honesty and clarity in your videos, and these two just nail it.
my man 3b1b was spawncamping this video 💀
Literally just watched your video on the topic too! @3b1b
You guys should have a couple photons together. 😏
Literally just watched your video too 😅😅
Just coming after watching your video, if you are reading this, know that you have my huge respect and keep up your work 🎉🎉🎉
I'm not a physicist so I can't weigh in on the technical side, but this was a really great video. A lot of educational content is so fixated on portraying the aesthetic of expertise that it misses out on the _process_ of expertise, and this is a great example of what that looks like, even if you don't wind up with a nice, clean answer to wrap things up.
I appreciate this so much!
This.
What a remarkable video.
Alpha Phoenix has recently posted similar content with a similar process. You really understand all the trouble he's gone to in gaining this knowledge. LookingGlassUniverse and AlphaPhoenix need to team up to muddle their way through the next physics problem!
A lot of educational content also tends to assume that the viewer is either completely new to the subject and can only digest gross simplifications, or has all the prerequisites for a university-level course. There's seldom much content for viewers that have a good phenomenological understanding of the subject but are missing the math.
12tone, since you're showing up on a physics video, is there any chance you could do a series on music theory for STEM majors? People who understand small integer frequency ratios and twelfth roots of 2, but stare blankly when you say "this resolves to that". (Fun fact, there is actually an intriguing bit of orbital mechanics that locks the orbital period of Pluto to be exactly a perfect fifth away from that of Neptune).
@@LookingGlassUniverse while your simulations are good, you can see that your first simulation clips show the 3 circle dots lagging behind but they start lagging more as time passes. This is not what we see when we see light slowing down because otherwise that would imply that given a larger volume of water, we would see light slowing down more (basically additively slowing) and at some point light will be absorbed by the water and we would see water being opaque. That does not happen. I am not sure if anyone has actually figured out why light slows down in different mediums. But I think it's because of gravity or space-time. From a photon's perspective, it does not experience time at all. The beginning and the end of the universe for the photon happens instantaneously as if time did not exist. For a photon, it always travels in a straight line too. Everything around it curves. So why then do we see light bending around a black hole? It's the same principle. For a photon it travels in a straight line and will never curve, but it has to maintain its speed, and because of the space-time curvature around a black hole it travels with the same speed but will have to do so in a curve, and thus we see it being curved. Well the important point is this space-time curvature is actually density. You can replace a black hole with something else, and add gas instead of just pure vacuum instead while maintaining the space-time effects that photon was experiencing, and it will behave the same way. This is the same as satellites experiencing slower time than people on Earth. This rate of flow of time changes depending on the density. In the case of light going through water, the difference will be compounded because photons are small enough for quantum effects of atoms to be affecting it (maybe my theory is implying that gravitons exist and there's graviton interaction happening between atoms and photons). That's why people won't experience slow rate of time if they are submerged in water (because we and any mass particle is too big), but for something which is massless, this is as good as traveling near a black hole where you see it curving.
If you consider light directly aimed at a center of a black hole, it's going to slow down and down till it reaches the event horizon at which point time stops and light also stops traveling. Now imagine light being incident perpendicular to the surface of water. It's the same exact thing (the angle of refraction is a different concept and not relevant to the scope of this). If we had different type of water with varying refractive indices, we could simulate what light must experience if it is aimed at a black hole. It all has to do with density and how time interacts inside dense material. Changing wavelengths or even phases doesn't help at all here, since it will completely break down if you consider the position of a single photon and track it from vacuum to water or from air to water, and then measure the speed.
Fantastic video! It's already been three weeks, so I'm not sure if anyone is still reading the comments, but I have three happy remarks to share:
1. Regarding the Ewald-Oseen Extinction Theorem, if we delve into the mathematics, it's not about the initial pulse being magically and continuously canceled. Instead, the initial pulse is canceled right at the outset, and the negation wave (already generated by the first layer of electrons) travels automatically alongside the initial pulse wave at the speed of light. Consequently, the rest of the electrons don't even "feel" any field traveling at the speed of light. I hope this explanation makes the whole intuition much more acceptable.
2. You demonstrated how significant results are actually achieved. By delving a bit more into simulation and discussing the results with a mathematician, you could have independently discovered the Ewald-Oseen Extinction Theorem. This showcases that great results stem from a physicist's intuition and the meticulous pursuit of an idea.
3. I understand your reluctance to use plane waves, considering they exist indefinitely everywhere. However, under Maxwell's equations, questioning the physical possibility of the superposition of plane waves is not valid since they are mathematically equivalent. Philosophically speaking, when two physical events are equivalent, they indeed, should be described by the same mathematics. However, when the same mathematics can be interpreted as representing two different physical events, it doesn't necessarily imply that both must be real. I hope this perspective offers some solace. :)
Adding a bit to point 1: under the framework of Maxwell's equations, we might not even need to delve into atoms or electrons. This is because the negation wave is a purely mathematical consequence of the "smoothed" electric/magnetic permeability of the medium. The use of a group of "electrons" in simulations is essentially an approximation of the Microscopic Maxwell equations (even though more "real" ).
Doesn't the Ewald-Oseen Extinction Theorem also show that the binary star argument for the independence of the speed of light from the speed of the source does not hold if the light hits an intervening gas cloud?
Ewald-Oseen treats the medium as a continuum of dipoles, which implies a uniform continuum of positive & negative charge, which can't for a in the body of the medium, as the charges will cancel except at the boundaries, and there would be speed-of-light delay for the effects of excess charge at the boundaries. A real medium is made of of rather discrete atoms, with gaps in between. There is no accounting for the leading edge of a light pulse light slowing down in these gaps. We can even align our light pulse's path through a crystal structure so that it has an unobstructed path between layers of atoms. The oscillating electrons can never _completely_ cancel the leading edge of an electromagnetic pulse. But they can diminish the leading "tail" (or "nose") of the pulse to so near zero as to be undetectable.
As it turns out, in the strictest sense, information is _always_ transmitted at vacuum _c,_ the speed of causality in relativistic QFT, and you will always have a nonzero probability of detecting a photon after a delay of L/c from the time the photon enters the medium, to a detect at distance L on the other side of the medium.
I've heard that negative results get published much rarely than positive ones. This makes this video even greater! We need more like this one. After all, stating difficult questions without straight answers is what gets us to advance.
Sadly, that is more the rule than the exception. It would help a lot if research funding terms either required publication regardless the outcome, or after some period of time, the funder would publish that the study was commissioned, and what the hypothesis was. So if the researchers didn't publish, others would know to ask questions.
We def need a Journal of Negative Results. Especially since we don't need to use dead trees for that any more. There are a lot of negative results, but that's partly because there's no Journal of Negative Results! Also that needs to be moderated ...
As an AMO prof I’ve always taken the Feynman explanation at face value and I loved to see you tackle it head on. Thank you. These videos do a wonderful job of how to think like a physicist but more importantly, that it is ok to be wrong bi intend to share this with students the next time I teach from Matter and Interactions.
Thank you so much for the lovely comment. Matter and Interactions is still one of my absolute favourites- but you're right, we can't take things written in textbooks for granted
@@LookingGlassUniverse you shouldn’t say prove when it comes science. Science never proves nothing.
Great analysis! I've been thinking about this same problem (off and on) since 2017, but have had almost no time to actually work on it. This video might inspire me to spend the time (and also give me a bit of a head start).
Hey, crazy!
Please do. I would love to see what you can figure out. You're one of the very best at this sort of thing.
Teaser!
If you do take it up let me know, that’d be amazing :)
I have the impression from these two videos (I am not a scientist) that each electron blunts the front of the pulse a tiny bit, which would explain the "coincidence" of why the cancellation effect should be so exact - I think I get that. The "coincidence" I don't get is that the sum of the wave interference from the wake of the original pusle, from the surrounding electrons, reproduces the original pulse to the extent that it looks like it's the "same" light but slower, hence a slower information speed. But why is the information preserved at all?
The reason I'm posting this as a reply to Nick's comment is because it reminds me of his video about mirrors: light from the angle of incidence hits the silver atoms, which in response radiate in ALL directions, and the sum of their waves at the angle of reflection just happens to exactly reproduce the light from the angle of incidence. I didn't really get the WHY of that, either. Is it a similar effect here, or am I just embarrassing myself?
I love this. Lots of others in the comment are saying this, but I have to agree - I love that you're going into how you go about doing science (idea -> hypothesis -> experiment -> analysis - and also lots of false leads and false starts and looking up other references, and the fact that, no matter what the math says, if the experiments show something different then that's what's ultimately real), and then despite all that you only end up with a partial result. But not only is it the try-fail cycles that I like, but also your explanations are in-depth enough that it's very easy to follow your thought processes (and I was totally convinced by your explanation and was just as mystified as you were at the end of Part 1). It feels like we're not only being told about the process, but shown it and taken through every major step of the way.
I would love to poke around to see if I can get any further with the intuition of where that funny double peak is coming from, but I don't know if I'll find the time... I hope someone else can get to something!
Thank you so much! I'm weirdly very happy to hear that you were also confused at the end of part 1. I wanted to take people on the journey and the emotions so I'm glad it worked :)
I didn't want you to be right, I wanted you to teach me something. You excelled. These two videos were exceedingly worthwhile. Imagine what else we don't know because someone thought it might be embarrassing to share.
The Ewald-Oseen extinction theorem seems to exactly about this topic. The electrons produce a second wave that (somehow, I don't know how) cancels out the original wave, while also producing a new wave that appears to travel at a slower speed.
The wikipedia page also mentions "extinction length", i.e. how far into the medium the original light has to travel until you can consider it negated.
Interesting. Never had heard about this. But that seems the exact answer to the original question.
However, note that the mere existence of a nonzero "extinction length" means that the leading edge of the pule is never _completely_ extinguish in the strictest sense, as at any point along the way we can treat that as the starting point of a pulse and extend that for the give extinction length. So the extinction length simply tells us a distance at which for all practical purposes the leading edge will be undetectable.
Ewald-Oseen treats the medium as a continuum of dipoles, which implies a uniform continuum of positive & negative charge, which can't for a in the body of the medium, as the charges will cancel except at the boundaries, and there would be speed-of-light delay for the effects of excess charge at the boundaries. A real medium is made of of rather discrete atoms, with gaps in between. There is no accounting for the leading edge of a light pulse light slowing down in these gaps. We can even align our light pulse's path through a crystal structure so that it has an unobstructed path between layers of atoms. The oscillating electrons can never _completely_ cancel the leading edge of an electromagnetic pulse. But they can diminish the leading "tail" (or "nose") of the pulse to so near zero as to be undetectable.
As it turns out, in the strictest sense, information is _always_ transmitted at vacuum _c,_ the speed of causality in relativistic QFT, and you will always have a nonzero probability of detecting a photon after a delay of L/c from the time the photon enters the medium, to a detect at distance L on the other side of the medium.
I think an important thing to remember is that if the light is doing work on the electrons by moving them, then it must be transferring energy to them, at least temporarily. Thus, the original wave should lose energy as it travels, and if the energy loss just some % per length, then you would get an exponential suppression of the original wave.
Jackson probably has an explanation of this somewhere -- sections 7.8 and 7.9 look promising, but I'm sick right now, and understanding Jackson is too much work for me to do right now \:D.
There's also a QFT-style explanation involving the difference between "real" photons (which correspond to the vacuum solutions of Maxwell's equations) and "virtual" photons (corresponding to propagators/the Green's functions of Maxwell's equations) that I could try to type up if people want.
Not even energy loss necessarily. Elastic scattering as per light in water doesn't lose energy, but it excites electrons, because the preservation of kinetic energy is maintained by directional change. Thing is, aren't we then back to the idea she put down at the beginning of last video that light doesn't slow because its taking a longer path..because that sounds like a longer path to me, if photons repeatedlychange directuib even if there is a lot to do with phase cancellation we must add to this.
@@jorgepeterbarton I would say that the process of scattering is equivalent to absorption-emission for this specific ondulatory model. Even if this experiment is a case of elastic scattering and the hole system doesn’t lose energy, the analythical vacuum pulse does, it is just reemited by the medium by the exact same amount.
If I am right, the scattering explanation (for a wave model) was right since the beginning. It is just that the phase superposition is preferent in one direction (which doesn’t have to be the same as vacuum's since there is refraction).
I don't know about QFT but I guess the mechanics are similar to photonics. Is that correct?
A little late to the party but:
If it's still an open question, why c is smaller in a medium than in vaccuum I would be glad to provide an explanation (I'm a physicist working in kinda this area). All the puzzle pieces are already given in this and 3blue1browns video. The key is the harmonic oszillator. However a satisfying explanation would take some time (maths, physics, simulation). But if you're interested I would get back to you some time before christmas.
Awesome handle!
I'd be really excited to read/watch/listen/imbibe whatever comes of this comment.
Please!
I'm also late to the party - but here are my two cents: from the theoretical end of things, I think a crucial ingredient are the so-called 'macroscopic' Maxwell equations, which I find surprising never getting mentioned in videos on this topic. There's also the matter of, if light 'slows' down in a medium, that's akin to say its quantum is a _massive_ photon, so that we need something like Proca's equations to properly explain it - which, IMHO, has something or the other to do with symmetry breaking (i.e., the medium is responsible for breaking the _conformal_ invariance of light in a vacuum).
It's not so hard to accept that the original wave is rapidly (exponentially) extinguished in the medium, and you're only left with the slower radiated light field. But I agree that to then say that "light travels slower in the medium" seems a bit misleading as it's more like a synthesized light, rather than an unmolested light wave.
Yes, the electron interaction somehow converts the original light energy into re-radiated and thus delayed light. There is no need for the electrons to send out a signal at the speed of c to cancel the original light wave.
I prefer my light molested , it stops me getting cancer.
I’m an electronics and RF person so I was fascinated by your journey, knowing that using a 100m length of coaxial cable, a switch and a battery plus an oscilloscope you can easily measure the ‘slowing of c’ - known in my field as the velocity factor - typical value being 0.535 for RG58 coaxial cable. We also use on a daily basis antennas that form their beams by delaying the signal passing to different elements - using electronics for antennas that need to change their beam direction rapidly, or just pieces of coaxial cable for fixed delay lines. The variable we’d look at is the permittivity of the medium, and as far as light as an EM wave propagating in a vacuum, air or water this is the critical parameter.
You might like the fact that we can do the same thing with light in what is aptly named optical phased arrays.
Of course RF and light are just the same thing.
I don't think that a pulse moving along a wire counts as a photon. Isn't the pulse in a piece of coax an alternating magnetic and electric field with the energy exchanging between the two. It wouldn't work if there was not the copper conductor? And since there is resistance there is a time constant for the energy to go from the electric field (capacitance) and magnetic field (inductance). It's not the same thing as light until it leaves the wave guide?
@@petewright4640 Yes I agree - it’s a varying electric and magnetic field - and a photon is…?
@@Richardincancale If you connect a capacitor and an inductor in parallel and inject some electrical energy then the energy cycles between being stored in the magnetic field of the inductor and the electric field of the capacitor. That occilation is not a photon. A coax cable is like a string of LC circuits connected in series.
@@petewright4640 Yes a coaxial cable can be approximately modelled as a series of LC and R, but it’s a model. The actual propagation mode of RF is as a TEM (transverse electric magnetic) wave. Check out some references from a Google search for “wave propagation in coaxial cable”
This is really awesome, thank you! It's so wonderful to see the uncertainty and tenacity at play, combined with the willingness to concede when you've got it wrong. I actually also really appreciate how you can dare to challenge whether 'definitive' sources have it right at all, then go about trying to convince yourself rather than taking the word of some text or video at face value.
I am a game developer who's been learning physics over the last few years, and often go through these moments where I can go from being so convinced I've nailed something, to thinking I know nothing, then oscillating between these two while developing a deeper understanding of things. Keep up the great work, really enjoy your content!
There's a few things I can recommend that could help. Now you've written your own code you might consider downloading a PIC (particle in cell) code that'll model the incident field and particle response for you. For your own code you might also be able to use the huygens-fresnel principle (calculates the vector E field from a series of points at a new point) to speed it up. I've written something similar previously and nearly everything was a vector or matrix operation so pretty fast. Well, faster than I expected.
Thirdly, is it right to model a pulse as a sum of plane waves in this case? Isn't it more accurate (and conceptually easier) to model the pulse as the product of a single cosine and a gaussian envelope? Then you should see the envelope travel at dw/dk but the phase at w/k? In fact you might even be coming afoul of violating the slowly varying envelope approximation (SVEA) and having an envelope function would let you easily test pulses of different number of wavelengths per envelope.
Hello. Is your code on github? do you mind sharing a link please?
Wouldn't the pulses differ fundamentally from a continuous beam anyway? The electron light that is emitted keeps up with the original pulse, there is nothing to lag, or to continually produce other waves.
i feel like you did get the answer with the simulation. And it's the same thing as was with the veritasium vs electroboom argument about the lightbulb puzzle (i'm assuming you know it and have seen all Mehdi's videos).
So, the electromagnetic field travels with c, but the amplitude that arrives "immediately" with c isn't big enough to detect. What any equipment is able to detect is the peak of the wave in the pulse which arrives later - with the speed 3/4 c.
That...sounds really plausible to a layperson like me. I did see all the lightbulb videos, so I understand what you mean. If you are right...then she's also right that the light 'hits' the other side of the water tank at the same time as light through a vacuum. And then it's also right that the actual detection (at a big enough amplitude) is indeed the phase speed of the combined wave.
But...is that consistent with refraction?
so, the distinction I am seeing is that she had a problem with electrons conspiring to 'perfectly' cancel out the c wave. But rather, you are suggesting that perfect cancellation is like an unobtainable limit it tends toward but never reaches, so dependant on the material and size of material, its reduced to a miniscule but varying amount?
@@jorgepeterbarton I'm saying that the front part of the pulse wave that looks like /\_ gets stretched to a shallower and shallower form the further in the material the pulse travels - with the peak travelling at 3/4 c and the needle "front" is travelling at c. it gets so shallow, it's basically undetectable - it's amplitude is going to be below the natural noise level (which in reality will never be a pure mathematical zero).
I think you're right. The graphic at 18:46 seems to show exactly this. The front peak moves at the speed of light in a vacuum, but peters out to undetectable fairly quickly. Nevertheless, it seems that this tiny peak would arrive at the other side of the water at c, but just be undetectable.
I've had the same question after watching 3b1b's video and he recommend viewers to come here. I love your video! And I think your video answers your own question more than you've given yourself credit. Basically after watching your video, I've now understood that 1) the front of the original light travels at c, as you've assumed 2) the front leaves some of its energy behind at each layer of electrons 3) which will emit the energy back (hence water is transparent) 4) but will emit to all directions hence the emitted light will be slower and slower, 5) and lastly, the original front of the light would lose energy quickly until it is undetectable.
for 5), looks like you worked really hard to try to show the effect with either math or computer simulation - but I think we could attack the math from a different angle. As long as each layer of electron reduces energy of the front of the light, it will become indetectable or effectively 'cancelled out'.
@16:32 "I revisited my old code and it was terrible...I decided to scrap the whole thing and rewrite it in a few days."
Thank you for this high quality content! After watching it, I think I finally got what happens:
I believe the answer may already be in the video: my hypothesis is that, just as the incident wave influences the electrons in water, eliciting a secondary wave in response, the electrons themselves affect the electromagnetic wave (after all, what we are analyzing is the oscillation of the electric field), acting as a damping mechanism for the primary wave, which "decays" after a few layers of electrons. Thus, the primary wave reaches the end but becomes undetectable, and what is detectable is the resulting wave from the interaction. Therefore, the simulation should also incorporate the effect of electrons on the electric field in the space through which the wave passes.
These videos were a fascinating rollercoaster and gave me an intuitive sense of what we mean when we say "light slows down in a medium". My take away is that "c" is a constant in any medium if we think about it only as the "wave velocity of the EM field". But the "apparent" velocity of the "speed of information" slows down in a medium simply because the group velocity resulting from the original wave, and subsequent waves induced by charges in the medium, add to create an apparent new clean slow wave. But it is not really a new single clean wave, it is just the group wave. And this "speed of information" in a medium is confirmed be to slower by your LIDAR measurements, which rely on the group pulse to determine distance. So "c" is constant, and the "maximum" speed of information is "c". Even for the single pulse example at the end, you have to pick a point on the pulse to represent the wave front in order to ask the question "when does the light reach the end?". Your simulation shows the apparent resulting peak lags the non-medium peak, again showing the "speed of information" is slower in the medium. I think the semantics you pointed out in the beginning are key.
The constant "c" has nothing to do with light. It's the max. speed at which causality between two systems can occur. I would avoid the term "information". It has no use in physics and it's actually rather counterintuitive even in information theory (random sequences aka noise contain the most information, constant sequences have almost none with exception of their length). The actual speed of light in a medium, OTOH, is strongly variable.
Thanks a lot for the videos. It is so rare to see how a physicist thinks since we usually see the completed results only. I am so happy to join your journey of the light speed in a media. And I hope we can see the follow up of your journey to understanding the world. Thanks again! 😃
I LOVE how you're doing all these videos about light, and your backgrounds and backdrops all have interesting lighting. Like the light coming out of that clear cylindrical thing, the lights on the wall in the background, etc. it's all so interesting and very fitting
You totally nerd-sniped me for the weekend, congratulations! Tonight I was apparently talking in my dream about fourier and light pulses in a medium.
The closest intuitive explanation I could come up with is an analogy to a bunch of coupled series LC circuits. Driving them below resonance (where circuit acts capacitively) will cause the voltage to lag behind the current and slow down the propagation of the signal similar to what happens in media with n > 1. Driving them above resonance (where circuit acts inductively) will cause the voltage to precede the current and apparently speed up the propagation, but only apparently because we find that the circuit acts as a transmission line when we try to transmit information and modulate the signal.
Thinking about light in terms of voltage and current may seem like a stretch, but I can convince myself (and no one else) that it's equivalent to thinking about electric and magnetic fields and their interaction described by Maxwells equations.
I agree actually. I think your analogy holds up very well. After all, the free-space propagation of a signal is actually the same thing as a transmission line (yeah, it spreads out more in free space, and therefore dissipates more quickly at a receiving point, but the transmission is very similar). After all, free space does have a characteristic impedance - 377 ohms. Just like a transmission line does. Now, compare how signals are affected by a more capacitive transmission line and how light is affected by a material with a higher dielectric permittivity than air/vacuum - the maths are identical.
Yeah I got nerd sniped really bad too!
I like your LC analogy and how it imulates Maxwells equations. It also demonstrates the phase velocity of infinite signals can lead or lag the input signal but an impulse is always delayed by the network.
You just flew to the very top of my favorite TH-cam channels list, and didn't even break a sweat.
I know this is about physics and stuff, and really important. But seeing that you care so much that your voice starts to break down at the end really makes me want to give you a hug.
These kind of questions have been boggling us for a long time, and will continue to do so for even longer still. You did a great job, weather it is conclusive or not.
Honestly the coding journey felt like a microcosm of this whole process… like trying to find an intuitive answer for these questions was its own kind of personal growth! I loved seeing the whole process of testing different hypotheses and every step was more satisfying; the simulation was so cool to see working. The stopwatch reminded me of the early videos with the white rabbit and reminded me how much this channel has grown too, and this video really reminded me of how lucky we are to see people like Mithuna confiding honestly about the uncertainty at each step. I’m inspired again to do something with science, and I hope to see someone get to the homework at the end 😸
PS: The 3b1b video also tries not to give a false sense of understanding, as some math TH-camrs give warnings about. Still, I wasn’t going to chase down the derivation for the 90° phase shift until this video showed how hard it is; it's been fun to see all the other people in the comments who HAD to peruse the Feynman lectures, even experts with ideas about chapter 30!
Thank you so so much for this really sweet comment, it reminded me how much has changed with these videos and how much I learnt along the way, but also made me nostalgic. I hope people realise I am assigning them homework with this video!
I love your bravery of doing a public experiment and publishing the results even when the results do not match your hypothesis. I wish more people would be more concerned with exploring reality and trying to understand it like you, and less concerned with being right all the time.
Thanks for this! I had this same question/hypothesis after watching grants video but it’s clear the answer now. The medium produces destructive interference for the original light. When new a combination of light is created in the next layer, the destructive interference also applies to that and hence it that slowly propagates the light backwards. Even though the original light still exists it’s almost completely cancelled by light from the electrons.
As mentioned in Grants original video, When a photon passes an electron, it immediately induces it to generate its own photon at 90degree phase shift to the original. Because it’s the light that induces it and it’s not independent, it’s always 90° to whatever resultant light is going through the medium, and even though it’s small, it slowly deconstructs the original wave until it no longer exists, replaced by light that’s always phase shifted 90 back
@@MrChinleungyau Woudln't that suggest that light traveling through a short amount of transparent material would be slowed less (per distance) than through a thicker piece of material, since there have been fewer interactions and less time for the destructive interfererence to result in a phase shift ?
Wow, these two videos and the one by 3Blue1Brown taught me to understand something really deep which I thought I had down, but... understood as little as apparently almost everybody else.
What I find most awesome about them is how you included all the wrong turns and frustrations on the way to figuring this out instead of just presenting the result. That is not just only a great way to teach, but also gave the videos an emotional depth that had me absolutely gripped while watching them... or maybe the emotional depth is just the thing that makes your teaching style so great.
This is a great exploration of a very cool problem! I'm a phd student in computational electromagnetics and am very familiar with this kind of scientific computing. I'd be happy to help work on that code of yours to make it more efficient if you'd like another set of eyes on it!
wow, that was mind blowing. i have the feeling that you explained in an intuitive way why light slows down in a medium. even if you weren't able to explain in detail the results of the last simulation about the light pulse. thanks for all that work, i feel less ignorant.
Long time fan of your work! Really enjoyed your approach of challenging what we take for granted.
Perhaps this was mentioned in a previous comment, but for high frequency/wavenumber, you should recover the speed of light in vacuum for both the phase and group velocity. This assumes you are using something like Sellmeier’s equation or the harmonic oscillator response in the FLP, both of which are essentially lowpass filters. Perhaps the frequency of the wave packet was too low in your simulation.
This suggests that the impulse response should travel at the speed of light (in vacuum), as the frequency tail will play an important role. This works in a continuous medium which simplifies computation (pen and paper or simulation). Also, the effect is already visible in 1D, so I was not fully convinced by the argument of different electrons transverse to the beam contributing to delay. If you’re looking for inputs/bibliography, did you try forums like Physics SE? It would be easier to share equations.
Anyway, can’t wait to see your next video!
Hi! I would love to hear more about this- is there any resources you recommend? Feel free to email me at looking dot glass dot universe at gmail
Thank you!
Your videos are engaging mini movie rollercoasters of narrative; perfect little wave packets of photonic physics.
I really love your channel, because;
a) I’m equally as fascinated by the physics of light and energy, and
b) you are transparent about the challenging and laborious processes involved in driving your own understanding, AND
c) you bring the viewer on an emotional journey through that process.
The surprising side effect of these two videos, for me, is the somewhat calming realisation that it ok to wonder about what many would consider the most basic things, not understand them, be wrong and slowly figure it out even after studying this stuff for years and getting a PhD ...
Nobody understands physics, but lots of people build models that match the data.
@@DumbledoreMcCracken It is a pointless statement.
@@qewqeqeqwew3977 yes yours is. Care to try again?
Now I want to know the answer so much! I have been watching your videos for a while now and you explain things very nicely and in a manner that is simple to understand, without sacrificing nuance! If anything new comes up on this topic please make a new video about it!!!
It's so easy to think you understand something until you examine it closer, thanks for these two videos!
T-H-A-N-K Y-O-U !!!!!
Even your struggle helps my struggle to understand 'information velocity', 'phase velocity' and 'actual light velocity'
Doesn't the speed of light in a medium depend on the wavelength? From googling the refractive index should increase with smaller wavelength, so maybe simulate with higher frequencies to get a more pronounced effect? Also it looks like you are doing your simulation in real-time? If so, just do it off-line and dump the simulation steps to a file, maybe just every 100th and then visualize that, as a suggestion.
Your persistence is truly commendable.... Wish I had 1% of that patience
No one writes code correctly the first time.
That's what mediocre programmers want everyone to believe.
And with simulations like this it's hard to verify and debug, because you don't really know how the code should behave.
Depends on the complexity of the code. Primitive codes often work 1st try. The downside is they are pretty much useless in real world application.
No, it's not really the "complexity," it's the size of the code. Large software projects are written by multiple programmers, which naturally include some whose skill is mediocre.
@@brothermine2292 That is correct. I should have used the term "size" or "length" of the code.
It's really nice to see a video where someone genuinely didn't see know the answer. Really enjoyed this. Keep up the good work!
Honest reporting of results with methods is the heart of science. You feel badly because you know someone has figured this out but you have not yet. But that's nothing to feel badly about. Not accepting what others tell you as an answer is the (ok maybe "a") key to keeping science alive. This kind of video is as at least as important as explanatory videos which follow accepted science.
In the "linear restoring force" model each electron, at least initially, experiences 0 restoring force, so it can be thought of as a free electron if we're talking about very low time scales (small fraction of a light wave period).
A free electron tends to (partially) cancel out any field passing through it (because it accelerates with the electric field, and thus emits an opposing electric field).
In fact we know (I think?) an electron gas is completely opaque.
Maybe that's enough to explain the complete suppression of the "fast" component of the light? It takes time for the electron to move away from its initial position sufficiently to start "feeling" the effect of the lattice, and thus transitioning into mode of pi/2 phase shift (after initially starting at 0 phase shift) relative to the electric field of the light that "drives" it.
That's a really good point. The restoring force is proportional to the distance away, while (in the steady state plane wave case) the light's force is strongest when the displacement is zero. I will have a think about this!
@@LookingGlassUniverse wait are you sure? I think the opposite is true: in the steady state we expect the net force to be 0 at displacement 0 (because double derivative of sin is -sin). My point was to consider what happens when we're *out* of steady state, when the initial pulse arrives.
I'm an AMO physicist and this reminds me of a time I was co-running a course on special relativity with a professor. He wasn't satisfied with the explanation of the twin "paradox" in the course material and that we should come up with another one . After weeks of us both researching, we concluded that neither of us really understood it and just admitted that to the students. A very humbling but valuable experience. Great video!
From what I recall from a university course I took on modern physics, the twin paradox works because each twin has a different reference frame from which it appears the other twin is aging slower. Let's say in this world where we've developed rockets that can instantly accelerate to a fraction of the speed of light, Adam goes off to space at 0.4c relative to Earth, while his twin Bill stays on Earth. While they are moving relative to each other, each reference frame says the other twin is younger, because they disagree on which points are "simultaneous". Neither one is actually correct. It's only because of acceleration, and changing reference frames, that we can find that one twin is definitively younger.
We want to compare Adam and Bill's ages, so the twins have to reunite on the same reference frame.
(a) We could say that five Earth-years from now, Adam decides to head back to Earth at the speed of 0.4c. Once he reenters Earth's reference frame, he will be younger and it will appear that his time has slowed down for the ten Earth-years they've been apart.
(b) But you could also say that, Earth has managed to double the speed of their instantly-accelerating rockets in the five years since Adam left Earth, and now Bill decides to catch up to him in the latest-technology 0.8c rocket. Five years later, Bill slows his rocket to half-speed and docks on Adam's rocket. Now Bill is the one who's younger, as his reference frame has always been 0.4c relative to Adam's. [I suppose the "years" in this scenario would be relative to Adam's perspective, if we want this scenario to be symmetrical to (a).]
(c) Or perhaps Adam and Bill both decide after five years to meet each other in rockets going 0.4c toward each other, whereupon they land on the planet Causality, which is traveling 0.2c from Earth in the same direction that Adam left! Now they're both the same age after all, since they were both traveling at 0.2c the whole time, relative to Causality's reference frame.
The bit that's always confused *me* is why the speed of light was ever suspected to be the maximum speed of causality anyway. Weren't the thought experiments leading up to it something like "You shouldn't be able to tell your speed in an inertial reference frame, and you wouldn't be able to see the light in your rocket if you're going faster than light"? Surely this can't be about light produced inside the rocket, because if light speed weren't a universal constant, the light coming from the light bulbs in your vehicle would be sped up along with the rocket, and there'd be no problem seeing anything from turning on a light (just like you wouldn't stop hearing things while riding in a supersonic vehicle). But if it's external light, then what's the problem with not being able to see light that's coming from a star that's moving faster than light speed away from you?
It feels as though there was some other reason that Einstein intuited light speed would be the same as the speed limit of the universe, and that particular kind of thought experiment is just some question-begging justification for that.
@@michaels4340 It was an experimentally observed fact, due to the Michelson-Morley experiment. It was also hinted at by Maxwell's equations, which predict a speed for light but don't say what it's relative to. Einstein's thought experiments weren't a proof of the constancy of c; they were him taking it as an axiom and exploring the consequences of it.
Best explanation in print imo: Don Koks "Explorations in Mathematical Physics" section 7.3
I think your original explanation for the reason the light doesn't slow down has the right spirit. Only that, the only light that keeps in lockstep, as you say, is the forward scattered one (electron in line). You can show that this one has to always be opposite in phase to the drive (optical theorem), so this light will be reduced while it travels and disappears eventually. The light that is left comes from the other electrons, arriving slightly later. But this process repeats as the combined field drives further electrons, so gradually the front edge of the light gets eaten out, slowing down the pulse. The Feynman explanation is taylored to the long time steady state, but what you want to describe is the first transient. The intuition you get out of it doesn't always apply.
Thank you for this! This is what I thought originally, but the issue seemed to be that the phase of the electrons in the centre line is the same as the phase of the original light is the refractive index is greater than 1. Do you know how to deal with that case?
@@LookingGlassUniverse sure, that's what I meant in the end of the comment. The scattered field is in phase in steady state, but for you what matters is the short time response
@@LookingGlassUniverseyou could show it by repeating the forced oscillator calculation in the Feynman notes, but with a force that is a delta function in time for example. The restoring force doesn't have time to respond. Personally, I think the best argument for this is just energy conservation. If the scattering is in phase, the drive would get amplified indefinitely and there are no other fields fast enough to catch up to it.. it must be out of phase
@@LookingGlassUniverse here is another argument. The value of the index of refraction depends on the frequency of the light. When the light first hits the electron, how does it know what the frequency (and the index of refraction) is? It's going to take at least a period for the electron to realise this and start responding with the expected phase. This shows you that the concept of index of refraction is not relevant for what the scattered field looks like immediately when the field hits.
This and the other video are just fantastic. The real nitty gritty of understanding a concept in physics through theory, experiment and finally computation. I've always just taken the slow-down of light in water at face value...now I'll have to think about why!
In the cumulative sum of electron-interacting light, wouldn't the distance traveled be longer due to interactions resulting in non straight paths?
Yes! But as long as some of the light going on the shortest path is still there (and hasn't been cancelled out) then some of the information will still travel the shortest path. But as long as the short path's light is cancelled then yes, the light's gone a longer way
Is there really some light going the shortest path? In a lecture Feynman taught that electrons going from A to B always travel through the whole universe and the observed result is the sum of all probabilities. Isn't it the same with light? I think to answer this question there must be some quantum mechanics involved. The problem is that nobody really understands quantum mechanics. Maybe GPT 8 will give us an answer
Wonderful video! Pharmacist/Programmer here. I think there might be a decent intuitive mechanical analogy in SEC. Size exclusion chromatography (SEC) separates molecules[colors] based on their size by filtration through a gel[glass] in a column under e.g. water pressure. Separation occurs when molecules of different sizes are included or excluded from the pores within the gel matrix. A given size molecule may travel directly through the gel material, but with smaller size it is very unlikely and undetectable. The average molecule will zig-zag through lots and bring down the measurable group velocity. The smaller molecules find more pores to travel through. SEC is used to separate the molecules by size, by measuring their time to traverse the gel.
I have watched both yours and 3Blue1Brown’s videos, and spent several hours thinking about it, and I have arrived at what I believe to be a satisfying explanation as to why the information speed of the pulse light slows down.
As per 10:30 in your original video: th-cam.com/video/yP1kKN3ghOU/w-d-xo.html the light created by an electron responding to light would be the equal and opposite wave. This would cancel out, but as 3Blue1Brown says in this section of his video: th-cam.com/video/KTzGBJPuJwM/w-d-xo.html the restoring force on the electron from the medium causes the resultant wave to be weaker (typically) and out of phase.
However when the electron is at equilibrium (i.e.: before the pulse reaches it) the restoring force would be zero, and for the first instant that the pulse reaches it the reaction wave would exactly cancel out the arriving wave, as that repeats in the many layers of material, it eats away at the front of the wave.
Thanks for an almost satisfying answer. It may well be holes in my understanding stopping it from being completely satiating. Maybe you can help?
What exactly the phase of the electron light is and why, is something I am still a little unsure of. Can you elaborate at all? Perhaps for an idealised case with no restoring force and a more realistic case.
In 3b1b's video, he said the phase was retarded by 90 degrees, whereas here it was said to be out of phase. Is there something about negative charges that I should be thinking about? Perhaps producing inverted waves? It also surprised me to hear that there was no delay in the arrival of the wave and the production of the secondary wave. I thought this would involve infinitely fast acceleration of an object with mass. But I suppose if it is the acceleration of the charge (not it achieving some speed) that produces the wave there is no reason there has to be a delay between the arrival of a force and the production of the wave.
Your input would be appreciated, thanks!
Your nerdiness is contagious, and I am really struggling to keep myself from exploring your code and trying to see what I can do to speed it up hahah
Coming from Computer Science and having worked as a Software Engineer for 8 years now, I do sometimes miss these nerdy assignments we did in CS classes like Algorithms 2 and 3, where you approach the limits of physical hardware and you have to start thinking hard to make shortcuts!
Here is a question though: in Maxwell's equations, the speed of light is just 1 over the sqrt of the product of the electric permittivity and the magnetic permeability. Maxwell calculated the speed of light based on the measured permittivity and permeabililty of the vacuum, features that were already understood from experiments with electricity and magnetism.
But you can calculate permeability and permittivity for any material, and indeed we routinely do In electric engineering and other scientific fields, although it seems like those numbers are usually calculated for very different freqencies than the visible light range. But the refractive index of a material is actaully calculated based on the permittivity and permeability values. Permittivity "is a measure of how well the molecules of substance align, aka polarize, under an electric field. The better the molecules polarize, the more that substance resists the electric field." According to one googled source.
So from that perspective, it seems like we understand why C slows down in transparent materials quite well, without needing to resort to addional EM waves, quantum effects, or anything else.
So what is going on here? Is this just a classical representation that doesn't get at the underlying complex physics? Is it just a restatement of the same problem from a different perspective? Or is it really as simple as: materials have intrnal polarity and thus internal electric fields, and the stronger the electric field is, the slower an EM wave (aka a light wave) will propogate through it? This seems so much like it could be the right answer, and it's so simple. Yet if true, why doesn't it show up in these physics explanations?
There's a very quick, intuitive explanation of permittivity here at 2:00, which...totally makes sense to me th-cam.com/video/DkqdNUTMrHc/w-d-xo.html
Yes, you got it right. its ε0 & μ0 that determine the speed of light. In transparent materials the Permeability & Permittivtity is different from vacuum which decrease the speed of light. People like to make physics unnecessarily complicated.
I would think that this is an oversimplified classical explanation, considering this is part of the same model that produced the ultraviolet catastrophe. It works for predicting the result quite well but only if you don't poke at the details.
I don't think your explanation actually explains why permeability and permittivity are linked to refractive index, only that they are linked.
The classical result should have been enough to convince her that the effect is readily observable. But, to me, it has no explanatory power. It just says materials have these properties that were determined empirically, and using these properties we can predict the propagation speed of electromagnetic waves through the medium.
I think your argument is correct. When it comes to most materials, I think the front speed is going to be c as you originally expected. But if that front gets worn down as you suggest, it won't be detectable. It could be fun to redo your experiment with different amounts of water to see if you can demonstrate that the detectable front goes discontinuously from v < c to v = c. I suspect the lidar won't be sensitive enough to capture this though.
The best textbook that I think explains what is happening is "Absorption and Scattering of Light by Small Particles" by Bohren and Huffman. It was the first source that taught me about the Ewald-Oseen theorem---when I learned about it it did feel like learning about a conspiracy related to the scattering of light.
I have tried myself an experiment with single photons, the HOM interferometer. Then you put a piece of glass in once of the arms and the dip shifts by the amount the single photons get delayed in the glass. I can try it with a bit of water in the way and see how much it changes.
Taught, not "thought."
Thank you so much for this great recommendation! It sounds like it probably has the answer in it!
That's incredible that you have a HOM interferometer, I'd love to hear about the result. My email is on my about page!
That the open questions in today's physics, like the nature of gravity, the lack of a unified theory, the crisis in cosmology, and the nature of dark matter without viable alternatives, must be considered parts of that physics, is self evident. That all the attempts on answering them remain unsuccessful, makes every new question all the more important! I think your openness and willingness to ask every question, is precisely the approach that is needed!
I think the captioning for this video is for the first video
I love your honesty.
The way I think about it is via the actual derivation of the vacuum speed of light from Maxwell's equations. There, c is found to depend on the permittivity and permeability of free space. In other words, the strength of the electric and magnetic fields in response to charges and currents are just natural constants. Now, when we introduce a medium, the response changes. You can see this with dielectrics where the induced polarisation reduces the magnitude of the field. These medium responses change the permittivity and permeability constants, and hence the speed of light. I think that reducing this medium response via the superposition principle has caused the problems here. If you imagine a medium as being composed of a continuum of springs, the response of the medium will depend on the spring constants. These spring constants are always less that those of the vacuum due to screening. This is all covered in gorey detail in Panofsky and Phillips, Classical Electricity and Magnetism, although I doubt that this will aid your intuition. I think that considering disturbance propagation in an elastic medium is much easier to grasp.
I would give consideration to why light has a speed in free space.
That should be critical to understanding why the speed changes in other media.
That's just how massless particles work in this universe. They all move at c, they cannot do otherwise. And all massive particles are slower than c.
Now c is 1/sqrt(ε0μ0), with the electric constant ε0 and the magnetic constant μ0, but I think c is likely the more fundamental one.
@@KaiHenningsen You could say the same exact thing about the speed of light in water... I think we're all looking for an explanation rather than an equation.
She touches on briefly in the previous video. c is the speed of causality, and it makes sense for it to also be the speed of light in a vacuum. Why causality has a speed? We don't really have an explanation, that's how the universe is, but that simple idea explains a lot of things. Attempts to model light as a wave travelling an a medium has been done before. It was, in fact, the leading theory (luminiferous aether) before special relativity turned out to work much better. Nowadays, explaining why some things go slower than c is the hard part, that's how we got the Higgs field and all that stuff.
@@gubx42It just seems unlikely to understand why the speed changes when you don't understand why there's even a speed to begin with.
And I think it's funny that the aether has been dismissed only to be replaced with "free space" which has properties. Isn't it just a different name for the same thing?
So I think that thinking in terms of electrons is a far cry short of what's needed to understand the speeds of light.
There is necessarily something far more extraordinary happening. The very nature of spacetime and light and their relationship must be revealed.
Light appears to transcend spacetime and in some way also be entangled with it.
@@FaithLikeAMustardSeed The problem is that the speed of light (c) is the same everywhere, including on things that move. This is hard to reconcile with the idea of light being a wave traveling through a medium since the relative motion of the medium itself would have to be taken into account.
Its great to see your journey through what i have thought is one of the hardest concepts in physics. The interaction of light and matter. During my PhD i was given a great book on light and matter called QED by you guessed it Richard Feynman. You might enjoy it.
Maybe the light isn't _really_ slowing down from its perspective but actually traveling farther.
Consider Kelvin's Knot Vortex Theory of atoms.
Of course the frequency dependence would have to be accounted for (perhaps a short-circuiting of certain crossings or something like that).
Yes Naomie, I think you are on the right track. Regarding frequency dependence, could it be that wavelengths larger than the distortions in space (that are the atoms) do not have to traverse those distortions.
Consider this 1D string, with distortions representing the matter:
___________/\_____/\_____/\_____/\_____/\___________
Wiggle the string with a wavelength shorter than the distortions
like ---^^^^^--- and those waves will traverse the distortions.
But wiggle the string with a wavelength longer than the distortions
like ___/‾‾‾‾‾\___/‾‾‾‾‾\___ and those waves will not need to traverse the distortions.
See my other comment.
Thanks so much for making this video. It takes courage to present one’s struggles rather than a neat and tidy solution all completely figured out. It is fun to watch a ten minute TH-cam video where someone achieves something wonderful with little apparent effort, but it leaves the viewer with a distorted view of reality and frustration when they themselves face adversity. I’m speaking from experience.
To me, it seems that your ultimate question was, “If the speed of propagation through the field is always constant, what can make the ACTUAL propagation (the delivery of information from point A to point B) slow down?” This line of inquiry fascinates me, making me wonder if it might have wider implications. Could this be related to the phenomena whereby the quantum electromagnetic field permeates the universe, with a constant maximum speed of information propagation, and yet for different frames of reference the propagation (the speed of light) differs relative to the global frame of the field? I.e. the speed of light measured in all different frames in motion is the same. To make this work, there would also have to be something that makes clocks run slower or faster in each reference frame. But since clocks are nothing but mater elements propagating through their own respective quantum fields, perhaps the same principles would apply. It probably is not related, but it is interesting to me to consider.
Thanks for making this video!
Feel free to correct me if I'm wrong:
The original pulse should fall off exponentially. As it's the first to interact with each layer of electrons, they'll cancel out a percentage of the original wave (through their secondary wave). As each layer does that, the pulses amplitude should fall off exponentially.
This fall off happens at the same time the slower wavefront is created from constructive interferance behind the dwindling first pulse.
This would mean *some* light does travel at c, but it drops off very quickly.
That's at least my intuition, but again, please feel free to correct me.
That's my intuition as well! The secondary wave produced by the jiggling electrons is in the opposite direction of the original wave, and so will create almost perfect destructive interference with the original wave (as more and more layers cancel off more and more of the original wave). The end result is that the front edge of the pulse still moves at speed c, but with such a tiny amount of energy that it's undetectable; the main energy of the pulse will only arrive much later.
The mystery that still needs to be explained is why the cancellation happens in such a perfectly predictable way every time - I don't have a good intuitive reason for why the bulk of the energy should arrive after a very predictable delay. Water and glass aren't crystals, so a good explanation can't depend in any way on the symmetry or perfect spacing of the "layers" of electrons.
This was what I thought too, till I realised that if the refractive index is great than 1 (which is most of the time) the electron wave actually reenforces the light- which is mind bending. I don't understand it at all
@@LookingGlassUniverse that's really interesting - could that be explained as a "layer effect" coming from the many electrons in the layer that are farther away? My hypothesis is that the very front edge of the light pulse will only be affected by the closest electrons in the layer it passes (since the waves from the other electrons in the layer don't have time to reach it), and the secondary wave from these close electron will cause destructive interference, flatting the front of the pulse. But the contributions from the further away electrons take longer to reach the same spot, and they combine in a way that interferes constructively with the original pulse. So the combined electron wave has the effect of surpressing the front edge of the pulse and boosting the back edge of the pulse, with the apparent result that (1) the pulse is delayed, and (2) for the section of the pulse that "remains," the phase agrees with both the original wave and the electron wave, so it looks like the electron wave is reinforcing the light. Does this explanation run into issues somewhere?
@@LookingGlassUniverse Re the simulation. Remember energy conversation. The EM energy in the delayed wave comes from the initial wave. The exact details don't matter - the first wave must die out as the delayed wave is created.
Such a great video! It brought me weeks of joy appreciating the wonders of the world. As a beginner in physics, I recently came across the concept of "Quantum Decoherence" (en.wikipedia.org/wiki/Quantum_decoherence) which seems to partially explain the slowing down phenomenon in your video. On one hand, under the influence of the environment (such as water or other media), the degradation of quantum characteristics and the enhancement of classical particle behavior can account for the decrease in speed. On the other hand, I got some feeling of the transition from infinite wave plane to a pulse: when the mathematical expression on an infinite time axis (perfect "coherence") undergoes "decoherence" due to the method of laser generation, interference from the propagation medium, or even observation behavior, lead to a degradation in wave characteristics. Recently, I have been trying to use this naive understanding to understand classical phenomena like the double-slit interference without bothering the complex partial differential equation calculations 🙂
21:56 how to fix the bad framerate of your simulation: If you, instead of recording your simulation with a screen recorder, save all the different slices after rendering each iteration, as screenshots, and then later stitch them together, you can get a really smooth animation, especially if you select a small enough dt.
It wasreally interesting to follow through your struggle with those experiments and simulation. I certainly undestood more than in other videos, which are also great, but I'm easily getting lost with all the sinus formulas and angular/vector graph comparisons. Your rather visual and "slo-mo" way of explanation is much more intuitive for me. Also I must admit I got distracted by your beauty quite a few times :) Anyway, subscribed.
Gotta get the only optics YT channel (that I know of) Hugens Optics in here.
He commented on the part 1 video actually. He said he thinks the range finder with the red laser actually just used triangulation. Edit: And now it looks like he's seen this one too.
I've enjoyed all of your videos over the years but I especially like this one.
I'm sure there are many fans of your channel who can help out with programming, me included. I often spend midnight hours watching videos like yours and 3blue1brown, I'd be more than happy to help out.
Thank you so so much- I would love that! I have it on my github but I'm going to write up a doc on what factors need to go into the simulation so that people can write their own (probably much much better) version. github.com/mithuna-y/speed_of_light_in_a_medium/tree/main/multiple_layers
everything about this is adorable except for the for loop
Love the video! =D
In astronomical observations, particularly of pulsars, we observe a phenomenon known as dispersion. This is characterized by a time delay in the observed light, which is dependent on the frequency of the light. This dispersion serves as observational evidence for delay in information speed.
As a side note, from the photon's frame of reference, the time experienced is always effectively zero, due to the relativistic effects at the speed of light.
Is the dispersion caused by intervening matter? I am under the impression that in a theoretical perfect vacuum, there would be no dispersion. Dispersion happens in transmission lines also (like coaxial cable, for example).
Please please make regular videos. I love listening to you talk. It puts me in a good mood
This is a great project and some great work! This is really a question that's been bugging me for a long time, and while it's a bit disappointing (and understandably frustrating for you) that you did not manage to find a definitive answer, you should be super proud of all the work you've done and the insights they brought to you (and everyone who watched your videos).
Hopefully, someone will take on the challenge and deliver a final explanation for all the curious mind around here :)
Null results are a result. ^.^
Thank you so much! Yes, I would love to know the answer
Great effort and honesty. Keep it up. The process of light slowing down in materials is ultimately explained in quantum field theory which describes the interactions of the fields involved in the process(photon, electron, quark up and quark down), but it would be too computationally expensive to predict the refractive behavior of a material with those equations, that's why they further abstracted it with density functional theory, which still doesn't do quite a good job.
I think what your simulation is missing is the phase/frequency dispersion of a medium, AKA it's complex-valued index of refraction. The refractive index of gamma rays through anything is basically "1", but the limit of refractive index as frequency --> 0 is basically infinite.
Thanks! In the simulation about midway you can see the dispersion happening- or ‘chirping’ as it’s also called. The previously peaked red wave becomes a much wider wave. I didn’t include complex refractive indexes because the video was too long, but they account for absorption
Fantastic videos ! Thanks to you i realized I didn't really understand the slowdown of light in matter. I'm quite sure that there are many other examples of physics phenomenon that everybody takes at face value but if we really digged down we'd find out that we don't really.
understand.
Congratulations for your great work and honesty !
I love how some effects can be so self-evident in the spectrogram but so counter-intuitive in the time domain.
This made me excited to go do the lab report I've been avoiding for a week ❤
I love that the answer in the end is just "I don't know". The journey matters just as much as the destination, if not more. This video and the previous one are both excellent.
An explanation to why light slows down in material medium:
The electrical permittivity and magnetic permeability, which basically means how easily electromagnetic (EM) force is propagated through the EM field, is different from the vacuum. This happens due to the presence of charges in the medium, hence Feynman's explanation comes in handy and is correct. Also, you can use plane waves in your explanation, since mathematically every wave is equivalent to a sum of plain waves. DO note that I said MATHEMATICALLY, meaning we can describe the real phenomena more easily, even though plane wave are not real. You correctly explained the problem when you got the answer for plane waves, just needing to use Fourier SERIES to then get the real signal.
Why series instead of transform you may ask. Fourier transform, as the name implies, transform a function to it's correspondent in the dual space. The Fourier series is the expansion of a function into sines and cosines, similarly to how a Taylor series expands a function into a polynomial.
Cool video! This is my favorite kind of science vid, the intersection of physics, research and programming. I'm glad you made the video despite things not panning out like you wanted, very neat watch even to someone like myself who's not much of a physics knower.
From a simulation perspective, something that might be worth looking into are "Finite Difference Time Domain" and "Finite Difference Frequency Domain". As a computer science researcher that works with waves a lot I can say those methods impressed me a lot. Though they're a bit too optimised to be particularly comprehensible for understanding in my opinion. If looking into those methods proves too confusing, I generally recommend trying to code up a lattice simulation of electrodynamics. That is to say, breaking space into a discrete grid and looking at the physics from the perspective of space instead of the perspective of the waves / particles. You can create a full wave simulation using just convolutions. That is to say, each pixel in your grid can only see the pixels surrounding it and moves in respect to them.
I found this video strangely moving. You put so much time and effort into your research. But it seems like you learned many valuable things along the way. Thank you for sharing the journey.
Thank you so much :)
Amazing! Thank you and 3blue1brown so much! Your series' have improved my understanding of light 10-fold.
I think you came soooooo close to the final answer right at the end. Your simulation showed that while the speed of light doesn't change, the speed of the resulting *interference pattern* does.
That is to say: yes: the resonant responses interfere to perfectly cancel the original light wave.
In terms of the original explanations you discussed - this is closest in analogy to "the light gets absorbed then re-emitted" because for the electrons to resonate, they have to absorb energy from the original light source.
As for why the light doesn't scatter... yes it does! Sort of. You can see the laser inside the water from all directions, meaning some light must radiate in all directions from every point. However most of the light is parallel to the original light source because at the microscope scale the laser approximates an infinite plane (think of how many trillions of atoms wide that laser is).
Right... This is an approach I wasn't quite thinking about. So if it weren't for the re-admitting of light then the medium would be opaque due to the loss of energy in the original wave?
@@PulseCodeMusic Well I know for certain the light has to conserve energy.
If the matter had no charge there would be no interaction with the light (assuming no direct collision, though IDK what that even means at this scale).
Anything with a charge is going to vibrate in response to the light. For the charged particle to vibrate it has absorbed some energy.
The charged particle can either re-emit that or absorb it as heat. But this getting beyond my level of knowledge of physics because at this scale what is heat but vibration? Perhaps "heat" in this context means converting the energy to a different frequency?
Of course the magnitude of the effect comes into play. There can be energy absorption and transmission (think of shining a light through a piece of paper) - it depends on the rate of absorption and thickness of material.
@@003Jetfire it definitely doesn't give all the energy in back to the wave that continues through the material as half of that wave goes in the opposite direction. The question is, how much energy is lost. I would love to see this simulation but minus the secondary light to see how far the original light got. If it decays quickly then that's your answer.
"I don't know the answer" should be the most exciting thing in the world for a scientist, its sad that our society has made you feel badly about something that needn't be bad at all. I was thrilled watching this and inspired to learn more about it myself now, thank you
Love your honesty and scientific process in this video. Shows clearly how much work, deep understanding and perseverance goes into your physics work. Light is enigmatic, but even Einstein was stumped at how mysterious it is, and remains so to this day!
Frustrating twists and turns and at the end you have more questions than answers. Sounds like science!
Sounds like a blooper reel.
This is very much how it felt when I was doing research ahaha
About a quarter of the way through this video I was thinking, wow what a phenomenal representation of the experience of being a working scientist. Still though, it's missing the part where you try to make a computer model and at first it seems great but it ultimately doesn't work and your sanity erodes until you eventually give up and question whether you even deserve to probe into the secrets of the universe. Whether this whole enterprise has been arrogant and your human mind can never dream of brushing up against the roots of existence. So you give up for a while and have a huge crisis over it but then you look at your code with fresh eyes and realize that while you should not be allowed within ten feet of a computer (not that this will stop you) you absolutely deserve to probe the secrets of the universe and you fix it and it's one of the best feelings you've ever had in your life. You know, science.
Anyways, well played.
One of the best videos I've seen on this site btw. I'll be showing my students.
Honestly, you gave so much more information on why light slows down in a medium than Dr. Don from Fermilab.
Absolutely incredible video and it pairs so well with 3b1b's recent upload!
Thank you!
which of your simulation files is proving to be the bottleneck? Maybe one of us programmers can make a PR to enhance your simulations. Stellar video and really appreciated how candid it is
The one that's just a pile of for loops is this one: github.com/mithuna-y/speed_of_light_in_a_medium/tree/main/multiple_layers
I would absolutely love if you're interested in improving it! I'm going to write up a proper explanation of what I did so others can take the idea and simulate it in a better way
Really loved your videos on the speed of light through water. I think that you have come to the same conclusion I have: Incumbent physics does not understand how light propagates in general, and that the inability to apply the incumbent models to transmission through transparent media is the red flag exposing this inconvenient truth.
If you try to simplify things by assuming the propagation of a single photon, then things become even more obvious. The whole idea that the light "jiggles" the electrons means that it must be imparting energy to those electrons. That can only happen if the photon loses energy. According to the E = hf equation, this means that this "primary photon" must experience a reduction in frequency as it traverses the water. Also, any wave emitted by the jiggled electrons can only be as photons. Again, their frequencies must be different from that of the original photon. It is not credible that these "secondary photons" would be angled in exactly the right direction to now again interact with the primary photon.
Regardless, if this mechanism was at play, the photons emerging on the far side of the water would have a different frequency to that of the primary photon.
The Fourier transform is a very useful mathematical way for engineers to calculate the measured effects of wave-like phenomena, but we should be weary of believing it is telling us something about fundamental physics.
It would also be instructive to take into account effects like the change of light speed in still and flowing water.
I believe that the honest answer to your question is that incumbent physics does not understand the phenomenon either.
I love when reality contradicts me
It’s kind of fun :)
Wow, very interesting. It's a much more difficult question to really answer for certain than expected. I would hope you keep at the problem, as a definitive result, especially with a good simulation, would certainly be very valuable scientific research for everyone. Great job!
As the pulse travels, the layer that it has reached emits a secondary wave not only in the forward direction, canceling the incoming light, but also backwards towards the other layers that the pulse had passed. This back and forth emission causes the same slowing down as in the infintie-duration case.
I'm not sure if there's any mistakes in this explanation but here I go. I think the whole original wave is destroyed and a slower one is created is the correct explanation. First, let us consider a wave of light travelling through a straight line of electrons, but first we will only consider the response waves that the electrons generate in the same direction of the original wave. This response wave is some multiple of the original wave, say 10%. So the second electron would see 90% of the original wave, the next would see 89%, etc. Eventually the wave will be completely annihilated.
For any wave, this means that it will cancel out with the response waves that are travelling in the same direction.
This doesn't quite explain how the slower wave is generated, but i guess an argument would be that the remaining waves which don't travel in the same direction in the original wave can be added together to create another wave in the original direction at speed c, however it will be pushed back by a phase shift because it took an indirect path. And then the same argument applies
Hopefully that makes sense??
Sorry if it was mentioned already, but the conspiratorial cancellation of the incoming wave by the electron induced waves was mathematically proven by Ewald-Oseen. See, for example, section 2.4.2 in Born & Wolf's Principles of Optics.
That's an impressive project for a "first code" project!
You are awesome. Was waiting for your new video. Can't wait to watch this in it's entirety!
I really appreciate your painstaking search of a convincing truth on this argument!!! that me think the best for you and for your Phisics Theory career. These videos let me literally jawdropping seeing all 3 in just one shot!. I really hope you can come up to an acceptable solution, that, for your behavior, could only mean to finally explain the phenomena. Thanks for sharing! Hope my best wishes to you!
2:41
The plane waive represents the timeless quality of a photon. Because of the very nature of its speed, it has no time component. Because of that, any experiment you do with light has to take into account that from the moment that photon was emitted, it is no longer in your reference frame in regards to time.
All things are experienced by the photon in the same instant it is created. Hence why it both does and does not slow down when passing through a medium. You increase the distance traveled so from our reference point outside that solid medium, it slows down.
Have a look at Cherenkov radiation. Excited particles basically blasting through a medium without regards to the refractive index of that material... creating a blue light.
I'm very much enjoying your videos as you look at these things experimentally rather than theoretically.
Great stuff.
16:24
Send him a bottle of his favorite adult beverage. Best advice anyone could have possibly given you.
When faced with adversity, always try and turn your failures into success... either yours or someone else's.
Only way to do this is to let colleagues (or the internet) in on your failures or confusion.
You are Waaayyyy smarter than I am. Mathematically you have such a gift and such a firm grasp on this that it has me subscribing to see what else you are on about.
The only thing you lack is what you are embarking on now... experimentation.
I was blessed to have worked for nearly two decades in an incredibly well funded industrial lab environment where for a period of about 5 years I was working on the EXACT thing you are wrestling with now.
That's what actually had me click on this pair of videos... and I'm glad I did.
26:09
A brilliant and humble admission. I hope you continue to revisit this from time to time as I too would LOVE to know the exact reason(s) for what we have both seen experimentally.
So cool, just watched both videos and I really want to congratulate with you for all these efforts. I was like "no way she is getting into coding to simulate it", but you actually did, and with great results (even though you didn't vectorize the code haha). Btw, I agree with you, the answers is still not satisfactory and it still would look like it wouldn't actually slow down...Damn. But maybe is as you said, the first front might be chipped away but many subsequent "layers" of electrons. This is actually very interesting and your model really makes sense. I always supposed that there actually was a "correct" physical answers to this question, but that, given its complexity, everyone was just working its way around it; you really make it look as if we really don't know what's going on. I think that's crazy for such an important thing in physics.
Really loved these two videos. They are actually inspiring.