I don't know why light slows down in water

Supported by Screen Australia and Youtube through the Skip Ahead initiative.

Links to the other videos mentioned:

Experiment:

Code:

References:
The Feynman lectures- “Ch 31: On the origin of refractive index” and “Ch 48: Beats”

[bluebrown]

So glad this is finally out! I always appreciate the combined honesty and clarity in your videos, and these two just nail it.

[tone]

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.

[brownbird]

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. :)

[userxt]

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.

[toddzimmerman]

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.

[corykiesling]

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.

[TheViolaBuddy]

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!

[Zinurist]

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.

[the-nick-of-time]

@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." <- Spoken like a true programmer, you're clearly a natural :)

[Kitchen]

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.

[ScienceAsylum]

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).

[Richardincancale]

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.

[undefinednan]

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.

[Mofessor]

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.

[LightPariah]

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.

[DukeBG]

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.

[MarkRawling]

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.

[time-trader]

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 ...

[PsyPhoda]

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.

[robertwalkley]

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!