Lie groups are my favorite thing in all of mathematics, and gauge theory is my favorite thing in physics. E8 and all its connections to other subjects is one example of how amazing this subject can be.

It would be a coup de grace of the highest order, just the crowning intellectual achievement of mankind, if we could stumble upon a theory of everything explaining the entire Standard Model, just by fiddling around with how to fit SU(3)xSU(2)xU(1) fits inside E8 or whatever.

But I guess it’s not going to happen.

I’ll level with you. I know how to use QED to compute the cross section of a scattering reaction. But I do not remember, or perhaps never knew, what the QED theoretic description of classical wave mechanical phenomena like diffraction, reflection, refraction, and dispersion look like.

Well… actually of those phenomena, I think diffraction is fine. A single waveform will exhibit diffraction. It doesn’t entail any interactions. A single photon can still exhibit a diffraction pattern. It doesn’t mean that the photon has changed directions or circled around or in any way accelerated. The only reason you might think so is that you’re thinking of photons as billiard ball type classical particles, but of course they are not, they are quantum particles with spread out wavefunctions.

Dispersion I guess is just scattering combined with absorption re-emission (and as we discussed, even scattering is itself a form of absorption & re-emission). But as for reflection and refraction? Those are the phenomena that Entropius was pointing to elsewhere in this thread. I remember how those look in terms of solutions to Maxwell’s equations and boundary conditions, but that’s classical wave mechanics. I do not remember how to translate that into the language of QED.

QED is a fundamental theory, so I assume that a description exists, and of course because I know what QED looks like, so I am certain that it will still be true that in this description, photons will be absorbed & emitted by charged particles, but photons will not interact with photons. However beyond that I cannot say much. How do we describe reflection of light in a mirror as photons scattering off electrons? I don’t know exactly.

One thing I can say is that generally classical states are modeled in quantum mechanics as coherent states, which are eigenstates of the annihilation operator. They look something like exp(N)|0> where N is the number operator, which means that they are states with a superposition of 0 photons, 1 photons, 2 photons, etc. They don’t have a well defined number of particles. So maybe if you want a QED theoretic description of reflection, you can have it, but you won’t be able to talk about specific numbers of photons. But again, I don’t know the details of this.

I wonder whether this concept of classical waveforms as coherent states with a superposition of all numbers of particles will help at all with this philosophical debate about whether two photons are the same particle or not, or about whether you can have a universe with only 3 photons

complex numbers are just numbers in a plane instead of a line. saying you don’t believe in i is like saying you don’t believe in “up”

Look bro. Your top level comment that I replied to was generally correct, and also very helpful. I liked it. I liked the suggestion for people to look at the Feynman diagrams. I agreed with it. I upvoted it.

I hope I’m not giving you the impression that I’m taking a personal issue with you. I’m not. I like you and I hope we’ll still be friends when this is all over. I promise to read Discworld soon.

The only quibble I had with what you wrote was this one sentence:

So for a photon to change course, aka accelerate, it does it by absorbing a virtual photon and emitting another.

Photons do not absorb virtual photons. And real on-shell photons do not interact. In Compton scattering and 1 loop photon-photon scattering, you can think of photons emitting e+e- pairs. But never do they emit or absorb other photons.

Maybe that’s not what you meant with that sentence, and I misunderstood. If that’s the case, my bad. Maybe you didn’t need the explanation. If someone else made the same misunderstanding reading your comment that I did, then maybe my comments will help them even if you don’t need them. Or if not, if it’s just me being dumb, well c’est la vie.

Cheers bro.

I am indeed denying the existence of photons interacting with virtual photons. I am also saying there is no tree level photon-photon interaction of on shell photons. Neither Compton scattering nor Bhabha nor pair production nor pair annihilation involves a photon-photon interaction. There is no photon-photon vertex in QED. There is no tree level Feynman diagram that you can look at and say “this is, at least philosophically, a photon changing its momentum”.

There is a 1 loop diagram that represents photon-photon scattering. But even that doesn’t have any photon-photon vertices, instead it is mediated by electron-positron pair.

Non-abelian gauge bosons (gluons) couple to themselves. So does gravity (gravitons). Abelian ones (photons) do not.

Photons don’t accelerate. They are emitted or absorbed. That’s their only interaction.

The electromagnetic field does have a force carrier. It is the photon.

The photon mediates the force between electrically charged particles. It cannot mediate any reaction between two neutral photons.

the speed of light expressed in units of distance per time, is a dimensionful quantity so it probably doesn’t mean anything to say some theory does or does not predict a value for it. The value is entirely determined by how big you choose your yardsticks and sundials to be, which is arbitrary convention.

It is only meaningful to talk about theoretical predictions of the values of constants if they are dimensionless, like the fine structure constant.

However relativity does suggest as a natural point of view that space and time are just orthogonal directions in a unified spacetime. In this point of view, relativity gives you the option of measuring your timelike and spacelike coordinates with the same yardstick (which you may still choose arbitrarily). And then relativity does predict its value. It’s 1. No units.

There is no tree level photon-photon interaction. Photons scatter off electrons (or any other charged particle), not off neutral photons.

Ok but photons don’t change direction either. Treating photon scattering as an individual particle accelerating due to an applied force, well that’s just not a correct description of how perturbative QED models photon interactions.

The fact that light cannot change speed is one of the core axioms of relativity

Photons cannot accelerate

The point wasn’t that ranged attacks or siege or cavalry weapons are more important than melee weapons, though depending on the battle or the century, that may well be true.

The point was that when it comes to melee, the weapons used by your infantry was never swords. Swords are prestige weapons, expensive and heavy, wielded by wealthy knights and nobility for ceremonial purposes, duels, or tournaments. The king cannot afford to equip a thousand infantry with swords (the way you see in movies like Braveheart or LotR), and even if he could, the infantrymen have neither the skill nor strength to wield them for an extended duration.

Swords weren’t the weapon of last resort. They just weren’t included in the loadout at all, of the soldiers engaging in melee combat. So what did they use? Spears. That’s probably why the OP says spears are king.

But take it with a grain of salt cause I don’t actually know anything about medieval warfare. It’s just a thing I heard.

Modern conceptions of medieval warfare drastically overestimate the amount of usage that swords saw in battle. At least that’s a thing I’ve heard.

For the record, I don’t think safari works this way. Every incognito window has its own session I believe

but the encryption keys are not stored on the 1password cloud systems

1password user data is encrypted, right? so even if a hack had allowed a bad actor access to user pw databases, it’s not like they would’ve just scored everyone’s passwords… right?

Ah. Thanks.

I don’t get it. Are those toppings controversial? What even are they? Pickles?

Zuckerberg owns %14 percent of the 2.5 billion shares of the trillion dollar company.

Yes, he could retire and live off a slice of the profit for the rest of his life. But that’s nothing. Anyone with a few tens of thousands of shares of a healthy company can do that. That massively understates the scope of his holdings.

Facebook could never turn a profit again. Revenue could fall off a cliff. And Zuck could borrow against the value of his assets to get paid handsomely for the rest of his life.

Heck he could shut down Meta and liquidate the company for pennies on the dollar and still have more money than most people see in 100 lifetimes.

I suppose the elements formed by fusion of hydrogen are pretty fixed. It’s mostly helium. Only the rate depends on the pressure and temperature of the fuel.

So I don’t know whether fusion happens in an accretion disk. But if it does, the elements formed are mostly helium, and a few other light elements at trace amounts.