[jdbburg]

In classical electromagnetism photons (light) do not interact, period. But in quantum mechanics the photons can briefly fluctuate into electron + positron pairs which allow them to interact with each other. But the probability for interacting is very small AND you need enough energy to make the electron positron pair (for the Breit-Wheeler process), so it is very rare in practice.

I am not sure about the "time" the photons collide, but the interesting thing is that the Breit-Wheeler process is what determines the opacity of the universe - since high energy photons traveling through the universe can hit low energy photons from the cosmic microwave background and convert (disappearing) into an electron positron pair.

[jerf]

This is a good example of one of the errors that I often see in what is otherwise the best scientific writing, which is either forgetting to specify what a certain model says, or simply straight up forgetting/confusing that a certain model isn't reality.

Maxwell's equations say that light doesn't interact. Maxwell's equations are known to be wrong in that way. They're still a very good simplifying case that you can do very well with using, by all means, just like Newtonian physics in the right conditions, but they aren't the way reality works. Maxwell's equations also have no place to put a gravity term, yet gravity clearly affects light.

The one I probably see the most often is articles about black holes confidently speaking about "what goes on below the event horizon" from an Einstein relativity point of view, which is where you get all the singularities and ring singularities that lead to different universes somehow, etc, again either forgetting to point out or simply forgetting entirely that those are the specific predictions of Einstein relativity, which is known to be inadequate to describe the inside of a black hole. It is certainly fair to discuss that theory's predictions, and whatever really is happening in there, relativity will certain shine some sort of light on it, but it is a mistake to present it simply as "what happens on the inside". The model is known to be broken here.

I am working out how to phrase this in a way that makes sense to the HN crowd because this tends to ruffle feathers when I say it, but this is all what should be well-known stuff. It's not like I'm "denying science" when I say this; quite the contrary! It's "denying science" when you insist the known-by-science-to-be-broken models are in fact not broken where the science is pretty clear that they are.

[whatshisface]

>Maxwell's equations also have no place to put a gravity term, yet gravity clearly affects light.

The place to put the "gravity term" is in the coordinate system that Maxwell's equations take place in, and the definition of the derivative which is implicitly brought in via the curls, divergences, etc. That's general relativity, and Maxwell's equations are already fully compatible with it.

>[this tends to ruffle feathers when I say it] ... It's "denying science" when you insist the known-by-science-to-be-broken models are in fact not broken where the science is pretty clear that they are.

People are probably taking issue with your use of the words "broken" and "wrong," because you're describing a car that says 90mph on the dealership's sticker but can't go 900mph as "broken," or a one pound lump of beef as "wrong," because although the butcher said it weighed a pound, and you were charged for a pound, it'd be nice if it were two.

[jerf]

Yes, if you add relativity to Maxwell's equations, you get relativistic Maxwell's equations. Ultimately not particularly relevant here anyhow since it's QM describing what's going on here, not relativity.

I don't deal in automotive metaphors because they rarely enlighten, so I'll just stick with, yes, they are broken in those places, and are not suitable for unqualified claims about the nature of reality. This isn't about what would be nice if it were true or slight exaggerations, it's about the models being broken by being applied outside of their domain in an unqualified manner. That's exactly not how they are wrong. They are wrong in a much stronger manner.

And what's more, their strong brokenness is scientific consensus, not some sort of whacky theory. Whack theorization is what you're doing when you take these models, apply them in a domain they are known to be broken in, then claim this is the absolute truth about what is going on.

[ChrisLomont]

> relativity to Maxwell's equations, you get relativistic Maxwell's equations

Maxwell's equations imply (special) relativity, so there's nothing to be added. Maxwell's equations imply the speed of light is the same in all reference frames, which is all you need to derive special relativity.

That is why people of the time were trying to understand how this can ben so, why the did things like Michaelson-Morely to look for invariance/ether, and why so many of the terms used in relativity predate relativity, since they were invented to handle that Maxwell's Equations had this invariance.

Basically, Maxwell's equations, as written were relativistically invariant, thus compatible.

[tsimionescu]

Special relativity is (partially) predicted by Maxwell's equations, and they are fully compatible. They are instead incompatible with classical mechanics.

GP claimed that Maxwell's equations are missing a term for gravity/mass, which would be the domain of General Relativity. This is more complicated, as it's true that they didn't predict gravitational lensing. But, they are still compatible with GR, as GR modifies the coordinate system, and Maxwell's equation in the GR curved space-time coordinate system do predict gravitational lensing.

GP also pointed out that Maxwell's equations are not compatible at all with QM, as they incorrectly predict that photons can't interact. Here there is no way to save them - Maxwell's equations are just an approximation, and the actual laws governing the behavior of light are substantially different, only reducing to ME in certain approximations (just like classical mechanics is not compatible with either QM or SR/GR, except as an approximation of either of the two others).

[radicalbyte]

> or simply straight up forgetting/confusing > that a certain model isn't reality.

That's partly to do with the way that high school science is taught. If we made the context clear at all times then people would have a better grounding.

[tgb]

I find your comment confusing. What exactly is the "good example" you're referring to? The person you are replying to appears to have done exactly what you are saying to do, by my reading, so I'm wondering what you're referring to.

'The map is not the territory' is the phrasing I've heard: https://en.m.wikipedia.org/wiki/Map%E2%80%93territory_relati...

[rootbear]

Thank you! I was curious about exactly this. But now I have a new question. If a photon is sufficiently energetic to be capable of briefly fluctuating into an electron-positron pair, does that imply that it would, over a long distance, be slower than c, since the e-p pair can't travel at c for the brief moment it exists?

[jdbburg]

The structure of the photon (here meaning the fact that it can fluctuate into an electron positron pair) is what leads to the speed of light being c and not something even larger. So your intuition is somewhat correct, except that the effect is "already taken into account" when we first learned what the speed of light was. Also, a photon can do this fluctuating even if it doesnt have a lot of energy, since the electron positron pair can be virtual - i.e. they have almost no mass and live only for an instant before annihilating back into a photon

[vlovich123]

Hmm... is the right mental model then that the photon has a speed higher than C in its photon state but on average it's C due to the fluctuation into an electron/positron pair? I would imagine that's the wrong model because there's contradictions that arise (e.g. the speed of light would vary with the energy of the photons so that those not fluctuating would have a higher speed but that's not the case AFAIK). Is this just "quantum mechanical weirdness" or do we have an "intuitive" explanation for how the speed of light and this fluctuation interplay?

[tsimionescu]

I don't think this is right at all. C is a universal constant, and it is not in fact known for sure whether light travels at c or just below (whether photons have a mass). However, individual photons in certain conditions can absolutely move at speeds lower than c. If photons of different energy move at different speeds, this would be detectable by firing the photons at the same far-away mirror, and measuring how much time it takes for each photon to return (on average).

[shoemakersteve]

That's really interesting. What's this effect called? I'd love to learn more about it. This topic fascinates me to no end!

[earthscienceman]

Wait. I did a physics undergrad but I never asked myself this question. How is it possible that the EM fields from photos can't interact with each other? Doubly funny, I did my undergrad research for the PHENIX experiment.

[whatshisface]

Phillips gave you a good answer, but another good answer is that Maxwell's equations are linear; forbidding any interaction between solutions f and g because if L is a linear operator, L[f+g] must = L[f] + L[g].

[jdbburg]

This is what we are taught in high school / college as the super-position principle

[earthscienceman]

Oooo. Wow. This is a great answer, thanks for explaining it that way.

[acchow]

Where do they teach physics like this? Anywhere?

[whatshisface]

I feel like this would be mentioned in a typical undergraduate wave mechanics course taught in a typical American university, but I have not been to enough undergraduate wave mechanics courses in enough American universities to know, really.

[leephillips]

Fields are abstractions that ease the calculation of the forces on charges caused by the positions and motions of other charges. The charges interact, but the fields don’t; there is nothing “there” to interact. (This is classical EM.)

If you are in a room with two charges, the electrostatic field at any point is the addition of the fields from each charge. There is no extra interaction term.

[at_a_remove]

Photons are EM fields -- self-propagating ones, like a glider in the Game of Life. The electric field changes, creating a magnetic field, but the magnetic field changes, creating an electric field. Use sines for the functions and you can see how the function just keeps re-appearing.

Now, combine that with the superposition principle ... photons pass through one another under most circumstances because of this (unlike gliders).

[vlovich123]

Stupid question I’m sure, but do our estimates for the total amount of matter in the universe account for this effect? Could this effect end up being the source of dark matter? Or is too infrequent to generate enough matter to explain the discrepancy?

[whatshisface]

If by "this effect" you mean particles fluctuating so that every field has at least some role to play in every interaction, it also applies to empty space, which has a nonzero energy density due to its own fluctuations. In fact, empty space has an enormous energy density due to this stuff. It is so enormous that it's implausible, and that's considered to be one of the major unsolved problems in physics.

If by "this effect" you mean radiation occasionally interacting to produce particles, that actually doesn't change the amount of gravity in the universe when it happens, because energy is what gravitates and it's conserved in particle interactions.

https://en.wikipedia.org/wiki/Cosmological_constant_problem

[jdbburg]

Not a stupid question. However, I think that this process (whether it is included in calculations or not) shouldn't contribute to the dark matter issue. Electrons and positrons are "normal" matter and if they are anywhere near e.g. a star, they will contribute to the plasma around the star and therefore be visible. Also, even if it were not visible, my intuition is that the process is too rare to produce enough mass to account for the dark matter

[simonh]

Best estimates are that photons only make up about 0.005% of the energy density of the universe. There's just not enough of them.