I then kept reading things that tell me photons don't interact, which saddened me because I like the question. This now appears to not be the case, is there a specific condition under which photons can interact like this?
I then kept reading things that tell me photons don't interact, which saddened me because I like the question. This now appears to not be the case, is there a specific condition under which photons can interact like this?
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.
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.
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.
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.
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.
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).
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.
'The map is not the territory' is the phrasing I've heard: https://en.m.wikipedia.org/wiki/Map%E2%80%93territory_relati...
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.
Now, combine that with the superposition principle ... photons pass through one another under most circumstances because of this (unlike gliders).
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.
Even if in the same vicinity, and time, eg same apartment building, subway, street, driving down the road, there is often zero interaction.
Really, humans interact very rarely too. Yet, humans do interact, in meaningful ways. Thus, it is likely the same for photons.
This theory also explains why, with the rarity of human interaction, I am unmarried. In fact, it probably explains it on multiple levels.
There is no absolute clock in the world; we can only know about what happened where and when by looking.
A way to understand this (and special relativity) is from an information-theoretic perspective, and to think of c as the “Mach number” of free space, nothing more and nothing less.
So imagine that you couldn’t see but could only know about what happened where and when by hearing. All those phenomena (foreshortening, frequency shift, apparent time dilation) would be exhibited though the speed of information travel would be much lower. You have probably experienced the equivalent of blue shift/red shift yourself by listening to a high speed vehicle.
Change the medium from ordinary air to something with a different density and all these phenomena will be detectable, even though the speed of sound will be different.
I guess if you wanted to pose that question in a framework where a medium where the speed was less than c, and photons, could exist simultaneously, you would want an effective field theory (maybe). But you will have to get someone else who knows more than me to explain that. :-)
But the photons really shouldn't have rest mass.
It might be a pedantic argument on my part, but still, it is worth being clear on this point.
[1] https://en.wikipedia.org/wiki/Invariant_mass#Collider_experi...
Those are the first few sentences in the article I already posted.
> The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, it is a characteristic of the system's total energy and momentum that is the same in all frames of reference related by Lorentz transformations.[1] If a center-of-momentum frame exists for the system, then the invariant mass of a system is equal to its total mass in that "rest frame".
Those are the first few sentences in the article he already posted.
I know what your position is. I'm just not sure that the quote from his article supports your position.
I will grant you that if you take the energy-momentum equation and apply it to such a system as a whole, and plug in the total energy (non-zero) and the total momentum (zero), then out comes a non-zero mass. I just am unclear on whether that's a valid thing to do. (I also don't know that it's not valid.) Can you make a convincing case that it's reasonable to apply that equation in that way?
> Can you make a convincing case that it's reasonable to apply that equation in that way?
Even hpcjoe did not object to that, only to the name "rest mass" for the result. We saw that the number you get out was useful upthread, because it allowed predicting if pair production can occur or not.