Does a single unique photon ever not travel at c in the same inertial frame?
I think that “stuff” that makes light go slower is adding to distance traveled (something like bouncing the photon around in a house of mirrors before letting it out the other side) or is modulating the field by taking up and giving back energy. At least these are two examples of how “slowing” of light is modeled. The distance traveled in the house of mirrors does slow a photon down if you just measure when it went in and when it came out. The taking up and giving back energy isn’t the same photon, at least that’s how energy transistions in EM can be modeled. The EM field absorbes a photon, which is now gone, and may give one back, a new one, at a different group or phase velocity. How you use general relativity to view them in a material, I have no idea.
I’m stuck on the apparent problems with applying the Lorentz transformation to a photon. I don’t think it makes sense to apply them to a photon. I guess what I’m getting at is that photons have zero mass and possess energy. A zero mass object at rest at less then the speed of light is really nothing. You can add energy to nothing and get the energy back but, I don’t think it’s going to create a photon.
You can apply a field to a material and create photons but, I think they “pop” into exsistence with a velocity c. Talking about moving photons from rest to c, I don’t think happens or even makes sense.
I beleive there are materials though which you can slow light down to the point where you can walk faster then it.
In fact my brother is in grad school and the project he’s working on involves slowing light down. I beleive he’s doing research for the telecommunicaitions industry.
I think we must be careful what we mean by light and photons. Photons in a vacuum travel at c with regard to the inertial reference frame they are in, and with regard to any other inertial reference frame too, for that matter. That is, the velocity of a photon with respect to anthing that has any mass is always c. The relative velocity between a photon and a moving mass is c, and the relative velocity between that same photon and another mass that is moving differently is also c.
We can see through a window, and can speak of light traveling through the window, but it’s not made of photons in the same sense. The electrons in the window pass light by converting it into mechanical vibrations. The electrons have an elastic resistance to displacement that relates to the dielectric constant of the window glass (or whatever). We refer to the speed of light slowing in the window, and speak of the index of refraction as a speed divider that is specific to the transparent substance, but this is more a shorthand way of dealing with the conversion of the light to mechanical vibrations and back again. In fact, you can estimate the index of refraction from the dielectric constant and the density.
Another consequence of this is the way the impedance mismatch at the surface of a transparent substance will reflect some of the light, and the way polarization depends on orientation around the optical path for rays of light that strike such a surface at a nonperpendicular angle.
Thank you confirming that a photon always travels at c in any inertial frame.
Your point about speed of light and speed of photons being different is something that is commonly missed. Do you know of some material that is accessible to a lay person that would explain the difference? Addtionally, do you have any citiations that I can use to support that photons always travel at c in any inertial frame?
There’s this German chap by the name of Einstein; kind of obscure but you might check him out. He did a bit of work in this area along with a few other guys like this crazy frog named Poincaré, that Finian wonk FitzGerald, and some Lithuanian called Minkowski (don’t laugh, that’s his real name) and I think Einstein might have got some kind of award or medal or something, but actually not for this minor and possibly crackheaded theory.
You’ll note that there isn’t an American in the bunch, which is more than a little suspicious and not just slightly unpatriotic, but there are also a few other guys who are true blue Americans like John Archibald Wheeler and Richard Feynman who did some modest if little known work in trying to make Special Relativity jive with this totally insane theory about how particles are actually just little waves and everything is just a big smear of probability. Don’t listen to anything from this nutsoid called Gell-Mann, though; it’s clear from the name that he’s some kind of shyster who is just trying to extort money from the Swedes, and he has cribbed heavily from the childish fiction of Charles Dodgson for his alleged theory of “quantum chromodynamics”. Like that even means anything. Sheesh, people are gullible. You’d think those eggheads in Pasadena would get a clue, but they keep hiring those street corner schitzophrenics, probably out of pity to keep them off the street.
This may be extremely ignorant on my part, but does it make sense to consider the rest mass of a photon infinitesimal, rather than zero? So that when you apply the formula for it’s mass/energy at C, you get a finite value?
>What is the relative velocity of a photon to another photon?
Uh… c… Wait, mangeorge, do you know otherwise? I have a vague recollection about you being all over this - are you?
But it has to be c. It can’t be any less. And it can’t be any more, not without disrupting causality. That is, if photons can move with relative velocities above c, they could also put effects after their causes.
The citation about photons in inertial frames at c would be Einstein’s 1905 paper on the electrodynamics of moving clocks. I have an english translation here somewhere. I use it in a PowerPoint presentation about PowerPoint presentations, pointing out that Einstein only needed two heirarchical type styles to explain this work, so when PowerPoint suggests your own slide show use 5 levels, it’s overkill.
Curiously enough, zero, as least as far as an observer in the reference frame of the photon (either one) is concerned. Since a photon is moving at c, it cannot be said to experience the passage of time, and therefore time rate of change. It can gain or lose energy relative to an external reference frame along its path from conception to terminus, but it cannot “perceive” motion. We idealize a photon as a particle in terms of its interaction with other systems, but from the point of view of the photon, it is one long geodesic curve that exists in simultaneity, with the rest of the universe being a smear along a space-like path through time.
Externally, the difference in velocity between two photons is a simple exercise in vector trigonometry, and in fact is the only particle (aside from the color confined gluons, unobservable gravitons, and speculative exotic or supersymmetry particles like photinos) for which the Lorentz transformations on Newtonian mechanics can be reduced to their classical mechanics, and velocity can be calculated as a simple superposition of trigonometic vectors in three dimensional space. In simple terms, photons behave in this way exactly like classical particles (provided that local space is flat and mass-free in accordance with SR) and the math becomes trivial. However, there’s no way for an observer to actually see a free moving photon without interacting with it, and by interacting with it, he destroys it.
A funny business, this. Even stranger than a Wodehouse novel.
I am merely your humble servent, but thank you for the accolade.
Strange, but fun. Until the aspirin runs out.
But two photons approaching? Both are at c, as is closing as Napier states. I understand that, but still.
Even Hawking once confessed to a little problem with that.
Wait, wait, wait. What do you mean by “the reference frame of the photon”? If you mean the reference frame that moves with the photon, i. e. the reference frame with respect to which the photon’s velocity is zero, then that’s a nonsensical specification for a reference frame, isn’t it? That would certainly not be a reference frame that could have an observer in it.
True; I was just addressing the hypothetical question of what an observer, could he (or at least some massless element of consciousness) ride along with the photon, would see, and the result is that he wouldn’t see any movement at all or otherwise percieve the passage of time. In reality, no real massy object can go c, and so that interpretation of the question is meaningless for any practical purpose.
I have a question for stranger on a train. Does he believe that c and photons are the same thing? I’m not smart enough to prove that a massless particle with energy has to have a velocity c relative to any inertial frame. If stranger would be so kind, please demonstrate how massless particles with energy must have a velocity c in any inertial frame. Hand waving and invoking the names of Nobel Laureate’s (except when it’s to add an equation) is greatly discouraged.
First of all, c is a constant, and a photon is a particle. Photons move at c, but that doesn’t make them the same thing.
Second, what you are asking for is the Theory of Special Relativity. There is plenty of information available on line (the Wikipedia article linked isn’t the best but isn’t too bad), at the library, bookstore, and local university. It’s both beyond the scope, and too extensive of a topic for me to cover in sufficient detail in this forum. If you want to understand Special Relativity–and while it’s a theory that can be understood with nothing more than a grasp of high school trigonometry and the bare fundamentals of calculus, it’ll take more than a few column inches to explain thoroughly–I’d recommend checking out Einstein’s Relativity: The Special and the General Theory and Feynman’s *Six Not-So-Easy Pieces: Einstein’s Relativity, Symmetry, and Space-Time*. There are a vast number of other popular science and entry level texts that cover Special Relativity as well–I find Brian Greene to be a fairly accessible read–but it’s not something you’re going to “get” from a single reading in a few minutes.
So the energy of a photon doesn’t depend on its velocity
But from relativity we know that:
E = mc[sup]2[/sup] / (1-v[sup]2[/sup]/c[sup]2[/sup]) [sup]1/2[/sup]
And since the photon’s mass = 0 its E = 0
But we know that’s not true. So what’s the story?
The only way these two equations can be reconciled is for v in all reference frames to = c. Because in that case the second equation is indeterminate, meaning the energy can be anything at all and so it can = hf just as it should.
Ok, so from SR kinematics I can say that a massless particle can exist and have have energy but only if it has v=c, which I had to realize after getting E=0/0 (applying the Lorentz transformation to a massless particle traveling with v=c) and deriving the more general form of E from the difference of E and momentum and noting that if m=0 then E=pc can be true if v=c. And this proves that massless particles with energy can exist and must travel at c. This is the basis of a proof a massless particle must travel a v=c in all inetial frames?
My original intent with my question was to get some support on the invalidity of applying the Lorentz transformation on a massless particle. Which I guess I got. I also still need to reconcile photon velocity and slowing of light in the context of relativity (SR or GR). Can a photon have a velocity other than c in a non-inertial frame? I don’t think it can.
