I’m sure this is a dumb question but here goes. I gather from several places that mass and energy are equivalent and are in fact different forms of the same thing and one can be converted to the other, eg atomic explosions. Now for my question. As I understand it photons have energy, some have high-energy. If energy is equivalent to mass how is it possible that photons have no mass?
I don’t have an answer, but I do have a questoon on an additional aspect of this issue. If light has no mass, how is that gravity has an effect on light?
For the 2nd question gravity impacts the shape of space so photons moving through it (taking the path of least action) follow the curves induced by the mass. They don’t get “pulled” in.
I don’t see any intuitive problem with the idea that mass and energy are (in some sense) equivalent, or different forms of the same thing, but the nature of a photon is that all the mass-energy is in the form of energy.
It may also help to note that the energy in a photon certainly can be converted to mass, but the massive particles that result from this are not photons.
Photons aren’t massless in that sense. They have energy and are affected by gravity for example. When physicist use the word mass, nowadays, they mean the rest mass. This is a measure of the energy content of something at rest (i.e., in the same frame of reference as you). But there is no frame of reference in which photons are at rest.
The oft-cited formula E = mc[sup]2[/sup] written in terms of rest mass is E[sup]2[/sup] = p[sup]2[/sup]c[sup]2[/sup]+m[sup]2[/sup]c[sup]4[/sup].
For normal slow particles this is approximately E = mc[sup]2[/sup]. The other portion is kinetic energy. For photons and others with zero (rest) mass, there is only kinetic energy.
Here’s a paper/essay that addresses your question almost exactly as you put it. It’s not very long either and even I mostly understood it. 
http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html
I am personally less interested in how a photon could have energy and momentum but no mass, and more interested in whether we know for certain that it’s true. This essay states that it’s impossible to prove that a photon has exactly zero mass, but it states that if photons had mass then certain phenomena like the behavior of magnetic fields would be different. That sounds good enough to me.
Even with Newtonian gravity, you might expect massless photons to be affected by gravity - quoting some guy in this post https://boards.straightdope.com/sdmb/showpost.php?p=21637878&postcount=6
"The force on an object due to the Sun’s gravity is F=GmMs/r2 (where m is the mass of the object and Ms is the mass of the Sun).
The acceleration due to a force is a=F/m. Notice that m cancels out, leaving the acceleration/deflection proportional to the mass of the Sun and the distance - and nothing else. As Chronos suggested, it is possible therefore to take the limit and conclude that the same deflection occurs for zero mass as would occur for an incredibly tiny mass. "
Now, in fact, the effect of gravity on photons turns out to be different than the naive Newtonian calculation above, but that’s another story.
Please feel free to attack this dumbed-down attempt at answering the OP:
If photons had mass, it would be impossibly difficult for them to move as fast as the speed of light. Yet, by definition, they do move as fast as light, because they are light, literally. Thus, it must be that they have no mass to slow them down.
IANAP, but it’s my understanding that:
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Photons are massless because they’re traveling at a speed of c.
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Photons are traveling at a speed of c because they’re massless.
And for the weird one:
Measure the mass of photon A: it is zero.
Measure the mass of photon B: it is zero.
Measure the mass of photon A and Photon B (together): it is non-zero.
“Why are photons massless?” is the wrong question. It is better to ask, how do certain particles gain their masses in the first place (example: Higgs mechanism)
That is correct, Crafter_Man. Given two or more photons, unless they’re traveling in exactly the same direction, the combination of them will have mass, even though no single photon individually does.
Keeve, that’s an oversimplification. The c that shows up in the equations of relativity shouldn’t really be thought of as The Speed of Light; it should just be thought of as The Fundamental Speed. Anything that travels at exactly The Fundamental Speed must be massless, and anything that’s massless must travel at exactly The Fundamental Speed: That much is true. What does that mean for light, though? Well, we think that light is massless, and so it travels at The Fundamental Speed… but we might be wrong. If instead the photon has some extremely small but nonzero mass, then it doesn’t have a single speed, any more than one can talk of The Speed of Car or The Speed of Baseball. If the photon has a mass, then it can travel at any speed, depending on its energy. But if its mass is extremely low, compared to the energy it typically has, then its speed will be very, very close to The Fundamental Speed.
Likewise for anything else that depends on the mass of the photon: A mass would result in changes to electromagnetic fields, too, but those changes would also be very small, if the mass were small enough. And so we measure things like the speed of light and the electric and magnetic fields at various distances, and so on, and we always (so far) find that they’re what we expect, to within the limits of our measurements, and so we know that the mass of the photon must be very small at most, less than some very tiny value. But for all we know, there might actually be some very small deviation from what we expect, too small to be detected in the experiments we’ve done so far, so we can’t rule out the possibility of mass.
If it turns out the The Speed of Light is even a tiny bit slower than The Fundamental Speed, then it is possible that there might be something else, other than light, that can go faster than light, without overstepping The Fundamental Speed.
This Other Thing would be able to reach destinations faster than its departing image. In other words, someone at the destination would greet the actual arrival of The Other Thing, yet simultaneously see The Other Thing still at home on its launch pad getting ready to depart.
Does modern physics really allow for that? No snark here, it’s a question of history that I’ve often wondered, but only now have I been able to phrase it clearly: Who was it that equated The Speed Of Light with The Fundamental Speed, and on what basis?
James Clerk Maxwell, I suppose. His equations predict a finite propagation speed of electromagnetic waves, determined by the permittivity and permeability of free space. He also proposed that light was electromagnetic in nature.
Although it though it took Einstein later to explain that the values governing the propagation of EM waves could not give a larger value for the speed of light than c, Maxwell’s equations would give slightly different results if light did not move at exactly c. So I give the nod to him even if he didn’t realize at the time that his equations imply a fixed speed to the universe and that light moves at this speed.
Fifty kudos to whoever provides an intuitive minimal-math explanation for this factor of two!
Minimal-math explanation: Einstein’s explanation of gravity is different from Newton’s, especially in some extreme cases, and photons are an extreme case.
What, you want me to put a number in my explanation? Then it wouldn’t be minimal-math any more!
Keeve, we also think that gravitons (the particles of gravity) are massless, and in fact our best bound for the mass of the graviton is several orders of magnitude stronger than our best bound for photons. So even if anyone found evidence that the photon does have a tiny nonzero mass, we’d still expect the graviton to be massless, and thus travel at the Fundamental Speed.
As for something getting to us before we “see” it, that only happens if you restrict “seeing” to light. And the only reason one might do that is that we happen to use light vision as our primary sense. Really, it wouldn’t be any more problematic than things getting to us before we hear them, which is nowadays quite routine. If somehow we had evolved gravitational-wave senses, then we’d talk of “seeing” things when the gravitational waves reached us.
If you’re going this route, it’s best to think of c as being the Speed of Causality, or the Speed of Information: If you get information to you faster than that, there’s some reference frame where you broke causality and got information about an event before that event happened. Light has nothing to do with it except that it’s currently the fastest way we have to transmit information, as Chronos said.
That is interesting. Reminds me of something I read ages ago on a popular science book (might be by Feynman?): when light passes through more than one medium, the bending of the path taken by the light we measure is because the photon “goes” from A to B through the “fastest” combined path in both media*. Does that mean that when passing though a prism (like the Pink Floyd cover) red light travels slower than violet light? And if so, how come there is a difference in light speed in a medium like glass but not in a vacuum?
- My hazy memory is that the photon travels through all possible paths simultaneously interfering with itself in a way that results in this optimum path trajectory. Of course I may remember wrongly or the effect may be due to something completely different: do you happen to know? Hope this is not hijacking!
Given that explanation, is there anything in existence that doesn’t get affected by gravity?
I’m pretty sure not, since under GR gravity is not so much a force as something that specifies the shape of spacetime. So when we perceive as something being bent by the force of gravity, it’s really better conceived as something continuing unperturbed by any force but passing through a bend in spacetime.
But we have no reconciliation between GR and QM, so… this isn’t perfect.
The title question is still unaddressed: Why are photons massless? Why can’t we have a photon with mass?
It’s masslessness is neither accidental nor arbitrary, but rather it is required by the mathematics behind the Standard Model of particle physics.
The Standard Model is built by starting with a set of non-interacting particles. All particles are represented in the theory as “fields” – mathematical objects that can take on different values at different points in space and time. The values are complex numbers.
A certain type of symmetry is then imposed on the system (or if you like: on the mathematical expression describing the system). This symmetry, called a gauge symmetry, is esoteric and can come in different varieties, but the simpliest version amounts to having the physics remain unchanged when the fields’ complex numbers are rotated around in complex number space.
The gauge symmetry is imposed in such a way that the amount of rotation can be different at different points in spacetime. It turns out that the theory does not immediately satisfy this symmetry, so if we want to impose it, we have to add something. The precise thing you need to add turns out to provide particle interactions and “force carrier” particles like the photon, but these force carrier particles must be massless, or else you can’t satisfy the gauge symmetry.
To get the full Standard Model, you need to impose a more complicated set of gauge symmetries, and the resulting counterterms in the theory give the strong, weak, and electromagnetic forces and provide for force carrier particles – the “gauge bosons”. These bosons would all be massless if not for the Higgs mechanism. The minimal Higgs mechanism in the Standard Model, which is consistent with all experimental observations to date, gives mass only to the weak interaction’s gauge bosons (W and Z). Of note, the photon must stay massless due to the simple nature of the specific gauge symmetry that corresponds to electromagnetism.
So, if the photon were to have even a tiny tiny mass, it would require new physics beyond the Standard Model. This is, of course, all the more reason to look for evidence of photon mass.