Ask Question. Asked 10 years, 9 months ago. Active 6 years, 8 months ago. Viewed 22k times. Could you explain this to me in a short and mathematical way? Improve this question. The question is different, the answers are different. In fact, the "duplicate" question has NO answer that tells why it is believed that photons are massless. And the question is one of some interest. In addition to the current literature i.
Jackson has a discussion of this question and the question here has attracted 5 answers, none from a less than rep author, and with a total of 9, reputation. Reopen the question. It is not an axioma as far as I know. Is this why any body with a mass can't escape a black hole? Add a comment. Active Oldest Votes.
Improve this answer. Correspondingly, the force among such neutral particles decreases quickly with the distance. In fact, the decreases is faster than the power law because the gluons self-interact so they are confined, too.
The mass of colored objects is a subtle thing - it depends on the RG scale and the masslessness is only relevant at very short distances, much shorter than the proton radius QCD scale where the confinement starts to matter.
Einstein's equations show that in order for mass to travel at the speed of light would take an infinite amount of energy. So, you asked Crazy Peanut how he knew that neutrinos did not travel at the speed of light. Now, what exactly are quantum fields anyway? Essentially, the defining features for most quantum field theories are more or less the following:. Now, in the case of quantum electrodynamics, it is a gauge theory with the symmetry group U 1.
This U 1 -group which also gives rise to conservation of electric charge also has a gauge field associated with it, which is the electromagnetic field well, technically it is the vector potential of the EM-field. Well, great, we now know what a photon is, but what does any of this have to do with the photon not having any mass? The defining property here is that a photon is classified as a gauge boson.
It actually turns out that mathematically, there is no way to add a mass term for the photon without breaking gauge symmetry, which is what the whole Standard Model is practically based on. Other gauge bosons such as the W and Z bosons can, however, obtain a mass regardless through something called spontaneous symmetry breaking and the Higgs field, but this does not occur for the photon. So, in fact, the quantum field theoretical explanation for why a photon does not have mass is that gauge symmetry forbids it.
Therefore, if we want quantum electrodynamics to work like it should and also agree with experiments, the photon cannot have a mass this is quite an important point as all experimental evidence also suggests the photon to be massless. Even though these lead to some very interesting consequences in, for example electromagnetism for massive photons, electromagnetic waves should have three polarization states , they simply do not correspond to reality or anything that has been experimentally verified apart from the superconducting phenomenon, which is a whole other story.
This of course indicates that the mass of a photon is also extremely small it could likely be proven to be exactly zero, if it was possible to measure it accurately enough. Such is the case with light. Furthermore, if the object travels at some speed v that is less than the universal speed limit c , we can always choose a reference frame traveling along with the object so that the object will be at rest in this reference frame.
Therefore, an object that can never be at rest must always travel at the universal speed limit c, because this speed has the interesting property that once an object goes a speed c in one reference frame, it goes the speed c in all reference frames. In summary, all objects with no mass can never be at rest and must travel at speed c in all reference frames.
Light is such an object, and the universal speed limit c is named the speed of light in its honor. But light is not the only massless object. Gluons and the hypothetical gravitons are also massless, and therefore travel at speed c in all frames. How can an object have momentum without mass?
By this definition a beam of light is massless like the photons it is composed of. However, if light is trapped in a box with perfect mirrors so the photons are continually reflected back and forth in both directions symmetrically in the box, then the total momentum is zero in the box's frame of reference but the energy is not.
Therefore the light adds a small contribution to the mass of the box. This could be measured--in principle at least--either by the greater force required to accelerate the box, or by an increase in its gravitational pull. You might say that the light in the box has mass, but it would be more correct to say that the light contributes to the total mass of the box of light.
You should not use this to justify the statement that light has mass in general. Part of this discussion is only concerned with semantics. It might be thought that it would be better to regard the mass of the photons to be their nonzero relativistic mass, as opposed to their zero invariant mass.
We could then consistently talk about the light having mass independently of whether or not it is contained. If relativistic mass is used for all objects, then mass is conserved and the mass of an object is the sum of the masses of its parts. However, modern usage defines mass as the invariant mass of an object mainly because the invariant mass is more useful when doing any kind of calculation.
In this case mass is not conserved and the mass of an object is not the sum of the masses of its parts.
0コメント