Since gluons are located within nucleons and immediately outside of them, how do experiments determine parameters like their speed? Is it possible we could be assuming they travel at the speed of light since they are massless, but in reality they travel faster/slower than light?
Particle Physics – How Do We Know that Gluons Travel at the Speed of Light?
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Because in special relativity and in terms of conserved momentum and energy velocity is given by:$$\vec{v} = \frac{\vec{p}c^2}{E},$$ and energy and momentum are related by:$$E^2 = \left(mc^2\right)^2 + (pc)^2,$$ giving: $$\vec{v} = \frac{\vec{p}}{\sqrt{\left(mc\right)^2 + \left(\vec{p}\right)^2}}c.$$ There is no real momentum, $\vec{p}$ that can give a velocity $\vec{v}$ higher than $c$, and only infinite momentum gives $v=c$ when $m\neq0$.
For the specific question you have, the individual gluons cannot accelerate, but the frequency of gluons traveling in one direction can be different than the frequency of the gluons traveling in the other. This gives the box of gluons, on average, a momentum and kinetic energy. The inertia of the box is a property it has, again averaged over a time long enough for the gluons to bounce back and forth, that is caused by the way gluons reflecting from a moving wall will change frequency in a way that exerts a force on the wall and changes the frequency of the gluons.
It's a classic undergraduate physics problem to calculate the change in frequency caused by the Doppler effect of light reflecting off of a moving object. The momentum and energy needed to cause that change in frequency have to come from somewhere, and it comes from the force exerted on the object the light reflects from.
Either the structure of space-time has no speed limit (unbounded relative velocities would then be possible), or the structure of space-time has a maximum speed (limitation on the maximum relative speed possible).
The first case corresponds to Newtonian space & time. We know that this is incorrect for fast moving objects, and evidence has been accumulating since before Einstein's work of 1905.
The second case, where there is a speed limit, is explained by Einstein's Special Relativity. Here the maximum speed is c, which also happens to be the speed that light travels.
To consider the cosmological case of the expanding universe, one needs Einstein's General Relativity. Here we have a dynamic space-time, which responds to local density of matter and energy. From observation it is known that the cosmos is expanding, and the further away (in time and space), the faster it is moving away from the observer, such as us. There are two elements to this motion: one is ordinary motion, the other is due to the expansion (stretching) of space.
The stretching of space is not limited by the speed of light, and thus there are elements of the cosmos which used to be observable, but which now have attained speeds, due to the expansion of space, such that they can no longer be seen.
For details, see How Can the Universe Expand Faster Than the Speed of Light?
Best Answer
Gluons, like quarks, are bound inside nucleons. However, it's not quite correct to think of either quarks or (especially) gluons as being little particles inside a nucleon. Before addressing questions about their speed, it's important to appreciate the limitations of the idea that they are particles — or classical waves, or anything else to which we might normally apply a concept like "speed".
Quantum chromodynamics (QCD) is expressed in terms of quark and gluon fields, not particles. Particles are phenomena that the model predicts when the conditions are right. The only particles that QCD predicts under ordinary conditions are mesons (like pions) and baryons (like protons and neutrons), both of which are "color neutral". In that context, I don't know of any natural sense in which qualities like "speed" can be attributed to individual gluons, because I don't know of any natural sense in which a meson or baryon is made of individual gluons! Mesons and baryons are a different kind of structure composed of quark and gluon fields. Even the usual cartoon of a proton being made of two up-quarks and a down-quark isn't quite accurate. It's good enough for some purposes (like the Bohr model of the atom), but a proton is more accurately described as a quantum superposition of many different combinations of quarks (and gluons), like three up-quarks and one anti-up-quark and a down-quark.
One of the most direct manifestations of individual quarks and gluons is in a phenomenon called jets. This phenomenon occurs, for example, when an electron and positron (anti-electron) are smashed together with a center-of-mass energy between about 5 GeV and 45 GeV (the GeV is a convenient unit of energy is particle physics; it stands for "giga electron volts"). In this energy range, the result is often two back-to-back "jets" of hadrons (mesons and baryons). QCD predicts that this will occur as the result of the electron and anti-electron annihilating each other and producing a quark and anti-quark moving away from each other in opposite directions. But since quarks (and anti-quarks) are confined under ordinary conditions, they don't get very far before they become "clothed" with other quarks and gluons, resulting in two back-to-back jets (bunches) of many color-neutral particles instead.
At the higher end of this energy range, above about 20 GeV, we occasionally see three-jet events, with three jets of color-neutral particles propagating away from the point where the electron and anti-electron annihilated each other. This is also predicted by QCD, which describes it as the creation of a quark, and anti-quark, and one gluon, all initially flying away from each other. This can't last for long, though; they quickly "clothe" themselves with other quarks and gluons, resulting in three jets of color-neutral particles instead.
(By the way, to check these things while I was typing them, I referred to page 24 in chapter 1 of Renton's book Electroweak Interactions. But I still accept responsibility if I've said anything inaccurate.)
So, how fast does a gluon move? Well, considering the high energies involved in the collisions that produce these jets, the final particles tend to be moving away from the collision point at very nearly the speed of light, even though most of them have mass. I'm not sure the "bare" gluon lasts long enough to really constitute a well-defined particle (maybe an expert can chime in and quantify this — or correct me if I'm wrong), in which case the concept of "speed" is once again not quite appropriate.
So, do gluons move at the speed of light? Before we can answer that in a meaningful way, we have to find a condition under which gluons exist as individual particles long enough for the concept of "speed" to make sense... and that's not as easy as it sounds.