# Reason why only massless particles can travel at speed of light?

I have read this question:

Do all massless particles (e.g. photon, graviton, gluon) necessarily have the same speed $c$?

And the answer by WetSavannaAnimal aka Rod Vance:

"Incidentally, if we confine massless particles, e.g. put light into a perfectly reflecting box, the box's inertia increases by E/c2E/c2, where EE is the energy content. This is the mechanism for most of your body's mass: massless gluons are confined and are accelerating backwards and forwards all the time, so they have inertia just as the confined light in a box did. Likewise, an electron can be thought of as comprising two massless particles, tethered together by a coupling term that is the mass of the electron. The Dirac and Maxwell equations can be written in the same form: the left and right hand circularly polarized components of light are uncoupled and therefore travel at cc, but the massless left and right hand circular components of the electron are tethered together. This begets the phenomenon of the Zitterbewegung - whereby an electron can be construed as observable at any instant in time as traveling at cc, but it swiftly oscillates back and forth between left and right hand states and is thus confined in one place. Therefore it takes on mass, just as the "tethered" light in the box does."

So is this the reason why anything with mass, like our body, that has "massless gluons are confined and are accelerating backwards and forwards all the time, so they have inertia just as the confined light in a box did", so the gluons are confined, so they must travel back and forth between some kind of confining container, a "wall" or something?

Question:

1. As this body would speed up, as it reaches speed c, the gluons inside it will not be able to "accelerating backwards and forwards all the time", because they are already at speed c and the "wall/container" they are confined in is already moving at speed c in a direction, so the gluons would never reach the confining wall anymore? So they cannot have inertia anymore, and so the body cannot have mass anymore? (just like in SR, the photon clock, the photons can't reach the mirrors anymore, so time seizes to exist too)
2. So as anything that reaches speed c, will (or must have no rest mass in the first place) lose its rest mass?

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.

• ok, but where you say "that is caused by the way gluons reflecting from a moving wall will change frequency" there you say they have to bounce off a wall. So if the wall moves with c, the gluons still can't reach it. So they can't bounce back from it. So there will be no change in frequency, no inertia? Oct 26, 2016 at 20:44
• The wall has to have mass. In the case of gluons in a proton, the wall is provided by the potential generated by massive quarks - the quark mass being set by a different mechanism. Oct 26, 2016 at 22:39

The idea that rest mass of matter can be attributed to massless particles oscillating back and forth is interesting, but not mainstream physics.

As far as I know, the origin of mass is a bit of an outstanding problem.
https://en.wikipedia.org/wiki/Mass_generation

So speculating based on an answer that is itself speculation might not get you too far.

One thing we do know is that if you were to accelerate something to close to the speed of light, the kinetic energy shows up as a significant fraction of the inertial mass. This makes speeding up the particle even harder, more and more of the energy shows up as inertial mass making things harder and harder. To reach the limit of the speed of light would require an infinite amount of energy.

For a particle with mass $$m > 0$$ we have the relativistic equation:

$$E = \frac{mc^2}{\sqrt{1-v^2/c^2}}$$

this implies that:

$$v = c\sqrt{1-\frac{m^2c^4}{E^2}}$$

in the limit $$m\to 0$$, we see that $$v\to c$$ for finite energy. In addition, for $$m>0$$ necessarily we have $$v

On the other hand, the gluons that hold the quarks together are virtual gluons, not real ones (so they are not limited to move at the speed of light, since they must not necessarily satisfy $$E^2 = p^2c^2 + m^2c^4$$), for that reason, the argument cannot be applied, because these gluons are not real and can move at any speed, including superluminal speeds.