Is the momentum of a massive particle traveling at the speed of light zero?

[RAD4921]

I know this isn't a deep discussion and the thread will be short but this question has been bothering me for a while and I hope the moderators won't terminate it.

Are photons the only massless particles that travel at the speed of light? Diagrams of the standard model do not reveal the answer to this and the physics forum is my last hope. Thanks
RAD

 

[Hootenanny]

Currently it is accepted that the photon and the gluon are both massless particles. The graviton [if it exists] is predicted (quantum theory of gravity??) to be massless, but as yet no observations have been made and the related theories are still a bit 'shaky'. The evidence to support the massless photon is basically rock solid, the gluon somewhat less so I believe.

Edit: Oops I believe I forgot to answer your actual question. All massless particles must, acording to the standard model which obeys SR, travel at the speed of light due to the very fact that they are massless.

 

[Schrodinger's Dog]

And to add any particle with mass as I understand it cannot travel at c, due to the energy required to achieve c.

Interesting side note and spoilered so as not to confuse the issue

https://www.physicsforums.com/showthread.php?t=152855

 

[Hootenanny]

Interesting side note and spoilered so as not to confuse the issue
[spoiler removed from quote]

Seems very interesting, I may have a read of that paper this weekend if I get chance.

 

[rbj]

i remember Meir pointed out a link to some study that put an upper limit on the (invariant) mass of a photon and it wasn't zero. it was something like 10^-50 kg. it seems to me very dissatisfying that the speed of particles of light or E&M in general do not fly by at the same speed as the wavespeed of E&M but it might not be so rock solid.

 

[Parlyne]

i remember Meir pointed out a link to some study that put an upper limit on the (invariant) mass of a photon and it wasn't zero. it was something like 10^-50 kg. it seems to me very dissatisfying that the speed of particles of light or E&M in general do not fly by at the same speed as the wavespeed of E&M but it might not be so rock solid.

An upper bound like that just means that our methods of measuring the photon's mass can't measure a mass smaller than that. This means that the photon could have a mass as small as 0 kg or as large as 10^-50 kg, and we just wouldn't be able to tell the difference with any equipment that exists today. The existence of a non-zero upper bound does not mean that the photon actually has a non-zero mass.

 

[ZapperZ]

An upper bound like that just means that our methods of measuring the photon's mass can't measure a mass smaller than that. This means that the photon could have a mass as small as 0 kg or as large as 10^-50 kg, and we just wouldn't be able to tell the difference with any equipment that exists today. The existence of a non-zero upper bound does not mean that the photon actually has a non-zero mass.

Parlyne has brought up an extremely important point. In many cases, this is the limit of the resolution of the best experiment that we have today. This upper limit has continued to become smaller and smaller as our experimental method improves. It certainly does NOT mean that it has a mass, it is just that the experiment has not detected anything LARGER than that upper limit value.

The same is done with experiments measuring the possible variation in c (see Recent Noteworthy Papers thread). Each of these experiment will quote the upper limit in the variation of c, meaning that the experiment does not detect any various above and as low as that value. Again, this upper limit value continues to fall as the experiments become better.

Zz.

 

[rbj]

An upper bound like that just means that our methods of measuring the photon's mass can't measure a mass smaller than that. This means that the photon could have a mass as small as 0 kg or as large as 10^-50 kg, and we just wouldn't be able to tell the difference with any equipment that exists today. The existence of a non-zero upper bound does not mean that the photon actually has a non-zero mass.

i agree with everything you're saying (and i trust that the rest masses of photons are exactly zero), but just to point out that it would be more satisfying if there was some independent confirmation that they really are 0 (and that we can simply equate the speed of photons to the wavespeed of E&M and never need think of any qualification to that). it's sort of like we expect the speed of gravity to be the same as the speed of light and it was measured to be within +/- 20% of the speed of light which is still consistent with GR but it would still be nice if the coffin was nailed shut on it. [from a percentage POV, which is worse?]

edit: actually, thinking of it, i think now that we are more secure in the rest mass of photons being exactly zero from measuring the speed of photons as indistiguishable from c than the sloppy 20% range of error (s.d.?) regarding the relative speeds of gravity and E&M.

 

[rbj]

All massless particles must, acording to the standard model which obeys SR, travel at the speed of light due to the very fact that they are massless.

not to disagree (because equivalence is a bidirectional arrow), but i like to think of cause and effect as the other way around. first postulate that photons travel at speed c (since that is what is observed to a high degree), then you get the result that their rest mass is zero.

 

[nakurusil]

i remember Meir pointed out a link to some study that put an upper limit on the (invariant) mass of a photon and it wasn't zero. it was something like 10^-50 kg. it seems to me very dissatisfying that the speed of particles of light or E&M in general do not fly by at the same speed as the wavespeed of E&M but it might not be so rock solid.

There is no way of measuring an "exact zero" experimentally. In this context it is important to notice that all experiments that expect a null result (mass of the photon, MMX, etc.) are represented by a series of experiments whose results "converge" towards zero. A "perfect" zero is not attainable due to the experimental error of the instruments involved.

 

[cesiumfrog]

Are photons the only massless particles that travel at the speed of light?

In special relativity, the momentum of a particle is expressed by a four-vector. This vector is 1) parallel with the particle's four-velocity, and 2) has length proportional to the particle's rest mass (EDIT: these are properties, not a definition). This implies that "travelling at speed of light" and "massless" are synonymous.

 

[nakurusil]

In special relativity, the momentum of a particle is expressed by a four-vector. This vector is 1) parallel with the particle's four-velocity, and 2) has length proportional to the particle's rest mass. This implies that "travelling at speed of light" and "massless" are synonymous.

While it is true that "travelling at speed of light" and "massless" are synonymous, you would be hard pressed to prove that this is a consequence of your above defintion of the 4-momentum. On the other hand, if you gave the correct defintion of the 4-momentum as in $$P=\gamma m v$$ with $$\gamma=\frac {1}{\sqrt{1-v^2/c^2}}$$ then...a massive particle traveling at c would have a momentum of...fill in the blanks.