Friar Bellows

Guys, I don't care if you "derail" the thread. That's what threads are for. I don't own the thread.

Answerer

Hey Friar, I don't think the relativistic mass question works for any rest mass travelling at the speed of light. Anyway, do the photons really discovered to have rest mass?

Friar Bellows

True. However, an extremely small rest mass could get very close to the speed of light with very little effort (i.e. initial energy), so close that we (experimentally) might not be able to tell the difference.

No, we don't know. The experiment described in the article established only an upper limit to the rest mass, not a lower limit. I expect that the photon rest mass will be zero, but it's fun to think about the implications of a small but nonzero photon rest mass.

Kenny

To chime in with another off topic, thread derailing comment , many physicists consider the whole notion of “effective mass” to be a misguided one. Mass, IMHO, should be defined in such a way that it is Lorentz invariant. I’m not sure exactly what it is supposed to even mean to speak of a concept of “mass” that changes from reference frame to reference frame or a sort of “mass” that is completely undetectable in the reference frame in which the object being spoken of is at rest. In fact, just exactly how would one go about measuring the “effective mass” something has in any way that is distinct from how one would measure its momentum? Why not just drop the whole notion of “effective mass” and just stick to talking about relativistic momentum (p = mv/SQRT(1-(v/c)^2))? Let’s just scrap the whole notion of “effective mass” and the “m = m0/SQRT(1-(v/c)^2)” equation that goes along with it – we don’t need it and, IMO, it creates more conceptual problems than it solves.

God Bless,
Kenny

Friar Bellows

True, but some don't. See for example:

"In defense of relativistic mass," T.R. Sandin, Am. J. Phys. 59 (11),
November 1991

Wolfgang Rindler, (Letter to the Editor) Physics Today, 43, #5 (May, 1990) p. 13

I don't think the use of "relativistic mass" necessarily causes any conceptual problems but I do think it can confuse students of the subject. But I prefer invariant or rest mass when I speak about mass.

lpetrich

If a photon has nonzero rest mass, then that would screw up a convenient physical symmetry called "gauge invariance". However, gauge invariance could be rescued by introducing some new particle which gives mass to the photon the way that the predicted "Higgs particles" give mass to the W and the Z particles, which have a photonlike role in weak interactions.

This would come about from that particle having a nonzero ground-state value of its field. It would act like a marble in a bowl with a hump in the middle; when one places the marble on the hump, it rolls off to a point on the ring-shaped minimum. That motion in the bowl would then couple to the electromagnetic field, giving it a rest mass.

However, the strength of that particle's field must be extremely small, at least if one judges from the various limits that can be put on the photon's mass by observation of large magnetic fields.

If the photon had a finite mass, then any electromagnetic phenomena would have an exponential decline ~ exp(-r/lp) where r is the distance from the source and lp is the photon's Compton wavelength.

From Jupiter's magnetosphere, one infers that lp must be at least a few tens of millions of km in size; this implies a mass limit of 10^-16 eV

And from the extent of galactic magnetic fields, one infers that lp must be at least hundreds of parsecs in size; this implies a mass limit of 10^-25 eV.

lpetrich

However, there is no theoretical principle that would be sacrificed if neutrinos were massive. In fact, their being nearly massless by elementary-particle standards is a serious puzzle, because one would naturally expect them to have masses similar to those of their corresponding electronlike particles (e, mu, tau).

However, various Grand Unified Theories feature possible solutions; the favorite one is a "seesaw" mechanism, which posits that there are additional very-massive "right-handed" neutrinos in addition to the "left-handed" ones that we observe. The usual sort of mass mechanism mixes left-handed and right-handed, and it interacts with this all-right-handed mass to produce very low masses for the neutrinos that we observe.

Jesse

lpetrich:
If the photon had a finite mass, then any electromagnetic phenomena would have an exponential decline ~ exp(-r/lp) where r is the distance from the source and lp is the photon's Compton wavelength.

If the photon had a finite mass, would that also mean the electromagnetic force would have a finite range, like the strong and weak forces?

lpetrich

Here is a nice page on neutrino mass, though a rather technical one.

Here are the various neutrino mass limits:

Laboratory:

m(nu-e) < 5.1 eV (tritium beta decay)
m(nu-mu) < 160 keV, pi -> mu + nu-mu
m(nu-tau) < 24 MeV, tau -> 5pi(pi0) + nu-tau

No convincing laboratory evidence for neutrino oscillations. These are produced by a weak decay producing a mixture of different neutrino mass states. These states then oscillate at different frequencies due to their different masses, producing different mixtures of the weak-decay states.

However, the solar-neutrino deficit is consistent with neutrinos oscillating from one flavor to another (nu-e to nu-mu/nu-tau and back), as demonstrated in the Mikheyev-Smirnov-Wolfenstein calculations. The resulting neutrino mass is about a few*10^-3 eV, and the mass-state-weak-state mixing angle is most likely a few degrees, though a relatively large angle cannot be excluded.

And there is suggestive evidence of oscillations in observations of neutrinos produced by cosmic-ray-atmosphere collisions, but that is inconclusive.

As I'd mentioned earlier, the favorite theory for the smallness of neutrino masses is that there are very massive superheavy neutrinos, perhaps somewhere around 10^12 GeV. The masses of neutrinos become

m(nu) = m(typical)^2/M

where

m(typical) is from a few MeV (e) to a few hundred MeV (mu) to a few GeV (tau) and

M is the mass of those superheavy neutrinos.

Using these masses for elementary particles,

m(e) ~ 0.5 MeV
m(down) ~ 7 MeV
m(up) ~ 3 MeV

m(mu) ~ 106 MeV
m(strange) ~ 120 MeV
m(charm) ~ 1.2 GeV

m(tau) ~ 1.8 GeV
m(bottom) ~ 4.2 GeV
m(top) ~ 174 GeV

I find

m(nu-e) ~ 10^-10 - 10^-8 eV
m(nu-mu) ~ 10^-5 to 10^-3 eV
m(nu-tau) ~ 3*10^-3 to 30 eV

The mass of the muon-neutrino is about right for the MSW mechanism for the solar-neutrino deficit.

lpetrich

That's right -- its range would essentially be "lp", my writing of the photon's Compton wavelength. And it would get a finite range the way that the weak and the strong forces do (oversimplifying a bit for the strong force).