The relativistic equations of energy and momentum forbid the possibility that anybody with nonzero rest mass reaches the speed of light because both quantities tend to infinity. In the case of the photon and neutrino, the problem is saved annulling their masses, so that the equations lead to an indetermination, and opens thus the ability to assign the value E = pc for both quantities. But on the other hand, the measurements indicate that neutrinos have nonzero mass. The question is how this theoretical dilemma is resolved.
There isn't any theoretical dilemma. Until 1998, it was thought that neutrinos were massless-so they traveled at the speed of light. However there wasn't any particular reason that forbade neutrinos to be massive, or required them to be massless. Since it was known that their mass is very small, the simplest hypothesis, that was, also, consistent with experiments, until 1998, was that the mass was, in fact, zero.
The absence of right handed neutrinos means that their putative mass terms require a slightly more complicated mechanism (the seesaw mechanism) but that is understood theoretically. There are currently experiments that try to test whether neutrinos could acquire their mass through Yukawa terms or not (whether they are not their own antiparticle, or they are).
Since 1998 it is *known* from the discovery of their flavor oscillations that neutrinos are not massless-therefore they don't travel at the speed of light. However their masses are so small, that their speed is *very* close to the speed of light.
On the other hand, there is a theoretical reason the photon is massless and that is gauge invariance: the unbroken U(1) symmetry of the Standard Model ensures that the photon remains massless-thus, it travels at the speed of light in vacuum.
Dear Stan.
First of all, thanks for your response. But I now can think of other questions: :
1) measurements of the speed of neutrinos are consistent with this idea that you express?.
2)Effectively does its speed is less than the photon?.,
3)Or are they so close that the difference in speed is less than the measurement error?.
Carlos.
(1) Yes, from supernova measurements and from oscillation measurements.
(2) Typical supernova measurements show this
(3) No.
What that means is that the neutrinos that we do observe have energies that are so much larger than their rest energies, that their sped is very close to the speed of light-even if the rest energies aren't *exactly* zero.
The question is, rather, why are they so much lighter, in comparison to other particles.
Why their masses are so much smaller than the masses of the other leptons is not known.
They can have any energy, above their rest energy. The fact that this latter is very ``small'', compared to a typical lepton mass, implies that they are, typically, relativistic.
The real question is to understand their mass spectrum. This is, for the moment, an open problem. Cf. here: https://indico.in2p3.fr/getFile.py/access?contribId=198&sessionId=4&resId=0&materialId=slides&confId=9116
for a very recent presentation on what is known.
Hi Stan.
Do you have any publications available that detail the process and the results of measurements of the speed of neutrinos?. will be very grateful if you send me the paper or a link.
Here is a paper by the OPERA collaboration, where they've fixed their systematics:
http://arxiv.org/pdf/1212.1276v2.pdf
Dear.
I was reading the article about the measurements of the speed of neutrinos with the OPERA detector, the conclusions are the following: "The OPERA experiment after the improving of the timing system, has confirmed the result reported in [3], showing no significant deviation of the muon neutrino velocity from the speed of light. The present result is: delta (t) = (0.6 ± 0.4 (stat.) ± 3.0 (syst.)) ns, giving the limit -1.8 × 10-6
This simply shows that muon neutrinos are so relativistic that with the techniques used it's hard to measure their velocity as different from that of light. That's all. If the mass is very small (which it is) then this isn't a surprising result. Detectors have a finite resolution. This calibrates the detector.
Dear stan.
But this measure implies that we can not say with precision up to 10exp-6 that the speed of neutrinos is different from the light.
So, my question is whether there are alternatives theories to the Standard Model and conventional RG that can explain how a particle with mass can move at the speed of light. I can even say that carrier particles of interactions, such as the weak bosons and gluons, they have mass and they move at the speed of light. Is not this one of the mismatches of the Standard Model?
A massive particle *can't* move at the speed of light. If its mass is very small, however, as is the case for neutrinos, it is difficult to measure the speed very precisely. That's all. It's a technical issue, not a conceptual issue. No physical principle says that one must be able to measure the speed of an object to a given accuracy. The question that can arise is, given a measurement, that, always, has a finite accuracy, what conclusions can we draw from it? The answer here is that neutrinos are ultra-relativistic particles and this is consistent with all we know about them. We expect that, if it becomes possible to perform the experiment more accurately the difference between the speed of the neutrinos and the speed of light will *increase*, confirming that they are, indeed, slower.
Depends on what ``supermassive'' is supposed to mean. What is the issue with ``supermassive bosons''?
I'm just doing the devil's advocate. I have no problem with the concept than you express. the problem is that the bosons W and Z have masses much higher that the neutrinos, as the gluons. However, they are carrier particles of interactions and thereby, its characteristic velocity is c (from theorical point of view). what do you think about this?
Gluons are massless (SU(3) color is not broken). They are confined, of course, so it's tricky to talk of their velocity. In the deconfined phase this would be the speed of light.
The W and Z are massive (SU(2) x U(1) is broken) and move with velocity much less than c. There isn't any principle that says that interactions are transmitted at the speed of light.
ok. thank you very much again for your time. See you later.
Cordialmente
Carlos.
Carlos, quizás encuentre interesante la demostración que hago de que una partícula acelerada puede superar la velocidad de la luz sin contradecir las transformaciones de Lorentz, ver artículo adjunto.
Article Trajectories in space-time M4: Reinstating the Newtonian Time
Ok Ivan. Muchas gracias. Apenas pueda lo leo y si logro entender le cuento mi opinión.
Saludos.
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