Massive neutrinos don't travel at the speed of light-that statement's just wrong.

Dear Stam,

The view that massive neutrinos don't travel at the speed of light is the present collective view of the physics community. It was not always this way. For years the community sad that the neutrino did travel at the speed of light, and formulated the Standard Model incorporating this fact based on experimental data. Measurements from Fermilab yielded the speed of light with a precision of 4x10-5, and those from Supernova 1987A a precision of 2x10-9 (see Photodynamics in the Open Access Journal of Phys Math 2018 Vol 9:4). The experimental data did not change. In fact, as time goes on, and the experiments get better, the precision just gets better with smaller and smaller experimental error. Experimental error always exists. You should not hide behind it.You can't even measure the speed of an actual photon with infinite precision. Does this mean that light does not travel at the speed of light? The measured speed of neutrinos is always c to experimental error, not a scatter of speed as if you were measuring the speed of electrons. Slow neutrinos have never been seen. Where have all the slow neutrinos all gone?

Then with the solution of the Solar neutrino problem with the introduction of the concept of neutrino oscillation in 1967 (see Photodynamics) all this began to change, (in spite of the experimental facts confirming that they did travel at the speed of light with improving precision), because neutrino oscillation cannot happen unless neutrinos have mass, and everybody "knows" that massive particles can not travel at the speed of light in violation of Einstein's E = mc^2. Because of this, the long accepted position that neutrinos travel at the speed of light and have no mass (Standard Model) was flipped to the present position that they do have mass and that they therefore do not travel at the speed of light because of the 2015 Nobel Prize in Physics confirming that neutrino oscillation actually occurs. The present position of the physics community is not being driven by the experimental facts, which actually oppose the accepted position. The present position is driven solely by a false belief that Einstein's E = mc^2 applies to particles that travel at the speed of light, just as it applies to atomic particles. This is not true. Einstein's E = mc^2 does not apply to any particle that travels at the speed of light. There is no need to deny the experimental facts that neutrinos travel at the speed of light to preserve Einstein's E = mc^2. Einstein's E = mc^2 will continue to apply to atomic particles as it always has. It just does not apply to lightspeed particles, and never has.

This is the central finding of Photodynamics. There presently exists a mathematical and experimental error in the special theory of relativity which has now been there for more than 100 years. It has to be and will be corrected whatever your views on neutrino oscillation. Photodynamics identifies the location of this error, explains how it was generated, and eliminates it. The result is an error-free special relativity, working as it was meant to work, and much more powerful than ever before. All it requires is the acceptance of the truth, namely that lightspeed particle dynamics are governed by the laws of Photodynamics, and atomic particle dynamics by the Einstein relation.

Please re-read my paper on Photodynamics (t is available on this site or on line) and judge for yourself whether or not I am telling you and others the truth. I would love to have your agreement. I only ask you to let me know any specific error in the paper applicable to the argument above, and to vote again if needed.

Thanks for your interest,

Bob Martineau

When it was assumed that neutrinos were massless, this implied that they traveled at the speed of light. Now it's known they're massive, which implies that they don't travel at the speed of light. However their mass is so small, compared to the mass of all other particles, that the deviation of their speed from the speed of light is very hard to measure. Indeed it hasn't been measured directly, simply because it's much easier to deduce it indirectly.

What does matter is the oscillations between flavor eigenstates, that would be absent, were the neutrinos massless-that's the important issue, not the fraction with which their speed differs from that of light.

Indeed the measurement of such oscillations is another way to probe Lorentz invariance and deviations from it.

The Standard Model, that is consistent with global Lorentz invariance, can accommodate massive as well as massless neutrinos-if they're not their own antiparticles. Their mass is acquired by the Brout-Englert-Higgs mechanism, with a very small Yukawa coupling. No problem.

If the neutrinos are their own antiparticles, then they can't acquire their mass that way, but the mechanism by which they could is known (the ``seesaw mechanism'', e.g. https://nuss.fnal.gov/lectures/RabiM_1.pdf). This is an extension to the Standard Model, not a contradiction to it; it's completely consistent with what's known already. The details matter, so finding which variation is, in fact, realized is an open problem-better to focus on that.

It's straightforward to describe effects that would violate global Lorentz invariance in the Standard Model (cf. http://www.indiana.edu/~lorentz/kostelecky/faq.html). These don't have anything to do with describing the fact that neutrinos are massive, however. The statement that massive neutrinos imply violation of Lorentz invariance is, simply, wrong. The statement that violation of Lorentz invariance would imply that neutrinos were massive is meaningless, since mass is a Lorentz invariant quantity.

The statement that there's some ``mathematical error'' in special relativity is, trivially, wrong; and the statement about any experimental deviations is equivalent to non-zero values for the coefficients of the terms that describe them in the extensions to the Lagrangian of the Standard Model. These have been written down and their effects, on known processes, can be calculated. Their values are consistent with zero and inconsistent with any non-zero value.

There is ongoing research on the hierarchy of neutrino masses e.g. Article The neutrino mass hierarchy from oscillation

It's well known that the relation E=mc^2 doesn't make sense for particles that travel at the speed of light-that's nothing new.

Dear Stam,

Let me focus on your last paragraph. I disagree that the fact that Einstein's E = mc^2 = m(0)g c^2, where g is the Lorentz gamma factor, does not apply to lightspeed particles is well known. Most physicists apply the Einstein relation to both lightspeed (type 1 ) and atomic (type 2) particles. In order to justify this mathematically, they say that the rest mass of a photon m(0) has to be zero to avoid m(0)g being infinity for all photons since g is infinity at light speed. Then if m(0) is zero, the photon would have zero energy and momentum if its speed were less than c. That is the origin of the present understanding that the photon has a zero rest mass and can only travel at the speed of light. Do you agree with me on this being the source of the present understanding? If not, why does the community hold the false position that the photon has a zero rest mass and can only travel at the speed of light, a 100 year old position which is demonstrably wrong, theoretically (mathematically) and experimentally. That is the central error and motivation for making that error that I am trying to convince the physics community to correct.

Please answer the question: Why does the physics community say that the photon has a zero rest mass and can only travel at the speed of light?

Sincerely,,

Bob