Neutrino Mass

A Note on Special Relativity

In special relativity, the speed of light, is always measured to be the same no matter frame you are in. This is odd.

In special relativity light travels at the same speed in all frames of reference. In Newton's world, this is not true. In Newton's picture, a moving observer would see a different speed of propagation for light than would a stationary observer. This comes about because Newton assumed that time runs at the same rate for all things in the Universe, that is, there is some central (preferred) clock in the Universe. The upshot of having the speed of light the same for all observers has some interesting consequences.

• Measured quantities depend upon whether the observer is moving or is stationary. For example, depending on who does the measuring, the following quantities for observers can change:
  • the rate of flow of time
  • the energy of a moving object
  • the lengths of objects
  • ...

Consequences for Neutrinos

Because the mass of an object approaches infinity as its speed approaches c, an object that has mass cannot travel at the speed of light, c. Only objects which have zero mass can travel at the speed of c. Light particles (photons) are massless.

• If neutrinos are massless, then they would also travel at the speed of light, c. This means that once we take into account the fact that neutrinos are produced before the optical outburst in a supernova, then the neutrinos from SN1987A should have arrived at precisely the same time as the photons arrived.

  Let's consider SN1987A for a second.

  So, even for the generous estimate for the lag of 1 day (which is not inferred by the data at all), the speed of the neutrinos was exceedingly close to c and there can be no inference from this exercise that neutrinos have mass.

• There is another test we can apply which may be more sensitive. If neutrinos are massless, then they will travel at the speed of light, c. This is interesting because this would also mean that neutrinos travel at one speed, c, independent of how energetic they are (this is like a photon). If neutrinos have mass, however, then how fast they travel depends upon their energy (this is like more normal particles (i.e., particles with mass) like electrons, protons, neutrons, ...)
  • This has the consequence that the more energetic neutrinos should arrive before the less energetic neutrinos. Is this effect found in the data? Let's see.
  • Well, maybe. But it is not compelling. But, anyway, carrying through on the exercise says that if the entire spread of ~12 seconds in arrival times reflects different propagation speeds because the neutrinos had different energies, then we infer that the mass of a neutrino cannot exceed

    mass(neutrino) ~ 0.002 - 0.004 % of the mass of an electron

    This is an exceddingly small number but Terrestrial experiments still place stricter limits on the mass of a neutrino. However, as Colgate put it, if we get a nearby supernova from which we will detect many more neutrinos, then we can expect to get a much better estimate of the maximum possible mass of the neutrino.