Particle Physics Question?

Question

If we know that the rest mass of any particle is E = mc^2 then can somebody explain the following:

It was observed that a pion decays into a muon, and that their momentum was conserved. However their energy was NOT conserved. Thus it was hypothesized that there is another product of decay to conserve the energy. This new particle had to have zero mass for it to have no momentum - since momentum = MV. Thus they come up with the nuetrino to conserve the energy. However, since the nuetrino has no mass, how can it have energy? - Remember, E = mc^2 !! This has been puzzleing me for a while now!!! any help at all would be great.

Answer 1

Two points:

1. It was thought at the time of its introduction that the neutrino had no mass.

However, we now know that there are three types of neutrino, that they can in fact "oscillate" between different types, and that their EXTREMELY SMALL masses --- as well as the material they may pass through --- play a significant role in the way and the rate at which they do change their character.

(In fact, SOME mass, no matter how small, is actually needed in the currently accepted theory of "neutrino oscillation." Without any mass, it simply couldn't work. So the logic is that BECAUSE they have mass, "oscillation" is possible; conversely, the detection of "oscillations" CONFIRMS that they have mass --- but it doesn't CAUSE them to have mass, the causal connection is quite the reverse.)

This also means that neutrinos DON'T travel with speed 'c', but rather with speeds generally VERY, VERY LITTLE LESS THAN 'c' for the energies generally associated with their production and/or detection.

How close to 'c' they still travel for detectable energies was first checked really tightly in an ASTRONOMICAL CONTEXT! (In fact the "observations" themselves were done, extremely serendipitously, by after-the-fact examination of results found at a certain time in underground physics experiments. Those particle physics experiments were trying to set limits on the proton's lifetime.)

The circumstances were these: neutrino bursts of very short duration were received from Supernova1987A at essentially the same time, at THREE different places on Earth. Once it was realized that neutrinos might possibly have been detected from this supernova, they were looked for and found in the records of the particle detection experiments. The set-ups also recorded both energies and arrival times, so that any spread-out in time could be compared with their energies, all of this presumed spreading-out in time (only of order seconds or fractions of a second) having taken place while travelling for ~ 155,000 years from the Large Magellanic Cloud to Earth --- truly a mind-blowingly small separation. The limits placed on that, and on the neutrino masses, were far tighter than those in any then existing terrestrial physics experiments.

Our understanding of neutrino physics really advanced around 1985-86 with the so-called MSW "neutrino oscillation" effect as an explanation of the solar neutrino problem. Much more recently, "neutrino oscillations" have finally been observed from both atmospheric neutrinos and from collections of calibrated neutrino-producing accelerators, in both cases with the neutrinos passing through different path-lengths in the Earth itself. This has enabled very much tighter limits to be put on neutrino masses.

2. Now going back to the original time of the neutrino's introduction. AS Einstein showed, any particle, whatever its mass, satisfies:

E^2 = p^2 c^2 + (m_0)^2 c^4,

Where E is its total energy , p its momentum, and m_0 its rest-mass.

You can see that when p = 0 (particle at rest) you get E = m_0 c^2. (Also, for slow speeds, you'd find E = m_0 c^2 + (1/2) m_0 v^2, the sum of rest-mass energy + Newtonian kinetic energy.)

But you can also put m_0 = 0 in this equation; that tells you that
E = pc, which was in fact already deduced from Maxwell's equations for electromagnetic radiation in the late 19th century. While that was first realized for electromagnetic waves, it applies, of course, to (massless) photons.

Thus, the argument employed at the time the neutrino was thought to have zero mass was that its momentum and energy were connected by E = pc.

By the way, the expression you give for momentum is itself only valid for slow speeds with v << c. At higher speeds, a particle with mass has momentum like that you wrote, but DIVIDED BY the ubiquitous relativistic factor of sqrt(1 - (v/c)^2). So, the momentum becomes exceedingly large as v --> c. (That's why it gets harder and harder to accelerate any more.)

However, for speeds very close to c, the dominant term in the (E, p, m_0) connection is given by E = pc with the m_0 term a very minor correction. If m_0 actually equals zero, that "correction" term drops out altogether, leaving you simply with E = pc.

And finally, a correction: it was ACTUALLY first observed that NEITHER energy NOR momentum were apparently conserved in certain reactions/decays. However, the idea that an UNSEEN particle might be involved led to seeing what could do the job, leaving the mass to be determined as part of this process. It then turned out that for the other measurements that could be made, the mass of the unseen particle would have to be absolutely minute, by the standards of the day, and its speed essentially indistinguishable from 'c.' It couldn't be the photon (somehow not seen), because this unseen particle also had to have spin 1/2. So, basically, that's how an idealized 'massless,' spin 1/2, neutral particle that only travelled at speed 'c' was postulated. (It was ultimately christened "the neutrino," or "little neutral one," by Fermi.)

I hope this explanation has helped.

Live long and prosper.

Answer 2

Massless particles like photons can indeed have momentum. For example, light hitting a surface can actually exert pressure on it even if photons have no mass. In quantum field theory, photons are the gauge bosons for the electromagnetic force, and actually do "exchange momenta". You must incorporate quantum physics to express momentum of massless particles.

The irony is that it turns out that neutrinos do have mass after all, as inferred from solar neutrino detection experiments. However, the existence of such tiny neutrino mass has no bearing on the pion decays leading to the deduction of the existence of neutrinos.

Answer 3

actually it was just found in the last few years that neutrinos do actually have a very miniscule mass. It was determined that neutrinos flavor oscillate, which creates a very tiny mass to them. the only way its been seen so far is by measuring the differences between the squares of the eigenstate mass. for example the difference in Eigenstate 1 and 2 is 0.000079 eV^2, which is incredibly tiny but does still have a mass.

Answer 4

Hi. The neutrino can ONLY travel at 'c' so it has no rest mass.