Massless particles

[elas]

yourdadonapogos

 

E = mc2 only applies in very specific circumstances. The correct equation remains E2=m2c4 + p2c2.

 

You did not mention that the Classical Electron Radius (CER) is one of those "very specific circumstances". Knowing that explains why it applies throughout my work; it is of course because in the CLF model the CER is used as the base measurement of particle radii. This is confirmed by using the same CLF equation to calculate proton and neutron radii, the result being in agreement with the proton and neutron radii found by experiment.

 

Listening helps, but, it does not always provide the complete answer; but, even a little help sometimes goes a long way.

[Riogho]

To answer the question implied by the title, the only "massless particle" is the photon.

 

The photon has no rest mass.

 

It does however, have mass.

[swansont]

The photon has no rest mass.

 

It does however, have mass.

 

No, it has relativistic mass. You have to define your terms. In physics, the default for mass is rest mass.

[Riogho]

Photons are traditionally said to be massless. This is a figure of speech that physicists use to describe something about how a photon's particle-like properties are described by the language of special relativity.

 

The logic can be constructed in many ways, and the following is one such. Take an isolated system (called a "particle") and accelerate it to some velocity v (a vector). Newton defined the "momentum" p of this particle (also a vector), such that p behaves in a simple way when the particle is accelerated, or when it's involved in a collision. For this simple behaviour to hold, it turns out that p must be proportional to v. The proportionality constant is called the particle's "mass" m, so that p = mv.

 

In special relativity, it turns out that we are still able to define a particle's momentum such that it behaves in well-defined ways that are an extension of the newtonian case. The vector p is no longer proportional to the vector v (although they do both grow or shrink together), but these two vectors do still lie in the same direction; so we can define the ratio of the length of p to the length of v to be the particle's "relativistic mass" mrel. Thus

 

p = mrelv .

 

When the particle is at rest, its relativistic mass has a minimum value called the "rest mass" mrest. The rest mass is always the same for the same type of particle. For example, all protons, electrons, and neutrons have the same rest mass; it's something that can be looked up in a table. As the particle is accelerated to ever higher speeds, its relativistic mass increases without limit.

 

It also turns out that in special relativity, we are able to define the concept of "energy" E, such that E has simple and well-defined properties just like those it has in newtonian mechanics. When a particle has been accelerated so that it has some momentum p (the length of the vector p) and relativistic mass mrel, then its energy E turns out to be given by

 

E = mrelc2 , and also E2 = p2c2 + m2restc4 . (1)

 

There are two interesting cases of this last equation:

 

If the particle is at rest, then p = 0, and E = mrestc2.

If we set the rest mass equal to zero (regardless of whether or not that's a reasonable thing to do), then E = pc.

 

In classical electromagnetic theory, light turns out to have energy E and momentum p, and these happen to be related by E = pc. Quantum mechanics introduces the idea that light can be viewed as a collection of "particles"--photons. Even though these photons cannot be brought to rest, and so the idea of rest mass doesn't really apply to them, we can certainly bring these "particles" of light into the fold of equation (1) by just considering them to have no rest mass. That way, equation (1) gives the correct expression for light, E = pc, and no harm has been done. Equation (1) is now able to be applied to particles of matter and "particles" of light. It can now be used as a fully general equation, and that makes it very useful.

 

Because the energy of a particle just equals its relativistic mass times c2, physicists have learned to economise the language by only ever referring to a particle's energy. When they use the term "mass", they mean rest mass. This is purely a linguistic convention. When the two sorts of mass are referred to together, relativistic mass is usually written m and rest mass is written m0. But when only rest mass is being used, then the word "mass" is assumed to mean rest mass, and it tends to be written simply as m.

[Mr Skeptic]

No, it has relativistic mass. You have to define your terms. In physics, the default for mass is rest mass.

 

Fred56, remember when I said you should say "relativistic mass" when you meant "relativistic mass"? This is why. Using that one extra word will save all of us the annoyance of much disagreement and using a whole lot more words.

[Fred56]

So the 'correct' term is "equivalent relativistic mass", if referring to photons of energy? "mass equal to" doesn't cut it? Unless you're Albert Einstein?

This might be why cosmologists don't refer to mass very often...

(please excuse any sarcastic tone, I really can't help it -and they won't let me out of the ward)

[swansont]

You have to drop the notion of "If Einstein said it, it must be so." Science is a group effort. Albert wrote those papers a hundred years ago and a lot of refinement has happened since.

 

Yes, scientists can be anal about such things. We try not to say speed when we mean velocity, (and vice versa) or transpose heat and thermal energy, and a bunch of other terms. They aren't interchangeable, and you can get the wrong answer (both numerically and conceptually) if you use the wrong term.

[Mr Skeptic]

I'd use "equivalent mass" and "equivalent energy" only if I were converting mass to/from energy.

[elas]

swansont

 

You have to drop the notion of "If Einstein said it, it must be so." Science is a group effort. Albert wrote those papers a hundred years ago and a lot of refinement has happened since.

 

Yes, scientists can be anal about such things. We try not to say speed when we mean velocity,

 

So what do we mean when by the term mass, According to Jammer in "Concepts of Mass" this is the unanswered question.

Taken together with MacGregor's "the Enigmatic Electron" where the Classical Electron Radius is used as a base measurement for particle radii and you have an argument that supports the sort of ideas developed in my work, now confined to the Junk Forum. I explain mass and energy on

http://69.5.17.59/lnr%20E.pdf

This meets the demands of Jammer, confirms the ideas of MacGregor, and produces the same result as Einstein's short equation; the equation that applies to the electron.