# Mass-less particles? How can that be?

1. Oct 30, 2011

### narrator

Hi,

Not sure if this is the correct forum for it. Pls move if not.

I've read and heard several times about mass-less particles, such as photons, and that in some calculations, you give them mass just as an intermediate step. But my question is, how can any particle be mass-less? Or is it that their size is so insignificantly small that any mass would be immeasurable?

Also, I imagine that even subatomic particles must have mass, even if it can't be measured. Or is "mass" somehow in the nature of how particles react to each other?

Thanks

2. Oct 30, 2011

### Staff: Mentor

Moved to the relativity forum because massless particles are a feature of relativistic mechanics.

3. Oct 30, 2011

### phinds

Mass, in the sense that you almost certainly mean it, is what is more formally called "rest mass". Photons don't HAVE a rest mass because they are never at rest. Photons have energy and E=mc^2 can be looked at the other way round to say m = E/c^2 so they have an equivalent mass.

EDIT: by the way, I find it interesting that your bugaboo is mass-less particles, whereas mine is point particles. Because of what I said above, I'm perfectly fine with particles that have no rest mass, but elections have mass and they are"point particles" so have no dimensions. That's the one that makes MY head hurt.

4. Oct 30, 2011

### Sam Gralla

The notion of a massless particle comes from quantum field theory. You shouldn't think of it like a normal particle except without mass. Instead, it's an excitation of a quantum field.

In general relativity the notion of a "photon" is really a stand in for "the geometric optics limit of Maxwell's equations". This topic is not adequately covered in most textbooks, but Wald gives a very clear treatment in chapter 4.

5. Oct 30, 2011

### Sam Gralla

All this stuff makes people's head hurt because textbooks are sloppy and don't explain things clearly. "Point particle" is just a stand-in for "body whose size is small compared to the curvature scales of its surroundings". True point particles (i.e., delta function stress energy on a worldline) do not exist in general relativity. (There is a theorem by Geroch and Traschen.) Mathematically, this is because the equations are nonlinear. Physically, this is because collapse to a black hole must occur before a point particle could be made.

6. Oct 30, 2011

### Matterwave

There is, in fact, a problem with self-energy for point particles (they are infinite...), but the fact that no information can travel faster than the speed of light would seem to limit you to point particles because if you had a particle with some physical extent (even miniscule), then the fact that that particle must act like a rigid body would mean information transfer across the particle's width instantaneously.

I'm sure there's a resolution somewhere, but indeed this is a conundrum.

7. Oct 30, 2011

### phinds

So you are saying that an electron has non-zero radius? I'm not sure "radius" can even be applied to an electron since it isn't actually a little tiny billiard ball, but I'm old school clasical physics and still have a hard time w/ quantum ideas.

8. Oct 30, 2011

### Sam Gralla

Oh, no, an electron is another intrinsically quantum object--an excitation of a quantum field. The best classical physics can do is consider an extended body that is small compared to the scale of variation of the external field. Since people have done this and found that the Lorentz force law holds, one would expect/hope that electrons follow this law, too (which is of course experimentally verified). But you can't derive electron motion from classical physics. The best solution really would be to have a QED-based derivation in the classical limit, but as far as I know nobody has done that satisfactorily.

Sorry if my first statements weren't clear.

9. Oct 30, 2011

### atyy

10. Oct 30, 2011

### phinds

OK, that makes sense to the extent that I can follow it (limited) but then WHY are electrons called "point particles" if they aren't really points? It seems very misleading (of course that wuoldn't be the first scientific term to be very misleading big bang)

11. Oct 30, 2011

### Sam Gralla

ooh somebody citing my papers! =)

The first of those summarizes our attitude pretty well. Indeed in footnote 4 we say "Of course, the body of most interest to experimental phenomena, the electron, is an intrinsically quantum mechanical object. Our results will apply to electrons only to the extent that a classical description of the motion of an electron can be justified." In the rest of the paper we just talk about smooth distributions of classical charged matter.

phinds wrote:

"but then WHY are electrons called "point particles" if they aren't really points? It seems very misleading (of course that wuoldn't be the first scientific term to be very misleading big bang)"

Well, the term "point particle" is used in a lot of different ways by a lot of different people. Particle physicists sometimes use it just to mean that electrons are not composite particles (at least, no more fundamental structure has yet been discovered). But I agree that it's bad terminology, not least because in quantum mechanics particles would at best only be "points" if they happened to be in a position Eigenstate.

But at least within classical physics, point particle almost always means delta-function stress-energy supported on a worldline (i.e., a delta function in space but not time), and you won't catch too many people saying "electrons are point particles". Instead, you'll hear "we model the electron as a point particle", which is much more clear/sensible/correct.

12. Oct 30, 2011

### phinds

Thank you Sam, that was helpful.

13. Oct 30, 2011

### atyy

Thanks Sam. I especially enjoyed the first of those two papers. Too bad I'll never be able to cite them in my work - I'm a biologist, and the closest thing to Maxwell's equations I use is Thevenin's theorem.

14. Oct 30, 2011

### narrator

I don't recall hearing the term "point particle" before. What is the term meant to infer? It makes me think of a speck that is too small for my eyes to give it any dimension.

Thanks for the above answers folks. Much of the discussion provokes further thoughts. One that stood out as I read, relates to "rest mass", or more particularly, electrons, since they are never at rest. What is it that makes them perpetually move?

15. Oct 31, 2011

### Phrak

Massive particles? How can that be?

The OP asks why particles are massless. I want to know how they could possibly be massless.

16. Oct 31, 2011

### Chalnoth

Well, mass doesn't have anything to do with size. Basically, in particle physics we typically separate the energy of a particle into two components: the energy internal to the particle and the energy due to the particle's motion.

The energy internal to the particle is its rest mass, which is usually just called "mass" these days. The energy due to the particle's motion is its kinetic energy. You can get the right answer for the total energy of a particle by using this equation in special relativity:

$$E^2 = m^2 c^4 + p^2 c^2$$

Here $E$ is the total energy, $m$ is the particle's mass, and $p$ is the particle's momentum. The velocity of a particle can be extracted as follows:

$$v = {p c^2 \over E}$$

You can see that this works pretty easy for a classical particle that has a mass energy much, much larger than its kinetic energy, because $p=mv$ and $E = m c^2$ when $v$ is small:

$${p c^2 \over E} = {mv c^2 \over mc^2} = v$$

With these definitions, your zero-mass particle simply has $E = pc$, which is another way of saying that its energy is equal to its momentum, which, if we plug it into the velocity equation means:

$$v = {p c^2 \over E} = {p c^2 \over pc} = c$$

Does that help you to see what is meant by mass in relativity, and how we can deal with massless particles?

17. Oct 31, 2011

### narrator

So it's a convention of the math rather than an actuality?

18. Oct 31, 2011

### Chalnoth

Sorta kinda.

Many particles have zero rest mass, meaning they have no internal energy. Most of the time we simply refer to rest mass as mass.

19. Oct 31, 2011

### narrator

Basic question, I know, but what constitutes having or not having internal energy? On the surface, the notion makes sense, but that could just be my preconceptions.

20. Oct 31, 2011

### Chalnoth

Generally it's just energy that is not related to the particle's motion, and could come from a number of sources.

For example, most of the mass of a proton is mostly not made up of the mass of the quarks, but instead it is in the binding energy of the quarks. One extremely rough description of what's going on here is that you have quarks and the gluons between them, and those gluons act sort of like "springs", and the energy due to tension on those springs makes up most of the mass of the proton. This description isn't entirely correct, but I can't think of a better description without going into the quantum weirdness in detail.

Another thing that can give particles mass is an interaction with an external field. The most mundane example of this is electrons in a solid. When an electron moves through a metal, for instance, its negative charge pushes on the positive charges of the nuclei. Depending upon the specific properties of the solid in question, upon how the electron and the motion of the atoms interact with one another, you can end up with an effective mass of the electron that is very, very different from the electron's mass in free space. In some cases, it can even have a mass as great as that of a proton (which has about 2000 times the mass of an electron in free space).

This is similar, at least in concept, to the idea of the Higgs mechanism whose interaction gives particles the mass which we usually think of as being intrinsic (as a side note, it turns out that if you try to do quantum field theory with particles that have intrinsic masses, you end up with a contradiction...so it is generally expected that all particles are intrinsically massless, and their masses only arise as a result of interactions).