# Mass-less particles? How can that be?

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

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

phinds
Gold Member
2021 Award
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

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.

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.

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.

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.

Matterwave
Gold Member
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.

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.

phinds
Gold Member
2021 Award
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.

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.

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.

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.

phinds
Gold Member
2021 Award
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.

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)

Why not? I thought you did that here? I guess I misunderstood?
http://arxiv.org/abs/0905.2391
http://arxiv.org/abs/1002.5045

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.

phinds
Gold Member
2021 Award
Thank you Sam, that was helpful.

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.

Well, the term "point particle" is used in a lot of different ways by a lot of different people.

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?

Massive particles? How can that be?

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

Chalnoth
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?
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?

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

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

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

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.

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.

Chalnoth
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.
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).

atyy
The classical counterpart of a photon is an electromagnetic wave.

Electromagnetic waves travel at the same speed regardless of their frequency - this called "no frequency dispersion".

Through quantum mechanics, massive particles have wave counterparts with frequency dispersion that is mathematically related to their classical mass.

Since an electromagnetic wave has no frequency dispersion, its corresponding quantum particle, the photon, is said to be massless.

Electromagnetic waves and photons do carry energy and momentum.

As a technical note, it is possible for massless classical particles to exist. However, the reason we relate classical electromagnetic waves to massless particles is best seen through quantum mechanics.

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...so it is generally expected that all particles are intrinsically massless, and their masses only arise as a result of interactions).

Thanks Chalnoth.. pitched right at my level too :)

Seems my preconceptions were heading somewhat in the right direction. I was thinking of the proton and electron (and even the neutron) and how they act in concert like little engines because they interact with each other and with neighboring particles, and are perpetual because of conservation of energy (And I don't imagine there is friction, as we normally understand it, at the atomic level). Similarly with quarks and gluons (although I am given to understand that conservation of energy is perhaps not so apt at that level).

So, is the proton without an electron, or the quark without a gluon, considered at rest? Or is its potential still in the mix somehow?

Massless means it has no mass at rest. Consider the property of photon which is a wave packet in EM field. Imagine that if there is no propagation it's just plane EM field which I don't think have any discernable mass.

While travelling it is considered to have equivalence momentum which is E=pc.

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).

Does the Higgs field itself have nonzero rest mass?

Chalnoth
Does the Higgs field itself have nonzero rest mass?
Yes. Otherwise we would have seen it. I am unsure as to where this mass is expected to come from, though an obvious way would be a self-interaction with the Higgs field.

Yes. Otherwise we would have seen it. I am unsure as to where this mass is expected to come from, though an obvious way would be a self-interaction with the Higgs field.

Yes? I did ask whether it were non zero rather than zero, so I'm confused. Perhaps you inverted the answer to my question(?).

Anyway, we can ask both whether the Higgs field is intrinsically massive, or acquires mass, itself through self interaction. I'm not sure how you answered these.

Chalnoth
Yes? I did ask whether it were non zero rather than zero, so I'm confused. Perhaps you inverted the answer to my question(?).

Anyway, we can ask both whether the Higgs field is intrinsically massive, or acquires mass, itself through self interaction. I'm not sure how you answered these.
The Higgs field is a scalar field. Scalar fields act like force carriers. In order for us to not see this force (which we don't), the Higgs particle must have non-zero rest mass. In fact, it must have a pretty large mass.

But this doesn't mean that it has intrinsic mass. I don't think anything can have intrinsic mass in quantum field theory.

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

What forum was it in? It's a feature of quantum mechanics. Technically speaking, pure relativistic mechanics doesn't model massless particles, instead it has waves and particles that have mass. See also the reply by atyy.

PAllen
What forum was it in? It's a feature of quantum mechanics. Technically speaking relativistic mechanics doesn't have massless particles, instead it has waves and particles with mass. See also the reply by atyy.

That depends on point of view. One can take SR circa 1905 and seamlessly add tachyons (with various well known isuues). Similarly, one can seamlessly add massless particles, in a unique, consistent way. In another thread on this, it was shown how SR perfectly accommodates even massless charged particles (which don't exist per standard model); that is, there is a consistent way to treat force on charged massless particles in SR. None of these extensions to 1905 SR involve QFT. Thus, in the sense of being non-quantum, they are usually considered classical SR.

If you relate energy to frequency of photons, you are obviously sneaking in a quantum phenomenon. However, you can bring this in, without bringing in the whole machinery of QFT.

So my way, of looking at this is that as long as you don't deal in quantum fields, you are doing classical SR. This is admittedly not the only way of looking at it, but it is a common, accepted, way of looking at it.

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The Higgs field is a scalar field. Scalar fields act like force carriers. In order for us to not see this force (which we don't), the Higgs particle must have non-zero rest mass. In fact, it must have a pretty large mass.

But this doesn't mean that it has intrinsic mass. I don't think anything can have intrinsic mass in quantum field theory.

The idea makes some sense, even if it is quatum mechanics. Is there a model for how the Higgs field itself has mass, or simply a required parameter of some sort?