# Relation between total energy and rest mass

1. Jan 15, 2010

### ZirkMan

Is there a direct relation between the relativistic mass (total energy) and rest mass?

In other words, can we say a proton has higher rest mass than an electron because a proton-antiproton annihilation would produce that much more energy than electron-positron one? And the ratio of energy content of these two annihilations will be the same as respective ratios of their rest masses?

Judging from http://www.wolframalpha.com/input/?i=proton+electron this is true and the ratio of their MeV/c^2 masses to their kg masses is the same.

Then why do we need the Higgs when we know that rest mass is directly proportional to the total energy contained in a particle?

2. Jan 15, 2010

### jety

We know about the ratios you mentioned because we measured them, not because a theory predicts them. "The Higgs", as you call it, is a theoretical effort to explain the mechanisms standing behind the phenomena of particles having mass.

In other words, we have a phenomenological description, not a theoretical explanation( as of yet).

3. Jan 15, 2010

### ZirkMan

Don't we? And what about high energy gammas pair production, where for E > 1.022 MeV an electron-positron pair is formed which then usually annihilates into 2 gammas of energy ~0.511 MeV. See: https://www.physicsforums.com/showthread.php?t=366068 Isn't this a direct energy to rest mass translation? We can infer from this that 0.511 MeV of Energy is equal to 9.109382x10^-31 kg of rest mass. This also predicts that for a proton creation you will need at leas 938.27203 MeV of energy. Does the Higgs mechanism try to explain why this total energy creates exactly the proton and not for example a super heavy neutrino or something else?

4. Jan 15, 2010

### jety

I don't know, maybe someone else does.

5. Jan 15, 2010

### vela

Staff Emeritus
We know how much energy turns into how much mass and vice versa, but what we don't know is why mass exists in the first place. Why aren't all particles massless like the photon? When you write down the equations that describe a fundamental interaction, if you put in a term that represents the mass of a particle, it ruins the symmetry needed to describe the interaction, so it seems like all particles should be massless. But obviously, that's not the case. The Higgs mechanism explains why some particles gain this property we refer to as mass, and it does so without ruining the symmetries needed to describe the fundamental interactions.

6. Jan 15, 2010

### ZapperZ

Staff Emeritus
Thinks about it this way. e-p have mass. Yet, when they annihilate each other and produce photons, those photons have no mass. Yet, the energy accounting remains constant, i.e. both before and after, the total energy is identical. The conversion of the energy does not account for why one form of it has mass, while the other does not.

Zz.

7. Jan 15, 2010

### ZirkMan

Isn't this because the energy contained in them is in a mode where it can move with slower relative velocities than c? Even a photon has momentum (and therefore certain inertia) which is one aspect of mass. Even a photon is affected by gravity. What aspect of mass we can't explain?

8. Jan 15, 2010

### ZirkMan

When the two antiparticles collide (with their relative velocities always lower than c) isn't all their mass converted into the kinetic energy of the radiation? Photons don't have rest mass because all their energy is in a form of kinetic energy and it cannot move slower than c in that mode (in vacuo). Therefore by definition of rest mass they should have rest mass 0 because they cannot exist at rest without transformation into an energy mode that can. And when that transformation occurs some of that pure kinetic energy is converted into rest mass (c-v). Or not?

9. Jan 15, 2010

### vela

Staff Emeritus
But why should that "mode" exist at all? Why do some particles have mass and others don't? Why does the electron have a mass of 0.511 MeV/c^2 as opposed to, say, 1 MeV/c^2? There are all sorts of things about mass that aren't understood.

10. Jan 15, 2010

### ZirkMan

Yes, these are good questions. But is this what the Higgs mechanism is trying to answer? If yes, then OK, I understand its ambition. But I thought its ambition is just explain why there is a rest mass at all. And I just don't see why we need the Higgs to explain just that.

11. Jan 15, 2010

### vela

Staff Emeritus
There's essentially no difference between those questions.

I'm not sure how you think $E=mc^2$ explains the phenomenon of rest mass.

12. Jan 15, 2010

### ZapperZ

Staff Emeritus
Er... rest mass is an invariant concept. Something could be moving at 0.999c, and STILL has the same rest mass value.

A photon has zero rest mass. An electron has a non-zero rest mass. When an an energy equivalent to the electron's rest mass is converted into photons, there's no mass. In the search for the Higgs, it isn't really a "particle" that they are looking for, but rather symmetry-breaking process.

Edit: just to make sure we are clear on this. The higgs mechanism that has been in the news lately is the mechanism that might endows leptons (or those participating in the electroweak symmetry breaking) with mass. It doesn't explain why, say, nucleons, have mass. The latter have been speculated to have mass due to how gluons couple with the quarks (i.e. QCD takes over). Different mechanism. See, for example, S. Dürr et al., Science v.322, p.1224 (2008).

Zz.

Last edited: Jan 15, 2010
13. Jan 15, 2010

### ZirkMan

Yes, once you make it stop again it will return to the same value of its rest mass. No problem with this.
Exactly, and my question is why do you expect something that cannot be at rest by principle to have a rest mass? How would you measure it?
Thank you for this information, I didn't know this.

14. Jan 16, 2010

### ZirkMan

Actually I was not right not having a problem with this.
I think it all comes down to the question of (non)invariance of rest mass. In a previous thread see https://www.physicsforums.com/showthread.php?t=368133 we have discussed wheather there is something that is invariant in the relativity theory. We came to conclusion that no, that total energy is conserved but not invariant. And now this concept of invariant rest mass has been pointed out.

Can anybody please describe how can rest mass of particle with 0,99c relative velocity to the frame of measurment be invariant (not changed) to the rest mass of the same type of particle at relative rest? How would you make such measurment (calculation)? Maybe I just don't understand what the rest mass is.

Last edited: Jan 16, 2010
15. Jan 16, 2010

### Char. Limit

Rest mass, I believe, is the mass when velocity is 0. I'm pretty sure that doesn't change.

16. Jan 16, 2010

### jety

When an e-p pair turns into two photons, their rest mass (energy at rest) is given to the photons, as well as the rest of their energy, that is "stored" in the form of kinetic, and potential energy. This comes from the law of energy conservation:
E(rest masses)+E(kinetic energies)+E(potential energies)=E(g1)+E(g2)
where g1 and g2 the two photons, respectively. As you can see, the rest mass is a constant, and does not depend on velocity.

17. Jan 16, 2010

### ZirkMan

That's what I thought too. But then it is not invariant because the frame where relative velocity is 0 is only one frame out of many. Change a frame and the relative kinetic energy will change and with it the total (measured) energy. But rest mass being invariant should not change. So if it is really invariant what you wrote should not be true because invariant means "that which doesn't change in any frame of reference under the given transformation".

18. Jan 16, 2010

### ZirkMan

But when the velocity is > 0 the rest mass becomes practically indistinguishable from other forms of energy which add to the total energy. Again, how would you measure (calculate) rest mass for v>0 without bringing the measured object back to v=0 and measure its rest mass there?

19. Jan 16, 2010

### jety

One calculate the kinetic and the potential energies of the particles, knowing their speed it should be simple, then measure the energies of g1 and g2. The difference between the two is the rest mass (of the two particles)
E(rest masses)=E(g1)+E(g2)-E(kinetic energies)-E(potential energies)
since the electron and the positron have equal masses,

E(e)=E(p)=E(rest masses)/2

20. Jan 16, 2010

### ZirkMan

In other words, Rest mass is all the energy that is left once we subtract the energy related to motion = rest energy.

Let's come back to the original problem of photons not having rest mass and this being a big problem for which we don't have a theory yet.

Photons as we know is energy in a frame with unchanging relative constant velocity c (in vacuo).
Since it has been proven many times that you cannot change this relative velocity to any other value than c (in vacuo) in any frame of reference you cannot directly and by experiment measure its rest mass. If you do it by calculation using the method where you subtract all energy related to motion you will get the value of its rest mass (energy) being 0.

That means that even if photons would have a non-zero potential rest mass all their energy is in a form of kinetic energy. Thus we have a mechanism where rest mass is capable of converting itself into kinetic energy up to the point where rest mass=0 and vice versa where purely kinetic energy is transformed into a non-zero rest mass as demonstrated in the gamma electron-positron pair creation.

The total energy in this transformation is conserved but the rest mass is not because it is not invariant in respect to transformation to frame of refference where v=c. Does this solve the particles with mass and massless particles problem? You tell me.