Relation between total energy and rest mass

[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?

 

[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).

 

[ZirkMan]

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).

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?

 

[jety]

I don't know, maybe someone else does.

 

[vela]

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.

 

[ZapperZ]

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?

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.

 

[ZirkMan]

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?

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?

 

[ZirkMan]

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.

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?

 

[vela]

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.

 

[ZirkMan]

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.

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.

 

[vela]

But why should that "mode" exist at all? Why do some particles have mass and others don't?

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.

There's essentially no difference between those questions.

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

 

[ZapperZ]

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?

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.

 

[ZirkMan]

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

Yes, once you make it stop again it will return to the same value of its rest mass. No problem with this.

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.

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?

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.

Thank you for this information, I didn't know this.

 

[ZirkMan]

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

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.

 

[Char. Limit]

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

 

[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.

 

[ZirkMan]

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

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".

 

[ZirkMan]

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.

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?

 

[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

 

[ZirkMan]

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

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.

 

[Vanadium 50]

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.

This is not a big problem. And we've had a theory since 1905.

 

[ZirkMan]

This is not a big problem. And we've had a theory since 1905.

So why do we need the Higgs boson to give particles mass?

 

[jety]

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.

Mass is not as easy concept as it may seem.

Photons don't have rest mass. What makes You think that they do? They do, however, have mass, but we can't call it rest mass, that would be incorrect.
Evidently, photons interact with celestial bodies through gravitation. Therefore, they have mass. True, we cannot measure it directly, but we can measure it indirectly. That also proves that photons have mass.
How can we tell that this mass is not a rest mass? At this point I have to clarify something, in order to answer that.

(In physics, mass (from Ancient Greek: μᾶζα) commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: inertial mass, active gravitational mass and passive gravitational mass. In everyday usage, mass is often taken to mean weight, but in scientific use, they refer to different properties.[wikipedia:mass]

Don't let yourself confused, active gravitational mass is the same property as passive gravitational mass. They both determine the force, at which two heavy objects are pulling into one another. But this kind of property is now irrelevant. What matters now is the property to which we refer to as inertial mass. )

Inertial mass is the property of an object to resist acceleration. When an object with inertial mass is accelerated, it not only resists acceleration, but even gains inertial mass. As we come closer to the speed of light, inertial mass goes to infinity(according to special realativity).
Inertial mass = (rest mass @ zero speed)

Do photons have inertial mass? NO! They don't resist acceleration at all. They are born at the speed of light. I think that if there is a property that tells us if a particle can be accelerated, then photons simply lack this property. Let me illustrate this.

property rest mass | gravitational mass | can be accelerated
photons - + -
particles + + +

Photons don't have rest mass, because they don't resist acceleration.

How can we (indirectly) measure the mass of photons? We can measure their change of impulse in the case of the Compton-effect and Deflection from a mirror. Neither of these processes require the absorbtion of the photon. Since p(g)=m(g)*c
m(g)=p(g)/c
It is a bit more difficult, but if you don't believe me, research for yourself.

P.S. It may be true that photon is a somewhat mis-taken particle. The wiki tells that each of the three masses are equal, but it does not say anything about the photon. Is this statement true for the photon? I would be glad to hear some opinion on that. I think not, because photons, as opposed to non-massless particles, respond to external forces differently.
When a force is applied to a photon, it changes wavelength, not speed. When a force is applied to a particle with nonzero rest mass, it resists acceleration. It is a conceptual difference, and it is important, because this difference is in the root of Your problem.

 

[ZirkMan]

jety, thanks for a nice summary of what has been said. You are right that we need to hear from someone whose knowledge is beyond of what wikipedia can tell us.

We still don't know what kind of mass is the problem the Higgs mechanism is trying to solve and what is its relation to the total energy and rest mass.

 

[jtbell]

Photons don't have rest mass. What makes You think that they do? They do, however, have mass, but we can't call it rest mass, that would be incorrect.

Many "lay-people" seem to be drawn to the idea of "relativistic mass of a photon" (via $E = hf = mc^2$) like moths to a candle flame. Nevertheless, I have yet to find any modern scientific literature (journal articles, textbooks, etc.) that use this concept of photon mass.

Evidently, photons interact with celestial bodies through gravitation. Therefore, they have mass.

No. In general relativity, gravitation is an effect of spacetime curvature. An object does not need to have mass in order to "follow" the curvature of spacetime. It doesn't even need to have mass in order to "produce" spacetime curvature, which comes from the stress-energy tensor, whose components arise from momentum and energy.

 

[jety]

Therefore, the very principle of mass becomes useless in terms of general relativity.

 

[ZirkMan]

Many "lay-people" seem to be drawn to the idea of "relativistic mass of a photon" (via $E = hf = mc^2$) like moths to a candle flame.

If nothing else, they gain some mass while flying around it and some energy when burned. Finally there is nothing left of them but massless radiation

Anyway, I found a nice FAQ on the topic of mass of a photon here: http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html

As for the Higgs mechanism, it seem to be a mathematical construct to "explain why the Z and W particles which carry the Weak Interactions are so heavy while the photon which carries Electromagnetic forces is massless" (which is not because you can bring it to rest and measure its rest mass in a form of a real electron created from it a moment ago). So the Higgs boson and field will remain a theoretical math issue bearing no relation to reality .. until, of course, they find in the LHC. Then we have to readjust our lay-relativity world-view.

 

[ZapperZ]

If nothing else, they gain some mass while flying around it and some energy when burned. Finally there is nothing left of them but massless radiation

Anyway, I found a nice FAQ on the topic of mass of a photon here: http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html

As for the Higgs mechanism, it seem to be a mathematical construct to "explain why the Z and W particles which carry the Weak Interactions are so heavy while the photon which carries Electromagnetic forces is massless" (which is not because you can bring it to rest and measure its rest mass in a form of a real electron created from it a moment ago). So the Higgs boson and field will remain a theoretical math issue bearing no relation to reality .. until, of course, they find in the LHC. Then we have to readjust our lay-relativity world-view.

This is utterly backwards.

The Standard Model, as it stands, considers all of the elementary particles as being "massless". The different types of "Higgs" bosons are what endows them with mass (be it either all, or some). Finding the Higgs reaffirmed the track that the Standard Model is on. It is when it is NOT found that a lot of "readjustment" will have to be made, because it means that there's something that the Standard Model has severely missed.

Were you alive when the search for the top quark was going on? Try looking for some of the writings back then, and you'll see some similarity with that as well. So I'm not sure why this search for the Higgs has become an issue that deserve such derision.

You will note that if you try to measure the mass of an electron that is in your semiconductor, you will see that it has been endowed with a different mass than the bare mass. In fact, I can give you a heavy-fermion material and you'll find that the mass that you measure can be up to 200 times the bare mass! Analogous mechanism!

Zz.

 

[atyy]

Many "lay-people" seem to be drawn to the idea of "relativistic mass of a photon" (via $E = hf = mc^2$) like moths to a candle flame. Nevertheless, I have yet to find any modern scientific literature (journal articles, textbooks, etc.) that use this concept of photon mass.



No. In general relativity, gravitation is an effect of spacetime curvature. An object does not need to have mass in order to "follow" the curvature of spacetime. It doesn't even need to have mass in order to "produce" spacetime curvature, which comes from the stress-energy tensor, whose components arise from momentum and energy.

Try section 1.16, p24 of http://books.google.com/books?id=MuuaG5HXOGEC&dq=rindler+relativity&source=gbs_navlinks_s

 

[ZirkMan]

This is utterly backwards.

The Standard Model, as it stands, considers all of the elementary particles as being "massless". The different types of "Higgs" bosons are what endows them with mass (be it either all, or some). Finding the Higgs reaffirmed the track that the Standard Model is on. It is when it is NOT found that a lot of "readjustment" will have to be made, because it means that there's something that the Standard Model has severely missed.

This is actually a nice endpoint of the debate. It seems the more deeper one is trying to go armed only with logic and a sense of model consistency the more one hits theories which do no longer seem to describe observable reality but instead working mathematical models of that reality that seem to give the best predictions of experimental outcomes. Although the difference may seem subtle the departure from the observable (in sense of imaginable) to purely mathematical is a world of difference from which also this conflict of what is backwards and what is not arises.

Isn't the Higgs boson or for example virtual photon only a mathematical construct that helps the theory in some way but which has not any direct connection to observable and thus reality? No real Higgs bosons exists nor any real photons are being exchanged in the mitigation of the EM force. I think this is the root of the problem and even some physicists don't realize these things are not real in a sense that they can say "hey, there are those H. bosons that are real and are everywhere just like electrons in a electric spark and they give everything its mass". Or are they?

You will note that if you try to measure the mass of an electron that is in your semiconductor, you will see that it has been endowed with a different mass than the bare mass. In fact, I can give you a heavy-fermion material and you'll find that the mass that you measure can be up to 200 times the bare mass! Analogous mechanism!

Zz.

From my (observable) point of view what is real is mass=energy and change in mass is change in energy (or its form). Or is there a violation of this principle in this particular case? Isn't the mass gain of the electron directly proportional to its total energy change?

 

[ZapperZ]

From my (observable) point of view what is real is mass=energy and change in mass is change in energy (or its form). Or is there a violation of this principle in this particular case? Isn't the mass gain of the electron directly proportional to its total energy change?

What "observable"? If we use your own argument, I could turn this around and argue that this is nothing more than a mathematical construct as well! After all, the mass-energy change IS mathematical in description AND quantity. Furthermore, you buy into some classical field and not quantum field not for any physical reason, but simply based on a matter of tastes.

I think you give hand-waving argument too high of a status.

Zz.

 

[ZirkMan]

Yes, you are right, you could say that. Maybe the problem is that I cannot imagine how the e=mc2 is compatible with this other (Higgs) concept of mass. When I make such connection and the two models will reconcile the Higgs reality will become the Reality. But until then I have to hand-wave: Help me understand it :)