Hot and cold

[Michael]

And net momentum is unchanged while energy increases. If momentum is mass*velocity and energy is 0.5*mass*velocity^2, how did one remain the same while the other increased ... are my terms too classical?

I would not say that they are "too" classical, but rather that's the common way to express it. As I said before, I tend to prefer to think of it as an increase in internal kinetic energy that doesn't actually change the number of molecules, and therefore changes nothing related to "rest mass".

Since heat is essentially a photon, we're basically debating the whole "does a photon have rest mass" question all over again IMO.

What am I missing? Is it the "system" part? Maybe a system of particles would produce a different type of result. I'll need to ponder this a bit.

Essentially as I understand the argument, the basic claim is that while a single photon has no rest mass (just kinetic energy) a "system" (however that's defined) contains such mass. I guess I will need to read a few references on that idea to get a better handle on the concept.

 

[sfs]

That may very well be true, but do you have a reference for the suggestion that a "system" of photons has rest mass? I haven't read anything like that before.

Take a look at this wiki article section. (Or you could take my word for it -- I used to do this sort of thing for a living. This is basic relativistic kinematics.)

 

[sfs]

Uh. There's something very intriguing in what you've said here, but I'm not sure I've grasped it well enough yet to ask a question.

A "system" of photons has a rest mass. Hmm. Can you elaborate on what that "system" is?

A system is any set of particles that you choose to treat together. Consider a single neutral pion, sitting at rest. It has zero momentum, a mass of 135 MeV/c[sup]2[/sup] (which is how particle masses are generally expressed), and therefore an energy of 135 MeV. The pion decays into two photons, as they are wont to do. By conservation of energy and momentum, the entire system still has an energy of 135 MeV and zero momentum. Each photon has an energy of 67.5 MeV and a momentum of 67.5 MeV/c. The vector sum of the momenta is zero, however, since the two photons are emitted back to back. So the pair of photons still has a rest mass of 135 MeV, based on the definition of rest mass I gave previously.

Because energy and momentum are each conserved, and because the energy and the momentum determine the rest mass, the rest mass of a system is always conserved. (The rest mass is also an invariant, i.e. has the same value whatever reference frame it is observed from. So you would get the same rest mass if the pion had been traveling at 0.9c -- but the math would be a bit more complicated.)

And net momentum is unchanged while energy increases. If momentum is mass*velocity and energy is 0.5*mass*velocity^2, how did one remain the same while the other increased ... are my terms too classical?

This part is purely classical. The net momentum of the body that's being heated doesn't change, because the body's velocity hasn't changed. Suppose it's a glass of water you're heating. Each molecule of water will move faster as the temperature increases, meaning the kinetic energy in the water increases. But the momentum of the entire mass of water is still zero, because the glass is just sitting there in your microwave (or wherever). More formally, energy is a scalar quantity while momentum is a vector, so the energies of the molecules all add, while the vector sum can be zero.

Because, say we start with m = 0.5 and v = 0.5. So, p = 0.25. Then say after heating m = 0.6. If p doesn't change, then v = 0.25 / 0.6 = 0.4167. So, initially E = 0.0625 and finally E = 0.0521. So energy decreased, not increased.

Here you can't use the classical formula for energy, since you're dealing with a relativistic effect; the energy includes not just the bulk kinetic energy of the object, but the internal energy gained by heating. You're better off taking v and p to be zero, and then calculating the change in mass for a given change in energy, using the definition of rest mass.

 

[Resha Caner]

As I said before, I tend to prefer to think of it as an increase in internal kinetic energy that doesn't actually change the number of molecules, and therefore changes nothing related to "rest mass".

Ah, but either you didn't mention rest mass or I missed it. I wasn't thinking in terms of rest mass. If that is your criteria, I now understand you.

It's a bit like saying, yes a gas will occupy different volumes at different pressures, but I don't think of it that way because I'm only thinking of atmospheric pressure.

Anyway, at least I understand better what you're saying now.

 

[Resha Caner]

The net momentum of the body that's being heated doesn't change, because the body's velocity hasn't changed. Suppose it's a glass of water you're heating. Each molecule of water will move faster as the temperature increases, meaning the kinetic energy in the water increases. But the momentum of the entire mass of water is still zero, because the glass is just sitting there in your microwave (or wherever). More formally, energy is a scalar quantity while momentum is a vector, so the energies of the molecules all add, while the vector sum can be zero.

I must have been tired last night. I realized this very thing this morning, so I'm with you now.

 

[Resha Caner]

Take a look at this wiki article section.

Very cool. I think I get it, but it will take awhile before I can make my own paraphrase.

At this point, it seems similar to the previous post on vectors vs. scalars. A single photon is always moving at the speed of light. Were it to be brought to "rest", it's energy would be zero - hence, no rest mass.

However, if you have two photons whose velocity vectors sum to zero, that "system" is at "rest". Hence, the energy of that system (a scalar), can be equated to a mass scalar.

 

[Michael]

A system is any set of particles that you choose to treat together. Consider a single neutral pion, sitting at rest. It has zero momentum, a mass of 135 MeV/c[sup]2[/sup] (which is how particle masses are generally expressed), and therefore an energy of 135 MeV. The pion decays into two photons, as they are wont to do. By conservation of energy and momentum, the entire system still has an energy of 135 MeV and zero momentum. Each photon has an energy of 67.5 MeV and a momentum of 67.5 MeV/c. The vector sum of the momenta is zero, however, since the two photons are emitted back to back. So the pair of photons still has a rest mass of 135 MeV, based on the definition of rest mass I gave previously.

Because energy and momentum are each conserved, and because the energy and the momentum determine the rest mass, the rest mass of a system is always conserved. (The rest mass is also an invariant, i.e. has the same value whatever reference frame it is observed from. So you would get the same rest mass if the pion had been traveling at 0.9c -- but the math would be a bit more complicated.)

That was a very helpful explanation. Thanks.

 

[Wiccan_Child]

It doesn't have more mass, but it has more energy, which is analogous to mass. It's an ongoing question as to whether a very hot object of mass M is inherently heavier or more gravitationally attractive than a very cold object of mass M - that is, does energy warp space?

 

[Michael]

It doesn't have more mass, but it has more energy, which is analogous to mass. It's an ongoing question as to whether a very hot object of mass M is inherently heavier or more gravitationally attractive than a very cold object of mass M - that is, does energy warp space?

That seems to be the key question alright. I've been arguing that the total number of molecules doesn't change, therefore the actual "rest mass" never changes. I tend to look at it as a pure kinetic energy transfer. If however that extra energy "system" does in fact "warp" spacetime (say due to faster movement of particles inside the atom lattice), where does that leave us? That internal momentum might be considered a type of "mass" in the sense that it "may" have the potential to warp spacetime, albeit via "internal momentum", not simply particle pass. It's an interesting question IMO and it comes right back to your question of does that additional internal movement equate to a small additional warping of spacetime?

 

[sfs]

It doesn't have more mass, but it has more energy, which is analogous to mass.

By any definition of mass I've ever seen in physics, a hot object has greater mass than the same object when cooler -- provided Special Relativity is correct, which we have every reason to believe is the case at this point.

It's an ongoing question as to whether a very hot object of mass M is inherently heavier or more gravitationally attractive than a very cold object of mass M - that is, does energy warp space?

Could you provide some references to this as an ongoing question? Pretty much all of modern physics has to be wrong if energy doesn't contribute to gravitation: something like 99% of the mass of ordinary matter comes from binding energy, not from bare particle masses.

 

[Wiccan_Child]

By any definition of mass I've ever seen in physics, a hot object has greater mass than the same object when cooler -- provided Special Relativity is correct, which we have every reason to believe is the case at this point.

Relativity contradicts quantum mechanics, and physicists tend to hedge their bets on QM rather than GR.

Could you provide some references to this as an ongoing question? Pretty much all of modern physics has to be wrong if energy doesn't contribute to gravitation: something like 99% of the mass of ordinary matter comes from binding energy, not from bare particle masses.

Energy doesn't exist in a pure form, it's only the behaviour of particles (potential and kinetic energy). We can't weigh a glob of energy, but we can way a hot thing and a cold thing - and they're the same weight.

Also, binding energy doesn't provide anywhere near 99% of the mass of an object; its mass is mostly, if not entirely, the particle itself.

 

[sfs]

Relativity contradicts quantum mechanics, and physicists tend to hedge their bets on QM rather than GR.

More precisely, almost all physicists think that GR is a good low-energy approximation to some quantum theory of gravity. What you're suggesting, however, is that GR is completely wrong even in the low-energy/low-mass regime. Do you have any kind of theoretical or experimental justification for doing so?

Energy doesn't exist in a pure form, it's only the behaviour of particles (potential and kinetic energy). We can't weigh a glob of energy, but we can way a hot thing and a cold thing - and they're the same weight.

They should be the same weight, to within our ability to measure the weight, since the change in weight from heating is so small. Where energy changes are larger, as in nuclear reactions, however, we can indeed measure the change in mass, and it is exactly what is predicted by theory. Are you suggesting that the theory is completely accurate everywhere that we can test it, and suddenly stops working at lower energies? What kind of physics argument is that?

Also, binding energy doesn't provide anywhere near 99% of the mass of an object; its mass is mostly, if not entirely, the particle itself.

The mass of an object comes almost entirely from the mass of its constituent protons and neutrons. The mass of the proton is 938 MeV/c[sup]2[/sup]; the mass of its constituent up and down quarks totals just about 10 MeV/c[sup]2[/sup], with the rest being contributed by the QCD binding energy. That's 99% binding energy.

 

[Wiccan_Child]

More precisely, almost all physicists think that GR is a good low-energy approximation to some quantum theory of gravity. What you're suggesting, however, is that GR is completely wrong even in the low-energy/low-mass regime. Do you have any kind of theoretical or experimental justification for doing so?

No. I'm saying that GR contradicts QM: they are mutually exclusive. For instance, they contradict each other on the nature of a black hole's singularity (specifically, density).

They should be the same weight, to within our ability to measure the weight, since the change in weight from heating is so small. Where energy changes are larger, as in nuclear reactions, however, we can indeed measure the change in mass, and it is exactly what is predicted by theory.

Do you have a source for this?

Are you suggesting that the theory is completely accurate everywhere that we can test it, and suddenly stops working at lower energies? What kind of physics argument is that?

Since I'm not making that point, your question is moot.

The mass of an object comes almost entirely from the mass of its constituent protons and neutrons. The mass of the proton is 938 MeV/c[sup]2[/sup]; the mass of its constituent up and down quarks totals just about 10 MeV/c[sup]2[/sup], with the rest being contributed by the QCD binding energy. That's 99% binding energy.

Fair enough. It's been a while since I've mucked about with quarks

 

[sfs]

No. I'm saying that GR contradicts QM: they are mutually exclusive. For instance, they contradict each other on the nature of a black hole's singularity (specifically, density).

Sure, you're saying that, but you're also saying that GR is wrong that energy contributes to mass (something that is true in both GR and SR) and to gravity. This means you're saying that GR is not just wrong in the extreme limit, but completely wrong about pretty much everything, at all energy levels. That's a much more sweeping claim.

Do you have a source for this?

Look up Cockcroft and Walton. I think they measured the change in mass in their 1932 Proc Roy Soc London paper (A137: 229-242). That was a good part of the reason they won the Nobel Prize.

Since I'm not making that point, your question is moot.

Then what point are you making? You've chucked out two of the central theories of modern physics, Special and General Relativity: both of them imply the equivalence of energy and mass (in one case inertial mass, in the other gravitational mass). That in turn means you've wrecked QED and QCD; I suspect you've also eliminated every class of theory that's been proposed as an alternative to GR. So what exactly is it that you're suggesting?

Fair enough. It's been a while since I've mucked about with quarks

If energy isn't equivalent to mass, where do you think the mass in ordinary matter comes from?

 

[Resha Caner]

Love the debate. It's not something I expected, that, as Wiccan stated, the mass of a hot object is an "ongoing question."

Also, I didn't realize there was a contradiction between relativity and QM. So, relativity is only, as sfs said, a "good approximation" for low energy states? That confuses me because I thought classical physics was a "good approximation" of low velocity, macro-scale events, whereas relativity served better at speeds approaching light ... which I would think is pretty high energy. I guess I thought QM only really came in to play for small scale physics - stuff approaching uncertainty.

Even more interesting is that gravity is at the center of it all - the very thing that has been puzzling science since Grog dropped a rock on the foot of his fellow Neanderthal. So I guess gravity is still the BIG question.

But is there another "question"? For instance, I believe the blackbody puzzle was a big player in leading to QM. Is there a similar "question" that is plaguing physics right now? I'm not really thinking of the Higgs boson and the 1001 other questions physicists toy with. I mean, is there some underlying root question ... for example an attempt to show that energy has gravitational attraction?

 

[Wiccan_Child]

Sure, you're saying that, but you're also saying that GR is wrong that energy contributes to mass (something that is true in both GR and SR) and to gravity. This means you're saying that GR is not just wrong in the extreme limit, but completely wrong about pretty much everything, at all energy levels. That's a much more sweeping claim.

I never said that energy doesn't contributes to mass. Matter-antimatter annihilations are evidence enough of that.

Look up Cockcroft and Walton. I think they measured the change in mass in their 1932 Proc Roy Soc London paper (A137: 229-242). That was a good part of the reason they won the Nobel Prize.

Then what point are you making? You've chucked out two of the central theories of modern physics, Special and General Relativity: both of them imply the equivalence of energy and mass (in one case inertial mass, in the other gravitational mass). That in turn means you've wrecked QED and QCD; I suspect you've also eliminated every class of theory that's been proposed as an alternative to GR. So what exactly is it that you're suggesting?

I never chucked out GR - I said that, when push came to shove, GR and QM are mutually exclusive, and GR is most likely to be false. That doesn't mean it's chucked out, any more than post-1905 physicists simply stopped using Classical Mechanics. It's obviously very, very useful - but, as it stands, probably wrong somewhere along the line.

If energy isn't equivalent to mass, where do you think the mass in ordinary matter comes from?

The Higgs boson.

 

[Wiccan_Child]

Love the debate. It's not something I expected, that, as Wiccan stated, the mass of a hot object is an "ongoing question."

Also, I didn't realize there was a contradiction between relativity and QM. So, relativity is only, as sfs said, a "good approximation" for low energy states? That confuses me because I thought classical physics was a "good approximation" of low velocity, macro-scale events, whereas relativity served better at speeds approaching light ... which I would think is pretty high energy. I guess I thought QM only really came in to play for small scale physics - stuff approaching uncertainty.

CM is good for low-speed, middle-sized things. QM is good for the very small, SR for the very fast, and GR for the very large and the very massive (and SR is a part of GR). Since QM and GR deal with different things, they rarely interact. But in the case of black holes, you have something very heavy (GR) and something very small (QM). They don't agree.

 

[Resha Caner]

CM is good for low-speed, middle-sized things. QM is good for the very small, SR for the very fast, and GR for the very large and the very massive (and SR is a part of GR). Since QM and GR deal with different things, they rarely interact. But in the case of black holes, you have something very heavy (GR) and something very small (QM). They don't agree.

Is there a book that discusses the conflict? ... not something post-grad that would start over my head.

(edit) Hmm. After a little digging, it seems string theory has been proposed as the means to resolve the conflict between GR and QM. Is that right - that if string theory works out as expected, the issue will be settled?

 

[sfs]

I never said that energy doesn't contributes to mass. Matter-antimatter annihilations are evidence enough of that.

What you said was "It doesn't have more mass, but it has more energy, which is analogous to mass." It sure sounded like you were saying that the energy wasn't contributing more mass.

I never chucked out GR - I said that, when push came to shove, GR and QM are mutually exclusive, and GR is most likely to be false. That doesn't mean it's chucked out, any more than post-1905 physicists simply stopped using Classical Mechanics. It's obviously very, very useful - but, as it stands, probably wrong somewhere along the line.

Again, what you wrote was, " It's an ongoing question as to whether a very hot object of mass M is inherently heavier or more gravitationally attractive than a very cold object of mass M - that is, does energy warp space?" Your question here is equivalent to asking whether GR has any validity at all, since if hot objects don't warp space, then the field equations of GR are wrong -- not wrong in the sense of being an imperfect approximation, but completely wrong. Here, though, you are saying that those equations are very useful. I'm still not seeing these as consistent.

The Higgs boson.

The Higgs (assuming that is the mechanism of mass generation) produces the bare quark masses I mentioned. Where does the other 99% of mass come from?

 

[Michael]

Again, what you wrote was, " It's an ongoing question as to whether a very hot object of mass M is inherently heavier or more gravitationally attractive than a very cold object of mass M - that is, does energy warp space?" Your question here is equivalent to asking whether GR has any validity at all, since if hot objects don't warp space, then the field equations of GR are wrong -- not wrong in the sense of being an imperfect approximation, but completely wrong. Here, though, you are saying that those equations are very useful. I'm still not seeing these as consistent.

As I see this argument, it *appears* to come back to the notion of a change in momentum *within* the atomic lattice structure and whether or not that additional movement equates to a change in the total mass of the object. Unless GR theory suddenly drops off the map inside the atom (not a given IMO), it *seems* as though that additional movement would in fact have some influence on the total mass of the atoms. It would likely be an infinitesimal amount of change.

As I see it, this is a "one test is worth a thousand expert opinions" moment. Is there a physical test we might devise that would settle such an issue?