Is Relativistic Mass Still Relevant in Modern Physics Discussions?

[Aer]

Your posts are getting more and more stupid every time you post.

Again, Aer, please don't be a jerk.

I was merely providing my expert analysis in trends.

I am not considering the curvature of space by the object! Holy crap.

I didn't say you were, I was just qualifying my own statement about the equivalence principle, since the argument wouldn't quite work for a very large object like a planet.

You are referring to gravitational mass! That is what the weak equivalence principle is all about. See http://www.npl.washington.edu/eotwash/equiv.html , gravitational mass is only mentioned in the Newton analysis and the weak equivalence princple. Nowhere is "gravitational mass" mentioned in the GR (i.e. equivalence principle) interpretation. Notice all you need to know is highlighted in red on the page, perhaps specially for you: spacetime itself is curved.[/color]

This is what you and pervect do not understand. Gravity is not a force in General Relativity. The idea of gravity as a force is a Newtonian concept that Einstein abondanded with his General Relativity Theory.

equivalence principle:states that there is no experiment a person could conduct in a small volume of space that would distinguish between a gravitational field and an equivalent uniform acceleration. This principle is the foundation of General Relavity.

Seems to me that's exactly the same as my statement that "if the object is sitting on a scale in an elevator that is accelerating through empty space at 1G, the scale's reading should be the same as if the elevator was sitting on the surface of the earth, according to the equivalence principle" (assuming the elevator is considered to be a small volume of space).

There is no experiment that can be done that would detect a difference between the two - however, gravity is not a force. That is the entire point of the equivalence principle. To explain how gravity is like a force, yet it is not. It is merely the curvature of spacetime. All objects (with and without mass) follow the same curvature. Now if you had a light particle bouncing back and forth on a scale in your accelerating frame, it is not going to measure a mass on the scale. However, photons still follow the curvature of spacetime created by gravity.

I didn't say that this was the equivalence principle, just that it's a necessary consequence of it.

But it is not a necessary consequence because all objects regardless of mass with follow the same path from the curvature of spacetime as defined in General Relativity. The gravitational mass and inertial mass equivalence is explained by the "weak equivalence principle" which Galileo proved. Again, check http://www.npl.washington.edu/eotwash/equiv.html .

Huh? According to wikipedia the weak equivalence principle says that "The trajectory of a falling test body depends only on its initial position and velocity, and is independent of its composition." That is obviously not what I was talking about.

This only proves what I've thought all along. You have no idea what the hell you are talking about.

So, effectively you are attributing a force to gravity just like I said.

No I'm not.

Yes you are.

And I never said anything about treating gravity as a force, as you say, general relativity does not treat it as such.

Good, you are learning.

Sure, but different objects still have different gravitational masses, which can be measured by seeing the force they exert on a scale sitting in a gravitational field. And again, the equivalence principle shows the reading on the scale in a gravitational field must be the same as the reading on a scale in an elevator undergoing uniform acceleration (which in that case is measuring inertial mass).

You still don't get that this has no relevance to the relativistic mass subject we are discussing.

Do you agree that SR predicts a hot brick will have slightly more inertia than a cold one, again because it has a slightly higher rest energy?

Thermal energy is kinetic energy on the atomic level (not subatomic level which is quantum physics). Since kinetic energy has no effect on an objects rest mass, neither will thermal energy. And yes I realize there is a long history of assuming thermal energy is considered apart of the rest energy in E₀=mc².

All this talk about gravitational mass is useless. It has nothing to do with relativistic mass which is the issue here. You say that relativistic mass is useful. I say it is not useful. agrees with me:

In the earlier years of relativity, it was the relativistic mass that was taken to be the "correct" notion of mass, and the invariant mass was referred to as the rest mass. Gradually, as special relativity gave way to general relativity and found application in quantum field theory, it was realized that the invariant mass was the more useful quantity and scientists stopped referring to the relativistic mass altogether.

The accepted usage in the scientific community today (at least in the context of special relativity) considers the invariant mass to be the only "mass", while the concept of energy has replaced the relativistic mass. In popular science and basic relativity courses, however, the relativistic mass is usually presented, most likely due to its conceptual simplicity.[/url]

Just in case you need a summary: Kinetic energy does not add to the mass of an object, relativistic or not because the concept of "relativistic mass" is wrong.

 

[JesseM]

You are referring to gravitational mass! That is what the weak equivalence principle is all about. See http://www.npl.washington.edu/eotwash/equiv.html , for example:

Other predictions

* The equivalence of inertial mass and gravitational mass: This follows naturally from freefall being inertial motion.

Or see the section on the equivalence principle from the hyperphysics website:

Experiments performed in a uniformly accelerating reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating reference frame which is situated in a gravitational field where the acceleration of gravity = g = -a = intensity of gravity field. One way of stating this fundamental principle of general relativity is to say that gravitational mass is identical to inertial mass.

The physicists who wrote the http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909014.pdf that we were discussing earlier also describe the GR equivalence principle in this way in the introduction:

The principle of equivalence—the exact equality of inertial and gravitational mass—is a cornerstone of general relativity, and experimental tests of the universality of free fall provide a large set of data that must be explained by any theory of gravitation. But the implication that energy contributes to gravitational mass can be rather counterintuitive.

Anyway, all that I'm really talking about here is the reading on a scale for an object placed in a gravitational field. If you don't want to call this reading "gravitational mass", you don't have to, although I think most physicists would, even in the context of general relativity. All I'm saying is that this reading will always be the same as the reading for the same object sitting on a scale which is undergoing uniform acceleration in deep space, a reading which is usually understood to be a measurement of the "inertial mass". Regardless of whether you disagree about the usage of terminology, do you disagree with this physical claim about the readings of scales in different settings? If you don't disagree with me on any physical question, then all you're doing is quibbling over the standard meaning of certain terminology, and the quotes above suggest you're wrong about that anyway.

This is what you and pervect do not understand. Gravity is not a force in General Relativity. The idea of gravity as a force is a Newtonian concept that Einstein abondanded with his General Relativity Theory.

Of course I understand this, and I'm sure pervect does too. I never said anything about gravity being a force in GR. If you think that talking about an object's gravitational mass implies you're treating gravity as a force, I disagree (and I think the quotes above suggest physicists would disagree too), and I never intended that implication.

There is no experiment that can be done that would detect a difference between the two - however, gravity is not a force. That is the entire point of the equivalence principle. To explain how gravity is like a force, yet it is not. It is merely the curvature of spacetime. All objects (with and without mass) follow the same curvature. Now if you had a light particle bouncing back and forth on a scale in your accelerating frame, it is not going to measure a mass on the scale.

A box containing a photon bouncing back and forth between mirrored walls would weigh a little more than an empty box on a scale undergoing uniform acceleration in deep space, and the increase in inertial mass of the box should be equal to the energy of the photon (as measured in the box's rest frame).

But it is not a necessary consequence because all objects regardless of mass with follow the same path from the curvature of spacetime as defined in General Relativity. The gravitational mass and inertial mass equivalence is explained by the "weak equivalence principle" which Galileo proved. Again, check http://www.npl.washington.edu/eotwash/equiv.html .

OK, I admit I was a bit fuzzy on the weak vs. strong equivalence principle definition, that page suggests that in general relativity, the weak principle (that inertial mass and gravitational mass are equal, ie that the reading on a scale would be the same whether the scale was undergoing uniform acceleration in deep space or at rest with respect to a gravitational field) would just be a special case of the strong equivalence principle (that the results of all experiments would be the same whether an observer was undergoing uniform acceleration in deep space or at rest with respect to a gravitational field). But even though the weak equivalence principle predates relativity, it is still a part of relativity as suggested by the quotes I gave above, and it is in fact an obvious consequence of the strong equivalence principle. So again, my original physical argument, that if inertial mass is proportional to total energy than gravitational mass (ie the reading on a scale for a bound system in a gravitational field) must be too, still stands.

Do you agree that SR predicts a hot brick will have slightly more inertia than a cold one, again because it has a slightly higher rest energy?

Thermal energy is kinetic energy on the atomic level (not subatomic level which is quantum physics). Since kinetic energy has no effect on an objects rest mass, neither will thermal energy. And yes I realize there is a long history of assuming thermal energy is considered apart of the rest energy in E₀=mc².

Kinetic energy certainly has an effect on the rest mass of a compound object, provided you use the standard definition of "rest mass" for compound objects. But to avoid quibbling over definitions, do you agree that relativity predicts the inertia of a compound object whose parts have greater total kinetic energy in the compound object's rest frame (like a hot brick) will be larger than than the inertia of the same compound object when its parts have lesser total kinetic energy in the compound object's rest frame (like a cold brick)?

All this talk about gravitational mass is useless. It has nothing to do with relativistic mass which is the issue here. You say that relativistic mass is useful. I say it is not useful.

My argument is not about the utility of relativistic mass at all, it's just about the fact that the measured weight/inertia of a compound object is proportional to its total energy in its own rest frame (which is not the same as the sum of the relativistic masses of all its components in this frame, since there may be potential energy involved as well). You have been denying this for a long time--I originally jumped into this thread just to question the following statement by you:

Then we have people like pmb_phy claiming a contained gas's weight is a measure of the rest mass of the particles PLUS the kinetic energy they possess. UMMM - NO! That's wrong, the weight is only a measure of the rest mass of the particles and nothing more.

Do you now admit that you've been wrong all along, and that the weight (as measured by a physical scale) of a bound system is not just a measure of the rest mass of the particles that make up the system, but is in fact a measure of the system's total energy (including kinetic and potential) in its own rest frame, at least according to the theory of relativity?

agrees with me:

In the earlier years of relativity, it was the relativistic mass that was taken to be the "correct" notion of mass, and the invariant mass was referred to as the rest mass. Gradually, as special relativity gave way to general relativity and found application in quantum field theory, it was realized that the invariant mass was the more useful quantity and scientists stopped referring to the relativistic mass altogether.

The accepted usage in the scientific community today (at least in the context of special relativity) considers the invariant mass to be the only "mass", while the concept of energy has replaced the relativistic mass. In popular science and basic relativity courses, however, the relativistic mass is usually presented, most likely due to its conceptual simplicity.[/url]

Just in case you need a summary: Kinetic energy does not add to the mass of an object, relativistic or not because the concept of "relativistic mass" is wrong.

I don't know what you mean by the "mass of an object"--as always, I would say that the "rest mass" of a compound object is defined to be equal to its total energy in its own rest frame, and this is not in general the same thing as the sum of the "relativistic masses" of its components, so the quote above is irrelevant, since I haven't been defending the use of "relativistic mass" in the first place. I provided many quotes earlier in this thread to show that this was indeed the standard way of defining "rest mass" for a compound object whose parts may be in motion relative to one another, and you provided zero to support your claim that I was wrong. In any case, regardless of issues of terminology, it is certainly true that according to relativity, the weight (as measured by a physical scale) of a compound object is proportional to its total energy in its own rest frame, regardless of whether the scale is accelerating in free space or is at rest in a gravitational field.

 

[Aer]

Well, it is mentioned on the wikipedia entry on general relativity, for example:

Or see the section on the equivalence principle from the hyperphysics website:

In both instances, the context of the "weak equivalence principle" is meant.

This follows naturally from freefall being inertial motion.


And of course, what I originally said: "Tests of the weak equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. These experiments demonstrate that all objects fall at the same rate when the effect of air resistance is either eliminated or negligible."

But this is beside the point - gravitational mass has nothing to do with our discussion of relativistic mass!

This is what you and pervect do not understand. Gravity is not a force in General Relativity. The idea of gravity as a force is a Newtonian concept that Einstein abondanded with his General Relativity Theory.

Of course I understand this, and I'm sure pervect does too.

Well, of course you are wrong about pervect, but I'll accept that you understand if you say so. Anyway, from pervect "However, the various Christoffel symbols with time components that describe 'curved'/distorted space-time can be reasonably interpreted as 'forces'". See, he thinks there is some 'interpreted forces' involved with gravity.

A box containing a photon bouncing back and forth between mirrored walls would weigh a little more than an empty box on a scale undergoing uniform acceleration in deep space, and the increase in inertial mass of the box should be equal to the energy of the photon (as measured in the box's rest frame).

There is no reason to believe this! A photon is massless. It doesn't make sense to say a photon has 'no mass in its rest frame' because the the frame at v=c is not defined in relativity. However, a photon does have energy which is a result from quantum mechanics NOT relativity. For relativity, E=γmc² and γ=1/0 which is undefined. Relativists use E²=(pc)²+(mc²)² which is derived from E=γmc² and p=γmv. They then take the QM result that pc=hf and plug it into E²=(pc)²+(mc²)² with m=0 to get E=hf. Nowhere do they say that a photon has relativitic mass in order to explain the energy. In fact, relativistic mass m_r is undefined for a photon since m_r=γm = 1/0*0=0/0=undefined!

So again, my original physical argument, that if inertial mass is proportional to total energy than gravitational mass (ie the reading on a scale for a bound system in a gravitational field) must be too, still stands.

And what value does this argument even have with relativistic mass? You seem to have gone off topic just a bit.

Kinetic energy certainly has an effect on the rest mass of a compound object, provided you use the standard definition of "rest mass" for compound objects.

I don't accept the defintion of rest mass you've provided - it's really that simple. You think all energy is included in the rest mass when in fact we've shown with the photon example that to think of energy and mass interchangably is very wrong.

Mass and energy are only interchangable on the quantum level. So this excludes thermal energy as well as kinetic energy within compound objects.

But to avoid quibbling over definitions, do you agree that relativity predicts the inertia of a compound object whose parts have greater total kinetic energy in the compound object's rest frame (like a hot brick) will be larger than than the inertia of the same compound object when its parts have lesser total kinetic energy in the compound object's rest frame (like a cold brick)?

Any inertia of the parts within the compound object have no bearing on the whole. Your logic is flawed.

My argument is not about the utility of relativistic mass at all, it's just about the fact that the measured weight/inertia of a compound object is proportional to its total energy in its own rest frame

Which would have to include the relativistic masses of all the objects contained within! Energy and mass are only interchangable on the quantum level. It was thought long ago that they were interchangable on the macro level because there was no concept of the quantum level. Modern relativity has revised this thinking. Kinetic energy, thermal energy, potential energy all have no bearing on the mass of a particle. The only mass is the rest mass - period and this mass is only interchangable at the quantum level. So you and anyone you can find to support your position, is wrong and applying outdated thinking.

Do you now admit that you've been wrong all along

NO! You obviously need to do a little reading of modern relativity.

I don't know what you mean by the "mass of an object"

Of course you don't!

The mass of any object is a function of the gravitational field the object creates. Or rather, the strength of the gravitational field an object produces is a function of the object's mass. What clearer definition do you need?

I would say that the "rest mass" of a compound object is defined to be equal to its total energy in its own rest frame

And you and everyone you can find to support this, would be wrong.

Think of it this way: you can put 10 free particles in a volume of space that are all whirling around with great velocity. They do not create any greater curvature of the spacetime around them than if they were just at rest in spacetime because the curvature each particle creates is a function of the rest mass of each. Now put a box around them and call it a compound object. You'll have to assume that the box is massless compared to the particles (these are very heavy particles!). Now the curvature of spacetime around them has not increased any yet the rest mass, by your definition, of the compound object (box with particles inside) is much greater than the rest mass of the sum of the rest mass of each particle combined. And of course, all this makes absolutely no sense whatsoever unless "mass" is the ill-defined "relativistic mass" in which case we are not talking about "rest mass" at all.

If you cannot understand this, you are hopeless.

It shouldn't have even taken such a drawn out discussion.

But nevertheless, I predict you are going to post another ignorant reply.

 

[learningphysics]

What astounds me about this thread is that Aer, you're making claims and disagreeing with concepts that all relativists accept.

This thread really has nothing to do with the use of relativistic mass. It is simply JesseM desperately trying to help you understand a simple point: The inertia of a compound object in its rest frame is proportional to its total energy in its rest frame... This is equivalent to the definition of rest mass as total energy in the rest frame divided by c^2.

You have a hot brick at rest... the force you have to exert to accelerate it is greater than the force required to accelerate the same brick with the same acceleration when it's cold at rest. Do you agree or disagree?

 

[Aer]

What astounds me about this thread is that Aer, you're making claims and disagreeing with concepts that all relativists accept.

All relativists? Maybe retarded relativists...

This thread really has nothing to do with the use of relativistic mass. It is simply JesseM desperately trying to help you understand a simple point: The inertia of a compound object in its rest frame is proportional to its total energy in its rest frame... This is equivalent to the definition of rest mass as total energy in the rest frame divided by c^2.

No, this thread is all about relativistic mass. Read the OP! Also, this discussion stems from JesseM's very first post in this thread:

Then we have people like pmb_phy claiming a contained gas's weight is a measure of the rest mass of the particles PLUS the kinetic energy they possess. UMMM - NO! That's wrong, the weight is only a measure of the rest mass of the particles and nothing more.

Are you sure about that? the last question from this FAQ says that the apparent inertia of a black box filled with a gas will increase as the temperature increases, which I would think would mean the weight would increase as well

rest mass of the particles PLUS the kinetic energy = relativistic mass!

You have a hot brick at rest... the force you have to exert to accelerate it is greater than the force required to accelerate the same brick with the same acceleration when it's cold at rest. Do you agree or disagree?

Of course I do not agree with this outdated concept. You must remember that mass and energy were thought to be interchangable on the macro-level long ago. That is not the case today as it was realized it is only valid at the quantum level. However, there are still misguided fools out there such as yourself.

 

[learningphysics]

All relativists? Maybe retarded relativists...

No, this thread is all about relativistic mass. Read the OP! Also, this discussion stems from JesseM's very first post in this thread:


rest mass of the particles PLUS the kinetic energy = relativistic mass!

Of course I do not agree with this outdated concept. You must remember that mass and energy were thought to be interchangable on the macro-level long ago. That is not the case today as it was realized it is only valid at the quantum level. However, there are still misguided fools out there such as yourself.

You really don't have a clue do you? You haven't even worked through the math or gone through any of the derivations...

Find me one physicist with a phd that doesn't say that the rest mass of a hot brick is greater than the rest mass of the same brick when it's cold.

That wikipedia quote you used just shows you really don't understand what JesseM has been saying, and neither do you understand the quote.

 

[JesseM]

In both instances, the context of the "weak equivalence principle" is meant.

Call it whatever you want. My original point was just that the equivalence principle of general relativity implies that the weight of an object in a gravitational field must be proportional to the inertial mass, and since special relativity predicts that the inertia of a compound object is proportional to its total energy in the object's own rest frame, the equivalence principle alone is enough to tell us that the weight of a compound object in a gravitational field is also proportional to its total energy, without any further consideration of the details of GR.

But this is beside the point - gravitational mass has nothing to do with our discussion of relativistic mass!

You seem to have this confused idea that I have been trying to make some point about relativistic mass. I haven't--go back and look at my previous posts on this thread, my point was always focused on inertia and weight being proportional to total energy for a compound object, and also the terminological issue that "rest mass" is traditionally defined as total energy for a compound object. The discussion has dragged on for as long as it has because you keep making statements which seem to contradict this, such as this, from post #9:

Then we have people like pmb_phy claiming a contained gas's weight is a measure of the rest mass of the particles PLUS the kinetic energy they possess. UMMM - NO! That's wrong, the weight is only a measure of the rest mass of the particles and nothing more.

Or this, from post #21:

the mass of an object is its total energy in its rest frame

should be "the mass of an object is the sum of all its constituents' rest masses".

Or post #24:

Just to be clear, are you claiming for sure that the inertia of a black box filled with gas won't appear to increase when the temperature increases, or are you just not certain either way?

OK - let me state that I cannot be certain, but according to mass as it is defined, the answer would be that the mass of the gas would not appear to increase.

Or post #28:

No, not if you use the definition given by Tom Roberts, where the "rest mass" of a composite object is defined as its total energy (divided by c^2, presumably) in the center-of-mass frame.

Very well, then his definition of "rest mass" is not the proper definition of "rest mass"

Or post #29:

that says that the inertia of a composite object (its resistance to being accelerated) will be a function of its total energy, not just the energy of the rest mass of all the constituent particles:

The acceleration of an object is only properly measured in it's rest frame which implies the total energy is the rest energy.

Or post #41:

I'm confident that the same force will not accelerate your car as quickly as if the objects in your car were moving slower (in the center-of-mass frame of the car), ie the inertia of the car will be different, since two expert sources have said this is true.

I'd be more than happy to see these sources. This would do nothing but undermine the foundations of SR and probably neccessitate modifications to GR.

I could keep going, but you get the point. You have been consistently denying both my physical claim that the inertia and weight of a compound object is proportional to its total energy, and also my terminological claim that the standard definition of "rest mass" for a compound object is its total energy in the object's rest frame. Neither of these points has jack squat to do with relativistic mass! I am happy to accept the judgement of most physicists that "relativistic mass" is more confusing then helpful and should therefore be avoided in physics discussions, and in fact I've pointed this out on other threads prior to this one--see this post, for example.

Well, of course you are wrong about pervect, but I'll accept that you understand if you say so. Anyway, from pervect "However, the various Christoffel symbols with time components that describe 'curved'/distorted space-time can be reasonably interpreted as 'forces'". See, he thinks there is some 'interpreted forces' involved with gravity.

Well, I'm not a GR expert, perhaps there is an alternate way to interpret the mathematics, or perhaps pervect is just saying that the effects of curved spacetime come to resemble forces in some limit (as they must, since GR is supposed to reduce to Newtonian gravity in certain limits). I'm remembering something that physicist Kip Thorne says on p. 397 of his book Black Holes and Time Warps:

Is spacetime really curved? Isn't it conceivable that spacetime is actually flat, but the clocks and rulers with which we measure it, and which we regard as perfect in the sense of Box 11.1, are actually rubbery? Might not even the most perfect clocks slow down or speed up, and the most perfect of rulers shrink or expand, as we move them from point to point and change their orientations? Wouldn't such distortions of our clocks and rulers make a truly flat spacetime appear curved?

Yes.

[He then goes on to describe how a field that changes the length of rulers and speed of clocks could give exactly the same predictions as the usual curved spacetime picture in the case of a black hole]

What is the real, genuine truth? Is spacetime really flat, as the above paragraphs suggest, or is it really curved? To a physicist like me this is an uninteresting question because it has no physical consequences. Both viewpoints, curved spacetime and flat, give precisely the same predictions for any measurements performed with perfect rulers and clocks, and also (it turns out) the same predictions for any measurements performed with any kind of physical apparatus whatsoever. For example, both viewpoints agree that the radial distance between the horizon and the circle in Figure 11.1, as measured by a perfect ruler, is 37 kilometers. They disagree as to whether that measured distance is the "real" distance, but such a disagreement is a matter of philosophy, not physics. Since the two viewpoints agree on the results of all experiments, they are physically equivalent. Which viewpoint tells the "real truth" is irrelevant for experiments; it is a matter for philosophers to debate, not physicists. Moreover, physicsts can and do use the two viewpoints interchangeably when trying to deduce the predictions of general relativity.

...

The curved spacetime paradigm is based on three sets of mathematically formulated laws: Einstein's field equation, which describes how matter generates the curvature of spacetime; the laws which tell us that perfect rulers and perfect clocks measure the lengths and the times of Einstein's curved spacetime; and the laws which tell us how matter and fields move through curved spacetime, for example, that freely moving bodies travel along straight lines (geodesics). The flat spacetime paradigm is also based on three sets of laws: a law describing how matter, in flat spacetime, generates the gravitational field; laws describing how that field controls the shrinkage of perfect rulers and the dilation of the ticking rates of perfect clocks; and laws describing how the gravitational field also controls the motions of particles and fields through flat spacetime.

...

The exemplars of the curved spacetime paradign include the calculation, found in most relativity textbooks, by which one derives Schwarzschild's solution to the Einstein field equations, and the calculations by which Israel, Carter, Hawking, and others deduced that a black hole has no "hair." The flat spacetime exemplars include textbook calculations of how the mass of a black hole or other body changes when gravitational waves are captured by it, and calculations by Clifford Will, Thibault Damour, and others of how neutron stars orbiting each other generate gravitational waves (waves of shrinkage-producing field).

...

The flat spacetime paradigm's laws of physics can be derived, mathematically, from the curved spacetime paradigm's laws, and conversely. This means that the two sets of laws are different mathematical representations of the same physical phenomena, in somewhat the same sense as 0.001 and 1/1000 are different mathematical representations of the same number. However, the mathematical formulas for the laws look very different in the two representations, and the pictures and exemplars that accompany the two sets of laws look very different.

As an example, in the curved spacetime paradigm, the verbal picture of Einstein's field equation is the statement that "mass generates the curvature of spacetime." When translated into the language of the flat spacetime paradigm, this field equation is described by the verbal picture "mass generates the gravitational field that governs the shrinkage of rulers and the dilation of the ticking of clocks." Although the two versions of the Einstein field equation are mathematically equivalent, their verbal pictures differ profoundly.

It is extremely useful, in relativity research, to have both paradigms at one's fingertips. Some problems are solved most easily and quickly using the curved spacetime paradigm; others, using flat spacetime. Black-hole problems (for example, the discovery that a black hole has no hair) are more amenable to curved spacetime techniques; gravitational-wave problems (for example, computing the waves produced when two neutron stars orbit each other) are most amenable to flat spacetime techniques. Theoretical physicists, as they mature, gradually build up insight into which paradigm will be best for which situation, and they learn to flip their minds back and forth from one paradigm to the other, as needed. They may regard spacetime as curved on Sunday, when thinking about black holes, and as flat on Monday, when thinking about gravitational waves. ... Since the laws that underlie the two paradigms are mathematically equivalent, we can be sure that when the same physical situation is analyzed using both paradigms, the predictions for the results of experiments will be identically the same. We thus are free to use the paradigm that best suits us in any given situation.

A box containing a photon bouncing back and forth between mirrored walls would weigh a little more than an empty box on a scale undergoing uniform acceleration in deep space, and the increase in inertial mass of the box should be equal to the energy of the photon (as measured in the box's rest frame).

There is no reason to believe this! A photon is massless. It doesn't make sense to say a photon has 'no mass in its rest frame' because the the frame at v=c is not defined in relativity. However, a photon does have energy which is a result from quantum mechanics NOT relativity. For relativity, E=?mc² and ?=1/0 which is undefined. Relativists use E²=(pc)²+(mc²)² which is derived from E=?mc² and p=?mv. They then take the QM result that pc=hf and plug it into E²=(pc)²+(mc²)² with m=0 to get E=hf. Nowhere do they say that a photon has relativitic mass in order to explain the energy. In fact, relativistic mass m_r is undefined for a photon since m_r=?m = 1/0*0=0/0=undefined!

Again, I said nothing about the photon's relativistic mass, only that its total energy (which, as you say, is given by E=hf) contributes to the inertia/weight of the box, according to relativity. Any physicist would agree that this is what relativity predicts.

So again, my original physical argument, that if inertial mass is proportional to total energy than gravitational mass (ie the reading on a scale for a bound system in a gravitational field) must be too, still stands.

And what value does this argument even have with relativistic mass? You seem to have gone off topic just a bit.

Again, look back over my old posts, you'll see I was never focused on anything related to "relativistic mass", my focus has always been on pointing out that you are making claims about weight/inertia that disagree with the predictions of relativity, and also that you are not using the standard definition of "rest mass" for compound objects. You didn't give me a definite answer, do you agree or disagree "that if inertial mass is proportional to total energy than gravitational mass (ie the reading on a scale for a bound system in a gravitational field) must be too"?

Mass and energy are only interchangable on the quantum level. So this excludes thermal energy as well as kinetic energy within compound objects.

I have always said that I wish to avoid talking about the "mass" of a compound object since we can't even agree on how that's defined, and just talk about physical questions like what a scale will read when you put that compound object on top of it. Relativity predicts that the reading on the scale will be proportional to the sum of the rest masses of all the components plus the sum of their kinetic and potential energies, as seen in the compound object's rest frame. I don't know, and don't really care, whether you'd call this an "interchange of mass and energy". But if you disagree with this claim about the reading on a scale, then you're just ignorant of the predictions of relativity. I'm sure you could do a purely classical relativistic calculation to show this, like considering a box full of ball bearings which are bouncing around in a box and imparting little impulses (which could be analyzed using relativistic kinematics) to the scale whenever they hit the box's floor, and then calculating the average reading on the scale as a function of the average velocity of the ball bearings in the box's rest frame.

But to avoid quibbling over definitions, do you agree that relativity predicts the inertia of a compound object whose parts have greater total kinetic energy in the compound object's rest frame (like a hot brick) will be larger than than the inertia of the same compound object when its parts have lesser total kinetic energy in the compound object's rest frame (like a cold brick)?

Any inertia of the parts within the compound object have no bearing on the whole. Your logic is flawed.

It's not just my logic, it's also Einstein's--remember, the example of a hot brick weighing more than a cold one was from one of his papers.

My argument is not about the utility of relativistic mass at all, it's just about the fact that the measured weight/inertia of a compound object is proportional to its total energy in its own rest frame

Which would have to include the relativistic masses of all the objects contained within!

No, there is no need to make use of "relativistic mass" when calculating the total energy of the compound object. One could just calculate E = \sqrt{m^2 c^4 + p^2 c^2} for each component and then add them up, along with whatever potential energies are involved.

I don't know what you mean by the "mass of an object"

The mass of any object is a function of the gravitational field the object creates. Or rather, the strength of the gravitational field an object produces is a function of the object's mass. What clearer definition do you need?

As I understand it, all forms of energy contribute to the curvature of spacetime--so a hot planet would produce a slightly stronger gravitational field than a colder but otherwise equivalent planet, and likewise a compressed spring would produce a slightly stronger gravitational field than a relaxed version of the same spring.

I would say that the "rest mass" of a compound object is defined to be equal to its total energy in its own rest frame

And you and everyone you can find to support this, would be wrong.

How can "everyone" be wrong about an issue of how a term is defined? The symbol-string R-E-S-T-M-A-S-S has no inherent meaning, it means whatever physicists choose it to mean. Even if you have defined "rest mass" for a single particle, that does not lead you to a single unique definition of "rest mass" for a collection of particles which do not share a common rest frame, you have to make a choice of how you want to define rest mass for such a compound object. What I am saying is that the standard definition used by physicists is that it means the total energy of the compound object in its rest frame, and I provided a number of credible sources to show that this is the standard definition.

Think of it this way: you can put 10 free particles in a volume of space that are all whirling around with great velocity. They do not create any greater curvature of the spacetime around them than if they were just at rest in spacetime because the curvature each particle creates is a function of the rest mass of each.

As I understand it, general relativity says that all forms of energy contribute to something called the "stress-energy tensor" which determines the curvature of spacetime. For example, see this post by physicist John Baez where he's discussing how kinetic energy and potential energy contribute to the stress-energy tensor--at the end he says, in response to a comment by someone else on the group:

>It would seem that only "kinetic" energy contributes
>to gravitation in GR. Is that correct?

No, both kinetic and potential energy contribute.

And of course, all this makes absolutely no sense whatsoever unless "mass" is the ill-defined "relativistic mass" in which case we are not talking about "rest mass" at all.

I have said over and over that it is total energy in the compound object's rest frame, not "relativistic mass", which determines the inertia and which is defined as the compound object's "rest mass". Do you think the notion of total energy is ill-defined?

 

[JesseM]

rest mass of the particles PLUS the kinetic energy = relativistic mass!

It's true that you can call this the "relativistic mass" if you wish, but there's no need to do so. You could also just use the equation E^2 = m^2 c^4 + p^2 c^2, where m is the rest mass and p is the relativistic momentum, and you will get the same answer for the total energy as if you had used the equation E = Mc^2 where M is the "relativistic mass". Remember, the dispute over "relativistic mass" is just an aesthetic one about whether the term is misleading or not, it's not as if any calculation involving relativistic mass will actually give different results from an analogous calculation that doesn't, and any statement involving relativistic mass can be replaced with an equivalent one involving only concepts like rest mass, relativistic momentum and energy.

Of course I do not agree with this outdated concept.

Again, it's only "outdated" for aesthetic reasons, it's not as if physicists using relativistic mass made any different predictions about the results of any actual physical experiments than physicists who don't. Both would agree that the inertia of a compound object is equal to total energy, regardless of whether they calculate this by summing E = \sqrt{m^2 c^4 + p^2 c^2} + P or by summing E = M c^2 + P for each component (P is the potential energy of each component).

 

[Garth]

The term 'relativistic mass' requires the addition of 'kinetic energy' to 'rest mass'. As kinetic energy is frame dependent this is a frame dependent (3+1)D space + time perspective. In this perspective the energy required to accelerate a body to high velocity reappears as an apparent increase in inertial mass according to E = mc²- "the faster it goes the harder it is to push".

The term 'mass' to mean simply 'rest mass' as an invariant quantity is consistent with the 4D energy-momentum of a particle being conserved and frame invariant. This is a frame independent 4D space-time perspective. Therefore this may seem the more 'pure' form to a relativist working with frame independent space-time. The energy used to accelerate an object to high velocity is redefined and absorbed by the time dilation suffered by that object as observed by the 'stationary' observer. (The 'gamma' factor)

However physics is actually done by a physicist locked into one particular frame, or another, and not 'frame independent'. Therefore from the perspective of a real experimenter the use of 'relativistic mass' may be the more obvious to use. It is a matter of choice; so long as you know the full implications of the perspective you select both systems should be equivalent.

Garth

 

[learningphysics]

The term 'relativistic mass' requires the addition of 'kinetic energy' to 'rest mass'. As kinetic energy is frame dependent this is a frame dependent (3+1)D space + time perspective. In this perspective the energy required to accelerate a body to high velocity reappears as an apparent increase in inertial mass according to E = mc²- "the faster it goes the harder it is to push".

The term 'mass' to mean simply 'rest mass' as an invariant quantity is consistent with the 4D energy-momentum of a particle being conserved and frame invariant. This is a frame independent 4D space-time perspective. Therefore this may seem the more 'pure' form to a relativist working with frame independent space-time. The energy used to accelerate an object to high velocity is redefined and absorbed by the time dilation suffered by that object as observed by the 'stationary' observer. (The 'gamma' factor)

However physics is actually done by a physicist locked into one particular frame, or another, and not 'frame independent'. Therefore from the perspective of a real experimenter the use of 'relativistic mass' may be the more obvious to use. It is a matter of choice; so long as you know the full implications of the perspective you select both systems should be equivalent.

Garth

The thread has long since stopped being one about the use of 'relativistic mass' but one that contests what relativity actually physically predicts.

A hot brick at rest according to special relativity has greater rest mass than a cold brick at rest (the same brick after being heated up while leaving its center of mass motionless). This is being contested by Aer as being an outdated concept of special relativity.

 

[Aer]

since special relativity predicts that the inertia of a compound object is proportional to its total energy in the object's own rest frame

How many times do I have to tell you this? Special Relativity does not and cannot speak directly for a compound object. In fact, the relation E₀=mc² is independent of special relativity as was proven http://www.arxiv.org/PS_cache/astro-ph/pdf/0504/0504486.pdf . For a compound object, you just think that the total energy is proportional to its mass, in much the same way you think thermal energy adds to an objects mass. It does not and cannot because mass and energy are only indistinguishable on the quantum level.

my point was always focused on inertia and weight being proportional to total energy for a compound object

Do you think using the term weight changes what you are saying any? It doesn't, weight just implies a certain mass in a certain gravitational field. To say that the weight will change is to say that mass will change because one thing is for certain, the gravitational field of the Earth is not changing due to your little "compound object".

and also the terminological issue that "rest mass" is traditionally defined as total energy for a compound object

As I've told you repeated - I believe that is incorrect because thermal energy is a considered a rest energy for any object and thermal energy cannot and does not in any way add to an objects mass.

You must remember that mass and energy were once thought to be interchangable on the macro-level which is what you are doing here and what is what was done long ago when "relativistic mass" was thought to be the true mass. Slowly, but surely relativistic mass has been done away with since it has been realized that mass and energy are not interchangable on the macro-level, this only applies to the quantum level. Unfortunately it is still widely believed that energy and mass are interchangeable on the macro-level which is what lead you and others to come to the incorrect conclusion that the rest mass of a compound object (you may include all objects storing thermal energy as a compound object because that truly is what thermal energy is) will be greater than the sum of the rest masses of all the constituent parts.

The fact that you say any of the following just shows you do not understand the context of the statements. Might I suggest a course in reading comprehension? Because yours is truly deficient!

I'll play your little game just to show you how dumb your remark is saying that these statements are contradictory!

should be "the mass of an object is the sum of all its constituents' rest masses[/color]".

This is what I said above and is what I've said all along.

OK - let me state that I cannot be certain[/color], but according to mass as it is defined, the answer would be that the mass of the gas would not appear to increase[/color].

The statement in blue was to let you know that there is no experiment to back up any claims. The statement in red is the same as the first statement above because the gas would not increase since the total mass is the sum of all the constituents' rest masses or as I said above the mass of an object is the sum of all its constituents' rest masses[/color].

Very well, then his definition of "rest mass" is not the proper definition of "rest mass"

Because to use his definition of rest mass, one must include thermal energies and kinetic energies to get the rest mass of a compound object whereas I say the mass of an object is the sum of all its constituents' rest masses[/color]

The acceleration of an object is only properly measured in it's rest frame which implies the total energy is the rest energy.

There is no mention of rest mass here, however - as I've said, thermal energy is included in an ojbects rest energy but does not contribute to an objects rest mass because the mass of an object is the sum of all its constituents' rest masses[/color] and thermal energy is proportional to the kinetic energy of atoms within a system or as you like to call it, a compound object.

This would do nothing but undermine the foundations of SR and probably neccessitate modifications to GR.

Because if kinetic energy within a system added to the system's rest mass, then kinetic energy would be a form of mass which it clearly is not. Because there is no greater curvature of spacetime just because an object has kinetic energy so therefore the mass of an object is the sum of all its constituents' rest masses[/color].

All clear? I am sure you still don't understand, so I will be here to continue to try to teach you.

I could keep going, but you get the point.

Actually, you made my point, so I guess I do get it but somehow you don't - funny how that turned out.

Well, I'm not a GR expert

Well one thing is for sure, I certainly didn't think you were an expert in GR because if you were, then you would clearly understand that there is no way kinetic energy or thermal energy can add to the curvature of spacetime.

Again, I said nothing about the photon's relativistic mass, only that its total energy (which, as you say, is given by E=hf) contributes to the inertia/weight of the box, according to relativity.

You say that the presence of a photon adds to the weight of the box as if that is different from saying it adds to the mass of the box. There is no difference and photons do not add to the mass of anything. Do you really think that photons create curvature in spacetime?! I think you need to take a course in General Relativity.

I was never focused on anything related to "relativistic mass", my focus has always been on pointing out that you are making claims about weight/inertia that disagree with the predictions of relativity, and also that you are not using the standard definition of "rest mass" for compound objects

This is where your failure in knowledge exists. You seem to think there can be multiple definitions of "rest mass". There cannot. In fact the only definition that makes any sense when dealing with relativity is the one linking rest mass to the curvature of spacetime as described in General Relativity. No kinetic energy or thermal energy (which is another form of kinetic energy) can add to the curvature of spacetime, that was why relativistic mass was abandoned because not all energies added to an objects mass. Kinetic energy regained its place over relativistic mass which initially replaced kinetic energy when relativity was first conceived.

It's not just my logic, it's also Einstein's--remember, the example of a hot brick weighing more than a cold one was from one of his papers.

What part of the following paragraph do you not understand:

You must remember that mass and energy were once thought to be interchangable on the macro-level which is what you are doing here and what is what was done long ago when "relativistic mass" was thought to be the true mass. Slowly, but surely relativistic mass has been done away with since it has been realized that mass and energy are not interchangable on the macro-level, this only applies to the quantum level. Unfortunately it is still widely believed that energy and mass are interchangeable on the macro-level which is what lead you and others to come to the incorrect conclusion that the rest mass of a compound object (you may include all objects storing thermal energy as a compound object because that truly is what thermal energy is) will be greater than the sum of the rest masses of all the constituent parts.

I'll be glad to clarify.

As I understand it, all forms of energy contribute to the curvature of spacetime

Well you understand wrong. Kinetic energy does not and cannot contribute to the curvature of spacetime. Thermal energy is just a form of kinetic energy so therefore your hot planet model is false.

As I understand it, general relativity says that all forms of energy contribute to something called the "stress-energy tensor" which determines the curvature of spacetime. For example, see this post by physicist John Baez where he's discussing how kinetic energy and potential energy contribute to the stress-energy tensor--at the end he says, in response to a comment by someone else on the group:

No, that was Daryl McCullough making the comments. This is hardly a good source for anything, a message board?

Kinetic energies/Thermal energies do not contribute to the curvature of spacetime. Only matter (i.e. atoms) contributes to the curvature of spacetime. You need only take a look at some fundamentals of General Relativity borrowed from this site:

* The speed of light is a constant independent of the velocity of the source or the observer.
* Events that are simultaneous as seen by one observer are generally not simultaneous as seen by other observers, so there can be no absolute time.
* Each observer can define his own proper time -- the time measured by a good clock moving along his worldline.
* Observers can assign times and positions to events not on their worldlines using radar observations.
* Every observer will see his clock running faster than other clocks which are moving with respect to him, and this is a mathematically consistent pattern required by the properties of radar observations.
* As a result, the unaccelerated worldline between two events will have the longest proper time of all worldlines connecting these events.
* In the presence of gravity, the worldlines of objects accelerated only by gravity have the longest proper times.
* Gravity requires that spacetime have a non-Euclidean geometry, and this curvature of spacetime must be created by matter. [/color]

It's true that you can call this the "relativistic mass" if you wish, but there's no need to do so. You could also just use the equation E^2 = m^2 c^4 + p^2 c^2, where m is the rest mass and p is the relativistic momentum, and you will get the same answer for the total energy as if you had used the equation E = Mc^2 where M is the "relativistic mass".

You really have no idea do you?

E = M c^2 is properly written as E = \gamma m c^2

E^2 = m^2 c^4 + p^2 c^2 is derived from E = \gamma m c^2 and p = \gamma m v If you don't believe me, look it up. Better yet, just plug in p = \gamma m v to E^2 = m^2 c^4 + p^2 c^2 and you'll get E = \gamma m c^2. The fact that you define M=γm is not really all that significant except for when you go to the force equation F=ma and try to use your "relativistic mass" and say that F=Ma. Well that just doesn't work because F=γ³m would be the actual equation you get if you start from fundamentals. It is not a matter of style, it would be the same as if I defined a "relativistic velocity", V as γv and used this "relativistic velocity" in equations where ever γv used to appear. Of course I will get the same results, but that doesn't make "relativistic velocity" any more meaningful - In fact it just confuses the issue.

Now let's see you come up with a feasible explanation for why you say a compound object will have a greater rest mass than the sum of all the constituents' rest masses in the following context:

you can put 10 free particles in a volume of space that are all whirling around with great velocity. They do not create any greater curvature of the spacetime around them than if they were just at rest in spacetime because the curvature each particle creates is a function of the rest mass of each. Now put a box around them and call it a compound object. You'll have to assume that the box is massless compared to the particles (these are very heavy particles!). Now the curvature of spacetime around them has not increased any yet the rest mass, by your definition, of the compound object (box with particles inside) is much greater than the rest mass of the sum of the rest mass of each particle combined. And of course, all this makes absolutely no sense whatsoever unless "mass" is the ill-defined "relativistic mass" in which case we are not talking about "rest mass" at all.

 

[JesseM]

How many times do I have to tell you this? Special Relativity does not and cannot speak directly for a compound object.

Nonsense, it can speak for many types of bound objects. For example, if you had a box full of small ball bearings which collide elastically with the walls of the box and with each other, then you should be able to analyze the collisions using relativistic kinematics, and calculate the average force which with the bottom of the scale pushes on a scale that is being accelerated--do you disagree that SR could handle this? Likewise, do you disagree that SR could handle a situation involving classical particles bound by classical electromagnetic forces?

In fact, the relation E₀=mc² is independent of special relativity as was proven http://www.arxiv.org/PS_cache/astro-ph/pdf/0504/0504486.pdf .

OK, but the derivation uses the assumption of an object emitting electromagnetic wave packets, and classical electromagnetism was already a Lorentz-invariant theory even before relativity was discovered, so in a way it's not surprising that E=mc^2 can be derived from electromagnetism. (but note that pre-relativistic physicists would only have believed that Maxwell's laws held exactly in a single frame, the frame of the luminiferous ether, and that in other frames they'd have to be modified by a Galilei transform; presumably the derivation of the paper only works in a frame where Maxwell's laws hold exactly. And if you assume from the start that Maxwell's laws hold in every frame, then you are forced to assume SR is true!) The paper also points out that the theory of electromagnetism can be used to analyze the inertia of a compound system, namely a box filled with gas particles that emit electromagnetic radiation:

However, as a historical and logical exercise, one may also ask how equation (5) could have been generalized if it had been discovered prior to Special Relativity. Such a generalization follows from a simple thought experiment. Imagine a box filled with warm gas, whose thermal energy ultimately resides in the kinetic energy of the atoms. At the time, this picture was controversial but at least some physicists (e.g., Boltzmann) held to it. Light is emitted from two holes in the box, similarly to the situation in § 2. The energy of the light packets is drawn from the kinetic energy of the atoms in the box, some of which now move more slowly. By equation (4), the box has lost not only energy, but also mass. However, since the box contains no inter-atom potential energy, the mass (i.e., inertia) of the box must be the sum of the mass (inertia) of the atoms in it. As the number of these has not changed, the mass of some of the atoms must have been reduced by exactly the amount of reduced mass of the box, which is exactly the same as the kinetic energy lost from these atoms divided by c^2. That is, kinetic energy also contributes to inertia.

For a compound object, you just think that the total energy is proportional to its mass, in much the same way you think thermal energy adds to an objects mass. It does not and cannot because mass and energy are only indistinguishable on the quantum level.

Read your own reference, it's saying that the fact that kinetic energy contributes to inertia can be derived using classical electromagnetism, there is no need for quantum interactions where one type of particle turns into another type with a different rest mass.

my point was always focused on inertia and weight being proportional to total energy for a compound object

Do you think using the term weight changes what you are saying any? It doesn't, weight just implies a certain mass in a certain gravitational field. To say that the weight will change is to say that mass will change because one thing is for certain, the gravitational field of the Earth is not changing due to your little "compound object".

The weight of a compound object is not simply proportional to the sum of the rest masses of the particles that make it up, if that's what you're saying. Again, one can just use SR to define the inertia of a compound object being accelerated in free space, and then by the equivalence principle this must be proportional to the compound object's weight in a gravitational field. And thermal energy can be shown to contribute to inertia without bringing in QM, as explained, for example, in that paragraph of the paper you mentioned.

and also the terminological issue that "rest mass" is traditionally defined as total energy for a compound object

As I've told you repeated - I believe that is incorrect because thermal energy is a considered a rest energy for any object and thermal energy cannot and does not in any way add to an objects mass.

You are talking about "an objects mass" as if the word "mass" has some obvious meaning and there are no subtleties in how to define "mass" for a compound object. But as I've pointed out, there are different possible ways one could choose to define rest mass for a compound object--one could define it in terms of the sum of the rest masses of its parts, or one could define it in terms of the object's inertia in its own rest frame, or one could define it in terms of its gravitational pull on other objects. If you take the first option, then it would be true that thermal energy does not add to the compound object's mass, but if you take the second or third option, then you will be forced to define the "rest mass" of a compound object in terms of its total energy (in its own rest frame) divided by c^2. And physicists do in fact define rest mass for compound objects this way, as I've shown in numerous references.

You must remember that mass and energy were once thought to be interchangable on the macro-level which is what you are doing here and what is what was done long ago when "relativistic mass" was thought to be the true mass.

Nonsense. Einstein, for example, never liked the concept of "relativistic mass", but it was him who said the example of a hot brick weighing more than a cold one. Again, the idea that all energy contributes to inertia can be derived using classical electromagnetism, and I think it could also be derived just using relativistic kinematics as in my example of a box filled with ball bearings which collide elastically. Anway, as I pointed out in another post, the case against "relativistic mass" is just an aesthetic one, a physicist using this concept won't make any different predictions than one who doesn't--does your comment above suggest you are disagreeing with that? If so, you are misunderstanding the debate about "relativistic mass" in a very basic way, it is not a debate involving different predictions about the results of any experiments.

should be "the mass of an object is the sum of all its constituents' rest masses[/green]".

This is what I said above and is what I've said all along.

Yes, and this is what I've been disagreeing with you on all along. So stop trying to portray me as if I've been defending the use of "relativistic mass", because I haven't. I've just been trying to correct your ignorance about what relativity predicts for the inertia and weight of a compound object.

Also, didn't you at least admit that the mass of a compound object is not the sum of the rest masses of its parts in the case of a deuteron nucleus consisting of one proton and one neutron? I suppose you would continue to make the confused argument that this is just a quantum effect, but in any case it shows that your statement above is not true in all cases.

You say that the presence of a photon adds to the weight of the box as if that is different from saying it adds to the mass of the box. There is no difference and photons do not add to the mass of anything. Do you really think that photons create curvature in spacetime?! I think you need to take a course in General Relativity.

Hell yes photons contribute to the curvature of spacetime, it's you who needs to do some actual research before confidently proclaiming things you have obviously never actually looked up. For example, on this page it's mentioned that two photons would attract each other gravitationally according to GR, and in http://www.iidb.org/vbb/showthread.php?t=65536 from another board someone asks about whether photons gravitate, and someone responds with a reference to the literature:

Richard Tolman and others investigated this question not long after the general theory of relativity was invented. Let me dig up the reference:

On The Gravitational Field Produced by Light, Tolman, Ehrenfest and Podolsky, Physical Review, 37, 602-615.

You can also check out Tolman's classic textbook Relativity, Thermodynamics and Cosmology. There's a section in there which discusses this topic.

(The link he gives is dead, but there's an archived version of the link here.) This same Tolman reference is mentioned on https://www.physicsforums.com/archive/t-13745_Does_Light_Have_Mass?.html thread, where pmb_phy says:

Yes. Since light has energy and energy has mass then light will generate a gravitational field. An example was given in

On The Gravitational Field Produced by Light, Tolman, Ehrenfest and Podolsky, Physical Review, Vol(37), March 1, 1931, pg 602-615

See --
http://www.geocities.com/physics_world/grav_light.htm

Also in the thread, Tron3k links to this paper by physicists Gerard 't Hooft and M.B. van der Mark which first shows a calculation of why the inertia and weight of a box filled with gas would be greater as the temperature increases (confirming my earlier claim about the box filled with ball bearings), and then shows a corresponding calculation for a mirrored box filled with photons, confirming that the inertia and weight of this box will be greater than if the box were empty.

This is where your failure in knowledge exists. You seem to think there can be multiple definitions of "rest mass". There cannot. In fact the only definition that makes any sense when dealing with relativity is the one linking rest mass to the curvature of spacetime as described in General Relativity. No kinetic energy or thermal energy (which is another form of kinetic energy) can add to the curvature of spacetime, that was why relativistic mass was abandoned because not all energies added to an objects mass. Kinetic energy regained its place over relativistic mass which initially replaced kinetic energy when relativity was first conceived.

It's not just my logic, it's also Einstein's--remember, the example of a hot brick weighing more than a cold one was from one of his papers.

What part of the following paragraph do you not understand:

You must remember that mass and energy were once thought to be interchangable on the macro-level which is what you are doing here and what is what was done long ago when "relativistic mass" was thought to be the true mass.

Einstein always rejected the concept of relativistic mass, so this has no bearing on what I said above. Also, as I've pointed out, if you're under the impression that physicists who use the concept of relativistic mass actually made different predictions about the results of any experiments than physicists who didn't, then you're badly confused about what the whole debate over relativistic mass is actually about.

Well you understand wrong. Kinetic energy does not and cannot contribute to the curvature of spacetime. Thermal energy is just a form of kinetic energy so therefore your hot planet model is false.

Once again, you're speaking authoritatively based on nothing but your own intuitions, obviously without having checked any references or done any derivations to see whether it's actually true that kinetic energy doesn't contribute to spacetime curvature in GR. Can you provide a single reference for that? I bet you can't.

For example, see this post by physicist John Baez where he's discussing how kinetic energy and potential energy contribute to the stress-energy tensor--at the end he says, in response to a comment by someone else on the group:

>It would seem that only "kinetic" energy contributes
>to gravitation in GR. Is that correct?

No, both kinetic and potential energy contribute.

No, that was Daryl McCullough making the comments.

No, the post's heading says:

Subject: Re: Stress-energy tensor
* From: baez@galaxy.ucr.edu (John Baez)

The comment is in response to one by Daryl McCullough, so in the section I quoted, it was McCullough who said "It would seem that only 'kinetic' energy contributes to gravitation in GR. Is that correct?" while it is Baez who replies "No, both kinetic and potential energy contribute".

This is hardly a good source for anything, a message board?

If the person making the comment on the message board is a renowned physicist and GR expert, then I'd say that's a pretty good source. But since you have zero sources for your claim that kinetic energy doesn't contribute to gravity in GR, and I'm sure you have never studied the subject in detail, why are you so confident?

Kinetic energies/Thermal energies do not contribute to the curvature of spacetime. Only matter (i.e. atoms) contributes to the curvature of spacetime. You need only take a look at some fundamentals of General Relativity borrowed from this site:

* The speed of light is a constant independent of the velocity of the source or the observer.
* Events that are simultaneous as seen by one observer are generally not simultaneous as seen by other observers, so there can be no absolute time.
* Each observer can define his own proper time -- the time measured by a good clock moving along his worldline.
* Observers can assign times and positions to events not on their worldlines using radar observations.
* Every observer will see his clock running faster than other clocks which are moving with respect to him, and this is a mathematically consistent pattern required by the properties of radar observations.
* As a result, the unaccelerated worldline between two events will have the longest proper time of all worldlines connecting these events.
* In the presence of gravity, the worldlines of objects accelerated only by gravity have the longest proper times.
* Gravity requires that spacetime have a non-Euclidean geometry, and this curvature of spacetime must be created by matter. [/color]


You really have no idea do you?

He does not say that the curvature of spacetime is created only by matter, he's just saying that matter curves spacetime. The author of the above paragraph, Ned Wright, also says on this section of his site that the vacuum energy density, which is a type of energy that's definitely not in the form of rest mass, contributes to the curvature of spacetime:

The magnitude of the negative pressure needed for energy conservation is easily found to be P = -u = -rho*c2 where P is the pressure, u is the vacuum energy density, and rho is the equivalent mass density using E = m*c^2.

So vacuum energy can be treated as interchangeable with an equivalent density of matter for the purposes of calculating gravitational effects. He also mentions that in GR, the pressure of a collection of matter or energy contributes to the curvature of spacetime too:

But in General Relativity, pressure has weight, which means that the gravitational acceleration at the edge of a uniform density sphere is not given by

g = GM/R^2 = (4*pi/3)*G*rho*R

but is rather given by

g = (4*pi/3)*G*(rho+3P/c^2)*R

Obviously Wright would not agree with you that it's only energy in the form of rest mass which contributes to the curvature of spacetime. But if you don't believe me I could email him if you like.

E = M c^2 is properly written as E = \gamma m c^2

E^2 = m^2 c^4 + p^2 c^2 is derived from E = \gamma m c^2 and p = \gamma m v If you don't believe me, look it up. Better yet, just plug in p = \gamma m v to E^2 = m^2 c^4 + p^2 c^2 and you'll get E = \gamma m c^2 Yes, I understand that the equations E = \gamma m c^2 and E = \sqrt{m^2 c^4 + p^2 c^2} are equivalent, that was my whole point.

The fact that you define M=?m is not really all that significant except for when you go to the force equation F=ma and try to use your "relativistic mass" and say that F=Ma.

Complete strawman, I have never made the argument that you can plug relativistic mass into Newton's force equation F=ma. I have no idea where you're getting this, you'll certainly never find any statement remotely like that in any of my posts.

 

[quantumdude]

I am closing this thread.

In the first place, a great deal of latitude was given with the unfortunate choice of the title. Typically threads that are addressed to a single member are either locked or deleted outright. The PM system is supposed to be used for that.

Second, the disparaging tone taken by the author is unacceptable.

And third, it is quite obvious that this thread is going nowhere fast.