Exploring Relativistic Mass with pmb_phy: A Conversation on Its Relevance

[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".

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

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.

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.

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

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 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.

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.

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.


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.