Dynamic Mass of Photon: E=mc^2 & hv

[JustinLevy]

Correct, it is good to see that you finally understood the problem statement.
My point was (go back and read the post) that for this particular case the approach works.

No, you previously very clearly stated that the mass did not increase. In suddenly changing your opinion now you are trying to make it sound like you always claimed it did increase. And on top of that, condescendingly implying that I was the one claiming the invarient mass didn't increase and you proved me wrong... a complete switch-a-roo. It is because of attitude like this that it was easy to tell you were a sockpuppet of the banned clj4.

Everyone makes mistakes, but unless we can admit to ourselves that we've made a mistake, we can't learn from them. I hope you can take this with you in the future and I wish you well.

While the discussion is now ended, I would still like to help you learn the results here as you are still misunderstanding some pieces.

As such, m'>m, m'=m or ... m'<m !
Surprise, surprise, the photon doesn't always add to the invariant mass of the system!

That is incorrect. The simple solution given before is general. You can translate to any inertial frame and the photon will still be there. So translate to the rest frame of the box, and calculate the result of adding the photon in that frame. The result as shown previously is that the invarient mass increases. Always.

3. It is a bad idea to use thought experiments in the style "photon in the box", which give variable results depending on initial and final conditions, depending on momentum directions in order to prove that "photons can contribute to the invariant mass of a system". Because sometimes they don't add any mass and other times they even subtract, thus making the whole issue muddled.

No, add a photon to a closed system and it will always increase the invarient mass. Please, please take the time to think this through so you can gain something from this discussion.

I have expunged "relativistic mass" and "photon contribution the the invariant mass of a system " from my course notes and I am very happy with the results.

I somehow doubt such course notes exist. Assuming you are indeed clj4, who admitting he is Adrian Sfarti when I mentioned I believed Sfarti's papers would get rejected from inclusion in last year's Grossmann Meeting on General Relativity published conference proceedings, then the only record I could find of you ever teaching was as a guest lecturer in a CS course.

If I am wrong, feel free to email me (bj0umow02@sneakemail.com) and I appologize in advance.

Also, I appologize about my comments on Sfarti's papers as there was no way for me to know you were him at the time. Actually, it is usually rare for presented material to be withheld from conference proceedings, so they probably will go through fine. It is too time consuming to adequately peer-review conference proceedings, but if they do make comments on your papers, I hope you take them to heart and stop believing that you are defending the mainstream view against a sea of "crackpots" even though many people have taken time to help point out how your arguements actually conflict with current mainstream theory. People aren't "out to get you", they are trying to help you learn.

I wish you good luck in your endeavors and hope you never lose the thirst for learning.

==================================

Returning to the original topic, there was a question I had that got buried earlier:

Going back to the hollowed mirror sphere example pervect brought up, the photons add an energy density inside, but also apply pressure on the walls of the sphere which would strain the sphere. Is there someway to show how this pressure/strain would add to the inertial mass of the sphere, or would that somehow be double counting the effect of the photons?

 

[Hurkyl]

What I call useful I'm sure you will have another idea of what is useful. I call "useful" that which gives the correct answer for any legitimate question in relativity.

Requiring one to write "rest mass" instead of "mass" has the benefit of added precision and the drawback of being more cumbersome. I define this requirement to be useful iff the benefit outweighs the drawbacks.

When I talk about the "usefulness" of relativistic mass in this context, I mean in the above sense: does the notion of relativistic mass have sufficient utility to justify encumbering the notion of rest mass?

The term you used has that meaning. I recommend that you just say what you mean instead of using glossy language.

Er, I did. Equivocation is one of the standard logical fallacies.

 

[pervect]

Returning to the original topic, there was a question I had that got buried earlier:

Going back to the hollowed mirror sphere example pervect brought up, the photons add an energy density inside, but also apply pressure on the walls of the sphere which would strain the sphere. Is there someway to show how this pressure/strain would add to the inertial mass of the sphere, or would that somehow be double counting the effect of the photons?

I talk about this in an arrticle I wrote for the wikipedia. (For those who care about such things, I need to point out that this should only be considered to be wikipedian reviewed and not peer reviewed).

http://en.wikipedia.org/wiki/Mass_i...simple_examples_of_mass_in_general_relativity

If you consider the simplest case of an isolated sphere, the tension terms in the walls of the sphere are exactly counterbalanced by the pressure terms in the interior of the sphere, and they make no net contribution to the Komar mass of the sphere + photons.

So if you have an empty sphere, and add photons to it, the mass of the system of sphere + photons increases by E/c^2, where E is the energy of the photons you added to the sphere.

I don't think I go into all the gory details, see for instance http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/pressure_vessel.cfm for how to compute the stresses in a sphere.

Also note that one particular type of mass from general (and not special) relativity is being used in this calculation, a type of mass known as Komar mass.

GR does not have a single, general definition of mass, but has several different definitions that apply under different circumstances.

The Komar mass formula is one of the simplest, and applies to any static system, such as our mirrored sphere. (Actually, with enough care, the Komar formula can also be applied to stationary systems, like rotating spheres or Kerr black holes, but some of the details get a bit more complex).

It should be noted here that we are using the Komar formula, and that for the isolated sphere it gives the same answer for mass as the special relativistic formula.

The simpler special relativistic formula could actually be used here - note that for the isolated system of sphere + photons it gives the same answer. Note also that the SR formula does NOT have any pressure terms - there are only momentum and energy terms in the SR formula.

It greatly simplifies things to consider the mass only of an isolated system - you can get numbers for the mass of a non-isolated system, but you should realize that they are coordinate dependent.

 

[cesiumfrog]

That is not a change in definition. I was explaining what the general formula for momentum was and that reduces to what you call the "ordinary" momentum for a single particle. [..] There is also an article in the Am. J. Phys. Called "The inertia of stress" [..] And there is no reason to keep referring to it as "generalized relativistic mass"

Regardless of whether Pete's "generalisation" is reasonable, it is distinct from the usual concept of relativistic mass. (And why haste to sacrifice the niceties of that mass concept, except to use invariant mass instead?)

That article considers some material that is painted with electric charge. The article basically presumes the total relativistic mass of the system to be (naturally) the relativistic mass of the material ($m_r$) plus the mass-energy required to pull the electric charge distribution onto place. The total energy/momentum result by multiplying that with $c^2$ or with its velocity.

Then the article claims* to demonstrate obtaining the same results by calculating the momentum as "$m_r$v + stress momentum + field momentum (E x B)" and the energy as "$m_r c^2$ + stress energy + field energy ($E^2 + B^2$)". (In this sense the article concludes that there is inertia in stress, as in mass and in classical EM fields).

Now, Pete seems to be asserting that (when we consider individual components of this system) the stress term should be associated with the intervening material (rather than with the external charge distribution applying the forces.. which is presumably ascribed only the field's energy/momentum). It isn't shown whether or not the intervening material actually behaves as having increased inertia physically.

*The technicalities seem a bit odd, I'll look into the references a little - the whole stress thing seems like a hack to avoid a paradox which other authors claim never existed..

 

[pmb_phy]

*The technicalities seem a bit odd, I'll look into the references a little - the whole stress thing seems like a hack to avoid a paradox which other authors claim never existed..

Modern authors over the last 40 years seemed to have left this part of relativity out of there texts for the most part. The only one that comes to mind is Rindlers 1982 intro to SR text. It appears that new students wouldn't touch a book that was written before they were born, supposeldy they believe that they can't learn anything from them that they can from a newer text. But such texts by, say, Moller are a gem of a textbook. I myself haven't even gotten to read Moller but that's due to a lack of access and a lack of $.

Pete

 

[robphy]

It appears that new students wouldn't touch a book that was written before they were born, supposeldy they believe that they can't learn anything from them that they can from a newer text. But such texts by, say, Moller are a gem of a textbook. I myself haven't even gotten to read Moller but that's due to a lack of access and a lack of $.

Pete

Apparently, this is Moller's text:
http://www.archive.org/details/theoryofrelativi029229mbp

(Off main topic:
Recently, I've been interested in old pre-1925 relativity books, especially those pre-GR books. It's interesting and inspiring to see the physical, mathematical, philosophical, and pedagogical approaches taken to understand relativity back then. And it certainly is possible that some idea or technique which has not been continued in the modern textbooks can be useful for pedagogy or even cutting edge research.

One of the most interesting are the works of A.A. Robb, starting with his 1911 book "Optical geometry of Motion" http://www.archive.org/details/opticalgeometryo00robbrich
which (I think) was the first to use the word "rapidity" (for the Minkowskian analogue of angle) and has the foundations of the Bondi k-calculus and the beautiful but not well-known formula for the interval between a local event and a distant one in terms of three clock readings from a radar experiment [as featured in texts by Synge, Geroch, and Burke]. Some of his other books: http://www.archive.org/search.php?query=robb AND (geometry OR relativity) suggest that he was one of the first to emphasize the causal order... in fact, recovering practically all of the structure of Minkowski spacetime from the causal order... in a methodical but tortuous way.
)

More from archive.org: http://www.archive.org/search.php?query=subject:Relativity. Enjoy.

 

[pmb_phy]

Recently, I've been interested in old pre-1925 relativity books, especially those pre-GR books. It's interesting and inspiring to see the physical, mathematical, philosophical, and pedagogical approaches taken to understand relativity back then. And it certainly is possible that some idea or technique which has not been continued in the modern textbooks can be useful for pedagogy or even cutting edge research.

Thanks for that insightful opinion Rob!

There was some comments before about a gas of massless photons which had mass itself and the weight of a box of such a gas. There was an article published on this topic

The mass of a gas of massless photons, H. Kolbenstvedt, Am. J. Phys. 63(1), January 1995

I have this one and am in the process of placing my journal files on CD. Since this one was already scanned and on disk I thought I'd post it. Its a very interesting read!

http://www.geocities.com/physics_world/Kolbenstvedt_1995.pdf

Best wishes and enjoy

Pete