# Talk:Photon/Photons and Mass Debate5

## User:Ati3414

User:Ati3414 (User:12.36.122.2), it is clear that your modus operandi is to spread wierdness about all the ways in which everything that we've all learned about relativity is wrong (Mass in special relativity, Time dilation, Transverse Doppler effect, Ives-Stilwell experiment, etc.). I understand the frustration you must feel, when just about everything you post gets immediately reverted, but maybe that's telling you something about how disconnected your views are from the accepted mainstream. That doesn't mean you're wrong, but that might be a hypothesis you should consider more seriously. It's getting tiresome. Give it a break. Dicklyon 22:35, 8 August 2006 (UTC)

The above comment with my signature is not as I originally wrote it. Ati didn't like it and deleted it, and I respected that. Please don't post things with my signature, when you could just as easily post your own comments. Dicklyon 16:37, 11 August 2006 (UTC)
Yes, the insertion attributted to you belongs to a well known sock puppet by the name of Gregory9, one of the lowest beings on this planet. He should be banned for this last trick. Ati3414 17:10, 11 August 2006 (UTC)
Actually, it was my content, with your name removed. But I agreed with letting you remove it, as it diverted attention from wiki issues to your larger outside problems. I don't think he should have put it back under my name, but I do understand what drives people like him and me to "low" tactics as you call it when normal civil tactics fail. Dicklyon 19:44, 11 August 2006 (UTC)
Welcome back, Kevin. Up to your old tricks? Do I need to talk with your professors again?Do you want lt. Frost to give you a call and remind you that you should stay away? Ati3414 14:10, 11 August 2006 (UTC)

Dicklyon, you have done nothing wrong by posting that. Ati3414 however has done something wrong, as no one is supposed to delete user comments. I saw he complained about his name being used (even though, as you stated, it is obvious who he is), so out of respect of his complaint, I removed his name (even though he continually uses mine). Dicklyon, I appologize if that change upset you, but don't let Ati3414's threats get to you. Speak your mind freely.

Ati3414, speaking of threats, as I already told Lt. Frost (and he agreed) I have not broken any laws. Trying to enforce a mutual contract is not harassment. However, what you did: making threats, calling the police, and harassing someone's employers, all in an attempt to get someone to back down on an agreement for your financial gain... That is a serious crime of felony extortion (punishable by up to 2 yrs in jail as well as fines). It is ridiculous (and a show of your character) that you believe that is an acceptable means of resolving a dispute. After talking to Lt. Frost, I decided to not press charges if he made the seriousness of your actions aware to you, and told him if you ever did it again I would immediately press charges.

Apparrently his talk with you didn't sink in, as you are now threatenning the same thing.

I already gave into your threats once: I voided a previous agreement just to get you to agree to shut up. Remember this: To keep the agreement all you had to do was refrain from contacting me, or posting on the site that started this nonsense. YOU chose to violate this. Don't try to blame your predicament on me. Your bad choices are what got you in trouble. And I hope one day you will finally learn to accept responsibility for your choices and actions. Gregory9 18:52, 11 August 2006 (UTC)

I believe that this conversation does not pertain to the physics of the photon, nor to techniques for presenting it to a lay audience. Please carry it out on your own talk pages or (if you do know each other) in person, or — dare I say it? — swallow your pride and leave your retorts unspoken. Forgive me, but I don't care to know who did what when with whose sock-puppet; the whole affair leaves me sad and heart-sick. Please stay focused on the question at hand (how and when to apply "relativistic mass" to massless particles, see part 2 below), and leave all else behind. Willow 20:37, 11 August 2006 (UTC)
You are completely correct. The discussion of our dispute shouldn't be on this talk page (and really, shouldn't even be on a user talk page). I should have ignored his comments, and I will in the future. As far as I'm concerned, any discussion of this dispute on wikipedia will end here and now.
As for how to best present the physics, since it appears several are seriously discussing it now, I'll add my comments for that below. Gregory9 21:29, 11 August 2006 (UTC)

## A way out of the labyrinth (part 1: physics)

It's easy to recognize that there are many really smart people here, who have devoted much time and effort to understanding light and photons. I think we'll all be happier and more productive, however, if we confine our remarks to physics and the best methods for explaining it to Wikipedia's readers, all the while keeping those two topics distinct.

Believe it or not, I think we all now agree on the physics, specifically that (1) the rest mass of a system is increased when it absorbs energy in any form; and (2) the rest mass of a system is not changed if the form of its internal energy is changed. One example is that of the equilibrating blackbody box mentioned above. Perhaps a simpler example would be a box initially filled with a plasma of positrons and electrons and no photons; the electrons and positrons will gradually annihilate each other, forming photons, but the rest mass of the box — as seen from outside — will not change. This is a good example because the electrons and positrons have rest mass, whereas the photons are massless.

Since (I think) we all agree that this is true, we can safely drop the discussion of the physics, and turn to the pedagogy (next section, stay tuned). Willow 14:15, 11 August 2006 (UTC)

But I doubt we all agree that this is true. We now Atti if he's willing to sign off on the idea that a box which contains a positron-electron pair which anihilate, does not change mass, inertia, and weight now that it contains two photons instead. SBHarris 15:18, 11 August 2006 (UTC)
Sure , as long as you phrase it correctly to say that now the box contains the energy 2E where E is the energy of one photon and you do not attempt to say that the mass of each photon is E/c^2Ati3414 15:27, 11 August 2006 (UTC)
We never said the mass of each photon is E. We said the mass of the 2 photon SYSTEM is 2E. Which it is, box or not. SBHarris 15:31, 11 August 2006 (UTC)
Ati, if you want to be constructive, you need to criticize what the text actually says, and provide an alternative encyclopedic sentence or paragraph that you believe is better. Criticizing it for what it does not say, calling it "junky", and asking for it to be deleted is not constructive in helping to get to a version that we can all agree is clear and correct. In this section, you could just say you agree with the physics as present above (if you do), and then move you issues with the pedagogy to the next section. If you're not willing to do this, you should be written off as uncooperative and the rest of us should move on. Dicklyon 16:48, 11 August 2006 (UTC)
I did, all that needs to be done is to take out the parens in "For example, a mirrored box containing a gas of photons, or even a single photon, with total energy E will have greater rest mass (by Δm = E/c²) than if the box did not contain this energy." Ati3414 17:15, 11 August 2006 (UTC)
Oh, I see, it's the amount of mass corresponding to the photon energy that is in question. Is it that the energy is undefined? Or that the mass added is not energy over c^2? Or what? I still remain perplexed abokut how this E/c² bothers you; I thought we were in agreement on the physics, but maybe not. Dicklyon 17:26, 11 August 2006 (UTC)
"For example, a mirrored box containing a gas of photons, or even a single photon, with total energy E will have greater rest mass than if the box did not contain this energy." OK? I wrote this for you about 10 times. This is the corrected statement Ati3414 17:27, 11 August 2006 (UTC)
And why do you object to quantifying the amount of mass that the energy E adds? Dicklyon 19:46, 11 August 2006 (UTC)

If I understand correctly, Ati3414 objected to the confusion that might result in readers if the Photon article associates the rest-mass addition ${\displaystyle \Delta m={\frac {\delta E}{c^{2}}}}$ of a photon to a system directly with the photon itself, which is massless. Thus, it is really a problem of how to present the physics, rather than any misunderstanding of the physics itself. I hope that we can now lay the physics component of our discussion to rest. Our goal is to reach consensus on Photon, not work out who said what when on its Talk page, right? And I feel consensus coming on, don't you? Oops, gotta run, I'm needed elsewhere Willow 20:51, 11 August 2006 (UTC)

His objection to the inclusion of the parenthetical "(by Δm = E/c²)" seems to be based on the idea that someone might use the incorrect value for E (like using 3E where the correct number is sqrt(8)E for his example). Ati, is there more to it than that? Should be easy to clarify if that's all it is. Dicklyon 21:21, 11 August 2006 (UTC)

## A way out of the labyrinth (part 2:pedagogy)

OK, it seems like the actual point of contention is the following: Is it enlightening or confusing to introduce the concept of "relativistic mass" for massless particles such as the photon?

Clearly, some people have argued here for "enlightening (keep)" while others have argued for "confusing (delete)". I suggest a middle way, in which

1. "relativistic mass" is eliminated from the main sections describing the properties of the photon; but
2. we include a short section at the very end of the article that describes the concept of relativistic mass as applied to massless particles and its applications. Such a paragraph is probably necessary, since at least a few readers will likely have encountered some reference to the "relativistic mass of a photon", which we should put into the context of the present-day approach.

Here is my reasoning. As noted above in the survey of physics textbooks, and also in the FAQ's cited at mass in special relativity, the concept of "relativistic mass" is deprecated. It is not used by working physicists, nor is it taught to physics students as a fundamental concept. Moreover, judging from the Pauli and Sommerfeld sources, and from the fact that Einstein himself never used it, it seems fair to say that "relativistic mass" has never been the predominant method for describing relativistic mechanics, at least not since Planck introduced the energy-momentum 4-vector in 1906 (Verh. Deutsch. Phys. Ges., 4, 136). However, the concept of "relativistic mass" does have one pedagogical advantage, in that it provides a ready explanation of why we humans can never exceed the speed of light.

However, this pedagogical advantage does not carry over to photons, since of course light moves at the speed of light. I have seen one use of "relativistic mass" (although it was never called that) in the derivation of the gravitational red shift for lay people. However, given the confusion that will inevitably arise when lay readers read that a massless particle has mass, I personally feel that "relativistic mass" is too dangerous to use in the main text of Photon. It leads to questions like those quoted in the FAQ's cited at mass in special relativity, e.g., "If I go fast enough, will I turn into a black hole?"

In my own experience, I have never seen a scientific article that applies the concept of "relativistic mass" to a massless particle. I can't claim to have surveyed the literature, however. Perhaps its proponents can provide references to primary literature, e.g., Phys. Rev. Lett.? It would be nice to know the fraction of scientific papers involving massless particles that apply "relativistic mass" to them.

As an aside, the unqualified equation ${\displaystyle E=mc^{2}}$ almost always refers to the rest energy of a particle, at least in my experience; the more general equation ${\displaystyle E=\gamma mc^{2}}$ is used for the total energy of a particle. In the publications that use the relativistic mass, the latter equation is generally written as ${\displaystyle E=m_{r}c^{2}}$, i.e., with an "r" subscript to clarify for readers that it's the relativistic mass.

Hoping for a happy ending to the debate, Willow 15:00, 11 August 2006 (UTC)

I'm not convinced we need a whole section; as I said earlier, a footnote would be fine. But it should be placed at the first mention of photons having zero mass (and be neutrally worded). This is not a textbook but a reference work, so discussions of "pedagogy" are out of place, and there's no such thing as concepts being "too dangerous" to mention because people might get the wrong idea. --Trovatore 15:23, 11 August 2006 (UTC)
The most common place E = mc^2 is used is to calculate binding energy in nuclei, where we work in the COM frame. We there use ΔE = Δm c^2 to describe the rest mass lost, and it's also understood that this Δm mass lost also gives the energy liberated by the bomb. What isn't discussed much is that this energy continues to retain its mass, so the equation is correct for the heat and light also-- mass of the bomb is constant until heat and light are drained away. It's just that the active forms of energy ARE allowed out, and are not generally weighed. All this is done in the COM frame, where rest mass is the same as total energy. In such circumstances, mass is not "converted" to energy. Mass is conserved, because it is IS the same as total energy (relativistic energy). All that happens in the COM frame is that one kind of energy is converted to another. But all of them continue to be associated with rest mass (weightable mass), just as in the equation above. Due to being in the COM frame, the momentum terms never enter in. SBHarris 15:29, 11 August 2006 (UTC)
The point is that there are a lot of cranks running around sayig that the photon mass is E/c^2, so, if we have badly phrased entries, like "photon in a box", we end up with a junky encyclopedia.Ati3414 15:31, 11 August 2006 (UTC)
Not necessarily. Energy is weighable in systems without being localized (kinetic energy being a perfect example). So if you accept it with kinetic energy, you can accept it with photons. Just point out that it's a system property, and the mass increase doesn't reside with any *particular* photon, but only with systems of them (or systems containing them). SBHarris 15:34, 11 August 2006 (UTC)
Lots of cranks running around is a problem you can take on elsewhere. For here, please quote any part of the article that you think can be improved, and then your suggested improvment. Dicklyon 16:50, 11 August 2006 (UTC)
I gave you the suggestion about 10 times: edit out the parens in the sentence "For example, a mirrored box containing a gas of photons, or even a single photon, with total energy E will have greater rest mass (by Δm = E/c²) than if the box did not contain this energy. ". Ati3414 17:13, 11 August 2006 (UTC)
Why should we delete this sentence when the math shows that it's perfectly true? We can add that the increase in mass is not due to any photon rest mass. It's simply the photon energy showing up as rest mass, in this system.
OK, yes, you have. Is there some other mass contribution you would put there? Or essentially zero, or just he rest mass of the photon? Is this a difference on the physics, or on the pedagogy? Sounds to me like we have NOT converged on the physics, but maybe others see it differently. Dicklyon 17:29, 11 August 2006 (UTC)
You can't be any more explicit. Remember the exercise that we run together with Sbharris? "A simple exercise" tells you that whatever increase is dependent on the momentum. The exercise that you collaborated with SBharris also proves the same thing. So, you are best off leaving the sentence as I suggested. Ati3414 17:38, 11 August 2006 (UTC)
The increase is dependent on the energy also, since E = cp. Systems of photons have a rest mass, which in the COM frame happens to be their total energy/c^2. There you are. SBHarris 17:49, 11 August 2006 (UTC)
The exercise you botched a couple of times showed total energy at 3E while the invariant at :${\displaystyle {\frac {{\sqrt {8}}E}{c^{2}}}}$ . Unless you have a new defintion of total energy. Ati3414 17:57, 11 August 2006 (UTC)
Nobody ever claimed the total energy of the system should be 3E. We all agreed on what it was, after we got the calcuation details right, and we all agreed it had to be computed in the frame of the COM of the closed system; then we calculated the rest mass of the system by dividing by c^2. Why knock down silly strawmen that don't have anything to do with anyone's actual position? The answer we agreed on is still the total energy over c^2. So we DO agree on the physics. Just disagree on what that E was about. Can we all agree that it's energy as evaluated in the frame of the system, clarify that, and get over our problems? Dicklyon 18:12, 11 August 2006 (UTC)

Thank you, I think we have now established that we do actually agree on the physics. As stated above, the rest mass of a system does not change if the form of its internal energy changes. So the rest mass of an (infinitely rigid) box would not change even if an atom bomb went off inside of it. Great, I think we can move on.

The question still before us seems to be whether (and when) to mention the "relativistic mass" of a massless particle. Contrary to what Trovatore seems to be saying, I believe that it's a worthy goal to write Wikipedia articles as carefully as possible to avoid misunderstandings by our readers. I personally do not see any compelling reason to mention "relativistic mass" within the main text of Photon, and several reasons (outlined above) why we should not. Therefore, I recommend that "relativistic mass" be discussed at the end, with the goal of placing it in context and clearing up any misunderstandings about the physics that the readers may have picked up in outside reading. However, before deciding, we should wait until its proponents have argued for the pedagogical usefulness of "relativistic mass", or provided references of scientific articles that apply "relativistic mass" to massless particles. Do we all agree? Willow 16:42, 11 August 2006 (UTC)

I absolutely agree that we should write articles as carefully as possible, to avoid misunderstandings. That's different from writing pedagogically, that is, as if you were teaching a course. Instructors teaching a course often tell less than the whole truth, at least for a time, to avoid time-wasting and off-topic discussions in the classroom.[1] I've never really agreed with that procedure, and try to avoid it in my own teaching, but I do sort of understand it in that context. It has no place here. --Trovatore 17:10, 11 August 2006 (UTC)
1. ^ As an example, it's common to make a flat statement in low-level courses, such as College Algebra, that "you can't divide by zero". Of course, if you go far enough, you find that there are meaningful and important contexts where you can, such as the Riemann sphere. What I did, when I taught that course at North Texas, was say something like "you can't divide by zero", but add a verbal footnote, something like "well, there are contexts where you can, but we won't get to any of them in this course". Now, they didn't really need to know that, but it's a matter of principle: Other things being equal, I prefer not to lie to my students.

Wonderful! Then we're in full agreement, at least as far as our goals for the article. I also favor completeness, even if not all readers can grasp all the points. I try to handle the difficult-to-understand topics by gradually building up to them, laying out a "honey-trail to enlightenment", starting with the basics that everyone can follow. Unfortunately, I fall short of my intentions all too often. :( Here at least we can help each other out in crafting good presentations of the concepts. Willow 18:15, 11 August 2006 (UTC)

Yes, of course in general, simple concepts should come first and difficult ones later. Just the same, we should keep in mind that it's a reference work; we want to be clear but we're not teaching. For the benefit of readers who want to be taught (or to self-teach) we can provide resources in "further reading" or "external links". If you want to write a textbook on the subject, there's Wikibooks.
I am not insisting that the notion of relativistic mass must appear in-line at the first mention of mass, or indeed in-line anywhere in the article. A footnote is fine. As for clearing up misunderstandings of the relationship between relativistic mass and rest mass, that's no longer about photons, so the link to mass in special relativity should take care of it. --Trovatore 18:24, 11 August 2006 (UTC)

I completely agree with Trovatore and Willow about the goals for the article. I favor completeness.

The issue as I see it is that some wish to say "The photon has no mass. Period." The problem is that this will not make it clear for the lay person, as it just leaves them with more questions as there appears to be conflicting information. For example, even a single photon "has a gravitational force" (causes curvature of space according to GR). The lay person may ask: "Is that not mass?" Or they hear that a system of photons has non-zero (invarient) mass. Or they read that a box with a photon has more (invarient or rest) mass than the same box without a photon. Or that the (invarient or rest) mass of an ion decreases after emitting a photon, yet the (invarient or rest) mass of the system (ion + photon) remains the same (so, the lay person argues: How can we possibly say the photon has zero invarient mass, and no rest mass?). It is often subtle questions like this that lead people to refer to an information source in the first place. Completeness is the way to go.

The point is, we need to accept that the statement "the photon has no mass" needs qualification to allow a layperson to understand. But before we can get to that, much arguing between ourselves seems to be about definitions... so to get that out of the way:

• rest mass - IF an inertial frame exists where the net momentum of the system is zero (ie it is at rest), the rest mass is DEFINED as E/c^2 in this frame. Note that this means a photon does not have rest mass (not that it is zero, but that this term does not apply to photons or other particles with zero invarient mass as there is no frame in which they are at rest).
• invarient mass - the norm of the energy/momentum four vector. While different inertial observers will disagree on the energy or momentum, this value is the same (invarient) for all inertial observers. The invarient mass is the same as the rest mass if the invarient mass is non-zero.
• relativistic mass - the relativistic mass of a system is the energy of the system divided by c^2. Different inertial observers disagree on this value. (Note: I rarely have heard this applied to particles with zero invarient mass. Instead I usually heard it referred to as "equivalent mass" of the particle (for instance when discussing light 'bending' in a gravitational field) and in those cases the meaning is clear from context.)

I believe most scientists would agree with these definitions, if we are having issues on definitions, state so now.

So two things 1) Can we agree we need to add a qualification to the statement of a photon's mass for it to make sense to the lay person? (not what qualification, let's just start by agreeing we need one) 2) Can we agree on the definitions above, and agree to specify which mass we are referring to while discussing this issue? (to stop the annoying miscommunications) Once we agree on these two things, we can finally get to the heart of the matter:

• Where should the details of such qualifications be put? Is it really appropriate on this page, or should we mention some common questions and refer to another page for details?
• What qualifications should be made?

Hopefully we can move forward in this matter, -- Gregory9 22:14, 11 August 2006 (UTC)

### implemented way out

My try is in place, except I wasn't quite sure what to do about the "Molecular absorbtion" section, which has some now-redundant language. The "box" section I simply removed, since I think, as Xerces pointed out long ago, it's not really about photons per se. Feel free to put the "box" section back if you think it's useful, but please consider keeping the rest of the edit, including the miscellaneous copyedits (removal of scare quotes, "nonzero mass" rather than simply "mass" when "nonzero" is what's meant, removal of piped links when wiki syntax makes them unnecessary, stuff like that). --Trovatore 07:11, 12 August 2006 (UTC)
I think it's OK, though I never understood why the "box" as composite system was a stumbling block. I made a few edits to it to clarify the relationship, as I understand it, to the more modern formulation that doesn't have the notion of relativistic mass in it. Please check it. Dicklyon 19:24, 12 August 2006 (UTC)
Well, there wasn't anything really wrong with the "box" section; it's just not clear that it belonged in an article called "Photon". It's not really about photons; it's about mass and relativity. The "composite systems" section, it seems to me, has the same problem. --Trovatore 19:44, 12 August 2006 (UTC)
Just the fact that a photon can add mass to a system seems very relevant to me, especially in light of the extent to which some people have a hard time accepting it. In that sense, a photon is the standin for massless particles more generally. Dicklyon 21:03, 12 August 2006 (UTC)
Oh, here's another thought -- how about moving "box" to mass in special relativity? It might be a more natural fit there. Note to anyone who does this: Please make sure you note in the edit summary that the text came from this article. Otherwise there's no record of authorship, which is likely a violation of the GFDL. --Trovatore 07:39, 12 August 2006 (UTC)

The "box" example is just a special case of the composite system, so I don't think we need that section. However, it may be useful to just add one sentence to the "composite systems" giving the box as an explicit example (because right now, it is a bit abstract, and as Dicklyon mentioned: "some people have a hard time accepting it". So it is probably worth it to quickly mention a concrete example.)

However, an explicitly explained example would be great for the mass in special relativity article... showing that when considering components of a system, relativistic mass is additive, but invarient mass is not, etc.

Also, one last thing for the photon, shouldn't we mention something about the non-zero "gravitational mass" (the fact that even a single photon will create curvature in spacetime according to GR). This is another common question regarding different interpretations of the photon's "mass" that comes up. If there is no good place to add it in the article, maybe we should just add it to the footnote and point to the GR article. What do you think?

-- Gregory9 18:39, 13 August 2006 (UTC)

## Ati no longer with us

I think Ati had some kind of break and was threatening another user and got himself blocked. Thus, we can write whatever we like about the mass of a collection of photons. I suggest we write the truth. Two wrongs don't make a right, but three lefts do. Life is complicated. That's no reason to dumb it down to child level. Photons have no mass, but some residual of their energy shows up AS MASS, in systems which contain 2 or more of them traveling in different directions. That mass can be calculated. There we are. SBHarris 05:43, 14 August 2006 (UTC)

I suspect he'd be having a fit over the new section "Transfer of invariant mass between systems", as it makes the mistake he warns against, of essentially attributing the relativistic mass E/c^2 to the photon without being careful about the different frames that make the E values possibly different at emission and absorption. At least, that's what I think his issues may have at their root. Anyway, I edited it; someone please check and see if I'm right. Dicklyon 04:57, 16 August 2006 (UTC)

## Wording of footnote, serenely ;)

Hi, I'm OK with not having a full section describing the application of "relativistic mass" to photons, but I do think we need to clarify for Wikipedia's readers which definition of mass is "mainstream", don't you agree?

Based on the survey of standard physics textbooks I carried out above, the usage in early literature by Einstein, Planck and others of that era, and my own familiarity with the modern scientific literature, it seems fair to say that the "relativistic mass" of a photon is not now — and never has been — a mainstream concept in physics. I have not found a single instance of it by name, although perhaps others will be able to cite such instances in Phys. Rev. or similar sources. So that's why I'm uncomfortable with calling it an "older concept, not much used anymore"; that phrasing suggests that it was once a mainstream concept that has now fallen from favor. Based on my reading, it was never even mainstream to apply "relativistic mass" to massive particles such as electrons (a handful of physicists adopted that approach), to say nothing of massless particles such as the photon.

The FAQs cited at mass in special relativity and the quotes from textbooks contained therein, also support this viewpoint.

However, I'm willing to listen to other viewpoints — particularly if they cite scientific references! ;) Perhaps my wording was strong, but I do favor being accurate at the expense of a few extra words, as I think you do, too, from what you said above. Let's find a good compromise. :) Willow 23:06, 15 August 2006 (UTC)

P.S. I can only get to the computer now and then; other, less happy duties are occupying my time. So please forgive me if I don't reply immediately.

The wording of the footnote as of this writing (and even the mere fact that the text is in a footnote, as opposed to the main text) should be adequate to indicate which one is "mainstream". The fact that physicists are not very fond of the usage is not really a fact about photons; it's a "meta" sort of consideration, and distracting. It would be different if it actually made a difference whether you describe things in terms of invariant mass or relativistic mass, but since it doesn't, let's just describe the two usages and be done with it. What readers do need to know is what unqualified "mass" means in scientific literature, but that is adequately covered by the current text. --Trovatore 23:17, 15 August 2006 (UTC)

## Rest mass

http://www.iop.org/EJ/abstract/0034-4885/68/1/R02

Thoughts on the paper?