Talk:Mass in special relativity/Archive 1

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Archive 1

Archive 2

Archive 3

Rest mass VS relativistic mass

From the "Some reasons for abandoning the notion relativistic mass" we have:

One is forced to make statements like "The rest mass of a photon is zero", which sounds slightly odd because a photon can never be at rest, it always travels at the speed of light.

1) the statement isnt clear. I assume the author means "travels at c". But, this is also just not true as a photon going through any material like fiber optics or water or a bose-einstein condensate slows down dramatically in the last instance to within human walking speed. . Differences in the speed of light are the reason behind refraction.... delete, yes ?

Hfastedge 22:26, 27 Jun 2004 (UTC)

True, but irrelevant to the issue at hand. If you prefer change the statement to include "in a vacuum" (where the speed is indeed c). -- Fropuff 02:40, 2004 Jun 28 (UTC)

Relative mass is an example of trying to think of a concept (mass) in one paradigm (relativity) in terms of the old paradigm (classical Newtonian mechanics). It's an indication that the person isn't fully thinking relativistically but is still using a mishmash of nonrelativistic and relativistic concepts. Phys 21:23, 12 Nov 2004 (UTC)

Relativistic mass is an outdated term - see the "editing POV" comment below. Also, photons always travel at c, however in mateials - the photons get absorbed, reemitted and bounce around between atoms in irregular (but predictable macroscopically) patterns. However, during their travel - they are always going the same speed - c. Think of a car along a twisty road vs an airplane taking the straight path - even if the car had the same speed as the airplane, the airplane would always get to the destination faster. Fresheneesz 06:38, 22 November 2005 (UTC)

If you drop the notion of relativistic mass, then there is only 'mass'. The qualifier 'rest' is no longer operative. The statement becomes, "The mass of the photon is zero," which is accurate and not confusing.Kbk (talk) 15:44, 23 January 2008 (UTC)

Force equation question.

F=ma is OK, but when using relativistic force(F) and relativistic mass(m), there should also be relativistic acceleration(a), which has lorentz factor hidden inside. Using newtonian acceleration in a relativistic equation and then stating that the incorrect result is proof against relativistic mass is incompetence. I suggest to re-write the "F=ma" paragraph to be supporting for relativistic mass or to delete it.

Shouldn't the equation $F=\gamma {\frac {d(mv)}{dt}}$ read as $F=m{\frac {d(\gamma v)}{dt}}$ ?

After all, m is constant and $\gamma$ is an implicit function of t. Alfred Centauri 04:01, 28 May 2005 (UTC)

No, we're assuming that the velocity is constant. For the velocity to vary (i.e., acceleration), we require general relativity, not special. - mako 22:38, 17 July 2005 (UTC)

If v is constant, mv is constant too, and therefore d mv is zero, and so is F. Something wrong?--Army1987 07:35, 24 August 2005 (UTC)

Yeah, that crossed my mind after I submitted the last comment. I forget how this stuff works, and I'm not exactly yearning to review. (I don't think I've had to use this force equation, though it may apply in some sort of "relativistic rocket" problem.) Things don't make much sense when you try to formulate relativity in terms of Newtonian mechanics, but that's the equation given in books -- the book I have at hand doesn't explain much, but it does note that you have to use the chain rule when differentiating:

F={\frac {d(mv)}{dt}}=m{\frac {dv}{dt}}+v{\frac {dm}{dt}}

- mako 18:45, 24 August 2005 (UTC)

The correct equation is of course F=dp/dt. Since p=mγt, the γ goes inside the derivative. -lethe ^talk 22:24, 25 November 2005 (UTC)

NPOV?

It seems to me the article is making an argument, rather than merely reporting usage. One can make an opposing argument, but that side is not being presented. I think it would be more NPOV if it was less strident about the advantages of the more modern usage. As the article does make clear, the older usage is still sometimes used, even by physicists, and one can argue in its favor also. Gene Ward Smith 22:19, 21 Jun 2005 (UTC)

The goal was to report modern usage. However, it seemed appropriate to put the modern usage in a historical context and explain why this usage developed. I wasn't trying to present a POV although I certainly see how it could be intrepretted that way. -- Fropuff 23:29, 21 Jun 2005 (UTC)

The reasons for abandoning the notion relativistic mass are not convincing:

1. Pro-View: One is forced to make statements like "A photon has no rest mass", which sounds slightly odd because a photon can never be at rest.

Anti-View: Lene Vestergaard Hau of Harvard University and Ronald L. Walsworth and Mikhail D. Lukin of the Harvard-Smithsonian Institute have managed to brought light particles to a halt and then sped them back up to their usual speed.

2. Pro-view: The idea of mass increasing with velocity leads many to believe that the internal structure of a quickly moving object is somehow altered. However, the standard view of relativity is that the internal structure of an object is always unchanged, and that the different quantities measured by different observers for energy and velocity are simply the same reality seen from different points of view.

Anti-View: The quantum vacuum may in certain circumstances be regarded as a type of fluid medium, or aether, exhibiting energy density, pressure, stress and friction. This may alter the internal structure of an object.

3. Pro-View: The idea of relativistic mass combined with the notion of Lorentz contractions leads some people to the incorrect conclusion that an object traveling fast enough will form a black hole. However, by the very principle of relativity, if an object is not a black hole in one frame (its rest frame) it cannot be a black hole in any other frame either.

Anti-View: Some suggested that black holes were created during Big Bang and were tiny, some as light as 0.0000001kg. The density of matter as it crosses the event horizon varies inversely to the mass of the black hole, the miniscule nature of which had enormous pressures applied to create them. There is no evidence of their existence, but Hawking believes that these black holes could have evaporated.

4. Pro-View: If one wishes to retain the notion that mass measures the "resistance" to acceleration, then mass can no longer be treated as a scalar quantity. This is because it is easier to accelerate something perpendicular to the direction of motion than parallel to the direction of motion. In effect, an object would have more mass in one direction than other.

Anti-View: This is a misconception on the transverse and longitudinal stress in special relativity or fluid dynamics.

5. Pro-View: The primary reason that most physicists chose to abandon relativistic mass in favor of the rest mass is that rest mass is a Lorentz invariant quantity — it is the same in every reference frame. Strictly speaking, it is the time-like component of a four-vector (the energy-momentum four-vector). A four-vector is a Lorentz invariant quantity, but its individual components are not.

Anti-View: This is only one of the possible mathematical approaches. Richard Feynman was surprised that this was common though useful. (Feynman Lectures Vol 1 Section 16-1 Relativistic Mass)

I don't see a need for this pro- and anti-view stuff. Relativity is such a strange thing that there exist a wide variety of approaches to understanding it, some which work better in some situations than others. That said...

1. "A photon has no rest mass." That's just a terminology issue. As long as the concept is clear, it's okay. As Feynman says (v1 17-7), "If it is a particle of zero rest mass, what happens when it stops? It never stops!" The note about slowing light is a completely different kettle of fish: Bose-Einstein Condensate and quantum interference. Special relativity for the beginner stays in the classical realm.

2. This "internal structure" stuff is just not understood enough to say anything about it. And what about something like the electron? Scattering tests have established the point charge property of the electron down to a very small radius. Just how does this "quantum vacuum" change a point particle anyhow?

3. I can't say I remember the exact discussion from A Brief History of Time, but I do not see what primordial black holes have to do with relativistic mass.

4. Fluid dynamics? Eh?

5. Well, that's the most important aspect of the invariant mass: it's invariant. Note that the four-vector itself is not invariant. Only the scalar product of two four-vectors produces an invariant quantity. And I looked through the Feynman lectures 16 (and 17) and didn't see anything like you mentioned.

- mako 06:41, 10 July 2005 (UTC)

It is because there exist a wide variety of approaches to understanding, as you mention it, we should be more open-minded to new development instead of suppressing other views.

But some approaches are more valid than others, and these "anti-views" are just plain nonsense. You can tell kids that babies are delivered to doorsteps by storks, and they'll believe that—until they know better.

We can mention the various modes of interpretation, but only if we note their caveats. Science does not cleanly delineate into pairs of opposing viewpoints; particularly for something as old and established (it's the World Year of Physics 2005 for a reason) as relativity. - mako

"Plain nonsense" from Richard Feynman, Albert Einstein, Stephen Hawking, Paul Davies, Lene Vestergaard Hau...!? Wow, you'll be a great, revolutionary physicist!

I'm afraid you're missing the point here. I appreciate the sarcasm, but I'm saying that those numbered points are nonsensical. But anyway:

Feynman - Feynman uses the relativistic mass, and in the Lectures he does say "surprisingly enough", but that was probably in the context of the lecture, which used a Newtonian-relativity approach to a 2-body problem. He hasn't introduced four-vectors yet.
Einstein - He rarely used the relativistic mass himself.
Hawking - A Brief History of Time is a popular work, with very little math.
Davies - He's a popular science author.
Hau - As I already said, that's getting into quantum effects, which are outside the scope of this article.

Anyway, I'm working on a rewrite which I hope will clear this subject up. The one main point (that is not as heavily emphasized in the article as it should be) is that popular and other math-simple approaches to relativity, or relativistic "extensions" to Newtonian mechanics, tend to use the relativistic mass as a conceptual aid. The full-blown four-vector approach tends to use matrix notation, which a popular audience is not so likely to be familiar with. - mako 22:21, 17 July 2005 (UTC)

Many have been so passionate on this debate, it could be more political than you could imagine... Don't underestimate Richard Feynman...

Usage examples

I don't think the usage examples are helpful at all. To illustrate what I mean, suppose I list every single paper from the past 5 years from arxiv.org:hep-ex -- I would bet none of them use the relativistic mass. Sure it would show current usage, but it wouldn't be very useful. The article already says enough about usage; a bit about the (almost nonexistent) controversy could be added, but isn't really necessary. - mako 02:29, 27 July 2005 (UTC)

In a recent survey by Gary Oas (arXiv:physics/0504110), 477 out of 637 textbooks and various other works still rely on the concept of relativistic mass. You should not meddle around here as you're a mathematician instead of physicist, or at least do more homework first!

And what, may I ask, are you?

As for me, I'm neither a mathematician nor a physicist: I'm an electrical engineering major. I am however working with the people who wrote hep-ex/0502040, so I am doing physics at a particle accelerator site.

If you would read the paper you cite, it argues that the usage of the relativistic mass should be dropped. This doesn't support your argument. Perhaps you should solidify your position and actually defend it, instead of resorting to ad hominem attacks. - mako 23:57, 27 July 2005 (UTC)

We should not cover the truth, just like Gary Oas, who revealed that 477 out of 637 textbooks etc adopted RM, including Nobel Laureates like Leon Lederman, Richard Feynman, Martinus J.G. Veltman, Julian Schwinger, Robert Laughlin and so on. On the contrary, it is a shame that many physicists employed tactics like "Relativistic Mass is unfashionable, or outdated" as arguments. BTW, I am a physicist, reading more than 400 books and papers, and published a paper on this before. No, I'm not a promoter or destroyer of relativistic mass, afterall this concept is not created by me, and this is why I provide you Gary Oas's paper, which does not support RM. So, don't cover up the references to the public! Gosh, I'm not going to look at this website anymore...

Buh bye. -- CYD

Relativistic mass and mass in rest OK

With the formulation of the theory of the special relativity of Albert Einstein the concepts of relativistic mass were introduced, m, that depends on the speed of a frame of reference in rectilinear movement uniform and mass in rest, m₀ that talks about to a frame of reference taken in rest. These two states, for the inertial marks, that is to say, nonsubject to forces, are symmetrical due to the relative character of the movement. Of such form, that of its equivalence origin the equivalence between kinetic energy and mass, that was extended by heuristic route to all class of energy. For example, in a frame, the mass of a body, that in opposite directions absorbs the same amount and frequency of electromagnetic energy, increases its mass. The called modern relativity, that constitutes a revision of special relativity rejects the concepts of relativistic mass and mass in rest that it replaces and it unifies by invariant mass, that is, of a mass whose magnitude is independent of all frame of reference and result of transformation of the Lorentz. This revision is controversial, to see: Chapter 3 The energy has mass:

The law of the inertia of the energy and the speed of the gravity. October, 2004.

Editing POV

None of the information on this page is opinion. It is a current fact that relativisitc mass is a term that is rarely used in physics anymore - for the reason that it leads to confusion - but mostly because rest mass is used in so many equations - while relativistic mass is a much less useful (and less measureable) quantity. WAS, not to be inflammatory, but you really shouldn't edit a page giving me support just when we're having an argument about this issue. Since you like sources so much, heres a couple (look for the word outdated):

If you look up similar things about relativistic mass you'll find numerous references to the "outdated", "antiquated", and "obselete" term. I hope the sources help. Thanks. Fresheneesz 06:31, 22 November 2005 (UTC)

Rest mass is more convienient in particle physics in general. Relativistic mass is more convienient some of the time especially in nonparticle physics. The fact that equations are equivelent whether one uses one or the other and that computers do most of the actual number crunching mean there is NO debate among physicists about which term to use. Whatever is most convienient is used. When invarience is needed, rest mass is used. When actual behavior is being discussed, the relativistic mass is what is actually MEASURED.

http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html is the point of view of Philip Gibbs in 1997. It says "By convention relativistic mass is not usually called the mass of a particle in contemporary physics so it is wrong to say the photon has mass in this way. But you can say that the photon has relativistic mass if you really want to. In modern terminology the mass of an object is its invariant mass which is zero for a photon." He is right about convention and the use of "mass" for PARTICLES. But it is also true that by convention in contemporary physics, the "m" in E=mc squared refers to relativistic mass. Which mass to assume is all about convenience (and convention).
http://www.answers.com/topic/relativistic-mass quotes wikipedia.
http://relativistic-mass.borgfind.com/ says "However, the fact that some relativity courses continue to use relativistic mass demonstrates that this is a matter of opinion." Wikipedia doesn't take sides, making arguments. We do present encyclopedic arguments made by others. Physicists do NOT argue over this.
http://www.tardyon.de/mass.htm says "In this document, the word "mass" will refer to the thought of "inertial mass", as initially intended by Newton when he first included it as a component of a classical mathematical equation. In that form, "mass" is simply a natural resistance to any change in the current state of motion of any specific part of existence." The author is wrong in thinking "inertial mass" = "rest mass". WAS 4.250 17:37, 22 November 2005 (UTC)

Please refer to the article's external links. - mako 18:58, 23 November 2005 (UTC)

WAS, your last post seems to confirm that "mass" means conventionally "rest mass". In arguing that it is an opinion, a convention at one point *was* the best way to do something according to some people - an opinion. But when it becomes a convention, it is no longer an opinion, but a tool used to make communicating easier. Perhaps in thinking the convention is the best way is an opinion - but the convention is *not* opinion.

Also, when you meanioned that the author writing this is wrong in thinking "inertial mass" = "rest mass", he never said that. He said inertial mass *is* the inertia of an object - which is what relativistic mass is. Not like that is relavent to the argument or anything...

In conclusion, can we now decide how to use this convention - and how to edit this page so that it makes sense? I think that it would be good to say that E is rest energy, and *then* note that in history, the m in that expression was relativistic mass. What do you think WAS, and anyone else? Fresheneesz 00:50, 25 November 2005 (UTC)

I'd like to see the page reverted to its original state (meaning -- no offense -- before you guys came along). If you look at the rest of Talk, you'll see that I've been "custodian" of this page for a while. I also wrote much of what WAS considered POV; I consider it a telling of straight facts. A lot of what I do on WP involves cleanup, POV included, and I feel that I have a pretty good sense of what constitutes POV. I am willing to argue about presentation here on Talk, but wholesale blanking is a reactionary thing to do. And regarding the arguments above, the rest mass and the rel. mass are both used in particle physics, as they are merely concepts in relativity. The rest mass is important because it is an intrinsic property of a particle. The rel. mass (people call it "energy" instead of mass nowadays) is what you measure in certain kinds of detectors. - mako 00:53, 27 November 2005 (UTC)

I agree, all of my edits were compromises between the "original" and new edits. Fresheneesz 05:27, 28 November 2005 (UTC)

I notice that a few remarks in the article are not facts but POV or worse. I'll make a few small improvements in the coming days. Harald88 22:15, 6 May 2006 (UTC)

Newton's laws

I want to remove the comment about Newton's laws remaining unchanged when you use relativisitc mass. Newton's first law remains unchanged whether you use relativistic mass or not, while Newton's third law becomes very difficult to keep and is usually thrown out due to the relativity of simultaneity, whether you use relativistic mass or not. The only place relativistic mass is relevant is

f={\frac {dp}{dt}}

and

p=mv.

The first equation is Newton's second law, the second is simply the definition of momentum. There seems to have been some confusion earlier about whether the γ should be inside the derivative. It certainly should go inside, as I think is clear from this equation. -lethe ^talk 22:33, November 25, 2005 (UTC)

"concept" example

I'd like to keep the exposition of the "concept" section simple, without reference to relativistic mass before we've even defined it. Any good way to set up the observer and mass without bringing in too much complexity? - mako 09:45, 30 November 2005 (UTC)

"Mass* and energy in this theory also depend on velocity."

"*Modern physics teachers prefer to redefine mass such that it is velocity independent."

Gerard't Hooft. In search of the ultimate building blocks, (Cambridge University Press, Cambridge, 1997), p.17 He received 1999 Nobel Prize in physics for work in electroweak interactions.

Gerard't Hooft is wrong! Modern physics teachers and Wikipedia's contributors on relativistic mass, who are experts in other fields, prefer to redefine mass such that it is velocity independent.

And the subject is ...

What is the subject of this article??

Is it the relativistic mass in itself?
Is it a comparaison of the relativistic mass with others acceptions of mass?
Is it a nomenclature of every concepts of mass that exist from the begining of physics till today?
Is it an argumentation of what is good and what is no good between the different concepts?
Something else?

More I read the article and the talk page, more I'm confuse! Please help the poor reader that i am!
24.202.163.194 03:21, 27 December 2005 (UTC)

You're right, I've always felt that this page lacks a clear topic. I propose a move to the title Mass in Special Relativity, as that is what the page is really about; more tellingly, rest mass redirects to this page. The current title seems to make this article a lightning rod for controversy. - mako 07:59, 28 December 2005 (UTC)

I agree with you. This new title is more in the heart of the problem than the actual one, which is not bad in itself, but the subject is larger than just the relativistic mass who should be a section of the new article. Perhaps the new article should be even larger and have the title 'Mass in physics'. But, being more a collaborative style than a contributor style, I prefer to wait for the opinions of others contributors to make a final decision. 24.202.163.194 16:23, 28 December 2005 (UTC)

The page will be moved shortly if there are no further objections. - mako 00:02, 5 January 2006 (UTC)

Mass in special relativity would be fine. Note the naming conventions with respect to capitalization. -- Fropuff 00:28, 5 January 2006 (UTC)

Aye. - mako 09:06, 5 January 2006 (UTC)

Kinetic energy section of the article

E = Mc² being a special case where v = 0, then $\gamma$ = 0 also, and E = Mc² reduce to E = mc². So, the following demonstration is not valid. That's why it has to be removed and replaced by a valid one.
What do you think of that?
24.202.163.194 04:23, 28 December 2005 (UTC)

E = Mc² is valid for v not equal to zero; that's the whole point of the relativistic mass. I guess the page still needs some rewriting to make the concept clearer. - mako 07:59, 28 December 2005 (UTC)

For the validity of this demonstration, I have to make a further investigation into this subject. And, as much as possible, have the point of view of others contributors. 24.202.163.194 16:21, 28 December 2005 (UTC)

I'd just made a quick check up, and I am happy to tell you that you are right for E = Mc², M being the relativistic mass and not the rest mass. So, it is not a special case: that's was my mistake. Wrong reading! Thank you to have pointing it to me, and sorry for the perturbation! 24.202.163.194 17:09, 28 December 2005 (UTC)

Regarding the demonstration itself, my first investigations show me that it is not appear to be a stricly rigorous one, because they (physicists) do it with E and Eo at first, after they define m and m0 (or M and m here) base on their previous equations, and they finish by E = ym0c² ( E = yMc²). In the article, we begin by their end. But, even so, we can keep the one we have, for the moment, because their demonstration is very long and it would take an article by itself! 24.202.163.194 17:52, 28 December 2005 (UTC)

Gravity & Relativistic Mass

Sidestepping the pros and cons of whether the notion of relativistic mass is useful or not, and accepting that one could just talk about relativistic momentum and avoid the whole mess ...

... I have a question: does the gravitational force exerted by an object increase as it approaches the speed of light? I would suspect not -- but I have no good clue one way or another.

If not, that would be a very solid argument in favor of the anti-mass faction.

MrG (Greg Goebel) / 27 february 2006

Here are some references:

1. the theory had to combine the following things: (i) From general considerations of special relativity theory it was clear that the inert mass of a physical system increases with the total energy (therefore, e.g., with the kinetic energy). (ii) From the very accurate experiments, it was empirically known with very high accuracy that the gravitational mass of a body is exactly equal to its inert mass.” “ Autobiographical notes by Einstein published in 1949

2. A moving body with rest mass M gravitationally may attract nearby objects with an increase mass, (gamma)M or 2(gamma)M depending on the direction of velocity or approach. (Olson, D. W. & Guarino, R. C. (1985). Measuring the active gravitational mass of a moving object. Am. J. Phys., (53) 661

CL / 28 february 2006

Here's an abstract for the Olson paper. The authors note that it's only valid for a special case. (This question may be more general relativity than special.)

Food for thought: If you go too fast do you become a black hole?. - mako 10:09, 28 February 2006 (UTC)

Nice response -- very often the reply to "I ask this question out of ignorance" tends to focus on "ignorance" instead of "question".

Einstein's comment is a bit confusing because I would think "inert mass" would mean "rest mass", but when he says that it "increases with total energy" ... well, that throws a spanner in the works. The second comment is straightforward: yes "relativistic mass" does imply greater gravitational force.

However, suggesting that this may be more a GR question than an SR question makes me want to back up a bit. Not being a physicist getting seriously into GR is not a step I am inclined to take. If Einstein complained about the math ...

Reminds me of the time I was thinking about SR paradoxes and started wondering about what would happen if two remote starships began to accelerate in the same direction in step. I quickly realized I was out of my depth; when I found out I was reinventing Bell's Paradox I didn't feel so bad.

I would like to leave this thread in place for a while to see if it attracts further comment.

MrG (Greg Goebel) 01 mar 06

Everybody: I've had to fix the "relativistic mass" concept section because it was trying to say that faster objects increase gravitational field due to their "relativistic mass". This is the way that lies toward the idea that objects become so massive with speed that they might form a black hole. Wrong. In the rest frame an object is not a black hole, so it can't be a black hole for anybody else, either. That would be a paradox, so it's obviously wrong.

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html

The only time kinetic energy shows up as increased gravitational field is when it's the kinetic energy in a SYSTEM where the sum of momenta is zero. Otherwise, kinetic energy shows up as relatistic mass and as increased momentum, but not as gravity.

As for inertia, inertia is a tricky concept depending on how you define it. The only inertia of a body connected with its gravitation is the inertia it presents in its rest frame, which is to say, its center of momentum frame inertia. Inertias in other frames (and in different directions even in the same frame, when it's a moving one) don't agree with each other, as shown in this section. So which of these different inertias would be connected with gravity? Another paradox. The answer is "none." Only invarients (like invarient mass) are connected with gravity, because an object can't be, and not be, a black hole at the same time.

I might add that it's quite possible for two different inertial observers to see different gravitational pulls from the same mass in relativity, but this is a strictly directional thing caused by the overall shape of the gravity field being "squashed" in the sideways direction, as seen by moving observers. The same thing happens with electric fields and moving charges. However, just as the total charge in relativity is conserved and invarient to different observers, so is the mass and the gravitational field. An increased field in the transverse direction is compensated for by a decreased field in the direction of motion, and so the integrated total comes out the same for all observers. Still no black hole! Sbharris 01:38, 9 April 2006 (UTC)

Just noticed this old discussion. What is really needed here is a page on "mass in GR". I'm working on one, actually :-). Much of it will be considerably more technical, with a long discussion of Komar mass and a short discussion of Noether's theorem, but I plan to include a section with questions like this in it as well.

The situation is not as simple as the above remark makes it.

Consider a pressure vessel containing a gas. If we add energy to the system by heating up the gas, the system gains energy, does not gain momentum, and hence gains mass. The only difference between the pressure vessel containing a hot gas and a cold gas is due to the motion of the molecules. See also http://arxiv.org/abs/gr-qc/9909014. Thus motion can affect the gravitational field, this makes it different than charge.

There are some technical issues here too. The standard interconversion of curvature into forces requires a static metric, something that's lacking with a moving mass.

Pervect 20:21, 9 August 2006 (UTC)

Erroneous claim?

"the rest mass is an intrinsic property of an object" appears to be erroneous: according to SRT the rest mass increases with temperature, because the speed of the parts increases. Note: it might be that the article uses a different definition of "intrinsic", but its meaning should be both clear and consistent in one and the same article. Harald88 14:01, 6 May 2006 (UTC)

Maybe better to say "invariant". Mass is never intrinsic, rather density is intrinsic, and mass is extrinsic. Temperature is instrinsic, by the way, so the fact that mass depends on temperature doesn't contradict anything. -lethe ^{talk +} 14:09, 6 May 2006 (UTC)

That sounds better - but if that new phrasing is correct (and likely it is), then the Wikipedia definition of that term, Invariant (physics), is also erroneous. How should invariance be formulated so that it fits with a body that is increasing in temperature? Harald88 17:47, 6 May 2006 (UTC)

We're always talking about closed systems here, and I've fixed up the Invariant (physics) section to make that clear. If you let energy or momentum in or out of your system, they're obviously not conserved!

I'm afraid that that doesn't help: "relativistic mass" is in that sense also invariant. The way I understand it - and I propose to reformulate it accordingly - is that "invariant mass" is invariant under changes of coordinate systems. Harald88 19:17, 6 May 2006 (UTC)

Noooo! See the Wiki on mass in special relativity. When we say relativistic mass we generally mean the total relativistic energy/c^2. It varies with inertial frame/inertial observer. Only the invariant mass (which is not the same thing, and is the relativistic mass only in the COM frame) is invariant (ie, Lorentz-invariant, ie, the same in all inertial frames).Sbharris 23:11, 6 May 2006 (UTC)

mass in special relativity happens to be what we are editing. And apparently you misread what I wrote, for I fully agree with your last statements... Harald88 18:47, 9 May 2006 (UTC)

Both density and mass are intrinsic quantities of objects, so long as the system is closed and we're not adding or subtracting stuff (like heat energy and therefore rest-mass) surreptitiously. If you don't close the system, mass changes and usually density does also. You can't just talk about an "object" in a loosey-goosey fashion. For any of this to make any sense, it has to be an isolated "well-defined object", with nothing spalling or flaking or boiling or radiating off it. Sbharris 19:06, 6 May 2006 (UTC)

Hmmm, it occurs to me that density is not intrinsic, even to closed-system objects. They can always expand and contract spontaneously, due to phase changes and what-not. Mean density is intrinsic to closed systems, but only because mass is invariant, and if you define your system/object volume, so that it also is invariant. Sbharris 19:11, 6 May 2006 (UTC)

A property of an object is intrinsic if it doesn't change when you have two objects. Density and temperature are intrinsic, mass is not. A property is extrinsic if it doubles when you have two of them. Mass and volume are extrinsic. A property is invariant if it doesn't depend on your reference frame. Mass and temperature are both invariant, density and volume are not. -lethe ^{talk +} 20:50, 6 May 2006 (UTC)

Um, you're confusing your terms with the technical thermodynamic meanings of the terms intensive quantity and extensive quantity. Intrinsic and extrinsic are somewhat loosely defined terms of ordinary language. Don't use them when you really mean intensive and extensive. My revenge for your spelling pettiness :). Sbharris 22:48, 6 May 2006 (UTC)

Wow, you're right. I stand corrected. I'm sorry. -lethe ^{talk +} 02:42, 7 May 2006 (UTC)

Wow, the article invariant (physics) is pretty confused about invariants versus conserved quantities. It claims that acceleration is invariant under Galilean transformations. Whoa! -lethe ^{talk +} 20:56, 6 May 2006 (UTC)

Ok it looks like we're getting somewhere, thanks for the comments! I'll now correct "intrinsic" to "invariant" but will not yet link it until invariant (physics) has a compatible definition (I hope that Lethe agrees to do a little effort there). Harald88 22:03, 6 May 2006 (UTC)

I'd certainly be happy to take an axe to that article, but first we have to decide what's to be done with it. My point is, I'm not sure we have a need for an article called invariant (physics). This article is about invariance and its relationship to conserved currents. It might be best merged with Noether's theorem or covariance and contravariance. What do you think? -lethe ^{talk +} 02:42, 7 May 2006 (UTC)

I think Invariant (physics) should be merged into Covariance and contravariance. —Keenan Pepper 07:31, 7 May 2006 (UTC)

That makes sense as there are too many small articles around. As invariance is used independently of covariance, that article could be renamed "Invariance, covariance and contravariance" (or simply "Invariance and covariance"). Harald88 08:38, 7 May 2006 (UTC)

I was planning a rewrite of covariance and contravariance at some point. Maybe it's time I got back to that. -lethe ^{talk +} 07:55, 7 May 2006 (UTC)

I think Invariant (physics) should remain separate, since: 1) invariance is an important principle in physics (conservation laws, symmetries etc.) and this article could be expanded alot, and 2) covariance and contravariance appears to be mainly a mathematical discussion, not physics. Rotiro 07:27, 25 May 2006 (UTC)

gravitational field?

"invariant mass is the only type of mass which is connected with a gravitational field".

Apart of the fact that GRT doesn't really belong in this article, I think to have seen otherwise; and it's ambiguous if active or passive gravitation is meant. Please provide the source and the corresponding equation, thanks! Harald88 22:44, 6 May 2006 (UTC)

Well, the statement really should have read something like "invariant mass" is the source of the total gravitational field. There are "gravitomagnetic" effects for masses moving past at high velocities, just as there are magnetic effects from charges moving past at high velocities (this effect makes a charge look like a bigger charge, but only to the transverse observer--- other observers see a SMALLER charge). But total space-integrated charge is an invariant in relativity, and so is mass. But the mass that is invariant (frame invariant) is the invariant mass, which is the mass you see in the COM frame of your system. There's a discussion in chap 22 of MTW. The short argument is that you can't make something into a black hole by going past it really, really fast. You can't even make it LOOK like a black hole, because the effective gravitomagnetic increase in "mass" is proportional to gamma, so the field can't get infinite. Sbharris 23:23, 6 May 2006 (UTC)

Your statement that "the effective gravitomagnetic increase in "mass" is proportional to gamma" corresponds to what I meant: that happens to correspond to "relativistic mass", not "invariant mass". Thus it remains obscure what argument there would be for preferring the use of either m or M=γm in GRT equations. Harald88 23:51, 6 May 2006 (UTC)

Thus I now take out the corresponding paragraph:

For example, invariant mass is the only type of mass which is connected with a gravitational field (thus, no matter how fast an object goes, it cannot become a black hole because of relativistic mass).

If someone knows a way to rephrase it so that it is correct (either as Wikipedia statement or quote), please go ahead - but don't forget to indicate its relevance for this article about SRT. Harald88 18:38, 8 May 2006 (UTC)

Well, how about invariant mass as the "source" of a total gravitational field? It's clear you can go by an electron very fast and see a larger electric field in your direction, but that's more or less an effect of your squished spacial coords. The source of the field is the (dressed) charge of the electron, and that doesn't change from frame to frame, because you correct for it. There's an invariant there.

The source of a g field far out from an object is the integrated S-E tensor, and by the time you get far away from an object (low field limit-- linearized approximation to GR), that total flux through spacial boundary doesn't change, either. There's a sort of Poisson's equation for gravity-charge just as there is with electric charge. And the gravity charge is the rest mass or invariant mass that you're far away from.Sbharris 19:58, 8 May 2006 (UTC)

It's still not clear what prevents M=gamma*m (or E=M*c^2) from being the source of the gravitational field (which equation can't you write in that form?), nor what that has to do with Special relativity.

Note also that mass is not invariant like charge: an electron cloud of N electrons has a total charge of N*q_e, but total mass > N*m_e due to their kinetic energies. What will its total gravitational field be? Harald88 20:21, 8 May 2006 (UTC)

strange remark

"A more crucial flaw is that γ is undefined for v = c; in other words, these equations are not valid for photons."

-> It's a flaw of what exactly? Or, to put it differently: Is it also a "crucial flaw" of invariant mass that F=ma is not valid for photons?! Harald88 23:18, 6 May 2006 (UTC)

photons don't have invariant mass unless in pairs, or confined. And if confined, they would be expected to show mass m = E/c^2 (see the end talk section in mass) and no doubt the same inertial mass F/a. In this case, the acceleration just induces the same Dopper shift that the g field does in my example. The photons hit the end of an accelerated box a little harder, and it feels just like mass. Sbharris 23:56, 6 May 2006 (UTC)

Photons do indeed have an invariant mass. It is zero. I once again urge you to stop peppering Wikipedia with this nonstandard notion that mass includes kinetic energy. -lethe ^{talk +} 07:23, 7 May 2006 (UTC)

Just wanted you to remind you of the state of our conversation as of May. See the remark above. Do you still agree with it? Or have you learned something since? Sbharris 15:51, 17 June 2006 (UTC)

I concede that the concept of invariant mass of a system of particles is indeed used. I was wrong when I said it wasn't. -lethe ^{talk +} 16:44, 17 June 2006 (UTC)

Thank you for that, but usage is by far the least of the problem. Read the paragraphs above. I'm reminding you that systems of photons have mass, and you're flatly denying it, and telling me I'm peppering Wikipedia with the nonstandard notation that mass includes kinetic energy (which by now I hope you'll see is a yawner of an idea). You removed my example in which a pair of photons become a pair of leptons, without change in mass of the system, because you apparently believed it was just wrong physics. Well, it's not wrong. It's correct, and it's illustrative of an important point about the invariance and conservation of MASS, which is the subject here in this article on MASS. I'm not trying to publicly bust your chops here, but I am trying to get you to see the reason for my frustration in dealing with you on this topic. Please try to be a little more flexible when next you revert an example of mine, because you personally find the physics or conclusion surprising. Consider instead that the problem may be that you haven't had contact with the ideas being explained. Use this Wiki as a chance to learn something about physics, rather than a chance to be obstructive. Sbharris 17:38, 17 June 2006 (UTC)

Can you provide me with a diff of the particular reversion you're referring to now? I'm finding your remarks a little hard to follow out of context. -lethe ^{talk +} 18:20, 17 June 2006 (UTC)

You reverted a number of my edits on April 14 in mass. See the long discussion the Mass: Talk section (Mass of compound systems) which follows that, on that date. Most of your claims there are just wrong. If you'll go back and read them, and then again read the edits you reverted me with, in the light of our following discussion, it may refresh your memory. Briefly, you kept saying that colliding objects which stick increase in mass, and I pointed out that this is not true of you consider the system mass (including the kinetic energy of the particles) before the collision. You said system mass was a nonstandard concept and reverted me. But you're wrong-- it is a standard concept. You left on the MASS page an "example" where massive particles are made of massless photons, which is a reversion of my example pointing out that a system of two photons which makes such particles, DOES have a mass. You denied this (you also deny it just above on THIS page on 7 May, even though it's perfectly clear what I mean). And so on. Sbharris 19:05, 17 June 2006 (UTC)

So you mean for example this edit? Well nothing that stayed in the article was wrong, which is what you were claiming at the time, but I do recognize that there are two ways of talking about mass, and your way is indeed standard (and, yes, I was wrong when I said it was not), so it should have a place in the article. I do understand your frustration, and I sympathize. But please understand this: you "corrected" the article which you said contained mistakes. It is not a mistake to refer to mass the way I do. So I saw you "correcting" something which I knew to be correct, called it "confused" in your edit summary. I still know that there is nothing wrong with that description. Invariant system mass is not the only way of speaking. -lethe ^{talk +} 20:28, 17 June 2006 (UTC)

There's nothing nonstandard about it. I've referred you to MTW's gravitation, where there are many discussions of the T⁰⁰ term in the stress-energy of "stuff." Mass (here I mean invariant mass) does include kinetic energy most of the time (by which I mean, for most of the things in our normal experience, and for most of the objects and particles and in physics, too). The ONLY cases where this isn't certainly true (though it still might be true) is in the case of the massless particles (photons and gravitons if there is such a thing as a graviton) and (presumably) for the leptons as well, since they have mass but no sub-particle structure (or at least, none so far found at the energy scales we have been able to explore). But a large fraction of the mass of hadrons including the familiar baryons like neutrons and protons, is kinetic energy. And yes, that's in their rest frames. So some large fraction (though perhaps not all) of ordinary atoms and objects is kinetic energy of quarks. And that would still be true at absolute zero. You're weighing pure energy of motion because these things are systems in motion, even at "rest." And by the way, the invariant mass of photons is generally non-zero, since we rarely examine them one at at a time. So long as there are more than one, and they not moving in the same direction, photons have mass. The sun radiates 4 million tons of photons a second, and even the Earth radiates a couple of kilos of them per second. That's all invariant mass. The sun gets less massive by that amount. Presumably its G field decreases happens for near observers as this happens (for example, the Earth no doubt gravitationally feels the pull of (4.4 million tons x 500 seconds) of photons inside its orbit, but loses the pull of anything outside that)Sbharris 18:25, 8 May 2006 (UTC)

What is that about? It's well known and even explained here that the kinetic energy of the parts is included in both m and M. It's even possible that all mass is kinetic in origin (wave theories of matter). Harald88 08:49, 7 May 2006 (UTC)

If it's in the article that rest mass can come from kinetic energy, then the article is wrong. This may be true for composite systems with nonzero temperature, but it is completely false for fundamental particles.

Give it up! If it's true for neutrons and protons and atoms and paperweights, what does it MATTER if it might not be true for your last "fundamental particle" holdouts, like electrons?? "Rest mass" is NOT just a concept we ONLY apply to photons and leptons, and that's all. "Rest mass" is a concept which we apply to hadrons and atoms and ordinary objects. So let's just get on with it, and note that it includes kinetic energy much of the time (indeed, most of the time). Saying it CAN doesn't mean it ALWAYS MUST. But if it usually does, I think the article should certainly discuss it! Sbharris 18:25, 8 May 2006 (UTC)

As for your suggestion that all rest mass comes from kinetic energy, well that is in contradiction to the fact that some particles have nonzero rest mass when their kinetic energy is zero. -lethe ^{talk +} 09:41, 7 May 2006 (UTC)

It is correct (and not "may be true") that rest mass includes kinetic energy from parts in composite systems, and at first sight the article explains this very well. Note that the concept of mass is not limited to fundamental particles, just as the concept of length isn't limited to such either. But apparently you know the structure of fundamental particles, while I thought that nobody knows! What causes their mass (according to which publication)? Harald88 13:40, 7 May 2006 (UTC)

For a single particle, there is a distinct difference between the rest mass and the total energy/relativistic mass. The former includes only the energy content of the particle in its rest frame, while the latter includes its kinetic energy. Thus, here is an example of a system where the rest mass does not include kinetic energy (and this explains the use of the word "rest" in the phrase "rest mass"). So at least for systems which are not composite, it's simply not true, what you're saying.

As for where mass comes from, if you like, I can point you to some papers about the Higgs mechanism. If I do that, will you point me to some papers about this "mass comes from kinetic energy" theory? -lethe ^{talk +} 16:25, 7 May 2006 (UTC)

I don't have such theories at hand, but I can search for them. And we seem to speak different languages: I know of no evidence that the energy content of particles is composed of some kind of "rest energy" instead of some kind of "kinetic energy" - insofar such terms have meaning at that scale. Note also that IMO your use of the word "rest" does not correspond to the common use: I'd say that "rest" means that the centre of mass has a speed equal to zero in the chosen reference system. Harald88 22:48, 7 May 2006 (UTC)

I would also agree with you and say that "rest" means that the centre of mass has speed equal to zero. An electron has energy .511 MeV in its rest frame. This provides evidence that the energy content of particles is composed of rest energy instead of kinetic energy. Now, shall I give you some references for the Higgs mechanism? I'm eager to read about your "all mass is kinetic" theory. -lethe ^{talk +} 23:01, 7 May 2006 (UTC)

As I told you, don't have such a theory and don't have one at hand (perhaps Sbharris does), but I expect that one day there will be a satisfying wave theory of matter. That is perhaps incompatible with the Higgs theory, but perhaps not (think of the wrongly posed question of "particle or wave" nature of matter). If you have a better reference at hand for the Higgs mechanism, please add it to Higgs boson. Harald88 07:10, 8 May 2006 (UTC)

The wave theory of matter has been well-known for about 100 years, it's known as quantum mechanics. It is not at all incompatible with the Higgs mechanism, which admits a quantum formulation. I wonder what you meant when you said "It's even possible that all mass is kinetic in origin (wave theories of matter)"? I guess you were just speculating about some hypothetical models that have not been published yet, which you expect to be published soon? Since we're only allowed to talk about established physics here in these articles, I'm not sure what relevance your putative theory has to this discussion. To sum up: rest mass is not kinetic energy content. As for better references for the Higgs mechanism, better than what? It's in every QFT textbook. -lethe ^{talk +} 08:01, 8 May 2006 (UTC)

To the contrary: I reject speculation presented as fact - WP:NOR, nor do I propose to include any speculation. Let's stick to the subject matter. You claim that no kinetic (dynamic) energy is contained in particles. However, this is obviously controversial, as waves are kinetic by definition. Of course, your claim may be quoted as opinion, if it's notable and a good source is provided. Apart of that, that the rest mass of a body includes its kinetic energy is widely acknowledged and also explained in this article. If you think something is wrong, please discuss it.

And about Higgs, once more: we're editing an encyclopdia. If you have some improvement to make, please add it in Higgs boson.

That's all. Regards, Harald88 18:24, 8 May 2006 (UTC)

Nothing I have said in this thread should be regarded as controversial. It's standard material in any physics curriculum.

Firstly, let me say that I'm glad we agree on the utility of the WP:NOR policy. Therefore, let us no longer speak of your theory that "all rest mass comes from kinetic energy".
Second, as for your comment about waves: you haven't got it quite right. A field excitation can be wavelike and still be at rest. Therefore to say "waves are kinetic by definition" is incorrect. Modern physics understands all matter as having wavelike properties, but some of those properties are more subtle than waves in the ocean. Welcome to quantum mechanics. I assure you once again that my claim that matter has energy content even when it is at rest is not controversial, rather it is your claim "waves are kinetic by definition" that is not only controversial, but actually wrong.
Thirdly, that the rest mass of an object includes its kinetic energy is a controversial claim, at least that is my contention, which I was trying to discuss with Sbharris before you interjected with you "all mass is kinetic energy" theory. Then I went off into a sidetrack with you about whether all mass is kinetic. But I haven't forgotten the original point. So I agree with you, if something is wrong, it should be discussed here on this talk page, and that's exactly my intention. That original point was this: is kinetic energy always included in rest mass (nevermind that there is also always a non-kinetic component). I claim that the answer is obviously "no", as can be seen by considering fundamental particles. Sbharris may disagree. I'd like to get this issue hammered out with him.

No, only that part of the total kinetic energy which remains in the COM frame of the system is included in "rest mass." That works for composite particles (hadrons) and composite systems (like atoms and bottles of gas and paperweights). For massive "fundamental particles" (electrons, neutrinos), if they prove to be fundamental, that component is obviously zero. But the kinetic energy of stuff and its radiation can be a big thing, if it's a very energetic reaction. There's one point in the Feynman lectures where he talks about the mass of an atomic bomb, where he notes that if you take all the residua of an atomic blast, cool it down, and weigh it, it will weigh less, by about a gram. But he didn't put in that part about collecting and cooling for nothing. He was actually being precise without seeming to be. He had a way of being offhand and informal, without being wrong. Because he knew what he was doing. Let's see if we can repeat this on Wikipedia. Sbharris 19:41, 8 May 2006 (UTC)

I am pleased to discover that reading the first sentence of the above comment, I think you understand exactly what the issue is. I wonder now what the point of that long digression about "kinetic waves" was, but nevermind. Yes! The point is, Sbharris, and apparently you agree, contend that mass should be defined to include the kinetic energy in the COM frame. I contend that this definition is non-standard and should not be used on wikipedia. Now all we need to do is choose a talk page and start a new section and figure it out. -lethe ^{talk +} 19:52, 8 May 2006 (UTC)

Fourthly, as for your invitation to me to improve the article on the Higgs mechanism, well, once I'm finished defending this article, and the hundred other tasks I have on my todo list, I will be sure to take you up on it. In the mean time, I only brought up the Higgs mechanism because you challenged me with " But apparently you know the structure of fundamental particles, while I thought that nobody knows! What causes their mass (according to which publication)?". I assure you that there is a well-regarded theory about what causes mass, and it has been published in literally thousands of papers since Peter Higgs came up with it in the 60s. And it has nothing to do with "all waves are kinetic". -lethe ^{talk +} 19:02, 8 May 2006 (UTC)

I did not propose a theory, but instead tried to explain to you in different ways that your Higgs-based theory isn't to be proposed as the only and absolute truth in Wikipedia - but I'm repeating myself. Of course the source of your "mass is fundamentally static" theory is appreciated. According to the Higgs article, "The Higgs boson mass has not been measured experimentally." Thus please don't present your inferences from that theory as a fact in a Wikipedia article. At the moment it's just an opinion or belief.

You didn't propose a theory? Then what exactly were you referring to when you said "It's even possible that all mass is kinetic in origin (wave theories of matter)."? I'm quite curious. It sounded to me like you knew of a theory which explained the origin of mass as a form of kinetic energy. Now you say you never proposed any theory. What gives? Also, please don't put words in my mouth. I never said that the Higgs mechanism was the "absolute truth", nor did I propose to put the Higgs mechanism in wikipedia (it's actually already here). The Higgs mechanism is part of the Standard model, which is the most accurately verified scientific theory in the history of Man. Nevertheless, you are correct: the Higgs boson itself has not been directly observed. There are plenty of other mechanisms for breaking symmetry (technicolor, little higgs, etc). None of them have been experimentally verified, and so none of those models should be sold as "the absolute truth". In fact, that phrase may not have much meaning. The only scientific consideration is whether the model agrees with experiment. I'll let you know which of the Higgs mechanism and its competitors is the closest next year after the LHC goes online. -lethe ^{talk +} 21:19, 8 May 2006 (UTC)

Again, I contrasted your speculation with alternative speculation, in a fruitless attempt to make you aware of it... and indeed I did put words in your mouth to make you aware of the similar words you had put in my mouth - again, to no avail.

Happily we seem to agree on what statements to make in the article and what not - and that's the only thing that matters here. :-) Harald88 18:56, 9 May 2006 (UTC)

Of course we all agree that "matter has energy content even when it is at rest" since here we're talking about the object as a whole - it's also true for a gyroscope in a box. But I'm surprised to find that, according to you, "mass should be defined to include the kinetic energy in the COM frame" is not generally agreed on. All books and articles I have seen about it either just state it as a fact or explain why, for example [1] reminds the reader of the fact that "When a stationary body is heated its mass increases, and yet this increase is clearly relativistic — a consequence of the increased motion of molecules". It will be interesting to see counter claims. Harald88 20:52, 8 May 2006 (UTC)

In relativity, force and acceleration are not necessarily parallel. How can you divide F/a then? —Keenan Pepper 07:28, 7 May 2006 (UTC)

That complication is independent of the choice between m or M. And obviously, as Newton's equations apply to matter only, they are unsuited for photons. OK I'll rephrase that sentence. Harald88 08:49, 7 May 2006 (UTC)

Newtonian energy?

"the Newtonian energy which consists uniquely of the kinetic energy".

I only know classical energy equations and they include potential energy. Thus:

1. Is the above sentence correct? (reference?)

2. Is the above sentence relevant for this article on mass?

Thanks, Harald88 09:13, 7 May 2006 (UTC)

The discussion in which that text is found is about free particles. For a free particle, the only energy is kinetic energy. This is not at all clear from the text though. -lethe ^{talk +} 09:39, 7 May 2006 (UTC)

If I rememeber well, I was taught that in classical physics for example chemical energy may also be included, thus I doubt that it is generally accepted as correct; and its relevance escapes me. Thus I propose to simply delete that phrase. Harald88 13:43, 7 May 2006 (UTC)

Mass of an empty box with reflecting walls

It should be noted in the discussion about photons that even if there are no photons in a box with reflecting walls, there is still a contribution to the mass from the zero point energy (related to the Casimir effect). Count Iblis 21:36, 8 May 2006 (UTC)

Probably it's up to you to write that sentence, and please include a reference (is zero point energy to be included in mass?). Harald88 18:59, 9 May 2006 (UTC)

Invariant mass

Moved to Talk:Mass#Invariant_mass. Please, let's keep the dispute in one place.

Why should we keep the dispute in one place when you're making changes to multiple articles? Just hold off doing one till we get to the other, since the same issues of physics are being discussed.

From the revised article:

When discussing the mass of composite systems such as a pair of interacting particles, a little care must be taken. If the constituents can be distantly separated, then one can define the mass of the system to be the sum of the rest masses of the constituents. Using this definition, one finds that the mass of the system will generally not be conserved. Over the course of a reaction, the mass of the system can increase or decrease, as the mass of the particles is converted to energy or vice versa.

As you know, I'm strongly opposed to this entire idea, which is confusing. "If the constituents are distantly separated??" How distantly does that have to be? What a bizarre notion. How low does the pressure in a bottle of gas have to go before the kinetic energy of the molecules no longer contributes to its mass?

Second, although before relativity people naively assumed that the mass of a system was the sum of the rest masses of particles which compose it, relativity itself shows this to be flatly wrong, so let's just note that it's wrong, and get on with it. It's so much easier to say that the old notion of summed rest masses was wrong, and relativity is the reason.

Third, "over the course of a reaction the mass of the system can increase or decrease as the mass is converted to energy or vice versa". That's true only if you let the energy out, and the system isn't closed. The increase or decrease has nothing to do with mass-energy conversion. It's due to opening the system. If you close the system, mass is conserved, and invariant and end of story. So neat, so true, so useful to the working physicist, and something you won't now find in the Wiki, because you removed it. How about you put this back? Sbharris 20:31, 16 June 2006 (UTC)

Would you stop reverting edits without consideration?

When the mass of a system is not the sum of the rest masses of particles which make it up (for example a helium atom has less mass than 2 protons, 2 neutrons, 2 electrons) the reason is because energy has been lost from the system when it was assembled. No energy is "converted to mass". It's simply lost and not weighed. If it wasn't lost, it could be weighed, and then mass of the system would not change.

Similarly, when radium decays, the mass of the cooled decay products (ie, decay products at rest), is less than the mass of the radium. The difference represents energy lost to the system. If the energy were retained, no mass loss of the system would occur.

People have known that the mass of systems is not the same as the rest mass of their constituents (classical conservation of mass), since Einstein pointed out that they should different slightly according to E/C^2 where E is energy LOST FROM THE SYSTEM. That is why this notion is still used in calculation, but it's merely the historical understanding. So point that out. It's not a present "theory". It's the historical theory. It's the theory that relativity overturned. Sbharris 21:46, 16 June 2006 (UTC)

The energy is not lost. If a particle decays into two moving particles, and you measure the two moving particles' rest masses, you will find a lesser mass. The two particles still have all their energy in the form of kinetic energy. No energy is lost. -lethe ^{talk +} 22:19, 16 June 2006 (UTC)

Yes, indeed. But in that case, no mass is lost from the system, either. The kinetic energy counts, and contributes to system mass. See the point? Sbharris 11:01, 17 June 2006 (UTC)

sum of rest mass is not historical

Sbharris, please consider that perhaps there may be two usages; both current. One is the sum of the rest mass, which goes along with the mass defect and the nonconservation of mass; the other goes with the invariant mass and conservation is maintained. Also, why do you keep adding the phrase "in relativity theory"? What information is that supposed to convey? What other theory would we be considering in this article? -lethe ^{talk +} 22:15, 16 June 2006 (UTC)

The article, being about SR, should presumably talk about the new results which SR brings to physics, which a check of the rest of the article, finds that indeed it does! So why stop here, in this section on systems? Before 1900, it was expected that the mass of a system would be the sum of masses of the pieces of the system, and that was called the conservation of mass (or matter). That should be labeled as the old conservation of mass theory. It's not used any more, except as a classical reference, which is what the mass "defect" is-- really a classical reference. It's a defect which would be expected on the basis of the old pre-relativistic theory, but which is explained perfectly well in relativity as the mass of the energy which leaked out of the open system, when we made the thing whose mass is "defective."

Here are some references:

Griffiths, Introduction to Elementary Particles, 1987:
Except in elastic collisions, mass is not conserved. In the old terminology we would say that relativistic mass is conserved, but rest mass is not.
Streater and Wightman, PCT, Spin and Statistics, and All That, 1964:
the interaction may produce new bound states whose mass would ordinarily be expected to be less than m₁ + m₂, but which in principle could also be greater.
Sexl and Urbantke, Special Relativity and Relativistic Symmetry in Field and Particle Physics, 1992:
the relativistic version of the conservation laws has shown that only the sum of kinetic energy and rest energy is required to be conserved. If there are no further conservation laws implying further restrictions, then the conservation of rest mass to energy (or the other way around) will have to be expected in collisions. [...] conversion between mass and energy may be observed and tested in many kinds of experiments in the domain of elementary particles."

These three references all use the concept of mass defect, of mass in a collision defined to be the sum of the rest masses of the reactants. I also found a book that dealt in the invariant mass of the collision, thought you'd like to know. -lethe ^{talk +} 22:40, 16 June 2006 (UTC)

The references are okay as far as they go, but they don't say what needs to be said, which is that the defect we're talking about results from our sloppy handling. We let mass escape from our system, and lo we find that we have a mass "defect." It's sort of like poor bank security resulting in a "cash reserve defect" because the cash went out the door in your teller's pockets. It doesn't imply nonconservation of dollars.Sbharris 23:22, 16 June 2006 (UTC)

That's not true. Mass defect is not about closed systems and energy escaping. It's simply a different convention. -lethe ^{talk +} 06:54, 17 June 2006 (UTC)

It's a bad convention that produces wrong numbers (which are the defect). The error turns out to be due to mass escaping. Since the origin of the defect is so simply to explain (the escaped energy carries away the mass of the mass defect) why not note it? —The preceding unsigned comment was added by Sbharris (talk • contribs) .

Sure, they merely mean that the new terminology uses mass always to mean "rest mass". And rest mass is not conserved. But that's new-new. In the really old terminology (pre-relativity) mass IS conserved. You even label is "surprising" that it isn't. And indeed it was to the people of 1907 or whatever. But emphasize that this is the result of SR. —The preceding unsigned comment was added by Sbharris (talk • contribs) .

On this point we seem to have perfect agreement. The first reference defines the word "mass" to mean rest mass, and rest mass is not conserved. The amount of nonconservation is called mass defect, and is what I've written about in the article. Now, since this is an article about SR, every statement in the entire article is about SR. What's relevant to the sentence under debate is not whether we're talking about SR or Newtonian physics, but rather whether we define mass to be the rest mass of the constituents or the invariant mass of the system (or, god forbid, the relativistic mass). -lethe ^talk+ 09:39, 17 June 2006 (UTC)

Define it as you like, but note it's a bad definition, an old definition, and SR gives a better one where mass defect is seen as merely mass which has absconded. —The preceding unsigned comment was added by Sbharris (talk • contribs) .

On this matter I disagree. I think it is neither bad, nor old (at least no less current than other defs). -lethe ^{talk +} 11:23, 17 June 2006 (UTC)

Yeah, but again (as in all other examples) the differences here are all due to having open systems. Mass is conserved even in SR, if systems are closed. So note HOW and WHY mass is not conserved in SR-- it sneakily leaks out as heat and energy. —The preceding unsigned comment was added by Sbharris (talk • contribs) .

Mass is not conserved in a closed system, if you define mass to be the rest mass of the constituents. -lethe ^{talk +}

Actually it is conserved in closed systems, EVEN if you just sum rest masses and don't add or subtract anything else. Take a bunch of rest masses at rest, stick them in a system, don't add or subtract energy or mass, close it, and let any reaction you want happen in there, and the final mass of the system WILL actually be the sum of the rest masses you put in. Including nuclear reactions. "Mass defects" result from summed rest mass being converted to other types of mass in systems (like kinetic energy, heat, radiation, whatever) and then allowed to escape. —The preceding unsigned comment was added by Sbharris (talk • contribs) .

The mass in the system is, according to one definition, the sum of the rest masses. It's not that the other forms are allowed to escape, it's simply that they are not counted in this definition. -lethe ^{talk +} 11:23, 17 June 2006 (UTC)

This definition is used currently. It has nothing to do with escaping heat energy. Streater and Wightman are talking about a closed system of interacting particles. -lethe ^{talk +} 09:33, 17 June 2006 (UTC)

Well, here's a shock, but actually they aren't. You haven't quoted them saying specifically they are, and if they do, they're wrong. When particles interact, the system does not gain or lose mass in the COM frame, which is the frame you measure mass, usually. Gains or losses there are due to leakage. Two particles with kinetic energy can stick and become a particle with more rest mass than either of the inputs. The very best example is two photons which have NO rest mass and turn into and electron and positron. But the SYSTEM of photons DOES have rest mass (or as we call it, invariant mass) and that turns out to be just enough to equal the total mass of the of the leptons. —The preceding unsigned comment was added by Sbharris (talk • contribs) .

Streater and Wightman are not wrong. The mass of a system may be measured in the COM frame, but the mass of a particle is measured in the particle's rest frame, irrespective of what system it may be a part of, what other particles and interactions may be present. The sum of these numbers may change, while the invariant mass of the system does not. -lethe ^{talk +} 11:23, 17 June 2006 (UTC)

But what's the point? If you're lax about what energy you let in and out, you can make a particle or bound system of any rest mass you like. And name it Bill.Sbharris

Loose language in the last sentence. The first sentence has it right. Sum of kinetic and rest energy (and some other stuff) is conserved. And that's mass. And mass is conserved unless you let your kinetic and other energy leak out of your system. And that's the mass "defect." But as I said before, it's a mass defect like the weight defect in a burned log with ashes that weigh less. It doesn't imply nonconservation of mass. It just means you didn't keep track of your mass and it went up the chimney. —The preceding unsigned comment was added by Sbharris (talk • contribs) .

Sum of kinetic energy and rest energy is not mass, unless you want to talk relativistic mass mγ. -lethe ^{talk +}

It is both in the COM frame. Sum of kinetic energy and rest energy and potential energy and all other kinds of energy in a compound object ARE what you weigh as the mass, since you weigh in the COM frame. Yes, they are also the relativistic mass (total E/c^2), which is agreed a bad concept, but in this special case the relativistic mass is also the rest mass of the compound object (not the sum of the rest masses of its parts, but the mass of the whole thing, as you'd weigh on a scale). Like the mass of a nucleus or atom or box of gas. That's because relativistic mass (and energy) IS ordinary mass (and "rest energy" for the compound system) in the COM frame, which is (again) the frame you're in if you're weighing something. It is the minimal mass (or if you like, energy) you can get by choosing reference frame. All other frames give you more energy. —The preceding unsigned comment was added by Sbharris (talk • contribs) .

Right, but the cited sentence never mentioned COM frame. -lethe ^{talk +} 11:28, 17 June 2006 (UTC)

Well, it missed an opportunity, then. Total energy is conserved (with regard to reactions), but it is not invariant. Neither is sum of rest masses (usually). But the total mass of closed systems is both conserved and invariant. Since this is an article about mass, wouldn't it be nice to point out that, instead of insisting on using outdated definitions of mass which are constructed peicemeal, and which do change. Focus on conserved quantities where you find them. —The preceding unsigned comment was added by Sbharris (talk • contribs) .

OK, well we're not arguing about whose definition of mass is the best, we're arguing about whose definition is used. It's nice that invariant mass is conserved and invariant, but it can't tell you much about constituent particles, so not everyone uses it. Thus there are two definitions presently in the article. I claim that this definition, in terms of rest mass, is not some historical relic, but rather is in current usage. Furthermore, it has nothing to do with closed vs. open systems. -lethe ^{talk +} 12:34, 17 June 2006 (UTC)

The sum of rest energy and kinetic energy as measured in the COM frame is the invariant mass, but that's not quite the same as what's mentioned in the cited sentence. -lethe ^{talk +}

Which cited sentence?? Since the mass in the COM frame is the invariant mass, it's the mass calculated for every frame, and which can be weighed directly in the COM frame, which is the rest frame of the object. It's what we ordinarily MEAN by mass of objects. It happens also to be total relativisitic energy/c^2 (which makes you think at first we're going down that ugly road), but that's only a special a trick of the COM frame, and isn't true of any other frame. —The preceding unsigned comment was added by Sbharris (talk • contribs) .

The sentence I'm referring to is Sexl and Urbantke's "only the sum of kinetic energy and rest energy is required to be conserved". This sum is conserved in all reference frames, and that's what Sexl and Urbantke refer to. You respond that this sum is mass, but that's not true. This sum is mass when measured in the COM frame, but in all other frames it is not, even though it is still a conserved quantity in other frames. This conserved sum, in arbitrary frame, is what Sexl and Urbantke are referring to. -lethe ^{talk +} 11:28, 17 June 2006 (UTC)

Finally, mass defect is not due to nonclosed systems, rather it's due to which quantities you choose to define as your mass. -lethe ^{talk +} 09:42, 17 June 2006 (UTC)

Well, yes, if you define your composite mass as something which is wrong, there will be a "defect" between that, and what turns out to be reality. The difference turns out to be escaped mass. I can "define" the mass of the ash of a fire as the mass of the wood and kindling I put into it, and then talk about a "mass defect" when my ash doesn't come out to what I think it should be, and what went into it. But that's just a silly way to go about reality. Make your definitions fit the facts, not the other way around. Note that the old definitions were slightly wrong and didn't fit facts (rest masses weren't quite additive when heat/radiation/energy was allowed to escape), and the new definitions from SR give the right numbers.Sbharris 10:58, 17 June 2006 (UTC)

The question of "right" and "wrong" does not apply to terminology, which is determined solely by convention. It is, in my opinion, not silly to talk about wood losing mass while it burns. I don't want to debate whether this definition is right or wrong. The only debate left to have is whether it is found in the literature. My claim is that the three references support it. -lethe ^{talk +} 11:33, 17 June 2006 (UTC)

mass is converted into energy

Harald, when a reaction causes a change in mass of the participating particles, it is because some of their mass is converted to energy. This energy need not be radiation, it can be potential energy. The entire point of the segment is that mass can be converted into energy. This is a common way of describing things, and I don't understand why you don't like it. -lethe ^{talk +} 08:12, 17 June 2006 (UTC)

But in an article about systems, we need to take note of the fact that when "rest mass" of a system of particles (at rest to each other as well) is "converted" to "energy" (here we mean something other than the rest energy of the particles), that energy does not stop contributing to the mass of the system until it is allowed to escape it. That's true if it's kinetic energy, radiation, potential energy, whatever you like. Again, put a nuke in a box and blow it up on a scale, and according to SR the scale won't budge, so long as the box holds. Sum of rest masses is now very different, but the particles are no longer at rest, and everything else in the box counts as rest mass OF THE SYSTEM (aka invariant mass).Sbharris 11:11, 17 June 2006 (UTC)

Lethe, I agree that some people use that poor formulation, but see below. Harald88 08:19, 17 June 2006 (UTC)

mass is not identical to energy

One editor here doesn't understand that energy isn't mass, and so he keeps on reverting to the poor statement that mass can be "converted" into other forms of energy. As most of us know, energy can be converted from one form into another and it can also escape a system, but energy can't be "converted" from mass, just as it can't be "converted" from electricity. Harald88 08:16, 17 June 2006 (UTC) In particular, mass is a measure of energy content, as Einstein so strikingly explained in 1905. Pretending that mass is a measure of energy content and is itself a form of energy, leads to the contradiction that a form of energy is a measure of its energy content. That kind of confusion is unhelpful. Harald88 08:26, 17 June 2006 (UTC)

It's not a contradiction if you make a distinction between the mass of systems and the mass of particles. The mass of systems in their COM frame is its total energy/c^2, aka the relativistic mass AND the invariant mass (for that one frame only). That's because this is the frame where the m(rel) is minimized, and becomes m(rest) or m(invariant). Only part of that is the rest masses of the particles in the system. —The preceding unsigned comment was added by Sbharris (talk • contribs) .

Although I roughly agree with your argument (with the exception that we don't really know if the same is also valid for particles, eventhough you claim it isn't so), that was not really the issue here. This was more subtle: how to formulate the relationships between matter, mass, energy and radiation in a clear and consistent way. However, when only writing that "rest energy can change", the argument is incomplete in the way that you state; and the more precise phrasing of "rest energy" highlights the incompleteness of the statement. Harald88 00:05, 18 June 2006 (UTC)

Look, I have no problems with the way the article treats the mass of particles. The problems with m(rel) and m(rest) are well laid out. The problems come when we get to mass of systems, where basically m(rest) corresponds to m(invariant)-- that COM frame m(rel) which is also m(invariant) is the lowest m(rel) for that system you're ever going to see, from any inertial frame. Since it's E(rel)/c^2 it includes rest masses, kinetic energy, potentials, heat, radiation in the system, whatever. But E(rel) for that system in any OTHER frame is larger! This is the minimal E(rel)-- the best you can get. And because it's the COM frame mass, it's what you weigh.

Now if we want to go through all the problems of giving two conventions for masses of systems, we can do that. But I think the one with the addition of rest masses is a waste of time, because it's not the one we ever measure. The only mass of any system we ever measure is the one we CAN measure for enclosed systems in the COM frame, and that includes everything-- heat, kinetic energy, potential, the whole enchilada. It may be less or more than the rest masses of identifiable particle consituents, but at least it can be measured. It's what we've historically CALLED the mass of systems, because it's what we WEIGH when we weigh a system. As for sytems of unbound particles, we can calculate the system mass by adding up rest masses, but that's going to give us a wrong answer for what we'd weigh if we could weight it (and also for what we'd weigh if the system sprang from some single particle of indentifiable rest mass). So again, when we calculate this, we want to calculate the invariant mass of the system, not add up rest masses of components.

Finally, invariant mass of closed systems is both invariant and conserved, and that's more than you can say about most physical properties. So it deserves to be given top billing. It's the mass associated with all the energy inside a sphere, E = mc^2, if only the sphere is at rest in front of you. That's pretty easy to understand for the lay person, so it should be put that way. In fact, if you do, the reader will probably begin to wonder how many "fundamental particles" are just that kind of thing. They're at "rest" but how much of their mass is the rest mass of their constituents, such as quarks. And the answer is we don't know, but probably not much. Sbharris 00:52, 18 June 2006 (UTC)

OK, I see that we essentially agree. Harald88 10:16, 18 June 2006 (UTC)

Your suggestion that invariant mass is the only one we can measure is not very accurate. How will you measure the system invariant mass of a scattering of a tau particle off of a positron, for example? In such an experiment, there is no bound state, and the only masses that can be measured are the rest masses of the constituent particles. -lethe ^{talk +} 11:59, 18 June 2006 (UTC)

This whole mess is why I put in a substantial addition about the mass of systems. Deleting it didn't help, because it explained all the questions we're arguing over, and now we're arguing over them again. If you'd all read the examples I gave again, you'd quite asking the same questions, I think. Invariant mass of a system is a measure of the minimal energy content of a system (the minimized one you see in the COM frame). But it may contain more or less mass than the sum of the rest masses of the paticles used to construct the system. —The preceding unsigned comment was added by Sbharris (talk • contribs) .

What if I say rest energy instead? -lethe ^{talk +} 08:33, 17 June 2006 (UTC)

That's perhaps unusual... but certainly better. However, now that we have increased clarity, it's also easier to see that the argument is incomplete, see above.

But sorry for interrupting (and my lack of tact); I'm sure that the two of you can complete it (for example you may give as additional example a temperature increase). Harald88 00:05, 18 June 2006 (UTC)

proposed edits

Current:

In popular science and basic relativity courses, however, the observer-dependent kind of relativistic mass is usually still presented, due to its conceptual simplicity and the fact that certain equations from nonrelativistic mechanics retain their form (namely, Newton's second law). Einstein's famous equation E = mc^2 \,\! remains generally true for all observers only if the m\,\! in the equation is considered to be relativistic mass. It is true for invariant mass, only in specific circumstances to be discussed.

Proposed:

In popular science and basic relativity courses, however, the observer-dependent kind of relativistic mass is usually still presented. Einstein's famous equation, E=mc^2, is generally true as written only if the m in the equation is considered to be the relativistic mass. A slightly different and more complicated form of this equation, E^2 - p^2 c^2 = m^2 c^4 is required when invariant mass is used.

Arguments:

Newton's second law, F=ma, does NOT work when invariant mass is replaced with relativistic mass. This is pointed out later in the article.

The "conceptual simplicity" of relativistic mass is highly debatable. We can objectively agree that it relativistic mass is commonly used in popular science, and that Einstein's famous equation E=mc^2 uses relativistic mass.

Current:

The main benefit of using the relativistic mass is that the formulas

$F={\frac {dp}{dt}}\!$ and $p=mv\,\!$

from nonrelativistic mechanics retain their form, and are valid for relativistic situations when used with M in place of m. The first equation is Newton's second law, the second is simply the definition of momentum.

Proposed:

The main benefit of using relativistic mass is that the formula

p = mv

does not need to be modified.

Argument: F = dp/dt is always true, regardless of whether one uses relativistic or invariant mass. It's the basic defintion of force. Thefore F=dp/dt is not an argument for using relativistic mass.

I am also looking for a way to improve the discussion on "conservation of mass". The way I would describe the situation is that energy and momentum are conserved, and that the mass of a system is re-computed from its energy and momentum via the relationship m = sqrt(E^2 - (pc)^2) / c^2.

Most specifically, the mass of a system is not the sum of the masses of its parts. Energy and momentum do have the property that the total energy of a system is the sum of the system-component energies. Momentum behaves similarly. Mass does not behave in this manner.

Invariant mass (including that of systems) is separately conserved as well, in any frame, so long as the system is closed (but that also is a caveat for energy and momentum). While it is true that the mass of system is not the sum of rest masses of system parts, the mass of the system (or object, simple or compound) is its total energy/c^2 in the COM frame, which is useful, and in any case can be computed according to the invariant formula, and doesn't change. That's the main reason to use it as the definition of "mass," rather than relativistic mass.

It's certainly true the F = dp/dt remains true under all definitions of mass. Relativistic mass is used to try to make p = mv remain true (as you point out), and also to try to make E=mc^2 remain true in all frames. But as noted in the article, p=mv isn't all that useful and in any case is true only in the direction of v. Having E = mc^2 defined true for all frames simply redefines "mass" as total relativistic energy/c^2, and that's not very useful because we already have total relativistic energy to do that job. With m = invariant mass, E = mc^2 remains true in the COM frame only, but since that's the frame we usually work in with compound objects (it's the only frame in which they can be weighed on a scale, for example), invariant mass actually does most of what we want, and keeps E=mc^2 for most situations, too. That's confusing, because people are told that E=mc^2 is not true in general, except for simple single resting masses. But it has much wider application. Heat an object or a can of gas on a scale, and E = mc^2 still remains perfectly correct. Both E and m simply increase. The same happens in a chemical reaction or even for a nuclear bomb which liberates heat. E and m would remain constant if you didn't allow the heat and radiation to escape. S B H arris 19:46, 30 July 2006 (UTC)

I've made the edits I proposed - I think that by snipping a lot of material, I've improved the flow of the article.

Please sign your entries by adding four tildes in a row: "S B H arris 18:24, 5 August 2006 (UTC)". I would probably agree that your edits have improved the flow, but at the cost of decreasing the knowledge content (as is ever the case, truth and clarity are conjugate variables). The reader needs to clearly undertand that E = mc^2 is also perfectly true for systems in the COM frame, which is most things. Most people actually believe that when you blow up a nuke, the mass decreases. They teach this is school. Strickly speaking, this is wrong. Mass doesn't decrease until you let the energy of the explosion "out". The mass you weigh for the bomb is invariant and constant and conserved. It's the same AFTER the explosion. It doesn't decrease until you remove the heat and light, THEN the heat and light has the mass you're "missing." So you can't get rid of mass in the COM frame. It's conserved. Since this is an article on mass in relativity, this needs to be highlighted so the reader understands it completely. Anyway, I've added some bits which I hope do the job. S B H arris 18:24, 5 August 2006 (UTC)

Similarly, the purpose of the force equation was to stress that Newton's force law remains valid with relativistic mass. That is worth stressing because of some common misconceptions that have appeared in recent literature (don't people read old literature nowadays?). Thus I'll reinsert a remark about that. Harald88 11:26, 6 August 2006 (UTC)

I like the final result - I think the article is considerably more focused now. Meanwhile I've made a very minor edit to add a hyperlink, and a slightly less minor edit to explain that the relativistic energy momentum equation is a generalization of E=mc^2 (as was promised earlier). Pervect 20:23, 6 August 2006 (UTC)

I'm okay with the result, which gets in the necessary info. I originally put the section on mass of systems in after the E-m-p equation, because it's a little easier to introduce, as a sumation of this. But it can be done as it's done here. S B H arris 20:37, 6 August 2006 (UTC)

contradiction

The article now states an apparent contradiction (and it's for sure an inconsistency in presentation of facts) about the current use of relativistic mass. Now I don't have an oversight of all modern books and courses, so I don't know which statement is more correct:

"In [...] basic relativity courses [...] the observer-dependent kind of relativistic mass is usually still presented"

or,

"The concept has been eliminated from all modern physics textbooks as confusing and inappropriate."

At least these two POV's should be combined, insofar as they are verifiably correct; probably the best place is in the section of the first statement. Thus I now remove both from the article space, until it has been sorted out. Harald88 19:16, 7 August 2006 (UTC)

FYI, the user who made the changes about elimination of "relativistic mass" in modern textbooks is the same one who yesterday derided the discussion of photons in a box in the photon wiki, as being a "college textbook exercise." IOW, he's really concerned with textbooks when it suits him to be, but otherwise not. My question: Do we really care about pedgogics here, or should be move it all to an isolated section ("Stuff they teach or used to teach, which was confusing and no longer used by professionals")? S B H arris 21:05, 7 August 2006 (UTC)

The point is that you are using an obsolote notion (relativistic mass/ rest mass) in order to support your POV on the calculation of the "photon in a box" which in turn is something that you picked up off a FAQ for beginners. Do you have any references, other than the FAQ, that what you are writing about the photon "mass" in general is verifiable? A reference to an experiment published in a peer refereed journal on the "photon in the box", the "photn mass" being non-zero, the photon having "relativistic mass" please. Ati3414 00:24, 8 August 2006 (UTC)

This is pretty basic physics. Here's the standard equation for the invariant mass of two photons of energy E1 and E2 [2] (units of c=1 are used). Note that for angles of 180 degress, the mass is simply m^2 = 2E1*E2. If the photon energies are equal, the invariant mass of the pair is 2E. S B H arris 00:41, 8 August 2006 (UTC)

What I'd like to see, but it's too much work!

I'd like to see the explanaton of invariant mass given first. We tell people that it is modern practice to use invariant mass, and then the article spends a lot of time explaning relativistic mass, which while not wrong is a bit dated.

This strikes me as being too much work for the amount of gain, though. Pervect 05:57, 10 August 2006 (UTC)

Historically the article started out with a long discussion by somebody who loved the concept of relativistic mass, and was distrustful of invariant mass. After much arguing, we finally got it to the state you see, but it was a long haul. Personally, I'd also like to present invariant mass first as well, then move to invariant mass of systems. S B H arris 22:16, 10 August 2006 (UTC)

photon-like particles that aren't photons?

I find "other particle moving at the speed of light" puzzling: what particles other than photons move at the speed of light? Harald88 21:46, 10 August 2006 (UTC)

Gluons S B H arris 22:12, 10 August 2006 (UTC)

Gravity waves move at the speed of light. So if gravitons exist, they are massless and move at the speed of light. Neutrinos were thought until recently to be massless. They are very nearly so and move so close to the speed of light that the neutrinos from a supernova explosion arrived at Earth before the light did. Some theories say that all particles are massless in their "bare" condition and only gain mass as a result of interactions, especially with the Higgs boson. JRSpriggs 03:12, 11 August 2006 (UTC)

Thus hypothetical particles... OK why not! Harald88 12:23, 11 August 2006 (UTC)

Proper number of links per article per tech term ??

Another editor (AySz88 \^-^) and I have been having a discussion about proper number of links to have per technical term (such as invariant mass) in an article such as this. We agree that the proper number is somewhere between EVERY one, and ONLY ONE per article (the first one). The other editor has a reasonable approach to this idea, so I'm going to paste his suggestions right here. This should keep us out of a link-delink war, at least for this article. [And I'm seriously thinking of going to the WP:PUMP or the vague Wikipedia:Manual of Style (links)#Overlinking to propose a better general guideline for hyperlinks in tech stuff, too, so that other physics pages get treated the same way].

Anyway, I'll agree not to link any more than one tech phrase per (my!) screen, and if anybody wants to delink stuff up to once per section, I won't object. Personally, it doesn't bother me if EVERY use of a tech term is hyperlinked, though I understand if some people find it annoying if it is, and others if isn't. I certainly find it annoying if anything OTHER than tech terms are linked (for example, day of month dates). But I know some people OCD about that also. Anyway, what say you all? S B H arris 01:03, 14 November 2006 (UTC)

Overlinking. Hello; about the links, repeating the links is definitely okay if it has been a while since the last time the word was used, but repeating links every paragraph or so is not necessary especially if every paragraph is discussing those same subjects. There isn't a reason to repeat a link in, for example, the second and fifth paragraphs of a section, especially if one would need to read the second paragraph of the section anyway to understand paragraphs which follow (and if this isn't true, the section should probably be split into two). Personally, I think that there should be no repeats within a section, and no more than two per screen if the sections are very short. The section about this in the Manual of Style is Wikipedia:Manual of Style (links)#Overlinking, but it's somewhat vague.
Keep in mind that "a page" can be different depending on your display resolution - you might see only one link per page while I (working on 1280x1024) might see twenty on a screen. Most people seem to use something close to 1024x768.
Also, "relativistic mass" redirects back to the exact same article, so I removed all the links to it.—AySz88 \^-^ 00:11, 14 November 2006 (UTC)

Link everywhere: I say you can't link too much. --Michael C. Price ^talk 08:18, 14 November 2006 (UTC)

At risk of violating WP:POINT, I've fixed your last statement to reflect your view. Is that helpful? You may be interested to know that WP:MOS does not agree with you, nor do most editors, nor do I. Most words don't need to be linked (though they could be, as you can see above), because we all know perfectly well what they mean in context. Second, even overlinking odd words too much detracts from the usefulness of linking other odd words, because it's like crying wolf (or simply crying) too many times. It's like too many italics. Good linking is like good swearing. Or like spice in cooking. Too much and you totally spoil the whole efffect, and the whole point. Which is of course a kind of emphasis. S B H arris 21:25, 12 May 2007 (UTC)

Vague Sentence

I think this sentence is a bit vague: "The invariant mass is calculated excluding the kinetic energy of the system as a whole, while the relativistic mass is calculated including it." Although this sentence is true, it might lead readers to believe that invariant mass completely excludes kinetic energy, when in fact, it is important whether the constitute parts of a system are actually moving with respect to each other. Any opinions on whether this sentence should be changed? --Armaetin (talk) 08:27, 10 March 2009 (UTC)

Well, it does say kinetic energy of the system as a whole. What this means is kinetic energy of the system-as-a-whole as calculated using the velocity of the center-of-mass. I'll tweak it. S B H arris 02:37, 25 October 2009 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Mass in special relativity/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

This article has passed Ed Gerck's Wikipedia Test Count Iblis 00:02, 2 June 2007 (UTC)

Last edited at 00:02, 2 June 2007 (UTC). Substituted at 21:33, 3 May 2016 (UTC)