Talk:Mass in special relativity/Archive 3

Experimental proofs missing
Article does not contain any experimental proofs or corresponding references. The "proofs" included are only theoretical derivations. Article should contain the proofs of mass increase and experimental proofs of quantitative validity of relativistic mass equation. I am not saying, that the relativistic mass physical effect does not exist. I am saying, that there are no experimental proofs of quantitative validity of relativistic mass equation. Without that relativistic mass equation is only a theory. Softvision (talk) 17:55, 12 August 2009 (UTC)


 * Even if "relativistic mass equation" were only a wild hunch, if it is sufficiently referenced, it is ok. Sufficient references are provided for "relativistic mass equation" as the consequence of a theory, so it is ok. Now, look at the pointers on your talk page and start aquainting yourself with the Wikipedia policies. In other words, please stop abusing article talk pages. Thank you. DVdm (talk) 18:37, 12 August 2009 (UTC)


 * DVdm, I do not consider you as serious person. Experimental proofs are pride of any theory. If such experimental proofs exist, it could be useful to present them in article. Softvision (talk) 18:54, 12 August 2009 (UTC)


 * Yes, If you have a reference for an experimental proof, then provide it, but don't complain about the article not having one.
 * Other han that, I don't really care how you consider me. Just start trying to consider the Wikipedia policies as serious policies. DVdm (talk) 19:01, 12 August 2009 (UTC)


 * Ok. Message to editors : Please add experimental proofs of quantitative validity of relativistic mass equation, it would enhance the quality of the article. The same relates to relativistic momentum. Softvision (talk) 19:06, 12 August 2009 (UTC)


 * DVdm, this is the proof ? I know that you don't care. Softvision (talk) 19:38, 12 August 2009 (UTC)

This article has become amazingly POV
This article used to be a good example of how a fair and neutral discussion of such a topic should be - which is also what Wikipedia stands for. But although this HAS BEEN so about one year ago (see the archives), now it is undeniably making propaganda for a Single Point Of View, complete with manipulative claims like "The term relativistic mass has also been used historically" (erroneous, as at least last year in discussions here it was fund to still be in use!) and "mistakenly used that way by some" which constitutes Original Research. In short, currently this article may serve as a good counter example of how a Wikipedia article should NOT be (see WP:NPOV of what needs to be done in order to respect Wikipedia requirements). Harald88 (talk) 07:58, 21 October 2009 (UTC)


 * Go ahead, help yourself and then remove the POV-tag. - DVdm (talk) 08:54, 21 October 2009 (UTC)


 * OK, I admit that my approach to ask others to do the corrections sounds a bit lazy - it's just that this month I'm very busy. Harald88 (talk) 15:52, 22 October 2009 (UTC)


 * DVdm were you being sarcastic when you gave the above link to authors who themselves are apparently not able to do a Google book search on relativistic mass? Anyway, as a reminder I copy here again what may well be the most recent (although not peer reviewed) statistics, provided by an anti-relativistic mass author: . Amazingly, although slowly less physics books use "relativistic mass", he also found that in the period 2000-2005 there were twice as many books on relativity that used relativistic mass than books that did not! Harald88 (talk) 17:36, 31 October 2009 (UTC)



We could do one more re-write, if you want to treat both types of energy and mass equivalently. There are two types of mass: relativistic mass (M_r) and invariant/rest mass (M_i). The last is Lorentz invariant, the first is not, but both are conserved for single observers, through time, in isolated systems. To go with them, there are two types of corresponding energy: relativistic/total energy (E_r) and rest/invariant energy (E_i).

Now the equation E = mc^2 (or E = m if you use units c=1) is generally true so long as you remember to equate the right types of energy with the right types of mass, so E_r = M_r, and E_i = m_i. All you need to remember is that when mixing the terms, you need to add momentum terms to get from E_r to m_i, and thus, all four energy and mass types are equal only when total system momentum is zero:

E_r = M_r = E_i = m_i (when p = 0). Which handily leads to E_r = m_i in the COM frame only, something that leads to much confusion for those who think E_r = m_i must be generally true.

Anybody interested in a re-write that treats these all on an equal footing, from the beginning?

S B Harris 19:04, 20 December 2009 (UTC)

Math Font for Greek symbols
Momentum is generally represented by the Greek rho (ρ) rather than the lowercase Latin p, but there is no lowercase rho available in the math font without it throwing a parsing error. This seems like a critical weakness given the abundance of lowercase Greek letters within mathematics. —Preceding unsigned comment added by Fulvius (talk • contribs) 11:02, 4 January 2010 (UTC)


 * As you can verify in the article and in any physics book, momentum is generally represented by the Latin p. DVdm (talk) 11:23, 4 January 2010 (UTC)

style of article
This article is in my opinion not intelligible to the intelligent layperson for whom it is presumably intended, as experts will have their own sources. It may be a difficult topic, but the excellent article on the (not unrelated) Twin Paradox shows that it can be done. Escoville (talk) 16:09, 19 June 2010 (UTC)
 * What do you think of mass energy equivalence, which can be read in parallel, or as an introduction? This article is basically about mass-energy equivalence but with the additional complication of needing to explain the two kinds of mass-definition (rest/invariant mass vs. relativistic mass). That inevitably adds complexity here. S  B Harris 18:20, 19 June 2010 (UTC)

Fundamental problem with this article and related ones
Conservation of mass is a concept which is a bit of a cheat with respect to today's understanding of energy, mass, and the mathematical descriptions of the particles and interactions which constitute a physical system. To get an idea of what I am talking about, please see this short article by Frank Wilczek. To quote Wilczek, "Mass is a property of isolated particles, whose masses are intrinsic properties -- that is, all protons have one mass, all electrons have another, and so on. [...] There is no separate principle of mass conservation." This is evident in the treatment of mass in quantum theory, where a mass is a multiplicative factor in an interaction term of the Lagrangian. Mass has a completely different character than energy, which is an eigenvalue of the Hamiltonian. Conserved quantities in quantum theory are observables (Hermitian operators) which commute with the Hamiltonian, and their eigenvalues are the possible measured values of these conserved quantities. Mass measurements are not to my knowledge quantities which can be represented as eigenvalues of such operators, and therefore mass is not a fundamentally conserved quantity. Tim Shuba (talk) 02:49, 1 October 2010 (UTC)
 * Invariant mass is obviously conserved, since it's invariant. It can't change in any frame, so long as nothing is added or removed from the system. Relativistic mass is frame-dependant, but it's just (relativistic energy)/c^2, so it's as conserved as the energy is. No, there's no separate principle of mass conservation, as it's the same thing as energy conservation (no matter what sort of energy you're talking about). See the Mandelstam variables. The invariant mass is just the square root of Mandelstam's s. S  B Harris 03:35, 1 October 2010 (UTC)


 * I agree. The article by Wilczek is more of an interest in order to understand the classical limit, than special relativity. About measurement, I would say that the four-momentum p of a system is obviously a bona fide observable that commutes with the Hamiltonian of an isolated system (because the lagrangian should be invariant under translations) and we have that m^2 = p^2, so mass is obviously an observable. But it could be that I need to rethink my argument about the classical limit posted here. Count Iblis (talk) 03:53, 1 October 2010 (UTC)


 * The momentum p as an operator is an observable, but p = -i hbar d/dx. Much different than the classical four-momentum. Tim Shuba (talk) 05:27, 1 October 2010 (UTC)

Invariant mass or relativistic mass?
In the section 'Modern view' it says:

The invariant mass is the ratio of four-momentum to four-velocity: :$$ p^\mu = m_0 v^\mu\,$$

This seems an error (unless I interpret this equation incorrectly). Should be relativistic mass rather than invariant mass, right? JocK (talk) 03:29, 17 December 2010 (UTC)


 * No it is indeed invariant mass that is the ratio of four-momentum to four-velocity. See the article on four-momentum-- especially in the end sections where it talks about its invariance and relationship to four-velocity. S  B Harris 10:08, 19 December 2010 (UTC)


 * I have restored the section and added a source. DVdm (talk) 11:14, 19 December 2010 (UTC)


 * Thanks, that makes it much clearer. (I interpreted the four-velocity as (c, v), i.e. the four-vector that contains the bare velocity components in the spatial directions, and hence without the time dilation factor gamma.) JocK (talk) 15:39, 20 December 2010 (UTC)


 * No, that doesn't work out, since 4-velocity is always c-- so the components must be (gamma*c, v(1), v(2), v(3)) or else there's no "room" to make the length/magnitude of 4-v to be "c" when the v's have real values. It's only (c, v) when v = 0. S  B Harris 19:16, 20 December 2010 (UTC)
 * You mean (gamma*c, gamma*v), right? JocK (talk) 23:39, 22 December 2010 (UTC)
 * Wups, yes. 4-v = gamma* (c,v). S  B Harris 23:49, 22 December 2010 (UTC)

single sided "modern view" and one-sided controversy
The "modern view" and "controversy" only provide a one-sided POV. It should provide both opinions - best by contrasting Okun 1990 (already there) with Sandin 1991 (currently omitted):

http://ajp.aapt.org/resource/1/ajpias/v59/i11/p1032_s1

Even the physics FAQ - which is expected to express the mainstream view - references Sandin: http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html. Thus it appears that the FAQ now provides a more NPOV discussion than Wikipedia...

In addition, the article is in want of some restructuring: the same controversy appears twice, and even Einstein's preference is mentioned twice in this article. Harald88 (talk) 08:33, 12 April 2011 (UTC)

Einstein Quote Attribution
I think that the Reference (16) for the Einstein Quote should be C G Adler, Does mass really depend on velocity, dad? Am J Phys 55, 739 (1987) If you check the present reference, it notes that the quote used there is from the Adler paper, and if you check footnote 26 in that paper it notes that the author obtained permission from the Hebrew University of Jerusalem, Israel to publish this previously unpublished quote. In the interest of full disclosure I am the author, Carl G Adler, and for that reason I am putting this note here, in case there is some objection to the change I suggest.74.196.39.46 (talk) 20:47, 28 December 2011 (UTC)


 * Good idea, but I propose that you add it in stead of replacing it. That way we have a wp:primary source (yours), and a wp:secondary source (the current), which is the preferred kind of source in Wikipedia. - DVdm (talk) 21:03, 28 December 2011 (UTC)
 * By the way, I have already the wp:WEASEL phrase with a factual one. - DVdm (talk) 21:24, 28 December 2011 (UTC)

Does mass actually increase?
According to what I have read and understood it doesn't! Lorentz's factor nothing but is a coefficient of increase in the force applied dependent of the velocity of given momentum, just like coefficient of linear expansion or specific heat capacity. Mass does not change at higher velocities, it just appears to do so for more force is applied to get the same acceleration than that was applied at lower velocities. — Preceding unsigned comment added by 59.95.206.170 (talk) 13:59, 4 February 2012 (UTC)


 * Please sign your talk page messages with four tildes ( ~ ). Thanks.
 * Rest mass doesn't change. There is also an old-fashioned concept, called relativistic mass, which is the rest mass multiplied by the gamma factor, which obviously increases with velocity, but only for the one who does the measuring of that velocity. So this concept doesn't say anything about the intrinsic properties of the object. It's all explained in the article. Actually, it is more or less what the entire article is about. - DVdm (talk) 14:23, 4 February 2012 (UTC)

Conservation of Mass
A few weeks ago I contributed to the page, synchronising with the conservation of mass page, and the mass / matter pages, on the Einstein's relations. However, the contribution has vanished, edited back to how it was before the contributions. The issue is that the whole business of invariant mass and relativistic mass is silly. The choice of some people to differentiate matter and mass is not the consensus of contemporary physics. Instead, the mathematics that everybody uses makes things very clear about what is what.

In particular, Einstein's famous equation should be written as E^2 - p^2 = m^2 (for people to use, that is). In it, if you are talking about one, and only one, particle, then the right hand side is called the rest mass of the particle, and it pretty much pins down the identity of the particle (if the particle is real -- a virtual particle may disobey the Einstein relation altogether). The conservation laws, however, are the conservation of energy and momentum -- this set of 4 quantities (one for energy, three for momentum) are individually conserved, conserved absolutely, and conserved for all vertexes of Feynman diagrams (that is, virtual particles may disobey Einstein relation, but must still conserve these 4 quantities exactly). However, the value observed for E and p are not comparable between frames -- although all observers can measure the E and p of a system in their own frame and agree on their conservation, they cannot agree with the measurements of other observers. The only way to compare, is to construct this m^2 value using the Einstein relation above, which is why it is known as the invariant mass.

However, the invariant mass is not conserved (conserved only through the conservation of energy and momentum, and the Einstein relation, the latter of which can be violated). In particular, a positron and an electron may annihilate to produce two photons, and you can see how two point masses are changed into massless particles, signifying the violation of the conservation of mass / matter.

Notice, however, the caveat -- mass can only be created or destroyed if you are talking about systems of particles. It is easy to prove that, if all you have is one particle in the beginning and at the end, then Einstein's relation must hold as it is, pinning down a mass to a mass, and massless to massless. So, it is important to know how systems of particles are actually dealt with. In practice, it is really simple -- for each particle in a system, write down its (E,p) as a 4-vector. Add them all up to get ( sum E, sum p ). Now, we apply Einstein's relation to this final 4-vector. (The articles already includes this part in it.)

Yes, the Einstein relation then makes it sensible to talk about invariant mass of systems, which is conserved by the Einstein relation. However, it loses the creation and destruction of matter -- in particular, it loses how two photons somehow generate a mass. Moreover, this invariant mass is of no experimental use except in seeing whether we have beams of particles energetic enough to produce new and heavy particles. (Notice, "energetic enough" -- it will be obvious shortly.) It is also rather gut-wrenching for people to talk about mass creation / loss.

Instead, it is far nicer to notice something about the Einstein's relation. Other than talking about the rest mass of a single particle, one can notice that, Einstein's relation immediately implies E^2 - p^2 = m^2 = (E_2)^2 - (p_2)^2, where E_2 and p_2 are the energy and momentum measurements (of the same system) in another frame, then the definition of the centre of momentum frame is precisely that p_2 = 0. i.e. E^2 - p^2 = (E_cm)^2. That is, it is far more natural, and as convenient as using the invariant mass, to talk about centre of momentum energies instead of masses, which are confusing.

In particular, the E_cm way of talking about things, make it clear that it was the energy stored inside the electron and positron (that we had previously interpreted as their rest masses), that is liberated as light energy. Then there is no more the possibility of mistaking the conversion of mass to energy that feature so prominently right at the top of all these pages.

This formulation is particularly nice because the rest mass of elementary particles serve as identification tags (whenever they are non-zero). Their speciality turns up in particle physics integrals, something that NEVER happens with systems of particles' centre of momentum energy E_cm. This is also a reason why we should frown upon, not just relativistic mass (which, because Newton's Laws in relativistic form is really unwieldy to use, does not appear in textbooks other than classical electrodynamics, and even then, usually derived in the Lagrangian method, that does not care about relativistic mass), but to also frown upon invariant mass for systems of particles. Basically, anything other than the rest mass of fundamental particles, should be slowly ejected from the physics terminology. It also makes it clear that the distinction between matter and mass is just plain silly -- it is an inferior attempt at a solution to the same problem as being careful would automatically solve. i.e. The described solution not only solves it better, but also solves a lot more than it could ever hope.

Also, note that it is not the rest mass of fundamental particles that gives rise to, and is acted upon, by gravity. Instead, it is the energy, usually a large of which is stored within the rest mass. So, this is actually better for use in General Theory of Relativity too. So, stop deleting my contributions. — Preceding unsigned comment added by 115.66.236.172 (talk) 08:44, 18 May 2013 (UTC)


 * Please sign your talk page messages with four tildes ( ~ ). Thanks.
 * As I said on your talk page, I reverted the edit because it was not sourced - see wp:Verifiable sources and wp:Original research. - DVdm (talk) 09:22, 18 May 2013 (UTC)
 * That will take some time as I try to extract the sources from textbooks. These are not controversial ideas. However, contemporary physics does not even want to address the issue, because it is so completely solved -- you cannot even find it in the notes. Wish me good luck finding it in journal article form, since it is so old. The mathematics that I have given here (see above), already proves it for all.
 * The edit was rightfully reverted as an unnecessary WP:editorializing. Even worse, it was aimed to create an impression that a controversial concept of the “mass increase” was never a part of physics, although so named “relativistic mass” was ubiquitous in early works. Incnis Mrsi (talk) 09:26, 18 May 2013 (UTC)
 * You are referring to the wrong edit. That was not me. The breaking of the Law of Conservation of Mass was a gigantic part of early relativistic quantum physics. But to think that we have not figured it out, that there is still controversy, is a mistake. Secondly, it is good practice to slowly get rid of old controversies and bad ideas from the past. For example, current thinking in mathematics directly teach the convergence of series, so that we no longer tempt ourselves into thinking that the results of series outside their region of validity are to be trusted with our lives, and more like curiosities instead. Similarly, a prominent disclaimer that mass is not exactly conserved, but is a measure of stored energy, is warranted, but not any more than that. I would much rather like it to be called Invariant Energy (thus shifting the controversy there), but alas, I do not get to choose, in my lowliness. I will, once I get the chance and power to do so. So, keep the section on relativistic mass, because there are still mentions of that dreaded concept. And keep the invariant mass thing too, but denounce them the same way that relativistic mass is denounced. 115.66.236.172 (talk) 18:21, 18 May 2013 (UTC)
 * Really not “you” from the same IP address? Maybe your little brother, spouse, or child? Should I guess which of numerous edits from the same IP is “yours”?Register please – when you ceased to sprinkle IPs, dates in your patented “few weeks ago” format, and other junk to our brains, we’ll become more collaborative and could pay some attention to your content proposals. Incnis Mrsi (talk) 19:56, 18 May 2013 (UTC)
 * Thanks to the 1st world giving themselves all the IP addresses, ENTIRE COUNTRIES have to restrict themselves to sharing a MEASLY TWO IP addresses. And what part of Maths showed to you, proven in front of your face, do you not understand? 115.66.236.172 (talk) 15:58, 19 May 2013 (UTC)
 * You are not interesting in making all of your “E^2 - p^2 = m^2 = (E_2)^2 - (p_2)^2” readable for me → I am not interested in deciphering your insights and evaluating their merits for the article. Incnis Mrsi (talk) 16:23, 19 May 2013 (UTC)
 * Then you cannot be taken seriously. Why should we care about what you think, if you are unwilling to examine the case critically? I am not giving you unverifiable junk; its truth can be ascertained by just evaluating the mathematics and seeing that no leaps of faith had been taken. 115.66.236.172 (talk) 08:35, 20 May 2013 (UTC)
 * This is not a forum. We are not here to present and examine cases. We are not even allowed to do that. See our policies on wp:verifiability and wp:original research. If you can present wp:reliable sources, we can discuss those. Otherwise this discussion is —in the Wikipedia sense— off-topic. See our wp:talk page guidelines. - DVdm (talk) 08:45, 20 May 2013 (UTC)

Same dimension ?
Somewhere in the article there are some inaccurate statements about some quantities having the same dimension due to the use of natural units. I have removed the inaccuracies in accordance with the introduction of natural units article which says :While (the omission) has the apparent advantage of simplicity, it may entail a loss of clarity due to the loss of information for dimensional analysis. The apparent symplicity (also claimed in this article) leads to confusion due to loss of info re dimensional analysis. I'll remove again the claim of simplicity and same dimension which is a clear illusion created by natural units system.--5.2.200.163 (talk) 17:17, 26 January 2016 (UTC)
 * I don't agree that this is an illusion or just an impression. In natural units, m, p and E do indeed have the same dimension and they are expressed in the same units, so they are not just numerical values. And of course, the equations are simplified (not just shorter). See for instance "... expressions and calculatons are much simplified if one uses natural units." and "... mass, momentum, energy and wave number all have the same natural dimension M"
 * I will rephrase the first sentence along the source. If you have a source that supports something interesting beyond this, we can of course add some more.
 * Now, there is something horrible about the current sentence "If m > 0, then there is the rest frame, where p = 0, this equation states that E = m as numerical values."
 * So, I propose the following:
 * 
 * When working in units where c = 1, known as the natural unit system, all the relativistic equations are simplified and the quantities energy, momentum, and mass have the same dimension:
 * $$m^2 = E^2 - p^2 \,\!$$.
 * The equation is often written this way because the difference $$E^2 - p^2 $$ is the relativistic length of the energy momentum four-vector, a length which is associated with rest mass or invariant mass in systems. Where m > 0 and p = 0, this equation again expresses the mass-energy equivalence E = m.


 * DVdm (talk) 18:37, 26 January 2016 (UTC)
 * Assuming this is ok for everyone, I went ahead. Let's not just revert again, but discuss first. - DVdm (talk) 08:20, 27 January 2016 (UTC)
 * I agree with discuss first. There are several remarks on the proposal: 1) natural dimension is a good (although ad-hoc) qualifier whose absence generates confusion, there is no way the mentioned quantities could have the same dimension unless natural (system of units), 2) the absence of natural from the text of the source looks like an error in the source, 3) similar (same-dimension)ness is to be found: by considering c=1, time has the same dimension with space s=(c=1)t. Then what is the unit of space-time in SI and natural units?--5.2.200.163 (talk) 15:09, 28 January 2016 (UTC)
 * I have some trouble parsing the structure of your sentences. Is English not your first (or second) language by any chance?
 * If you think there's an error in the source, feel free to propose another one here. Let's see what other contributors think. - DVdm (talk) 15:18, 28 January 2016 (UTC)
 * What exactly is the parsing difficulty? You mean somehow the artificially generated adjective (same-dimension)ness that expresses the property of having the same dimension? (Or could it be written same-dimension-ness?)
 * The aspect I want to underline is that the word natural must not be missing from your proposed rewording.--5.2.200.163 (talk) 15:56, 28 January 2016 (UTC)
 * The second point is about the same dimension of space and time which follows from the use of natural units. Is it valid?--5.2.200.163 (talk) 16:04, 28 January 2016 (UTC)


 * As far as I can see the word "natural" is present in the new wording.
 * I don's see where the article says "same dimension of space and time" in the new wording. DVdm (talk) 16:16, 28 January 2016 (UTC)
 * But is it present in the term natural dimension M (as you wrote above before the quote putting a ref tag) )?--5.2.200.163 (talk) 13:37, 1 February 2016 (UTC)
 * Concerning "same dimension of space and time" (as a logical consequence of the use of natural units) I think the discussion could be continued at Talk:natural units. There must a be consistency between wikiarticles.--5.2.200.163 (talk) 13:43, 1 February 2016 (UTC)
 * Sorry, but I don't see any problem with the current text in the article, and I really have no idea what exactly you are trying to say. - DVdm (talk) 14:08, 1 February 2016 (UTC)
 * The problem is that there is no such thing as the misleading term same dimension for quantities that have clearly different dimensions like mass and energy. The phrasing that must appear if you insist on same dimension is same natural dimension. Either the term natural dimension appears explicitly in the place I've indicated or else the mentioning of just same dimension should be omitted.--5.2.200.163 (talk) 16:15, 1 February 2016 (UTC)

The concept of same natural dimension is a kind of a twisted one with no special significance, but so is the natural units system which is nothing more than a convenient shorthand/scriptology in order to not carry long/cumbersome formulae throughout mathematical derivations. This fact and the misleading appearance of simplicity should be clearly mentioned in article to be consistent with natural units article which clearly states the misleadingness.--5.2.200.163 (talk) 16:21, 1 February 2016 (UTC)


 * Ah,(sound of penny dropping) now I get it. Ok, I have inserted the word . It's in the source too, so no problem. - DVdm (talk) 16:26, 1 February 2016 (UTC)
 * Ok. I was intending to insert the word myself as I see in the above italicized quote. I see that you've done it before me.--5.2.200.163 (talk) 16:37, 1 February 2016 (UTC)

Outdated/upside down view in article
The article seems to suggest that the rejection of relativistic mass is the minority view. Not so, as John Roche "What is mass" European Journal of Physics 2005 pp 225 points out over 60% of modern authors use rest mass, and just use m with no subscript. Roche argues that relative mass is an artifact. Hence article has an upside down focus. I am not really dead (talk) 22:02, 17 February 2016 (UTC)

Terminology
I've reduced the lede to a manageable size by the simple device of farming out the definitions in it to the terminology section. This makes for a better use of summary style for the article, but it introduces a bit of redundancy. I leave it to other editors to fix this. &mdash; Charles Stewart (talk) 11:17, 12 April 2016 (UTC)