Talk:Energy–momentum relation

Relativistic Mass

The notion of relativistic mass is highly misleading, misused by many people, and has been discarded by most modern scientists. It should be removed from this article. Using it to teach people causes more confusion in the long run than the good it does. The only thing preventing me from giving a link to this article to my students as a good resource is the presence of the relativistic mass notion. — Preceding unsigned comment added by 50.25.85.90 (talk) 18:52, 29 January 2023 (UTC)

As a Physics student, I agree. At our university, we got rid of "relativistic mass" years ago, reducing it to a footnote in the lecture notes in freshman physics saying effectively "it's confusing, we avoid it". Unfortunately, the obsolete notions of "invariant mass", "rest mass", and "relativistic mass" are so engrained in that article, that one would have to edit the entire article to avoid inconsistency :-/ PointedEars (talk) 13:20, 15 March 2024 (UTC)

Untitled

The article says :

In particle physics, energy is typically given in units of electron volts (eV), momentum in units of eV/c, and mass in units of eV/c2

But, eV is a unit, but c is a number. How does this work? Ptarjan (talk) 07:29, 16 August 2009 (UTC)

c is also a unit. It can be used as a unit of speed or velocity; which in SI units, has units of m/s.218.186.9.246 (talk) 14:55, 3 August 2010 (UTC)

Isn't momentum the product of mass and velocity? Surely then, in a massless object, momentum too is nil? —Preceding unsigned comment added by 61.9.146.174 (talk) 11:55, 10 December 2010 (UTC)

For objects with mass, you're right, momentum = mass x velocity, ${\boldsymbol {p}}={\boldsymbol {m}}{\boldsymbol {v}}$.

For massless photons, we need another equation: ${\boldsymbol {p}}={\boldsymbol {h}}\nu$, where ${\boldsymbol {h}}$ is the Plank constant and $\nu$ is the frequency of the photon.

Think of it this way (this is an analogy, not the actual truth): For a photon, the mass is zero, but the apparent speed is ∞ (sort of). We can multiply zero by ∞ and get a reasonable answer, in some cases, by using a different form of maths, calculus - here, we end up with a different equation. Hope this helps a bit! Cosmogoblin (talk) 21:58, 11 September 2016 (UTC)

For objects with mass, the momentum is ${\boldsymbol {p}}={\boldsymbol {\gamma }}{\boldsymbol {m}}{\boldsymbol {v}}$ where ${\boldsymbol {\gamma }}$ is the Lorentz gamma factor. The Newtonian version ${\boldsymbol {p}}={\boldsymbol {m}}{\boldsymbol {v}}$ is an approximation valid only at low speeds.George Dishman (talk) 10:27, 5 January 2022 (UTC)

LaTeX for lead equation

Latest revision as of 20:01, 3 July 2013 Maschen (the lead eqn should stand out ideally in LaTeX and compare the code $E^{2}={(pc)}^{2}+{(mc^{2})}^{2}$ to E² = (pc)² + (mc²)²)

I can see the benefits of using LaTeX, but the downsides are

1. the page sometimes displays the latex code and then starts rendering it only after most of the rest of the page is loaded/rendered, at least on some/my browser
2. it doesn't render at all in the boxes that pop up when u hover over a link to this article (i think that's an option) and probably other similar things that only show the 1st paragraph; the most important part of the intro is silently absent.
3. the symbols in the text don't look like the ones they supposedly refer to in the equation (i guess it's the computer modern font -- when i used latex 24 years ago i always used to switch it to times roman or helvetica/arial instead). it would be more consistent (though not recommended) to change all the in-text symbols to LaTex as well :-)

If it's just an issue of standing out, i'm sure we could make it bigger/bolder/whatever. DavRosen (talk) 01:19, 4 July 2013 (UTC)

It's simple - use HTML for inline equations (unless special symbols are needed), and LaTeX for displayed equations. In order of the points:

1. Is that a problem? The same happens for all pages using LaTeX. The equations still load up.
2. It happens to on my browser, not sure why it can't (in general) just because it's in a table box. There are numerous places on WP where the box is used to frame equations and it wouldn't make sense to change all those equations to HTML. In mathjax the \boxed parameter does work, but not for PNG rendering. If needed, the reader can zoom in to see details for the one equation.
3. Changing inline HTML to LaTeX just for "consistency" is an unnecessary incredible waste of editing time and energy because LaTeX inline simply looks jarring, and similarly for changing all displayed formulae from LaTeX to HTML (which wouldn't even work in general because large fractions/roots/summations/integrals etc. are too awkward in HTML while they're too easy in LaTeX). It is inconsistent anyway to have displayed HTML and LaTeX in the same article. Obviously, if possible the LaTeX fonts (in WP and related projects) would be changed to something that matches the surrounding text (so that we don't have two diametric opposites - Arial and Computer/Latin Modern Roman), but it still isn't even in 2013...

Hope that clears it up. Best, M∧Ŝc²ħεИ_τlk 07:32, 4 July 2013 (UTC)

In flat Minkowski space, the relation is:

  E² = (pc)² + (mc²)²      (1)    

where c is the speed of light, and

I'm not saying we should do exactly that, but just that the box etc can go in a template and something like {{math}} could go inside?

DavRosen (talk) 16:38, 4 July 2013 (UTC)

I should soften my previous stance and personal preferences which shouldn't take priority over other people's. The issue is simply fonts, not physics.

By all means, we could use the {{bigmath}} inside the box, which seems to achieve what you want in one template, implemented now. ^_^ M∧Ŝc²ħεИ_τlk 18:31, 4 July 2013 (UTC)

With {{bigmath}}, the equation is still absent from the pop-up previews! My experiment didn't have that problem because it just used html <br> to set it on its own line, rather than a block structure like an html table. Logically, the equation could be inline (the article would still make sense) but we would like to display it on an isolated line for readability, emphasis, etc. By putting it in an html table, bigmath has taken away the possibility of it being rendered in a situation where block structures aren't rendered (like a preview). So then we have a preview that is missing its most important part. DavRosen (talk) 19:44, 5 July 2013 (UTC)

You wanted HTML and that's obviously not going to have the same pop-up/zoom-in image like with mathjax, with or without {{math}} templates... M∧Ŝc²ħεИ_τlk 08:46, 6 July 2013 (UTC)

Pop-up/zoom-in image like with mathjax shouldn't be necessary except for more complex equations, which probabably shouldn't be in the lead section anyway. Maybe the lead section should favor compatibility and accessibility, while the rest of the article can use the full-blown math display. BTW, what do you think about using the inherently-superscripted unicode characters as in "c²" -- too small?

Speaking of notation, I'm thinking the lead section would be clearer if it always used the explicit subscripts as in m₀ and E_Tot. At the end of lead section we can say we're dropping the subscripts for the remainder of article.

DavRosen (talk) 21:28, 9 July 2013 (UTC)

Unicode subscripts and superscripts are discouraged by WP:MOSMATH. If you are not satisfied with defaults of <sub> and <sup>, then you can use CSS to control them (both in a bare wiki and {{math}}): c² c² c² c² c². Incnis Mrsi (talk) 18:55, 12 July 2013 (UTC)

To answer:

• Not sure if DavRosen wants the pop-up preview or not, but as mentioned just now by DavRosen and in my point 2 above it's not essential since the equations are simple. So, can we forget about previews in the lead?
• I would just prefer to use LaTeX for all displayed equations (lead included) and HTML for very simple inline symbols and expressions (lead included). It looks weird to have one style (HTML/LaTeX) in the lead and another for the rest of the article (more generally and worse would be random styles all over the place). It's that simple. Why would displayed LaTeX be less accessible than HTML in the lead? It's no different than the rest of the article. Articles like vorticity equation and mass matrix use displayed LaTeX in the lead and it fits comfortably with the rest of the article.
• Yes, superscripts of symbols as glyphs generally do not match ^... and are discouraged for this reason, I would just use ^... for all superscripts.
• As for total/rest etc energy and mass, it is simple enough in my experience to just use E = mc² for total energy and mass, and E₀ = m₀c² for rest energy and mass. The "total"/"tot" etc subscripts are not necessary since the formulae are supposed to be explicated in words, and should by default emphasize what quantities are total/rest etc. and in which reference frames, as such the subscripts would clutter the equations, but it's not bad or wrong to include them either. (We shouldn't tie up the reader with the irrelevant "relativistic energy/mass" concept - it's the total and rest energy and mass that is fundamentally important).

But, I will leave the typography and notations to the editors of this article. BTW, there are some editors that actually change inline HTML to LaTeX (see for example [1])...M∧Ŝc²ħεИ_τlk 21:48, 12 July 2013 (UTC)

(outdent) I meant that there's a trade-off between using native vs latex equations, and the decision *could* go a different way in the lede, which should be a standalone summary that has the widest possible readership, with symbols that actually match between the equations and the inline, with equations that can be read aloud by screenreaders and searched for as text and copied-pasted into a document and then edited, but no complex equations, vs. the rest of the article which usually does have more complex equations but also is directed at a somewhat narrower audience who may be more accustomed to the way latex works in wikipedia and how to copy the source.
Also, I do want the pop-up of the article itself to be readable, which means the lede can't use unrenderable latex, but I'm less concerned about whether the popup of a link to a specific non-lede section is readable, as links from one article to a specific section in another is less common and less essential than the the ability to simply link to an article.
DavRosen (talk) 23:04, 12 July 2013 (UTC)

Subscripts for E and m

Maschen, you point out that it's simple enough "to just use E = mc² for total energy and mass, and E₀ = m₀c² for rest energy and mass".

But that's not what's being done in this article, which uses E to represent the total energy but a bare m to represent the rest mass, which may be a common convention but it's confusing when you're trying to talk about all four combinations of total vs rest with mass vs. energy in the same sentence, as in

..... E_[TOT] = m_TOTc² relates total energy (E or E_TOT) to total (relativistic) mass, while E₀ = m_[0]c² relates rest energy to rest (invariant) mass (m or m₀),

where I resorted to square brackets and referencing both with and without the subscripts in order to try to be consistent with the main eqn (1) while still explicitly distinguishing rest from total. I'm thinking this paragraph may be the only one that needs this distinction, so maybe I should use explicit subscripts in that paragraph (maybe shorten TOT to T), saying that I'm doing so, and then saying that they'll be dropped in the rest of the article.

Or maybe best to switch only once: start the lede with the explicit subscripts 0 and T to avoid ambiguity, and then after this paragrah, or at the end of the lede/begining of the 1st main section say that we're dropping them.

BTW, the importance of that paragraph is that it dispels the notion that E=mc2 isn't correct in general without the momentum term, which is only the case if you (mis-)apply it with mixed meanings as in E_[Tot] = m_[0]c²

DavRosen (talk) 22:59, 12 July 2013 (UTC)

You asked:

"Speaking of notation, I'm thinking the lead section would be clearer if it always used the explicit subscripts as in m₀ and E_Tot. At the end of lead section we can say we're dropping the subscripts for the remainder of article."

and the answer was partially a proposal to use no subscripts for total quantities, and 0 for rest quantities, throughout.

The use of square brackets/no square brackets, "total"/"tot"/ect. subscripts, and combinations, is really clumsy, cluttered, will only confuse readers by requiring continual explanation of notations (and the reader must then keep track), and it's not even necessary (I've never seen any textbook or course go further than a zero and/or possibly "total" subscript, have you?).

This is correct:

"The energy-momentum relation in flat spacetime, for a massive object of rest mass m₀ (with corresponding rest energy E₀ = m₀c²), is:

$E^{2}-(pc)^{2}=(m_{0}c^{2})^{2}$

and if the object moves at three-velocity u = (u_x, u_y, u_z) with magnitude |u| = u in the lab frame:

$E=\gamma (\mathbf {u} )m_{0}c^{2}$

is the total energy of the moving object in the lab frame,

$\mathbf {p} =\gamma (\mathbf {u} )m_{0}\mathbf {u}$

is the momentum of the object in the lab frame with magnitude |p| = p, and:

$\gamma (\mathbf {u} )={\frac {1}{\sqrt {1-{\frac {\mathbf {u} \cdot \mathbf {u} }{c^{2}}}}}}={\frac {1}{\sqrt {1-\left({\frac {u}{c}}\right)^{2}}}}$

It the Lorentz factor. Some authors use relativistic mass defined by:

$m=\gamma (\mathbf {u} )m_{0}$

although rest mass has a more fundamental significance, and relativistic mass will not be referred to in this article."

Later, I'm going to simplify the notation throughout and make it coherent. M∧Ŝc²ħεИ_τlk 08:41, 14 July 2013 (UTC)

Two refs:

• J.R. Forshaw, A.G. Smith (2009). "7". Dynamics and Relativity. Manchester Physics Series. John Wiley & Sons. ISBN 978-0-470-01460-8.

uses m₀ for rest mass,

• D. Kleppner, R. J. Kolenkow (2010). "13". An Introduction to Mechanics. Cambridge University Press. ISBN 978-0-521-19821-9.

uses m for rest mass.

M∧Ŝc²ħεИ_τlk 09:02, 14 July 2013 (UTC)

Misleading image?

I don't mean to be dismissive. The image File:Energy-Mass-Momentum Pythagorean Relationship.jpg in the lead may have pedagogy, but it doesn't mean much. It shows the relation geometrically by the Pythagorean theorem which applies in Euclidean space, when actually the energy-momentum relation is the magnitude of a four-vector in Minkowski space. Sooner or later I will draw another to represent the hyperbolic nature of the relation (not circular) and replace, or possibly just delete the one in the lead. M∧Ŝc²ħεИ_τlk 09:02, 14 July 2013 (UTC)

I agree: this JPEG crap is not worthy in all senses; I even had an intention to post about it myself. Do you know a geometric proof of pseudo-Euclidean Pythagorean theorem? Incnis Mrsi (talk) 11:00, 14 July 2013 (UTC)

Sorry, no geometric proof for now...

All I was getting at above was the length of a vector in Euclidean space vs the length of a vector in Minkowski space (which is the E-p relation), which are not the same, rather than emphasizing any "Pythagorean relations". M∧Ŝc²ħεИ_τlk 11:13, 14 July 2013 (UTC)

Then try to draw something along the lines of this old plot, but with more emphasis on the relation. Incnis Mrsi (talk) 12:14, 14 July 2013 (UTC)

The diagram illustrates equation (1) correctly (edit: it should have m₀ now, not just m), doesn't it? I.e. the version for flat spacetime. The pythagorean theorem applied directly to the diagram gives eqn (1). You could draw a "4-d" version of it for the more general relation in the "General relativity" section....DavRosen (talk) 07:15, 15 July 2013 (UTC)

You miss the point. The JPEG crap suggests that E is something like a magnitude of a vector, and that this vector changes its direction depending on p for fixed m. Whereas E is actually a 4-d vector projection, not a magnitude. For this insignificant gain of illustrating a trivial quadratic relation the image invokes completely wrong connotations. Incnis Mrsi (talk) 07:28, 15 July 2013 (UTC)

Looks to me like a triangle designed to illustrate a (trivial) quadratic relation between three scalar quantities -- I don't see anything that suggests that it has to do with vectors or their direction or magnitudes. I guess I'm not clear on who the readers of this article are. I don't think wikipedia has a concept of an "advanced" article whose readership is assumed to (a) not need any "trivial" visual aids, and (b) who will assume that the triangle must be meant to imply something more sophisticated. Maybe if the symbols in the diagram were italicized as they should be, it would be clearer to the sophisticated reader. DavRosen (talk) 08:20, 15 July 2013 (UTC)

Sorry for the delay. The diagram is ready and it will be replaced. M∧Ŝc²ħεИ_τlk 09:05, 15 July 2013 (UTC)

IMHO anybody would not be upset were you to upload images tomorrow, but indeed I detest “E'” and “p'” and have a vomit because of them. Could you learn that prime (symbol) is not an apostrophe? Also, for which reason do you make variables of sans serif muds? To me, it is a design of morons. Incnis Mrsi (talk) 09:39, 15 July 2013 (UTC)

You changed the fonts... I have always used and liked sans serif for Latin (Arial because it is standard and looks clean), and used and liked serif for Greek (clearer than thick and horrible sans serif Greek). What is wrong with sans serif for Latin? (I don't care too much about apostrophes...) M∧Ŝc²ħεИ_τlk 09:56, 15 July 2013 (UTC)

If you like Arial, the feel free to revert to it, but don’t reinstate apostrophes. Actually, my opposition to sans is primarily caused by problems with “I” (sans “l” is also ugly, but happily it is superseded with ℓ in math). Incnis Mrsi (talk) 10:45, 15 July 2013 (UTC)

No need to revert, I have converted the Greek to Times new roman, and all symbols to curves, so we can see the nicer times new roman and not the default fonts rendered in WP images. I also agree that "l"/"I"/etc. glyphs are unclear in sans serif (not serif - "l"/"I"/etc. ). M∧Ŝc²ħεИ_τlk 10:51, 15 July 2013 (UTC)

more about lead section

Maschen, I think the early part of the lede is hard to follow now, too long, and too technical in its 2nd paragraph. Especially since the first paragraph now has no trace of any information about the relationship itself or its form, the reader has to go to the 2nd para to find the relation and then that should still be a simple paragraph before getting into details. I don't see how rearranging the main eqn with a minus sign helps. Definitions of eqn 1's symbols are scattered, m_0 before it, and for p the reader has to go down five lines (two being additional equations) and find it in the middle of that line. I think it's good practice to state what each symbol represents (not necessarily a complete definition or derivation which can be later) all together and immediately without being separated by a lot of additional symbols needing to be defined. And not introducing any other symbols or equations until afterwards, if possible. For example, E can be said to be the total energy without immediately writing out the equation $E=\gamma (\mathbf {u} )m_{0}c^{2}$, which could be part of the derivation of the main relation but doesn't need to be this soon.

I think something like the following is much clearer (note that all four symbols in the equation are defined immediately within the same sentence below the eqn, with no new symbols or terms introduced until those 4 all been mentioned.

E² = (pc)² + (mc²)²

(1)

where c is the constant speed of light, E is total energy of the system, m₀is the rest mass, and p≡|p| is the magnitude of the total relativistic momentum,

p = γ(u)mu ,

of the system traveling at 3-velocity u. The 3-momentum here includes the Lorentz factor γ(u), not just the classical definition mu.

DavRosen (talk) 08:06, 15 July 2013 (UTC)

Yes, I've been meaning to rewrite the lead and reword in a few places. Trying to make all the symbols and notation coherent without making a single mistake is a bit much for one edit. M∧Ŝc²ħεИ_τlk 09:05, 15 July 2013 (UTC)

Thanks, Maschen. Isn't moving the momentum term over to the energy side a bit unconventional? We shouldn't do it just because we may prefer it that way. DavRosen (talk) 17:50, 15 July 2013 (UTC)

Apologies for not replying to this before. The main reason for:

$E^{2}-(pc)^{2}=(m_{0}c^{2})^{2}$

is because it's directly the equation for the norm of the 4-momentum, and both sides as it stands are invariants and hence readily applicable for calculations. The other rearrangement:

$E^{2}={(pc)}^{2}+{(m_{0}c^{2})}^{2}$

is probably more recognizable, and we could have this in the lead, but it's hardly different to the former rearrangement so I kept that. We can change the current lead equation to the second rearrangement here.

BTW, I have sounded bitey/ignorant throughout the posts, but your paragraph in the lead about E = mc² provides clarifying points not included elsewhere in the article. Thanks for writing it! M∧Ŝc²ħεИ_τlk 22:16, 15 July 2013 (UTC)

I think it's important to keep the first occurrence in the most recognizable form, not just a form equivalent to it. Later you could mention or use the other form, maybe just when it's helpful in relation to use of the 4-momentum, or maybe completely switching to it starting at the end of the lede or somewhere else, at which point we would state that we're doing so. DavRosen (talk) 16:49, 16 July 2013 (UTC)

Proposal: move the segment with the numbered points on the mass-energy equivalence relation down to the special cases section, where such explications should ideally be made, and replace in the lead with a shorter sentence or two, like:

"A famous consequence of special relativity is the equivalence between mass and energy, given by the infamous equation E = mc², although this applies to massive particles. The energy-momentum relation absorbs the mass-energy equivalence relation for massive particles, and with the inclusion of momentum, the total energy is related to the rest mass for all particles, thus providing the energy of massless particles correctly as well."

Or words to that effect. Seems better for a lead. Agreed? M∧Ŝc²ħεИ_τlk 15:05, 17 July 2013 (UTC)

Maschen, I just noticed your last post. I think the numbered sections (or improved/condensed versions thereof) are important to summarizing where and how this topic fits into the bigger picture including mass-energy equivalence and of course the classical limit and kinetic energy. I think it's very helpful to understand that this relation is a generalization of classical kinetic energy (with rest-mass-energy equivalence) to the case of relativistic speeds. That is, it shows what energy is contributed by motion beyond just the rest energy.

I was thinking that some of the paragraphs nearer to the end of the lede aren't necessary for understanding the big picture of this topic and could be moved down into some sections. In my mind, everything through the paragraph "A more general form of relation (1) holds for general relativity." (where it is now), constitutes a self-contained and reasonably-complete summary of this topic and answers the critical question "what is the energy-momentum relation and what other concepts does it most closely relate to and how?". But I'm flexible on this -- can some of those lower paragraphs be moved and/or shortened to their essentials within the lede? DavRosen (talk) 17:01, 17 July 2013 (UTC)

Perhaps the numbered points could stay, moving it down would probably induce unnecessary repetition in the "special cases" section.

Well, I agree some of the material after the "A more general form of relation (1) holds for general relativity." statement could be easily be moved down, but it's important to provide motivation for the need of this equation in relativistic mechanics and particle physics and I subconsciously included the invariant equation for E, p, E′, p′ there. IMO the statement about relativistic QM and QFT should stay in the lead. The points I wrote about the derivations of the equation were accidentally placed before the heading of the first section and should be moved down. M∧Ŝc²ħεИ_τlk 21:21, 17 July 2013 (UTC)

more about the new image at the top

I like the new diagram from above discussion, but it seems a bit too technical to be at the top with the lede (in fact it appears above and before the lede text if you have a narrow screen). I don't think most readers will be able to follow it until after they digest the lede and certain other parts of the article, and then they have to notice the connection with the diagram/caption. Can the diagram be moved down into one of the sections? (Or if not, then can its caption be shortened and refer the user to a particular section for more explanation, and maybe moved to near the bottom of the lede so it simply appears next to the Contents rather than alongside/above the very first introductory sentences of the lede.) DavRosen (talk) 18:31, 17 July 2013 (UTC)

Fair enough. The caption is of course too long and some of it should ideally be spilled into the main text. Also, it doesn't mention that φ and φ + η are the rapidities of the blue and green frames respectively. It would be fitting in the 4-momentum section. M∧Ŝc²ħεИ_τlk 21:21, 17 July 2013 (UTC)

Rest mass etc.

The page starts with

"the familiar mass-energy relation in both its interpretations: E = mc2 relates total energy E to the (total) relativistic mass m (alternatively denoted mrel or mtot ), while E0 = m0c2 relates rest energy E0 to rest (invariant) mass which we denote m0"

Per Lev Okun "The concept of mass" Physics Today June 1989 that statement is far from a forgone conclusion. That article has obviously not been read by the authors of this page. Hence the disputed flag. Please read that, it is straightforward, and fix. I am not really dead (talk) 15:22, 16 February 2016 (UTC)

I've taken the label off the article. The flag reads "This article's factual accuracy is disputed." and implies there is something wrong with the physics. It is only that the approach is disputed, not the accuracy. The 1989 aricle by Lev Okun, (Okun, Lev (June 1989). "The Concept of Mass". Physics Today. 42 (6): 31–36. doi:10.1063/1.881171.) is an opinion piece and was very controversial at the time. I think Okun has a good point, but many current texts use rest mass as in this article and it should remain. StarryGrandma (talk) 01:32, 11 October 2016 (UTC)

Potential energy in flat spacetime

Under the equation there is a note saying that a factor V for potential energy needs to be added, but above that it says the equation is "assuming the special relativity case of flat spacetime". If spacetime is flat is the potential energy zero? (I'm over my head here.) RJFJR (talk) 21:15, 27 April 2018 (UTC)

When and by who was the relativistic energy relationship published

Many uses wikipedia as source of information. Wikipedia is often very useful. However there is a big job left to point to references who and when important formulas where published. This article contains a series of references but not a single reference on who came up with this relation first. I assume possible Einstein? And no reference of when first published. I do not understand why this has so low property for wikipedia editors? This is not only about this page, but about many pages on wikipedia describing important mathematical relations in physics and other fields, often totally lacking any info about who and when it was discovered. I find this also impolite. It is like having a long page about the Mona Lisa painting without even mention who painted the picture. QuantitativeGeometry (talk) 20:12, 25 December 2018 (UTC)

It is told in the article that Dirac was the first to mention the relativistic energy momentum relationship. Please refer to a paper that show this and not only much older books that claim so. Is this in the 1928 Dirac paper on the electron, if so I could not see the relativistic energy momentum relationship there, at least not on the form mention in the wiki article. — Preceding unsigned comment added by QuantitativeGeometry (talk • contribs) 23:17, 5 January 2019 (UTC)

Hello. I don't actually know the answer but I can assure that Einstein didn't discover this. Because he mentioned L/C^2 ( L is radiation which is equal to mass ) . So for sure he never mentioned this. Intelligent boy 13 (talk) 15:03, 10 February 2022 (UTC)

I believe that Lev Okun goes into the history of early relativistic kinematics and it was Richard C. Tolman who gave us the energy-momentum relation in final form, about 1912. Unfortunately, it was also Tolman who suggested that we modify "mass" to "relativistic mass" m_rel = (E_rel)/c^2)" which would make E = mc^2 correct all of the time and disregard the momentum terms. This is not very helpful as you end with two kinds of masses (see Mass in special relativity and since relativistic mass goes up and down with energy in a system in various frames it looks like mass is "converted" to energy. High velocity particles in this view become more "massive" instead of the modern view that they stay the same mass but pick up momentum as v(gamma) and not just v. They don't get "fatter." Or even more massive. Just harder to stop (more momentum). Most important, since rest mass and system invariant mass are invariant, they are useful, but relativistic mass is not invariant, so it's less useful.

Poor Einstein didn't like "relativistic mass" and said so. But he was also a victim of the idea that mass is "converted" to energy (and said so at the end of his life when "explaining" the bomb), when what is really happening is that particles are converted to energy (and vice versa), so "matter" may be converted to various types of energy but rest-mass cannot (instead the energy keeps the rest mass as invariant mass). Also (as in the A-bomb) potential energy can be converted to heat and light (exothermic chemical and nuclear reactions) but the mass does not change until the heat and light are removed, along with THEIR mass (but then it's not a closed system so no conservation law applies anyway). That's true of a chemical reaction in a sealed system on a scale (but you can't measure masses that small) and an atom bomb after you cool the products down (but that's too difficult). Einstein always thought in terms of his initial 1905 thought experiment where an object gives off two photons in opposite directions (so we maintain p = 0) and loses mass. But Einstein might not have known that although one photon has no mass, two photons in opposite directions and energies have p = 0 and thus DO have an invariant mass. That's the mass the object is missing! So mass conservation is a product of special relativity also, so long as you use rest-mass and system invariant mass. Einstein's object loses mass only because he ignores the mass of the photons after they are emitted, assuming that if each is zero mass, both will be zero mass also! Wrong! Einstein's experiment actually happens with neutral pions which decay to two photons with the same (invariant) mass. But we see one reason that a massive pion can't ever decay to ONE photon!

The fallacy that mass is lost (unless you lose it by letting it out of your system!) or converted to mass-less energy, has crept into the mass-energy equivalence article, although our two articles mass in special relativity and energy-momentum relation (this article) are still okay. Read the end of the first one for insight. The relevant paragraph of the first article has to be fixed, but I wanted to introduce the problem here before doing it. The idea that mass is converted to energy in physics (a misreading of E=mc^2) is one of more persistent myths in physics-- still taught in some intro college classes. But not in SR relativity texts like Taylor and Wheeler. Anyway, discuss here before you-all jump on me for fixing this, in this article. SBHarris 04:11, 22 March 2022 (UTC)

Repeating the same

Who arranges it: In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating any object's rest (intrinsic) mass, total energy, and momentum:...

holds for a system, such as a particle or macroscopic body, having intrinsic rest mass m0, total energy E, and a momentum of magnitude p,

you can't read it — Preceding unsigned comment added by 31.183.229.101 (talk) 22:26, 4 January 2020 (UTC)

I'm surprised no one has fixed this yet, you are right, the statement is a run-on sentence and is hard to read. It is odd how you naturally interpret these things without noticing until you go back to critically read. Footlessmouse (talk) 05:24, 26 August 2020 (UTC)