Talk:Mass–energy equivalence/Archive 5

Mass-energy equivalence should be matter-energy equivalence
Although terminology like "mass-energy equivalence" and "interconversion of mass and energy" is common, it is nevertheless incorrect.

Mass is an extensive property of matter. It is also an extensive property of energy. If you take a small isolated system containing matter, and weigh it, and if the matter inside the isolated system then gets converted to energy, and you weigh that isolated system again, there will be no change in its weight. If the matter within the isolated system had a mass of N grams, the mass of the resulting energy is also N grams.

So mass cannot be converted into energy. Really, it's matter that can be converted into energy. The mass of the resulting energy is equal to the mass of the matter that we began with.

Even physics researchers sometimes use sloppy language, figuring that everybody understands that it's not mass, but matter, that can be converted into energy. But they misjudge their audience, and the result is confusion everywhere. The result is an entire Wikipedia article that uses confusing language.

Rahul (talk) 01:08, 2 March 2017 (UTC)


 * The literature and most part of the web seem to disagree with you:
 * {| class="wikitable" style="text-align: center"

! Google !! Scholar !! Books !! Web
 * "Mass-energy equivalence"
 * 2,220
 * 7,170
 * 142,000
 * "Matter-energy equivalence"
 * 65
 * 186
 * 27,900
 * }
 * 27,900
 * }
 * }


 * - DVdm (talk) 07:55, 2 March 2017 (UTC)


 * I'm skeptical of a search that just counts the number of Google hits. This type of search can be used to prove a lot of wrong things. Also, please note that I'm not denying that "mass-energy equivalence" is used. Rather, it's used by researchers who expect their audience to understand that it means something other than its literal meaning. The average Wikipedia reader would misunderstand this phrase. Rahul (talk)


 * Exactly how would you "weigh" energy? Weight is not the same as mass, let alone energy.--Jasper Deng (talk) 09:04, 2 March 2017 (UTC)
 * You can weigh energy, but please be cautious when phrasing such a question -- you're implying by your question that I mentioned weighing energy, and I did not. If this were a conventional discussion forum, you would have quoted me as saying "weigh that isolated system". It's hard to weigh energy alone -- it usually is found in conjunction with matter, so you would weigh both of them together. Typically the isolated system in this experiment would be an insulated box that you would weigh. Inside the box would be some combination of matter and energy, and the weight you get will be the weight of both. Also note that it's hard to convert matter into energy in a box that you can weigh, so this is obviously a hypothetical experiment that would be hard to actually do. We're essentially talking about exploding some sort of nuclear device inside an insulated box and weighing the box before and after. Rahul (talk) 21:17, 2 March 2017 (UTC)
 * I think then it's important to distinguish between the rest mass and the "relativistic" mass defined in this article. You are correct that the latter is conserved in an isolated system, but as soon as kinetic energy is gained by objects in the system (as observed from our reference frame), their relativistic mass is no longer the same as the rest mass. Now what do we need to do to measure the rest mass? We'd have to bring the objects in the system to rest with respect to our reference frame, i.e. robbing them of any kinetic energy they might have, which isn't allowed since we assume the system to be isolated. In order to gain that kinetic energy, their rest mass had to decrease (where else would you get the energy?). In other words, rest mass would not be a measure of the inertia of the system as-is, but is what we usually call "mass" in common parlance. You are, however, completely correct that the "relativistic" mass is invariant in a closed system relative to a given frame of reference.--Jasper Deng (talk) 22:32, 2 March 2017 (UTC)
 * By all means, let's be clear whether we're referring to rest mass or what you call "relativistic" mass (which I just call "mass" in my insulated box analogy). My point still remains that mass never appears and it never disappears, so mass does not convert into anything. The relativistic mass of a particle increases as the particle accelerates, but that increased mass does not appear out of nowhere -- something else must lose the same amount of mass somewhere, so again, mass does not interconvert. Rahul (talk) 04:28, 3 March 2017 (UTC)
 * Well the dominant viewpoint is that "mass" without further qualification refers to rest mass.--Jasper Deng (talk) 05:19, 3 March 2017 (UTC)


 * I have no quarrel with "mass" being used to mean "rest mass" in the Article, just so long as this is consistently done throughout the article, and the definition is made clear in the beginning. In my daily life, however, I use "mass" to mean "whatever you measure when you weigh something", and that (in the case of my insulated box example) is what you have described as the relativistic mass. Consider for a second a hot frying pan. Its relativistic mass is a few picograms higher than its rest mass. If the average person thinks about it, he will instinctively consider the relativistic mass the mass of the frying pan, because that's what he would measure if he could weigh it (accurately enough) on his kitchen scale. (Ignoring air currents etc.) The rest mass cannot be measured in his kitchen, because he would have to cool the frying pan down to absolute zero first. Oversimplifying a bit, we can say that the rest mass of the frying pan is a hypothetical quantity, while the relativistic mass is real (as opposed to hypothetical) because it's actually measurable at a temperature that can be achieved in our kitchen. If we're going to use terms like "mass" in a manner that is not intuitive to the average person, then we should be very, very clear up front that we are doing so in any text intended for a lay audience. Rahul (talk) 07:17, 3 March 2017 (UTC)
 * I have a different perspective. I believe most folks interpret mass as something not dependent on an object's velocity, which is the classical view. The concept of inertia is less intuitive to those who have not taken physics, especially in relativity, so my opinion is that pedagogically, the physical definition of mass as a measure of inertia (which, to be clear, is the one I consider most fundamental) takes a backseat. The article explains that the equation $$E = mc^2$$ is only valid when m is taken to be the rest mass, and is a special case of the more fundamental and general identity $$E^2 = (mc^2)^2 + (pc)^2$$. In fact, the latter identity is also only valid when m is taken to be the rest mass.--Jasper Deng (talk) 08:05, 3 March 2017 (UTC)
 * Rahul, energy and mass are both merely quantitative *properties* of an object. The object is ultimately *composed* of quantum particles, some of which may be considered matter and some of which may not, e.g. photons can be considered "radiation" particles instead of matter. You can't "convert" matter to a property of matter!  You can't convert any particle to its own property!  You can convert some particles (matter or not) to some other particles (matter or not), but in both cases they have the same energy and the same mass both before and after the conversion.  The problem is that you are considering something like light to *be* (a type of) energy -- in fact light *has* a property called total/relativistic energy (and an equivalent/proportionate one called its total/relativistic mass), just like matter does, but light is not a form of energy (nor of mass) and matter is also not a form of energy (nor of mass). You can't "weigh energy" because energy isn't an object that can be weighed.  Energy and mass are both quantities that are merely the *result* of a measurement made on an actual system/object.  You can weigh a system composed of particles (protons, photons, etc.), or measure its mass or equivalently its energy. Energy and mass are in fact the *same* physical property, but for historical reasons we use these terms according to different manifestations of this property.  If we are measuring the work or heat that can be performed by a system, we usually call it energy, and if we are measuring the inertia or the strength of interaction with a gravitational field, then we call it mass, but they are always proportionate if measured in different units, or identical if measured in the same units. DavRosen (talk) 00:51, 3 March 2017 (UTC)


 * What an interesting discussion! Sadly, Wikipedia is not a good place for this, as we're shoehorning a discussion into wiki software. Anyway, when the average person reads a Wikipedia article, they are not going to easily make sense of quantum particle-based mathematical models containing abstract energy or mass terms. They will, however, easily relate to the example I gave, which could be restated as: "If you take a perfectly insulated box containing matter, and weigh it, and if the matter inside the box then gets converted to energy, and you weigh that box again, there will be no change in its weight."  So why don't we try to make this Article use everyday analogies to make physics understandable to the lay person? The interconversion of matter and energy is understandable with my box analogy. The alleged interconversion of mass and energy by contrast has no real-life analogy. Rahul (talk) 04:28, 3 March 2017 (UTC)
 * His point is that you can't convert matter to energy and vice versa, since the latter is a property of the former, whereas mass and energy are in fact manifestations of the same thing.--Jasper Deng (talk) 05:18, 3 March 2017 (UTC)


 * I invite you to consider the journal reference below (sorry for the crude formatting, I'm not a Wikipedia expert and anyway this is the Talk page so I won't invest any time with wiki markup below). Rahul (talk) 07:47, 3 March 2017 (UTC)

BEGIN CITATION

Energy has Mass: A common misunderstanding is re-examined.

Hermann Bondi and C B Spurgin.

Physics Bulletin, Volume 38, Number 2, 1987.

http://iopscience.iop.org/article/10.1088/0031-9112/38/2/024/pdf

BEGIN EXCERPTS

The incorrect notion that mass can be converted to energy probably owes its origin to simplified popular accounts of nuclear fission processes, where emphasis is laid on the fact that the particulate fission products of uranium have a total rest mass somewhat less than that of the uranium atom and initiating neutron, while a very considerable amount of energy seems to have appeared from nowhere (as kinetic energy of products, energy of photons etc). But this energy has mass equal to the mass that seems to have disappeared. The energy has not come from nowhere; it was formerly present as potential energy of the arrangement of protons and neutrons prior to the fission — potential energy which has been diminished by the rearrangement into more stable fission products. It is the loss of this potential energy which gives rise to the apparent reduction in mass which is observed if one ignores the mass of the energy released. Potential energy has diminished and kinetic energy has increased. Mass of potential energy has diminished and mass of kinetic energy has increased. Energy has been conserved and mass has been conserved, each separately.

...

The best way to appreciate Einstein's conclusion is to realise that energy has mass. The best way to express it is to say that the mass of energy E is m, given by m = E/c².

Students should be taught that:

(i) energy has mass;

(ii) energy is always conserved;

(iii) mass is always conserved.

They should be warned against believing erroneous statements that mass and energy are interconvertible, and they should be urged to avoid such terminology as 'the equivalence of mass and energy'.

END EXCERPT

END CITATION
 * Let me ask you an elementary question. What is mass a property of? What is energy a property of? I consider the notion that "energy has mass" to be absurd, because it is matter that has mass.
 * If you really want, I could ask professors at my university (which is one very well-known for physics, having two elements named for it), but I doubt they'd disagree.--Jasper Deng (talk) 07:56, 3 March 2017 (UTC)


 * If you want to invest some time, and if your campus has easy access to online reference materials, perhaps you could do a citation search, and look for any journal articles that cite the one by Hermann Bondi and C B Spurgin (above), and see if there are other articles that agree or disagree with their assertions. Such citations will be very useful in improving the Article. But by all means if your professors have any insights supported by reliable published references those would be helpful. Re the notion that "energy has mass" being absurd, simply consider my insulated box again. Suppose it contains matter and antimatter particles that annihilate one another after you have weighed the box. The box now contains (almost) pure energy. Does the box weigh the same? If it does, you're weighing energy (after subtracting the weight of the box itself). If you can weigh something, it must have mass. Energy has mass. Try to find the entire paper by Hermann Bondi and C B Spurgin (cited above). — Preceding unsigned comment added by Dhesi (talk • contribs) 08:51, 3 March 2017 (UTC)
 * It is not true that the stuff left in the box "is energy" or "is almost pure energy". What's left in the box are photons, which *have* have a property called energy!  The original matter and antimatter already had that same property -- there is no difference in this respect.  It is no more true that photons "are" energy than that the original matter & antimatter "are" energy.  Energy (or its equivalent, mass) is equally a property of both!  DavRosen (talk) 08:58, 3 March 2017 (UTC)
 * As an example of how absurd that statement is, can you even tell me the "momentum of the energy"? Conservation of momentum is, after all, the original motivation for the notion of relativistic mass. You are attempting to frame a property of matter as a property of a property of matter.
 * You cannot define energy without matter, anymore than you can define momentum without matter. When you annihilate, you don't have the matter disappear. True, the result is often zero-mass particles, but they're particles nonetheless. The energy hence evolved is then an attribute of those particles.--Jasper Deng (talk) 09:28, 3 March 2017 (UTC)

OK peeps. This talk page is for discussing improvements to the article. Not a general discussion as to the meaning of "mass", "matter", "Energy" and whatever, see WP:NOTAFORUM. The article is supported by reliable sources and we do not do our own original research here. You could discuss on Reference desk/Science if you are struggling to find references and welcome to continue here if there are changes that you feel are needed to the article that are supported by sources. Best wishes Polyamorph (talk) 10:00, 3 March 2017 (UTC)
 * But this discussion is related to whether we should accept 's suggestion. He provided a reference, after all. --Jasper Deng (talk) 10:02, 3 March 2017 (UTC)
 * Then simple answer is no. We should use the term that is supported by the reliable sources which are cited in this article. Polyamorph (talk) 10:12, 3 March 2017 (UTC)
 * I agree. This is not the place to discuss interpretations of a paritcular —likely wp:UNDUE— source. Discussions of this kind tend to never end. - DVdm (talk) 10:33, 3 March 2017 (UTC)
 * This is not a discussion involving original research, but rather, that the terms used may mislead a lay reader. As another example, consider: "[I]f a body is stationary, it still has some internal or intrinsic energy, called its rest energy, corresponding to its rest mass." This would be clear to a physicist. A lay person would assume that the mass of book resting on a table in his living room is its rest mass. But the physicist knows, and a lay person does not, that this assertion either assumes absolute zero or assumes that the thermal energy is negligible for the calculation. Throughout the article implicit assumptions are made designed for physicist readers, not for lay persons. it's this type of misunderstanding that Bondi and Spurgin are addressing in the cited reference when they address what students should be taught (which you incorrectly suggest is wp:UNDUE). It's true that the Wikimedia software is poorly designed for discussions, but that's a reflection on the software, not on the discussion. — Preceding unsigned comment added by Dhesi (talk • contribs) 20:02, 3 March 2017 (UTC)
 * You started this section saying "matter-energy equivalence" when that has been clearly established to be absurd, as is your later "energy has mass". Your intuition argument is weak at best, because like I said, people don't think of mass as something dependent on velocity. Additionally, thermal energy of an everyday object is rather neglible compared to the rest energy: a heated clothes iron is basically not any harder to lift up than one cooled by liquid nitrogen. And I highly suggest you actually read WP:UNDUE because it does not say what you think it says. Your source is a small minority viewpoint.--Jasper Deng (talk) 20:14, 3 March 2017 (UTC)

I'm closing this discussion. If you want to talk more on this please take to Reference desk/Science. Thanks. Polyamorph (talk) 20:39, 3 March 2017 (UTC)

Universe design
Mass and energy works alternative due to force. Force generate by formula 0=-0/-0 to create universe. 0= null sign. Its also involved in dark matter. Its nothing but some parts of null inside in something. Prashant Nanda 14:52, 14 March 2017 (UTC) — Preceding unsigned comment added by Twisindia (talk • contribs)

Already in his relativity paper
User seems to have a grammar-related problem with the phrase Already in his relativity paper "On the electrodynamics of moving bodies", Einstein derived..." and wants to replace it with In his relativity paper "On the electrodynamics of moving bodies", Einstein had already derived...": We briefly discussed this on their talk page in the (now removed section) Grammar. I argue that
 * Original version:, 27 Nov 2015
 * Revert #1:, 10 Feb 2017
 * Revert #2:, 26 April 2017
 * Revert #3:, 2 May 2017
 * this changes the emphasis and the meaning of the sentence,
 * there's nothing really wrong with the grammar,
 * it is how the relevant literature formulates it (2000+ hits of Google Scholar, and almost 70000 hits of Google Books)

Thoughts? - DVdm (talk) 07:08, 2 May 2017 (UTC)


 * DVdm is absolutely wrong. The usage, "Already X did Y" is a typical misunderstanding of correct English grammar seen in those who have learned English as a second language. The edit does NOT change the meaning of the sentence. What it clearly does is rewrite the sentence to say what it is intended to say, i.e., that in Einstein had, a previous paper, already done whatever." The usage DVdm insists upon is ridiculous and would never be tolerated in an in-print encyclopedia. River Styx 23  12:03, 2 May 2017 (UTC)
 * The construction is not "Already X did Y", which would be bad indeed. The construction is "Already in X, Y did Z", which is used in more than a sufficient number of relevant scholarly articles and books. - DVdm (talk) 12:56, 2 May 2017 (UTC)


 * Compared to "In X, already Y", the construction "Already in X, Y" puts more emphasis on timing, which seems appropriate in the present context. I don't see any grammatical problem here. If there is, please cite a reliable source. Paradoctor (talk) 14:06, 2 May 2017 (UTC)


 * I wonder if this an American v. British problem. To my British ears, RiverStyx23's version sounds much better and easier to understand. Separating the adverb "already" from the verb "derived" just makes the sentence confusing. There is also an issue of verb tense. In British English, the pluperfect "had derived" should be used instead of the simple perfect "derived". (See http://www.oxfordlearnersdictionaries.com/definition/english/already under "British/American".) This webpage http://www.ef.co.uk/english-resources/english-grammar/present-perfect-ever-never-already-yet/ suggests that "Already can be placed before the main verb (past participle) or at the end of the sentence". --  Dr Greg   talk  18:37, 2 May 2017 (UTC)
 * I don't think that http://www.oxfordlearnersdictionaries.com/definition/english/already applies. In that entry already is an adverb working on the verb, whereas in our article already works on "in his relativity paper". That is the essence of putting it in front. This subtle—but i.m.o. essential—emphasis is lost in RiverStyx23's version. - DVdm (talk) 18:52, 2 May 2017 (UTC)
 * Well in British English, "already" is an adverb and it acts on a verb ("had derived"), no matter where you put it in the sentence. Acting on "in his relativity paper" doesn't make sense to me. --  Dr Greg   talk  22:28, 2 May 2017 (UTC)
 * But adverbs can act on other things: "it was already late in the evening"—see, for instance, http://www.english-grammar-revolution.com/what-is-an-adverb.html . As you see, adverbs can also act on other adverbs, and "in his relativity paper" clearly is a "multi-word-adverb", as it can be replaced with a single-word-adverb such as, for instance, "here", as in "already here he did such and such". I think that grammatically this is clear-cut case. - DVdm (talk) 12:44, 3 May 2017 (UTC)
 * And see http://dictionary.cambridge.org/grammar/british-grammar/adverbs-of-time-and-frequency/already :
 * Less often, we put already in front position (before the subject). This is usually more formal:
 * Already more than fifty thousand tickets have been sold for Saturday’s cup final match.
 * And that is exactly the idea behind our original sentence. So, perhaps less often and more formally... as in an encyclopedia, and apparently in the literature, as we can verify with the google Scholar and Books searches.
 * More frontal alreadies in, for instance http://sentence.yourdictionary.com/already - DVdm (talk) 12:54, 3 May 2017 (UTC)

'Equivalence' is wrong term.......
e = mc^2 does not assert equivalence. How could mass and energy possibly be the same thing when there's blatantly a c-squared involved. They are interchangeable not equivalent. CMJAWHM3 (talk) 14:18, 18 April 2017 (UTC)CMJAWHM
 * But the literature seems to have no problem with the term equivalence:
 * {| class="wikitable" style="text-align: center"

! Google !! Scholar !! Books
 * "Mass-energy equivalence"
 * 2,760
 * 7,210
 * }
 * - DVdm (talk) 16:11, 18 April 2017 (UTC)
 * Also, "equivalent" is not the same thing as "identical". &mdash; Amakuru (talk) 22:00, 30 April 2017 (UTC)
 * - DVdm (talk) 16:11, 18 April 2017 (UTC)
 * Also, "equivalent" is not the same thing as "identical". &mdash; Amakuru (talk) 22:00, 30 April 2017 (UTC)

Equivalence as a term for mass/energy is perfectly fine; as they are both relativistic variables - whereas the speed of light is not. Therefore they are interchangeable. — Preceding unsigned comment added by 110.23.6.200 (talk) 09:56, 12 May 2017 (UTC)

To expand on my above comment.

Equivalence as a term for mass/energy is perfectly fine; as mass and energy are both relativistic variables - whereas the speed of light is not. Therefore mass and energy are interchangeable, and also directly proportional to; each other, kinetic energy, and momentum. Perhaps the confusion about whether or not "equivalence" is the right term comes from the fact that mass has an inversely proportional relationship to the speed of light (as mass = E/C^2), whereas energy does not. The equivalence and interchangeability of mass and energy is also reasonably well substantiated by the practical examples section of the article. Dr. Jim Stanley. — Preceding unsigned comment added by 110.23.6.200 (talk) 10:11, 12 May 2017 (UTC)

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Why is the speed of light squared?
It's very hard to find a simple answer to this, and the article doesn't help. One physicist told me it's related to the square in the formula for momentum (mass times velocity squared). Another told me it's ultimately derived from formula for calculating the relationship between the lengths of the sides of an equilateral triangle. Tony (talk)  13:48, 17 December 2017 (UTC)
 * Well it's not to do with momentum, as that is mass times velocity, not velocity squared. It's actually the simplified form of the energy–momentum relation: $$E^2 = (pc)^2 + (m_0c^2)^2$$ For stationary bodies p (the momentum) is zero, and the equation simplifies to the familiar $$E = m_0c^2$$.
 * So, using the Pythagorean theorem for a right triangle, if you plot $$m_0c^2$$ and $$pc$$ as the "legs", the length of the hypotenuse is equal to $$E$$.  --Jules  (Mrjulesd) 14:28, 17 December 2017 (UTC)


 * Derivation in c = 1 units, where c only appears as a dimensionless rescaling parameter. Count Iblis (talk) 14:34, 17 December 2017 (UTC)

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Mathematical error
Article states that 9.0 × 10E16 Joules per kilogram is equivelent to 25,000 GWH/kg.

My repeated calculations give 25 GWH/kg.

But I am a lousy mathematician.

But this is an important error - if it is an error.

Can someone cleverer than I please check my result and reverse my correction if necessary (and tell me where I was wrong:- james@jbryant.eu).

JMBryant (talk) 11:43, 8 December 2018 (UTC)


 * 9.0 × 10E16 Joules per kilogram = 9.0 × 10E16 W s / kg = 9.0 × 10E16 W 1/3600 h / kg = 25 × 10E12 Wh/kg = 25,000 × 10E9 Wh/kg = 25,000 GWh/kg. - DVdm (talk) 11:49, 8 December 2018 (UTC)
 * Steps:
 * 1 Joule = 1 W s
 * 1 s = 1/3600 h
 * 9.0 × 10E16 / 3600 = 25 × 10E12
 * 25 × 10E12 = 25,000 × 10E9
 * G = 10E9
 * - DVdm (talk) 11:55, 8 December 2018 (UTC)

The constant c
Unless I'm mistaken, c is not the speed of light. It is the universal speed limit, or universal constant. It happens to also be the speed at which light travels in a vacuum because light has no mass. But the speed of light varies with the medium, whereas c does not vary. --82.21.97.70 (talk) 22:37, 6 March 2020 (UTC)


 * Anyone who has seriously studied relativity knows this. But it becomes tiresome to constantly say "Energy equals mass times the square of the speed of light in a vacuum". In most transparent media, such as air, the speed of light is very close to c anyhow, so it does not matter much. JRSpriggs (talk) 01:52, 7 March 2020 (UTC)


 * c0, or c, is indeed the speed of light in a vacuum. The ratio of the speed of light in a vacuum to the speed in a nominated material is the refractive index of the nominated material. As JRSpriggs points out, the refractive index of gases exceeds 1.000 by only a very small amount. (eg. The RI of carbon dioxide is 1.00045.) Dolphin ( t ) 07:09, 7 March 2020 (UTC)


 * OK, if you guys are happy with that, then! Personally, I think it should be explained, even though these things are equivalent. --82.21.97.70 (talk) 22:53, 12 March 2020 (UTC)


 * Points: (i) "universal speed limit" is not commonly used in literature, and "universal constant" could refer to any number of constants; (ii) saying "in vacuum" gives the false impression that "the speed of light" refers to anything other than the speed in vacuum. Note the use of the word the in "the speed of light", rather than a which could mean the speed in various media. --Jules  (Mrjulesd) 23:20, 12 March 2020 (UTC)

A extraordinary confusion
Do mass and energy refer to the same physical quantity? If it does, then speed of light would be dimensionless according to the famous formula. Therefore, the formula itself implies ironically that mass and energy cannot be the same. So, I think the first sentence of the section "conservation of mass and energy" should be edited. Somebody400 (talk) 20:02, 15 January 2020 (UTC)


 * (Late response) @Somebody400 Please see Dimensional analysis and Mass-energy equivalence. Two quantities can be equivalent (up to a constant of proportionality) without being dimensionally equal. If you wish, visit Natural units to learn about how you can set the speed of light to unity in a self-consistent manner. Note, this is not helpful in most non-relativistic settings, but it does reveal that you can treat mass and energy as unambiguously equivalent. In SI units, for a stationary mass, they are proportional, and the square of the speed of light in a vacuum is the constant of proportionality. Footlessmouse (talk) 10:12, 22 August 2020 (UTC)

Binding energy and the "mass defect"
Hi all, I think this section should be completely rewritten or deleted. It contradicts the rest of the article, especially Conservation of mass and energy section, and it's contents are not echoed in the binding energy article or the mass defect section therein. Furthermore, there are no references I could use to determine what the authors meant in context. It is strange to claim that mass cannot be converted to energy, what about antimatter? The whole argument revolves around nuclear reactions, while in this case it's true that the binding energy exhibits mass and that is all that's being released, this ignores other phenomena. Massless photons do not have mass, neither do collections of them, that does not make any sense at all. Any thoughts? Footlessmouse (talk) 06:12, 24 August 2020 (UTC)
 * That section is correct as far as I can tell. How does it contradict the conservation of mass and energy? Mass and energy are conserved, and loss of mass in binding of atoms occurs. For example lets say you burn hydrogen and oxygen to produce water. Now if you measure the mass of the water at the same temperature as the reactants there will indeed be a mass loss. Why? Well the mass is a measure of the energy of the system. When the hydrogen and oxygen burnt they gave out energy (i.e. heat). If that heat is removed the system will have lost energy, and therefore it will have lost mass; the mass is the measure of the energy of the system. Thus with the binding energy mass is lost, as potential energy has been lost (the potential to have an exothermic chemical reaction).
 * Now consider the scenario where you burn hydrogen and oxygen, but no heat is lost because as it is in an isolated system. In this scenario there will be no mass loss. That's because there is no energy loss. Another way of thinking about this is that although potential energy is lost in the burning of hydrogen and oxygen, there will be a corresponding increase in internal energy due to the rise in temperature. Therefore, as the mass of the sytem is a measure of its energy, and there has been no change in the systems energy, there will be no change in mass.
 * The essential thing to remember is that the mass of a sytem is a measure of its energy. If you remember that, if a syetem loses energy of any sort, it will also lose mass. Also see Binding energy, bound system is typically at a lower energy level than its unbound constituents. "When a dispersed system [...] combines, [...] the total energy of the system must decrease by an amount $\Delta E$, the binding energy [...]. The decrease in the total energy of the system must, according to relativity theory, be accompanied by a decrease $\Delta M$ in its mass, where $\Delta M \, c^2 = \Delta E$." -- --Jules (Mrjulesd) 06:56, 24 August 2020 (UTC)


 * Hi @(Mrjulesd), if you have any sources that can corroborate the statements made in the section, please provide them. The template has been there for years and no-one can find any sources, apparently. Thank you for trying to explain this to me, unfortunately you did not answer my question. I understand how thermodynamics and binding energy works, I am a physicist. What I want to know, is how this statement can even kind of close to hold true in matter-antimatter annihilations.
 * This circumstance has encouraged the false idea of conversion of mass to energy, rather than the correct idea that the binding energy of such systems is relatively large, and exhibits a measurable mass, which is removed when the binding energy is removed.... Thus, no mass (or, in the case of a nuclear bomb, no matter) would be "converted" to energy in such a process. Mass and energy, as always, would both be separately conserved.
 * This is clearly at odds with the other sections and flies right in the face of Einstein's interpretation of mass-energy equivalence (as he holds "the principle of the conservation of mass [...] proved inadequate in the face of the special theory of relativity"). If mass is a measure of energy, what is the mass of the massless energetic photon? If this is how we want to interpret it, each photon has a mass of h-bar over the speed of light times its wavelength. Should we redefine photons to not be massless? It is a measure of a form of energy. This is where philosophy comes in and is outside the realm of physics. Interpretations of the equations with no manifestly observable repercussions have no bearing on physics. Footlessmouse (talk) 07:32, 24 August 2020 (UTC)

The important point is that, when you consider moving bodies, is that $$E=m\,c^2$$ only strictly works for stationary bodies. When considering moving bodies you need to use the Energy–momentum relation: $$E^2 = (pc)^2 + \left(m_0c^2\right)^2\,$$. Now the important point of this equation is that energy is not merely a function of the mass; it is also a fucntion of the momentum (p). Thus for moving bodies there is not a straight mass-energy relationship, as you must also consider changes in momentum if you want to calculate things correctly. Thus, although the photon is mass-less, it carries away momentum, and therefore, if the energy of the system is maintained (E), if there is an increase in the momentum (p), there must also be a corresponding drop in mass (m). This explains why a body emitting photons loses mass; the photons don't have mass, but do have momentum. Therefore the body emitting the photons loses mass. Now a very simple explanation is that "mass is converted into energy", but this ignores that fact that the familiar $$E=m\,c^2$$ only strictly works for stationary bodies; the best way to consider it is as a special case of the Energy–momentum relation when p=0. Then things should hopefully become clearer. There's a very good video on youtube which explains this, which I shall link to: -- --Jules  (Mrjulesd) 07:58, 24 August 2020 (UTC)
 * As I already stated I'm a physicist, I am not sure why you brought any of this up, it's more than a little insulting. I would be the world's most incompetent physicist if I didn't know the relativistic energy momentum relationship. But thank you for the high school physics lesson and link to elementary youtube videos that will not tell me anything. If you have recommendations, they should be textbooks, and if you have those, you might want to fill in some citations like the template asks for. Also, you're wrong, there's no such thing as stationary, there is only inertial. In the center of momentum frame, E always equals m*c^2. One more time, when an electron and positron annihilate, they start with theoretically measurable mass, and end with no theoretically measurable mass. There is no "conversion" only "transformation". Footlessmouse (talk) 08:06, 24 August 2020 (UTC)
 * See Electron–positron annihilation Footlessmouse (talk) 08:15, 24 August 2020 (UTC)
 * Look I'm sorry if you're finding this insulting. And I agree that it could use citations. But my essential point is that it isn't wrong. Although the common "mass is converted into energy" mantra is often used in elementary explanations, it does give rise to paradoxes. Consider an isolated system in which a body emits photons; but both the body and the photons are trapped inside this isolated system (where no mass or energy can leave or come in). Now if you use the "mass is converted into energy" you would expect the system to decrease in mass. But no change in mass would be observed. Now I think the simplest explanation would be that the mass of the system is a measure of its energy; as there has been no overall changes in energy in the system, therefore there is no change in the systems mass. Thus the paradox has been averted. I think that is an example of why "mass is converted into energy" isn't a good way of looking at things.
 * Also E always equals m*c^2, I can't agree with that at all. If a body has momentum the correct euation is $$E^2 = (pc)^2 + \left(m_0c^2\right)^2\,$$, the momentum of the body must be taken into account, unless the mass we are talking about is relativistic mass; but since relativistic mass is usually not taken to be a physical quantity, $$E=m\,c^2$$ is only a special case when p=0. And Electron–positron annihilation makes perfect sense if you use the correct equations, mass is lost by the election-positron pair, but the resulting photons have momentum, and the Energy–momentum relation is not violated. -- --Jules (Mrjulesd) 08:29, 24 August 2020 (UTC)
 * Please see Center-of-momentum frame. This is what is meant by inertial frames in special relativity. I am sorry if I didn't make myself clear on the topic, as I was not arguing that energy-momentum is violated, that would be highly unbecoming. It seems like you are arguing that invariant mass is not conserved in these equations, though, which is contrary to the topic in discussion and is my entire point (also, relativistic mass depends on the frame of reference). I do not condone the mantra "mass is converted into energy" but rather "mass is energy", there is a chasm of difference. I will search for reliable sources before continuing this discussion. It has been a while since any of my studies in special relativity, but I think the article's lax use of mass to mean invariant and/or relativistic mass might be part of the problem. I also have not been able to read the whole article, I saw the template, assumed I could help, and got very confused. Footlessmouse (talk) 08:42, 24 August 2020 (UTC)
 * I will try to get some citations too, they are clearly needed. -- --Jules (Mrjulesd) 09:10, 24 August 2020 (UTC)

I will look for better sources, but the first one I looked through I found this:
 * "$$E = \gamma mc^2$$, represents the total energy of a particle. This important equation suggests that even when a particle is at rest ($$\gamma$$ = 1), it still possesses enormous energy through its mass. The clearest experimental proof of the equivalence of mass and energy occurs in nuclear and elementary-particle interactions in which the conversion of mass into kinetic energy takes place. Consequently, we cannot use the principle of conservation of energy in relativistic situations as it was outlined in Chapter 8. We must modify the principle by including rest energy as another form of energy storage." Serway, Physics for Scientists and Engineers with modern physics, pg 1218, this was my intro to physics 1 and 2 book from undergrad days.

A well established, university used textbook for introductory physics for scientists and engineers. This source alone puts the burden of proof on the article. Footlessmouse (talk) 09:40, 24 August 2020 (UTC)

Also, here's good olld Griffith's from Introduction to Elementary Particles, page 101:
 * "In a relativistic collision, energy and momentum are always conserved. In other words, all four components of the energy-momentum four-vector are conserved. As in the classical case, kinetic energy may or may not be conserved... Please note: except in elastic collisions, mass is not conserved.*"
 * Note at bottom for *: "In the old terminology, we would say that relativistic mass is conserved, but rest mass is not".

Please note, the italics were transcribed exactly as in the book. This is a HIGHLY reliable source. You will have a very hard time doing better unless graduate-level texts in relativity point to caveats not mentioned. This is solid proof of the sections misdirection. Footlessmouse (talk) 09:59, 24 August 2020 (UTC)

To make my claim official: I propose this section is deleted in its entirety until such time as it can be rewritten in accord with current scientific understanding and consensus. The only references on the topic thus far directly contradict the section. I therefore contend that the section is in violation of Wikipedia's no original research policy and does not represent current widely accepted scientific views on the subject. Footlessmouse (talk) 10:16, 24 August 2020 (UTC)
 * Also note, for the record, "mass converts to energy" is incoherent from a scientific perspective, it is like saying "a red apple converts to an apple", why would you ever say that? "Mass converts to kinetic energy" is inherently correct and is most certainly allowed. Footlessmouse (talk) 10:37, 24 August 2020 (UTC)
 * Upon critically rereading, I think I see what it means: it is restricting the point of view to binding energy related systems without making it perfectly clear (it ignores relativistic collisions). The statements it makes sound general and will confuse readers (it confused me). Conversion of mass into kinetic energy and the fact that mass of composite matter is generally greater than the sum of the mass of its parts are fundamentally important to this topic. This section confuses everything, but I see now that it could maybe be fixed with a few qualifications and a couple of reworded statements (and references). I will try tomorrow unless others have something to add. Footlessmouse (talk) 11:41, 24 August 2020 (UTC)
 * Griffith's electrodynamics page 510 also says explicitly that what we call mass is rest mass and that modern terminology has abandoned the use of Einstein's relativistic mass. This is an even more celebrated source than the last and is very widely adopted for undergraduate courses in electrodynamics (it's wikiNotable). This requires editing more than just that section. Archaic terminology shows up in several places and only leads to confusion. Footlessmouse (talk) 12:22, 24 August 2020 (UTC)

Hey, @(Mrjulesd), I apologize if I came off as rude in any of this. I did not mean to bite. One of the biggest problems I had with article, though, was saying that mass is conserved in situations like matter-antimatter annihilations. You must pick or choose which picture to follow: either the matter-antimatter system is in a superposition with the 2-photons and are all ill-defined as they are trapped in an isolated box we cannot interact with (in this case, mass is conserved), or the annihilation results in two photons traveling in different directions and mass has been converted to kinetic energy in order to conserve momentum and energy. It is very confusing and unhelpful, in my mind, to talk about the mass being conserved by means of the two photons, and that view is not upheld in modern textbooks. The other main thing is, for statements of "relocating matter", the outgoing radiation doesn't have to interact with any matter, what if a single photon makes it all the way outside of the observable universe? Could you call mass conserved then? I think this is philosophy and is why modern jargon has evolved. Footlessmouse (talk) 07:51, 25 August 2020 (UTC)


 * If I may suggest. It is not helpful to talk about mass being conserved. What is conserved is energy (and linear momentum, angular momentum, electric charge, baryon number, etc.). Leave it at that. Energy is an attribute of matter and radiation. Matter does not "convert" into energy, but matter can convert into radiation (or vice-versa) having the same total energy. JRSpriggs (talk) 03:43, 26 August 2020 (UTC)


 * Thanks @JRSpriggs, I wholeheartedly agree! It only serves to confuse. The article before went very far out of its way to insinuate mass is always conserved (at least that's what it seemed to me). I have made sweeping edits to try to fix some of the terminology and add qualifiers to any attempt to talk about the conservation of mass in relativistic settings. I hope I did not step on anyone's toes and I mean no disrespect to any other editors, I know that editing technical articles is quite difficult and time consuming and there are many pages to edit. I am sure more can be done, but I am a bit happier with it now. Footlessmouse (talk) 04:38, 26 August 2020 (UTC)

name change
Mass–energy is not hyphenated with a dash - but with a other character: –. side by side: -–. this is not a character on the standard keyboard 201.229.12.77 (talk) 21:41, 9 October 2020 (UTC)


 * ❌ WP:MOS, the name is proper, Mass-energy equivalence already redirects to Mass–energy equivalence.Footlessmouse (talk) 22:01, 9 October 2020 (UTC)
 * True about keyboards, but there is a redirect here with a hyphen: Mass-energy equivalence. But anyway, its in accordance with MOS:ENBETWEEN, specifically In compounds when the connection might otherwise be expressed with to, versus, and, or between, and in this context I think the word would be "and". Hyphens indicate compound modifiers in this context, but I feel this is less relevant here. Jules  (Mrjulesd) 22:03, 9 October 2020 (UTC)
 * Sorry about the edit conflict. To expand some, a hyphen here (like the one on a keyboard) is inappropriate and violates WP:MOS, energy does not modify mass. The only possible debate is between en dashes and em dashes, and I agree that the em dash is the correct option.Footlessmouse (talk) 22:14, 9 October 2020 (UTC)
 * No worries about the edit conflict. For your information the article title actually uses the en dash in accordance with MOS:ENBETWEEN. Jules  (Mrjulesd) 22:22, 9 October 2020 (UTC)
 * My bad, I guess I was confusing en dash with the shorter hyphen, but I thought that looked long enough to be em. Okay, if policy says en dash then leave it at that. Footlessmouse (talk) 23:04, 9 October 2020 (UTC)

Unclear definition
From the section "mass in special relativity", the first sentence is accurate, but the second is confusing and should be omitted: "The rest mass of an object is the total energy of all the parts, including kinetic energy, as observed from the center of momentum frame, and potential energy. The masses add up only if the constituents are at rest (as observed from the center of momentum frame) and do not attract or repel, so that they do not have any extra kinetic or potential energy.[note 1]" I'm not confident about editing directly, but i think "centre of momentum frame" says it all, and while this applies it is not necessary to place constraints on the motion. Feydun (talk) 07:03, 11 February 2021 (UTC)


 * The gravitational field interacts with the stress-energy tensor. For a particle (or condensed object), see Stress–energy tensor. Written in terms of classical physics this would be (relativistic mass $$\frac{E}{c^2}$$, momentum $$\vec{p}$$, the dyad product of momentum and velocity $$\vec{p} \vec{v}$$). So this is not just a scalar mass or a vector quantity, but something a little more complicated. JRSpriggs (talk) 17:30, 11 February 2021 (UTC)

Major reworking and potential GA nom
Hi all, I have spent quite a bit of time going through and trying to organize and consolidate the article. (I apologize if I have blown up your watch feed) I also fixed all the decade old reference errors that prevented this article from being promoted to GA status. I removed a lot of duplicate material and quite a bit of material that read either like a textbook or an essay rather than an encyclopedia that also lacked citation was not easily findable. I rewrote many other parts for clarity, excluding unnecessary detail. If you believe I have made a mistake, please either correct it or let me know. Now that the material is consolidated, I hope it will be easier to work on each section to bring it up to standards. I need a break from editing this article for now as you reach a point of diminishing returns, but I would like to nominate this article for GA status in the coming weeks or months. I think it would be a great GA once everything is tidied up a bit and a few more references are added in. If anyone has thoughts, please let me know. Footlessmouse (talk) 05:32, 15 October 2020 (UTC)


 * Footlessmouse, while I agree that your October 2020 editions made the article generally more readable, they also resulted in unfortunate loss in Verifiability. It might have been caused by the extreme speed of your work and the number of editions (21 editions from 6:20 to 12:30 on 14 October 2020) . Never mind, let us analyse quietly what has happened.  What happened was that first the name of the Nomenclature section was changed - edition at 8:17, 14 October 2020 with the remark: (Nomenclature: rename to history and c/e).  This was followed by undoing revision 983447126 in the same minute (8:17). Next Nomenclature was moved into History with the following comment " move nomenclature into history, it is inherently historic and shouldn't be at the top of the page, IMO, but that's a different topic". Actually, the section had lost some of its initial coherence from the July 2012. This was due to a lot of effort various editors put into improving the section, which was done undoubtedly in good faith but the result could indeed have been described as disorder. The reason was that all those improvements were close to OR. Editors became interested and were trying to check the claim. Which could have been: Einstein used different symbols and his meaning was different from what has been reported in secondary and tertiary sources and he only wrote the equation after the World War II, still with a different meaning. True or false?
 * My intention when I first wrote this section in 2012 was to use the primary source in a way that would match Wikipedia rules for the use of this type of source. The rules say: "A primary source may be used on Wikipedia only to make straightforward, descriptive statements of facts that can be verified by any educated person with access to the primary source but without further, specialized knowledge. For example, an article about a musician may cite discographies and track listings published by the record label, and an article about a novel may cite passages to describe the plot, but any interpretation needs a secondary source." If passages from a novel can be quoted, then quoting symbols used in a primary source should also be allowed, together with a phrase or sentence from an article. I named the section Nomenclature because the preceding section used symbols present in secondary and tertiary sources which did not report the original form of the "most famous equation of the humankind". As I myself had suffered a shock years before when I found the original in a library, I deemed it necessary to spare Wikipedia users the feeling of being cheated for tens of years, first in schools and then by the source they trusted. It was necessary to inform the readers about the actual form of the original equation, even if textbook publishers were reluctant.  The first edit was made on 25 June 2012, undone for the lack of references, edited again on June 28th and the version from 7 July 2012 was as follows:

Nomenclature In Does the inertia of a body depend upon its energy-content? Einstein used V to mean the speed of light in a vacuum and L to mean the energy lost by a body in the form of radiation. Consequently, the equation E = mc2 was not originally written as a formula but as a sentence in German that meant if a body gives off the energy L in the form of radiation, its mass diminishes by L/V2. A remark placed above it informed that the equation was approximate because the conclusion was only justified if one neglected "magnitudes of fourth and higher orders" of a series expansion. In 1907, the einsteinian mass-energy relationship was written as M0 = E0/c2 by Max Planck and, subsequently, was given a quantum interpretation by Johannes Stark, who assumed its validity and correctness (Gūltigkeit). In 1925, Louis de Broglie assumed the correctness of the relationship "énergie=masse c2" in his Research on the Theory of the Quanta. However, Einstein, even after the World War Two, wrote E = mc2 in the title of his article intended as an explanation for a "popular reader". Now, after your editions, Wikipedia again denies (?!) the readers their law to knowledge and simply contributes to cheating readers and the production of fools who one day may become angry. Why? Because equations like that one have their cultural and philosophical impact. People use them in songs and poems! And the famous E=mc2 is not there - why?
 * Now, Footlessmouse, how to improve the article again? Do you think it would be OK just to show a photo of the original passage in German, as published in 1905? This should satisfy the requirements of "NO original research". The problem is: it is Wikipedia, so people will start editing it again, and you will have the same dose of OR or even more than there was before. And no respectable journal will publish the text. So what to do? A blog or a pdf, on the Academy, for example? --C. Trifle (talk) 01:05, 5 March 2021 (UTC)  In my opinion, there is no need for urgent corrections, because the whole story is anyway well over a hundred years old. So I am not going  to make changes to the Einstein: mass–energy equivalence (this is what remained of the old Nomenclature section) for some time. Please, consider in advance if you are going to repair it on your own.--C. Trifle (talk) 10:40, 5 March 2021 (UTC)

Light rays are gravitationally bent already in the Newtonian theory of gravity
"... Solar eclipse of May 29, 1919.[15][16] During the solar eclipse, the English astronomer and physicist Arthur Eddington observed that the light from stars passing close to the Sun was bent. The effect is due to the gravitational attraction of light by the Sun. " - Light is bent by gravity in Newtonian gravity already, only is it 50% of the ovserved angle. But the last quoted sentence implies that this is qualitatively new with the theory of relativity. --Felix Tritschler (talk) 10:14, 16 May 2021 (UTC)

Mass-Energy-Information equivalence
I don't have a background in physics but I feel like this should be included as a section in this article.

Under the link below there is a relevant paper: https://aip.scitation.org/doi/pdf/10.1063/1.5123794

5.226.81.106 (talk) 15:53, 28 October 2021 (UTC)

Mass conservation
Yes, mass is still conserved in special relativity! Not if you let it out of your system, of course (as heat or light) but nothing is conserved (not momentum, either) if you do that. Alas, Einstein's 1905 thought experiment does that, and even he thought mass is conserved to energy sometimes, not realizing that the photons have mass (as a system).

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 are still okay. Read the end of the first one for insight. The relevant paragraph of THIS article (Mass-energy equivalence) 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. S B Harris 04:27, 22 March 2022 (UTC)

This is not mass... this is a mess.
I think that everyone that wants to edit should read this paper first: On the Abuse and Use of Relativistic Mass by Gary Oas. Basically, he affirms the whole "relativistic mass" thing is wrong (and yes, he affirms that if a body has energy E and mass m (invariant mass, rest mass, the only mass there should be), then the equation E = mc² is just wrong). And he shows that there are almost no textbooks (not even introductory ones) today that use that concept. Edelacroixx (talk) 06:06, 11 July 2022 (UTC)
 * The equation E = mc² is perfectly correct and backed by the literature, provided it its clear from the context that this is a stuation where v = 0, which clearly is the case here. This is not mathematics, but physics, where the meanings of the variables are described in the text that accompanies the equations. - DVdm (talk) 08:55, 11 July 2022 (UTC)