Talk:Mass–energy equivalence/Archive 3

Archive 1

Archive 2

Archive 3

Archive 4

Archive 5

Essence-Energies distinction

I think that the Catholic Church believes in mass–energy equivalence, like in Einstein's formula, at least in spiritual terms. Meaning that energy can easily become an essence in itself, and that an essence can easily be equated as an energy. And this is true for God also. The opposite belief is called Essence-Energies distinction in Eastern Orthodoxy. ADM (talk) 03:32, 3 July 2009 (UTC)

If this is so, then the catholic church is probably confusing the spiritual term "energy" with the physical term "energy". The spiritual term "energy" is usually an "aura" or a "halo", which is a quality percieved by the observer, not a physical quality but a psychological quality that only seems physical. It has to do with assignations of value, not with physical properties like mass or charge. It has nothing to do with the physics quantity "energy" which is a quantitative measure of work and heat.Likebox (talk) 14:53, 3 July 2009 (UTC)

The matter of fact is the equivalence of the essences "energy" and "matter" (the thing which mass is a measure of) which is stated by Einsteins formula. From its long struggle with religion and the masses that cling to it, modern science has a great horror of metaphysics and stepping into its rightful role as the essential belief system of man. Some time ago I tried to add a statement that matter was condensed energy to this article (or matter don't remember which), a commonplace which is what's asserted by the formula and fairly well known in the age of nuclear weapons. This combines with the quite justified policy against OR and the standard coterie of small minded individuals who appoint themselves arbiter of topics to make any such contributions here subject to the random absence of such individuals which unfortunately is not the case with this article at this time. Therefore you cannot reasonably expect this thread to have a satisfactory resolution other than that WP:OR settles the matter. Lycurgus (talk) 18:21, 29 July 2009 (UTC)

what's with the ndash?

article should reside at Mass-energy equivalence. En dashes are for ranges of values, not for basic hyphenation. --dab (𒁳) 15:15, 8 October 2009 (UTC)

Agreed. --Jtgibson (talk) 19:51, 19 October 2009 (UTC)

No, actually, it was originally hyphenated and then moved to this name, appropriately, in June 2007. This isn't "basic hyphenation", it's a... well, I don't know the name for it (surely it has a name)... but for lack of a better name, a nomial juxtaposition. Like Guillain–Barré syndrome or the Michelson–Morley experiment. (One can find a million other examples.) Robert K S (talk) 18:05, 7 November 2009 (UTC)

Constituent quarks vs. symmetry quarks

The constituent quark says that the hadrons are made out of objects which carry quark quantum numbers, and come together in twos and threes to make mesons and baryons. I don't know why, but this was a popular way to describe the quark model in the 1970s and 1980s. It doesn't work in any quantitative way, and nobody was that naive in the 1960s. Constituent quarks are a figment of the theorists imagination.

U,D,S Quarks are too light to stay nonrelativistic, and the hadrons are not made out of quarks in the same way that an atom is made out of protons neutrons and electrons. Despite this being a total fiction, if you imagine that hadrons are made out of nonrelativistic quarks, many hadronic properties come out right for two reasons: 1. gluon loops are much more important than quark loops (QCD has a small value of 1/N), 2. low lying mesons have the same quantum numbers as quark current bilinears, while low lying baryons have the same quantum numbers as quark trilinears 3. The approximation is correct for the nonrelativistic heavy quarks C,T,B.

But Gell-Mann and Zweig both well careful to state everything in terms of currents and approximate flavor-SU(3) conservation laws, because they knew that the nonrelativistic approximation is lousy. To see that it is lousy, remember that constituent quark models imagine that the pion is two quarks, so it should be 2/3 the mass of a hadron with 3 quarks. That's nonsense, because the pion's mass is determined by the vacuum pion condensate.

This is why the SVZ rules are quantitative--- they start with the quark perturabtion theory, and then shove in the effects of the vacuum condensates to get the right hadronic properties. This is the only type of quark calculation which is correct enough to give masses of hadrons, although many authors pretended that naive-quarks work in the 1980s.Likebox (talk) 14:18, 10 October 2009 (UTC)

Interestingly, pions do have roughly 2/3 of the (charge radius) VOLUME of protons and neutrons (actually, if you figure (0.71/0.875)^3, it's closer to half). Still, there's something about all these energies and fields that effectively takes up space, and has a sort of semi-constant density. "Constituitive" is a state of mind, and depends on what property you're talking about. Gell-Mann was also satirized for being cagy about the reality of quarks, even when scattering experiments revealed 3 little "dense" objects moving around in baryons. Quarks are real in that sense. Most of the mass of hadrons is not in their quarks, sure enough, so that sort of "constitution" (by mass) is incorrect. The rest mass of a hadron-- a bound zero-momentum system, is due to other kinds of contained energy. >98% of it is relativistic kinetic energy and gluon fields, with the latter playing the role of a potential energy when the kinetic energy is played out (as it must be in any bound system). Think of three very light particles moving incredibly fast and bound with an incredibly strong field-- most of the system invariant mass is not the sum of the "particle" rest masses. Gluons don't even have rest masses.

The people who want to see hadrons "made" of quarks, are the the people who believe only fermions should be "matter" and want most ordinary "matter" to somehow "made" of "matter." Well, it isn't, so long as you're talking about mass. Most of the mass of matter is not matter, if by "matter" you mean "fermions." SBHarris 21:17, 18 November 2009 (UTC)

What you are saying is even more true if you consider total scattering probabilities of pions/protons as opposed to volume. If you look at the high energy total cross sections of pions vs. protons, the cross section of pions asymptotes to about 2/3 the cross section of baryons. This is puzzling, because the total cross section in the high energy regime is dominated by nonperturbative effects, namely the exchange of the pomeron, not by quark type effects. Quark type effects would be important for charge measurements, which involve a photon which doesn't couple to gluons. But pomerons are nonperturbative string-like things, which do not have any obvious reason to couple to individual quarks.

Still, some people have claimed that pomerons couple to quarks directly because of this experimental rule. This claim is controversial, but it is hard to say whether it is true or false barring a full understanding of the regge regime in QCD.

As an aside, while it is true that Gell-Mann said that quarks are "mathematical particles" and not "physical particles", if you look at these statements in the context of the time, all he meant is that quarks are permanently confined. The literature in the 1960s, following Wigner, defines a "particle" as something that can be isolated and studied at infinity, through scattering experiments. That means that permanently confined things like quarks and gluons don't count. In this point of view, to say that quarks are mathematical is just the same as saying that quarks can't be separated from hadrons. By contrast, Nambu for a while believed that quarks could be knocked out of hadrons at high enough energies (probably because he also believed that the quarks could be assigned integer electric charges).

There was a shift in thinking in the 1970s, where quarks became real as QCD perturbation theory was shown to be reliable at predicting jet phenomena. Then the definition of "particle" changed to include any short-distance excitation of a renormalizable field theory, not just the asymptotic scattering states. This shift was generational, and mostly went unremarked in the literature, but it makes Gell-Mann look kind of silly to the modern reader. I think that's a pity, because Gell-Mann was ahead of his time in believing in quark confinement.Likebox (talk) 22:07, 18 November 2009 (UTC)

No implication

I made this edit and this revert. The implication fails since it is not stated in the premisse that momentum and kinetic energy increase to infinity. As velocity keeps increasing to a limit value, nothing has been said about momentum and kinetic energy increasing to infinity. If both would increase to finite limits, it could be still be that they could be expressed as a constant times velocity resp. velocity squared. I don't say that they can, I just say that the preceding sentences are not sufficient for the stated implication. DVdm (talk) 20:26, 18 November 2009 (UTC)

This is physics, not mathematics, the requirements of rigor are not as strict. In this case, the momentum increases by the impulse provided by the force, and the energy increases by the work done by the force. These quantities are clearly unbounded in certain specific examples, even though the velocity is bounded.

A version of this argument appears in Einstein's paper, with the force provided by an electric field accelerating a charged particle. If you imagine an electron accelerated by a uniformly charged plate, the work done on the electron over time clearly grows without bound, since the potential energy of the electron goes to negative infinity. Similarly, the momentum also grows without bound since the back-reaction on the plate from the electron is constant in time, so that the total momentum transferred to the plate is as large as you want. Conservation of energy/momentum then gives you that the actual work/impulse on the electron become unbounded, even though the speed asymptotes to the speed of light.Likebox (talk) 20:47, 18 November 2009 (UTC)

"This is physics, not mathematics" => Right, but the statement is explicitly talking about equations here and the logic is clearly faulty. If you insist on having an implication, I propose we explicitize the ubounded nature of the increases. Like for instance:

• "... Its momentum and energy continue to increase without bounds, but its speed approaches a constant value—the speed of light. This implies that the momentum of an object is not a constant..."

Ok with you? DVdm (talk) 20:53, 18 November 2009 (UTC)

That's good.Likebox (talk) 20:54, 18 November 2009 (UTC)

Ok, I'll make the change. Cheers, DVdm (talk) 20:56, 18 November 2009 (UTC)

The article read 1218 on Nov 20 contains the sentence: "Note that 1 joule equals 1 kg·m2/s2." I believe this should not be M2/S2, but M/S2, which follows from the explanation of units given just afterwards, and is also a conventional measure of energy in the form of acceleration. 72.221.89.66 (talk) 17:21, 20 November 2009 (UTC)

It's correct as it is.Likebox (talk) 17:58, 20 November 2009 (UTC)

Grammar help.

In the section "Fast-moving objects and systems of objects", there was this sentence in the first paragraph.

    "This implies that in relativity the momentum of an object cannot be not a constant times the velocity," (Last sentence)

I changed it to the following quote:

    "This implies that in relativity the momentum of an object cannot be anything but a constant times the velocity,"

I changed it to be easier to read. I do not know, however, if it was correct in the first place. 76.206.218.125 (talk) 13:05, 15 December 2009 (Central-US)

Thanks for having spotted the error, but your correction sort of made it worse :-)

I have removed the superfluous word "not":

    "This implies that in relativity the momentum of an object cannot be a constant times the velocity,"

Cheers, DVdm (talk) 19:18, 15 December 2009 (UTC)

E=M?

As it says in the wiki "According to the theory of relativity, mass and energy as commonly understood are two names for the same thing, and one is not changed to the other. Rather, neither one appears without the other." Does that mean E=M? I do know a way that both E=M and E=MC^2 could both be true. If c=1. I also know how that might be true. Perhaps 1 lightyear and a year (the 2 parts of the speed of light) are equal. It is thought that time is a dimension. Distance is a dimension. So they can be equal. But is it? —Preceding unsigned comment added by 98.111.122.55 (talk) 19:01, 9 January 2010 (UTC)

It means all Mass is Energy x The Speed of Light Squared, matter is energy, and energy has mass. This was first famously proven during a solar eclipse, when it was finally observed that light could be bent by gravity. This has profound implications, for example it makes the energy in a unit of matter measurable. It also means that matter can not travel faster than light, an it also means that an enormous amount of energy can be released from a small unit of matter, such as in a nuclear reaction. --67.58.85.57 (talk) 11:01, 20 January 2010 (UTC)

Yes E=M if you use the same units for time and space so that c=1. This is so conventional in high-energy physics, people don't even mention it anymore.Likebox (talk) 03:13, 4 February 2010 (UTC)

What kind of mass and energy?

A new editor has decided that the lead should specify "invariant mass" and put in the edit diff: "m = rest mass, units and units don't need to be explained in the lead - this is general knowledge not limited to this formula." In fact, it is not only not "general knowledge"-- that is wrong. The statement is incomplete. Many physicists have used this formula with relativistic mass, in which case the energy simply becomes the relativistic (total) energy. Problems with the formula only arise when you use one kind of mass with the other kind of energy and your momentum is not zero. This is all explained in the rest of the article. There is some irony in the fact that the same editor has gone down placing "unreferenced section" tags on a number of sections, and these are indeed general knowledge not limited to this formula. Same justification, except this time, right. SBHarris 01:33, 18 February 2010 (UTC)

If you read the lead you will see that units are in fact still discussed, I have just made the wording more succinct. It was only the sentence about unit conversion that I was referring to as general knowledge. I'm not a new editor, I am just new to this article and have just as much right to edit it as anybody else. With regard to the vastly unreferenced sections, I put tags on them because everything on wikipedia needs to be cited by reliable sources. There is no Original research on wikipedia. All content on wikipedia must be cited no matter how much it might be considered to be general knowledge. I urge you to assume good faith and actually read what I have done as I personally perceive it to be an improvement. I will attempt to address the issue of citations in the purely uncited sections at a later date, in the meantime the unreferenced tags should remain. Polyamorph (talk) 07:20, 18 February 2010 (UTC)

P.S. since this is wikipedia we all have the ability to edit. If there is an issue where you think my changes are inaccurate then by all means adjust them accordingly. Polyamorph (talk) 07:26, 18 February 2010 (UTC)

Finally I was only going by what was already written in the lead where the internal energy was discussed. There was no mention of relativistic energy. I have no objection to adding a line to say that E becomes the relativistic energy if m is taken as the relativistic mass. Both cases should be cited anyway. Polyamorph (talk) 08:20, 18 February 2010 (UTC)

Ok, I have clarified that the equation is for a stationary body and added a sentence to say that m becomes relativistic mass and E is the relativistic energy for a moving body. Hopefully you are happy with that now. In physics we have to be specific about what parameters we are using. It was too vague before, I think it is much better now. The technicalities are described in the article so we don't have to go into too much detail in the lead, just summarise the key ideas. I think this article has the potential to be a very good article. It is a very notable topic and deserves to be improved. References are the number one priority. Polyamorph (talk) 12:49, 18 February 2010 (UTC)

Thanks. I wasn't meaning to suggest we have no references. It's just that a {cite} tag can be taken two ways in absense of an edit summary. One way is "True, but let's find a reference" and the other way is "I don't believe this, let's see a reference." Let's all agree that here, the first applies. Most of this stuff is in Taylor and Wheeler's Space-Time Physics or other texts, so it's matter of digging it out.

My use of the templates was not to judge the content but simply to mark it as uncited per wikipedia policy. I'm certain that the content can be cited to a number of generic sources. Each paragraph could be referenced to a particular page in a book for example. I'm also not suggesting the content is original reasearch, only that without citations it could be construed as being so. I don't believe for a minute that someone wrote those sections without consulting any sources. The templates should not be seen as an attack on your work but instead simply a suggestion on how to improve the article, see for example General relativity to see what Physics articles can achieve! Polyamorph (talk) 17:45, 18 February 2010 (UTC)

Request for BODMAS disambiguation.

E = mc^2

Is it: E = m(c^2) aka E = m*c^2

or

E = (mc)^2

The first. If you don't see parenthesis, the rule in algebra is to assume they don't exist (exponentials only apply to the immediately preceeding factor or variable). SBHarris 18:16, 2 March 2010 (UTC)

Confusing notation

Small change, but I'd suggest to replace the various "K.E.", as in

$K.E.={\frac {m_{0}c^{2}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}-m_{0}c^{2},$

with something like this:

$K_{E}={\frac {m_{0}c^{2}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}-m_{0}c^{2},$

I find the first notation really looks too much like a typo for "K.E" (K times E). I'm going to change it. 62.147.27.247 (talk) 21:11, 11 March 2010 (UTC)

Yes, but I think E_K is much better:

$E_{K}={\frac {m_{0}c^{2}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}-m_{0}c^{2},$

Go ahead. DVdm (talk) 21:16, 11 March 2010 (UTC)

You're both totally right and quicker than me: I have just looked up kinetic energy and was about to amend my suggestion with $E_{k}$ indeed. Er, note that they use a lowercase "k" not an uppercase one, thought. Thanks. 62.147.27.247 (talk) 21:20, 11 March 2010 (UTC)

Yes, lowercase is even better. Cheers - DVdm (talk) 22:17, 11 March 2010 (UTC)

I like what you guys did. Much better! CosineKitty (talk) 02:28, 12 March 2010 (UTC)

1905 derivation criticized

The correctness of Einstein's 1905 derivation of E=mc2 was criticized by Max Planck (1907), and also by Herbert Ives (1952), and also in a recent book (2008) by Hans Ohanian. http://discovermagazine.com/2008/sep/01-einstein.s-23-biggest-mistakes

I dunno if "Discover Magazine" is a reliable source for this. They make basic phyics mistakes all the time. Planck pointed out that ΔE=Δmc^2 should also apply to chemical reactions that liberate heat (I think in 1908) so he couldn't have had a terribly hard time with idea. SBHarris 20:48, 25 December 2009 (UTC)

Planck had no problem with E=mc2, as Poincaré had already published the formula in 1900. Planck however did not consider Einstein's derivation to be correct, neither do Ives nor Ohanian consider Einstein's derivation to be correct. In fact, it is impossible to prove E=mc2 for real mass, no one has ever rigourously done it. The formula can only be rigourously proved for the effective mass of radiation, as Poincaré had done. Einstein tried all his life to prove the formula for real mass but never did, as Ohanian writes in his book, all of Einstein's subsequent derivations of E=mc2 were false.173.169.90.98 (talk) 00:59, 26 December 2009 (UTC)

Using Newtonian kinematics plus the idea that the momentum of a photon (or even beam of light) of energy E, is E/c (which follows from Maxwell) than you can prove that an object which emits a beam of light of energy E loses mass with an amount = E/c^2. Presumably, an object that kept emitting light would lose all of its mass in this fashion and convert it's entire mass into light energy = Mc^2, where M is the initial mass. You can show all this without even any calculus.

http://en.wikipedia.org/wiki/Talk:Mass-energy_equivalence/Archive1#A_derivation_of_.CE.94m_.3D_E.2Fc.5E2_without_calculus

SBHarris 23:04, 9 January 2010 (UTC)

Einstein's argument is reproduced here, and is self-evidently correct. Planck and all those others were full of it.Likebox (talk) 03:11, 4 February 2010 (UTC)

The history section of this article makes it clear, based on painstaking reading of the original German documents, that Poincare did not understand Mass-Energy equivalence in 1905. He claimed that radiation carried momentum, which was well known already in the late 19th century. There have been decades of accusations about the accuracy of Einstein's argument--- but it is presented here, and anyone can check that it is correct in a few minutes. Frankly, it's embarassing that these claims still get trotted out today.Likebox (talk) 03:15, 4 February 2010 (UTC)

Ohanian's book is clear: E=mc2 cannot be rigorously derived from relativity - Einstein tried all his life and never could do it - read Ohanian's book. Poincaré correctly and rigorously derived e=mc2, from Maxwell's equations which is the only way it can be done. 173.169.90.98 (talk) 21:53, 21 April 2010 (UTC)

From another book by Ohanian (on electromagnetism), I get the idea that his point is merely that the traditional derivations of E = m c^2 depends on a notion of conservation of energy and momentum. The choice of that you call energy and momentum is then an assumption and the derivation depends on that. He says that a correct derivation requires techiques of QFT. I think he means (in that introductory EM book) that you need to apply Noether's theorem to space-time translations to find the conserved four-momentum. So, we can easily derive the expresiions for the conserved four-momentum and then we're done as it is then a trivial matter to show that mass is the same as rest-energy. Count Iblis (talk) 23:45, 21 April 2010 (UTC)

Can you cite a source for where that was ever done as you are claiming ? Perhaps you refer to Ohanian's claim that Von Laue had once made a little known derivation of e=mc2. Von Laue might have just been showing that e=mc2 was not inconsistent with relativity, without actually proving e=mc2. Note that Planck's 1907 derivation of e=mc2 used electromagnetic theory as did Poincaré in 1900. Poincaré correctly derived e=mc2 in 1900, same as Planck later did in 1907. Einstein never in his life ever correctly derived e=mc2 in a rigorous manner. 173.169.90.98 (talk) 03:21, 22 April 2010 (UTC)

Ohanian in his book "Classical Electrodynamics" actually derives Maxwell's equations from Coulomb's law and Lorentz invariance. So, deriving E = m c^2 from Maxwell's equations would be rather strange according to that logic. What he does in that book is to consider a glancing collision and assume that there exists a conserved momentum. He is ten led to the xistence fo a conserved four-vector, the zeroth component of this is then identified with energy and the valure of it in the rest frame is identified with the mass.

So, I'm wondering if he also objects to using Maxwell's equations (i.e. the formula for momentum in electromagnetic radiation) to derive E = m c^2. Count Iblis (talk) 15:55, 22 April 2010 (UTC)

That is the problem, 'identifying' a term as mass is not the same as rigorously proving it. Whenever e=mc2 is shown 'derived' from relativity it is always simply an interpreted 'identification' and not a rigorous derivation. E=mc2 cannot be rigorously derived from relativity, no one can do that. The only theoretically rigorous derivation of e=mc2 is from Maxwell's equations as done by Poincaré in 1900. 173.169.90.98 (talk) 21:32, 22 April 2010 (UTC)

Terajoules?

In the section: Mass–energy_equivalence#Practical_examples there is a mention that one gram will result in 89.8 terajoules. Is this not incorrect? Should this not be 89.8 Pentajoules? --Ceaser (talk) 03:05, 26 April 2010 (UTC)

One kilogram would correspond to 89.9 petajoules (no "n"). Remember that the unit of mass is the kilogram, not the gram. DVdm (talk) 07:52, 26 April 2010 (UTC)

Section explaining some common misrepresentations of the Mass-energy equivalence

It would be nice to have a section that treats some well-known abuses of the E=mc2 equation. For instance, I have heard that the formula says that "no body can travel at the speed of light or it would disintegrate", or things like that. I guess that there are many silly things that are said regarding this equation. -- Annonimous -- —Preceding unsigned comment added by 96.231.120.36 (talk) 06:12, 9 May 2010 (UTC)

Indeed, many silly things are said about it. The problem is of course that we need a reliable source backing up that such and such is (1) abuse, and (2) that it is also well-known, aka sufficiently notable to be included here. Tricky... DVdm (talk) 08:55, 9 May 2010 (UTC)

Photons and gravatons have relativistic mass?

Really? Is this really the majority belief on this subject?

"In relativity, all energy moving along with a body adds up to the total energy, which is exactly proportional to the relativistic mass."

"Even a single photon, graviton, or neutrino traveling in empty space has a relativistic mass, which is its energy divided by c²."

129.139.1.68 (talk) 18:16, 13 May 2010 (UTC)

Yes, it's the majority belief on the subject. A photon has relativistic mass, but not rest mass; they are different things. The relativistic mass is given by E/c^2, hv/c^2, or Pc. Relativistic mass is just another name for total energy, and is frame-dependent. I agree that there's no point in meantioning "gravitons" in this article. SBHarris 22:25, 17 October 2010 (UTC)

Okay, and let's point out early that mass is never converted to energy, and vice versa

One of the things I'd hoped this article would do, even starting with the lede, is to clear up the misconception about E=mc², which may be at the same time the most famous equation in the world, and the most misunderstood. While it is true that the poorly-defined entity "matter" can be converted into the poorly defined "energy" (pairs of fermions into guage bosons, or virtual particle fields into real particles, or kinetic energy into real or virtual particles, it is NOT true that mass can be converted to energy (or vice versa). Most people think E=mc² means mass-energy conversion (which never happens), and aren't aware of the definitional problems with "matter" energy conversion. This article is the place to sort that out. It's the article about E=mc², after all, and if I were writing the lede/lead, I'd point out somewhere that this equation does not mean what 99% of laymen (and secondary school teachers and even some scientists) will tell you that it means! That's important. SBHarris 17:20, 18 February 2010 (UTC)

All we need to do for this is to ensure that the article states clearly and concisely the correct meaning of the equation. We don't need to discuss the misconception in the article, we just make sure that the article is very clear about the correct interpretation. Polyamorph (talk) 17:59, 18 February 2010 (UTC)

But this may not be enough. Do you not think that encyclopedias, as teaching tools, are obligated to point out enduring myths, also? For example, see Independence Day (United States) where a paragraph points out the enduring myth that July 4 is the day Congress signed the declaration. Could that not simply be omitted, since the correct info is given in the rest of the article? Thus (one could argue) allowing the careful reader to INFER that the other is actually a myth? So we leave the myth-debunking as a exercise and puzzle? SBHarris 18:13, 18 February 2010 (UTC)

An encyclopedia documents the current state of human knowledge. You're correct that it is a teaching tool but we are not the teachers, people need to educate themselves based on the (hopefully) accurate information that we provide. I don't think we can assume that people are being taught incorrectly by professional teachers and try and compensate for this. I think instead we have to start at the beginning and assume that the reader has no prior knowledge of the subject. But I would agree that if the confusion between mass and matter is well documented in reliable sources as a common misconception then we could try to clarify the point but I think this can be done without dwelling on the issue too much. It is my opinion that this isn't necessary but I wouldn't object if others thought it was necessary. For example, the article could contain a sentence similar to "...matter (not mass as commonly beleived, see below) is converted into energy", and then could provide a short summary about how it is matter and not mass that is converted with a citation to a reliable source that discusses the misconception. Polyamorph (talk) 19:46, 18 February 2010 (UTC)

I'm skeptical about your distinction between mass and matter in E=mc². I'm pretty sure m literally means mass, whether measured as rest mass or relativistic mass. Einstein's theory predicts that even if you compress a spring, the extra potential energy increases the mass by the exact amount predicted by that formula. But it doesn't add any matter to the spring at all: there are just as many protons, neutrons, and electrons in the relaxed spring as in the compressed spring. CosineKitty (talk) 21:29, 18 February 2010 (UTC)

No argument: m here literally DOES mean "mass." Though Einstein almost always meant rest mass when he wrote "m", this equation also works for "relativistic mass" (γm), in which case the output is relativistic energy. You just can't mix the two kinds of masses and energies when momentum is non-zero (when it is zero they're all the same). The equation is popularly thought to apply to matter/energy conversions, however, as when kinetic energy of a particle in an accelerator is turned into the matter of new particles (a particle pair, say). BUT that's not what this equation is meant to describe. It does not describe transformations, per se. The equation has no way of telling what is, or isn't, "matter." Matter is poorly defined, and its various definitions are outside of relativity and what this equation can do. Matter (electrons, say) and non-matter (like kinetic or potential energy) both have "mass". This mass stays the same when one is converted to the other. The spring is a good example: when you compress it, adding potential, do you add "matter" to it? Who knows? You certainly do not add real particles, but it does have more mass, and one of the definitions of matter is what which has mass and takes up space. I dunno the answer-- it's not a really good question, but more a matter of semantics. But the extra energy you added has a mass (whether it is considered now part of the spring matter or not), and ΔE= Δmc² tells you how much extra mass it has for the energy you added, since that energy HAS mass (your muscles LOST that much mass-- you just transferred mass from here to there). Mass cannot be transformed-- only moved. Matter can be transformed, but it's hard to define. See matter for something on this controversy. See mass in special relativity for the two definitions of mass. SBHarris 23:11, 18 February 2010 (UTC)

I'm not an expert and what I am about to write is pure speculation...but...I was under the impression that the compression of a spring only goes to increase the energy of the spring, i.e. changes in the atomic bonding, electronic structure, density and volume changes etc. in the spring itself. But why would the mass change? Do you have a reliable source that backs up this assertion because I'm not convinced it is true. I think the point about matter-energy conversion was to do with e.g. anti-matter anihilation. In this case there is a complete conversion of the matter and anti-matter particles into pure energy. In this case it is the particles themselves that are transformed into energy, the particles are annihilated. That is my interpretation anyway, it might be complete BS. Of course, using nuclear fission as an example instead of a spring, there is a release of energy due to the difference between the sum of the individual masses of the nucleons and the total mass of the nucleus itself. In this case the energy E released is equal to the mass deficit m multiplied by c². In this case I can't see where any matter is converted into energy, it is purely a mass deficit that has no physical manifestation, so CosineKitty might have a point? Polyamorph (talk) 06:58, 19 February 2010 (UTC)

Hi Jdrewitt. I found something in one of my college textbooks: Modern Physics by Paul A. Tipler (1978) ISBN 0-87901-088-6. On page 31, it says: "Whenever additional energy ΔE in any form is stored in an object, the rest mass of the object is increased by ΔE/c²." It goes on to give an example of two masses colliding into a spring, compressing it. In the thought experiment, the spring has a hook that locks it in the compressed state after the masses come to rest. It says that the total rest mass of the resulting system has increased by E_k/c², where E_k is the total kinetic energy the two masses had before the collision. Tipler gives a derivation from first principles on page 32. (Note: I found the fourth edition of this book has this stuff on page 87, which can be seen online here.)

However, to play devil's advocate, it makes me wonder about where the mass goes when energy is converted into electromagnetic radiation (photons). They are supposed to be massless, though they do carry positive momentum. (This isn't brain surgery; it's even harder, ha ha!) CosineKitty (talk) 12:02, 19 February 2010 (UTC)

Ok you've convinced me about the increase of the restmass of the spring :) Tipler's an amazing introductory textbook for physics. Polyamorph (talk) 13:26, 19 February 2010 (UTC)

Yes, Tipler is correct. I can also explain what happens when some of the energy is converted to "massless" photons. Individual single photons are massless, but when added to systems, they add invariant mass. The reason is that whenever you have a photon PLUS something else, you can always find a reference frame where the total momentum is zero, and in that frame, the photon energy adds to the system invariant mass, just as though the photon itself had a rest mass. In these circumstances, you can "weigh" photons and get a meaningful answer (otherwise, with a single photon, the mass is frame-dependent and can be anything you like). So the energy of photons bouncing around in a box adds to a box's weight, just as the kinetic energies of particles in it does (this is very beautiful). It's all a consequence of total energy, invariant mass, and system "rest" mass all being the same in the COM frame.

Not quite so intuitive, but still the same principle, is the fact that two photons considered as a system, have a rest mass (invariant mass) so long as they're not traveling in the same direction. In that case, you find the frame where the photons are traveling exactly away from each other, and with the same energy (you can always do this), and in that COM frame their momenta cancel, and their mass (the invariant mass) is then just their combined energy (in this frame)/c^2. So one photon has no (rest or invariant) mass, but a pair of photons DO have a rest or invariant mass! For one photon, the mass is relativistic mass and thus totally frame-dependent, but for a pair, there's a minimum mass, which no choice of frame can remove. That's the invariant mass. It might as well be a rest mass.

This makes things tidy when an electron and positron annihilate-- the mass of the gamma pair which results is just the same as the mass of the two particles that gave rise to them, so mass is conserved. This happens also when an uncharged pion disintigrates into two photons.

You may wonder what would happen if a massive particle gave rise to just ONE photon, which has no rest mass, and the answer is, that it can't happen. Conservation of momentum forbids it, since a photon already has the minimum momentum for its energy, so the extra momentum has nowhere to go if a massive particle just gives rise to a single photon. This guarantees that you always have a 2-particle system to give you an "invariant mass" even when just one of the particles is a photon. The extra particle absorbs the extra momentum when a photon is created from some energy (say kinetic energy of a massive particle). An example is when one photon is produced by Bremsstrahlung of an electron interacting with a nucleus as in an X-ray machine-- the target nucleus absorbs the extra momentum, and also acts as the second particle in a 2-particle system, so that system mass is conserved thoughout the whole process, even when some electron kinetic energy is converted to the energy of a single photon. SBHarris 19:22, 19 February 2010 (UTC)

You want to point out early that mass is never converted to energy, and then go on to say that mass is converted in other parts of the article. —Preceding unsigned comment added by 70.238.158.11 (talk) 18:52, 2 August 2010 (UTC)

We say it in the very next paragraph in the lede. Mass cannot be converted to energy, but matter can be, and vice versa. That's using the "lepton" definition of matter, and the standard definition of energy, including kinetic energy, light energy, and so on. SBHarris 07:58, 3 August 2010 (UTC)

I'm sorry, I should have been more specific. In the "Efficiency" section, it says: "In theory, it should be possible to convert all of the mass in matter into heat and light (with the same mass), but none of the theoretically known methods are practical. One way to convert all rest-mass into usable energy is to annihilate matter with antimatter." And later: "Since most of the mass of ordinary objects resides in protons and neutrons, in order to convert all the mass in ordinary matter to useful energy, the protons and neutrons must be converted to lighter particles." Also: "This process would be an efficient mass–energy conversion at ordinary temperatures...". And finally: "A third known method of total mass–energy conversion is using gravity, specifically black holes." At first glance (like if a layman such as myself is reading this) it appears to say that you can convert "all the mass in matter" into "heat and light" (what I would call energy), or convert "rest-mass" or "mass in ordinary matter" into "usable energy". Admittedly, the parenthetical note in paragraph two, "with the same mass", helps to clear up that mass is liberated with/as energy. However, the last two examples given clearly state "efficient mass-energy conversion" and "total mass-energy conversion". A quick read of this text may lead, I believe, to the incorrect conclusion that mass is converted to energy. It may be better, for example, if the second paragraph in the Efficiency section started by saying something like: "In theory, it should be possible to liberate all of the mass-energy from matter in the form of heat and light. One way to accomplish this is to annihilate matter with antimatter". Or perhaps the text should read "efficient/total matter-energy conversion" instead of "efficient/total mass-energy conversion". Maybe I am making too big a deal of this, but I was a little confused when I read it the first time. —Preceding unsigned comment added by 70.238.158.11 (talk) 04:08, 5 August 2010 (UTC)

This seems to be endlessly confusing. Matter + antimatter can be converted to energy, as when proton and electron annihilate, so yes, matter and be converted to energy and vice versa. BUT, the energy of the photons or heat made when antimatter and matter annihilate still retains its mass. The SYSTEM of two photons from annihilation of an electron and a positron has the SAME mass as the electron and positron. Individual photons have no mass, but systems of them DO have mass. So mass cannot be destroyed or converted or got rid of; it's always there. It's conserved right along with energy. As the lede says, don't confuse matter with mass. When matter changes to energy and vice versa, the mass of the system stays the same, throughout the process.

I've had to go back to the efficiency section and rewrite it so that it never seems to imply that mass is made to disappear. Matter, yes; mass no. All that happens to mass is that it's moved, or appears in more active forms of movable energy. In nuclear bombs (both fission and fusion) no particles or matter is destroyed, but mass in the unexploded bomb first turns into relativistic mass of the kinetic energy of the fission fragments (and some also in the photons in the sytem, but it's only 2-3% of the released fission energy-- see the energetics section of nuclear fission), and then later this kinetic energy of hot fission fragments is converted to the mass of kinetic energy of cooler atoms (the mass of "thermal energy"). But no particles are really destroyed in a nuclear bomb (at least in the first instant), the way they would be in an antimatter bomb. And just because the kinetic energy is no longer relativistic (resulting in relatively large fractions of realtivistic kinetic energy mass increase from the fast fission fragments) doesn't mean it's not still there, as mass. It's just the mass of the heat of slower particles, and is eventually partitioned into the various types of energy that absorb heat capacity

If you want a metaphor for fission, imagine two baseballs floating in space connected by a compressed spring. We know that the compression of the spring increases its mass (the potential energy of the spring shows up as a more massive spring). When the spring is allowed to push the baseballs away from each other, what happens to the mass of this entire system? Nothing! Mass is conserved. The spring has less mass, but the two baseballs now have more. The mass of their kinetic energy is exactly the mass missing from the spring. The same thing happens in fission, just more energetically. SBHarris 21:39, 5 August 2010 (UTC)

Thanks Sbharris. I think I finally understand all of this. You can't convert mass to energy if they are equal. If E=m, you can't decrease (lose) m and expect E to increase because, of course, they would no longer be equal. No matter which metaphors we use to explain all of this, you can always fall back on E=m and remember that energy is mass. It's almost painfully simple. I just need to remember that mass is not just some quality that matter has- that can be traded for some quantity of energy (although I can trade matter for energy). Rather, mass is the energy that already exists in that matter. Mass-energy can move into and out of matter, but always remains conserved. So I guess mass-energy can exist freely (traveling at the speed of light) or bound up in the form of matter (traveling at any speed less than c). Also, the Efficiency section reads more clearly now. I didn't want to make more work for you, but I really thought it needed to be fixed. Anyways, I appreciate all of your help.

You've got it. Wherever mass or energy is, the other is also. It's matter (whatever "matter" is) that comes in and out of existence. Don't be too worried, because I've seen professional physicists mess this point up on popular astronomy programs, on NOVA. They also forgot that matter is not the same thing as mass, and ended up saying very confusing things. And there are a whole host of secondary science books that have it wrong, also. You really need to get into college books on special relativity before it's all sorted out, and becomes clear. And then you realize that even most scientists don't quite understand it! But now, at least, you do. SBHarris 21:37, 6 August 2010 (UTC)

Note that (11.37) asserts that the energy e of a particle of mass m has the value mc 2 when the particle is at rest. This is sometimes incorrectly cited to be the meaning of E = Mc 2. The true meaning is to be found in inelastic collisions, as the expression (11.36) of the necessity for a change in mass to compensate exactly for any change in kinetic energy: if kinetic energy is gained in the collision, total mass must go down; if kinetic energy is lost, total mass must go up. Secondly, I see that Wikipedia is a place for promoting the myths rather than common sense and true knowledge. It is much clearer to see in the political matters where capitalists promote their agenda through the well-payed intellectuals and, for the sake of "neutrality", Wikipedia (especially russian) prohibits any sources besides these "respected (and liberal) sources". --Javalenok (talk) 23:33, 26 December 2010 (UTC)

While I do not disagree with Mermin's math, his example is too complicated to use here. E=mc^2 has whatever meaning it has when you specify what type of E and m you're talking about, and if you use it correctly with these. In zero-momentum systems, these are all the same, so E=mc^2 is always true so long as the system is closed. It's true of particles at rest, like the neutral pion, where m is the rest mass of the particle. If it breaks up into two photons, the mass of the system (the invariant mass) is the same as the mass of the initial particle at rest. SBHarris 00:15, 27 December 2010 (UTC)

What the heck happened to the lead?

I know it's been a while since I visited this article, and even when I worked on it frequently the lead was always a point of contention and was in a state of flux, but the present lead is just unacceptable. "We call"? "Energy inside"? Somebody find something better in the history and do some CPR. Here's the lead as it now stands: "In physics, mass–energy equivalence is the concept that the mass[1] of a body is a measure of its energy content. What we ordinarily call the mass of a body is always equal to the total energy inside, up to a factor that changes the units." Robert K S (talk) 16:02, 12 September 2009 (UTC)

How about "That which one denotes by the ponderance of a body, vis-a-vis said body's coefficient of inertia in response to any indeterminate extent force upon said body, is tantamount to the additive conjunction of the energies hitherto placed within said body?" Seriously, what's wrong with simple language?Likebox (talk) 00:09, 18 September 2009 (UTC)

It would benefit if the article wasn't almost singularly fixated on the semantics of closed systems. For all intents and purposes, when people are talking about nuclear bombs and E=mc^2 they're referring to the mass of the system (being the atoms of the bomb) being lost. This is still true, once the dust settles. The resulting fissile or fused material will weigh less, as that mass/energy has been transferred as kinetic energy and "given" to something outside the system. Thus, the same amount of matter weighs less. Fixating on the vault analogy too much can be distracting, since practicality is still important here. —Preceding unsigned comment added by 24.16.68.248 (talk) 05:29, 7 January 2011 (UTC)

I have a similar opinion to Robert. Likebox, you seem to have more time than the rest of us to put your viewpoint on this article. You answer every point with a long discussion which I, and I suspect others, simply don't have the time to engage in (look back on these discussion pages and you will see what I mean). I work in a physics department and teach relativity. My own research is in astrophysics but I have consulted colleagues who do research in high-energy physics. I have not found a single one who agrees with statements like "mass and energy are the same thing" and "the mass of a body is a measure of its energy content" It seems to me that you have a minority point of view, with good intentions I know. Timb66 (talk) 23:36, 20 September 2009 (UTC)

If what you are saying is correct, you have talked to incompetent colleagues. Thankfully, they are not yet in the majority. This article serves to educate them. I am not confused on this issue, and the statements that you are objecting to are quoted directly from Einstein's paper.

The statement "E=mc2" is a statement that the inertia of a box, what you feel as its resistance to changes in velocity, is equal to the energy inside the box. When the energy goes up, the inertia goes up, and when the energy goes down the inertia goes down. That's the content of Einstein's paper, and that is what the lead says. There is absolutely no dispute about this by any knowledgable physicists.

If the body remains at rest throughout the energy transfer processes, this is an unambiguous statement. If the body is moving with a large speed, then you have to debate whether to include the kinetic energy, or to measure energy in the rest frame. This is the difference between "relativistic mass" (which is just the same as the energy), and "rest mass" which is the total energy in the rest frame of the system.

When you look at a quantum of a free quantum field, like that of an electron, the smallest nonzero eigenvalue of the Hamiltonian is the mass of the particle. The Hamiltonian is the energy of the system, the mass of the particle is the value of this energy (when the particle is at rest). When the particle is moving quickly, there is then the distinction between rest mass (or mass) and relativistic mass (or energy).

The reason I answer with a long discussion is because I am annoyed that there are so many people that are ignorant about this subject. Each person I discuss with can be made to understand, and then this person can educate others who come to this page. It is not for my own personal benefit, since I already understand it.Likebox (talk) 17:43, 21 September 2009 (UTC)

Also, please do not attribute to Robert your own idea that the lead is inaccurate. Robert was objecting only to the informal tone.Likebox (talk) 17:47, 21 September 2009 (UTC)

Right. "We call" is academic-conversational, not encyclopedic. "Inside" has no antecedent basis (inside what?), and so needs to be reworked. It is not at all clear what is meant by "up to a factor that changes the units". Let's get back to some older, clearer version of the lead. Robert K S (talk) 07:29, 25 September 2009 (UTC)

This is written for a person who doesn't know this, which is like a high school person. And, come on, you really don't know what "The energy inside" means?Likebox (talk) 05:18, 26 September 2009 (UTC)

"Up to a factor that changes the units" is surely physics-insider-speak of the worst kind, though. SBHarris 06:20, 26 September 2009 (UTC)

(deindent) The reason I believe it must be stated this way is because it must not give space to incompetent people who equivocate on the meaning of this identity. If the lead is not pissing ignorant people off, it's not any good.

This page has been visited many times by people who misunderstand mass/energy equivalence, and think of it as "conversion of mass to energy". This misunderstanding is common enough and persuasive enough that you need to hit it over the head with a hammer of obviousness. That's why I prefer the colloquial lead.

On the other hand, "up to a factor that changes the units" is no good. I'll change that to something more colloquial.Likebox (talk) 16:15, 26 September 2009 (UTC)

Why do you keep going on about "ignorant people"? This is an article about a basic concept in physics. It is going to be somewhat technical, but there is no need to make it more technical or long-winded than absolutely necessary, and especially the WP:LEAD should be as straightforward as possible. "Ignorance" doesn't enter into it.

It is true that the c squared is a red herring, as it is just a constant. Imho, the proper way of putting this is that in natural units, where c=1, the equation reads E=m, while in SI units, a rest mass of 1 kg amounts to about 90 PJ (the energy released by a 20 megaton bomb). --dab (𒁳) 15:24, 8 October 2009 (UTC)

I was just referring to the people who misunderstand the formula as saying that mass can be converted into energy, so that mass disappears and energy appears at the same moment. This false idea says that an atom bomb suddenly weighs less at the moment that it produces heat, and that the heat that is produced does not have any weight. This is the ignorant position. It is difficult for people who understand what is going on to realize that there are people who misunderstand things in this way, because it is so difficult to remember what it is like before you understood what was going on. In my experience, I was never told the correct version, always the incorrect one, by anyone who tried to explain the formula to me.

For this reason, I want to avoid technical language in the lead: to speak as clearly as possible. You have to say "heat weighs", "chemical energy weighs", "nuclear energy weighs", and even "potential energy weighs" (except that in this case it only weighs in the combined system that includes the fields responsible for the potential energy.Likebox (talk) 19:25, 8 October 2009 (UTC)

C is not the speed of light

In my high-school physics class it was repeatedly emphasised that "c" in this equation is not the speed of light, but a dimensionless constant that is numerically equal to the speed of light. If mass and energy are equivalent, one can if one wishes measure mass in joules and energy in kilograms. If c has dimensions, then kilograms and joules are not alternate measures for the same thing, and mass and energy are not equivalent. —Preceding unsigned comment added by 90.192.141.171 (talk) 19:24, 16 January 2011 (UTC)

This is not correct; your textbook may have said this as an oversimplification of the concept of consistent units. VQuakr (talk) 20:28, 16 January 2011 (UTC)

Then what you learned in your class was wrong, because kilograms and joules are not measures of the same thing; the former it a measure of mass, the other of energy. Energy is expressed in joules (1 J = 1 kg·m²/s²), mass in kilograms (kg). If you check what a joule is in base SI units, you will see they have the units of [mass]·[speed]², which is exactly what you would expect from E = mc². Measuring "mass in joules / energy in kilograms" is very unrigorous, at best an abuse of language. Saying "mass and energy are equivalent" is only right if you are working in natural units, or understand that c² is involved. Headbomb {talk / contribs / physics / books} 21:02, 16 January 2011 (UTC)

More tampering in the lede

As you will read in the section following the lede, mass is conserved in (special) relativity (for general relativity, we have to decide whether the gravitational field, and warping of space, is a net negative energy). Energy is also simply conserved in special relativity. Mass+energy is also conserved, therefore, but that is trivial. It's enough to say that the mass of a system cannot be changed, or its energy, either. Period. End.

ALL of the suggestings that "mass" can be changed to "energy" really don't mean "mass" they mean "matter" (fundamental massive particles, i.e., massive leptons and a few other compound hadrons like the neutral pion). These particles can be converted to photons, which individually have no mass, but no such system can be converted to one INDIVIDUAL photon. The photons are always created in pairs, and that pair has a mass. One cannot simply choose to create a pair of photons and then look at only one of them, because now one has broken the isolation of the system. Nor are system "masses" (such as the photons) simply additive in special relativity, because the systems may be traveling at some relative velocity to each other, and this must be corrected for before you add them. With photons you can't do that, since there's no way to ever look at each photon in its rest frame.

Anyway, annihilation is a fine way to demonstate intraconversion of matter and energy, if by "matter" you mean electrons + positrons, and by "energy," you mean photons. But the electrons and protons have a rest energy, as well as a mass, and their annihilation products (taken together) always have a mass also (as well as an energy of course. And so, neither mass nor energy changes during the annhilation process.

As is noted in the article (also see mass in special relativity, if you put a nuclear weapon in a super-strong box and put it on a scale and detonated it, the needle wouldn't budge. Now uncover a super-strong transparent window and let out some heat or light, and now the box will cool and its mass will drop. However, the system is no longer closed, and the heat and light you let out, now carries the mass that escapes. Whatever absorbs the heat and light, will gain in mass by exactly the amount of mass that the box looses. Mass goes "here to there," but isn't destroyed.

Understand this point, and you understand nearly all of E=mc^2. The only other tricky part is that E=mc^2 is only ALWAYS true in the COM frame, so make sure you stay there. In other frames where the system has a net momentum, if you insist that E is total energy, and m is invariant mass, THEN you must correct for the net momentum of the system in the frame you're in, and that merely makes the equation uglier. SBHarris 17:51, 3 March 2011 (UTC)

But our understanding of the atomic fusion matter accumulation process is that all the individual particles being accumulated have an amount of rest mass plus an amount "free energy" equivalent mass. And the problem is to accumulate the restmasses into a stable larger accumulated rest mass amount in spite of the tendency the free energy to resist this effort by creating unstable physical situations. So now mother nature needs a way to get rid of some of this excess free energy mass. So she creates an entity that can carry it away from the situation and we're telling her how it has to function. First we don't want to lose any of the accumulated rest mass, so she can't use that, and then she has to obey our laws of motion and only carry off the significant offending motion energy without disturbing the rest of the system. So we have the E = mc^2 formula, which I think should only be applied to the "free energy" mass, and a rather unreasonable restriction on mother nature as to how she wants to go about creating the atom.WFPM (talk) 15:20, 4 April 2011 (UTC) The previous identity is who my computer thinks it is if I tarry too long in composing my contribution

Well, you can think whatever you like, but that's not how it works! See the article on nuclear fission for some detail. All energy has mass, whether it's potential energy (as in a large nucleus) or kinetic energy (when the nucleus is fissioned). The total mass never changes in such a process, although it does change form. SBHarris 00:54, 4 April 2011 (UTC)

What I am trying to get at is that since we know that in reactions the smallest entities get the most energy, it is perfectly logical that the smallest entity would get the most energy. And why do we then have to go off the deep end by assuming that there is an entity with no mass and just energy? And in the course of accumulating the atomic matter the result is for the smallest entities to accumulate the most energy, and a reasonable human being would be willing to give up an amount of small entity matter in order to get rid of the contained energy, which I think is what happens in the sun. But no exit of rest mass!!!! That sounds like a mathematical gimmick.WFPM (talk) 15:33, 4 April 2011 (UTC) It is to be noted that the lost free energy value related to any accumulated mass is proportional to -GM/r, so we really don't ever know what the rest mass is except in a specific situation. In the CRC handbook, it is shown by the incremental neutron mass values that the rest mass of a neutron is lass than 1, and for 10Ne22 it is shown as 0.997539. So nobody knows what the rest mass of a neutron really is.WFPM (talk) 18:46, 4 April 2011 (UTC)

A photon adds rest mass to a system (for example a photon bouncing around inside a box on a scale) without itself HAVING rest mass. There's really no difference between this and the kinetic energy of gas molecules adding mass to a system (a box of gas on a scale) even though the kinetic energy of each molecule has no effect on ITS OWN rest mass. See the point? For a box of gas, the rest mass of the system due to molecular motion is never seen as rest mass of any individual molecule. Some of the rest mass OF THE SYSTEM is present without being attached to the rest mass of any given particle IN THE SYSTEM. You cannot sum rest masses of particles, each in some frame, and come up with a system rest mass. Neither mass nor energy (nor momentum, for that matter) are additive, or conserved, if you're allowed to switch frames at will, like that.

As for the rest mass of neutrons, it's defined for FREE NEUTRONS. When the neutron is part of a system it's not really permissable to assign a part of the system's total mass to any particular particle within it, even if the contribution is less than the free particle's rest mass (as in the case of bound neutrons) rather than more than the particle's rest mass (as in the case for gas molecules). Both of these approaches neglect to consider energy: positive (kinetic) energy in the case of the hot gas, and negative (potential) energy in the case of bound neutrons in a nucleus. SBHarris 19:41, 4 April 2011 (UTC)

Well alright. But I have a saying that chemistry is about what things are, and physics is about what things do. And if I have to pick out a choice of basic things, I'll pick things. Then they do things and have energy. And they can fool you into thinking that they are more than they are. And to rationalize all this we hire mathematicians, who are willing to prove that an infinitely long space can have a finite area. So if you believe in a neutron it is not important as to what it really is, because they will tell you what it does in their equations. And you're saying that a specific amount of warm gas has more mass than a cold gas, because you added energy which has mass to it. And I guess that I wont argue about it until you go on to say that there is no such thing as rest mass and that everything is just more or less condensed energy.WFPM (talk) 21:09, 4 April 2011 (UTC)

"Rest mass" is what you measure on a scale. All energy trapped in a system (where it has zero-total momentum) add rest mass to the system. Is this energy "condensed" or not? Who is to say? Looking at the system from the "outside" who are you to say what's going on inside it? That's as true of a box of hot gas as it is for (say) a proton. And yes, when antielectron (positron) annihilates electron a lot of "condensed energy" gets turned into photons. But the mass of the system remains the same, since two photons traveling in opposite directions have rest mass as a system (invariant mass). The equations of general relativity don't have any solution for mass-energy appearing or disappearing, so you can imagine that when electrons and positrons annihilate, their gravitational field doesn't just disappear.

Finally, chemistry is a branch of physics (chemists only get upset when you say it's JUST a branch of physics). Like all sciences, chemistry makes predictions. As Alan Turing noted a long time ago, all natural sciences are divided between boundary conditions (what IS) and the differential equations that carry that system forward in time (what things DO). As Lord Rutherford says, the first part is stamp-collecting (naming and categorizing and describing), and the second part is the job of physics (it is what we call physical law). SBHarris 21:22, 4 April 2011 (UTC)

My Kaplan on page 124 has a 1 page formulation of the concept that the conversion value for incremental mass to energy is E = Mc^2. But it isn't categorical about there not being a rest mass. And if you didn't have a concept of a mass with a unit increment value, I don't see how you could have ever started the conversion analysis in the first place. And I think the chemists are too arbitrary about what things are, and thus combine with the conservatism of encyclopedic discussion to hinder conceptual development. I once asked a senator how things ever get done in washington, and his answer was "we just muddle along".WFPM (talk) 01:02, 5 April 2011 (UTC)

The Kaplan described conversion actually is a "momentum to energy" conversion where an incremental amount of Mv is converted to incremental Mc^2. It takes advantage of the mathematics of the differential of a product (delta Mv). However, if the M value in the situation were to be zero, I cant see how it would be a correct derivation.WFPM (talk) 10:15, 7 April 2011 (UTC)

I wish I could get your interests in "boundary conditions" to include the structure of the EE6C12 atom. As far as I know the concept of the structure hasn't advanced much beyond that shown in the May, 1985 National Geographics article Qv.WFPM (talk) 10:26, 7 April 2011 (UTC) Also see graphic images of nuclides in CNO cycle.WFPM (talk) 20:17, 8 April 2011 (UTC)

Contradiction in the introduction

3rd paragraph, 2nd and 5th sentences contradict: "Mass–energy equivalence also means that mass conservation becomes a restatement, or requirement, of the law of energy conservation...Mass and energy are both conserved separately in special relativity, and neither may be created or destroyed." The first claims the conservation of energy is a restatement of the conservation of mass. The second claims the conservation of energy is separate from the conservation of mass. 82.7.88.93 (talk) 11:12, 18 May 2011 (UTC)Ali

I agree hast this has to be cleared up. The "conservation of mass" here means conservation of rest mass, and that follows from conservation of energy and conservation of momentum. This means that the first statement is not correct. Count Iblis (talk) 14:36, 18 May 2011 (UTC)

When the conservation of mass refers to "relativistic mass," then E=mc^2 is defined as "true" in all systems (not only the special system where total momentum is zero), which is the same as saying that m(rel) = E(rel)/c^2. Then, that statement IS true by defintion of what we mean by relativistic mass. So conservation of "relativistic mass" is a restatement of the conservation of total energy. However, of course, many people do not like the idea of relativistic mass. One argument is that it doesn't say anything that total energy doesn't say already.

Conservation of rest mass (invariant mass in systems) is a separate thing, and follows (as noted) from BOTH the conservaton of energy and conservation of momentum. Moreover, although energy and momentum are conserved, they are not invariant, but vary with the observer. But their combination (as a Minkowski norm) is a value that IS invariant, and is not only conserved, but ALSO is not-observer dependent, even though total energy and momentum ARE observer-dependent. The later are conserved for any given observer, but not all observers. But length of a Lorentz-invariant 4-vector is both conserved ANY invariant, so all observers not only agree that invariant mass doesn't change in time, but they all agree on its value, even when undergoing relative motion (two different properties). SBHarris 17:13, 18 May 2011 (UTC)

E=m.n^2? Maybe speed of neutrino should be used?

After discoveries that maybe speed of light is not the limit, maybe we should update the formula:

$E=mc^{2}\,\!$

like this:

$E=mn^{2}\,\!$

n - speed of neutrino. — Preceding unsigned comment added by Vstoykov (talk • contribs) 16:09, 23 September 2011 (UTC)

Only after it's been confirmed and reported in reliable sources! At the moment it's not a discovery, only a possible discovery. That in itself is notable though and has been reported in main stream press, so could deserve a mention. But it's not time to re-write the equations quite yet! Polyamorph (talk) 16:30, 23 September 2011 (UTC)

Of course I don't suggest to rewrite this article, this is just my hypothesis. Also maybe this formula should be updated:

$m_{\mathrm {rel} }={\frac {m_{0}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}\,\,.$

like this:

$m_{\mathrm {rel} }={\frac {m_{0}}{\sqrt {1-{\frac {v^{2}}{n^{2}}}}}}\,\,.$

If neutrino has zero rest mass in above formula, then n is speed of neutrino. If neutrino has non-zero rest mass in above formula, then n is constant larger than speed of neutrino (because neutrino don't have infinite mass when it is moving). Vstoykov (talk) 16:39, 23 September 2011 (UTC)

knol nonsense

An anon keeps adding the nonsense from his recently published knol. I reverted three times and tried to explain on his talk page and in my edit summaries at Planck constant, but to no good effect yet. Help? Dicklyon (talk) 04:18, 14 October 2011 (UTC)

mass vs. matter

The statement "Mass–energy equivalence does not imply that mass may be "converted" to energy, but it allows for matter to be converted to energy" is, I would say, incorrect because the complementary word to "matter" should be "radiation". A correct statement corresponding to what the editor was trying for is: "Mass–energy equivalence does not imply that mass may be "converted" to energy, but it allows for matter to be converted to radiation".

Spope3 (talk) 22:25, 30 October 2011 (UTC)

Good point, but many other sort of energy that are not matter can be made from matter. Matter can be converted to kinetic energy (though we more frequently see the reverse, in particle accelerator collision experiments, where kinetic energy is converted to particle/antiparticle pairs). Also, of course, matter can be converted to potential energy. All these types of non-material energy contribute to the invariant mass of systems. I'll add the caveat. SBHarris 00:06, 31 October 2011 (UTC)

Poor text

It is amaazing how this important concept is described with poor/careless choice of words. I have fixed one minor nonsense, but there are mauch more within. For example, the idea that the mass of Solar system is less than the sum of the masses of its components basaally makes sense, but the argumentation and the phrasing of the statement itself don't hold water. Unfortunately I lack expertise to write a correct yet "popular" dectiption myself. I would urge experts to review the text with a critical eye. —Preceding unsigned comment added by 71.146.72.134 (talk) 21:07, 18 December 2010 (UTC)

Well, careful, it may be that your conception is wrong. The basic reason that bound systems have less mass than they had before binding, is that the binding energy has been removed, and it has mass. Remove mass, and wind up with less mass. Very simple. If you want to unbind them, you have to add the energy back, which means adding the mass of the energy back, and so now your mass is larger. It's just a matter of mass/energy moving from here to there, not one changing to the other. Matter and non-material "energy" (light, kinetic energy, potential energy in fields, etc) may change back and forth into each other, but mass and energy never do this. As matter changes to energy, mass is unchanged and conserved (although some of it may fly off, and go somewhere else). That's this article's message, in a nutshell. SBHarris 01:38, 19 December 2010 (UTC)

Your reply does not address the OP's concern which is that the language used in this article is in some places clumsy. I agree with this but no more than any other article that has not yet attained GA status, a copy edit and in places re-write would help this article. Polyamorph (talk) 11:39, 27 December 2010 (UTC)

I think, the confusion comes from the fact that binding energy is greater when interacting bodies are farther (the bodies making up the system can make a greater work while approaching to each other -- ie, they can give more energy to an external system), whereas the word "binding" suggests rather the opposite. One should make this point clearer in the article (but I'm not a suitable person to).

Also, the words that "work is a form of energy" or that "work is removed (???) from the system" look quite confusing to me. I was told in a school that work can only be "done" and not "removed" -- it's energy that can be "removed" when work is "done". -- 91.122.83.75 (talk) 23:09, 15 December 2011 (UTC)