Talk:Conservation of mass

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Merged with "law of conservation of matter"

I redirected the conservation of matter article here, since the article there wasn't so great, and having the two was pretty much redundant. Vastly more articles linked to this article (Conservation of mass) than to the other. The article textlolo, of course, still preserved in the history of Law of Conservation of Matter.

The Wikipedia entry claims that mass and matter are EQUIVALENT to energy. Hmm. Have a think about that. There is a lot of confusion about Einstein's Law; it is often taken to mean that mass and energy are the same thing, which is not (necessarily) so; its significance is that it links the conservation of mass with the conservation of energy, which before Einstein were thought to be independent. In modern physics we accept that energy is conserved (but may be transferred) and THEREFORE mass is conserved (but may be transferred).

Well, I don't necessarily disagree, but the conservation of matter (which was taken to mean various kinds of fermions) gave us a chance to talk about the conservation of baryon number and lepton number and so on. You can't just make and destroy these things without their anti-counterparts, so far as we know (or have seen) and so this is something separate than just conservation of mass (which may include all kinds of energy like kinetic energy and photons which are their own antiparticles and may be made and split and whatever). So here was the place to talk about additional conservation laws that had to do with other quantum numbers. But maybe, as you say, it wasn't done so well. Einstein gave us overall mass conservation without the particle conservation. But maybe (and usually) there's something more to it than that. Something in addition. If you blow up a thermonuke, not only doesn't the total mass change (fi you keep the energy in) but the number of baryons and leptons doesn't either. Which is remarkable to me. Sbharris 07:09, 23 May 2006 (UTC)

Well, I'd be for getting rid of the above stub entirely, or else expanding it a LOT.

The problem is the word "matter." It's got problems, as noted above, because it's not total MASS. In relativity, single observers (in single inertial frames) measure momentum, total energy, and a combination of these called invariant mass (mass for short), all to be separately conserved, in reactions in closed systems. Whenever you see somebody talking about conservation of "energy-matter" you know they're really trying to talk about muddy circumstances in which "matter" has somehow been "turned into" energy, but the additive combination is conserved. But in that case, by "matter" they mean "a sum of rest masses of matter particles" which is complicated and somewhat articifical, because it's never what we measure in a system (where those particles are not at rest, and are often subject to terrific potential binding energies). The sum of rest masses is always something we calculate by taking rest masses out of a book and adding them up. You can actually do that to get the active energy released in nuclear reactions, and that's where this whole idea of "sum of mass-energy conservation" comes from. However, it's (as I said) artificial is some ways. By contrast, total momentum, total energy and invariant mass of many systems is measureable directly. If you have a system on scales, its total momentum is zero, the mass is what it weighs, and its total energy is mass times c^2. During a reaction, none of those things change, if you keep the system closed. That's the most simple kind of conservation. Nothing is converted to anything. Mass is conserved, momentum is conserved, and total energy is conserved.

So anyway, all this has to be explained. Some things in physics you should say a lot about, or else nothing at all. In between always gets makes you say something that is wrong. Steve 20:56, 19 June 2006 (UTC)

Conservation of mass, although not exact, is extremely important in sciences that does not deal with relativity (i.e. chemistry) and also physics from a historical perspective.

The section on "Mass conservation in the theory of special relativity" lacks context and overshadows the importance of mass conservation. Rather, it should be short section and linked to "Mass-energy equivalence". Hence it should NOT be merged with "Energy-matter conservation", as the two topics pertains to different scientific fields. Roger (sorry for not signing comment)

Previous comment is unsigned, however I agree. As a first step, I'm going to move the "historical section" in conservation of mass up front. It's hugely important, and is as approximately true (and as useful) as Newton's law of gravity. But the departures from it, now take up most of the present article. So a bit of rebalancing here needs to be done, with the bulk left to the relativity sections as "main articles". I'll make a first pass and let others have a shot.Steve 06:55, 21 June 2006 (UTC)

I also agree. In fact, I have on three separate occasions attempted a rewrite to highlight the importance of conservation of mass in chemistry and de-emphasize special relativity, which does after all have its own article, as you point out. I wasn't happy with my attempts and eventually gave up, but it still needs to be done. -lethe ^{talk +} 11:30, 21 June 2006 (UTC)

The whole section "Mass conservation in the theory of special relativity" doesn't seem to fit in the article. For one thing, it's unnecessarily long and convoluted. I suggest that the whole section be rewrittened to be much more concised, and linked off to another article for more information. Any objections? Roger

Have offloaded it to a separate article. The stuff in it is not completely duplicated in the conservation section in the article on special relativity, so I've merely added links there and here. At least it's not cluttering this one any more. Steve 06:38, 3 July 2006 (UTC)

Excised from introduction a sentence fragment and some redundant text mentioning special relativity: In a strict sense the law of conservation of mass/matter may be viewed as a naive approximation to reality. While conservation of energy equations from special relativity give the more appropriate relationships between energy and mass behavior. Gnixon 04:39, 28 July 2006 (UTC)

Well, I'm afraid you've managed to muck it up some in the process. Please read the end of the article! The mass of systems (when viewed by a single observer in their center-of-mass frame) IS conserved, even in relativity, and even in nuclear reactions. Yes, that includes alpha, beta, and gamma decay. In all of these, the moving alpha, the moving beta, and the gamma photon all contribute mass to the system, and so long as they remain part of the system, the system mass does not change through the whole process of nuclear decay. Of course it changes when the particle is let out of the system, but you can't expect conservation of mass in a system which isn't closed! Yes, that means that kinetic energy has mass in this context. Yes, that means that massless photons contribute mass in this context. And so on. SBHarris 03:26, 22 August 2006 (UTC)

I think they should be kept as two separate articles. Although I'm not a physics expert my understanding has been that they are different although energy can suposedly be converted to mass and vice versa. Zacherystaylor (talk) 16:11, 20 March 2014 (UTC)

Ficks Principle?

I came to wikipedia to look for Ficks principle, and this page is the closest thing to it. Considering I came here looking for info, I probably shouldn't be the person to add a whole page, or a section to this one. Ficks principle roughly states that the amount of a substance that enters a system (e.g. a mass) must equal the amount of that substance that leaves the system. Its used in physiology in measuring things like glomerular filtration rate. Someone should add a quick thing to this page, or add a fick's principle page since this is a pretty common topic. Thanks. Rjkd12 15:52, 28 November 2006 (UTC)

Fick's principle probably needs its own physiology stub, but it's too arcane to discuss much here. Mass-balance is used in dozens of ways in dozens of fields. Fick's principle is just mass balance, expressed as a time derivative, and as used in biology. I don't even know why it has a special name, except that perhaps physiologists were so excited to discover and use some simple calculus, that they couldn't help themselves. ;) SBHarris 16:15, 28 November 2006 (UTC)

I thought Fick's Law stated that the rate of Diffusion of a substance was equal to the Concentration Gradient of the substance: Rt of Dfsn = dC/dX.JeepAssembler (talk) 22:13, 31 March 2009 (UTC)JeepAssemblerJeepAssembler (talk) 22:13, 31 March 2009 (UTC)

Merging again from Law of Conservation of Matter

I've redirected Law of Conservation of Matter to here, as there appears to be consensus for merge. Here are the contents of the article which are not in this article. I can't make heads or tails of it:

"The difficulty in stating this law in terms of the word "matter" is that "matter" is not a well-defined word. Most definitions of matter require that it be comprised of ordinary fermionic matter, which is composed of fermionic particles such as neutrons, protons, electrons and positrons. Most definitions of "matter" include neither electromagnetic radiation (such as light or gamma rays) nor do not include forms of potential energy associated with static nuclear or electromagnetic fields. The problem, however, is that scientists now know that such fields represent an appreciable percentage of the mass of ordinary objects, and even of particles themselves when they are compound particles (i.e., hadrons). The kinetic energy of particles in ordinary objects such as the kinetic energy of atoms represented in heat, but also the kinetic energy of subatomic particles contributes to the mass of objects, even though such energies are also not usually considered to be matter."

el:Αφθαρσία της ύλης pl:Prawo zachowania ru:Закон сохранения sl:Zakon o ohranitvi

There was also more in the page history. Kla'quot 09:20, 9 March 2007 (UTC)

Just as well. The problems were in the definition of the word "matter" which isn't well-defined in science. Thus, the law of conservation of matter should indeed be redirected to the conservation of mass page, and the problems with the world matter continue to be discussed in the matter article. Which is as things now stand. The reason you can't make heads or tails of the above is probably because you're not a native English speaker, and in English, "matter" is not synonymous with "mass." Matter is a lose philosophical word from the old days before relativity, and is probably obsolete, like "phlogiston." Nobody knows or can agree on what it means, really. Mass is much better defined.

hard to understand!

i dont understand this! —Preceding unsigned comment added by Sarahis1313 (talk • contribs) 21:35, 2 October 2007 (UTC)

WikiProject class rating

This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:46, 10 November 2007 (UTC)

Removed a bunch of junk

Article states:

"In special relativity, the conservation of mass can not be cast as a simple statement of conservation of energy. For example, a system of two photons can be massless or have an inertial mass up to 2E/c², where E is each photon's energy (assumed equal), as a function of relative momentum orientation for the photons. However, such a system requires the observer to change. So, independently of the energy content being constant at 2E, the total mass may vary from zero to 2E/c². ."

Nowhere does Wheeler say this (quote page, please). The "system" described is not even the same system! A system in which two photons of energy E are going the same direction, cannot be converted to a system in which they are moving in opposite directions, by any change of the observer. They are two separate systems, and why should they have the same mass? As for their energies, you can't simply get system energy by adding up energies of parts of the system. Moving from a system in which photons are going in (almost) the same direction, to a system in which they are going in opposite directions, amounts to changing the observer. Doing this changes the energy of the system unless you change the energy of the photons at the same time. But doing both at once is hardly fair-- why would you expect to have ANYTHING conserved, if you're changing both obsever and photons seen by the previous observer TOO? I took this whole paragraph out, because it describes a series of experiments and observers, not anything held truly constant. Photons of energy E in opposite directios will have MORE energy than 2E for any other observer in which they don't go in opposite directions. Diminishing them so they don't results in a different system. SBHarris 04:30, 24 February 2008 (UTC)

Law, Oh Really

Shouldn't it be more apparent that more recent scientific theories much advertise against this so called law? Right now It's waaay down. Waaay down. It was on the simpsons by the way. PoorLeno (talk) 13:16, 10 March 2008 (UTC)

If you would read the article, you might get some help in your question. SBHarris 05:48, 2 April 2008 (UTC)

Epicurus?

While it's true that Epicurus held something like this, it's a little strange to cite him as the first to state such a view. This idea goes back to the pre-Socratic philosophers, several of the earliest of whom believed one basic substance was the foundational element of physical reality. Thales held that it was water, Anaximines that it was air, and Heraclitus that it was fire. Empedocles was the first to offer earth, air, fire, and water all as elements. Leucippus believed in fundamental atoms that were all differently sized and shapes but not divisible and neither created nor destroyed (and was actually the original source of Epicurus' atomism, from which his use here eventually goes back). All of these philosophers thought the basic substance of substances are not created or destroyed and that they've always been there and always will be there, just rearranging themselves differently. Parableman (talk) 14:37, 10 February 2009 (UTC)

I am reading Marcus Aurelius' Meditations which were written circa AD 180. Here is a quote from the text of the legendary Roman Emperor, written in Greek may I add... "Now every part of nature benefits from that which is brought by the nature of the Whole and all which preserves that nature: and the order of the universe is preserved equally by the changes in the elements and the changes in their compounds". Book II, 2nd paragraph, lines 17-20. Translated by Martin Hammond. Penguin publishing. Copyright 2006. (Jsboyarsky (talk) 17:12, 22 February 2009 (UTC))

Epicurus Source doesn't work

I got the "IE can't display this page" message. Perhaps the link is outdated? --JudelFoir (talk) 20:03, 3 October 2009 (UTC)

A strawman argument removed

I have removed the following unsourced section:

Criticisms: The conventional statement of the law of conservation of mass - that matter can neither be created nor destroyed - has been subject to wide criticism due to its apparant absurdity in stating that matter cannot be created-as it is not possible to define an entity which cannot be created - and also due to its self-contradition in stating that matter cannot be destroyed either. Critics have suggested that the statement of the law of conservation of mass be modified to reflect the fact that it merely defines the scope of the physical science, rather than purporting to make a universal statement which is obviously contradicted by the existence of matter in the universe.

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• Comment: as the LEAD makes very clear, matter is not well defined, and everyone agrees that if photons are not "matter" then matter is not conserved, and that it can indeed be created and destroyed. The criticism section would go better in the Wiki on "matter." Mass is conserved so long as energy is. If there's any criticism to the theory, it is that energy conservation depends on the rules of physics being time-invariant, and this may not be true for the universe through the Big Bang. Thus, it may well be that the mass of the universe has been conserved so long as the laws of physics have not changed-- but perhaps they have changed. At the Big Bang, they may have been something different. Thus, there is no requirement that the universe began with the same mass that it now has.SBHarris 22:08, 10 March 2009 (UTC)

What about Combustion?

During a combustion process in a closed system; it seems like the total mass of products (Vapors, ashes, etc.) would be less than the mass of the reactants.JeepAssembler (talk) 17:08, 31 March 2009 (UTC)JeepAssemblerJeepAssembler (talk) 17:08, 31 March 2009 (UTC)

No, it's exactly the same. The first experimenters to burn things (or let them rust) inside sealed glass bulbs while weighing them, were shocked, too. SBHarris 01:27, 1 April 2009 (UTC)

Who were they? and when? I thought modern Chemistry was invented by Priestly and Lavoisier in the 1760's. I would like to be read about the first combustion experiments.JeepAssembler (talk) 21:05, 1 April 2009 (UTC)JeepAssemblerJeepAssembler (talk) 21:05, 1 April 2009 (UTC)

I know this is an old thread, but I just want to clarify that the mass of the system will remain the exactly the same after combustion only if it's isolated with respect to all forms of energy input and output, not just the material parts like "vapors, ashes, etc." might suggest. If some of the energy released during combustion escapes from the system (e.g. glass bulb), even in the form of light, heat transfer, etc., then the system will have less energy and thus less mass than before. In practice, though, this decrease in mass will most likely be too small to measure.DavRosen (talk) 18:38, 12 July 2013 (UTC)

Closed vs. isolated systems

Unfortunately, closed system is a term that may mean "closed to matter but open to energy and work flow." Such systems DO change mass, since energy goes in and out, and energy always takes mass with it, in systems. But in totally isolated systems, mass does not change. That is true even if matter is converted to energy inside the system (particle annihilation for example).

There is a popular misconception that nuclear energy converts mass into energy, but it does not. Rather, energy is liberated and removed, and when the (cold) products are weighed, you can weigh the missing energy (because it's so large). But you could weigh it just as well if you went to where it was deposited, and so the mass has moved, not disappeared. If you draw your system boundaries largely enough, the mass inside them cannot change since nothing has escaped. For example, when a nuclear bomb was detonated underground (something we don't do anymore) the mass of the Earth did not change. Even though a big thermonuke (600 kilotons = 1 ounce) might liberate several ounces of heat and light, it doesn't escape. The bomb's mass loss there is the crust's gain (E = mc^2 again), and nothing changes. That's an example of mass conservation in an isolated system, even with a nuclear weapon. SBHarris 07:23, 7 November 2011 (UTC)

Hijacked by non-experts with possible ulterior motivations

This is a warning to casual reader of this page looking for scientific understanding of mass and its conservation. The page has been hijacked by people who prefer to mystify the discussion than give the simple statements. The revision history shows a variety of vandalism claims and reverse edits, while this talk page shows that one of the abiding contributors Steve adopts an unusual definition of "mass" thereby making the discussion cumbersome and confusing.

I am not bothering to edit the main article because it is likely be vandalised by these authors. Sorry, I am not Being Bold the way Wikipedia exhorts us to be.

The message is very simple :

1. In chemistry and physiology, being phenomena at low energies, mass can be taken to be conserved within the observational approximation needed.
2. In Special Relativity the only useful definition of mass is the rest mass. This makes mass or inertia a property intrinsic to the particle, independent of the frame of observation.
3. Rest mass is not conserved in interactions as particle types can change. That is, the sum of rest masses of initial reactants is not necessarily the same as that of the final products.

The classic example of the last point is electron and positron with total rest mass twice that of the electron can combine to produce two photons, the rest mass in the final state being zero. This mismatching of rest masses is still consistent with the law of conservation of energy.

That's all there is to it folks, you can read the continuously updated article at your own risk and amusement. Powstini (talk) 12:52, 23 February 2014 (UTC)

On the contrary, in special relativity, the "only useful" definition of mass is NOT the narrow "rest mass." The only useful definition of mass is invariant mass which (indeed) is the same as rest mass for single massive particles, but has no definition for systems of particles except invariant mass (the system rest mass when bound, the system mass in the COM frame when unbound). Yet most objects are systems of particles, not simple particles! So what does relativity do in discussing the mass of compound objects? When you weigh (or find the mass of, by balance beam) a system of particles (any ordinary object) you are measuring the invariant mass of the object, not the sum of rest masses of the particles that make it up. So you end up counting the mass of the photons inside a hollow object, and the kinetic energy of the particles moving in the object, too ("thermal energy"). Yet none of these has a rest mass, as individual photons have no rest frame, and kinetic energy disappears in any given particle's rest frame.

In the system of two photons, the invariant mass of the two photons (as a system) is the same as the invariant mass of the electron and positron that produce them, so invariant mass is conserved. If you put the electron and positron in a can, and let them annihilate while the can sits on a scale, as the photons bounce around inside the can, the number on the scale does not change. The photons also add inertia, gravitation, and so on (none which changes with the anihilation). That is because invariant mass is conserved, so long as you keep the system closed. But if you like open systems, nothing is conserved, so what's the point in discussing that?

As for your remarks about my "unusual" definition of mass in relativity, it is the same as adopted by Taylor and Wheeler in Spacetime Physics, a well regarded mathematical introductory text on SR for physicists. SBHarris 21:31, 20 March 2014 (UTC)

Conservation of mass/energy

Doesn't the law of their equivalence imply that we are talking about one and the same law? –St.nerol (talk) 15:37, 17 March 2014 (UTC)

The issue is that the law of conservation of mass may be a special case of the law of conservation of energy but historically it is a law relating to chemistry, basically saying mass is neither gained nor lost in a chemical reaction. As such it is one of the "laws of stoichiometry". As the article says it was proposed by Lavoisier and at that time classical physics had no concept of mass being interchangeable with energy.

The desire to mix these two closely related topics is understandable but from an encyclopedic pont of view it has made this a cluttered article. I would separate the article into two, perhaps:- "Conservation of mass (chemistry)" and "Conservation of mass(physics)" allowing both threads to develop separately. I would keep the Conservation of Energy separate. Axiosaurus (talk) 10:29, 12 April 2014 (UTC)

Oppose merge. I agree that Conservation of mass should be kept separate from Conservation of energy despite Einstein. Historically, mass is a separate concept not only in chemistry but in Newtonian physics and therefore in (mechanical) engineering.

As for conservation of mass (chemistry), yet another article seems a bit much, so I have compromised by creating a new subsection for the chemistry content. I left Lavoisier in the intro due to his importance in developing the concept, but Stas and his experimental confirmation work are less crucial, so I placed them in the new subsection. Dirac66 (talk) 02:22, 14 April 2014 (UTC)

• Oppose merge. Don't know why this subject keeps getting brought up. Keep them separate. 10stone5 (talk) 05:08, 5 September 2014 (UTC)

• Oppose merge. The early chemists like Lavoisier had no concept that addition or subtraction of light and heat from a system would make a mass difference, so their concept of conservation of mass was absolute and didn't require a completely closed system. It could be open to heat and light, so long as you didn't let "matter" (atoms or particles) in and out. And Lavoisier did a lot of that with sealed glass ampules that let out the heat of reaction, and he never saw a mass change. Now we know it was there, but just too small for this scale. And even today chemists know that tiny mass change is there, but they ignore it just as though it was wasn't there, and old-time mass-conservation laws were the same.

  We all know what happened with Einstein. He calculated that if a great deal of heat was let in or out of an open system, it would change mass, even if you closed it to atoms and particles. So the strict law of mass conservation (after Einstein) requires a closed system, because now heat and light change system mass, too. But only by a very little in chemical reactions, which is why chemists didn't notice it, and still ignore it. It requires the vast energy of nuclear reactions or decays to get a good fractional mass change, due to heat and light exchange only from a system. SBHarris 04:26, 10 September 2014 (UTC)

This article has been wrong since 1905

Mass is not conserved. It is energy that is conserved (in an inertial frame).

Here are four examples.

1. Antimatter and matter both have positive mass, and their annihilation results in zero mass, eg all the energy being converted to photons. Simplest example: electron + positron --> two photons.
2. The merger of two black holes has been observed, where a loss of 3 solar masses of mass occurs in an instant.
3. All nuclear reactions fail to conserve mass, with the size of the effect being of the order of 1% in fusion reactions. Mass is converted to kinetic energy and electromagnetic radiation
4. Even chemical reactions fail to conserve mass (but the fraction is very small < 1 part in a billion). Here the energy released is converted to kinetic energy and electromagnetic radiation (of much lower frequency than for nuclear reactions Elroch (talk) 14:56, 13 June 2017 (UTC)

This is covered in the article, for instance in section Conservation of mass#Generalization . DVdm (talk) 13:02, 13 June 2017 (UTC)

No, it is misrepresented in the article. The question to clarify this is "is anything being stated other than conservation of energy?" and the answer here is "no". To attempt to revive the notion of conservation of mass, it is twisted into a form which is exactly the conservation of energy within an isolated system.
What physicist would say that when an positron and an electron annihilate, MASS is conserved? What is the mass of two photons? To modern physicists, all mass is energy, but not all energy is mass. Far better to talk about rest mass and energy, as is the norm in physics, and to have an article about the obsolete law of conservation of mass and how it was revised in the early 20th century. Elroch (talk) 14:56, 13 June 2017 (UTC)

I second this. 92.196.123.224 (talk) 15:44, 12 December 2017 (UTC)

"is anything being stated other than conservation of energy?" Yes, conservation of momentum. And of course, mass is linked to energy and momentum with $E^{2}=p^{2}+m^{2}$. "What physicist would say that when an positron and an electron annihilate, MASS is conserved?" More than you'd think. "What is the mass of two photons?" $m={\sqrt {(E_{1}+E_{2})^{2}-|{\vec {p}}_{1}+{\vec {p}}_{2}|^{2}}}$. "To modern physicists, all mass is energy". I should hope that most modern physicists paid attention when being taught special relativity and understand the difference between the time-like component of four-momentum and its norm. — dukwon (talk) (contribs) 06:18, 13 December 2017 (UTC)

I second this, I read it today and it's extremely wrong in places. Elroch is right in that it misrepresents several things. It must have been written by a chemist who has little knowledge of relativity and quantum field theory. The article doesn't distinguish well between mass of constituents and mass of a system (the way a nucleon is a system to whose mass the binding energy between its constituent quarks contributes). At times it also gives hints of using relativistic mass (but since it's not formulated well, it isn't very obvious) - another hint that it wasn't written by someone who has formal training in relativistic physics. It should be deleted or completely rewritten. The only thing that remains useful about conservation of mass is that it's approximately true in chemistry (only approximately because the energies involved in chemical processes aren't significant) and lower energy physics (ie mechanics, fluid dynamics). It is false in nuclear physics already (this article wrongly says the contrary). 92.196.123.224 (talk) 15:44, 12 December 2017 (UTC)

The article seems to address most the points that Elroch made. Yet I second that the article is in very bad shape. Just reading the first paragraph is very confusing. It needs to be rewritten. Nevertheless, it should maintain the consistency of a introductory article to chemistry and classical dynamics, nobody should doubt that matter is not conserved, but that doesn't illegitimate this law is very practical in some case. This conservation law should be written with a very detailed and evident explanantion on why, how and in which situations this law works "fine". MaoGo (talk) 15:59, 12 December 2017 (UTC)

I rewrote some parts of the introduction. Hope it helps. Feel free to correct and sorry for the lack of description. — Preceding unsigned comment added by MaoGo (talk • contribs) 18:08, 12 December 2017 (UTC)

Annihilation

Sorry, but NOPE! to this law. Annihilation (both electron and positron have mass and they transform it to energy - electromagnetic stuff in time and space). No word "statistic", no to law.

37.48.8.177 (talk) 18:37, 10 July 2019 (UTC)mooph

“ For very energetic systems the conservation of mass-only is shown not to hold, as is the case in nuclear reactions and particle-antiparticle annihilation in particle physics. ”

This article. This is Wikipedia. Incnis Mrsi (talk) 18:48, 10 July 2019 (UTC)

started like this:

“ system closed to all transfers of matter and energy ”

Let's close (for some model, imagination) space around annihilation at the moment when electron and positron are SO near, that it starts in time (annihilation itself) and ends as soon as it's done (goes out of closed space). I ask: "How to close space and keep the system closed over there for some time"? IMHO impossible no matter how we scale... Transformation of mass to energy (and probably also backwards, which is very rare, because dominant factor we observe (using one of multiple forms of energy) is mass) just happens, even in larger statistically measured models, because it's not possible to close the system both EXTERNALLY and INTERNALLY in space and time, because space and time are both scaled, infinite and scaled with adequate infinite possibilities how to choose rules how to scale. :)

37.48.8.177 (talk) 19:05, 10 July 2019 (UTC)mooph

Perfect truth of the law

The law is perfectly true. For example, photons have relativistic mass and therefore, have mass. So, in annihilation, no mass is lost. However, in the particle, it is stated that the law is approximately true. What a unreliable source is Wikipedia for even a simple law! Somebody400 (talk) 13:27, 16 January 2020 (UTC)

@Somebody400: sure, the law holds if you call it the "conservation of relativistic mass" but (1) it is not the typical concept of mass that laymen are used to (2) how are people supposed to know it is about "relativistic" and not "rest mass"? (3) "relativistic mass" is a concept that has been abandoned, it is the same as energy/c^2 and (4) it still does not hold in general relativity. If you wish, you may propose a better phrasing and we can discuss it together here.--MaoGo (talk) 15:36, 16 January 2020 (UTC)

Due to mass-energy equivalence, the mass of an isolated system in a given frame of reference is conserved. It follows from the independent law of conservation of energy. Also, mass may not even be properly defined in general relativity. So, it may be better to keep general relativity out of this discussion. Somebody400 (talk) 16:04, 16 January 2020 (UTC)

Sure and all that is explained in the lead. I am not sure what the problem is.--MaoGo (talk) 16:08, 16 January 2020 (UTC)

Does this article need a FAQ? Comment

I've noticed a lot of questions on this talk page, but also a lot of edits to the article, that doubt that conservation of mass holds for isolated systems. I was thinking perhaps a FAQ is needed to explain why it holds under special relativity. A FAQ could go something like this:

---

Q. Why is invariant mass conserved in a isolated system?

A. For a isolated system, it must obey the energy–momentum relation:

$E_{\text{total}}^{2}=(pc)^{2}+\left(m_{0}c^{2}\right)^{2}\,$

Where $E_{\text{total}}$ is the total energy of the system (= rest energy + kinetic energy), p is the overall momentum of the system, $m_{0}$ is the invariant mass of the system, and c is the speed of light.

Now for an isolated system, both the total energy (by the law of conservation of energy) and total momentum (by the law of conservation of momentum) must both remain constant, as no mass or energy must come into or leave an isolated system, nor any outside momentum. Now since c (the speed of light) is a constant, this must mean that $m_{0}$ must also be conserved, and the overall invariant mass remains unchanged.

In other words, $E_{\text{total}}$ and p are both conserved for an isolated system; c is a constant; and so $m_{0}$ must also be conserved for an isolated system. By conserved I mean "no overall change with time".

Q. In an isolated system, a motionless emitter emits some photons (light particles). Since the emitter loses energy, it must also lose invariant mass. Photons have zero invariant mass. Therefore, surely the isolated system has lost invariant mass?

A. The solution to this problem is that you have to consider the system as well as the individual components (emitter and photons). Now if you look at the individual components separately, then yes invariant mass has been lost. But if you consider the system, the system has not lost invariant mass.

One way of looking at this is to consider the energy–momentum relation as above, but this doesn't explain why the system conserves invariant mass. However it can be explained by considering the following:

First of all we assume that the emitter was motionless before emitting the photons. Now while photons don't have invariant mass, they do have momentum. Therefore, by the the law of conservation of momentum, the emitter must recoil slightly. So therefore the system is at rest, since the system is in its original center-of-momentum frame because of conservation of momentum. How so? Well even if components of a system have motion, if the overall momentum of the system is zero then the overall system is at rest, and the energy–momentum relation simplifies to:

$E_{\text{total}}=m_{0}c^{2}$

This is because p is zero. Since $E_{\text{total}}$ is conserved for isolated systems, therefore $m_{0}$ must also be conserved, and the invariant mass remains unchanged. So even though the individual photons don't have mass, they do contribute to the mass of the system.

Now since the system has no overall momentum, it has no overall velocity, and no overall kinetic energy, and therefore $E_{\text{total}}=E_{0}$, that is all the overall energy of the system is rest energy. This is despite both the emitter and photons individually both having kinetic energy. But that reinforces why considering an overall system is very different to considering the individual particles of a system.

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Any thought on this? --Jules (Mrjulesd) 17:30, 25 September 2020 (UTC)