# What is the difference between mass-energy equivalence theory/law and the conservation of energy? **URL:** \ **Category:** Factual Questions\ **Created:** [November 29, 2016, 3:24pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379 "2016-11-29T15:24:23Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![davidmich](https://avatars.discourse-cdn.com/v4/letter/d/e56c9b/32.png) [@davidmich](https://boards.straightdope.com/u/davidmich)\ **Post date:** [November 29, 2016, 3:24pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/1 "2016-11-29T15:24:23Z")
Hi What is the difference between the mass-energy equivalence theory/law(e=mc2 and the conservation of energy law? I’m not quite sure about how they are related. I believe the latter is the first law of thermodynamics. How does e=mc2 support the law of conservation? I look forward to your feedback ---
**Author:** ![DrCube](https://avatars.discourse-cdn.com/v4/letter/d/a3d4f5/32.png) [@DrCube](https://boards.straightdope.com/u/DrCube)\ **Post date:** [November 29, 2016, 4:09pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/2 "2016-11-29T16:09:34Z")
I don’t see a conflict. Mass is energy, energy has mass, and both quantities are conserved. ---
**Author:** ![davidmich](https://avatars.discourse-cdn.com/v4/letter/d/e56c9b/32.png) [@davidmich](https://boards.straightdope.com/u/davidmich)\ **Post date:** [November 29, 2016, 4:33pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/3 "2016-11-29T16:33:11Z")
> [@DrCube](#): > > I don’t see a conflict. > > Mass is energy, energy has mass, and both quantities are conserved. So if I described Einstein’s equation e=mc2 as the law of conservation of energy, would that be technically correct? I somehow thought that Einstein’s equation was an improvement over the 1st law of thermodynamics or was it proof of it? I’m not quite sure. ---
**Author:** ![Chopsticks](https://avatars.discourse-cdn.com/v4/letter/c/cab0a1/32.png) [@Chopsticks](https://boards.straightdope.com/u/Chopsticks)\ **Post date:** [November 29, 2016, 4:33pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/4 "2016-11-29T16:33:47Z")
e=mc^2 simply tells you “if I take this kilogram of matter and somehow turn it into pure energy, how much energy do I get out.” Convservation of energy is that if you add up the types of energy in a reaction (heat, kinetic, mass equivalent, atomic bonds, etc) the total can’t change from before to after. If a neutron at rest decays to proton, electron, and antineutrino, there will be slightly less mass after the reaction. That lost mass uses e=mc^2 to convert to energy, and that energy gets parcelled out as kinetic energy in the particles, and photon energy if any photons are emitted. Eout = Ein. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [November 29, 2016, 4:34pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/5 "2016-11-29T16:34:42Z")
mass is energy. And it is conserved. You can “convert” energy to mass and back, because it’s really the same thing. But you can’t destroy mass=energy, or create it out of thin air. ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [November 29, 2016, 5:03pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/6 "2016-11-29T17:03:57Z")
> [@Chopsticks](#): > > If a neutron at rest decays to proton, electron, and antineutrino, there will be slightly less mass after the reaction. This is actually subtly misleading. If neutron decays, the sum of the mass of the proton, the mass of the electron, and the mass of the anti-neutrino will be less than the mass of the original neutron. But the mass of the _system_ of the proton, electron, and anti-neutrino will be exactly the same as that of the neutron. The trick is that in relativity mass is not additive unless the objects are at rest relative to each other. I.e. the mass of a system of two objects with masses m1 and m2 is not necessarily m1 + m2. ---
**Author:** ![DrCube](https://avatars.discourse-cdn.com/v4/letter/d/a3d4f5/32.png) [@DrCube](https://boards.straightdope.com/u/DrCube)\ **Post date:** [November 29, 2016, 5:17pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/7 "2016-11-29T17:17:37Z")
> [@davidmich](#): > > So if I described Einstein’s equation e=mc2 as the law of conservation of energy, would that be technically correct? I somehow thought that Einstein’s equation was an improvement over the 1st law of thermodynamics or was it proof of it? I’m not quite sure. It was neither. It is another law entirely. In fact, the equation by itself isn’t all that influential, it’s more a succinct illustration of the sort of thing Einstein’s relativity implies. > [@scr4](#): > > You can “convert” energy to mass and back, That’s not really how it works. Mass has energy and energy has mass, but they don’t “convert” back and forth. ---
**Author:** ![Doubticus](https://avatars.discourse-cdn.com/v4/letter/d/e56c9b/32.png) [@Doubticus](https://boards.straightdope.com/u/Doubticus)\ **Post date:** [November 29, 2016, 5:20pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/8 "2016-11-29T17:20:12Z")
My understanding is E=MC^2 shows how matter is energy. I think of matter as frozen energy. Conservation of energy just states that you can’t create energy, or destroy it, just change its form. Kinetic to heat for example. ---
**Author:** ![John\_Mace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_mace/32/185_2.png) [@John\_Mace](https://boards.straightdope.com/u/John_Mace)\ **Post date:** [November 29, 2016, 5:24pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/9 "2016-11-29T17:24:15Z")
> [@davidmich](#): > > So if I described Einstein’s equation e=mc2 as the law of conservation of energy, would that be technically correct? No. That just tells you the relationship between mass and energy, and how much energy is contained in a certain amount of mass. The conservation of energy law is not something we usually write mathematically, but it would go something like this: Delta E (for a closed system) = 0. That is, the amount of Energy in a closed system (a system no subject to outside forces) is constant. Same for momentum. But the key is that the system must be closed. If outside forces can act on it, then the total amount of energy can change. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 29, 2016, 5:28pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/10 "2016-11-29T17:28:29Z")
More precisely, the Law of Conservation of Energy states that the change in the energy contained within any bounded region is equal to the sum of all of the flows of energy across the boundaries of the region. In other words, if the energy in a region increases, it’s because energy entered the region, and if it decreases, it’s because energy left the region. ---
**Author:** ![davidmich](https://avatars.discourse-cdn.com/v4/letter/d/e56c9b/32.png) [@davidmich](https://boards.straightdope.com/u/davidmich)\ **Post date:** [November 29, 2016, 5:30pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/11 "2016-11-29T17:30:38Z")
> [@John\_Mace](#): > > No. That just tells you the relationship between mass and energy, and how much energy is contained in a certain amount of mass. The conservation of energy law is not something we usually write mathematically, but it would go something like this: > > Delta E (for a closed system) = 0. > > That is, the amount of Energy in a closed system (a system no subject to outside forces) is constant. Same for momentum. But the key is that the system must be closed. If outside forces can act on it, then the total amount of energy can change. Thank you John Mace. Thank you all. Perhaps someone would like to comment of the following: > **[Does E=MC2 disprove the first law of thermodynamics?](https://www.quora.com/Does-E-MC2-disprove-the-first-law-of-thermodynamics)** > > Answer: It will depend on how you define energy. If you define energy in a non-relativistic manner, the first law is wrong. The first law still holds if you accept the relativistic definition of energy, the one which includes the rest mass energy. Does E=MC2 disprove the first law of thermodynamics? It will depend on how you define energy. If you define energy in a non-relativistic manner, the first law is wrong. The first law still holds if you accept the relativistic definition of energy, the one which includes the rest mass energy. ---
**Author:** ![Crafter\_Man](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crafter_man/32/458_2.png) [@Crafter\_Man](https://boards.straightdope.com/u/Crafter_Man)\ **Post date:** [November 29, 2016, 5:33pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/12 "2016-11-29T17:33:11Z")
IANAP, but it is my understanding that E = mc[sup]2[/sup] simply says “Mass **IS** energy. If you have a mass of m (kg), it is E joules of energy.” ---
**Author:** ![Blue\_Blistering\_Barnacle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/blue_blistering_barnacle/32/3386_2.png) [@Blue\_Blistering\_Barnacle](https://boards.straightdope.com/u/Blue_Blistering_Barnacle)\ **Post date:** [November 29, 2016, 6:29pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/13 "2016-11-29T18:29:18Z")
I think they are related, but draw from different wellsprings. First law of thermodynamics is very fundamental, and tells you what to expect when you measure the energy in your system. I believe it relates to a fundamental symmetry we believe the universe has (with respect to time?). E = mc\*2 tells you how matter and energy are related in your system. (For most practical purposes, we ignore matter’s contribution to the system’s energy because it is (mostly) the same before and after, but this can sometimes become important, especially when nuclear processes are involved.) ---
**Author:** ![davidmich](https://avatars.discourse-cdn.com/v4/letter/d/e56c9b/32.png) [@davidmich](https://boards.straightdope.com/u/davidmich)\ **Post date:** [November 29, 2016, 6:39pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/14 "2016-11-29T18:39:34Z")
> [@Blue\_Blistering\_Barnacle](#): > > I think they are related, but draw from different wellsprings. > > First law of thermodynamics is very fundamental, and tells you what to expect when you measure the energy in your system. I believe it relates to a fundamental symmetry we believe the universe has (with respect to time?). > > E = mc\*2 tells you how matter and energy are related in your system. (For most practical purposes, we ignore matter’s contribution to the system’s energy because it is (mostly) the same before and after, but this can sometimes become important, especially when nuclear processes are involved.) Thanks Blue Blistering Barnacle I’ve seen a lot of reference to non-relativistic versus relativistic interpretations of transfers of energy to distinguish the two and a lot of debate. I’d really like more clarification on that. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 29, 2016, 7:36pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/15 "2016-11-29T19:36:13Z")
While we’re at it, the actual law isn’t even E = mc[sup]2[/sup]. It’s E[sup]2[/sup] = p[sup]2[/sup]c[sup]2[/sup] + m[sup]2[/sup]c[sup]4[/sup]. It’s only in the (relatively boring) case where p = 0 that it reduces to E = mc[sup]2[/sup]. ---
**Author:** ![Blue\_Blistering\_Barnacle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/blue_blistering_barnacle/32/3386_2.png) [@Blue\_Blistering\_Barnacle](https://boards.straightdope.com/u/Blue_Blistering_Barnacle)\ **Post date:** [November 29, 2016, 8:17pm UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/16 "2016-11-29T20:17:45Z")
> [@davidmich](#): > > Thanks Blue Blistering Barnacle > > I’ve seen a lot of reference to non-relativistic versus relativistic interpretations of transfers of energy to distinguish the two and a lot of debate. I’d really like more clarification on that. A crude example: Lord Kelvin was a really smart guy who did very important work in thermodynamics. He famously calculated the Earth’s age to be about 20-40 million years (too short to support evolution as envisioned by Darwin), based on the Earth’s interior temperatures and conductivity of rock. But he was unable to account for radioactivity (as it was not yet discovered). Radioactivity adds heat to the center of the earth (or to any very radioactive object- read ‘The Martian’ for creative application of this). But it’s not ‘adding’ energy to the earth’s interior- that energy is counterbalanced by small losses of mass during nuclear decays, where forces and velocities are such that relativistic effects become apparent. (Incidentally, there is a similar but far more miniscule loss of mass in exothermic chemical reactions, if everything is fully accounted for.) > **[Lord Kelvin](https://en.wikipedia.org/wiki/William_Thomson,_1st_Baron_Kelvin#Age_of_the_Earth:_geology_and_theology)** > > William Thomson, 1st Baron Kelvin, OM, GCVO, PC, FRS, FRSE (26 June 1824 – 17 December 1907) was a British mathematician, mathematical physicist and engineer born in Belfast. He was the professor of Natural Philosophy at the University of Glasgow for 53 years, where he undertook significant research and mathematical analysis of electricity,\[citation needed\] was instrumental in the formulation of the first and second laws of thermodynamics, and contributed significantly to unifying ph Absolute ... > [@](#): > > Thomson’s initial 1864 estimate of the Earth’s age was from 20 to 400 million years old. These wide limits were due to his uncertainty about the melting temperature of rock, to which he equated the earth’s interior temperature,[49][50]as well as the uncertainty in thermal conductivities and specific heats of rocks, Over the years he refined his arguments and reduced the upper bound by a factor of ten, and in 1897 Thomson, now Lord Kelvin, ultimately settled on an estimate that the Earth was 20–40 million years old.[51][52] His exploration of this estimate can be found in his 1897 address to the Victoria Institute, given at the request of the Institute’s president George Stokes,[53] as recorded in that Institute’s journal Transactions.[54] Although his former assistant John Perry published a paper in 1895 challenging Kelvin’s assumption of low thermal conductivity inside the Earth, and thus showing a much greater age, this had little immediate impact.[55] The discovery in 1903 that radioactive decay releases heat led to Kelvin’s estimate being challenged, and Ernest Rutherford famously made the argument in a lecture attended by Kelvin that this provided the unknown energy source Kelvin had suggested, but the estimate was not overturned until the development in 1907 of radiometric dating of rocks. ---
**Author:** ![davidmich](https://avatars.discourse-cdn.com/v4/letter/d/e56c9b/32.png) [@davidmich](https://boards.straightdope.com/u/davidmich)\ **Post date:** [November 30, 2016, 12:36am UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/17 "2016-11-30T00:36:55Z")
> [@DrCube](#): > > It was neither. It is another law entirely. In fact, the equation by itself isn’t all that influential, it’s more a succinct illustration of the sort of thing Einstein’s relativity implies. > > That’s not really how it works. Mass has energy and energy has mass, but they don’t “convert” back and forth. Thanks Dr. Cube. Why do I see the word convert used at all? What would be a better phrasing for what happens between mass and energy? ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [November 30, 2016, 1:23am UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/18 "2016-11-30T01:23:38Z")
In special relativity the conservation of energy, momentum and mass are all linked together and they can all be seen as coming from the translational symmetry of spacetime in special relativity. The mass though that is specifically conserved is the rest mass of an isolated system, which may include, some, all or part of its kinetic energy (depending on the system and the frame). Now, using the usual relativistic definitions, mass and energy are not synonyms in special relativity: mass is invariant (i.e. the same in all frames), whereas energy is frame-dependent (i.e. depends on the frame of the observer). However a portion of the energy of a massive system can always be identified as the mass, so it is not incorrect to see mass as a type of energy. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 30, 2016, 1:29am UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/19 "2016-11-30T01:29:11Z")
You can certainly say that energy is converted between different forms. Just like a battery converts chemical energy to electrical energy, or an engine converts heat energy to kinetic energy, so too can you convert between, say, nuclear binding energy (which is usually accounted as “mass”) to radiant energy (which usually isn’t). ---
**Author:** ![Blue\_Blistering\_Barnacle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/blue_blistering_barnacle/32/3386_2.png) [@Blue\_Blistering\_Barnacle](https://boards.straightdope.com/u/Blue_Blistering_Barnacle)\ **Post date:** [November 30, 2016, 3:31am UTC](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379/20 "2016-11-30T03:31:30Z")
> [@Asympotically\_fat](#): > > In special relativity the conservation of energy, momentum and mass are all linked together and they can all be seen as coming from the translational symmetry of spacetime in special relativity. The mass though that is specifically conserved is the rest mass of an isolated system, which may include, some, all or part of its kinetic energy (depending on the system and the frame). > > Now, using the usual relativistic definitions, mass and energy are not synonyms in special relativity: mass is invariant (i.e. the same in all frames), whereas energy is frame-dependent (i.e. depends on the frame of the observer). However a portion of the energy of a massive system can always be identified as the mass, so it is not incorrect to see mass as a type of energy. Is this a distinction between mass conferred by Higg’s mechanism vs relativistic mass in bound particle systems? Or is this something different? [Next page](https://boards.straightdope.com/t/what-is-the-difference-between-mass-energy-equivalence-theory-law-and-the-conservation-of-energy/773379.md?page=2)