# What do the units of energy measurement mean in E=mc^2? **URL:** \ **Category:** Factual Questions\ **Created:** [April 1, 2014, 6:11pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104 "2014-04-01T18:11:54Z")\ **Posts on this page:** 20\ **Page:** 3
**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:** [April 3, 2014, 12:13am UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/41 "2014-04-03T00:13:35Z")
You’re actually approaching a deeply significant point, there. We speak of two states of the collections of letters: The state where they’re all sorted into nice neat individual trays, and the state where they’re all jumbled up every which way. The jumbled-up one contains more information, so we say that that’s a higher-entropy state. But those aren’t really both the same sort of specification: In the sorted one, we’ve specified the state completely, but in the jumbled one, we haven’t actually specified it (in fact, this is essential to the concept), but just sort of vaguely described it. Really, entropy isn’t actually a property of the states themselves, but rather a property of the way we describe states. ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [April 3, 2014, 12:25am UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/42 "2014-04-03T00:25:05Z")
> [@Chronos](#): > > Wow, **Derleth** , that page you linked is an excellent textbook on special relativity. What’s it doing on an aviation website? Waiting for the day when we stop fooling around and put [Project-Orion-style nuclear bomb propulsion systems](http://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)) on Cessnas? [John Denker, the site’s proprietor and the author of that page, has a whole lot of other pages on physics.](http://www.av8n.com/physics/) I actually first came to it through his [wonderful introduction to Clifford Algebra](http://www.av8n.com/physics/clifford-intro.htm), which is an interesting way to join algebra and geometry; in particular, it contains complex numbers and quaternions as sub-algebras, replaces cross products (which only work in some dimensionalities) with wedge products (which work more generally), and allows us to state the Maxwell equations in one equation. It might work as a floor wax and a dessert topping, too, I don’t know. [He also wrote this nice little basic piece on the expansion of the Universe and some ideas connected with it](http://www.av8n.com/physics/expansion-of-the-universe.htm) and [this more complex piece about doing thermodynamics with differential forms.](http://www.av8n.com/physics/thermo-forms.htm) ---
**Author:** ![JWT\_Kottekoe](https://avatars.discourse-cdn.com/v4/letter/j/3ec8ea/32.png) [@JWT\_Kottekoe](https://boards.straightdope.com/u/JWT_Kottekoe)\ **Post date:** [April 3, 2014, 1:53am UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/43 "2014-04-03T01:53:32Z")
John Denker’s web site on the [physics of flight](http://www.av8n.com/how/) is by far the best thing I’ve ever read on the subject. ---
**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:** [April 3, 2014, 2:09am UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/44 "2014-04-03T02:09:40Z")
Well, yeah, but that’s something I’d expect on an aviation website. ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [April 3, 2014, 2:31am UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/45 "2014-04-03T02:31:32Z")
> [@ThisUsernameIsForbidden](#): > > How so? Really, I’m trying to figure this out. Because the case where all the As have to be together, all the Bs have to be together and so on is functionally no different from just having one of each letter. The block of As counts as one object, and so on. However many letters you have in total, you can only arrange them in 26! ways, just as you could if you only had 26 letters, one of each. Eg you could have FFFFFFFFTTTTTTTTDDDDDOOOOOOOOOO… or HHHHHHHHHJJJJJJWWWWWWEEEEEEEEEEEETTTTTTTTTT… but you couldn’t have KVEJSGOJSHSIGIWERCOOSFAWWSLKO… or ITWASADARKANDSTORMYNIGHTTHERAINFELL… (Waiting for someone to tell me I’m off with my 26! above. I always get permutations and combinations muddled) ---
**Author:** ![JWT\_Kottekoe](https://avatars.discourse-cdn.com/v4/letter/j/3ec8ea/32.png) [@JWT\_Kottekoe](https://boards.straightdope.com/u/JWT_Kottekoe)\ **Post date:** [April 3, 2014, 2:37am UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/46 "2014-04-03T02:37:42Z")
> [@Chronos](#): > > Well, yeah, but that’s something I’d expect on an aviation website. It’s the web site of a [brilliant physicist](http://www.av8n.com/physics/). His book on flight is just one of the many wonderful things on his site. I don’t know him, but I first came across his work more than 30 years ago and was immediately impressed. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [April 3, 2014, 4:44pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/47 "2014-04-03T16:44:51Z")
> [@JWT\_Kottekoe](#): > > It’s the web site of a [brilliant physicist](http://www.av8n.com/physics/). His book on flight is just one of the many wonderful things on his site. > > I don’t know him, but I first came across his work more than 30 years ago and was immediately impressed. Brilliant site/cite. Thanks. ---
**Author:** ![BrightNShiny](https://avatars.discourse-cdn.com/v4/letter/b/7bcc69/32.png) [@BrightNShiny](https://boards.straightdope.com/u/BrightNShiny)\ **Post date:** [April 4, 2014, 7:36am UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/48 "2014-04-04T07:36:07Z")
> [@lawbuff](#): > > To clarify again, since you can’t decipher plain language, the OP asked; > > I said M = MASS, C is speed of light in a volume squared (exponent of 2) > > There is NO, repeat, no METER as he suggests., the word METER is NOT in the equation. > E = mc2; there is no mass meter squared, it is mass **X** (times) C. > > Now, I if you can’t understand that, too bad! Lol. Multiple posters have explained to you why you didn’t answer the question, but now it’s clear that you don’t really understand the equation either. ---
**Author:** ![rsa](https://avatars.discourse-cdn.com/v4/letter/r/839c29/32.png) [@rsa](https://boards.straightdope.com/u/rsa)\ **Post date:** [April 4, 2014, 11:22pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/49 "2014-04-04T23:22:38Z")
> [@Chronos](#): > > What’s perhaps not so intuitive is the fact that a system with high disorder has high information, rather than the other way around. > [@Chronos](#): > > Really, entropy isn’t actually a property of the states themselves, but rather a property of the way we describe states… Is the confusion many people, including myself, have understanding entropy vis a vis information is that it is conflating two different concepts? I can see that the universe will have more entropy when it is a trillion years old, but I can’t see that it will have more information. That is, entropy is a **property** of the universe a trillion years from now. At that stage perhaps it takes more information to **describe** the universe and perhaps, also, the universe has more **potential** information, but it doesn’t have **the property** of more information. ---
**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:** [April 5, 2014, 1:05am UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/50 "2014-04-05T01:05:31Z")
If it takes more information to describe the Universe, that means that the Universe has more information. ---
**Author:** ![ThisUsernameIsForbidden](https://avatars.discourse-cdn.com/v4/letter/t/b4bc9f/32.png) [@ThisUsernameIsForbidden](https://boards.straightdope.com/u/ThisUsernameIsForbidden)\ **Post date:** [April 5, 2014, 1:38am UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/51 "2014-04-05T01:38:12Z")
What’s the point of saying it has it? ---
**Author:** ![rsa](https://avatars.discourse-cdn.com/v4/letter/r/839c29/32.png) [@rsa](https://boards.straightdope.com/u/rsa)\ **Post date:** [April 5, 2014, 1:38am UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/52 "2014-04-05T01:38:47Z")
Well I did say “perhaps”. I still need a little more explanation so that I can understand. It seems that in the far future I can describe all matter in the universe as in thermal equilibrium, gravitationally non-interacting, and distributed randomly (Cold, Dark, and Empty). The universe is still still expanding according to some mathematical formula. That’s not a lot of information is it? I guess there is more to it than this, but I’ve described a big chunk of the variables with some very simple statements. Also, is entropy only comparing points in time? IOW, the current universe is presumably much more dynamic than the far future universe. Doesn’t that dynamism encode much more information than a static universe? Sorry, this has always confounded me. ---
**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:** [April 5, 2014, 1:57pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/53 "2014-04-05T13:57:08Z")
> [@](#): > > I guess there is more to it than this, but I’ve described a big chunk of the variables with some very simple statements. You’ve summarized the interesting parts of the information. Doing this is a large part of what thermodynamics is all about. But it says less about the information itself than it does about our standards of what we consider “interesting”. ---
**Author:** ![lawbuff](https://avatars.discourse-cdn.com/v4/letter/l/13edae/32.png) [@lawbuff](https://boards.straightdope.com/u/lawbuff)\ **Post date:** [April 5, 2014, 3:58pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/54 "2014-04-05T15:58:13Z")
> [@BrightNShiny](#): > > Lol. Multiple posters have explained to you why you didn’t answer the question, but now it’s clear that you don’t really understand the equation either. He said; > [@](#): > > But what does a mass meter squared per second squared mean? M=Mass; C is speed of light in a volume exponent 2. Since the equation he posted is this, as read online, etc.; E=Mc2 NOT E= (M) (C)2. Mass is NOT multiplied by Speed of light then squared, it is C that is just squared. Example; 3 + 6 x (5 + 4) ÷ 3 - 7 = 3 + 6 x 9 ÷ 3 - 7 Since 5 and 4 are in parentheses, it is 9 /3-7, not starting from 3. Any clearer! ---
**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:** [April 5, 2014, 4:19pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/55 "2014-04-05T16:19:43Z")
Yes, we know what he said, and we know what you said, and what you said still has nothing to do with what he said. He knows that m isn’t squared, and never gave any indication that he thought otherwise. What’s the point of what you’re saying? ---
**Author:** ![UTejas](https://avatars.discourse-cdn.com/v4/letter/u/977dab/32.png) [@UTejas](https://boards.straightdope.com/u/UTejas)\ **Post date:** [April 5, 2014, 4:32pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/56 "2014-04-05T16:32:03Z")
> [@lawbuff](#): > > He said; > > M=Mass; C is speed of light in a volume exponent 2. > > Since the equation he posted is this, as read online, etc.; > > E=Mc2 > > NOT > > E= (M) (C)2. > > Mass is NOT multiplied by Speed of light then squared, it is C that is just squared. > > Example; > > 3 + 6 x (5 + 4) ÷ 3 - 7 = 3 + 6 x 9 ÷ 3 - 7 > > Since 5 and 4 are in parentheses, it is 9 /3-7, not starting from 3. > > Any clearer! Really? You think this whole thing was an order of operations thing? There’s no difference between the two things you just wrote. (m)(c)^2 = mc^2 = (m)(c^2). Unless written as (mc)^2, the standard notation implies the exponent acts on the c alone. That’s not the issue at hand here. The question was about UNITS. Specifically, what does it mean to say that some energy unit is equal to a mass unit multiplied by distance squared divided by seconds squared? This units question has been explained very well in this thread. A Joule (an energy unit) is equal to one kilogram \* meter^2 / second ^2. It is not clear why immediately, but the answer is that one can think of a Joule as the energy required (aka the work done) when one applies a force of one kg \*m / s^2 for a distance of one meter. Why is a force in units of kg \* m / s^2? Look at Newton’s second law. F=ma. An acceleration is measured in distance per second per second. ---
**Author:** ![lawbuff](https://avatars.discourse-cdn.com/v4/letter/l/13edae/32.png) [@lawbuff](https://boards.straightdope.com/u/lawbuff)\ **Post date:** [April 5, 2014, 5:56pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/57 "2014-04-05T17:56:34Z")
> [@UTejas](#): > > Really? You think this whole thing was an order of operations thing? There’s no difference between the two things you just wrote. (m)(c)^2 = mc^2 = (m)(c^2). Unless written as (mc)^2, the standard notation implies the exponent acts on the c alone. > > That’s not the issue at hand here. The question was about UNITS. Specifically, what does it mean to say that some energy unit is equal to a mass unit multiplied by distance squared divided by seconds squared? > > This units question has been explained very well in this thread. A Joule (an energy unit) is equal to one kilogram \* meter^2 / second ^2. It is not clear why immediately, but the answer is that one can think of a Joule as the energy required (aka the work done) when one applies a force of one kg \*m / s^2 for a distance of one meter. Why is a force in units of kg \* m / s^2? Look at Newton’s second law. F=ma. An acceleration is measured in distance per second per second. Well Albert, YOU tell us the answer then!! Can YOU tell me what the upside down V means? ---
**Author:** ![lawbuff](https://avatars.discourse-cdn.com/v4/letter/l/13edae/32.png) [@lawbuff](https://boards.straightdope.com/u/lawbuff)\ **Post date:** [April 5, 2014, 6:16pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/58 "2014-04-05T18:16:16Z")
Oh add, Filmore, the OP has not come back to tell that I am misunderstanding it, if he did HE could explain it better, you are interpreting it for him. Brightsunny was a smart aleck in post 8 anyway, soooo… I have no further need in this thread to fight with him or you. ---
**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:** [April 5, 2014, 6:30pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/59 "2014-04-05T18:30:46Z")
> [@lawbuff](#): > > Well Albert, YOU tell us the answer then!! Can YOU tell me what the upside down V means? It means exponentiation and in order of operations it comes before multiplication which is why mc^2 = (m)(c^2) rather than (mc)^2 ---
**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:** [April 5, 2014, 6:34pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/60 "2014-04-05T18:34:01Z")
> [@lawbuff](#): > > Oh add, Filmore, the OP has not come back to tell that I am misunderstanding it, if he did HE could explain it better, you are interpreting it for him. Brightsunny was a smart aleck in post 8 anyway, soooo… > > I have no further need in this thread to fight with him or you. Except that, even if you are unaware of orders of operation (which seems to be the case) also wrote “(mass)(meter^2/second^2)” right next to the sentence you took issue with making their meaning crystal clear, if it wasn’t already. [Previous page](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104.md?page=2) [Next page](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104.md?page=4)