# 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:** 2
**Author:** ![CC](https://avatars.discourse-cdn.com/v4/letter/c/f1d935/32.png) [@CC](https://boards.straightdope.com/u/CC)\ **Post date:** [April 1, 2014, 10:18pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/21 "2014-04-01T22:18:37Z")
> [@tracer](#): > > Energy is at least understandable. It’s work, that is, a force applied over a distance, hence Force x distance… I think that you need to make a distinction between energy and work. Work, yes, is a force moving through a distance. But energy is more of a capacity to exert a force. Kinetic energy may be gained by exerting a force through a distance, such as lifting up a bowling ball and putting on a shelf. And it may require energy to exert a force. But energy isn’t work, per se. ---
**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 1, 2014, 11:06pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/22 "2014-04-01T23:06:29Z")
Work is just a change in energy (or to be more precise, one form of change of energy). I don’t think that offers much potential for confusion. > [@](#): > > Quoth **tracer** : > > The one unit I have more trouble understanding is Entropy. I know what it means (the disorderliness of a system), but the units of entropy work out to “Joules per Kelvin”. I have trouble turning Joules-per-Kelvin into disorderliness in my head. That’s really just a historical accident, resulting from the fact that thermodynamics was the first field where we studied entropy. The actual quantity of interest is the thing that we call entropy, divided by Boltzmann’s constant (which also has units of joules per kelvin, so the units cancel out). What’s left is a dimensionless quantity, or if you prefer, a quantity measured in bits (or other information units). And it’s hopefully a little more intuitive to see a relationship between disorder and information. What’s perhaps not so intuitive is the fact that a system with high disorder has high information, rather than the other way around. The analogy I prefer here is a cabinet full of printers’ movable type. When all the A pieces are in one little drawer, and all the B pieces are in another little drawer right next to it, and so on for C through Z, the system is very highly ordered, but it also has no information content. Jumble all the pieces up, though, and they could end up spelling out absolutely anything: That’s a lot of information. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [April 2, 2014, 6:36pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/23 "2014-04-02T18:36:50Z")
> [@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. The analogy I prefer here is a cabinet full of printers’ movable type. When all the A pieces are in one little drawer, and all the B pieces are in another little drawer right next to it, and so on for C through Z, the system is very highly ordered, but it also has no information content. **Jumble all the pieces up, though, and they could end up spelling out absolutely anything: That’s a lot of information.** Definitely not so intuitive. I don’t see that there’s any information in a bunch of parts jumbled up randomly, even if it “just so happens” to spell out a line of Shakespeare. To extract any information from that, you would have to have an _á priori_ knowledge of what a line of Shakespeare looks like, just in order to recognize it – that is, the information content is already in your head, and not in the words that got spelled out. To contain any information, the line would have to tell you something that you might not already know. Some jumbled text that “could end up spelling out absolutely anything” doesn’t do that. (Unless you believe it’s your dear departed great-grandmother sending you a message from the other side.) ---
**Author:** ![lawbuff](https://avatars.discourse-cdn.com/v4/letter/l/13edae/32.png) [@lawbuff](https://boards.straightdope.com/u/lawbuff)\ **Post date:** [April 2, 2014, 7:36pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/24 "2014-04-02T19:36:37Z")
> [@BrightNShiny](#): > > To clarify for you, that doesn’t answer his question at all. Boy. To clarify again, since you can’t decipher plain language, the OP asked; > [@](#): > > But what does a mass meter squared per second squared mean? 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! ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [April 2, 2014, 8:33pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/25 "2014-04-02T20:33:52Z")
> [@lawbuff](#): > > Engy = mass x speed of light in a volume/vaccum squared. I’m still trying to figure out how you divide the speed of light in a volume by the square of the vacuum. ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [April 2, 2014, 9:20pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/26 "2014-04-02T21:20:11Z")
> [@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! It’s you who is not understanding the question. Assuming we are using SI units, then of course metres are in the equation, because c represents the _speed_ of light, and speed is measured in _metres per second_. So we have the mass, in kilograms, multiplied by the speed, in metres per second, squared. If you multiply that up then your energy term comes out in kg m[sup]2[/sup] s[sup]-2[/sup], which just so happens to be joules. Of course, if you wanted to you could specify the mass in ounces and the speed in miles per hour, but then you’d have to apply conversion factors in order to get the energy term to have the units you wanted: foot-pounds, say. SI units make these things a lot easier. ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [April 2, 2014, 9:32pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/27 "2014-04-02T21:32:54Z")
To expand on the above, it’s basically dimensional analysis. If you look at the units of what you are multiplying and dividing then you can work out what kind of quantity you have ended up with. To take a very simple example, it’s easy to tell that if you divide work, or energy (in kg m[sup]2[/sup] s[sup]-2[/sup], that is, joules) by distance (in m) then you get force (in kg m s[sup]-2[/sup], that is, newtons). And of course that makes sense because we know that work = force x distance. Similarly, you can express your car’s fuel consumption in [square metres](https://what-if.xkcd.com/11/). 🙂 Seems odd at first, but you’re just dividing a volume (of fuel used) by a distance (travelled by your car), so it stands to reason that you end up with an area. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [April 2, 2014, 9:34pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/28 "2014-04-02T21:34:43Z")
> [@Senegoid](#): > > Definitely not so intuitive. I don’t see that there’s any information in a bunch of parts jumbled up randomly… Two additional ways of thinking about this: - Imagine the neatly arranged letters getting scrambled around by a rambunctious toddler. If you look at the resulting jumbled situation, there is all sorts of information in front of you. Information on how exactly the toddler struck the trays, and when, and with what force… information on exactly how _that_ letter _Q_ hit the ground and bounced around. Such information isn’t all that interesting, and it may be hard to extract, but it’s there. - You can also think about how much information it takes to describe the system. If you wanted to write down instructions that could be used to reproduce the jumbled situation, you’d be writing things like, “A letter _H_ tile is positioned 32.3 inches to the east and 4.6 inches to the north of our reference point. The tile is face-up and it is rotated 130.8 degrees from north. Okay, now another letter _H_ tile is positioned…” There’s a lot of information packed into the pattern! It’s not terribly useful, but it’s there.\* ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [April 2, 2014, 9:48pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/29 "2014-04-02T21:48:53Z")
> [@Pasta](#): > > - You can also think about how much information it takes to describe the system. If you wanted to write down instructions that could be used to reproduce the jumbled situation, you’d be writing things like, “A letter _H_ tile is positioned 32.3 inches to the east and 4.6 inches to the north of our reference point. The tile is face-up and it is rotated 130.8 degrees from north. Okay, now another letter _H_ tile is positioned…” There’s a lot of information packed into the pattern! It’s not terribly useful, but it’s there.\* Yes, I think the key, which I dimly remember from my Further Maths A-level class, is the _compressibility_ of the information. If you have, say, the following set-up. with all the letters nicely grouped: **AAAAAAAAAAAAAAABBBBBBBBBCCCCCCCCCCCDDDDDDDDDEEEEEEEEEEEEEEEEEEEE…** then you can represent that as: **15A, 9B, 11C, 9D, 20E…** Whereas if you have them all jumbled up: **JYJRFGOEJNDDOTKLEAMCWHDRTTGEKUQSGDRHTHHUIUEJNJMFCSEWPKITWCNMDQSS…** then you can’t really compress it usefully. Therefore, the second grouping contains more information, because the simplest possible way of representing it is bigger than the simplest possible way of representing the first grouping. ---
**Author:** ![ThisUsernameIsForbidden](https://avatars.discourse-cdn.com/v4/letter/t/b4bc9f/32.png) [@ThisUsernameIsForbidden](https://boards.straightdope.com/u/ThisUsernameIsForbidden)\ **Post date:** [April 2, 2014, 10:07pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/30 "2014-04-02T22:07:11Z")
It takes more _particulate_ information to describe one system than the other, but that implies nothing about the quality of the information. If you broke everything down to the same particulate level, you would have the same quantity of information. I guess calling it “information” in the first place is something of a misnomer, since we expect it to be _informative._ To my mind, if you can explain a system more simply that gives you the same amount of information as if you were explaining it in an esoteric way that takes more time. ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [April 2, 2014, 10:14pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/31 "2014-04-02T22:14:04Z")
[This might be a bit more than the OP asked for, but this document shows how to derive E = mc² from the geometry of space-time.](http://www.av8n.com/physics/spacetime-welcome.htm) It goes on to do a lot more beyond that, because that’s a fairly trivial consequence, but it’s an important part of understanding where all this comes from. ---
**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 2, 2014, 10:20pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/32 "2014-04-02T22:20:01Z")
It’s not that a sequence of letters _does_ spell out any particular message. It’s that a sequence of letters _can_ spell out _any message at all_. Including, of course, a great many nonsensical messages. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [April 2, 2014, 10:37pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/33 "2014-04-02T22:37:00Z")
> [@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! The OP is asking for the units - energy mass and speed are not units. Joules, Kilograms and metres per second are units. ---
**Author:** ![hibernicus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hibernicus/32/2802_2.png) [@hibernicus](https://boards.straightdope.com/u/hibernicus)\ **Post date:** [April 2, 2014, 10:43pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/34 "2014-04-02T22:43:00Z")
> [@tracer](#): > > Energy is at least understandable. It’s work, that is, a force applied over a distance, hence Force x distance. > > The one unit I have more trouble understanding is Entropy. I know what it means (the disorderliness of a system), but the units of entropy work out to “Joules per Kelvin”. I have trouble turning Joules-per-Kelvin into disorderliness in my head. There is a related (and complementary) concept called “free energy” or “available energy” which may help to understand entropy in the thermodynamic sense. If you take the total internal energy of a system, only some of it is available to do work. The unavailable remainder is (entropy x temperature). So the reason entropy has units of J/K is that it is the ratio of the unavailable energy of the system to the temperature of the system. The increase in entropy associated with any real-world process is equivalent to a reduction in available energy and an increase in unavailable energy. ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [April 2, 2014, 10:45pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/35 "2014-04-02T22:45:36Z")
> [@Chronos](#): > > It’s not that a sequence of letters _does_ spell out any particular message. It’s that a sequence of letters _can_ spell out _any message at all_. Including, of course, a great many nonsensical messages. And of course a sequence of letters where all the letters of a given type are grouped together, as in my AAAAAAAAAAAAAAABBBBBBBBB… example above, can spell a lot fewer possible messages than one in which the letters are all mixed up. ---
**Author:** ![ThisUsernameIsForbidden](https://avatars.discourse-cdn.com/v4/letter/t/b4bc9f/32.png) [@ThisUsernameIsForbidden](https://boards.straightdope.com/u/ThisUsernameIsForbidden)\ **Post date:** [April 2, 2014, 10:49pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/36 "2014-04-02T22:49:13Z")
> [@Colophon](#): > > And of course a sequence of letters where all the letters of a given type are grouped together, as in my AAAAAAAAAAAAAAABBBBBBBBB… example above, can spell a lot fewer possible messages than one in which the letters are all mixed up. How so? Really, I’m trying to figure this out. ---
**Author:** ![zombywoof](https://avatars.discourse-cdn.com/v4/letter/z/9e8a1a/32.png) [@zombywoof](https://boards.straightdope.com/u/zombywoof)\ **Post date:** [April 2, 2014, 11:10pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/37 "2014-04-02T23:10:19Z")
> [@ThisUsernameIsForbidden](#): > > How so? Really, I’m trying to figure this out. Consider: AABB vs AABB ABAB ABBA BAAB BABA BBAA ---
**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 2, 2014, 11:14pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/38 "2014-04-02T23:14:23Z")
Wow, **Derleth** , that page you linked is an excellent textbook on special relativity. What’s it doing on an aviation website? ---
**Author:** ![Cartoonacy](https://avatars.discourse-cdn.com/v4/letter/c/848f3c/32.png) [@Cartoonacy](https://boards.straightdope.com/u/Cartoonacy)\ **Post date:** [April 2, 2014, 11:18pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/39 "2014-04-02T23:18:49Z")
More specifically, if you select four \*sequential \*letters from the string, there are only 5 possible combinations you can have: AAAA AAAB AABB ABBB BBBB But if you take four \*random \*letters from the string, there are 16 possibilities: AAAA AAAB AABA AABB ABAA ABAB ABBA ABBB BAAA BAAB BABA BABB BBAA BBAB BBBA BBBB ---
**Author:** ![ThisUsernameIsForbidden](https://avatars.discourse-cdn.com/v4/letter/t/b4bc9f/32.png) [@ThisUsernameIsForbidden](https://boards.straightdope.com/u/ThisUsernameIsForbidden)\ **Post date:** [April 2, 2014, 11:44pm UTC](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104/40 "2014-04-02T23:44:11Z")
Ok, so let’s say I have a string: AAAAAAAA No matter whether I choose 4 letters randomly or sequentially, there is only one unique sequence. So that’s the trivial case. Let’s say the string is: ABCDEFG You can obviously get more combinations that are unique no matter how you pick them (as long as you cannot choose the same letter 4 times). So I get that, but what I’m thinking is that each string has a specific letter in a specific location in the string. It takes up the same number of bits. So it must convey the same amount of information. If you randomly select 4 letters from the first string, twice, and you randomly select 4 letters from the second string, twice, your resultant strings take up the same number of bits. Granted, the difference is uniqueness, not amount of information. Unless number of bits doesn’t equate to amount of information. [Previous page](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104.md?page=1) [Next page](https://boards.straightdope.com/t/what-do-the-units-of-energy-measurement-mean-in-e-mc-2/685104.md?page=3)