# Help me understand E=MC2 **URL:** \ **Category:** Factual Questions\ **Created:** [August 3, 2001, 12:56pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760 "2001-08-03T12:56:06Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Aghris](https://avatars.discourse-cdn.com/v4/letter/a/ecccb3/32.png) [@Aghris](https://boards.straightdope.com/u/Aghris)\ **Post date:** [August 3, 2001, 12:56pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/1 "2001-08-03T12:56:06Z")
OK, I’m not a physicist, but I’m usually very interested in things like this. However, I can’t get my head around the following. Please bear with me: Given 1: Nothing can exceed the speed of light. The more an object approaces _c_, the heavier it gets, therefore needing more energie to accelerate, etc., etc… all the way to infinity. Given 2: Only light (and other EM radiation) can reach _c_, since this radiation doesn’t have mass. But it has energy though. Given 3: Mass and energy are basically the same, in a ratio of E=MC[sup]2[/sup], the famous equation of Albert Einstein. Now please explain: Light does not have mass, but does have energy. How can this be, since this energy, devided by c[sup]2[/sup], will result in a tiny fraction of mass. But if light even has this tiny fraction of mass, it will be infinitely large when the photon reaches lightspeed. Paradox, but I guess that rather than the physics being flawed, there’s an error in my train of thoughts somewhere. ---
**Author:** ![bryanmcc](https://avatars.discourse-cdn.com/v4/letter/b/eada6e/32.png) [@bryanmcc](https://boards.straightdope.com/u/bryanmcc)\ **Post date:** [August 3, 2001, 1:02pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/2 "2001-08-03T13:02:56Z")
E=mc^2 is a formula for interconversion of mass and energy. Just because i have 80kg of mass doesn’t mean that I am currently composed of umpteen bazillion joules of energy. It is, however, possible to **convert** my 80kg of mass into energy (theoretically, anyway). And it is possible to convert your happy little photon into a tiny fraction of mass. It just so happens that wiled it is a photon, it’s pure energy. Hope that helps. -b ---
**Author:** ![Phobos](https://avatars.discourse-cdn.com/v4/letter/p/3d9bf3/32.png) [@Phobos](https://boards.straightdope.com/u/Phobos)\ **Post date:** [August 3, 2001, 1:31pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/3 "2001-08-03T13:31:49Z")
Perhaps the confusion lies in that there is a difference between “regular” (or “rest”) mass and relativistic mass. FWIW, a photon is believed to have zero rest mass. Is there a physicist in the house? (silly question) ---
**Author:** ![bryanmcc](https://avatars.discourse-cdn.com/v4/letter/b/eada6e/32.png) [@bryanmcc](https://boards.straightdope.com/u/bryanmcc)\ **Post date:** [August 3, 2001, 1:44pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/4 "2001-08-03T13:44:32Z")
**Phobos** : I thought photons had zero mass while moving at c, but _did_ have rest mass? -b ---
**Author:** ![Phobos](https://avatars.discourse-cdn.com/v4/letter/p/3d9bf3/32.png) [@Phobos](https://boards.straightdope.com/u/Phobos)\ **Post date:** [August 3, 2001, 1:47pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/5 "2001-08-03T13:47:50Z")
I’ll just retract my comment about “relativistic mass” and offer this [link about the mass of light](http://math.ucr.edu/home/baez/physics/light_mass.html) instead. Hope it helps. I’m not 100% clear on this topic. ---
**Author:** ![Tripler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripler/32/21807_2.png) [@Tripler](https://boards.straightdope.com/u/Tripler)\ **Post date:** [August 3, 2001, 1:49pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/6 "2001-08-03T13:49:25Z")
> [@](#): > > \*Originally posted by Aghris \* > \*\*Now please explain: Light does not have mass, but does have energy. How can this be, since this energy, devided by c[sup]2[/sup], will result in a tiny fraction of mass. \*\* Take it a step back: Light is not what makes the energy, light _is_ the energy. What makes light is the shift of electrons. When an electron drops from one higher valence level to a lower one, there is energy released (imagine the potential energy is released) in the form of a photon. This photon can be released on any wavelength, but in order for us to see it, it has to be in the spectrum of visible light. . . Sorta like the electron falling down a flight of stairs, then yelling in pain. Except he can’t scream, he just yells out photons. At least, that’s how I remember it from college. . . Tripler I’m not a physicist, but I play one on TV. ---
**Author:** ![Aghris](https://avatars.discourse-cdn.com/v4/letter/a/ecccb3/32.png) [@Aghris](https://boards.straightdope.com/u/Aghris)\ **Post date:** [August 3, 2001, 1:58pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/7 "2001-08-03T13:58:14Z")
Thanks guys. I forgot to say in my OP: “Please use small words.” Although I can grasp the theory behind things (most of the time), I have some difficulty with the technobabble. Still, I’m confused. **bryanmcc** explained to me what I had come up myself only seconds after I hit ‘post’, but now the link that **Phobos** provided says that I’m at least partially right in my suspicions. Huh? ---
**Author:** ![Quercus](https://avatars.discourse-cdn.com/v4/letter/q/7ab992/32.png) [@Quercus](https://boards.straightdope.com/u/Quercus)\ **Post date:** [August 3, 2001, 3:32pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/8 "2001-08-03T15:32:03Z")
OK, here’s a shot an explaining it without big words or math (which I’d probably screw up anyway, being too many years away from my last physics class) Well, I put in an equation, but you can skip it. Think of it this way: A moving particle’s energy includes its rest mass energy (for a classical particle, think of it as the energy you need to create the particle in the first place), and its momentum energy (in classical physics, momentum is mass times velocity; this is the energy you need to speed it up). In fact, with p= momentum =mv you can rewrite E=mc2 to be E2/c2 = m(0)2\*c2 + p2 Where m(0) is rest mass. All those 2’s are supposed to be squared signs, by the way. Photons, it turns out, do have momentum, despite having no rest mass. This is one of the places where Newtonian physics just stops working, and you have to accept that’s the way things are. As they have real momentum, photons have energy, even though they don’t have any rest mass (Their energy is related to their wavelength, as Einstein’s first big success explained, but that’s another story). If you want more equations and derivations, a quick search found this site: [http://www.taylormade.com.au/billspages/relativity/relativity3.html](http://www.taylormade.com.au/billspages/relativity/relativity3.html) which goes through them all (if without a lot of explanation). Phobos’s link looks good, too. ---
**Author:** ![g8rguy](https://avatars.discourse-cdn.com/v4/letter/g/7cd45c/32.png) [@g8rguy](https://boards.straightdope.com/u/g8rguy)\ **Post date:** [August 3, 2001, 3:47pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/9 "2001-08-03T15:47:11Z")
The difference is basically one of terminology. When physicists discuss mass these days, they mean rest mass. As things are accelerated, their energy increases, but we don’t think of it as being an increase in the mass. That being said, from a modern viewpoint, the explanation is this: The famous E=mc[sup]2[/sup] is really just a special case of the more correct equation E[sup]2[/sup] = p[sup]2[/sup] c[sup]2[/sup] + m[sup]2[/sup] c[sup]4[/sup]. For an object with zero momentum (p=0), you get the original equation; it tells you the energy in the object’s rest mass. We would call it incorrect to apply that equation to a moving object, such as a photon (in a vacuum, a photon ALWAYS moves at speed c). Or, in preview, what **Quercus** said. ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [August 3, 2001, 3:54pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/10 "2001-08-03T15:54:11Z")
Any object having a non zero rest mass cannot have a velocity equal to the speed of light. (Strangely special relativity does _not_ say that \* “nothing can exceed the speed of light” \* i.e. tachyons) Light (photons) do not have a rest mass and therefore \* must\* travel at c in order to have energy. Einstein’s relativistically correct equation is actually E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] +p[sup]2[/sup] c[sup]2[/sup] where m = rest mass and p = momentum). This says that the energy of a photon is due to its momentum - not its rest mass - and that its rest mass equals 0. ---
**Author:** ![Tripler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripler/32/21807_2.png) [@Tripler](https://boards.straightdope.com/u/Tripler)\ **Post date:** [August 3, 2001, 5:14pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/11 "2001-08-03T17:14:27Z")
> [@](#): > > \*Originally posted by Quercus \* > \*\*This is one of the places where Newtonian physics just stops working, and you have to accept that’s the way things are. \*\* That’s an awesome sig line. . . Tripler I’m going to use it in my office somewhere 😃 ---
**Author:** ![b-side](https://avatars.discourse-cdn.com/v4/letter/b/90ced4/32.png) [@b-side](https://boards.straightdope.com/u/b-side)\ **Post date:** [August 3, 2001, 8:04pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/12 "2001-08-03T20:04:19Z")
Go to [http://www.davidbodanis.com](http://www.davidbodanis.com) The author gives attention to some physics on the site, but more for information on his book, which is billed as a biography of that oh-so-famous equation. I found it a good read for someone who barely got through Calc II in college - it’s sort of a ‘Physics for Poets’ approach. ---
**Author:** ![Aghris](https://avatars.discourse-cdn.com/v4/letter/a/ecccb3/32.png) [@Aghris](https://boards.straightdope.com/u/Aghris)\ **Post date:** [August 3, 2001, 10:02pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/13 "2001-08-03T22:02:13Z")
So, in short, what people are saying here is that photons indeed don’t have mass, but still become heavier when they travel at the speed of light (which they always do) and therefore do have some mass as things that move at speed of light become heavier? (there, try saying that in one breath ;)) If that is the case, is their relativistc mass in water (when light does slow down a bit) actually lower? (If things have more mass when they approach c, then the opposite must be true as well, right?) Sorry of I come across as a dim bulb, but this stuff interests me even though I probably can never grasp the full implications of things. Thanks for all the effort though. I appreceate it. (And I actually understood some of the equations) ---
**Author:** ![barbitu8](https://avatars.discourse-cdn.com/v4/letter/b/839c29/32.png) [@barbitu8](https://boards.straightdope.com/u/barbitu8)\ **Post date:** [August 3, 2001, 10:10pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/14 "2001-08-03T22:10:23Z")
> [@](#): > > \*Originally posted by Ring \* > \*\*(Strangely special relativity does _not_ say that \* “nothing can exceed the speed of light” \* i.e. tachyons) \*\* I’m not well versed in physics, but I’ve always been under the apprehension that nothing can be acclerated faster than the speed of light, not that nothing can exceed the speed of light. The theory is that tachyons existed at the birth of the Universe and have always traveled faster than C. ---
**Author:** ![g8rguy](https://avatars.discourse-cdn.com/v4/letter/g/7cd45c/32.png) [@g8rguy](https://boards.straightdope.com/u/g8rguy)\ **Post date:** [August 3, 2001, 10:44pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/15 "2001-08-03T22:44:09Z")
First off, **barbitu8** is correct in noting that relativity tells us that nothing can be accelerated even up to the speed of light. As I recall, it’s also true that a tachyon can’t be decelerated below the speed of light. Strictly speaking, if you could come up with a mechanism, there’s nothing to prevent creating more tachyons. > [@](#): > > So, in short, what people are saying here is that photons indeed don’t have mass, but still become heavier when they travel at the speed of light (which they always do) and therefore do have some mass as things that move at speed of light become heavier? No, what we’re saying is that photons never have mass in the sense that physicists mean. They have energy and momentum, but not mass. You could try to say that because photons have energy, and E=mc[sup]2[/sup] that photons have some odd sort of effective mass, but that’s not really the way to think about; you’re misapplying the equation. > [@](#): > > If things have more mass when they approach c, then the opposite must be true as well, right? Well, hmm… Things don’t really have more **mass** as they approach c, they have more **energy**. Mass is **a** form of energy, but not the only form. An electron always has mass-energy 0.511 MeV; it could get moving very very very fast and have basically as much energy as you wanted, but the mass-energy would STILL be 0.511 MeV. A photon always has mass-energy of 0, but it can have as much total energy as you want. ---
**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:** [August 3, 2001, 10:48pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/16 "2001-08-03T22:48:14Z")
Photons never approach c; any individual photon is always travelling at exactly c, nor more nor less. In a material other than vacuum, however (such as water), the average speed can be considerably lower. What’s happening here is that a photon is travelling a short distance between molecules at exactly c, and then gets absorbed by a molecule. A very short time later, it’s re-emitted, in the same direction (strictly speaking, you can’t say if it’s the same one, but it looks just like it). In other words, it always satisfies Einstein’s equation while it exists, but sometimes it doesn’t exist. ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [August 4, 2001, 3:08am UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/17 "2001-08-04T03:08:53Z")
The concept of relativistic mass is not wrong it’s just very misleading. When physicists speak of mass they are referring to rest mass, which is an invariant, whereas relativistic mass depends on the observer’s frame of reference. It also means that mass would be a vector rather than scalar quantity. In other words it would have a direction as well as a magnitude. A particle would have one mass component in the longitudinal direction and a different one in the transverse direction. If relativistic mass was the same animal as rest mass you could collapse a neutron star to a black hole simply by moving past it with a high enough velocity. Having said that it seems the term does have its uses when trying to explain some physical effects. ---
**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:** [August 4, 2001, 6:03pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/18 "2001-08-04T18:03:34Z")
> [@](#): > > Having said that it seems the term does have its uses when trying to explain some physical effects. There’s usually better ways to explain thos effects, though. If you’re talking about how energy goes to infinity as speed goes to c, then just say energy, not mass. If you’re discussing momentum, then instead of changing the mass around, you can introduce the proper velocity, which has the added advantage of generalizing easily to four dimensions. That is, 3-momentum is equal to (invariant) mass times 3-proper velocity, and 4-momentum is equal to mass times 4-proper velocity. ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [August 4, 2001, 10:14pm UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/19 "2001-08-04T22:14:34Z")
If you’re on an airplane (a very fast one) and you’re traveling at a velocity of dx/dt with respect to the ground, then your proper velocity is dx/dtau where tau is your proper time. I can see that PV easily transforms, and that it is the spatial part of a four vector, but I don’t see what its physical significance is. What does it represent that you on the plane would be concerned about? Or do I have this whole concept screwed up in my pea brain? ---
**Author:** ![Drake\_Christensen](https://avatars.discourse-cdn.com/v4/letter/d/96bed5/32.png) [@Drake\_Christensen](https://boards.straightdope.com/u/Drake_Christensen)\ **Post date:** [August 5, 2001, 8:24am UTC](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760/20 "2001-08-05T08:24:43Z")
I vaguely remember reading years ago that there was an experiment that recorded some sort of light effect from tachyons. I thought it had something to do with taking advantage of light’s reduced speed in most mediums. But Chronos’ reply doesn’t jibe with that very well. I just did a Google search on “tachyons physics glossary” and the first few hits said nobody as ever detected tachyons experimentally. [Next page](https://boards.straightdope.com/t/help-me-understand-e-mc2/74760.md?page=2)