View Question
 Question
 Subject: Einstein's Formula Category: Miscellaneous Asked by: buddy12349-ga List Price: \$25.00 Posted: 14 Apr 2005 14:28 PDT Expires: 14 May 2005 14:28 PDT Question ID: 509349
 ```In most equations, the factors have meaning. eg. Momentum = Mass * Velocity. So in Einstein's e=m*c^2, I get that e=energy, m=mass and that c=speed of light, but how/why does the speed of light get involved here (other than to have a big number)?``` Request for Question Clarification by welte-ga on 14 Apr 2005 15:40 PDT ```Hi Buddy12349, Have you looked at this Google Answer thread? http://answers.google.com/answers/threadview?id=477866 -welte-ga```
 ```Hello and thank you for your question. The best explanation that I've seen on the Web of how the speed of light gets into the formula is at Mass Energy Equivalence http://www.geocities.com/physics_world/sr/mass_energy_equiv.htm The algebra on that page gets a little confusing, but thankfully there's no calculus! Because Einstein used photons as an example of a body having a certain amount of mass and a certain amount of energy, and given that photons travel at the speed of light, his formula ended up with 'c' in it, and in fact c^2 The photon example turns out to yield a formula that's true for all matter, even matter standing still, and the c^2 stays in that formula too. Let me try to talk you through the calculation that's explained on that page. Einstein knew (because he had figured it out but actual experiments prove it to be so) that the the energy of a photon of light is a fixed multiple of its frequency. E = h * [greek letter 'mu'] The constant multiplier 'h' is called Planck's constant, and 'mu' is the frequency of the light [it looks like the letter 'v' but it isn't velocity, it's frequency]. The name of this principle is the photoelectic effect. So if two photons of frequency v jump off in opposite directions http://www.geocities.com/physics_world/sr/image_gif/sr13-im-01.gif the total energy of the two of them is E = hv + hv However, because of the Doppler effect [like the change in frequency of a train whistle as it moves toward you or away from you] the frequency of one photon is increased, relatively speaking, (call it v+) and the frequency of the other photon is decreased (call it v-). In other words, one photon is emitted in the +x? direction and the other in the -x? direction. The photons have frequencies v+ and v- respectively. The velocity of the body remains unchanged. Due to Doppler shift the photon moving in the +x direction is red shifted and the photon moving in the -x direction is blue shifted. http://www.geocities.com/physics_world/sr/mass_energy_equiv.htm And because of conservation of momentum, and the equal and opposite direction of the two photons, the total momentum is the same as it was before they jumped off. So if the starting condition had momentum zero (that is, we see it standing still at the start), the total momentum remains zero although both photons are now headed away from each other. This is where 'c' gets into the picture, because momentum is mass times velocity, and the velocity of each photon is the speed of light, 'c' The rest of the algebra on that page is pretty hard to follow, but you'll notice that the doppler shift formula [the one that has greek letter beta in it that I have to type here as 'B'] has a fraction ((1-B)/(1+B))^1/2 The ^1/2 in that formula is a square root, and the algebra requires squaring that as part of the solution, and that's how 'c' ends up being squared too. When you get to the end of the algebra, you discover that "if a body emits radiation having an energy E then there is a decrease in the body?s inertial mass in the amount Dm = E/c2. This holds even when the body is at rest. Therefore the mass of a body is related to its energy content [and a] body at rest has a rest energy E0 = m0c^2." ------------------------ Here's a scientific paper that does the actual calculation, not once but twice! Two exact derivations of the mass/energy relationship, E=mc2 http://arxiv.org/pdf/physics/0009062 I don't know if you'll find this paper easier or harder to follow. But here you'll see a relativistic formula that you might have learned in high school physics, the one that has (1-v^2/c^2)^(1/2) which is a measure of how an object's mass increases as its speed increases. This too turns out to tie up with E=mc^2 so at least if you accept the increase in mass formula (which like the photoelectic effect has been experimentally proven) then that also counts as an explanation of how the speed of light gets into the picture. ---------- I'll finish with an item of historical interest. The Past, Present and Future of the Mass Energy Equation E = mc^2 http://www.mrelativity.net/Papers/8/Sharma4.htm "Some scientists believe that Einstein should not be given credit as he has published an unreferenced paper deliberately hiding the previous discoveries and status of E=mc2. The mass-energy inter-conversion holds good universally e.g. in chemical reactions, nuclear reactions, reactions taking place in heavenly bodies and phenomena." Note also the last sentence above about the universality of the mass-energy conversion. That was the topic of the Google Answers question cited by welte-ga, and you'll note in the comments to the other question my consternation that the posted Answer seemed to say that matter doesn't really get changed to energy in a standard chemical reaction. But it does! Search terms used: "why c2" "why c squared" photon shift momentum Fadner, Am. J. Phys. Feb 1988 Thanks again for bringing us your question. If you think I can make this any clearer (although I've really done my best here) you may request clarification. Sincerely, Google Answers Researcher Richard-ga```