4 ms·

E = mc^2 is the energy contained within a particle of mass m, IF it is at rest (has zero velocity with respect to your frame). If it is moving, it's energy is g

by tanishq 11y ago

E = mc^2 is the energy contained within a particle of mass m, IF it is at rest (has zero velocity with respect to your frame). If it is moving, it's energy is given by E = ymc^2, where y (gamma) is 1/sqrt(1 - v^2/c^2). This may sound like the particle has somehow "gained" or "lost" energy just by switching frames, but so has everything else. The differences in energy have been kept the same, which is all that really matters. When deriving this formula for the energy it becomes clear that _any_ multiple of ymc^2 is conserved. We choose E = ymc^2 and not, say, E = 5ymc^2 because in the Newtonian limit (as speeds approach zero), the ymc^2 formula reduces to the well-known E = 1/2 mv^2, which is the kinetic energy of an object obtained from classical mechanics. I'd really recommend reading a mathematical treatment of special relativity, because you'll be exactly clear on where this formula comes from.

raziel2702 11y ago
I think the answer we want now is a non-mathematical one. It gets tiresome how most of the "answers" are just too afraid( or maybe naive?) to just say "we don't know" why the speed of light is the constant of proportionality in the mass-energy conversion equation. You can answer the "how" very well which is what the mathematical derivation is, and which is what most people are answering in this thread but you see that none of those answers start with "Because..." but rather just keep on spitting out more math. And what we want is an explanation for why c^2 is there and what it means. We don't know what it means, we haven't answered that question and we don't know how to answer it. It's similar to how pi keeps coming up in a lot of equations and we struggle to understand why.
- lumpypua 11y ago
  > I think the answer we want now is a non-mathematical one. I'm just an interested lay person, but my understanding is the past century of physics is a giant argument for trusting the math, and accepting it as explanation. If someone asks "Why does xyz act this way?" then the best answer for it, once you get to non-intuitive quantum scales is: "because the math says so." Dirac's prediction of the existence of antimatter, the Higgs, and pretty much all quantum mechanical behavior are great examples of this. Nima Arkani-Hamed, a kickass theoretical physicist, has a great lecture series on the philosophy of physics: • http://www.cornell.edu/video/nima-arkani-hamed-philosophy-of-fundamental-physics-1 http://www.cornell.edu/video/nima-arkani-hamed-philosophy-of... • http://www.cornell.edu/video/nima-arkani-hamed-philosophy-of-fundamental-physics-2 http://www.cornell.edu/video/nima-arkani-hamed-philosophy-of... In an aside, he mentions that he used to explain the Higgs field with analogies such like calling it a kind of "molasses" slowing down particles and giving them mass. He's stopped doing that, because the physical analogy is really misleading. The true reason the Higgs as we conceive of it exists is that it addresses mathematical issues in our treatment of bosons that have mass. The math said there was an issue. 50 years ago the math said the Higgs fixed it. It took 50 years and construction of the LHC, but now we've verified the existence of the Higgs.

by tanishq 11y ago

raziel2702 11y ago

I think the answer we want now is a non-mathematical one. It gets tiresome how most of the "answers" are just too afraid( or maybe naive?) to just say "we don't know" why the speed of light is the constant of proportionality in the mass-energy conversion equation. You can answer the "how" very well which is what the mathematical derivation is, and which is what most people are answering in this thread but you see that none of those answers start with "Because..." but rather just keep on spitting out more math. And what we want is an explanation for why c^2 is there and what it means. We don't know what it means, we haven't answered that question and we don't know how to answer it. It's similar to how pi keeps coming up in a lot of equations and we struggle to understand why.

lumpypua 11y ago
> I think the answer we want now is a non-mathematical one. I'm just an interested lay person, but my understanding is the past century of physics is a giant argument for trusting the math, and accepting it as explanation. If someone asks "Why does xyz act this way?" then the best answer for it, once you get to non-intuitive quantum scales is: "because the math says so." Dirac's prediction of the existence of antimatter, the Higgs, and pretty much all quantum mechanical behavior are great examples of this. Nima Arkani-Hamed, a kickass theoretical physicist, has a great lecture series on the philosophy of physics: • http://www.cornell.edu/video/nima-arkani-hamed-philosophy-of-fundamental-physics-1 http://www.cornell.edu/video/nima-arkani-hamed-philosophy-of... • http://www.cornell.edu/video/nima-arkani-hamed-philosophy-of-fundamental-physics-2 http://www.cornell.edu/video/nima-arkani-hamed-philosophy-of... In an aside, he mentions that he used to explain the Higgs field with analogies such like calling it a kind of "molasses" slowing down particles and giving them mass. He's stopped doing that, because the physical analogy is really misleading. The true reason the Higgs as we conceive of it exists is that it addresses mathematical issues in our treatment of bosons that have mass. The math said there was an issue. 50 years ago the math said the Higgs fixed it. It took 50 years and construction of the LHC, but now we've verified the existence of the Higgs.