luc Posted June 8, 2005 Share Posted June 8, 2005 Right now I'm reading Hawking's "The large scale-structure of space time", and he uses constantly a quantity called Energy-momentum, though I can't see it defined anywhere. I've also read in some forum that in GR, total energy is not conserved, but energy-momentum is conserved. I think that perhaps energy-momentum is (Total energy + magnitude of 4-momentum), but I'm not sure. What exactly is energy-momentum? Link to comment Share on other sites More sharing options...
swansont Posted June 8, 2005 Share Posted June 8, 2005 There's an energy-momentum 4-vector, comprised of E and the three spatial components of pc. The scalar product with itself gives you E2 - p2c2, which is the square of the rest energy. Link to comment Share on other sites More sharing options...
luc Posted June 8, 2005 Author Share Posted June 8, 2005 'kay, but I think that 4-momentum is the same as the energy-momentum 4-vector (at least is Special Relativity is that way). So energy-momentum is the magnitude of the energy-momentum 4-vector, is that what you're saying? Link to comment Share on other sites More sharing options...
swansont Posted June 8, 2005 Share Posted June 8, 2005 'kay, but I think that 4-momentum is the same as the energy-momentum 4-vector (at least is Special Relativity is that way). So energy-momentum is the magnitude of the energy-momentum 4-vector, is that what you're saying? I haven't read the book, so I can't say for sure. IN GR there is also an energy-momentum tensor, aka the stress-energy tensor. Link to comment Share on other sites More sharing options...
□h=-16πT Posted June 8, 2005 Share Posted June 8, 2005 'kay, but I think that 4-momentum is the same as the energy-momentum 4-vector (at least is Special Relativity is that way). The energy-momentum four-vector is the same as the 4-momentum vector. The 4-momentum vector has as its time component the energy of the frame and so gets its other name "energy-momentum" four-vector. Link to comment Share on other sites More sharing options...
Tom Mattson Posted June 8, 2005 Share Posted June 8, 2005 'kay' date=' but I think that 4-momentum is the same as the energy-momentum 4-vector (at least is Special Relativity is that way). [/quote'] That's right. So energy-momentum is the magnitude of the energy-momentum 4-vector, is that what you're saying? That's not right. The norm of a particle's 4-momentum is the mass of the particle. [math] p^{\mu}=(E,\mathbf{p}) [/math] [math] p_{\mu}=(E,-\mathbf{p}) [/math] Taking their inner product yields: [math] p^{\mu}p_{\mu}=E^2-p^2=m^2 [/math] where [math]p[/math] is the norm of the 3-momentum. Link to comment Share on other sites More sharing options...
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