Markus Hanke Posted March 16 Share Posted March 16 4 hours ago, md65536 said: It should be possible to contrive an example where the Newtonian forces are small, and the purely GR aspects dominate and give results that are the exact opposite of what Newtonian gravity predicts. How about an interior metric, such as FLRW - under the right circumstances, the distance between points in such a spacetime will increase over time (metric expansion), whereas under Newton the interior of energy-momentum distributions will always contract, but never expand (assuming there’s no effects other than gravity of course). Or how about something like a gravitational geon - a topological construct that is held together purely by gravitational self-energy, without the presence of any other energy-momentum sources at all? This particular solution relies entirely on GR self-interaction effects - under Newton, a completely empty spacetime without any gravitational sources cannot contain (or maintain) gravity. Any type of radiative spacetime should qualify too, since Newtonian gravity has no radiative degrees of freedom. At most you can have varying gravitational forces, but the oscillations of the force vector would be “longitudinal” (ie in the radial direction) and of a dipole nature, whereas in GR the effects are transverse and quadrupole. Or anything with angular momentum, since Newton can’t model frame dragging effects, and thus will give wrong trajectories for free-falling bodies around rotating objects. You can also give angular momentum to an interior spacetime, and get something like the Gödel metric - it contains a number of peculiar effects that I don’t think Newton would be able to replicate, and certainly not based on just invariant mass. 5 hours ago, md65536 said: The energy of the beams is frame-dependent, and as total momentum approaches zero, so does the energy. I’m not so sure about this - the energies and momenta are certainly frame-dependent, but their sums should never cancel. Since E=hf, there is no physically realisable frame in which either beam is seen to have f=0 by the other beam, so I think you will always get a non-vanishing net energy of each beam with respect to the other. So I think in Newton, the beams should always attract according to an inverse-square law, irrespective of their relative direction of motion. Note that what we are asking about is the attraction between the beams (ie of each beam to the other), not how an external test-particle is attracted to the two-beam system as a whole (which would involve the system’s invariant mass in Newtonian gravity). Link to comment Share on other sites More sharing options...
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