Question of the Week / Re: QotW - 21.09.13 - Where does the extra energy go when light is stretched?« on: Yesterday at 17:52:34 »
Excellently put. This was the gist of my post above.Will it make a difference if the change of wavelength is caused by expansion of space, compared to physical movement/velocity difference between transmitter and receiver?1. The receiver just receives radiation. If it gets a frequency of 100 Mhz for that radiation, that is all it cares about. The radiation will be 100 MhZ radiation regradless of how it came to be that frequency. We can redshift radiation in several ways. The receiver doesn't care if it was caused by space expanding or a relative velocity between the source and the receiver.
2. It's natural to suggest that space behaves just like Minkowski space and the source was moving away from us but it just doesn't work well.We seem to disagree on this point. It seems to work well enough if you keep it sufficiently local (where the scalefactor stays reasonably linear). A separation of 2 BLY seems to fall within this 'local' range, with the deviations being minor secondary effects. At larger distances, I agree it falls apart. You go out 7 BLY and suddenly the secondary effects start being significant. The universe expansion was still slowing 7 billion years ago. Out twice that far you start dealing with event horizons that cannot be described with an inertial frame. The secondary effects begin to dominate the primary ones, and the inertial model completely falls apart. I'm not proposing the Minkowski spacetime as a model for the universe at large. That is indeed quite easily falsified.
One of the main points of evidence for this would be the Hubble law. This suggests that the recession speed of distant galaxies can exceed the speed of light.Under the Milne model (which has been falsified), Hubble's law still stands, where Hubbles constant is exactly 1/time at all times. Galaxies don't have velocities greater than light because there are no galaxies further away than a fixed figure. Recession rates in the expanding metric can exceed c, but those rates are expressed as a rapidity, not as a velocity. Rapidity has no upper limit, so in expanding space, the distance between a pair of galaxies can increase at arbitrarily high rates. In the inertial frame, none of these galaxies has a relative velocity greater than c.
I'm saying this not because I support the Milne model, but because Hubble's law is not in fact evidence for expanding space. The acceleration is. You can't have that in flat space. Deceleration either for that matter since the symmetry must be broken.
So real visible galaxies like GN-z11 have recession rates over 2c, and since it is far enough away that an inertial model simply cannot be applied, one cannot really assign an inertial velocity to that, but if you could, it would be around 0.98c
General relativity offers an explanation for why the change in distance between us and distant galaxy with time can exceed the speed of light. This quantity is called the recession speed but it is NOT a velocity that anything has, it is just the rate of change of distance with time.We seem to be in agreement about that much.
In flat space, that quantity would have to be the magnitude of a velocity - it is essentially the definition of what a velocity is.Not that quantity, no. To convert a recession rate r to a flat velocity v of one object relative to the other: v=tanh(r), but I agree, it is fairly inappropriate to apply such a transformation over non-local distances since the transformation assumes spacetime is flat.
The pop articles never really explain the difference between recession rate and the speed something is moving, or more precisely, between rapidity and velocity.
3. The key issue being discussed in this thread seems to be the conservation of energy. We already know that total energy is a somewhat arbitrary quantity. We are only interested in CHANGES in energy and that is all that the conservation of energy concerns itself with. For example, if we have a system that consisted of some atoms then the kinetic energy of the atoms depends on the inertial reference frame we wish to use. We can give the atoms more energy just by using a different frame and boosting the velocity of all those atoms. This doesn't matter, we are only concerned with changes in the energy that might happen as the atoms interact, we don't claim to know or care about the actual energy that the system really had. Hopefully, that makes sense. If we don't consider everything in our system under one consistent inertial frame then the conservation of energy doesn't apply.[/quote]Exactly, and since the universe is not a system that can be considered under any one consisten inertial frame, there is no necessary conservation of energy in the universe, something which is rarely admitted, which is why I like the Carroll article, who comes right out and says it rather than trying to sweep the embarrassment under the rug.
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