Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: gsmollin on 16/03/2004 02:57:51
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The cosmic background radiation (CBR) has a dipole moment clearly measured to great precision. It corresponds to a blue-shift, and a matching, equal and opposite red-shift in the opposite direction. The only reasonable explanation is that this is a Doppler-shift caused by the earth's velocity with respect to the CBR of about 220 miles/sec., or 0.0012 c, if memory serves. The exact number is not the issue, just the fact that this is a rather pedestrian velocity by cosmological standards.
Now the cosmological principal states that observers in all parts of the universe should see the same universe when they look out at the sky.
When we look at distant galaxies, we see large recesional velocities, relativistic velocities, numbers on the order of 0.5 c.
What do astronomers on these distant galaxies see when they measure the CBR? The cosmological principal implies it should be a low number, on the order of 0.0012 c. I'm having some trouble understanding why this is true. I know that relativistic velocities add according to the special theory of relativity, but in that theory, if one train measured 0.0012 c velocity, relative to an embankment, and a second train measured 0.5 C relative to the first train, the second train would not measure 0.0012 c relative to the same embankment. This is more complicated, and involves general relativity, and expanding space issues.
If somebody knows of a paper that has treated this problem, I'd like to hear about it. Thanks.
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A little arthmetic with the age of the universe, 13.7 billion years, the hubble constant, Ho = 71 km/s/Mps, and the speed of light, c = 300 megameters/s, give some interesting results. The hubble expansion rate simplifies to 2.3x10(-18)/s. Multiply the age of the universe, 432x10(15)s, c, and Ho, and you get the recessional velocity of the cosmic background radiation. The number is 0.994c.
That simple multiplication is probably wrong, and I should go back and do a relatavistic calculation. I may have also just found an identity here. Anyway, it should be clear that the CBR is receding at nearly the speed of light. That should answer the original question. Astronomers on a galaxy receding at 0.5 C will see a CBR with a low dipole moment, of hundreds of miles/sec. They will see US receding from them at 0.5 C, and wonder what we see when we measure the CBR.
However, it brings up a few other questions. If the CBR is receding at such high speeds, it is highly red-shifted. We measure a 2.7 K black-body radiation that has been red-shifted. What is the non-red-shifted temperature? And could the extremely small variations we see be dependent on small variations in the recessional velocity. In other words, is the recessional velocity truely a constant, or does it have small perturbations that cause us to see small perturbations in the temperature?
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I don't know the answers to your questions, but I do know you must resort to relativistic calculations for this. I have read some on the CBR, but I've never seen any book that gives it a good treatment without being a hard-core technical paper (which I don't have the mathematics and patience to work through). I do know that the theory predicted the 3K temp before it was detected, and that is was initially detected by accident.
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John - The Eternal Pessimist.