|Mar7-07, 04:31 AM||#1|
On a sheet of paper draw four concentric circles, one outside the other.
Fill the innermost circle with dots. This is the CMB photons at the point in time when they were scattered throughout the early universe and first became liberated from the spreading dense matter cloud that scattered them.
At some point on the second circle mark the current position of the Earth 13 billion years later (but not necessarily 13.7gly from the point of the big bang)
The third circle is to indicate a distance of 13.7gly from the big bang and is only to illustrate the point that due to the expansion of space itself the universe is much larger than would be allowed by the velocity of light if space had not expanded as well.
The fourth outermost circle roughly illustrates the current size of the universe.
In the approximately thirteen billion years the universe has been expanding since the CMB photons were first liberated (the innermost circle) these photons have spread out uniformly throughout the current universe and are moving in all directions, predominately outward but some toward and some away from the Earth (and some back toward the big bang itself but very few actually returning to the point of the singularity). Of those that originally had a trajectory toward the Earth, some of them will arrive at this moment in time and contribute to the Wmap picture we see today.
As the universe continues to expand they also become more and more spread apart and fewer and fewer will arrive at any given time yielding a cooler and cooler picture of the CMB to any given point within the universe.
Is there any validity to this simplified view of how we witness the CMB we observe today?
|Mar7-07, 08:40 AM||#2|
or do you mean put dots all along the curved line that is the circle?
How you answer will determine whether or not there is some validity (in reply to your question about validity.)
Have you watched that computer animation of the balloon model at Ned Wright's website?
The little squiggles are CMB photons and as the balloon expands they actually get stretched out so they have longer and longer wavelength ("redshift") and to emphasize what is happening he makes the squiggles gradually change color and become more red.
I hope he still has that movie. I havent checked for some time.
Your circles could be schematic balloons.
A circle is a one-sphere (a sphere made of a one-dimensional line)
A balloon is a two-sphere (a sphere made of two-dimensional rubber skin)
A three-sphere is a three-sphere.
the best estimate of the radius of curvature of our current three-sphere is...?
I just checked---Wright has an improved version of the balloon movie:
|Mar7-07, 09:46 AM||#3|
In my understanding photons, while traveling in space-time, undergo no frequency change at all. All red and blue shift can be attributable to the distance between events in GR. It is not the photons that shift but instead the curvature, distance and speed differential between the space-time events of the emitter and absorber cause the absorber to measure a photon bluer or redder than the emitter.
Am I wrong?
|Mar7-07, 12:19 PM||#4|
so I take it you don't like the movie
in cosmology there is this basic day-one equation which you may have seen
1+z = a(t_receive)/a(t_emit)
this refers to the usual cosmology model with a scale-factor a(t) that you plug into the metric to get the timedependence of the metric.
t_emit is the time the photon is emitted
t_rec is the time the photon is received (usually the present)
the z we are talking about is the cosmological redshift z, not a doppler redshift. So the whole wavelength ratio (1 + z) is equal to the factor by which space has stretched during the flight of the photon
there are various geometrical ways to visualize, but this is a practical way that works----and it has a physical intuition supporting it: imagine Maxwell's equations working as the EM wave travels along and imagine the equations working in a space that little by little is expanding....
|Mar7-07, 11:11 PM||#5|
But that does not imply that the observed cosmological redshift is not a relativistic effect.
|Mar8-07, 12:30 AM||#6|
Jennifer, I hope you watched the movie and saw the little wriggles stretched out (redshifted) by the expansion of space. there's no better authority than Ned Wright.
But any beginning course on cosmology would give you that equation, often on day one or in the first week, and that says the same thing.
1+z = a(t_receive)/a(t_emit)
the ratio by which the wavelength is stretched out is exactly equal to the ratio by which space is stretched out.
this is a (general) relativistic effect.
So I will try to answer your question directly.
the packet of electromag wave energy, while traveling, DOES undergo a frequency change.
the curvature, the distance, the speed differential are NOT the determining factors. the determining factor, as the basic equation says, is how much space has stretched while the squiggle was swimming.
|Mar8-07, 01:59 AM||#7|
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