Effort to get us all on the same page (balloon analogy)
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Feb26-09, 04:17 PM
One of the first things you learn in an introductory cosmo class is not to think of the redshift as a doppler effect. It is not the result of some particular speed.
The formula involves the entire factor by which distances have been expanded during the whole time the light has been traveling.
1+z = size(now)/size(then)
Technically the index of size used is called the "scalefactor" usually written a(t) as a function of universal time. Intuitively it is just a handle on the size of the universe or (if that is too vague and undefined) the average distance between galaxies. The exact definition involves a differential equation modeling the growth of a(t), the expansion history of the universe.
So you get taught that
1+z = a(now)/a(then)
the factor by which distances have increased from the moment the light was emitted until the moment it reached our telescope.
Since z is the fractional increase in wavelength, that is the amount added to it, it must be that 1+z is the ratio by which wavelength(now) is bigger than wavelength(then).
So wavelengths have increased by the same factor that large astronomical distances have, during the same time interval.
Pop-sci journalism often misleads readers by presenting the redshift z as a Doppler effect.
Presumably the Doppler shift due to some particular recession speed at one moment in history. But it is not. It is the integrated stretch due to the whole history of expansion during the light's transit.
Just another instance of pop-sci media damage that we are constantly having to recover from.
Hmm, sounds like spacetime Doppler to me!!
I'm not being deliberately difficult, I should probably stick to doing sound for bands :lol: