Cosmo calculator-recession speed tutorial

[Jorrie]

One of the points of a paper I'm preparing is that it might account for the discrepancy between type 1A supernovae distances and redshifts.

What 'discrepancy' are you referring to?
AFAIK, redshifts are measured pretty accurately, but there are uncertainties in the distances to the SN1Ae used for calibrating the 'distance ladder' and hence in the value of H_0. I fail to see how knowing the Doppler shifts will improve that.

 

[JArnold]

I see now. There is a serious misunderstanding of terms. You and I are speaking a different language, in effect.

Marcus, I think I understand the language problem. "Doppler" effects are treated by convention in cosmology as shifts in wavelength produced by local peculiarities in relative motion that can be discounted in measuring cosmological redshift. I should have been clear that I'm referring to doppler redshift in the generic sense: Redshift in wavelength due to the recession velocity of the source, in contrast to redshift due to subsequent cosmological expansion.

Here's the problem as I see it. Relative velocity would, in principle, be a good measure of cosmological distance, but when it's derived from wavelengths, being derivative, it's prone to confusion and miscalculation. 1) When wavelength rather than velocity is used to calculate z, it's evident that recession velocity shouldn't be relativized, because cosmic expansion isn't relativistic. (It's commonly recognized that recession velocities can exceed c, and yet high-z is calculated relativistically.) In the measure of z in terms of the ratio of wavelength-then to wavelength-now it's clear that there's no relativistic limit that would diminish higher ratios, because space and recession velocities can, in principle, expand without limit. 2) Basing z on the ratio between wavelengths brings the problem that I've been struggling with: It doesn't distinguish the redshift due to cosmic expansion from the redshift due to the recession velocity of the source. Consequently, deriving distance from velocity and z as it's constructed only masks that fundamental problem. There must be a unique solution, given the usual parameters (age of universe, Hubble, etc), to discriminate the components of redshift (recession speed and cosmic expansion), but I've been unable to develop it.

 

[JArnold]

What 'discrepancy' are you referring to?
AFAIK, redshifts are measured pretty accurately, but there are uncertainties in the distances to the SN1Ae used for calibrating the 'distance ladder' and hence in the value of H_0. I fail to see how knowing the Doppler shifts will improve that.

As I'm sure you know, the 2011 Nobel was awarded to Riess et al for showing that the universe is accelerating, based on data that shows type 1A supernovae are, for example, about 25% fainter at z=.5 than redshift would indicate.

 

[Jorrie]

As I'm sure you know, the 2011 Nobel was awarded to Riess et al for showing that the universe is accelerating, based on data that shows type 1A supernovae are, for example, about 25% fainter at z=.5 than redshift would indicate.

Yes, but that was not because the redshift was measured incorrectly; it was because the models for converting redshift to distance were based on a non-accelerating cosmos (Lambda=0). By other means, not redshift, they found that those galaxies were farther (dimmer) than previously calculated by the (then) standard model. This essentially increased Ho and required Lambda to be greater than zero, otherwise the models did not fit all observations.

On your problem mentioned to Marcus (which he no doubt will explain in detail): "There must be a unique solution, given the usual parameters (age of universe, Hubble, etc), to discriminate the components of redshift (recession speed and cosmic expansion), but I've been unable to develop it".

You cannot use both expansion factor and recession speed in the calculation for distance, because they are just different views of the same thing (dependent variables). One can say that essentially recession speed is the apparent rate at which the proper distances between us and distant galaxies are increasing, which can exceed c. We should not apply the Doppler shift formula (relativistic or otherwise) to this speed.

 

[JArnold]

Where has it been agreed that Ho should be increased?

Regarding your comment about expansion and recession, I don't know to express my point more clearly than this: At the moment of emission, light can be highly redshifted due to the recession velocity of the emitter. SUBSEQUENTLY, depending on the time it takes for the light to be received, it will be redshifted due to cosmic expansion. The two bases of redshift are separate and independent.

 

[Jorrie]

Where has it been agreed that Ho should be increased?

Ho was still around 50 km/s/Mpc in the mid 1990s; today it is around 70 km/s/Mpc. It was the discovery of accelerating expansion that forced the increase.

Regarding your comment about expansion and recession, I don't know to express my point more clearly than this: At the moment of emission, light can be highly redshifted due to the recession velocity of the emitter.

No, light can only be highly Doppler-shifted if relative to its local area, the source has an extreme peculiar (non-Hubble) recession velocity, causing the Doppler shift. Galaxies typically do not have that; even adjacent clusters move relative to each other at no more than around c/1000, as Marcus also stated. In a z=0.5 galaxy, that accounts for a negligible amount. What we observe is all due to expansion, unless that galaxy is very nearby - like in the Virgo cluster, where we do not apply Hubble's law.

It is possible to approximate the cosmic redshift by a series of infinitesimal Doppler shifts between adjacent points in the line of sight, but AFAIK, that's not a common method any more. Take note that in such a case, the expansion factor is not used, so that we do not double-count.

 

[JArnold]

Jorrie, thank you for your patience. I was wrong, you were right. What finally made sense to me was a thought experiment (in the shower!): If the universe were to abruptly stop expanding, would a distant galaxy still recede, and have a redshift? The answer of course is no.

 

[Jorrie]

If the universe were to abruptly stop expanding, would a distant galaxy still recede, and have a redshift? The answer of course is no.

Yes, showers do some magic, sometimes...

But, note that such a case would have made no difference to our present redshift observation of distant galaxies; we would have to 'wait for billions of years' to notice the change. What we currently observe in terms of redshift is determined only by how much the universe has expanded since the time of the emission of those photons.

In any case, this is another (good) argument against Doppler shift due to recession velocity, at least as per the cosmological understanding of the terms. One can obviously also just look at the good old balloon analogy and "see the light"...