I Is the light from Andromeda truly blue shifted?

[TeethWhitener]

I don't think it's valid to apply Hubble's law at all, because the local group of galaxies is not a region of space with the average energy density of the universe as a whole. Hubble's law applies to the universe at the largest scale, where the average energy density applies, but not to every region of the universe, where different equations govern the local galactic kinematics.

Interestingly, Hubble derived his law using data for relatively close galaxies. How did he do this? Here's what Steven Weinberg says in The First Three Minutes:

His conclusion was that there is a "roughly linear relation" between velocities and distances. Actually, a look at Hubble's data leaves me perplexed how he could reach such a conclusion - galactic velocities seem almost uncorrelated with their distance ... In fact, we would not expect any neat relation of proportionality between velocity and distance for these 18 galaxies - they are all much too close. It is difficult to avoid the conclusion that ... Hubble knew the answer he wanted to get.

The average density of the Local group is about twice the average density of the universe (Ref1 Ref2). I’m curious now as to whether that counts as a big perturbation to the FLRW metric. My gut says probably but I’m not an expert.

Which is what I was unsure about: when you say Hubble’s law doesn’t apply, do you mean that the recessional velocity is insignificant/of the same order as local astronomical velocities, or do you mean that, because GR is nonlinear, the metric of an FLRW background plus local matter is sufficiently qualitatively different from the flat FLRW metric that Hubble’s law, or an analog of it, can no longer be derived from the metric?

 

[PeroK]

Which is what I was unsure about: when you say Hubble’s law doesn’t apply, do you mean that the recessional velocity is insignificant/of the same order as local astronomical velocities, or do you mean that, because GR is nonlinear, the metric of an FLRW background plus local matter is sufficiently qualitatively different from the flat FLRW metric that Hubble’s law, or an analog of it, can no longer be derived from the metric?

That's a good question. Hubble's law requires an evolution of the universe from the earliest time. In order for Andromeda to be moving away from the Milky Way at recession speed $v$ requires a long time evolution. It's not like a gravitational force that acts directly.

Look at it this way. Take two objects (Earth and Sun, say) and look at their behaviour today. Then, imagine their behaviour at a time in the future when the universal expansion is enormous. It makes no difference. The local behaviour will not change over time as the universe globally expands more rapidly. Unless the system remains part of the Hubble flow for billions of years, it simply does not have the accelerating background average recessional velocity. Not at all.

 

[Bandersnatch]

Interestingly, Hubble derived his law using data for relatively close galaxies. How did he do this? Here's what Steven Weinberg says in The First Three Minutes:

I'm a bit late to the party, but let me address this.
While today any small-scale region is most certainly not uniform, there was a time when it was. Galaxies that we see today are made of material that must have necessarily inherited the initial Hubble flow. It's not like all that matter hit brakes the moment the deviation from uniform distribution reached some arbitrary threshold.

Over the history of the universe, many objects have managed to bleed off the initial impulse and coalesce, collide, combine, begin approaching or orbiting one another. But the farther apart and smaller the objects, the longer it takes. For most of the galaxies used by Hubble in his paper, the dominant component of their motion is still the initial recession. Even though they are all technically in a single bound system.

And it shows when one plots them - the trend is clear, whether one uses Hubble's original, or modern, distance and velocity data (although it is more messy in the former case).
I'm not sure why Weinberg would say what he did there.

 

[mitchell porter]

I think the Quora poster is making a mess of explaining something that's true.

The Quora poster's answers are generated by ChatGPT.