Observers sending signals to measure expansion

[BWV]

TL;DR Summary

Help me understand expansion rate

Googling you find a current expansion rate of ~70 km/s or 0.0002C but of course we don't observe this with objects in the solar system as local gravity prevents this expansion - otherwise a distances would increase by a light second roughly every 71 minutes (maybe I’m missing some here conceptually?)

question is - how far apart would to observers sending signals to one another need to be in order to observe expansion? (assuming they could wait however long it took to send and receive the signal) - between here and Andromeda (after accounting for the trajectories of the two galaxies) or farther?

what about two observers floating in some intergalactic void - could they observe expansion at relatively small distances?

 

[phinds]

Googling you find a current expansion rate of ~70 km/s

This is not correct. You have specified a SPEED, not an expansion rate. The expansion rate is 73.3 km/s/Mpc. That is, the expansion SPEED is a function of distance. At 1 Mpc, it IS 73.3km/s but at 2Mpc it's 146.6km/s and at 3Mpc ... etc.

Also, whether or not expansion is happening in a given area of space is a function of what's IN that space. For bound systems, whether very large galactic clusters or a single non-clustered galaxy, it doesn't happen inside the cluster or galaxy but how far away it starts to occur will depend on how close something has to be to still be bound to the galaxy or the cluster.

SO ... there is no hard and fast numerical answer to your question.

 

[BWV]

thanks - so simply per above 2 observers 1 mpc apart floating in a much larger intergalactic void would observe their signals taking longer to send and receive proportional to space expanding at 73 km/s and the 6.5 million years for the round-trip signal?

 

[phinds]

thanks - so simply per above 2 observers 1 mpc apart floating in a much larger intergalactic void would observe their signals taking longer to send and receive proportional to space expanding at 73 km/s and the 6.5 million years for the round-trip signal?

I believe so, yes.

 

[PAllen]

thanks - so simply per above 2 observers 1 mpc apart floating in a much larger intergalactic void would observe their signals taking longer to send and receive proportional to space expanding at 73 km/s and the 6.5 million years for the round-trip signal?

Actually, a void isn't what you would want to observe this. A void would not be governed by the overall universe geometry (aside: advanced technical terms: the void would have pure Weyl curvature, while the FLRW geometry is pure Ricci curvature. Expansion is a feature of Ricci curvature and initial conditions. Ricci curvature requires a distribution of matter and/or energy). What you would want is a is large enough region to be not gravitationally bound, with average matter and energy density similar to the universe as a whole. And you would want the initial state of the observers to be not just any free fall trajectory, but ones consistent with the so called Hubble flow. Then you should observe the effect you describe.

What also might work is a 1 Mpc region filled with average matter/energy density embedded in a 'typical' region between galactic clusters. But I'm not sure this would really work if the region around this 1 mpc region is of substantially below average matter/energy density. So the only sure fire case is as above - effectively a typical region larger than a galactic cluster.

[edit: sorry, this is not really a B level answer, but I can find no simpler way to describe it without being substantially inaccurate]

 

[PAllen]

A perhaps useful analogy is the think about the surface of a golf ball. The general features of the cosmology (cosmological redshift, Hubble 'constant', expansion etc.) correspond to the overall average spherical geometry of the golf ball surface. This overall spherical character is irrelevant to the geometry of a region of a few dimples. Thus, cosmological behavior simply doesn't exist at smaller scales. And, stretching the analogy a bit, a void would be like taking a slice off a bit of the golf ball, leaving a flat region. This would thus have none of the overall spherical large scale average geometry.

Summary: cosmological behavior is large scale emergent behavior. It has no small scale consequences at all (contrary to a great many misleading suggestions that it does).

[edit: I forgot one key exception: the cosmological constant. To the extent that GR with a cosmological constant is correct, the cosmological constant influences behavior at all scales. However, this has nothing to do with applying the scale factor in FLRW metric at local scales, or even applying large scale curvature locally. It does mean, in principle, that orbits should be calculated using the cosmological constant version of Schwarzschild geometry. The effects of this, of course, are many many orders of magnitude less than what is observable, so no one does this. Recall how small the cosmological constant is for our universe in the reference model. ]