Expansion of the Universe ponderables

Sometimes I ponder things, and some of those ponderations lead me to suspect that I'm misunderstanding some of the fundamentals.

For the sake of discussion, let's take it as a given that the universe is expanding, and that the rate of expansion is increasing, and that eventually this will tear apart galaxies, then solar systems, then planets, then atoms in the "big rip."

Also, let's suppose that we had developed an exquisitely sensitive instrument that could measure the local rate of expansion and expansion acceleration.

Ponderable #1: Suppose I have an scientist floating in space and he measures the local expansion acceleration as 4E-12/sec^2. At that moment,another scientist flies past at C/2, and he also measures the local expansion rate. Would he also see 4E-12/sec^2? Part of me thinks that he'd measure the rate as being 5E-12/sec^2 due to time dilation, but if so, that implies a preferred frame to the universe and that seems really wrong to me. But is the expansion acceleration rate (is there a shorter name for it?) dependent on the reference frame? I'm having a little trouble even figuring out what that would mean. I've assumed the expansion would be isotropic, but is that necessarily true? Would one or both observers measure different expansion rates in different directions?

Ponderable #2 (and I think this is just a different perspective on #1): If I have 2 scientists and one is at the bottom of a deep gravity well while the other is far from anything (say, rural Iowa), would they measure different rates of expansion and expansion acceleration? Suppose I had a planet and a neutron star, both the same diameter but, of course, radically different masses. When the big rip came, would they fly apart at the same time as seen by an outside observer? And, if not, will black holes survive the big rip (from an outsider observer's perspective)?

Any help from those out there who actually understand these things?

Expanding universes of the type usually considered in cosmology do have a preferred frame (there are a few special exceptions, but they are exceptions). The best way to define the preferred frame is to say that in it, at any fixed time the density of energy is constant in space - apart from small fluctuations on large scales and, in rare places, large fluctuations on small scales (like planets, galaxies, black holes, etc.).

Whether the two scientists would "measure" different expansion rates is not an easy question to answer, because you haven't defined "local rate of expansion" carefully. If you tell me exactly what and how your devices measures, I can answer it - but "rate of expansion" a concept that really only makes sense in the preferred frame. Bear in mind that the earth is in fact moving rather quickly with respect to the frame (as it orbits the sun, and the solar system orbits the center of the galaxy) and yet earth-based scientists have no trouble measuring the expansion rate of the preferred frame.

As for the big rip, different things will get torn apart at different times in anyone's frame. I'm not entirely sure what happens to black holes at a big rip, but I doubt they are torn apart in any sense - instead, I expect that they simply grow until they take up all the space.

sol invictus said:

Expanding universes of the type usually considered in cosmology do have a preferred frame (there are a few special exceptions, but they are exceptions). The best way to define the preferred frame is to say that in it, at any fixed time the density of energy is constant in space - apart from small fluctuations on large scales and, in rare places, large fluctuations on small scales (like planets, galaxies, black holes, etc.).

Click to expand...

Thanks for responding.

sol invictus said:

Expanding universes of the type usually considered in cosmology do have a preferred frame

Click to expand...

<sigh> That's unsatisfying. Ah, well, I'd long ago learned that there's not a strong correlation between a statement's correctness and the degree to which it I find it satisfying (that whole 'death' thing is Exhibit A).

But having a preferred frame does make parts of it more comprehensible.

Whether the two scientists would "measure" different expansion rates is not an easy question to answer, because you haven't defined "local rate of expansion" carefully. If you tell me exactly what and how your devices measures, I can answer it - but "rate of expansion" a concept that really only makes sense in the preferred frame.

Click to expand...

Good question. I was thinking of local measurements, sort of "what is the rate of expansion right here." So, hmm, I could have two known weights attached by a long rod, and then accurately measure the (very, very small) tension in the rod. It would be difficult to remove small gravity gradient effects, of course. I was originally thinking of something with mirrors and interference patterns, but I'm not getting that to work right now.

Bear in mind that the earth is in fact moving rather quickly with respect to the frame (as it orbits the sun, and the solar system orbits the center of the galaxy) and yet earth-based scientists have no trouble measuring the expansion rate of the preferred frame.

Click to expand...

I've assumed that modern scientists are measuring the expansion rate on a very large scale (millions to billions of light years).

As for the big rip, different things will get torn apart at different times in anyone's frame. I'm not entirely sure what happens to black holes at a big rip, but I doubt they are torn apart in any sense - instead, I expect that they simply grow until they take up all the space.

Click to expand...

I was thinking that if the Big Rip proceeded according to the local passage of time, then since time appears to be stopped at the event horizon, a black whole would never appear to reach the Big Rip time. Of course, the outside observer would be flying away from the black hole at >>c, so he wouldn't see much anyway.

But I'll hold off on the "post-Rip universe" questions for the time being.

Perpetual Student said:

Click to expand...

You might have missed "of the type usually considered in cosmology"... I've never disputed (how could I?) that in homogeneous and isotropic FRW cosmologies, there is a special time slicing. The issue we were discussing in the other thread is a) whether such a cosmology actually describes our universe (answer: we do not and cannot know), and b) what the significance of the existence of that frame is more broadly (answer: probably zero).

dasmiller said:

Good question. I was thinking of local measurements, sort of "what is the rate of expansion right here." So, hmm, I could have two known weights attached by a long rod, and then accurately measure the (very, very small) tension in the rod. It would be difficult to remove small gravity gradient effects, of course.

Click to expand...

What that device would measure can always be regarded as "small gravity effects" - which is OK, because the expansion is a gravity effect as well, more or less. Such a device measures components of the Riemann curvature tensor. Two scientists in relative motion would in most cases measure different forces with it. But I wouldn't interpret that as a difference in local expansion rates.

I was thinking that if the Big Rip proceeded according to the local passage of time, then since time appears to be stopped at the event horizon, a black whole would never appear to reach the Big Rip time. Of course, the outside observer would be flying away from the black hole at >>c, so he wouldn't see much anyway.

Click to expand...

This whole business about time stopping at the horizon causes lots of confusion.... What I suspect you'd see is either that you'd fallen into the horizon (which happens in finite time, and you can see it happen in finite time) and then you get annihilated inside, or that you get annihilated at the rip before falling into any horizons. In the second case you wouldn't get to see anything else get ripped, because you yourself would be ripped before the light from anything else getting ripped could reach you.