Mass of Space (B but approaching I)

[PeterDonis]

how can you choose a different space coordinate for the distance across the galaxies vs the distance between the galaxies?

I didn't say you had to. I just said "separated by a distance of...". The point is simply that "distance" is coordinate-dependent.

 

[timmdeeg]

The point is simply that "distance" is coordinate-dependent.

While if we say "increasing distances" (standing for increasing redshifts) that's invariant, right?

 

[PeterDonis]

While if we say "increasing distances" (standing for increasing redshifts) that's invariant, right?

Increasing with respect to what?

 

[timmdeeg]

Increasing with respect to what?

increasing with respect to an arbitrary observer who measures the redshift of far away galaxies.

 

[PeterDonis]

increasing with respect to an arbitrary observer

This is too vague. With respect to what property of the observer?

 

[timmdeeg]

This is too vague. With respect to what property of the observer?

With respect to a co-moving observer.

 

[PeterDonis]

With respect to a co-moving observer.

With respect to what property of a co-moving observer? You are talking about a rate of change--"increasing". A rate of change relative to what? To put it another way, you are taking a derivative of something; with respect to what are you taking the derivative?

 

[timmdeeg]

With respect to what property of a co-moving observer? You are talking about a rate of change--"increasing". A rate of change relative to what? To put it another way, you are taking a derivative of something; with respect to what are you taking the derivative?

Hm, a rate of change relative to the proper time of the observer?

 

[PeterDonis]

a rate of change relative to the proper time of the observer?

Yes. But this will only be an invariant if it's the rate of change of an invariant. So the rate of change of the observed redshift with respect to proper time will be an invariant; but the rate of change of "distance" with respect to proper time won't be, because "distance" is not an invariant, it's coordinate-dependent.

 

[timmdeeg]

Thanks, that has been a helpful course!

 

[timmdeeg]

... but the rate of change of "distance" with respect to proper time won't be, because "distance" is not an invariant, it's coordinate-dependent.

If one talkes about the expansion of the universe without further details wouldn't then the sign of the rate of change of "distance" with respect to proper time be invariant?

 

[PeterDonis]

If one talkes about the expansion of the universe without further details wouldn't then the sign of the rate of change of "distance" with respect to proper time be invariant?

It can't be an invariant if "distance" isn't an invariant.

 

[timmdeeg]

It can't be an invariant if "distance" isn't an invariant.

So the sign of the observed rate of change of the redshift doesn't correspond to a certain sign of the rate of change of distance, that sign could still be positive or negative depending on the chosen coordinates if I understand you correctly.

 

[PeterDonis]

the sign of the observed rate of change of the redshift doesn't correspond to a certain sign of the rate of change of distance

No.

that sign could still be positive or negative depending on the chosen coordinates if I understand you correctly.

Not only due to choice of coordinates. The observed rate of change of the redshift depends on whether the expansion is accelerating or decelerating--or more precisely whether it was doing so when the light we are seeing now from a particular distant galaxy was emitted.

The observed redshift itself can be related to a "rate of change of distance", but the relationship is model dependent as well as coordinate dependent. The best way to interpret the redshift is not as telling you a speed of recession, but as telling you by what factor the universe has expanded since the light you are seeing now was emitted. But that, of course, involves the scale factor, which assumes that you have made a particular choice of coordinates (it isn't even meaningful in other coordinates).

 

[timmdeeg]

No.

Got it.

Not only due to choice of coordinates. The observed rate of change of the redshift depends on whether the expansion is accelerating or decelerating--or more precisely whether it was doing so when the light we are seeing now from a particular distant galaxy was emitted.

Ok, that I've been missing.
Thanks for your great explanation!

Quite often here in PF it comes to a point where someone explains expansion of the universe doesn't mean that space expands, it means increasing distances. This seems quite vague and with no reference to coordinate dependence. But it at least points to right direction. Would you agree to that?

 

[PeterDonis]

Quite often here in PF it comes to a point where someone explains expansion of the universe doesn't mean that space expands, it means increasing distances. This seems quite vague and with no reference to coordinate dependence. But it at least points to right direction. Would you agree to that?

Sort of. When you fill in the missing information about what "increasing distances" means, the coordinate dependence appears. So whether it "points in the right direction" depends on what your goal is.