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wolram

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how do we know that the expansion of space is universal ,rather than local to our observable portion of it?

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wolram

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maximus

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Originally posted by wolram

becuase we observe a redshift for almost every galaxy out there! i don't get what you mean by our local portion of it.

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drag

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We don't.Originally posted by wolram

how do we know that the expansion of space is universal ,rather than local to our observable portion of it?

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marcus

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Originally posted by wolram

two approaches to answering

1. the "Copernican axiom" or "we ain't special"

like, it would be very strange if the Earth had some privileged position in the scheme of things

so that everything was arranged an moving to look like it was expanding from our point of view but not from perspective of your average other galaxy. (its all a show put on for our benefit? whoah!)

people often call it "the assumption of mediocrity"

It isn't proven its like one of euclid's postulates that you start with.

Also to get cosmology off the ground in the area of mathematical models a further assumption of uniformity is made:

The universe is homogeneous and isotropic---in large scale on the average. That is it looks pretty much the same on very large scale looking in any direction (isotropy) and also if you shift over to your neighbor's perspective (homogeneity).

They assume there is no preferred direction and no preferred location (these are cousins of the basic Copernican prejudice and I don't mean to knock it but an axiom is a prejudice and we all have em)

2. There is another more pragmatic way that we can kind of tell.

The Hubble law is linear at the present moment.

This actually means that expansion would look the same from a neighbor's viewpoint as long as everybody is at rest w/rt CMB.

People who are "comoving" or have a common idea of what it means to be at rest also have a common idea of the present moment. One can define a "comoving" distance in the present

---also called the "Hubble law distance" because it is the idea of distance that works in the v = H

this law is linear. Linear expansion looks the same

everywhere

you can plot it out on graph paper and see---it is the old

raisinbread dough picture: when the dough is rising and expanding it looks the same to every raisin. each raisin sees

the others getting farther away

that is not so fine reasoning as the Copernican axiom of ordinariness or mediocrity---but it is some kind of practical

corroboration

great question as usual

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maximus

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Originally posted by marcus

you can plot it out on graph paper and see---it is the old

raisinbread dough picture: when the dough is rising and expanding it looks the same to every raisin. each raisin sees

the others getting farther away

i always use the old 'painting dots on a balloon' analogy, where (while being blown up) every point appears to be the center of expansion.

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wolram

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marcus

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Originally posted by wolram

LOL (ignorant) yes we do make a serious effort don't we?

heartily welcome from my part

the thoughtful question and the attempt to reply are two

sides of the same coin

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jeff

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Originally posted by marcus

1. the "Copernican axiom" or "we ain't special"...

I think wolram is right to appreciate the additional perspective your providing, but the answer to his question is still that we don't know.

Originally posted by marcus

They assume there is no preferred direction and no preferred location.

This is not meant as criticism in any way, but it's worth mentioning that isotropy implies homogeneity.

Originally posted by marcus

2. There is another more pragmatic way that we can kind of tell.

The Hubble law is linear at the present moment. This actually means that expansion would look the same from a neighbor's viewpoint as long as everybody is at rest w/rt CMB.

Be careful, copernican prejudice may be more insidious than you realize.

Originally posted by marcus

People who are "comoving" or have a common idea of what it means to be at rest also have a common idea of the present moment.

This elegant way of finessing the issue of comoving coordinates does make sense, but ony because of the isotropy in this important but special case. In general (and yes I'm sure you know this marcus, these remarks aren't aimed at you), just as in SR, simultaneity is an observer-dependent concept, and there are an infinite number of ways general spacetimes can be foliated by spacelike hypersurfaces. In this more general context, the analogy between comoving coordinates and "chronologically like minded" observers breaks down.

Originally posted by marcus

One can define a "comoving" distance in the present

---also called the "Hubble law distance" because it is the idea of distance that works in the v = H_{0}D law. this law is linear.

That's just a misleading artifact of working in comoving coordinates which hides the physical significance of hubble's law. Firstly, comoving coordinate distances unlike physical distances between points carried from slice to slice remain constant. Also, as I explained in another thread, the use of recessional velocities is in practice problematic due to the difficulty of separating out the gravitational component of redshift. It's really the basic linearity of the relation between physical distance - as opposed to comoving coordinate distance - and redshift implicit in hubble's famous relation that in terms of comparing with redshift data is unambiguous and for that reason should be used.

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marcus

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--------------------------------------------------------------------------------

Originally posted by marcus

One can define a "comoving" distance in the present

---also called the "Hubble law distance" because it is the idea of distance that works in the v = H

--------------------------------------------------------------------------------

I put "comoving" in quotes because it is Ned Wright's shortened expression for "comoving with the Hubble flow". This is the physical distance in the usual metric (called RW or FRW) and also what Wright often reminds readers is the "Hubble law distance" or the distance that works in the Hubble law.

I see we have some semantic trouble here. If you read Wright's discussion of 4 types of distance you will see what I mean by

RW (Robertson-Walker) metric distance or what Wright calls "comoving" or "Hubble law" distance.

I don't care if there are disagreements but it would be nice to have a common understanding of the meanings of words.

Originally posted by steinitz

This elegant way of finessing the issue of comoving coordinates does make sense, but ony because of the isotropy in this important but special case. In general (and yes I'm sure you know this marcus, these remarks aren't aimed at you), just as in SR, simultaneity is an observer-dependent concept, and there are an infinite number of ways general spacetimes can be foliated by spacelike hypersurfaces. In this more general context, the analogy between comoving coordinates and "chronologically like minded" observers breaks down.

There is only one foliation or slicing that is meant when one talks about observers comoving with the CMB or comoving with the Hubble flow. It is just a habit cosmologists have and the RW metric they use is built on that way of representing the 4D manifold as the cartesian product of a 3D space Σ with a time axis R, actually positive time 0 to infinity but call it R.

Another online intro to cosmology is by Eric Linder----he is even more explicit than Wright. Its part of the standard toolkit.

Maybe I will fish up the URL for Linder's "Cosmology Overview"

since it is very concise and corroborates Wright.

The Hubble law is not explicitly about redshift.

The gravitational redshift that light suffers when departing from a massive galaxy has already been removed by the time one gets to the Hubble law----whatever adjustments need to be made in the redshift are made. Calculating the relation between redshift and present real physical (i.e. comoving or metric) distance is not all that simple since it involves estimating PAST rates of expansion experienced by the light during its journey. I expect you know what I mean and can handle the mildly figurative language used here.

So the Hubble law is this simple linear relation between recession speed of a stationary object and distance, when both the recession speed and the distance are measured in the present in real physical (metric, i.e. "comoving w/rt expansion of space) terms.

It does not talk about the redshift or the light travel time (these things take more complicated calculation using assumptions like the famous 73 percent dark energy assumption, to relate to the Hubble law distance). It simply relates present speed and present distance to the present value of the parameter

v = H

Originally posted by steinitz

That's just a misleading artifact of working in comoving coordinates which hides the physical significance of hubble's law. Firstly, comoving coordinate distances unlike physical distances between points carried from slice to slice remain constant. Also, as I explained in another thread, the use of recessional velocities is in practice problematic due to the difficulty of separating out the gravitational component of redshift. It's really the basic linearity of the relation between physical distance - as opposed to comoving coordinate distance - and redshift implicit in hubble's famous relation that in terms of comparing with redshift data is unambiguous and for that reason should be used.

There are some things here that could use a little discussion.

But I shall just post my reply as it is. To resolve semantic differences one should, I guess, proceed in stages.

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marcus

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"Firstly, comoving coordinate distances unlike physical distances between points carried from slice to slice remain constant."

Indeed that is just what they do not do!

I am trying to understand how you came to that idea.

Is it possible that when you see the manifold written as a

cartesian product

Σ x R

you think that means that the metric is also a cartesian product?

This could be the source of the misunderstanding.

The metric is LIKE a cartesian product except that it has a

time-dependent scale factor a(t) in the space part.

This a(t) takes care of the expansion and indeed the

Friedmann equations concern themselves with this a(t)

and how it evolves thru time.

But though it is in a rough way like a cartesian product it is not one, and the comoving (w/rt Hubble flow) distance to a faraway point in space increases with time.

"Comoving w/rt Hubble flow or w/rt CMB or expansion of space" is a lot of words----wish we could simply say "comoving" as

Wright and Linder do, without risk of misunderstanding.

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