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Jul 25, 2000, 3:00:00 AM7/25/00

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I am completely at a loss at understanding what expands and what does not

expand in the expanding universe.

expand in the expanding universe.

My metre stick consists mainly of space. Does it expand?

If so, how can I ever become aware of the expansion of space, since I

would always lay off my stick the same number of times when measuring the

distance between two objects?

If my metre stick does not expand, then why not?

I am confused about whether massive objects are simply flying apart in a

pre-existing space as a result of a primordial explosion or whether the

space itself is expanding.

All help gratefully received.

Franz Heymann

[Moderator's note: Small, bound systems like rulers and galaxies don't

expand along with the Universe. This question is treated in detail

in the Relativity FAQ, at

http://math.ucr.edu/home/baez/physics/relativity.html and mirror

sites. Anyone who wants to participate in this thread should make

sure that they've read the FAQ. -TB]

Jul 25, 2000, 3:00:00 AM7/25/00

to

franz heymann wrote:

> My metre stick consists mainly of space. Does it expand?

No.

> If my metre stick does not expand, then why not?

It is bound together by incredibly strong subatomic and interatomic forces.

Just think, if these forces didn't exist,

your metre stick would be a gas (actually a quark gluon plasma)

and would expand for purely thermodynamic reasons.

But these forces are enough to overcome both that and the expansion of space.

In fact, gravity is enough to overcome the expansion of space.

The Sun is not expanding. The Milky Way is not expanding.

The Local Group [of galaxies] is not expanding.

Only the space between superclusters of galaxies is expanding.

> I am confused about whether massive objects are simply flying apart in a

>pre-existing space as a result of a primordial explosion or whether the

>space itself is expanding.

Space itself is expanding in the sense that

freefalling objects which were initially travelling side by side

would not remain travelling side by side as time went on.

-- Toby

to...@ugcs.caltech.edu

Jul 26, 2000, 3:00:00 AM7/26/00

to

In article <8lctfg$cc6$1...@lure.pipex.net>,

franz heymann <franz....@care4free.net> wrote:

> I am completely at a loss at understanding what expands and what does not

>expand in the expanding universe.

franz heymann <franz....@care4free.net> wrote:

> I am completely at a loss at understanding what expands and what does not

>expand in the expanding universe.

Rule of thumb: If something is bound together by some force, it

won't expand due to the expansion of the universe.

Here we even count gravity as a force, though the purists may disdain

us for it. E.g., a galaxy is gravitationally bound, so it doesn't

expand due to the expansion of the universe.

(The stars will eventually "boil off", as described in an article

I just posted in the "ionization" thread, but that's a different effect,

not caused by the expansion of the universe! To confuse the issue,

once the stars boil off, the galaxy is no longer gravitationally

bound, or even a galaxy - it's just a bunch of stars flying this way

and that, and these stars will eventually move apart due to the

expansion of the universe. But the rule of thumb is still true:

as long as the galaxy remains gravitationally bound, it won't

expand due to the expansion of the universe.)

> My metre stick consists mainly of space. Does it expand?

No: the stick is held together by some force, so it doesn't expand.

(Btw, it makes me very nervous to hear someone say that something

"consists mainly of space" - space is not an "ingredient" that things

can "consist of". I can just see the labels on diet foods: "Low fat!

99.99% pure empty space!"

Presumably you mean the old business about atoms being "mostly empty

space", but that's fairly misleading in its own way, since the

electron wavefunctions are packed pretty tight - it's the Pauli

exclusion principle that ultimately accounts for atomic matter's tendency

to resist compression. The electrons' electrostatic repulsion is relevant,

but the electrons and protons attract, so one really needs some other

argument to see why matter doesn't just collapse indefinitely. This

argument was figured out by Dyson and made rigorous by Lieb.)

While I'm at it, let me reiterate the moderator's wise suggestion:

before discussing this stuff further, read the FAQ!

> This question is treated in detail in the Relativity FAQ, at

> http://math.ucr.edu/home/baez/physics/relativity.html and mirror

> sites. Anyone who wants to participate in this thread should make

> sure that they've read the FAQ. -TB]

(I didn't write this, by the way, despite the fact that it's sitting

on my website.)

Jul 27, 2000, 3:00:00 AM7/27/00

to

Thank you Toby, You have successfully given me a way of thinking about my

worry

Franz Heymann

worry

Franz Heymann

Toby Bartels <to...@ugcs.caltech.edu> wrote in message

news:8lj99l$f...@gap.cco.caltech.edu...

> franz heymann wrote:

>

> > My metre stick consists mainly of space. Does it expand?

>

> No.

>

> > If my metre stick does not expand, then why not?

>

> It is bound together by incredibly strong subatomic and interatomic

forces.

[...]

[Moderator's note: Quoted article trimmed. -MM]

Jul 27, 2000, 3:00:00 AM7/27/00

to

In article <8lctfg$cc6$1...@lure.pipex.net>,

"franz heymann" <franz....@care4free.net> wrote:

> I am completely at a loss at understanding what expands and what

does not

> expand in the expanding universe.

"franz heymann" <franz....@care4free.net> wrote:

> I am completely at a loss at understanding what expands and what

does not

> expand in the expanding universe.

The distance between 2 points is what's expanding. Material objects

will accomodate for this, since they're always subject to the same laws

of motion -- which means the Earth's orbit is slipping off the

expanding fabric of space so as to retain its present size unchanged.

In terms of time, the distance between any two points A(t) and B(t)

will be equal to:

D x R(t)

where D is their distance at some standard time and R(t) is exactly the

same function of time which describes the altitude of a free-falling

object (relative to the center of the gravity source), which is falling

directly away or toward the source.

So the analogy is that the universe is expanding exactly as if

everything in the universe were flying out from a gigantic source of

gravity at a centrally located point.

A "point" is, here, technically being defined as a time-like curve of

constant coordinates (x, y, z) is one of the more commonly used

coordinate systems used to describe the expanding universe (i.e., the

one with the metric of the form ds^2 = dt^2 - R(t)^2 (3-D metric^2).

So, the answer to the question "define the Universe and give 3

examples" is, thus: the Universe is a solution to Einstein's Field

Equations, and the 3 examples are the 3 cases corresponding to (a) R(t)

describing a falling object which eventually stops and falls back, (b) R

(t) describing an object going at exactly escape velocity and (c) R(t)

describing an object which is going faster than escape velocity.

The universe is flying out at almost exactly escape velocity.

So the metric can be written almost exactly as:

ds^2 = dt^2 - K t^{2/3} (dx^2 + dy^2 + dz^2)

where K is some constant. The function R(t) is just a constant times t

to the 2/3'rds power. Therefore, distances are expanding as the

2/3rd's power of time.

None of this, by the way, includes the effect that the recently

discovered non-zero Cosmological Constant (which Einstein condemned as

his biggest blunder) has.

Sent via Deja.com http://www.deja.com/

Before you buy.

Jul 27, 2000, 3:00:00 AM7/27/00

to

In article <8lj99l$f...@gap.cco.caltech.edu>,

Toby Bartels <to...@ugcs.caltech.edu> wrote:

Toby Bartels <to...@ugcs.caltech.edu> wrote:

>Space itself is expanding in the sense that

>freefalling objects which were initially travelling side by side

>would not remain travelling side by side as time went on.

I think this is a misleading thing to say. It suggests that

the two objects in question will be pulled apart by the expansion

when in fact this is only true if the expansion is *accelerating*.

Suppose you live in an expanding FRW Universe. You put two test

masses down in such a way that their velocity with respect to each

other at some time is zero. To be precise, suppose you put them down

in such a way that a light signal emitted by one would be received by

the other with zero redshift. I assume that this is what you mean by

"travelling side by side."

(More technical assumptions: let's say the two objects are separated

by a distance that's small compared to the Hubble distance. That way,

the Universe won't expand much between emission and absorption of said

light signal. Without that assumption, the phrase "at some time"

above is problematic. But although the two objects are relatively

nearby, they're not gravitationally bound to each other; they're test

masses in a homogeneous FRW Universe.)

Many people's intuition is that the expansion of the Universe will

cause the two objects to start moving away from each other: as time

passes, they'll get "swept up" in the expansion and acquire redshifts

with respect to each other. But that's true only if the expansion is

accelerating; if it's slowing down -- for instance, if the Universe is

matter-dominated with no cosmological constant, as people believed

only a year or so ago -- they'll actually start to move towards each

other.

-Ted

Jul 27, 2000, 3:00:00 AM7/27/00

to

In article <8lnmqq$ag3$1...@Urvile.MSUS.EDU>,

John Baez <ba...@galaxy.ucr.edu> wrote:

John Baez <ba...@galaxy.ucr.edu> wrote:

>(The stars will eventually "boil off", as described in an article

>I just posted in the "ionization" thread, but that's a different effect,

>not caused by the expansion of the universe! To confuse the issue,

>once the stars boil off, the galaxy is no longer gravitationally

>bound, or even a galaxy - it's just a bunch of stars flying this way

>and that, and these stars will eventually move apart due to the

>expansion of the universe.

I don't agree with that last sentence. The stars will move apart

because their "initial" (post-boiling-off) velocities away from each

other are larger than the escape velocity. The expansion of the

Universe has nothing to do with it.

If you plunked down our Galaxy in the middle of empty, non-expanding

Minkowski space and let it evolve for a long time, the stars would

boil off and move apart from each other. The fact that the Galaxy

is in fact embedded in an expanding FRW spacetime doesn't enhance

that in any way.

(Well, actually, if there's a nonzero cosmological constant, as

current evidence seems to suggest, then eventually the boiled-off

stars start to accelerate away from each other due to the accelerating

expansion. But it's really the acceleration, not the expansion,

that's responsible for this effect. In a matter-dominated Universe

the expansion doesn't help the stars along at all.)

-Ted

Jul 28, 2000, 3:00:00 AM7/28/00

to

In article <2000072623...@rosencrantz.stcloudstate.edu>,

<t...@rosencrantz.stcloudstate.edu> wrote:

<t...@rosencrantz.stcloudstate.edu> wrote:

>In article <8lnmqq$ag3$1...@Urvile.MSUS.EDU>,

>John Baez <ba...@galaxy.ucr.edu> wrote:

>>(The stars will eventually "boil off", as described in an article

>>I just posted in the "ionization" thread, but that's a different effect,

>>not caused by the expansion of the universe! To confuse the issue,

>>once the stars boil off, the galaxy is no longer gravitationally

>>bound, or even a galaxy - it's just a bunch of stars flying this way

>>and that, and these stars will eventually move apart due to the

>>expansion of the universe.

>I don't agree with that last sentence. The stars will move apart

>because their "initial" (post-boiling-off) velocities away from each

>other are larger than the escape velocity. The expansion of the

>Universe has nothing to do with it.

Whoops! Thanks.

>If you plunked down our Galaxy in the middle of empty, non-expanding

>Minkowski space and let it evolve for a long time, the stars would

>boil off and move apart from each other. The fact that the Galaxy

>is in fact embedded in an expanding FRW spacetime doesn't enhance

>that in any way.

I see that you're right as long as the stars stay close enough

together that the flat-spacetime approximation remains good: in this

approximation, the expansion of the universe can be pictured as

simply the galaxies moving apart from each other at a rate proportional

to their distance... just like freely moving particles in ordinary

flat spacetime.

... so if two stars are moving apart from each other due to boiling

off, why then, they'll just keep moving apart at that speed - there's

no *extra* effect to worry about due to the "expansion of space" or

something like that.

[So far I'm just repeating what you're saying, in order to reassure

people that I learned my lesson.]

But now suppose, just for the heck of it, that the stars drift apart

to a distance where curvature effects matter. Surely their paths

will start to do something a big different in the Friedman-Robertson-

Walker metric than they would in flat spacetime. No?

Of course, for most purposes it's utterly silly to worry about

this, because as the stars boil off the galaxies, they will be

moving so slowly that it will take "forever" for them to get

far enough apart that the flat spacetime approximation ceases to

be excellent. Presumably this was your (very sensible) point.

But - in a feeble attempt to justify my silliness - remember that I

just posted an article about the end of the universe, and what we

can expect to happen in 10^20 years, or 10^66 years. For these

highly specialized purposes, it might be fun to know what happens

when the stars move so far apart that the spacetime curvature matters.

Is there an extra effect? What's it like?

Have any idea? I'm too lazy to work out the geodesics in the FRW

metric - especially since I stayed up late last night with John

Barrett doing an integral in oblate spheroidal coordinates in

hyperbolic space! It's very rare for me to do such calculations

these days, and I don't plan on doing antoher for at least a week.

But it should be possible to intuit the answer to *this* question

geometrically, without setting pencil to paper.

(I guess in the "Milne cosmology" that Matt McIrvin likes to talk

about - which is really just a solid lightcone in Minkowski spacetime,

viewed as an expanding universe in its own right - there would be

precisely *no* extra effect due to spacetime curvature, since this

spacetime is flat. And I guess this cosmology is the one suitable

to an expanding universe with *zero* stress-energy tensor. So throw

in matter.... hmm, now I'm guessing the extra effect will actually

act to *slow* the drifting apart of the stars!)

Jul 30, 2000, 3:00:00 AM7/30/00

to

In article <8lrnrc$2c71$1...@mortar.ucr.edu>,

John Baez <ba...@galaxy.ucr.edu> wrote:

>In article <2000072623...@rosencrantz.stcloudstate.edu>,

John Baez <ba...@galaxy.ucr.edu> wrote:

>In article <2000072623...@rosencrantz.stcloudstate.edu>,

>>If you plunked down our Galaxy in the middle of empty, non-expanding

>>Minkowski space and let it evolve for a long time, the stars would

>>boil off and move apart from each other. The fact that the Galaxy

>>is in fact embedded in an expanding FRW spacetime doesn't enhance

>>that in any way.

>

>I see that you're right as long as the stars stay close enough

>together that the flat-spacetime approximation remains good:

[...]

>But now suppose, just for the heck of it, that the stars drift apart

>to a distance where curvature effects matter. Surely their paths

>will start to do something a big different in the Friedman-Robertson-

>Walker metric than they would in flat spacetime. No?

Yes. And in fact, your guess below about what happens is exactly right:

>(I guess in the "Milne cosmology" that Matt McIrvin likes to talk

>about - which is really just a solid lightcone in Minkowski spacetime,

>viewed as an expanding universe in its own right - there would be

>precisely *no* extra effect due to spacetime curvature, since this

>spacetime is flat. And I guess this cosmology is the one suitable

>to an expanding universe with *zero* stress-energy tensor. So throw

>in matter.... hmm, now I'm guessing the extra effect will actually

>act to *slow* the drifting apart of the stars!)

Got it!

Of course, if there's a cosmological constant, that does act to push

the stars further apart, so they do accelerate away from each other in

that case. But in a matter-dominated Universe the effect of spacetime

curvature is to slow down their relative velocities.

Here's one way to think about it. In an expanding Universe, peculiar

velocities decay with time. (In case anybody's not up on the

terminology, "peculiar velocity" means "velocity with respect to

nearby comoving observers," and a "comoving observer" is someone who

is, heuristically speaking "at rest" in the expanding Universe.) So

the stars will eventually be at rest in comoving coordinates, and

their velocities relative to each other will simply be whatever

Hubble's law says they should be. In a matter-dominated Universe, the

expansion rate slows down with time, so the relative velocities of the

boiled-off stars get smaller as time passes; in a

cosmological-constant-dominated Universe, the opposite is true.

Things used to be so much simpler back when everyone thought the

cosmological constant was zero! You didn't have to put in all these

"but if there's a cosmological constant ..." clauses in everything you

said! Unfortunately, at the moment it looks like there actually *is*

a cosmological constant (or something very like it), so you can't get

away with leaving out those clauses anymore.

(By the way, I completely agree with Matt that thinking about the

Milne model is a terrific way to build up your intuition about

expanding spacetime. Everyone should go home and contemplate the

Milne model, right now!)

-Ted

Jul 31, 2000, 3:00:00 AM7/31/00

to

<t...@rosencrantz.stcloudstate.edu> wrote in message

news:2000072623...@rosencrantz.stcloudstate.edu...

> In article <8lnmqq$ag3$1...@Urvile.MSUS.EDU>,

> John Baez <ba...@galaxy.ucr.edu> wrote:

>

> >(The stars will eventually "boil off", as described in an article

> >I just posted in the "ionization" thread, but that's a different effect,

> >not caused by the expansion of the universe! To confuse the issue,

> >once the stars boil off, the galaxy is no longer gravitationally

> >bound, or even a galaxy - it's just a bunch of stars flying this way

> >and that, and these stars will eventually move apart due to the

> >expansion of the universe.

>

> I don't agree with that last sentence. The stars will move apart

> because their "initial" (post-boiling-off) velocities away from each

> other are larger than the escape velocity. The expansion of the

> Universe has nothing to do with it.

Just as I thought I was getting the idea, you have spoiled my way of

thinking: An earlier posting from Toby Bartels suggested that objects which

are bound to each other, like the cpmponents of my ruler, do not participate

in the expansion (relative to each other) Now you seem to suggest that

objects which were once bound but are no longer so, will also not

participate in the expansion (relative to each other). This seems weird to

me. The stuff out there appears to be of many kinds: That which is bound

to something, that which was once bound but is no longer and that which was

never bound to anything. Are you saying it is only the latter kind which

participates in the expansion?

>

> If you plunked down our Galaxy in the middle of empty, non-expanding

> Minkowski space and let it evolve for a long time, the stars would

> boil off and move apart from each other. The fact that the Galaxy

> is in fact embedded in an expanding FRW spacetime doesn't enhance

> that in any way.

>

> (Well, actually, if there's a nonzero cosmological constant, as

> current evidence seems to suggest, then eventually the boiled-off

> stars start to accelerate away from each other due to the accelerating

> expansion. But it's really the acceleration, not the expansion,

> that's responsible for this effect. In a matter-dominated Universe

> the expansion doesn't help the stars along at all.)

>

> -Ted

>

As a side line: The moderator's suggestion that I should have looked at

the FAQ (which I admit I haven't done yet) does not appear to be fully

vindicated, judging by the amount of correspondence which my naive quedtion

has generated!

Franz Heymann

[Moderator's note: Well, go look at it, right this very minute!! In

any case, my suggestion was not meant to imply that the FAQ had all

the answers or that no further discussion of this subject was

warranted; rather it was meant to ensure that participants in this

thread, having all read the FAQ, would be in a position to discuss

issues that go beyond what the FAQ covers. -TB]

Aug 1, 2000, 3:00:00 AM8/1/00

to

In article <8m1lp8$sk9$1...@lure.pipex.net>,

franz heymann <franz....@care4free.net> wrote:

franz heymann <franz....@care4free.net> wrote:

> Just as I thought I was getting the idea, you have spoiled my way of

>thinking: An earlier posting from Toby Bartels suggested that objects which

>are bound to each other, like the components of my ruler, do not participate

>in the expansion (relative to each other) Now you seem to suggest that

>objects which were once bound but are no longer so, will also not

>participate in the expansion (relative to each other).

I certainly wouldn't think of it this way! This makes it sound like

the history of an object determines its future, sort of like Oedipus's

past misdeeds causing his eventual doom. Nothing so fatalistic is

true, at least not in cosmology.

Suppose that you live in a matter-dominated expanding

Friedmann-Robertson-Walker Universe. All I mean by that barrage of

jargon is that matter is homogeneously distributed through space, so

that the geometry of space is the same everywhere, and that the main

thing influencing the expansion rate is the gravitational pull of

ordinary matter (not some icky cosmological constant or anything like

that).

Also, suppose that you're at rest in "comoving coordinates." All that

means is that you're not moving with respect to the expansion; in

other words, things look the same in all directions; in other other

words, your peculiar velocity is zero.

Finally, as long as we're supposing, suppose that you look out with

your telescope and see a distant object. You measure the speed (via a

Doppler shift, no doubt) of that object, and you find it's not moving

towards you or away from you. This object is not at rest in comoving

coordinates, of course: it's moving with respect to the stuff that's

just expanding along with the Hubble flow. (After all, if it were at

rest with respect to the expansion, you'd see a redshift in accordance

with Hubble's law.)

If you keep watching that object as time passes, you will find that it

starts to move towards you, not away from you. That is, it doesn't

get "swept up" in the expansion; it gets pulled in by your (and

everything else in your neighborhood's) gravity. Eventually,

it's going to hit you.

This is true regardless of the past history of the object and

regardless of how far away it is. I know it conflicts with

your (and most people's) intuition about expanding spacetime,

but that's what general relativity predicts.

-Ted

Aug 2, 2000, 3:00:00 AM8/2/00

to

t...@rosencrantz.stcloudstate.edu wrote:

>

> In article <8m1lp8$sk9$1...@lure.pipex.net>,

> franz heymann <franz....@care4free.net> wrote:

>

> > Just as I thought I was getting the idea, you have spoiled my way of

> >thinking:

..>

> In article <8m1lp8$sk9$1...@lure.pipex.net>,

> franz heymann <franz....@care4free.net> wrote:

>

> > Just as I thought I was getting the idea, you have spoiled my way of

> >thinking:

> This is true regardless of the past history of the object and

> regardless of how far away it is. I know it conflicts with

> your (and most people's) intuition about expanding spacetime,

> but that's what general relativity predicts.

Do you expect this analysis to hold in the emerging, more unified

models, even, say, in an approximate model of quantum gravity?

--

Frost Low Energy Physics

http://www.dcwi.com/~refrost/index.htm

[Moderator's note: Classical general relativity should be a good

approximation to quantum gravity in this regime, in order to

reproduce observations. So the expansion of spacetime should

happen in the same way in any good quantum gravity theory. -MM]

Aug 3, 2000, 3:00:00 AM8/3/00

to

Ted wrote for the most part:

>Toby Bartels <to...@ugcs.caltech.edu> wrote:

>>Space itself is expanding in the sense that

>>freefalling objects which were initially travelling side by side

>>would not remain travelling side by side as time went on.

>Suppose you live in an expanding FRW Universe. You put two test

>masses down in such a way that their velocity with respect to each

>other at some time is zero. To be precise, suppose you put them down

>in such a way that a light signal emitted by one would be received by

>the other with zero redshift. I assume that this is what you mean by

>"travelling side by side."

Actually what I meant was that the objects were so close

that we could pretend there was a local frame of reference including both

and according to which they were at some time both at rest.

>(But although the two objects are relatively

>nearby, they're not gravitationally bound to each other; they're test

>masses in a homogeneous FRW Universe.)

An important point.

We're really studying geodesics, not physical objects.

>Many people's intuition is that the expansion of the Universe will

>cause the two objects to start moving away from each other: as time

>passes, they'll get "swept up" in the expansion and acquire redshifts

>with respect to each other.

My intution too. I guess I was wrong.

Looking at some other threads here, I'm thinking like this now:

The statement I made about a local reference frame is good to 1st order,

but that turns out to not be strong enough to draw a conclusion.

If my statement about local reference frames is true to 1st order,

then (a) the particles have the same speed WRT the CMB to 1st order,

and (b) the particles measure no redshift WRT each other to 1st order.

Now, if (a) is exact, then they will separate with the expansion.

OTOH, if (b) is exact, then it all depends on the expansion's acceleration.

If something between (a) and (b) is true, it's something in between.

Is this correct?

If so, I can then say that space really is expanding

in that there is a field of local frames

(mathematically expressed by the FRW global time coordinate,

physically realised by the CMB) such that

particles at rest WRT these frames are growing farther apart.

Yes???

-- Toby

to...@ugcs.caltech.edu

Aug 3, 2000, 3:00:00 AM8/3/00

to

close enough an approximation, quantitatively, to predictions computed

from relativity equations for most regimes, even though the two

CONCEPTUAL MODELS are worlds apart?

If so, it seems overly speculative of you to hope to retain the concept

of "expansion of spacetime" intact across the transition from the old,

less unified models, to the new, more unified model.

Do you agree?

--

Frost Low Energy Physics

http://www.dcwi.com/~refrost/index.htm

They don't call it a paradigm shift for nothin'

Aug 4, 2000, 3:00:00 AM8/4/00

to

> > [Moderator's note: Classical general relativity should be a good

> > approximation to quantum gravity in this regime, in order to

> > reproduce observations. So the expansion of spacetime should

> > happen in the same way in any good quantum gravity theory. -MM]

>

> Is your comment here analogous to saying that the Newtonian model is

> close enough an approximation, quantitatively, to predictions computed

> from relativity equations for most regimes, even though the two

> CONCEPTUAL MODELS are worlds apart?

> > approximation to quantum gravity in this regime, in order to

> > reproduce observations. So the expansion of spacetime should

> > happen in the same way in any good quantum gravity theory. -MM]

>

> Is your comment here analogous to saying that the Newtonian model is

> close enough an approximation, quantitatively, to predictions computed

> from relativity equations for most regimes, even though the two

> CONCEPTUAL MODELS are worlds apart?

Yes

> If so, it seems overly speculative of you to hope to retain the concept

> of "expansion of spacetime" intact across the transition from the old,

> less unified models, to the new, more unified model.

>

> Do you agree?

No!!! Expansion of space-time is certainly one of the best verified

experimental fact about cosmology. A quantum gravity model, which wouldn't

predict any expansion (at least under some fraction of the possible initial

conditions) would be born-dead, I think (if I dare answering for MM..!).

To make this statement more precise, it is widely accepted that a theory of

quantum gravity would be very different from general relativity only for very

high energy densities (e.g. black holes, big-bang). For low energy densities,

where we don't expect quantum physics to play an important role, it should

reproduce the result of classical general relativity. A universe in homogeneous

expansion is something that happens when the matter density is low and constant

(as big masses can spoil locally the effect, by binding together objects which

should fall apart, as discussed in this thread). So homogeneous isotropic

expansion is certainly a regime where general relativity can be trusted.

Let me say now something more speculative!

Instead of being (like in GR) one of the many solutions of the equations of

motion, we might hope that an expanding universe could be predicted from

quantum gravity, as it should give us a sensible picture of the big-bang (which

GR is unable to do) and choose an expanding universe dynamically more or less

regardless of the initial conditions (for example, as the most likely scenario

with overwhelming probability w.r.t. others, to speak in quantum words).

Of course that's a dream up to now... but who knows!

Thank you for reading up to here...

Maxime

Aug 5, 2000, 3:00:00 AM8/5/00

to

In article <8m8hq7$a...@gap.cco.caltech.edu>,

>>Suppose you live in an expanding FRW Universe. You put two test

>>masses down in such a way that their velocity with respect to each

>>other at some time is zero. To be precise, suppose you put them down

>>in such a way that a light signal emitted by one would be received by

>>the other with zero redshift. I assume that this is what you mean by

>>"travelling side by side."

>

>Actually what I meant was that the objects were so close

>that we could pretend there was a local frame of reference including both

>and according to which they were at some time both at rest.

OK. That definition is a bit stronger than the one I gave above. My

definition only requires that they be not moving towards or away from

each other; yours has the additional requirement that they be close.

In hindsight, I should have included such a condition, since otherwise

my definition can get tangled up in time-delay issues. (If you see a

faraway object and it has zero redshift, does that mean it's

stationary with respect to you *now*, or that it was *then*?)

>The statement I made about a local reference frame is good to 1st order,

>but that turns out to not be strong enough to draw a conclusion.

>If my statement about local reference frames is true to 1st order,

>then (a) the particles have the same speed WRT the CMB to 1st order,

Either this is wrong, or I just mean something different from you by

"first order." The small quantity in question, I assume, is r/R,

where r is the separation between the two particles and R is the

Hubble distance. In that case, if particle 1 is at rest in comoving

coordinates, and particle 2 is at rest in a local inertial frame with

particle 1, then particle 2 will have a peculiar velocity (velocity

with respect to comoving observers at its location) of

v = Hr = c (r/R),

which is first-order in the small quantity.

>and (b) the particles measure no redshift WRT each other to 1st order.

>Now, if (a) is exact, then they will separate with the expansion.

>OTOH, if (b) is exact, then it all depends on the expansion's acceleration.

>If something between (a) and (b) is true, it's something in between.

>Is this correct?

If I'm understanding you correctly, then everything in this block

of text is true.

>If so, I can then say that space really is expanding

>in that there is a field of local frames

>(mathematically expressed by the FRW global time coordinate,

>physically realised by the CMB) such that

>particles at rest WRT these frames are growing farther apart.

>Yes???

Sounds good to me.

-Ted

Aug 5, 2000, 3:00:00 AM8/5/00

to

Toby Bartels wrote:

> Ted wrote for the most part:

>

> >Toby Bartels <to...@ugcs.caltech.edu> wrote:

>

> >>Space itself is expanding in the sense that

> >>freefalling objects which were initially travelling side by side

> >>would not remain travelling side by side as time went on.

>

> >Suppose you live in an expanding FRW Universe. You put two test

> >masses down in such a way that their velocity with respect to each

> >other at some time is zero. To be precise, suppose you put them down

> >in such a way that a light signal emitted by one would be received by

> >the other with zero redshift. I assume that this is what you mean by

> >"travelling side by side."

>

> Actually what I meant was that the objects were so close

> that we could pretend there was a local frame of reference including both

> and according to which they were at some time both at rest.

>

> >(But although the two objects are relatively

> >nearby, they're not gravitationally bound to each other; they're test

> >masses in a homogeneous FRW Universe.)

>

> An important point.

> We're really studying geodesics, not physical objects.

I think, that's precisely the point! If we don't consider their mutual

interaction, their respective geodesics will diverge. That's exactly what I

would call an expanding FRW universe, a universe where geodesics slowly

diverge.

Do you agree with that?

Aug 7, 2000, 3:00:00 AM8/7/00

to

In article <398A8868...@iph.unine.ch>, Maxime Bagnoud

<Maxime....@iph.unine.ch> wrote:

<Maxime....@iph.unine.ch> wrote:

>I think, that's precisely the point! If we don't consider their mutual

>interaction, their respective geodesics will diverge. That's exactly what I

>would call an expanding FRW universe, a universe where geodesics slowly

>diverge.

>Do you agree with that?

Not without additional stipulations. Objects' geodesics will diverge *if

they are at rest in comoving FRW coordinates*. But this is, locally

speaking, a quite arbitrary condition. In general their geodesics will

converge or diverge depending on their initial velocities.

--

Matt McIrvin http://world.std.com/~mmcirvin/

Aug 7, 2000, 3:00:00 AM8/7/00

to

Ted Bunn wrote in part:

>Toby Bartels wrote:

>>If my statement about local reference frames is true to 1st order,

>>then (a) the particles have the same speed WRT the CMB to 1st order,

>Either this is wrong, or I just mean something different from you by

>"first order." The small quantity in question, I assume, is r/R,

>where r is the separation between the two particles and R is the

>Hubble distance. In that case, if particle 1 is at rest in comoving

>coordinates, and particle 2 is at rest in a local inertial frame with

>particle 1, then particle 2 will have a peculiar velocity (velocity

>with respect to comoving observers at its location) of

>v = Hr = c (r/R), which is first-order in the small quantity.

I see what you mean. OK, how about 0th order?

That's enough, since a particle not at rest WRT particle 1 in any sense

might well have a peculiar velocity quite a bit larger than Hr,

so we really are saying something by claiming the 0th order term vanishes.

>>If so, I can then say that space really is expanding

>>in that there is a field of local frames

>>(mathematically expressed by the FRW global time coordinate,

>>physically realised by the CMB) such that

>>particles at rest WRT these frames are growing farther apart.

>>Yes???

>Sounds good to me.

Huzzah!

-- Toby

to...@ugcs.caltech.edu

Aug 8, 2000, 3:00:00 AM8/8/00

to

Matt McIrvin wrote:

Well, of course... Sorry. If the two particles are moving towards each other in

the first place, their geodesics will probably converge, I agree. That's not

really the situation I had in mind. I thought about initially parallel

geodesics (you will say that's a pretty unprecise statement), so "at rest in

comoving coordinates is probably a sensible definition for it and I agree to

what you're saying.

Thanks,

Maxime.

Aug 9, 2000, 3:00:00 AM8/9/00

to

In article <39900B7F...@iph.unine.ch>, Maxime Bagnoud

<Maxime....@iph.unine.ch> wrote:

<Maxime....@iph.unine.ch> wrote:

>Matt McIrvin wrote:

>

>> Not without additional stipulations. Objects' geodesics will diverge *if

>> they are at rest in comoving FRW coordinates*. But this is, locally

>> speaking, a quite arbitrary condition. In general their geodesics will

>> converge or diverge depending on their initial velocities.

>

>Well, of course... Sorry. If the two particles are moving towards each other in

>the first place, their geodesics will probably converge, I agree. That's not

>really the situation I had in mind. I thought about initially parallel

>geodesics (you will say that's a pretty unprecise statement), so "at rest in

>comoving coordinates is probably a sensible definition for it and I agree to

>what you're saying.

Actually, I think that "at rest in comoving coordinates" is not a sensible

definition for initially parallel geodesics. Objects that are at rest in

comoving coordinates in an expanding universe are moving apart to begin

with.

Suppose we define "initially parallel" timelike geodesics as those whose

greatest separation along a spacelike geodesic, measured from a certain

point on one of the timelike geodesics (and with the additional

stipulation that in a finite universe we have to measure the short way

round), does not change to first order under variation of the proper time

parameter of the point.

Then, I believe that objects with initially parallel geodesics, in an FRW

universe with no cosmological constant and positive matter density, will

fall together. It does not matter whether the universe on the whole is

expanding or contracting.

On the other hand, a cosmological constant can introduce the possibility

that they will move apart.

(Once again, it's helpful to think about the Milne model. This is just the

interior of a light cone in flat spacetime; in such a spacetime, initially

parallel geodesics will obviously not converge or diverge. Yet this is

also the zero-density limit of an expanding FRW cosmology. *Comoving*

geodesics will diverge, but only because the FRW coordinates that define

the comoving geodesics are built that way.)

Aug 10, 2000, 3:00:00 AM8/10/00

to

Matt McIrvin wrote:

> Actually, I think that "at rest in comoving coordinates" is not a sensible

> definition for initially parallel geodesics. Objects that are at rest in

> comoving coordinates in an expanding universe are moving apart to begin

> with.

Well, yes. I wasn't precise enough, again. I always have in mind this

stupid image of a sphere getting bigger and bigger and points on it

are slowly going apart. To translate this in words which really make

sense in a theory where only local coordinates are allowed is somehow

tricky.

> Suppose we define "initially parallel" timelike geodesics as those whose

> greatest separation along a spacelike geodesic, measured from a certain

> point on one of the timelike geodesics (and with the additional

> stipulation that in a finite universe we have to measure the short way

> round), does not change to first order under variation of the proper time

> parameter of the point.

OK.

> Then, I believe that objects with initially parallel geodesics, in an FRW

> universe with no cosmological constant and positive matter density, will

> fall together.

I was neglecting gravitational interactions all the way, focussing on

the effect of expansion. So, then OK, they will remain parallel

forever.

> It does not matter whether the universe on the whole is

> expanding or contracting.

>

> On the other hand, a cosmological constant can introduce the possibility

> that they will move apart.

>

> (Once again, it's helpful to think about the Milne model. This is just the

> interior of a light cone in flat spacetime; in such a spacetime, initially

> parallel geodesics will obviously not converge or diverge. Yet this is

> also the zero-density limit of an expanding FRW cosmology. *Comoving*

> geodesics will diverge, but only because the FRW coordinates that define

> the comoving geodesics are built that way.)

>

> --

> Matt McIrvin http://world.std.com/~mmcirvin/

Thank you, everything's getting slowly clearer.

Maxime

Aug 12, 2000, 3:00:00 AM8/12/00

to

In article <8msfmm$t0g$1...@Urvile.MSUS.EDU> you wrote:

: [snip other author]

: >Matt McIrvin wrote:

: >> Not without additional stipulations. Objects' geodesics will diverge *if

: >> they are at rest in comoving FRW coordinates*. But this is, locally

: >> speaking, a quite arbitrary condition. In general their geodesics will

: >> converge or diverge depending on their initial velocities.

:

: Actually, I think that "at rest in comoving coordinates" is not a sensible

: definition for initially parallel geodesics. Objects that are at rest in

: comoving coordinates in an expanding universe are moving apart to begin

: with.

: [snip other author]

: >Matt McIrvin wrote:

: >> Not without additional stipulations. Objects' geodesics will diverge *if

: >> speaking, a quite arbitrary condition. In general their geodesics will

: >> converge or diverge depending on their initial velocities.

: Actually, I think that "at rest in comoving coordinates" is not a sensible

: definition for initially parallel geodesics. Objects that are at rest in

: comoving coordinates in an expanding universe are moving apart to begin

: with.

I am very interested in direction of motion (apart or

together) of free moving objects, both in the expanding universe,

and in local General Relativity treatment of even the Earth's

gravitational field.

: Suppose we define "initially parallel" timelike geodesics as those whose

: greatest separation along a spacelike geodesic, measured from a certain

: point on one of the timelike geodesics (and with the additional

: stipulation that in a finite universe we have to measure the short way

: round), does not change to first order under variation of the proper time

: parameter of the point.

:

: Then, I believe that objects with initially parallel geodesics, in an FRW

: universe with no cosmological constant and positive matter density, will

: fall together. It does not matter whether the universe on the whole is

: expanding or contracting.

If two rockets are fired upward, one going quite a

bit higher than the other, both will be in inertial motion

after the fuel runs out.

The energy expended should give a clue as to what

the geodesics would be as time passes. The Earth observer

sees the rockets "falling" as they strike the surface, but

are they still not moving upward?

: On the other hand, a cosmological constant can introduce the possibility

: that they will move apart.

Does modern cosmology still assume "attractive" gravity

acting at those distances even though eveything is in inertial

motion?

Regards,

Joe Fischer

--

3

Aug 14, 2000, 3:00:00 AM8/14/00

to

In article <E13NKes-...@iglou.com>,

Joe Fischer <grav...@iglou.com> wrote:

Joe Fischer <grav...@iglou.com> wrote:

> Does modern cosmology still assume "attractive" gravity

>acting at those distances even though eveything is in inertial

>motion?

Modern cosmology isn't based on Newton's theory of gravity, if

that's what you are referring to.

Modern cosmology uses general relativity - usually with cosmological

constant, and sometimes with "quintessence" to spice things up.

If general relativity is right, Newtonian dynamics should be a

decent approximation in certain contexts, like the motion of

stars in a galaxy (ignoring black holes). But there are also

people studying MOND - Milgrom's "modified Newtonian dynamics",

a phenomenological approach to modifying Newtonian gravity aimed

at handling the missing mass problem.

A random sample:

Paper: astro-ph/9807023

From: san...@astro.rug.nl (R. H. Sanders)

Date: Thu, 2 Jul 1998 10:05:04 GMT (44kb)

Title: Resolving the virial discrepancy in clusters of galaxies with modified

Newtonian dynamics

Author: R.H. Sanders (Kapteyn Astronomical Institute, Groningen, NL)

Comments: Submitted to A&A, 4 pages, 3 figures, A&A macros

A sample of 197 X-ray emitting clusters of galaxies is considered in the

context of Milgrom's modified Newtonian dynamics (MOND). It is shown that the

gas mass, extrapolated via an assumed beta model to a fixed radius of 3 Mpc,

is correlated with the gas temperature as predicted by MOND (M_g proportional

to T^2). The observed temperatures are generally consistent with the inferred

mass of hot gas; no substantial quantity of additional unseen matter is

required in the context of MOND. However, modified dynamics cannot resolve the

strong lensing discrepancy in those clusters where this phenomenon occurs. The

prediction is that additional baryonic matter may be detected in the central

regions of rich clusters.

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