What expands?

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franz heymann

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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.

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]

Toby Bartels

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


John Baez

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

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.)

franz heymann

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Jul 27, 2000, 3:00:00 AM7/27/00
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Thank you Toby, You have successfully given me a way of thinking about my
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]

alfred_...@my-deja.com

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

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.


t...@rosencrantz.stcloudstate.edu

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Jul 27, 2000, 3:00:00 AM7/27/00
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In article <8lj99l$f...@gap.cco.caltech.edu>,
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


t...@rosencrantz.stcloudstate.edu

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

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


John Baez

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Jul 28, 2000, 3:00:00 AM7/28/00
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In article <2000072623...@rosencrantz.stcloudstate.edu>,
<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!)


t...@rosencrantz.stcloudstate.edu

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Jul 30, 2000, 3:00:00 AM7/30/00
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In article <8lrnrc$2c71$1...@mortar.ucr.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


franz heymann

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

t...@rosencrantz.stcloudstate.edu

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


Ralph E. Frost

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

> 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]


Toby Bartels

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


Ralph E. Frost

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

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?

--

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


Maxime Bagnoud

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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?

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


t...@rosencrantz.stcloudstate.edu

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Aug 5, 2000, 3:00:00 AM8/5/00
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In article <8m8hq7$a...@gap.cco.caltech.edu>,

Toby Bartels <to...@ugcs.caltech.edu> wrote:
>Ted wrote for the most part:

>>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


Maxime Bagnoud

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


Matt McIrvin

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Aug 7, 2000, 3:00:00 AM8/7/00
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In article <398A8868...@iph.unine.ch>, Maxime Bagnoud
<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/


Toby Bartels

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


Maxime Bagnoud

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


Matt McIrvin

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Aug 9, 2000, 3:00:00 AM8/9/00
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In article <39900B7F...@iph.unine.ch>, Maxime Bagnoud
<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.)

Maxime Bagnoud

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


Joe Fischer

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

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


John Baez

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Aug 14, 2000, 3:00:00 AM8/14/00
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In article <E13NKes-...@iglou.com>,
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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