# Exploring the Possibility of Velocity Beyond c

• Omega0
In summary: CMB) is at rest in these coordinates.In summary, in curved space-time, there is no speed limit between objects separated by some distance. The speed of light limitation is only a limitation at a single point. This is because in General Relativity, there is no single definition of relative speed at different points. There are many possible choices and no way to say which is better. This makes it impossible to answer the question of when there was a possible velocity between point A and B greater than the speed of light. Additionally, comoving coordinates do not work the same way as inertial coordinates in Special Relativity, and it is impossible to directly measure the speed of a faraway object when spacetime
Omega0
Hi,

Say c is a reliable constant in nature. From what point in time there was a possible velocity between point A and B > c?

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In curved space-time, there is no speed limit between objects separated by some distance. The speed of light limitation is only a limitation at a single point. That is, the speed limit in General Relativity is the statement that nothing can outrun a beam of light.

The reason for this is that in General Relativity, there is no single definition of relative speed at different points. There are many possible choices and no way to say which is better. What this means is that you can write down your equations one way and say that points A and B are moving away from one another at 0.5c, and then write them down another way and say they're moving away at 2.0c. So there's just no way to answer your question.

Chalnoth said:
In curved space-time, there is no speed limit between objects separated by some distance. The speed of light limitation is only a limitation at a single point.
No, I would call it a reference frame, this might be big, depending from the curvature.
That is, the speed limit in General Relativity is the statement that nothing can outrun a beam of light.
The reason for this is that in General Relativity, there is no single definition of relative speed at different points. There are many possible choices and no way to say which is better. What this means is that you can write down your equations one way and say that points A and B are moving away from one another at 0.5c, and then write them down another way and say they're moving away at 2.0c. So there's just no way to answer your question.
If you measure and you measure from your point of view 0.5c than you measure 0.5c. I expect out there the same equations. I can see the coordinate system. I can transform. GRT doesn't mean that everything is relative, it just means that it makes it more complicated to transform (compared with SRT).
If I go to the limit c then my measurement ends. After the limit c I still have a universe which I can't measure, right? When the object would move avay < c I could measure something...
Sorry but I see a logical break in "comoving coordinates"...

Omega0 said:
If you measure and you measure from your point of view 0.5c than you measure 0.5c.

Measure what? Local measurements are not a problem, and the limit of c applies to those. But how would you measure how fast an object a billion light years away is moving relative to you?

Omega0 said:
If I go to the limit c then my measurement ends.

Measurement of what?

Omega0 said:
I see a logical break in "comoving coordinates"...

I think you have a misunderstanding of them. They're perfectly logical, but they certainly don't work the same as inertial coordinates in SR do. It seems to me that you are expecting them to work like SR inertial coordinates; that is bound to lead to confusion.

Omega0 said:
No, I would call it a reference frame, this might be big, depending from the curvature.
There is no unambiguous way to make a global reference frame. And even if you decide upon a specific global reference frame, you still have multiple options for defining speed.

The only situation in which it makes sense to compare speeds far away is in flat space-time. In practical situations, this means distances much shorter than the space-time curvature.

Omega0 said:
If you measure and you measure from your point of view 0.5c than you measure 0.5c. I expect out there the same equations. I can see the coordinate system. I can transform. GRT doesn't mean that everything is relative, it just means that it makes it more complicated to transform (compared with SRT).
If I go to the limit c then my measurement ends. After the limit c I still have a universe which I can't measure, right? When the object would move avay < c I could measure something...
Sorry but I see a logical break in "comoving coordinates"...
It is fundamentally impossible to directly measure the speed of a faraway object when spacetime is curved. The speed has to be interpreted, and that interpretation varies depending upon how you write down your equations.

For example, one way to think of speed is to change in distance over time. There is a way to define a distance specifically: you can use the proper distance. But to do that, you have to make a choice of time: you have multiple choices of which time at point A corresponds to a time at point B. One way to do this would be to use the CMB: we can call the time the same if the CMB temperature is the same. Using this definition, the change in distance over time is and always has been greater than c for most of the visible galaxies (because there are more galaxies visible further away than nearby).

PeterDonis said:
Measure what? Local measurements are not a problem, and the limit of c applies to those. But how would you measure how fast an object a billion light years away is moving relative to you?
That's the point, how we measure this? How me measure which speed have current objects relative to us?
The history of the universe has to be taken into account, right?
I like to understand how I can have an accelerating unviverse and dark energy if I can't measure the spead? What measurement have we?
I think you have a misunderstanding of them. They're perfectly logical, but they certainly don't work the same as inertial coordinates in SR do. It seems to me that you are expecting them to work like SR inertial coordinates; that is bound to lead to confusion.
Maybe I gett something wrong but are not that comoving coordinates the same as SR inertial coordinates from a point of say a galaxy?
It is said (Liddle, An Introduction to Modern Cosmology) that effects of the expansion having effect only to objects millions of lightyears away.
But for me it makes no sense to say that this effect is not aware to us - to our galaxy our the solar system or us - the point is just, the effect is so very very small - it's a joke.
It would be a logical contradiction to separate the comoving coordinates from the phyisical coordintes in a way that you say: "Well, little things like solar systems or galaxies feel nothing - but on the long distances it is felt, space is evolving".
This doesn't work logically since then you would need to define from when the influence ends to work or begins.
Do I think right?
PS: It something like in QM, the proton doesn't care about the electron mass since the electon charge is so dominant - but the mass is there, if so very very small

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Omega0 said:
That's the point, how we measure this? How me measure which speed have current objects relative to us?

And the answer is that there is no way to measure the "speed" of an object a billion light years away from us, relative to us, because that concept is not well-defined.

Omega0 said:
how I can have an accelerating unviverse and dark energy if I can't measure the spead?

Because the "acceleration" of the universe's expansion is not defined in terms of the "speed" of distant objects. It's defined in terms of the universe's scale factor and the fractional rate at which it increases. We measure the increase of the scale factor over time by making various measurements of the light we receive from distant objects: the redshift of the light, the angular size of the objects on the sky, and their brightness. The observed relationships between these measurements tell us how the scale factor of the universe has behaved over time.

Omega0 said:
are not that comoving coordinates the same as SR inertial coordinates from a point of say a galaxy?

No. Objects at rest in comoving coordinates will be moving away from us in SR inertial coordinates centered on us.

Omega0 said:
It is said (Liddle, An Introduction to Modern Cosmology) that effects of the expansion having effect only to objects millions of lightyears away.

What this means is that objects close enough to use are not "comoving" in the global sense of the comoving coordinates used in cosmology; their motion relative to us is not determined by the expansion of the universe. For example, our "Local Group" of galaxies (our galaxy, the Andromeda galaxy, and a few other smaller ones like the Magellanic Clouds) are gravitationally bound to each other, so their relative motion is not due to the universe's expansion. To see objects whose motion relative to us is due to the universe's expansion, you have to look far enough away.

Omega0 said:
It something like in QM, the proton doesn't care about the electron mass since the electon charge is so dominant - but the mass is there, if so very very small

Not really. The expansion of the universe, in and of itself, is not a "force"; it's just the inertia of objects that were flying apart in the past. So objects which are gravitationally bound don't feel any small "force" pushing them apart.

The accelerated expansion, due to dark energy, can be thought of as exerting a small "force" even on objects that are gravitationally bound, like the solar system or the galaxy; but on those scales it is way, way too small to matter.

PeterDonis said:
And the answer is that there is no way to measure the "speed" of an object a billion light years away from us, relative to us, because that concept is not well-defined.
Okay.

Because the "acceleration" of the universe's expansion is not defined in terms of the "speed" of distant objects. It's defined in terms of the universe's scale factor and the fractional rate at which it increases. We measure the increase of the scale factor over time by making various measurements of the light we receive from distant objects: the redshift of the light, the angular size of the objects on the sky, and their brightness. The observed relationships between these measurements tell us how the scale factor of the universe has behaved over time.
Okay, this goes into the direction that I may unwrap the nots in my potentential misconception, thanks - but why does angular size play a role in an isotropic homogenieous universe? This should only play a role in a non-isotropic universe?
I feel not well if you insert into the model now the "brightness". How to solve the problem of the Olbers paradoxon?
Isn't it a horror to introduce a dimmer factor?
No. Objects at rest in comoving coordinates will be moving away from us in SR inertial coordinates centered on us.
What this means is that objects close enough to use are not "comoving" in the global sense of the comoving coordinates used in cosmology; their motion relative to us is not determined by the expansion of the universe. For example, our "Local Group" of galaxies (our galaxy, the Andromeda galaxy, and a few other smaller ones like the Magellanic Clouds) are gravitationally bound to each other, so their relative motion is not due to the universe's expansion. To see objects whose motion relative to us is due to the universe's expansion, you have to look far enough away.
This seems to be a misconception. Everything in the universe is bound to each other, in my point of view. The link can be broken but this demands to be out of the light cone. In my eyes it makes no sense to separate between local and global. If you are introducing a new coordinate system which you call "comoving coordinates" you are introducing something pretty interesting: You feel fine as you did with absolute space and time (or SRT). You have that expansion factor but who cares, we are in our "Local Group". Then we have the void. Now the expansion factor begins to work. Not before...
This is a clear conceptual break. If you have something in physics then it is very often smooth, except from symmetry breaking. So, do you break a symmetry here?
The expansion of the universe, in and of itself, is not a "force"; it's just the inertia of objects that were flying apart in the past. So objects which are gravitationally bound don't feel any small "force" pushing them apart.
So we are back again to the roots: We introduce an absolute background. After we have left Galileo transforms and Newtons absolute time we construct physics on expanding space-time-coordinates?
The accelerated expansion, due to dark energy, can be thought of as exerting a small "force" even on objects that are gravitationally bound, like the solar system or the galaxy; but on those scales it is way, way too small to matter.
Back again: Now a suddenly introduced "anti-gravitation influence" plays a role - but it is too small to matter.
Sorry, but this seems to me like a logical misconception.

Omega0 said:
why does angular size play a role in an isotropic homogenieous universe?

Because something that's farther away should have a smaller angular size, so angular size is an indirect measure of distance. Basically what I was describing is comparing various indirect measures of distance to determine the behavior of the scale factor of the universe.

Omega0 said:
How to solve the problem of the Olbers paradoxon?

That paradox is already solved by any model of the universe which either (a) gives the universe a finite age, or (b) gives objects further away increasing redshifts. Since our current model of the universe does both of these things, it is not subject to Olbers' paradox.

Omega0 said:
Everything in the universe is bound to each other, in my point of view.

Then your point of view is wrong, at least with respect to this discussion. It is true that, considered in isolation, two pieces of matter can affect each other gravitationally no matter how far apart they are. But the universe does not consist of two isolated pieces of matter. There is matter everywhere, and from the viewpoint of any isolated system (our solar system or our galaxy or our Local Group--any system which is locally gravitationally bound), the matter in the rest of the universe is, on average, distributed symmetrically in all directions. That means the average gravitational influence of distant matter on local systems is zero, by the shell theorem.

Omega0 said:
If you are introducing a new coordinate system which you call "comoving coordinates" you are introducing something pretty interesting: You feel fine as you did with absolute space and time (or SRT).

Comoving coordinates do no such thing. They are just convenient to use in cosmology because observers who see the universe as homogeneous and isotropic, on average, are at rest in these coordinates. There is no claim about absolute space and time involved.

Omega0 said:
You have that expansion factor but who cares, we are in our "Local Group".

I didn't say the universe was not expanding in our local region. I said that the relative motion of galaxies in our Local Group is not due to that expansion, because those galaxies are gravitationally bound to each other. See above for more on how that works.

Omega0 said:
After we have left Galileo transforms and Newtons absolute time we construct physics on expanding space-time-coordinates?

We aren't constructing the physics using any particular coordinates; that's not how GR works. You can describe the solution of the Einstein Field Equation that we use to model the universe in any coordinates you want; you will get the same predictions for all physical observables. (Note, however, that whatever coordinates you use must be able to cover a large enough region of the universe; local inertial coordinates centered on our galaxy, for example, will not do that, they will only cover our local region.) As I said above, we choose comoving coordinates because they are convenient: they make the description look simple so it's easier to work with.

Omega0 said:
Now a suddenly introduced "anti-gravitation influence" plays a role - but it is too small to matter.
Sorry, but this seems to me like a logical misconception.

It plays a role on large scales--large distances and long times. It is too small to matter on local scales and over short times. There's no logical problem.

I would strongly recommend that you take some time to learn what our current cosmological models actually say before posting further; you appear to have some basic misconceptions, and if you continue to push them as you have in your latest post you are likely to receive a warning. I would recommend checking out Ned Wright's cosmology tutorial and FAQ here:

http://www.astro.ucla.edu/~wright/cosmolog.htm

PeterDonis said:
The accelerated expansion, due to dark energy, can be thought of as exerting a small "force" even on objects that are gravitationally bound, like the solar system or the galaxy; but on those scales it is way, way too small to matter.
If I imagine the perfect fluid, then the accelerated expansion works at any scale, regardless how small. But in contrast to the fluid, our universe is homogeneus only on very large scales. A galaxy is gravitationally bound and its average matter density is much larger than the matter density of the universe. So, I would have expected, that the accelerated expansion exerts zero force, not a very small one on a galaxy. Am I wrong?

timmdeeg said:
I would have expected, that the accelerated expansion exerts zero force, not a very small one on a galaxy. Am I wrong?

Yes. At least, it does on our current understanding of dark energy, which is that it, unlike the ordinary matter and energy in the universe, is homogeneous even on the smallest scales. In other words, the dark energy density really is constant everywhere, on all distance scales, whereas the ordinary matter and energy density is only constant on very large scales.

I see, I didn't ask the right question.
Let me try again. According to Friedmann the dynamics of the the expansion of the universe depends on the amounts of matter density and lambda. Now, let's compare the effect of the expansion on the scale of a galaxy regarding two cases, both with the same matter denisity and lambda: (i) the universe is perfectly homogeneous and (ii) the universe shows a large-scale structure like ours. With (ii) we should distinguish the effect of the expansion on a galaxy and on a void of the same size.
Could you please explain the outcome?

Another question. There are two versions to explain why galaxies don't expand. Often people mention the gravitationally bound system, but others talk about overdensity. What is correct? I mean, if two stars orbit each other in a distance of galaxy scale (other masses very far away), it's a gravitationally bound system then and one can hardly talk about overdensity. Shouldn't one expext, that such a binary system participates in the expansion on much smaller scales?

I thought the effect of expansion occurred even on small scales but it was extremely small.

nikkkom
timmdeeg said:
According to Friedmann the dynamics of the the expansion of the universe depends on the amounts of matter density and lambda.

Yes, but the matter density is highly variable on small enough distance scales--the Earth is about 30 orders of magnitude denser than the average matter density used in the Friedmann equations. The lambda density, OTOH, is constant everywhere.

timmdeeg said:
let's compare the effect of the expansion on the scale of a galaxy regarding two cases, both with the same matter denisity and lambda: (i) the universe is perfectly homogeneous and (ii) the universe shows a large-scale structure like ours. With (ii) we should distinguish the effect of the expansion on a galaxy and on a void of the same size.
Could you please explain the outcome?

In case (i), the matter is evenly distributed everywhere (which is of course a huge idealization; the reason we have stars and galaxies today is that the matter was never exactly evenly distributed to begin with), so eveyr single piece of matter will follow an exact "comoving" worldline. Since "expansion" is defined in terms of comoving worldlines, any two pieces of matter, no matter how close together they are, will show the effects of expansion.

In case (ii), on small enough distance scales, the matter is much denser than the average over the universe, so even if the center of mass of a system like a galaxy is following a "comoving" worldline, the rest of the matter in the galaxy is not; the system as a whole is gravitationally bound. So, for example, even if we assume that the center of mass of the Milky Way galaxy is following an exact "comoving" worldline, individual stars are not; the solar system's center of mass, for example, is not following a "comoving" worldline; it's orbiting the center of the galaxy. So you won't be able to see the effects of expansion on the scale of the Milky Way, because there are no pieces of matter actually moving on "comoving" worldlines, so their relative motion won't tell you anything about the expansion.

In fact, from our observations, case (ii) applies up to the scale of galaxy clusters and superclusters. Our galaxy and all the others in our Local Group are part of a cluster/supercluster, which is gravitationally bound even on a scale of tens of millions of light years. So even if the center of mass of the supercluster is moving on a "comoving" worldline, individual galaxies are not. So to see the effects of expansion, we would need to look on a large enough distance scale to see multiple superclusters, and be able to compare the motion of their centers of mass (which will be the average motion of all their galaxies). If we assume each supercluster's center of mass is moving on a "comoving" worldline, then comparing their motion does tell us about the universe's expansion, because we are comparing different "comoving" worldlines.

timmdeeg said:
There are two versions to explain why galaxies don't expand. Often people mention the gravitationally bound system, but others talk about overdensity. What is correct?

Both. The reason there are gravitationally bound systems at all is overdensity; some regions started out slightly denser than others, and gravitational clumping greatly magnified those density differences, so that we now have gravitationally bound systems on multiple distance scales.

timmdeeg said:
if two stars orbit each other in a distance of galaxy scale (other masses very far away), it's a gravitationally bound system then and one can hardly talk about overdensity.

If the average density of the system containing the two stars, at the distance they're orbiting each other, is not greater than the average density in the universe a a whole, then they can't be gravitationally bound.

PeterDonis said:
So you won't be able to see the effects of expansion on the scale of the Milky Way, because there are no pieces of matter actually moving on "comoving" worldlines, so their relative motion won't tell you anything about the expansion.
Thanks for you answer. If I understand you correctly, this means that the Milky Way doesn't expand at all. And it should also mean that the 'force' which the dark energy exerts on all scales has zero (not marginal) effect on gravitationally bound systems.

I'm interested in this question, because I never understood this paper: http://arxiv.org/pdf/astro-ph/9803097v1.pdf
The authors claim that the cosmological expansion affects the solar system, the milky way ... .

timmdeeg said:
If I understand you correctly, this means that the Milky Way doesn't expand at all.

Correct.

timmdeeg said:
it should also mean that the 'force' which the dark energy exerts on all scales has zero (not marginal) effect on gravitationally bound systems.

It is not correct to say that dark energy has zero effect. Dark energy does affect which worldlines are "comoving" ones, so it does affect (by a very small amount) how much the worldlines of objects in a gravitationally bound system like the Milky Way deviate from being "comoving". This effect can be thought of as a very small amount of tidal gravity.

timmdeeg said:
I'm interested in this question, because I never understood this paper: http://arxiv.org/pdf/astro-ph/9803097v1.pdf

I believe we had a thread on PF some time ago about this paper; I'll see if I can find it. IIRC, the basic conclusion was that the paper was only partly right: dark energy can be thought of as creating a very small amount of tidal gravity (as above), but expansion in itself does not.

timmdeeg
PeterDonis said:
It is not correct to say that dark energy has zero effect. Dark energy does affect which worldlines are "comoving" ones, so it does affect (by a very small amount) how much the worldlines of objects in a gravitationally bound system like the Milky Way deviate from being "comoving". This effect can be thought of as a very small amount of tidal gravity.

Understand, thanks for providing a new insight!

First: I didn't want to attack you or any else. I just don't like things that are because they are.

PeterDonis said:
That means the average gravitational influence of distant matter on local systems is zero, by the shell theorem.
Correct.
Comoving coordinates do no such thing. They are just convenient to use in cosmology because observers who see the universe as homogeneous and isotropic, on average, are at rest in these coordinates. There is no claim about absolute space and time involved.
That's what I wanted to say, obviously in the wrong way.

I didn't say the universe was not expanding in our local region. I said that the relative motion of galaxies in our Local Group is not due to that expansion, because those galaxies are gravitationally bound to each other. See above for more on how that works.
I think I understand that galaxies are bound gravitationally to each other.
As I said above, we choose comoving coordinates because they are convenient: they make the description look simple so it's easier to work with.
It plays a role on large scales--large distances and long times. It is too small to matter on local scales and over short times. There's no logical problem.
Sorry if didn't find the right words - I just wanted to s
But there is an influence which is really really small (http://arxiv.org/pdf/astro-ph/9803097v1.pdf).
To say the effect is very very small, that's acceptable.
Otherwhise the transformotion between real coordinates and comoving coordinates would be pretty anstonshing...

To summarize: The effect locally is peanuts but its' existing.

Liking our description of the local universe is strictly optional. The observational evidence does not change. Only interpretations.

Omega0 said:
To summarize: The effect locally is peanuts but its' existing.
It depends on what you mean, if you say "effect". As Peter Donis explained, gravitationally bound systems don't expand (not even tiny), but experience a tiny tidal force due to accelerated expansion (second derivative of the scale factor ##> 0##), which makes a difference.

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"From what point in time there was a possible velocity between point A and B > c?

Always, at every time.

Lineweaver and Davis have a really nice discussion in the 2005 Scientific American [available online]: Misconceptions about the Big Bang.

"when the hot plasma of the early universe emitted the radiation we now see, it was receding from our location at about 50 times the speed of light." [I'm pretty sure that also means 'every location' and recession velocities were even faster earlier in time.]

Hubble's law predicts that galaxies beyond the Hubble distance recede faster than c. Today that's about 14B light years distant.

Again, Lineweaver and Davis:

"The velocity in Hubble's law is a recession velocity caused by the expansion of space, not a motion through space. It is a genewral relativistic effect and is not bound by the special relativistic limit. Having a recession velocity greater than the speed of light does not violate special relativity.

Finny said:
"From what point in time there was a possible velocity between point A and B > c?

Lineweaver and Davis have a really nice discussion in the 2005 Scientific American [available online]: Misconceptions about the Big Bang.

Copy of the article is here... Highly worthwhile, IMO.
http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

diogenesNY

PeterDonis: #16 posts...

"...Dark energy does affect which worldlines are "comoving" ones, so it does affect (by a very small amount) how much the worldlines of objects in a gravitationally bound system like the Milky Way deviate from being "comoving". This effect can be thought of as a very small amount of tidal gravity..."

Can you provide any reference online where this is discussed so I can understand the conclusion better? I'm particularly interested not so much in the detailed mathematics, but the assumptions.

In post 10, Timedeg posted my understanding until I read your posts referencing dark energy directly. His post says, in my won words, the homogeneous and isotropic assumptions which lead to FLRW model expansion don't apply in a local, lumpy environment. That's what I thought until now.

By coincidence I just reread two conflicting papers this morning. The Lineweaver and Davis Scientific American article referenced above allows for a tiny local change. They say, IS BROOKLYN EXPANDING,

"...in our universe the expansion is accelerating, and that exerts a gentle outward force on bodies. Consequently bound bodies are slightly larger than they would be in a non accelerating universe...

I also reread this morning a paper which seems to arrive at a different conclusion:

Expanding Space, the Root of all Evil, July 2007...
edit: http://arxiv.org/abs/0707.0380
This paper was utilized to support 'no local expansion' in a prior discussion here in the forums... Here is what they said, section 2.2 LOCAL EXPANSIONS

""..We should not expect the global behavior of a perfectly homogeneous and isotropic model to be applicable when these conditions are not even approximately met. The expansion of space fails to have a meaningful local counterpart'...because the physical conditions that manifest the effects described as the expansion of space are not met in the average surburban bedroom."...[nor Brooklyn, the Lineweaver Davis article.].

So even with uniform dark energy on all scales, is that itself a sufficient condition to cause local expansion?
thank you

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From the paper referenced in post #23:

" Recently (Anderson 1995; Bonnor 1996) there has been a revival of interest in the
question as to whether the cosmological expansion also proceeds at smaller scales. There
is a tendency to reject such an extrapolation by confusing it with the intrinsically unobservable
”expansion” (let us refer to this as ”pseudo-expansion”) described above.
By contrast, the metric of Friedman–Robertson–Walker (FRW) in general relativity is
intrinsically dynamic with the increase (decrease) of proper distances correlated with
red–shift (blue–shift). It does so on any scale provided the light travel time is much
longer than the wave period. Thus, the cosmological metric alone does not dictate a
scale for expansion and in principle, it could be present at the smallest practical scale
as real– as opposed to pseudo–expansion, and observable in principle..."

I don't get that statement. If one assumes a homogeneous and isotropic [ideal cosmic fluid], of course the metric covers all distances. This seems to be circular reasoning of the worst sort. Am I misunderestimating what they say here...probably! What does the light travel time and wave period have to do with the theory?

Thank you.

Finny said:
the homogeneous and isotropic assumptions which lead to FLRW model expansion don't apply in a local, lumpy environment

More precisely, they don't apply to matter in a local, lumpy environment, because the matter is what's lumpy. See below.

Finny said:
"...in our universe the expansion is accelerating, and that exerts a gentle outward force on bodies. Consequently bound bodies are slightly larger than they would be in a non accelerating universe...

That's because dark energy is not lumpy; it literally has the same exact density everywhere and on all distance scales. So dark energy is homogeneous and isotropic, even though matter is not.

It's not difficult to calculate the effect of expansion on the solar system, if expansion occurs on all scales. Using the value of 1/144% per million years for this purpose and the age of the solar system as 4.5 billion years would suggest the solar system has expanded by about 31.25% which implies the Earth has receeded from the sun by nearly 25% since life arose about 3.5 billion years. A change of this magnitude would easily show up in paleontological records. But, the evidence suggests the sun was actually about 25% fainter than now at that time. This in itself is sufficient to dismiss the expanding solar system hypothesis. Needless to say universal expansion st all scales would produce some very curious spectral lines in objects at cosmological distances. Thus, one is led to suspect expansion does not occur on lesser scales.

Finny, as you can see, I had the same concern until a few days ago. The key point in the context of gravitationally bound systems is to distinguish between 'expansion' and the effect of a tidal force. Expansion means continuously increasing distances between co-moving objects, whereas tidal forces caused by the dark energy (accelerated expansion) tend to stretch things a little bit, depending on their elastic properties. In my opinion it would be confusing for this reason to call the stretching of the before mentioned systems due to tidal forces expansion.

The statement of Lineweaver & Davis "...in our universe the expansion is accelerating, and that exerts a gentle outward force on bodies. Consequently bound bodies are slightly larger than they would be in a non accelerating universe..." regards tidal forces. Only in the not realistic case of linear expansion, there wouldn't be tidal forces.

Chronos: "This in itself is sufficient to dismiss the expanding solar system hypothesis."

interesting calculation; You sure there isn't an issue with a decimal point somewhere? That result seems awfully big...of course my 'intution' has led me astray before.

From the UCLA asto website:

"...Cooperstock et al computes that the influence of the cosmological expansion on the Earth's orbit asround the sun amounts to a growth by only one part in a septillion over the age of the Solar System."
[I've forgotten what a 'sepetillion' is, but it's got to be small!]
edit: I came across a comment about this calculation of Cooperstock in another paper...that is was merely a two body calculation. Don't know the significance of that.

Also, hasn't the CMBR source expansion resulted in a change of wavelength of about a thousand, that is from about 3,000 K to about 3K today...an expansion of about a thousand? Doesn't seem possible our tiny solar system could have expanded as much as the calculation seems to show??

Timedeg: Thanks for you most recent post...I need to go back and reread PeterDonis explanations here.
All I understand right now is [a] without accelerated expansionn, there is no force, dark energy/ cosmological constant is the source of accelerated expansion. With 99%+ of matter actually empty space, it's easy enough to imagine dark energy itself being uniform.

I have read several papers, some of which I quoted already; some favor and others oppose local expansion.
Some of these are likely ten years old..maybe insights have changed.

In papers that do not favor local expansion, their argument seems to be "sure you can do local calculations", but the 'homogeneous and isotropic' conditions assumed in the model do not apply locally. I know I have seen references to the effect that 'massive galaxies' and even galaxy clusters void the assumptions of the uniformity of theFLRW model on small scales. Maybe that view has changed?

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Finny said:
hasn't the CMBR source expansion resulted in a change of wavelength of about a thousand, that is from about 3,000 K to about 3K today...an expansion of about a thousand?

Yes. But the CMBR is not a locally bound system; it is very well approximated as a homogeneous and isotropic "fluid" of radiation filling the universe. So the overall dynamics of the expanding universe should describe the CMBR very well.

PeterDonis said:
Yes. But the CMBR is not a locally bound system; it is very well approximated as a homogeneous and isotropic "fluid" of radiation filling the universe. So the overall dynamics of the expanding universe should describe the CMBR very well.

Yes, no issue with that...Thanks for the observation, but I was on a different topic when I posted about the universe expansion by a factor of 1,000...merely wondering if Chronos' calculation wasn't wildly too big regarding the solar system in comparsion with such distant expansion. Now that I think about it, my comparison is not so good as his is in a much more recent timeframe. Mine started shortly after the big bang, his only 4.5B or so years ago...apples and oranges...

Anyway, no issue about CMBR being homogeneous and isotropic...fits that description well...lots better than matter I think. .

Finny said:
merely wondering if Chronos' calculation wasn't wildly too big regarding the solar system in comparsion with such distant expansion

The solar system is a locally bound system, whereas the CMBR is not. You should not expect observations of the two to show similar effects from the universe's expansion. Chronos' calculation was merely confirming that, by showing what "similar effects" would look like--i.e., what we would expect to observe if the solar system had expanded over the past 4.5B years at the same rate as the universe as a whole. Obviously it hasn't, which is why this calculation gives an answer very, very different from what we actually observe.

Finny said:
"...Cooperstock et al computes that the influence of the cosmological expansion on the Earth's orbit asround the sun amounts to a growth by only one part in a septillion over the age of the Solar System."

This calculation takes into account the fact that the solar system is a locally bound system. Chronos's calculation does not, which is why it gives a very different answer.

Finny said:
my comparison is not so good as his is in a much more recent timeframe. Mine started shortly after the big bang, his only 4.5B or so years ago...apples and oranges...

That makes a difference, but it still leaves a large variance between the expansion of the universe as a whole (which is, IIRC, about a factor of 2 over that time period) and that of the solar system (which is much, much, much less, as the Cooperstock calculation shows--see above).

Finny
I guess another interesting question would be what it would imply if we events propagating faster than the speed of light locally. Particles with negative mass? Tachyons? :)

How would you propose to detect tachyonz?

PeterDonis said:
This calculation takes into account the fact that the solar system is a locally bound system. Chronos's calculation does not, which is why it gives a very different answer.

That makes a difference, but it still leaves a large variance between the expansion of the universe as a whole (which is, IIRC, about a factor of 2 over that time period) and that of the solar system (which is much, much, much less, as the Cooperstock calculation shows--see above).

http://arxiv.org/pdf/astro-ph/9803097v1.pdf

Quote:

"However, it is reasonable to pose the question as to whether there is a cut–off at which systems below this scale do not partake of the expansion. It would appear that one would be hard put to justify a particular scale for the onset of expansion. Thus, in this debate, we are in agreement with Anderson (1995) that it is most reasonable to assume that the expansion does indeed proceed at all scales. However, there is a certain ironical quality attached to the debate in the sense that even if the expansion does actually occur at all scales, we will show that the effects of the cosmological expansion on smaller spatial and temporal scales would be undetectable in general in the foreseeable future and hence one could just as comfortably hold the view that the expansion occurs strictly on the cosmological scale. ...

The purpose of the present paper is to provide a clear quantitative answer to the problem. The motion of a particle subject to external forces in the (approximate) LIF using Fermi normal coordinates is analyzed. It is the locally inertial frame based on a geodesic observer and it continues to be locally inertial following the observer in time. This is the frame in which astronomical observations are performed, and we compute the corrections to the dynamics due to cosmology. In this paper, we assume that homogeneous isotropic expansion is actually universal and we analyze the consequences of this assumption."

If I understand Cooperstock et al correctly, they talk in the subjunctive mood. Their calculation is based on the assumption that the expansion occurs "at all scales", thus obviously including the solar system. So it seems the result that the expansion of the solar system is negligible (but not zero) doesn't prove or disprove this assumption.

They don't mention tidal forces at all and presumably their assumption is not related to tidal forces, because probably no one would doubt their existence on small scales like the solar system, following your arguments. From this I suspect that Cooperstock takes into consideration that it is an open question whether or not gravitational systems do participate in the cosmological expansion.
On the other side they mention "external forced"; what is the meaning, if not tidal forces. To me it's a puzzle, so I would be glad to know your opinion.

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