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Author Topic:   Motion in an expanding space
Ben!
Member (Idle past 1399 days)
Posts: 1161
From: Hayward, CA
Joined: 10-14-2004


Message 16 of 40 (181611)
01-29-2005 7:59 AM
Reply to: Message 4 by Sylas
01-28-2005 7:37 PM


Sylas,
I don't really get it.
The rate of expansion 70 km/sec/MPsec is called the "Hubble constant". The term is misleading, because the Hubble constant is not in fact a constant at all! It is a constant value through all space, but it changes with time.
Got it. No problem. But.. WHY does this constant change with time?
But what happens as time passes? In a simple zero density case, a galaxy at 1 MegaParsec distance, which is receding with the Hubble flow at 70 km/sec, will continue to recede at that same rate, even as it moves further away. So, taking a MegaParsec as 3*10^19 km, then after 4.3*10^17 (BC:changed) seconds, the galaxy will be 2 MegaParsecs away. This is about 14 billion years.
(Does than number sound familiar? It should! It is about the age of the universe, since the time when galaxies are at zero separation distance.)
OK... what does this mean? Does it mean that space has expanded to 1Mps since the big bang? I guess not, since the Hubble constant is changing in time. So, what does this mean?
At that time, the Hubble flow rate will be only 35 km/sec/MPsec. In other words, the flow rate is inversely proportional to age.
I've no idea how you got here. Clearly the "Hubble flow rate" is half of what it was as time doubled. But I have no understanding of the mechanism of WHY this would be.
Now there are a few more quibbles. A "cosmological constant" tends to maintain the Hubble flow at a fixed rate. As galaxies move further away, therefore, the rate of recession increases. In the extreme case this is what happens in so-called "inflation". If we have an inflationary expansion, so that the Hubble constant remains at 70 km/sec/MPsec indefinitely, then your answer is correct. (I think! I've only been learning about this myself quite recently.)
Whoa! Crazy! Now I'm really lost! But tell me this--if this "cosmological constant" didn't exist, and the "Hubble flow rate" was changing over time, then we WOULD see space "pull on" the particles--i.e. the particles would be seen to "accelerate" (i.e. change their relative velocity) without having any force applied to them.
On the other hand, gravity from mass in the universe tends to retard expansion.
Back in the crap hole. What?? How can gravity retard the expansion of space?? I can understand how it retards the expansion of mass, but .. space? How the heck does that work?
At present, there seems to be a small cosmological constant, but not enough for inflation, and also a small mass density which acts to retard expansion rates. So to a first approximation, we can just use the zero density model. Assume that the expansion of space is such that objects moving with the flow of expansion continue to recede at the same velocity as they move further away.
Shoot, lost again. I thought you said our universe was an inflationary universe (due to the cosmological constant). But then you say the cosmological constant is not enough for inflation. Which is it? Am I misreading?
Sorry for all the questions. i'll appreciate any comment that you make. I'll stop here for now, so that I avoid dousing you with further questions (i.e. the questions are raining down on you?)
Thanks,
Ben

This message is a reply to:
 Message 4 by Sylas, posted 01-28-2005 7:37 PM Sylas has not replied

  
Sylas
Member (Idle past 5261 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 17 of 40 (181620)
01-29-2005 8:45 AM
Reply to: Message 15 by Ben!
01-29-2005 7:36 AM


Good questions, Ben. I'll make an attempt to answer, and I'll warn you when I am likely to be a bit unreliable.
Ben writes:
What is a "local motion"? What reference frame defines "local motion" ? I don't get this at all. It doesn't fit with how I think about space. Would you mind to help me understand?
It turns out that at any point in space, there is one unique reference frame that fits easily with what we see of the universe.
The universe is filled with background radiation, coming from every corner of the sky. This is one of the major lines of evidence for the "Big Bang", and study of this radiation has been very useful in cosmology. It has the spectrum of a perfect blackbody radiator, with a supercold temperature of 2.725 degrees above absolute zero.
This radiation defines the rest frame. If you move through the radiation, it looks a bit hotter in the direction of motion, and a bit cooler looking back. In fact, the Sun is moving through this radiation at about 369 km/sec, and so from Earth, one half of the sky is just a bit hotter than the other half.
The velocity of 369 km/sec is measured with respect to the local rest frame of the background radiation. At any point in the universe, you can do the same thing; place yourself at rest with respect to the background radiation that fills the universe.
A set of observers spread through space, all of whom are at rest in this sense, are called the co-moving observers. They all recede from each other at a rate determined by the Hubble constant. That is, two co-moving observers at a separation of 1 MegaParsec will at the present instant be receding from each other at 71 km/sec.
A local motion means a motion with respect to the co-moving observer at your present location.
That is, the particles have a local velocity towards each other that exactly matches and cancels out the rate at which space is stretching between them.
I still don't get it. What is "local velocity" ? How is that different from "velocity" ? I can understand what it means for the two particles to be in the same inertial reference frame... but I think I'm missing something basic here.
Caution, I am approaching the limits of my ability again.
An inertial reference frame is a very important concept in special relativity, but it does not carry over to general relativity. In general relativity, the best we can manage is a local inertial frame. That is, for any point in space time, we can have different inertial rest frames centered on that point (but differing in velocity) that are a very good approximation to nearby spacetime, but become progressively less reliable as you move away.
Put another way, there is no inertial reference frame containing two particles that are 1 MegaParsec apart.
The notion of distance is dubious in general relativity. However, in cosmology there is a useful notion of proper distance. Basically, it is a distance between co-moving observers of the same age, all in a straight line and all adding up touching rulers. This distance expands over time. Hubble flow refers to the rate of increase of proper distance between co-moving observers at a point in time.
If you have a local motion, then you are effectively moving past a line of adjacent co-moving observers. Your velocity to another very distant point is in two parts. The local velocity is the rate at which you are passing by adjacent co-moving observers. The recession velocity is the rate at which proper distance is expanding between the observer you are next to right now and the distant observer. You add these to get the rate of change in proper distance to a distant observer.
Again, my standard reference for much of this stuff is Ned Wright’s Cosmology Tutorial. The notion of a comoving observer is discussed in the first section.
Cheers -- Sylas

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johnfolton 
Suspended Member (Idle past 5592 days)
Posts: 2024
Joined: 12-04-2005


Message 18 of 40 (181668)
01-29-2005 1:26 PM
Reply to: Message 14 by Sylas
01-29-2005 4:22 AM


Sylas, Your theory of space expanding appears to me to be just a measurement of the curvature of Space. The objects galaxies are moving in two dimensions, and the light is moving in 3 dimensions. If space is expanding then both light and the object would be moving in 2 dimensions.
You appear to be saying the galaxies are moving in two dimensions away from us at greater and greater speeds. That only the space between the galaxies are exibiting this two dimensional phenomenom of expanding space. I suspect what your actually seeing is how curved space is between the galaxies.
I think the galaxies are closer that they move in two dimensions, and the light that your basing their present distance has returned to earth on the space curve.
Space has thrown you a curve ball, and your scientists are calling it a fast ball. I think you got how fast an object is moving thru space in reverse. The galaxies are moving away from us primarily as a fastball(two dimensions), and its light is returning to us as a curve(three dimensions). Your only looking at it from 2 dimensions so you have this need to have space expanding.
I agree I don't know much about astronomy(you momentarily got my interest), but will have to agree with Einstein on this one.
I'm back to the lurking mode, cause what your saying does not make sense to me, unless were talking two dimensions, then you'd have to come up with expanding space to account for increasing distances.
http://www.phy.syr.edu/...modules/LIGHTCONE/einstein-gr.html
Curvature of Space in Two Dimensions
The idea of a curved surface is not an unfamiliar one since we live on the surface of a sphere. More generally, mathematicians distinguish 3 qualitatively different classes of curvature, as illustrated in the following image (Source):
http://csep10.phys.utk.edu/...2/lect/cosmology/geometry.html

This message is a reply to:
 Message 14 by Sylas, posted 01-29-2005 4:22 AM Sylas has replied

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Sylas
Member (Idle past 5261 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 19 of 40 (181698)
01-29-2005 4:09 PM
Reply to: Message 18 by johnfolton
01-29-2005 1:26 PM


You are not agreeing with Einstein. You are disagreeing with Einstein, and don't know enough to even recognize this. Your links are perfectly consistent with the information in this thread. They are trying to explain a basic point about relativity, without using heavy maths. Your comments about dimensions are incorrect. Galaxies and light are all moving in a a spacetime of three spatial dimensions and one time dimension. That spacetime is expanding. The association of curvature and expansion is much more complex than you represent; but in any case, whether curvature is positive, negative or flat (the three cases mentioned in your links) you still have the 71 km/sec/MPsec expansion. Curvature impacts on how expansion develops over time. It does not replace expansion as an alternative for the observations.

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Brad McFall
Member (Idle past 5033 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 20 of 40 (181907)
01-30-2005 6:20 PM
Reply to: Message 5 by CK
01-28-2005 7:52 PM


May I suggest "A Sophisticate's Primer on Relativity" by PW Bridgman; Weselyan University Press, Middletown, Conneticut 1962,1983?
It gave me a clear "operational" alternative to Einstein upto the Einstein,Podlosky,Rosen 1935 paradox as to Quantum Mechanics
The transition between pages 76-77 in this book is where ALL of my comments in the previous thread derived physically.

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Sylas
Member (Idle past 5261 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 21 of 40 (182030)
01-31-2005 9:55 AM
Reply to: Message 7 by Sylas
01-28-2005 8:16 PM


Sorry about the delay in posting this solution. The delay is due to my having some incorrect assumptions of my own!
The solution (which is the opposite to what I thought when I first posted!) is that the two particles do actually start to move apart from each other; at least if the current most favoured model for the universe is correct. The previously favoured model, before the discovery of accelerated expansion, was for the particles to approach each other! The puzzle I set for Charles was actually too difficult. Sorry Charles. There is a complication I neglected to consider in the first instance!
The reference I have been using, which has some undergraduate level maths, is Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects, by Tamara M. Davis, Charles H. Lineweaver, and John K. Webbc, at the Department of Astrophysics, University of New South Wales, Australia. I recommend it; it has excellent credentials, and is intended to help in teaching some physical consequences of expansion which are not always well understood.
People sometimes think that space pulls things along with it, somehow. It doesn't. Space just expands.
The problem I posed concerns two particles, which are held at the same fixed separation distance, while space expands. I assume that the particles are 1 MegaParsec apart, and that space expands at 70 km/sec/MPsec. This value is called H0, the Hubble constant.
The expansion of space means that there are 70 new kilometres of space between the particles every second. To remain at the same separation, the particles must have a local movement towards each other, of 70 km/sec, just enough to cancel the effect of expansion on separation distance.
If the particles are allowed to drift free of any forces, then to a first approximation they remain at a fixed separation. There is no force to accelerate the particles, so they keep moving locally at 70 km/sec. Space does not act to drag them in any direction. In the meantime, space continues to expand at 70 km/sec, so nothing changes, at least in the short term.
1. The Hubble constant is not constant. The Hubble constant H0, of 70 about km/sec/Mpsec, is not actually constant. It is a constant through all space, but it changes over time. How it changes depends on various properties of the universe. The most important properties are the density of the universe, and the cosmological constant. But in the absence of these two effects, the recession velocity of two galaxies, like a normal velocity in Newtonian physics with no forces, remains constant. This has the effect of reducing H. In fact, in this model H is simply the inverse of the age of the universe! We use H0 for H at the current instant.
Let’s consider how this changes things.
Let a million years pass by; which is about 3*1013 seconds. The galaxies that were previously one MegaParsec away from A are now on average an additional 2.1*1015 kilometers (70*3*1013) away, due to the expansion of space. A MegaParsec is about 3*1019 kilometers, so those galaxies are an additional 7*10-5 MegaParsecs away. But the rate at which space is increasing is still 70 km/sec between those galaxies and A. This means that the rate of expansion, after a million years, is now 70 km/sec for each 1.00007 MegaParsecs, which is 69.995 km/sec/MPsec.
Assuming that the local velocity of A and B remains 70 km/sec, they now will be approaching each other at about 5 meters a second.
Originally, I had hoped this would be enough to give a feel for what goes on. But it isn’t
2. Momentum decays. It turns out that just like the expansion of space gives photons a redshift, it also causes the momentum of any moving particles to decay. If the universe is empty of mass, so that galaxies maintain a fixed recession velocity as they move further away, it turns out that the decay of momentum matches the slowing of the Hubble constant, and the test particles in my problem statement remain at a fixed separation.
This means I was wrong in Message 4. I said that separation remains fixed in inflationary space. In fact, I should have said it remains fixed in zero-density case.
3. Mass retards expansion. It turns out that mass in the universe slows the expansion of the universe; a bit like pulling it in on itself. If we take into account the effects of mass, the expansion rate slows more rapidly than the local momentum, and so the test particles actually move closer together. This was the most favoured model for the universe up until several years ago.
4. The cosmological constant pushes expansion. Einstein’s equations allow for a so-called cosmological constant that accelerates expansion. Evidence presently suggests that there is small cosmological constant, at work in the universe. In this case, the expansion rate while momentum decays, and the particles will start to move away from each other as time passes. If current models are correct, then the cosmological constant is the more powerful effect; and the particles will indeed move apart from each other after release.
This is a pity; I was hoping for the opposite answer, to underline the fact that space does not pull on particles. Unfortunately, the current most favoured model for the parameters of the universe is such that the released particles will begin to move apart.
From hear on I get a little more technical, just to go into the answers in a little move depth. Proceeding is optional.

5. Scale factor, comoving observers. I’ve explained (Message 17) how background radiation defines a kind of natural rest frame anywhere in the universe. As particles move through space, we can calculate their momentum at any point with respect to their local rest frame at that point. This value for momentum is what decays. But note; the background radiation does not define a single inertial rest frame for the universe. General relativity does not have such a concept. The background defines many different inertial frames that work over small scales at each point in spacetime. These frames are called the co-moving observers.
There is a value called the scale factor of the universe, written a, that changes with time. This number represents how much space has expanded. It is defined to be one at the present instant, and at all other times is represents the factor by which distances between co-moving observers has changed.
Putting this in simple mathematical terms let R0 be the distance between two given comoving galaxies at the present instant. The scale factor after a time t is a(t), and the distance between the galaxies at time t can be given as R0*a(t).
The rate of separation for these two galaxies is thus R0da/dt, and the Hubble constant is always equal to (da/dt) / a.
For the simple case given above, the scale factor simple keeps increasing at a fixed rate, and so da/dt is a constant. Hence the value of the Hubble constant at any time is inversely proportional to the scale factor. H(t) = H0 / a.
6. Momentum inversely proportional to scale factor. This was my error; I initially neglected to consider this aspect of the situation.
Think first about background radiation. It fills the universe, from every direction. As space expands, the wavelength of the photons gets stretched as well. This has the effect of a redshift over time.
Photons have a momentum, inversely proportional to wavelength. Hence, as space expands, photons in space actually lose momentum. Their wavelength expands proportional to the scale factor, and so their momentum is initial momentum divided by a.
What about conservation of momentum, I hear you cry! What about conservation of energy! I’m not completely sure. One answer is that this may actually be compensated for by momentum and energy effects arising from the expansion itself. Another is that (hold on to your hat) conservation laws are only approximations anyway. The conservation laws are only defined locally, and in general relativity we don’t have a clear notion of a frame for the whole universe in which these laws can be easily expressed. Truth to tell, I don’t fully understand this aspect of general relativity yet, and don’t trust myself to give a good explanation. So for the moment, take it on trust, and we’ll see some consequences. I encourage interested readers to explore this further; and anyone who wants to take a stab at explaining conservation laws in the light of general relativity, fire ahead.
In any case, what I neglected to consider is that the same thing applies for particles moving at sub-relativistic velocities. Particles at motion gradually lose momentum with respect to their local rest frame, proportional to 1/a, just like photons.
Here is how I think about this.... as a moving particle moves into a frame for a new portion of space, there is an associated co-ordinate transformation, and with this transformation there is a loss of momentum just like we calculate different momentums depending on the different velocities of observers in normal Newtonian physics. That basically is what we have with moving particles. I am not really sure if this is a useful way to think about it, it seems to give the numbers that match theory.
7. The effect of momentum decay on particle separation. If we consider again the simple case in which receding galaxies retain the same recession velocity as space expands, then the rate of separation is proportional to 1/a, and so is the local recession velocity. Let t0 be the present time (the age of the universe) we have the relation a = t/t0 Thus both local velocity and recession velocity decay at the same rate, and the particles remain at the same separation.
8. The effects of mass. Einstein’s equations applied to the spacetime of the entire universe indicate that mass in the universe has the effect of slowing expansion. There is a certain critical value for mass density which is just enough to reduce the expansion rate to nothing in the limit, without quite being enough to halt expansion and let the universe re-collapse. Up until fairly recently it was thought that our universe had critical mass density, even though we were not sure where all the mass was. This has the effect of slowing the Hubble expansion
If the mass of the universe has critical density, it turns out that a(t) = (t/t0)2/3, and the released particles eventually approach each other.
9. The effects of a cosmological constant. This would need to be solved by numeric methods, as there is no simple analytic solution for scale factor. Basically, however, released particles do, eventually, start to recede from each other.
It is getting too late for me to run some sample numbers, so I’ll leave it at that for tonight.
Cheers -- Sylas

This message is a reply to:
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sidelined
Member (Idle past 5909 days)
Posts: 3435
From: Edmonton Alberta Canada
Joined: 08-30-2003


Message 22 of 40 (183286)
02-05-2005 1:58 PM
Reply to: Message 21 by Sylas
01-31-2005 9:55 AM


Sylas
It will be quite sometime till I catch up to the implications of this since my math is abysmal{Good news is I am working to improve it and am succeding} but there is a question that has floated in my head for some time concerning the equivalence of gravity and acceleration as put forth by a book I read on relativity that Einstein wrote.Since gravity is an acceleration experienced in the presence of mass is there some connection to the expansion of space and its local interaction with mass thT produce the acceleration we experience as gravity?
If space is expanding at a given rate{hubble expansion} does this expansion pertain to the space within atoms as well? Would this somehow mean that atoms are expanding with the universe but since the expansion is equal across all of spacetime then the relative sizes do not change and we cannot therefore measure a difference?
Please point out the error in my thinking since I am sure it is there but, as is the case with personal theories, it needs criticim of an evidentiary sort to drive them away. Thanks and I appreciate the links as I find them full of substance,though I do hope I will be able to better appreciate it as I realize my goals with math.
This message has been edited by sidelined, 02-05-2005 13:59 AM

This message is a reply to:
 Message 21 by Sylas, posted 01-31-2005 9:55 AM Sylas has replied

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Sylas
Member (Idle past 5261 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 23 of 40 (183300)
02-05-2005 4:38 PM
Reply to: Message 22 by sidelined
02-05-2005 1:58 PM


I'm quite dissatisfied with this thread. I do not think I have explained the matter well, and the explanation is more complex than really necessary. Sometime I might know enough to explain it better....
sidelined writes:
Since gravity is an acceleration experienced in the presence of mass is there some connection to the expansion of space and its local interaction with mass thT produce the acceleration we experience as gravity?
I'm not sure I understand the question.
I think the answer may be "no". Einstein's equations admit all kinds of solutions for the universe, depending on various parameters. With enough mass, expansion is slowed and eventually reverses to become a compression. With a cosmological constant, expansion accelerates and proceeds forever. With a careful balance of these features (which is what Einstein proposed) the universe is static, neither expanding nor contracting. Unfortunately, Einsteins model was unstable, and hence cannot explain an infinite static universe as he tended to assume.
The point is that in all of these models, on local scales mass continues to experience accelerations.
Expansion is not a separate thing that can ehlp explain local gravitational interactions. Rather, our current best theory of gravity represents gravity as acting upon spacetime to alter its geometry. Falling objects move along geodesics in spacetime. And on cogmological scales, the spacetime has global features like expansion, and a geometry (flat, open, closed).
General relativity is the model for both local and global aspects. The global expansion is not a separate thing that could stand as inducing the local interactions.
If space is expanding at a given rate{hubble expansion} does this expansion pertain to the space within atoms as well? Would this somehow mean that atoms are expanding with the universe but since the expansion is equal across all of spacetime then the relative sizes do not change and we cannot therefore measure a difference?
No. This is a common reaction, but in fact local forces, which move things through spacetime, are more than enough to hold things together while space is expanding.
This was been considered in considerable detail in a couple of posts in other threads. Have a look at Message 296. There is also a link to a good paper which calculates the effects of expansion on the gravitationally bound solar system. There is an effect, but it is far too small to detect. Gravity works to keep the orbit looking much the same, whether space is expanding, contracting, or remaining the same.
Cheers -- Sylas
This message has been edited by Sylas, 02-05-2005 16:41 AM

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Buzsaw
Inactive Member


Message 24 of 40 (183323)
02-05-2005 6:43 PM
Reply to: Message 22 by sidelined
02-05-2005 1:58 PM


Hi Sidelined. I asked the following similar specific question concerning the protons and electrons of atoms and expansion in post 297 of the GD which Percy answered in 298 and Silas answered in 299. It appears to me, by these answers of Percy and Silas, that they believe forces within things restrict the expansion of things like this which occupy space and the space which they occupy continues to expand through them, leaving the distances in and between the electrons and the protons within atoms constant, or maybe a better word is static/unchanged. From what I gathered of Silas's previous posts, however, that does not hold concerning the distances between galexies in the cosmos, because the gravitational forces within the cosmos is supposed to be insufficient to restrict the distances between galaxies caused by the alleged expansion of space.
Buz question in 297: "Even the minutest things like protons, electrons, and such occupy space. Do these expand with space?"
See Percy and Sylas's answers in GD thread posts 298 and 299.
This message has been edited by buzsaw, 02-05-2005 18:51 AM

In Jehovah God's Universe; time, energy and boundless space had no beginning and will have no ending. The universe, by and through him, is, has always been and forever will be intelligently designed, changed and managed by his providence. buzsaw

This message is a reply to:
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Eta_Carinae
Member (Idle past 4375 days)
Posts: 547
From: US
Joined: 11-15-2003


Message 25 of 40 (183325)
02-05-2005 7:08 PM
Reply to: Message 23 by Sylas
02-05-2005 4:38 PM


Sylas that is because.....
you got yourself into a pickle by formulating a question that you used an analytic solution to, but in reality it requires a numerical solution for.
You have to integrate numerically using the full Freidmann equation and values for Omega Lanmbda and Omega Matter like 0.73 and 0.27 respectively.
This message has been edited by Eta_Carinae, 02-05-2005 19:18 AM
This message has been edited by Admin_Eta, 02-05-2005 19:19 AM

This message is a reply to:
 Message 23 by Sylas, posted 02-05-2005 4:38 PM Sylas has replied

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Sylas
Member (Idle past 5261 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 26 of 40 (183326)
02-05-2005 7:16 PM
Reply to: Message 25 by Eta_Carinae
02-05-2005 7:08 PM


Re: Sylas that is because.....
you got yourself into a pickle by formulating a question that you used an analytic solution to, but in reality it requires a numerical solution for.
Right. The paper I have cited and tried to use does employ numerical solutions, and I could do the same myself from the formulae provided.
What I was trying to do... and failed... was give a simpler intuition for a potentially surprising result, with as little maths as I could get away with.
Part of the difficulty is that the (ΩM, ΩΛ) = (0.27,0.73) solution that is now widely cited as the best model consistent with current observations, will actually have tethered particles receding on release. Models from a few years ago with no ΩΛ component have tethered particles approaching on release.
By the way, welcome back. I've been writing a lot on cosmology recently, and I have badly needed your expertise! Watch your posting identity. You can select whether you are Admin or not in a post. You want to be back with the proles in this thread, I think.
Cheers -- Sylas

This message is a reply to:
 Message 25 by Eta_Carinae, posted 02-05-2005 7:08 PM Eta_Carinae has replied

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 Message 28 by Eta_Carinae, posted 02-05-2005 7:21 PM Sylas has replied

  
Eta_Carinae
Member (Idle past 4375 days)
Posts: 547
From: US
Joined: 11-15-2003


Message 27 of 40 (183327)
02-05-2005 7:17 PM


Just a general comment.
The global cosmic expansion involves the application of general relativity and the expression of the metric for spacetime in a Fermi-Robertson-Walker form. This intimately involves the concepts of global isotropy and homgeneity. These can be relaxed in other metrical forms and expansion derived but other mathematical problems crop up.
When you use GR in say solving forces between masses you have lost isotropy and homogeneity and you are solving a 'local' problem where the appropriate GR solution is say the Schwarzchild one.
The problem comes in combing them for a problem such as 'Does the cosmic expansion affect the spacing between atoms?'.
Since GR is inherently nonlinear (i.e. you cannot apply the principle of superposition) it is difficult to combine the two. If nothing else the two solutions involve different a priori assumptions.
This question has been talked about 'quietly' for years and somewhat swept under the carpet as a result.
If I remember, I'm too lazy to search, a guy called Cooperstock wrote a paper on this bout 3 years ago.
This message has been edited by Admin_Eta, 02-05-2005 19:20 AM

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Eta_Carinae
Member (Idle past 4375 days)
Posts: 547
From: US
Joined: 11-15-2003


Message 28 of 40 (183328)
02-05-2005 7:21 PM
Reply to: Message 26 by Sylas
02-05-2005 7:16 PM


You bugger....
how did you get the Omegas to display. I typed Omega out!!!

This message is a reply to:
 Message 26 by Sylas, posted 02-05-2005 7:16 PM Sylas has replied

Replies to this message:
 Message 30 by Sylas, posted 02-05-2005 7:46 PM Eta_Carinae has replied

  
Sylas
Member (Idle past 5261 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 29 of 40 (183333)
02-05-2005 7:45 PM
Reply to: Message 27 by Eta_Carinae
02-05-2005 7:17 PM


Re: Just a general comment.
The problem comes in combing them for a problem such as 'Does the cosmic expansion affect the spacing between atoms?'.
Yes! I alluded to this problem myself (or at least, I think I did, indirectly!) in one of my posts that I can't now find.
The paper I have cited several times (eg, in Message 286 of another thread) that calculates perturbations in the solar system arising from cosmological expansion has Cooperstock as one of the authors. It is
The influence of the cosmological expansion on local systems,
by F. I. Cooperstock, V. Faraoni, D. N. Vollick,
in Astrophys.J. 503 (1998) 61 (astro-ph/9803097)
The abstract reads as follows:
Following renewed interest, the problem of whether the cosmological expansion affects the dynamics of local systems is reconsidered. The cosmological correction to the equations of motion in the locally inertial Fermi normal frame (the relevant frame for astronomical observations) is computed. The evolution equations for the cosmological perturbation of the two--body problem are solved in this frame. The effect on the orbit is insignificant as are the effects on the galactic and galactic--cluster scales.
The paper seems to take a simplified approach, and simply assumes expansion is universal (as opposed to varying locally) and calculates the consequent pertubations on the Solar system and galaxy.
Is this the same paper you were thinking of? It does not seem to be quite the same thing, and I would very much like to see a reference that considers in detail the problems you mention.
I had a quick look, and just as a minor detail I found a wonderful page of Cooperstock quotations, which were apparently collected by admiring students in his relativity lectures. Cooperstock quotes.
Sounds like quite a guy!
Cheers -- Sylas

This message is a reply to:
 Message 27 by Eta_Carinae, posted 02-05-2005 7:17 PM Eta_Carinae has not replied

  
Sylas
Member (Idle past 5261 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 30 of 40 (183334)
02-05-2005 7:46 PM
Reply to: Message 28 by Eta_Carinae
02-05-2005 7:21 PM


Re: You bugger....
how did you get the Omegas to display. I typed Omega out!!!
Hit the "peek" button in the bottom right hand corner of a post to see how text was actually entered. I used HTML special character codes.

This message is a reply to:
 Message 28 by Eta_Carinae, posted 02-05-2005 7:21 PM Eta_Carinae has replied

Replies to this message:
 Message 31 by Eta_Carinae, posted 02-05-2005 8:00 PM Sylas has replied

  
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