Accelerating Expansion Threshhold

[tfb]

A popular "Science" TV program said "The accelerating expansion of the universe does not apply to structures as small as the Solar System". Why not? Is there a boundary, marker, or distance that limits where the accelerated expansion begins?
Thanks from an humble pupil,
tfb

 

[Bodicea]

Hi another humble student here, and newbie too, so hello everyone


I believe its the currants in a cake thing. The cake will expand whilst baking, but the currants dont. Its the fabric of space that is being pushed and pulled and the solar system is just being pulled along with it, but yet not affected by it.

 

[granpa]

same reason you don't expand.

 

[geronimo]

same reason you don't expand.

Ah, from your own frame of reference only, possibly so!

But I too want to know what this mysterious and possibly arbitrary limit or distance marker is. My intuition tells me there is not one but without such a thing the balloon and raisins in cake analogies have reached their limits. New analogy required, please, to lift our thinking to the next level.

 

[Janus]

The "Limit" occurs where the effect of expansion is less the effect of the mutual gravitational attraction of the bodies involved. Thus for our Solar system, our galaxy and even our local group or cluster of galaxies gravity dominates and they do not expand. Clusters of galaxies, on the other hand, are separated by enough distance that the effect of expansion dominates and they recede from each other.

 

[81+]

It seems to me that our galaxy, and our galactic cluster, has to either be expanding with the rest of the universe or it has to be contracting due to its own gravity. I would vote for our cluster to be expanding. All by itself, as I understand it, our galaxy remains constant in size due to its gravitational force counterbalancing its centrifugal forces due to its rotation. But if space (all of space) is expanding then the planets, stars, etc. in our galaxy are moving farther apart which reduces the gravitatioinal forces and at the same time increases the centrifugal forces.

Frank

 

[Vanadium 50]

While Janus is absolutely right, I would say that more generally, things don't expand when the forces holding them together are stronger than the expansion. For the solar system, it's gravity. For a ruler, it's chemistry. For an atom, it's electromagnetism.

 

[wolram]

My understanding is, EVERY unit of space, (whatever that is), is expanding every where, the space units between the atoms that make up your computer are expanding, but your computer doe's not expand because the atoms are help together with their binding energy,
which is far stronger than any (pressure) exerted by space units expanding.

I think of this like a field of ghost bubbles, each and every ghost bubble is expanding, each and every ghost bubble has a minuscule capacity to move matter, so minuscule that every other force can over come it.

 

[hellfire]

The topic is quite complex and the answer depends heavily on the cosmological model.
See In an expanding universe, what doesn't expand?.

 

[Orion1]

Newtonian cosmological model...


Consider a classical Newtonian cosmological model where the cosmological force is equivalent to the gravitational force:

Newton's universal law of gravitation:
[tex]F_g = m \frac{d^2 r}{dt^2} = - \frac{G m^2}{r^2}[/tex]

Newtonian cosmological constant force:
[tex]F_{\Lambda} = m \frac{d^2 r}{dt^2} = \frac{\Lambda m r}{3} \; \; \; \; \; \; \boxed{\Lambda = \frac{1}{dt^2}}[/tex]

Newtonian cosmological force is equivalent to gravitational force:
[tex]\boxed{F_{\Lambda} = - F_g}[/tex]

[tex]\frac{\Lambda m r}{3} = \frac{G m^2}{r^2}[/tex]

[tex]\boxed{\Lambda = \frac{3 G m_u}{r_u^3}}[/tex]

Would such a cosmological model evolve as completely diffuse particles?

Reference:
https://www.physicsforums.com/showpost.php?p=2023221&postcount=9"

 

[stevebd1]

I know that when it comes to calculating distances using redshift, the normal doppler redshift equation can be used for z<0.01 (0.14 Gly), the relativistic doppler redshift should be used for 0.01<z<0.1 and anything larger than z=0.1 should take into account cosmological expansion. For z=0.1, the relativistic doppler redshift equation gives a distance of ~1.3 Gly which is a fair distance before the effects of the cosmological constant kick in (while it could be said that the universe is still expanding within z=0.1, this is not a cosmological effect and more the actual effect of things simply moving away from each other rather than the space between them expanding, though some argue that there is no doppler effect and that all universal expansion is the consequence of space itself expanding).

http://hyperphysics.phy-astr.gsu.edu/hbase/astro/Hubble.html" (scroll down)

http://www.geocities.com/alschairn/cc_e.htm"

 

[Orion1]

Cosmological redshift...

These galaxies are not receding simply by means of a physical velocity in the direction away from the observer; instead, the intervening space is stretching, which accounts for the large-scale isotropy of the effect demanded by the cosmological principle. For cosmological redshifts of z < 0.01 the effects of spacetime expansion are minimal and cosmological redshifts can be dominated by additional Doppler redshifts and blue shifts caused by the peculiar motions of the galaxies relative to one another.

Doppler redshift is bound by special relativity; thus v > c is impossible while, in contrast, v > c is possible for cosmological redshift because the space which separates the objects (e.g., a quasar from the Earth) can expand faster than the speed of light.

FLRW spacetime (expanding Big Bang universe)
Cosmological redshift:
[tex]1 + z = \frac{a(t_0)}{a(t)}[/tex]

Universe radius:
[tex]r_u = 2 \cdot 10^{26} \; \text{m}[/tex]

Cosmological constant:
[tex]\Lambda = \frac{1}{r_u^2} = 2.5 \cdot 10^{-53} \; \text{m}^{-2}[/tex]

Cosmological constant solar system experimental limit:
[tex]|\Lambda_{ss}| \leq 10^{-46} \; \text{m}^{-2}[/tex]

The measurable lower limit cosmological constant range:
[tex]r_{ss} \geq \sqrt{\frac{1}{\Lambda_{ss}}} \geq 10^{23} \; \text{m}[/tex]

[tex]\boxed{r_{ss} \geq 10^{23} \; \text{m}}[/tex]
[tex]\boxed{r_{ss} \geq 1.057 \cdot 10^7 \; \text{ly}}[/tex]

Galaxy cluster radius:
[tex]\boxed{r_{gc} = 10^{23} \; \text{m}}[/tex]

The greater the distance, the greater the cosmological constant effect.
The greater the cosmological constant magnitude, the greater the local effects on gravitation.

Reference:
http://en.wikipedia.org/wiki/Redshift#Redshift_formulas"
http://books.google.com/books?id=xm...&oi=book_result&resnum=2&ct=result#PPA408,M1"
http://en.wikipedia.org/wiki/Galaxy_groups_and_clusters"

 

[tfb]

Wikipedia is not my idea of a source for ultimate truth. When space expands my ruler also expands. And the raisins and currants in my cake expand. Gravity will work against expansion, locally as appropriate. And even as my atoms expand, tempered by local gravity, I cannot be aware of my local expansion. And that's because my ruler expands.
Howzzat!?
tfb

 

[sylas]

My understanding of the matter is as follows; and I am particularly indebted to Wallace for helping me follow this. (Which is why I voted for him under cosmo in the current PF voting season.) Any errors, however, are my own. I am an egg.

Expansion is not a force to pull things apart. Expansion is simply the motion of things moving apart. Things moving apart from each other are expanding; things not moving apart from each other are not expanding.

The role of "space" is not some kind of fabric or influence that helps moves things around. To get really really simple: it is a name we use for the gaps between things.

The rate at which things move apart from one another (expand) can change over time, because of various forces that may apply. Gravity, for example, tends to pull things back together. If some collection of things is expanding, gravity will tend to slow the expansion down.

The solar system isn't expanding. It is not because gravity is hard at work preventing the solar system from being pulled apart; it is that gravity HAS pulled it together so that there is no expansion going on. Same for our galaxy, or our local group of galaxies. Gravity has pulled them all together so that they are gravitationally bound and not expanding.

A complication is "dark energy". Apparently there is a kind of energy within the vacuum that works a bit like a tiny "pressure" (and that might not be the best word) to push things apart. The tendency of dark energy is to accelerate expansion. So in a sense there is something, it seems, that is continually pushing things apart while gravity is pulling them together. But it is not the expansion that is doing the pushing or pulling. Expansion is just a description of how things are moving at present.

A further complication is that space is not as simple as we once thought. We need to use GR to describe it properly. It has properties... curvature, for instance. On really large cosmological scales, the expansion of the universe looks like an expansion of space itself, and seems to be an almost irresistible thought to think of space carrying all the "stuff" along for the ride. That is, space expands and that is pulling things apart, as if space where some kind of fabric to which "stuff" is attached.

I think a more credible idea is to think of "stuff" as pulling on space, rather than the reverse. As "stuff" moves apart, there's more space.

Cheers -- sylas

 

[Wallace]

Hi Sylas, I'd say you've got a pretty good understanding going there! I have a few comments and additions which will hopefully help.

The solar system isn't expanding. It is not because gravity is hard at work preventing the solar system from being pulled apart; it is that gravity HAS pulled it together so that there is no expansion going on. Same for our galaxy, or our local group of galaxies. Gravity has pulled them all together so that they are gravitationally bound and not expanding.

A key concept here is the Virial Thereom which describes the balance between kinetic and potential energy in a stable system. The systems you mention; galaxies, clusters (eventually) and solar systems are examples of 'virialised' systems in which this balance holds.

The early universe has small differences in density from place to place and you can imagine solving the Friedmann equations, which are normally taken to represent the whole universe, for a finite region which happens to be at a different density from the average. If a region is sufficiently overdense, it will eventually collapse (even if the overall universe does not) forming a galaxy or cluster or galaxies. Formally, the size of the region (its local scale factor) will go to zero at some time. However, the Friedmann Equations are a simplification, and in practice the virial theroem kicks in preventing the contractiong from proceeding once the kinetic and potential energy are in balance.

So, once a system is virialised the initial condition of expansion is 'forgotten' and the system is stable. In practice, the mergers of different systems is actually the cause of the build up of things like galaxies and clusters, rather than isolated collapse, but the same arguements about virialisation hold.

A complication is "dark energy". Apparently there is a kind of energy within the vacuum that works a bit like a tiny "pressure" (and that might not be the best word) to push things apart. The tendency of dark energy is to acceleration expansion. So in a sense there is something, it seems, that is continually pushing things apart while gravity is pulling them together. But it is not the expansion that is doing the pushing or pulling. Expansion is just a description of how things are moving at present.

This is not as much of a complication as you might think. The simplest model for dark energy is a cosmological constant in which the energy density of dark energy is constant. In the Newtonian limit this acts as a force which is repulsive and proportional to distance, so that Newton's law of gravity becomes

[tex] F = -GmM/r^2 + Cmr[/tex]

where the C is some constant. What this does therefore is slightly changes the balance involved in the virial theorem, but importantly there is still a stable balance point. That is to say, in the presence of dark energy, the Earth might orbit a little bit further from the Sun than without, but it still finds a stable orbit. Even in the presence of dark energy, there is no residual expansion in bound systems.

The complication that can arise is the case of dynamical dark energy, in which the energy density of dark energy is not constant. In this case in principle the balance of the virial theorem could change over time, however if the energy density of dark energy is slightly decreasing, then this actually means a virialised system would contract, rather than expand, due to dark energy. In practice, the energy density of dark energy compared to that of matter is very very tiny in a collapsed objects like galaxies and clusters, so you can completely ignore its effects when it comes to internal dynamics. So even in the case of dark energy, there is no expansion in bound systems.

The one exception is the case of 'phantom' dark energy, in which the energy density of dark energy increases without bound into the future. In this case bound systems can be torn apart, and in principle eventually even atoms and smaller particles cannot stay bound, leading to a 'Big Rip'. This is a cartoon model that is completely absurd and most dark energy theorists rue the day this one got into the pop sci imagination, but none the less it can't be ruled out from present observations. Note that even in the most extreme cases, none of this will start happening for Billions of years.

A further complication is that space is not as simple as we once thought. We need to use GR to describe it properly. It has properties... curvature, for instance. On really large cosmological scales, the expansion of the universe looks like an expansion of space itself, and seems to be an almost irresistible thought to think of space carrying all the "stuff" along for the ride. That is, space expands and that is pulling things apart, as if space where some kind of fabric to which "stuff" is attached.

I wouldn't worry too much about that. You can always replace 'curvature of space' with 'gravitational field' (at least in the Newtonian limit) and then things are usually easier to understand. I strongly believe that if you need to invoke GR concepts like 'curvature of space' in order to explain or understand basic concepts to do with the expanding universe then you have missed something somewhere. GR is necessary in order to get the numbers right, but not the concepts.

 

[twofish-quant]

One other way of thinking about it...

The first calculation that you do for how the universe behaves *assumes* that the universe is completely even and that matter is totally evenly distributed. You get a nice simple equation which describes the universe is evenly expanding.

Now this is an approximation, so the next calculation you do takes all of the lumpiness in the universe and calculates that as a correction to your first calculation. You get a more accurate answer but the calculation is a lot messier.

Now for things like the solar system where things are not very even at all, the basic assumptions you have totally break down.

One other way of thinking of this is imagine a gas. If you look at a large amount of gas then you can imagine the gas as being a continuous, uniform fluid, and that gets you the right answer if you are looking at large amounts of gas. If you are looking at an one atom, this is not going to work.

 

[twofish-quant]

When space expands my ruler also expands. And the raisins and currants in my cake expand. Gravity will work against expansion, locally as appropriate. And even as my atoms expand, tempered by local gravity, I cannot be aware of my local expansion. And that's because my ruler expands.

It's incorrect.

The reason people talk about "expanding space" is that the theory that people use to model gravity involves looking at gravity in terms of distortions in space, but it's really not necessary. You can get the basic picture of the expanding universe by using plain Newtonian gravity without thinking about expanding space at all.

What is going on is that to get the general behavior of the universe, you *assume* that matter in the universe is evenly distributed. Now for the universe as a whole, that's a pretty good assumption. If you look at the solar system, it's a pretty bad assumption.

It's the old physics joke "assume a spherical cow".

 

[tfb]

Please excuse my ignorance. But if ALL RULERS expand, dosen't all the math and theories simply become irrelevant?
tfb

 

[VooDooX]

Question... If the universe is expanding and a photon is on a part of the bit that is expanding would this cause the photon to exceed C? also is it possible for expansion (which i assume is going faster and faster due to as we have more and more space we have more and more space that's expanding it seems it should be exponential ) to exceed C?

 

[S.Vasojevic]

Question... If the universe is expanding and a photon is on a part of the bit that is expanding would this cause the photon to exceed C? also is it possible for expansion (which i assume is going faster and faster due to as we have more and more space we have more and more space that's expanding it seems it should be exponential ) to exceed C?

Whole mess is build up on the sentence "space is expanding". For almost all purposes, we can say that space is not expanding, but the galaxies are flying away of each other. As they move further away, there is more space between them by definition, but that does not mean necessary that space expansion is cause, it may very well be only consequence.

 

[twofish-quant]

There's no rule that keep two points in the universe from moving away from each other at faster than the speed of light. The rule is that it's impossible to transmit information at faster than the speed of light so if one galaxy shines a light at another, that light will never make it.

 

[sylas]

Hi Sylas, I'd say you've got a pretty good understanding going there! I have a few comments and additions which will hopefully help.

Thanks... it does help!

... I strongly believe that if you need to invoke GR concepts like 'curvature of space' in order to explain or understand basic concepts to do with the expanding universe then you have missed something somewhere. GR is necessary in order to get the numbers right, but not the concepts.

This is a really important point. I've come to agree with you on that. Earlier this year we got into a dispute on the [thread=323692]The Mechanism of the Cosmological Redshift[/thread], in which I had been emphasizing the importance of GR and querying you for rejecting the notion that expansion involves an "inherently relativistic process". It turns out, I think, that I was getting excessively hung up on details and not seeing the concepts sufficiently clearly.

And for tfb:

Please excuse my ignorance. But if ALL RULERS expand, dosen't all the math and theories simply become irrelevant?

Rulers don't expand.

Cheers -- sylas

 

[tfb]

sylas, by "rulers" I mean "by whatever means we use to determine distance".
From galaxy A to galaxy B can be shown to be increasing by an amount, over time, minus gravitational effects. That's a "ruler". Am I too naive to be in this discussion?
tfb

 

[sylas]

sylas, by "rulers" I mean "by whatever means we use to determine distance".
From galaxy A to galaxy B can be shown to be increasing by an amount, over time, minus gravitational effects. That's a "ruler". Am I too naive to be in this discussion?
tfb

The ruler isn't the distance between two galaxies! They are moving apart from each other. You see this, by measuring this distance between them. We do this with rulers (conceptually) that DON'T expand.

(Added in edit. If you dig into the measurements; we don't actually see the movement by measuring distance and seeing if it changes. We rather measure velocity, or rate of change of distance, using the Doppler effect. Distances are measured by a range of methods, all of which conceptually employ standard rulers, and rulers don't expand, pretty much by defintion. If it expands, it isn't a ruler.)

A major ruler is the light-year. The distance light moves in one year. This distance doesn't expand.

Whether you will benefit from this discussion or not depends on whether you actually recognize that you need to learn a few things. There's nothing wrong with not knowing everything, being confused or mistaken, or asking questions in a discussion to try learning.

What would be naive would be to make confident statements, or think that you are here to engage in argument or dispute. Trying to learn more, or making mistakes, is not a problem at all. Good luck with it; people here can help you understand more about this. They've helped me; I may be able to help you, and if I can't then others can.

Cheers -- sylas

 

[Ich]

There's no rule that keep two points in the universe from moving away from each other at faster than the speed of light. The rule is that it's impossible to transmit information at faster than the speed of light so if one galaxy shines a light at another, that light will never make it.

There's no rule to forbid that either, as the "velocities" cosmologists refer to in these models are not standard velocities. They are coordinate quantities that have no direct link to SR-like definitions.
For example, the Hubble sphere (where the coordinate velocity exceeds c) is not a horizon. One can easily observe objects that are further away, and one can even imagine objects out there that are stationary to us, if only their distance is determined by the very same operational method everytime you try.

 

[VooDooX]

Please excuse my ignorance. But if ALL RULERS expand, dosen't all the math and theories simply become irrelevant?
tfb

i think what he means is since space is expanding all the time any calculations we make now will be useless in 100 year or even tomorrow if its an accurate enough calculation example we make a probe to visit a far off star system not in our galaxy (i know i know 1000's if not 100s of 1000's of years away) but when the ship gets there the universe will have expanded and the galaxy won't be where it was supposed to be or take much longer to get there in the 15 billion years the universe has existed some light has traversed 60-80-100 billion light years riding the expansion so not to break the speed of light however that seems to make me believe that 2 objects on opposite sides of the universe are traveling away from each other at a rate faster then 6 times the speed of light? that means objects on each side are breaking the laws of physics if someone can explain why this isn't true please elaborate? and if we are already breakign the speed of light how do we know our measurements aren't all false

 

[twofish-quant]

I think that the resolution to this is to say "galaxies are moving away from each other *as if* space is expanding". But space isn't really expanding. It's a *metaphor* for what is going on that you shouldn't take too seriously.

 

[VooDooX]

ya but it seems to be expanding at 5.2X the speed of light please explain why i would be wrong in thinking that since in 15 billion years the universe expanded 156billion lightyears across if logic was true and matter went less then the speed of light wouldn't the max diameter be 30billlion lightyears across

 

[Wallace]

The 'law of physics' that says you can't travel faster than the speed of light only has a simple unambigous description locally. What that means is you can't overtake a light beam, and someone running at you is always coming at you slower than light.

But, when you are talking about the 'speed' at which something a long long way away from you is moving, things become a little tricky, because there is no universal way to define the distance between you or how fast their watch runs compared to yours. Since speed is the change in distance over the change in time, it means there is no universal way to even describe the speed of a distant galaxy in comparison to you.

If you use the simplest and most useful set of co-ordinate that are used in cosmology, the co-moving Friedmann-Robertson-Walker co-ordinates, then in those co-ordinates, galaxies will be moving away from us at 'faster than the speed of light' once you reach a certain distance. However, in other equally valid co-ordinates, this is not the case.

This is an issue than is often overlooked or swept under the carpet, but it's quite fundamental. Some people like to latch onto one co-ordinate system and interpret what it tells you in a literally way, and try and explain how it's okay for things to move faster than the speed of light. The reasons this is not the best way to go, is that doing so violates the very fundamental principle in relativity, which is the relativity of simultanaity. What this says is that different observers can disagree on whether two events occurred 'at the same time'. There are many thought experiments along these lines, check Google of other threads for details.

In a cosmological context, what this relativitiy of simultanaity tells us is that we cannot declare a universal instant, a 'now', that everyone in the Universe agrees on, freeze expansion, measure the distnaces, then let the expansion continue for a moment, freeze it again, measure the distances and therefore know the velocties. Relativity says that there is no singular way to do this process, and therefore no unique way to define distances.

Think about it this way. When you receive a photon from a distant galaxy, you know that the light was emmitted a long time ago. So if you want to know how far away that galaxy is, do you define the distance as how far away it is 'now' or 'then' when the photon was emmitted? Say you define the distance as how far away it is 'now'. How would you know what they distance is? You'd have to go out and measure it somehow, which would take at least as long as the photon took to get to you, by which time the distance would have changed once again! Over small distances we don't have this problem; you can measure the length of you arm with a ruler without worrying about the fact that it takes longer for the light to get to your eye from one end of the ruler than from the other. But over cosmological distances this is a fundamental issue, we can't make 'instant' measures of distance.

In practice, there are a number of different ways in which we define the distance to distant galaxies in cosmology, and none of them imply that distant galaxies move away from us faster than light would at that same distance. That would be the only way in which we could sensibly say that galaxies receed at faster than light, and that certainly doesn't happen.

There is a well meaning school of thought which holds that 'space can expand at faster than the speed of light', or something along those lines, which tries to explain how the FRW co-ordinate imply superluminal motion without violating the laws of physics. Your statement 'light has traversed 60-80-100 billion light years riding the expansion so not to break the speed of light' makes me think you've been influenced by this idea. What you need to realize is that that is just one way of thinking about how the expansion works, which uses the 'expansion of space' as a metaphor for the way in which the FRW co-ordinate operate. It's an approach that has its merits, but also some dangers, which you have discovered in your thoughts above.

In truth, what we have are instantaneous observations, which we use to constrain a model governed by general relativity. There are some fundamental principles in GR, such as 'general co-variance' that ensures you cannot describe any space-time by a unique set of co-ordinates. In order to fitting our model to data however, we have to decide on a set of co-ordinates to use. The most useful and easiest are the FRW co-ordinates, so we use those. What is important is the physics that is implied by the parameter values of our model, once we fit to data. What is not important is the details of how the distance co-ordinate of a distant galaxy changes with respect to the time co-ordinate. This is something that depends only on the co-ordinate system, which is completeley arbitrary.

So, I've rambled for too long, but I'll summarise:

-- Galaxies do not in a meaningful way, receed from us at greater than the speed of light. The only way they would meaningfully do so is if they moved away faster than a light beam at the same location sa the galaxy, which clearly does not happen. --

 

[Wallace]

ya but it seems to be expanding at 5.2X the speed of light please explain why i would be wrong in thinking that since in 15 billion years the universe expanded 156billion lightyears across if logic was true and matter went less then the speed of light wouldn't the max diameter be 30billlion lightyears across

Just a quick addition, since you both posted while I was compiling my essay :)

Remember that those numbers you are quoting '156 billion light years across' are co-ordinate distances; they are derived using the FRW co-ordinates, in a different co-ordinate system you'd get a different distance, even though you are describing the same underlying space-time (and the same underlying physics).

 

[VooDooX]

so in essence your saying its due to time dilation ?

 

[twofish-quant]

This is one of the reasons physics is interesting. A lot of the standard concepts and assumptions don't work. If you talk about a "distance" to a distant galaxies, you have to define exactly what you mean by "distance" and it turns out that there are about five or six perfectly reasonable definitions for distance, that give you different numbers.

 

[twofish-quant]

so in essence your saying its due to time dilation ?

It's actually more fundamental. What is "distance" and what is "time"?

For something that I can hold in my hand, 'distance" is what I'm measuring with a ruler and "time" is what I measure with a stopwatch. The trouble is that for a distant galaxy I can't take a ruler and run it all the way to the galaxy, and I can't easily take my stopwatch and measure something that is going on there.

So I have to come up with another definition of distance and another definition of "time" and it turns out that there are several different reasonable definitions that give you different numbers.

I should point out that this is completely separate from the expansion of the universe.

 

[Wallace]

so in essence your saying its due to time dilation ?

No, what I'm saying is you can't say it's beacuse of this or because of that. Let me give a more concrete example. Let's ignore gravity for a moment and imagine you've got two massless dots moving apart. If we define our co-ordinates using simple Minkowski space (which is equivalent to special relativity) then there is no curvature of space-time. Now, in these co-ordinates we can define one dot to be at rest at some chosen origin, and the other dot is moving.

At any given moment, specified by the time on the 'stationary' observers watch, we can work out the co-ordinate distance to the 'moving' dot. Since there is no gravity, this distance increases with time at a steady rate, at less than the speed of light. If we fire photons between the dots, we find they are redshifted, this is because due to time dilation, the moving dot's clock runs at a different rate than the stationary one. All very well and good.

But, we don't have to describe this situation in this way. We could instead define a co-ordinate system that itself expanded, such that both dots are at rest with respect to the co-ordinates. This is just the same as taking say a rotating reference frame in the case of something that is spinning, just in this case we take a convenient co-ordinate system for an expanding system.

Now, in this set of expanding co-ordinates, both dots are at rest. But if we fire photons between the particles, we see they are red-shifted. How does this happen? It turns out that in this new co-ordinate system, as a photon passes through spatial co-ordinates, it gets steadily streched. This is because in this co-ordinate system 'space expands', because the spatial co-ordiantes have a time dependance.

So, in the first case, the dots move apart and redshift is caused by time dilation and in the second case the dots are at rest and redshift is caused by the expansion of space. Both descriptions are correct and give you the same answer for the redshift, but if you tried to assert that something was 'caused by time dilation' someone could also choose a different co-ordinate system in which that thing was 'caused' by something else.

There are certain 'invariants' that do describe the underlying 'truth' of a given space-time, but these are not the co-ordinates.

Note that the only difference between my example and the real universe is the addition of gravity, which adds in addition effects but doesn't change the issues around co-ordinates and there interpretation.

 

[S.Vasojevic]

Wallace, very useful posts. You just answered at about a half of threads in a cosmology forum, in a very coherent fashion.