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NGC7319
2007-Jul-04, 11:47 PM
If, for arguments sake, the Universe was not expanding, would General Relativity and or Special Relativty still be valid?

In other words, does the curvature of space time rely on an expansive universe?

Thank you

George
2007-Jul-05, 12:00 AM
At the time both theories were introduced, Einstein, like the rest of mainstream science, accepted a traditional static universe (no expansion or contraction). At its inception, Einstein rejected the idea of an expanding universe as proposed by Lemaitre (and Friedman). Hubble's observations changed his opinion, however.

[How expansion changes the formulations is far beyond me, admittedly.]

NGC7319
2007-Jul-05, 12:06 AM
At the time both theories were introduced, Einstein, like the rest of mainstream science, accepted a traditional static universe (no expansion or contraction). At its inception, Einstein rejected the idea of an expanding universe as proposed by Lemaitre (and Friedman). Hubble's observations changed his opinion, however.

[How expansion changes the formulations is far beyond me, admittedly.]
Thank you. My understanding is that GR (And SR) didn't work for a static universe, hence Friedman and Lemaitre coming to his [Einstein's] rescue, but it is these technical formulations that I struggle with, too. :)

Perhaps it is possible to give a simple answer, or maybe I am being naive?

George
2007-Jul-05, 12:20 AM
Thank you. My understanding is that GR (And SR) didn't work for a static universe, hence Friedman and Lemaitre coming to his [Einstein's] rescue, but it is these technical formulations that I struggle with, too. :)
SR really had little to say about it as it significantly avoided the gravitational aspect (as I understand it).

Friedman and Lemaitre, independently I believe, realized the equations strongly supported a non-static universe; gravity could not be discounted when applied to the cosmos itself. Einstein countered with his cosmological constant but gladly abandoned it once he was convinced it was inappropriate.

Cougar
2007-Jul-05, 12:39 AM
If, for arguments sake, the Universe was not expanding, would General Relativity... still be valid?
Yes, I believe so.


Einstein's [GR] equations do not specify the universe; rather they may be considered a general framework within which you can construct many different model universes. - Tony Rothman (http://www.physics.princeton.edu/~trothman/)

Ken G
2007-Jul-05, 12:41 AM
I think the key issue was stability. GR cannot produce a stable static universe, not even with a cosmological constant. Positive curvature, due to strong gravity, tends to generate even more positive curvature as it evolves, and negative curvature, due to a state of expansion, tends to get even more negative. Keeping the universe "flat" is then like trying to balance a pencil on its head, so we look for dynamical solutions, like expansion.

NGC7319
2007-Jul-05, 12:55 AM
I think the key issue was stability. GR cannot produce a stable static universe, not even with a cosmological constant. Positive curvature, due to strong gravity, tends to generate even more positive curvature as it evolves, and negative curvature, due to a state of expansion, tends to get even more negative. Keeping the universe "flat" is then like trying to balance a pencil on its head, so we look for dynamical solutions, like expansion.
Ah, thank you. This makes good sense to me, apart from the fact that I do not understand the difference beteen negative and positive curvature! :doh:

Tensor
2007-Jul-05, 01:40 AM
Ah, thank you. This makes good sense to me, apart from the fact that I do not understand the difference beteen negative and positive curvature! :doh:

That's easy. Parallel lines will meet at some point in positive curvature. Think of a sphere, like the Earth. Lines that are parallel at the equator (like lines of longitude), will meet at the poles. They separate in negative curvature. Think of a saddle shape. Of course, in flat space, parallel lines neither come together or separate, they stay at a constant separation. It's a bit harder, of course, to visualize it in four dimensions.

George
2007-Jul-05, 02:37 AM
That's easy. Parallel lines will meet at some point in positive curvature. Think of a sphere, like the Earth. Lines that are parallel at the equator (like lines of longitude), will meet at the poles. They separate in negative curvature. Think of a saddle shape. Of course, in flat space, parallel lines neither come together or separate, they stay at a constant separation. I realize this popular approach is especially useful for observations of distant objects which help decide the shape we are in, so to speak. :) However, is it too simplistic to consider the universe as spherical with a net gravitational field either strong enough to pull it all back in or too weak to stop the initial outward thrust? It seems apparent that we are extremely well balanced, though we are now in an acceleration mode.

Jeff Root
2007-Jul-05, 03:08 AM
Before the acceleration of the expansion was discovered (1998),
it was calculated that the balance between gravity and expansion
rate must be precise to better than one part in
100,000,000,000,000,000,000,000,000,000,000,000. If gravity
were stronger by that amount, the Universe would have collapsed
by now. If it were weaker, galaxies could not have formed.

I don't know how the acceleration affects this calculation.

-- Jeff, in Minneapolis

George
2007-Jul-05, 04:51 AM
I don't know how the acceleration affects this calculation.
I would bet it greatly contracts that ratio. Sorta like seeing a tight-rope walker perfectly balanced, then discovering the spray from a fire hose is about to hit him.

Ari Jokimaki
2007-Jul-05, 05:00 AM
If, for arguments sake, the Universe was not expanding, would General Relativity and or Special Relativty still be valid?
In addition to already mentioned Einstein's static universe, there's more modern Hoyle-Narlikar-Arp variable mass hypothesis, which is said to contain all the local effects of GR, but universe is not expanding. VM hypothesis has been developed so that initial premises are the same as in GR, but as GR assumes that mass is always unchanging constant, the VMH removes that assumption and says that mass changes over time (starts from zero and increases when it ages). The resulting universe is static (not expanding), but the mathematics of the hypothesis gives GR if it is solved for local space-time conditions. But it should be noted that the VMH is an alternative hypothesis, and doesn't have many supporters.

Twinsun
2007-Jul-05, 06:15 AM
hmm by expansion I guess that the Universe doesn't change teh relativity theory cause in the end all it does is enlarging the space and flattening the space

NGC7319
2007-Jul-05, 03:35 PM
So, in summation, GR works much better for a dynamical (probably expansive) universe. There are alternatives, but these remain speculative and fringe

If gravity were stronger, things would have collapsed, and any weaker, galaxies would not have formed.

Oh, and the rate of expansion is accelerating, probably because it is difficult to strike a perfect a balance between the above?

Thank you for these clarifications.

Paragraph 2 reminds me of the planetary thing, where gravity attracts planets to the sun, but they do not collapse into it, because their own inertia spins them off, but these forces balance, ad infinitum. Is this a little counter-intuitive, or is astronomy meant to screw with your head? :)

ngeo
2007-Jul-05, 03:50 PM
I think the key issue was stability. GR cannot produce a stable static universe, not even with a cosmological constant. Positive curvature, due to strong gravity, tends to generate even more positive curvature as it evolves, and negative curvature, due to a state of expansion, tends to get even more negative. Keeping the universe "flat" is then like trying to balance a pencil on its head, so we look for dynamical solutions, like expansion.

Can GR produce a universe that expands at a constant rate?

Ken G
2007-Jul-05, 08:40 PM
NGC-- sounds like a good summary to me.
ngeo-- I've no idea! In principle, GR can do anything, but it might not seem plausible.

Tim Thompson
2007-Jul-07, 07:33 AM
Can GR produce a universe that expands at a constant rate?
Sure. One way is to make the cosmological constant a variable which gets smaller as the universe expands. If it gets smaller at the aame rate that the self gravitation of the universe gets smaller, the expansion rate should be constant. Another way is to ignore the cosmological constant, and add a scalar field to the stress-energy tensor, which matches the weakening self gravitation of the universe.

ngeo
2007-Jul-08, 04:37 PM
Sure. One way is to make the cosmological constant a variable which gets smaller as the universe expands. If it gets smaller at the aame rate that the self gravitation of the universe gets smaller, the expansion rate should be constant. Another way is to ignore the cosmological constant, and add a scalar field to the stress-energy tensor, which matches the weakening self gravitation of the universe.

If the scalar field is added, does that affect the way the observation of expansion is interpreted so there is no current acceleration, or can acceleration can be measured in other ways that don‘t need GR?

Tim Thompson
2007-Jul-08, 06:16 PM
If the scalar field is added, does that affect the way the observation of expansion is interpreted so there is no current acceleration, ...
I don't think there is a way to avoid the interpretation of accelerated expansion by adding a scalar field. But there are other ways to try ...


... or can acceleration can be measured in other ways that don‘t need GR?
It's not so much about needing GR, it's about the expanding universe cosmology. Ken G says even with a cosmological constant we can't make a static universe; I haven't heard that before, but since I am trying to leave on a long delayed vacation, I am not going to do the work to investigate the matter for a while. But I have been under the impression that a cosmological constant could do what Einstein wanted it to do, namely make the universe static (i.e., GR would then be compatible with a non-expanding universe).

Accelerated expansion is not an observation, it is a model dependent interpretation. The observations are the light curve, brightness & redshift of distant type-Ia supernovae. A cosmological model is used to derive a distance from the redshift, and that distance is used to derive an expected observed light curve & brightness, which are then compared with their observed counterparts. The comparison reveals that the observed brightness is lower than expected. so, either the SNe are farther away than we expect them to be, or some intervening material ("dust") dims the SNe, and we are not accounting for the effect. One might also doubt that type Ia SNe are "standard candles".

The weakest argument is the assumption that type Ia SNe are not standard candles. The SNe that are used in the studies are heavily selected to match the characteristics of "local", known type Ia SNe. So even if the overall class of objects is not as reliable a standard as we think, the ones selected for cosmological studies certainly are, and that's why the argument is weak.

There has been considerable effort on the dust problem, and it has been well established that no known type of dust can produce the observed effect. This is because dust does not just dim, it dims & reddens. There is no evidence of reddening in SNe light curves, only dimming.

With dust & non-standard SNe ruled out, the only interpretation left, in the context of expanding universe cosmology, is that the observd SNe are farther than expected. And that leads to an accelerating expansion.

So, the only way to escape the accelerated expansion interpretation is to escape first from the expanding universe cosmology. You can't use the SNe observations to reliably argue against an expanding universe, because we already know that expanding universe cosmology is consistent with the observations, when accelerated expansion is included. You would have to show that acceleration is unreasonable or unacceptable, in GR or expanding universe cosmologies, in order to break the link between the accelerated expansion interpretation and the observations.

The methods I outlined in my previous post will produce a univers that expands at a constant rate. But that would create a model that is inconsistent with observation. So such models would be discarded in any case.

ngeo
2007-Jul-08, 08:01 PM
I don't think there is a way to avoid the interpretation of accelerated expansion by adding a scalar field. But there are other ways to try ...


It's not so much about needing GR, it's about the expanding universe cosmology. Ken G says even with a cosmological constant we can't make a static universe; I haven't heard that before, but since I am trying to leave on a long delayed vacation, I am not going to do the work to investigate the matter for a while. But I have been under the impression that a cosmological constant could do what Einstein wanted it to do, namely make the universe static (i.e., GR would then be compatible with a non-expanding universe).

Accelerated expansion is not an observation, it is a model dependent interpretation. The observations are the light curve, brightness & redshift of distant type-Ia supernovae. A cosmological model is used to derive a distance from the redshift, and that distance is used to derive an expected observed light curve & brightness, which are then compared with their observed counterparts. The comparison reveals that the observed brightness is lower than expected. so, either the SNe are farther away than we expect them to be, or some intervening material ("dust") dims the SNe, and we are not accounting for the effect. One might also doubt that type Ia SNe are "standard candles".

The weakest argument is the assumption that type Ia SNe are not standard candles. The SNe that are used in the studies are heavily selected to match the characteristics of "local", known type Ia SNe. So even if the overall class of objects is not as reliable a standard as we think, the ones selected for cosmological studies certainly are, and that's why the argument is weak.

There has been considerable effort on the dust problem, and it has been well established that no known type of dust can produce the observed effect. This is because dust does not just dim, it dims & reddens. There is no evidence of reddening in SNe light curves, only dimming.

With dust & non-standard SNe ruled out, the only interpretation left, in the context of expanding universe cosmology, is that the observd SNe are farther than expected. And that leads to an accelerating expansion.

So, the only way to escape the accelerated expansion interpretation is to escape first from the expanding universe cosmology. You can't use the SNe observations to reliably argue against an expanding universe, because we already know that expanding universe cosmology is consistent with the observations, when accelerated expansion is included. You would have to show that acceleration is unreasonable or unacceptable, in GR or expanding universe cosmologies, in order to break the link between the accelerated expansion interpretation and the observations.

The methods I outlined in my previous post will produce a univers that expands at a constant rate. But that would create a model that is inconsistent with observation. So such models would be discarded in any case.


It seems right that GR including the cosmological constant is unable to produce a stable static universe:
http://en.wikipedia.org/wiki/Einstein_field_equations
“The cosmological constant term was originally introduced by Einstein to allow for a static universe (i.e., one that is not expanding or contracting). This effort was unsuccessful for two reasons: the static universe described by this theory was unstable, and observations of distant galaxies by Hubble a decade later confirmed that our universe is, in fact, not static but expanding.”
If GR is able to produce a model for a stable (i.e. constantly) expanding universe, I don’t think such a model necessarily needs to be immediately discarded since the universe also does not appear isotropic or homogeneous until around 200 megaparsecs - in other words, at the distances measured to produce the interpretation of accelerated expansion, the universe may have structure so doesn’t follow the cosmological principle. If the acceleration is taking place in in voids, it is taking place in regions with structure. If the supernovae are measured at around z = .4-.6, and 200 megaparsecs is equivalent to around z = .04, there seems to be room for uncertainty in any interpretation made according to the cosmological principle. This is not to say that acceleration is not taking place, but that it may be in regions within an overall constant expansion universe.

Anyway, thanks for the response, happy vacation!