[Little Bang]

CC I don't understand. You are a steady state guy and de Sitter's universe expands into nothingness? Or at least approaches nothingness.

[coldcreation]

Originally Posted by Little Bang

CC I don't understand. You are a steady state guy and de Sitter's universe expands into nothingness? Or at least approaches nothingness.

Hi Little Bang,

What do you mean by "nothingness"?



CC

[Little Bang]

The density of matter per cubic meter approaches zero.

[coldcreation]

Originally Posted by Little Bang

CC I don't understand. You are a steady state guy and de Sitter's universe expands into nothingness? Or at least approaches nothingness.

Which de Sitter model are you referring to, the 1917 model?

When you write steady state, do you mean the steady state theory (Hoyle, Bondi, Gold) or QSSC, other?


CC

[modest]

CC-
It's nice to see you arguing for a model that is not your own

In 1930 de Sitter admitted that neither solution (his or Einstein's) could represent our universe.
In 1931 de Sitter discovered Lemaître's solution and found it to be the "true solution"

Einstein came to the same conclusion. In fact, Einstein came to the conclusion that no static solution was valid because "the general structure of the Universe is not static"

[modest]

Originally Posted by Little Bang

CC I don't understand. You are a steady state guy and de Sitter's universe expands into nothingness? Or at least approaches nothingness.

Yes Little Bang, de Sitter's universe expands into nothingness. It expands to the point where 2 observers standing next to each other standing still would never see each other. However, it is a vacuum solution - if you add matter and fine tune the cosmological constant (like Einstein's) you can balance it out. His original model was just a vacuum he later added inertial and gravitational elements and a cosmological constant to see if it could in fact represent something 'real'. He came to the conclusion that it did not.

-modest

[coldcreation]

Originally Posted by modest

CC-
It's nice to see you arguing for a model that is not your own

The metric is only part of a model.

Originally Posted by modest

In 1930 de Sitter admitted that neither solution (his or Einstein's) could represent our universe.
In 1931 de Sitter discovered Lemaître's solution and found it to be the "true solution"

As I mentioned earlier, observations back in the 1930s (and in fact up to early 1990s) were simply insufficient to conclude which model or metric would best fit the real world. Even now (with the SNe Ia observations) it may be too early, but curvature has been observed, or at least a large deviation from linearity (whatever the interpretation or cause).

Originally Posted by modest

Einstein came to the same conclusion. In fact, Einstein came to the conclusion that no static solution was valid because "the general structure of the Universe is not static"

Tolman proved him wrong.

There are three static solutions (see above) as you now know.

Einstein also abandoned the idea of a flat, Euclidean universe with the advent of his general postulate of relativity.



cc

[modest]

Originally Posted by coldcreation

Tolman proved him wrong.

There are three static solutions (see above) as you now know.

Einstein also abandoned the idea of a flat, Euclidean universe with the advent of his general postulate of relativity.
cc

'Tolman proved Einstein wrong', that's funny! Einstein said that ALL static solutions are WRONG - including Tolman's list of 3. If Tolman is right and there are only 3 static solutions then they are ALL wrong according to Einstein.
'Tolman proved Einstein wrong'...

-modest

[coldcreation]

Originally Posted by modest

'Tolman proved Einstein wrong', that's funny! Einstein said that ALL static solutions are WRONG - including Tolman's list of 3. If Tolman is right and there are only 3 static solutions then they are ALL wrong according to Einstein.

-modest

You miss the point: The SNe Ia data.

In other words, the equations themselves do not allow us to determine which model best represents the real world: Only empirical observations can do that.

Tolman only proved that, in effect, three static solution were possible (in addition to the non-static solutions: the three Friedmann models, or FLRW).

So no one, not even Einstein, could have known which metric would eventually emerge victor. And again, we still may not know now, though the SNe Ia data is compelling, for a variety of possibilities (yes, even acceleration, lambda-CDM).


Do you wish to retract your geometrically flat, linear expansion regime claim in light of the SNe Ia data?





CC

[coldcreation]

.


So we have two views of nature, exemplified by either static solutions or non-static solutions to the Einstein field equations. In both species, there are (thought to be) three possible geometries: spherical, Euclidean, hyperbolic. And, in both cases, the geometry must be determined empirically.

In the case of the static metric, the geometry of the universe is directly determined by the mass-energy density of the universe which induces a nonzero curvature on the global spacetime manifold.

In the case of the non-static metric the recession velocity determines the geometric structure of the universe, resulting in a closed, flat, or open universe. The long-distance relationship to general relativity is that gravity determines the velocity, or rate of expansion. If there is enough force of attraction the velocity slows, causing a deceleration, and so on. Redshift, then, has virtually nothing to do with the general postulate of relativity or non-Euclidean spacetime.


An essential theme of general relativity is that the matter density of the manifold determines the space curvature. But to determine a fully viable notion of global curvature (and its raison d’être: the mass-energy density) that leads to the observed redshift, or “temporal displacements” requires some extrapolation from relativity, or at least an interpretation.

Einstein’s law of gravitation applicable to interstellar and extragalactic space must be supplemented with a hitherto poorly defined coefficient: the cosmological constant, lambda. Any definitive conclusions about the average mass-density of the universe or its geometric topology will undoubtedly have to include lambda, as the term represents an indispensable characteristic or property of spacetime.

Keep in mind, this is not obligatorily ‘new physics’ that introduces ad hoc concepts (dark energy) into a theory. This type of extrapolation is far less chimerical than the extrapolations based on Newtonian gravity or ‘relativistic’ instabilities leading conventional cosmologists to believe that space and time along with all the mass-energy in the entire cosmos were once upon a time wrapped up into one point of infinite density and curvature.


Light curves and redshift z of distant supernovae (SNe Ia) were raising the peculiar specter that Einstein’s constant was real. Remember that lambda (Einstein's so-called greatest blunder) was originally introduced to mediate equilibrium, staticity, in a gravitationally attractive, unstable universe. Yet, the observations had then to be interpreted in such a way that they would not viscerally oppose the finely tuned expansion of inflation, or Hubble's law, or even the favored critical Friedmann model.

The possibility that the new dark energy-like "greatest blunder" might revive some of the anti-big-bang rhetoric of the early 50s loomed. That is to say, confronted with choice of reintroducing the fudge factor or sacking eight decades of theoretical cosmology, physicists had to scramble fast, and scramble fast they did. It seemed the only way out was to change the constant.

If everyone is avoiding disagreement in order to save current theory, neither physicists from Cambridge England nor Cambridge Massachusetts are joining forces out of some resurrection of the old equilibrated romance between gravity and lambda. The mood at least in the United States is a quintessentially pragmatic one, emerging more out of a sense of self-preservation than a sentimental attachment to the cosmological constant as a kind of first principle.



CC