Quote:
Originally Posted by modest
Yes. I've read that he originally ignored them, then moved to actively arguing against their physical existence.
I don't think so. His argument, as best as I can recall, was that the angular momentum of some collapsing system would stabilize it before a black hole could form. ~modest
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I believe he could have used a different argument based on the fact that relativity defines the magnitude of a space-time curvature in a volume of space as being dependent on the magnitude of the gravitational potential in that volume.
However, the gravitational potential at the center of a mass is by definition zero therefore the according the concepts of relativity the space-time volume in the center of a collapsing star must remain flat. Additionally the space-time curvature caused by a gravitational potential would gradually increase as one moved outward from its center because the gravitational potential does. The fact that the space-time curvature at the center of a collapsing star must according to relativity remain flat suggests that space must contain some form of energy which counteracts the curving effects of a gravitational potential because the concepts of relativity mandates as just shown there is a limit to its ability to generate a space-time curvature.
Even though Einstein could not define its origins and how it interacted with a gravitational potential he knew it had to exist.
One reason why he couldn't may have been because it was not related to time or space-time property of space but to a spatial property of four *spatial* dimension.
Below is a reprint of the article
Dark energy: the cosmological constant which appeared in the
Imagineer's Chronicles. I believe it defines a mechanism in terms of four spatial dimension which may be related to the one Einstein was looking for.
"We have shown throughout this blog observations of our environment indicate the universe is composed of four *spatial* dimensions rather than of four-dimensional space-time as is suggested by Einstein's theories.
The recent discovery of Dark energy or a cosmological constant is one of those observations.
As Alexey Vikhlinin of the Smithsonian Astrophysical Observatory in Cambridge, Mass. wrote in the Scientific Frontline article Dark Energy Found Stifling Growth in Universe Dec 16, 2008:
This "study strengthens the evidence that dark energy is the cosmological constant. Although it is the leading candidate to explain dark energy, theoretical work suggests it should be about 10 raised to the power of 120 times larger than observed. Therefore, alternatives to general relativity, such as theories involving hidden dimensions are being explored.
Putting all of this data together gives us the strongest evidence yet that dark energy is the cosmological constant, or in other words, that 'nothing weighs something'," said Vikhlinin. "A lot more testing is needed, but so far Einstein's theory is looking as good as ever."
But the fact that Dark Energy or a Cosmological constant was discovered does not alter the fact Einstein introduced his cosmological constant because he was trying to make or "force" the universe conform to his expectations, rather than using theory to guide him to an understanding of its properties.
In the article "Why Space time?" Sept. 27, 2007 is was shown that it is possible to explain and predict all of the observed properties of relative motion including time dilatation, length contraction and mass increase as logically and consistently in terms of the geometry of four *spatial* dimensions as can be done in terms of the four-dimensional space-time geometry of Relativity.
Additionally it was show in the article “Gravity” Dec 15, 2007 it is possible to consistently define all the observed properties of a gravitational field in terms of a curvature in "surface" of a three-dimensional space manifold with respect to a fourth *spatial *dimension.
However, theoretically defining the universe in terms of four *spatial* dimensions as we have done in this blog and the paper The "Shadows" of four *spatial* dimensions means one does not have to "force" the integration of Dark energy or a cosmological constant into its theoretical structure as Einstein had to do to integrate it into Relativity.
If a gravitational field is a result of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension, as we are suggesting then reducing the mass of an object would reduce the magnitude of that curvature. However, this would result in the expansion of the "surface" of that three-dimensional space manifold. This would result in a physical expansion of the volume of the universe analogous to how removing the coils or curvature in a rope causes a physical expansion of its length with respect to three-dimensional space.
However, observations of our universe indicate Dark Energy expands the "surface" of space in a similar manner. This means that one can use a theory based on the existence of four *spatial* dimensions to guide them to an understanding of its properties rather than just expectations as Einstein had to.
Since the total mass in the universe is decreasing due to the nuclear reactions taking place in stars, the curvature associated with its gravitational field would also be decreasing. This means, according to this theoretical model the magnitude of this component of dark energy would be proportional to the quantity of mass the universe losses due to the nuclear reactions that occur within it.
However, the "concentration" of Dark Energy relative to gravitational energy would be, according to this mechanism defined by the equation E=mc^2c. This means its strength should be 1/c^2 weaker than gravitational forces. Therefore, because gravitational forces are much stronger than those of dark energy or the cosmology constant, the space between gravitationally bound objects would not appear to be expand.
This is consistent with the observation that its magnitude is about 10 raised to the power of 120 times smaller than predicted by Einstein's theories" and the fact that galaxies are not observed to be expanding, just the space between them. "
Later Jeff
Copyright 2009 Jeffrey O'Callaghan
