Quote:
Originally Posted by Jeffocal
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.
|
Not exactly. The value of potential does not determine the shape of the field, but rather how quickly potential changes. In a plot of potential in a star:
where the blue line is pretty much horizontal, space is pretty well flat. That's at the far left and the far right of the blue line (the center of the star and infinitely far from the star). These two areas have very different values of potential, but both have flat space because the shape (or strength) of the field is not determined by the value of potential, but how quickly potential changes with distance. The force of gravity is the
derivative of
gravitational potential energy.
Quote:
Originally Posted by Jeffocal
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.
|
Again, you're working under the assumption that the *value* of potential determines the force of gravity (or the strength of the field). That is not the case. You might think: "how much does gravitational potential change from one spot in space to the next spot in space?" If the change is not very great then the field is weak and nearly flat. If the change is a lot then the field is strong.
Quote:
Originally Posted by Jeffocal
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...
|
This is fine. Relativity describes 3 curved dimensions. If you want to say that they curve into a 4th dimension that is somehow hidden to us then that's not an unusual thing to think. It would be called extrinsic curvature. But, you still need time as a dimension—a curved dimension. It is the curvature of time that results in the gravity we feel here on earth. It is (as far as I know) an indispensable part of general relativity.
Quote:
Originally Posted by Jeffocal
Dear Modest
I'd like to thank you for taking the time to help me understand the depth of Einstein's genius.
I would also like to ask you a favor. I am receiving a military disability for a head trauma that affects my ability to comprehend explanations presented in a mathematical format. Could please, wherever possible try to use words to explain concepts.
|
Sure.
Quote:
Originally Posted by Jeffocal
The displacements responsible for the relativistic properties of space and time in both environments have a common element in the three spatial dimensions; therefore, their performance will be identical. The only difference between them is that one defines a displacement in terms of a time variable while the other in terms a variable spatial distance.
|
Well... if you're saying that space (the 3 normal dimensions that we know) is curved into a 4th 'hidden' dimension rather than being curved into time (which is the usual interpretation) then I think that's ok. You could also say that time has extrinsic curvature into this higher dimension.
Quote:
Originally Posted by Jeffocal
However, Einstein based the relativistic properties of time on the fact that the speed of light is constant for all observers. But distance equals velocity times time. Therefore could one quantitatively define the spatial distance a three dimensional space manifold moves with respect to a fourth *spatial* dimension by multiplying the speed of light with the relativistic time change predict by Einstein for a given situation.
If so could one plug that value into the field equation that Einstein developed to quantify his concepts in terms of existence of four *spatial* dimension instead of four-dimensional space time.
Thanks again Jeff
|
I don't really follow what you're saying there. The speed of light works as a conversion factor between space and time. To switch from space units to time units (or from time to space) you multiply or divide by the speed of light. There is no conversion factor between spatial dimensions, so this once again shows that time is a little different from the other dimensions.
~modest
