singularity

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However, we now know why inverse-square behavior is intrinsic to nature. [Any unbound phenomenon must spread in two dimensions as it propagates through a third spatial dimension and time.]

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Thank you for the enlightening replies. Couple final questions on this subject:

A. Is the law you refering to considered an axiom?
B. Do we have evidence it holds outside of our planetary system?

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>A. Is the law you refering to considered an axiom?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

No, it's mot an axiom because it is not an assumption. I referred to it as a principle because it comes from logic, although "principle" perhaps is too grandiose a term. The underlying axiom is that space is Euclidean, or at least sufficiently so that Euclidean space is an excellent approximation.

Elementary geometric considerations show that the area of concentric spherical shells increases with the square of distance from the central point. So any isotropic flux (whether particles or waves) must spread over an area that increases with the square of distance. If the amount of flux is conserved, its density per unit area must therefore vary inversely with the square of distance. So any isolated force that uses a flux to carry momentum from a source to a target must likewise diminish with the square of distance.

So this is a conclusion, not an axiom. But it has very few axioms that separate it from first principles.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>B. Do we have evidence it holds outside of our planetary system?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

For an inverse square law? Yes, all of stellar dynamics is of that character. Double stars are the simplest such application, with tens of thousands of orbits now known. Multiple star systems, eclipsing binaries, binary pulsars, open clusters, and globular clusters are other examples; although admittedly, the time scales for changes in the latter two are long, and the evidence that they obey an inverse square law is circumstantial. But even for galaxies, it has been demonstrated in numerical integrations that only an inverse linear law or an inverse square law are consistent with the forms we see. So the degrees of freedom here are severely constrained.

Within the solar system, the inverse square law holds in laboratory experiments, for spacecraft and debris ejected from spacecraft, asteroids and comets and their moons, and moons of major planets. Only on the smallest and largest scales we can observe is there reason to start questioning the inverse square character of gravitation. -|Tom|-

Thank you Dr. Van Flandern for your enlightening, precise answers.


I guess I'm now tempted to ask the following (maybe elementary) questions: (last, I promise)

If Gravity obeys flux laws wouldn't it be possible to amplify it or attenuate it via the use of other media? (ex. laser, maser effect?) Or even generate it artificially?

Why isn't there a Faraday cage for gravity?

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In principle, all those things are possible. But until we discover the graviton and learn to generate and control it, we won't have much success. The <i>Pushing Gravity</i> book provides as much insight as we presently possess into what kinds of engineering hurdles must be conquered to control and use gravity. Communications will surely be one of the early applications because the speed of gravity is apparently at least ten orders of magnitude faster than light. (See papers in Cosmology/Gravity on this web site.) -|Tom|-

Singularity may exist in only one form; the perfection of a single harmonious interaction. Within an "event-horizon", nothing but this harmony should exist, as far as we are concerned. Disharmonious elements (which dissapate energies) disappear into infinitisemal scales of existence. Harmonous elements, on the other hand, should reinforce their own energies to scales culminating in the event horizon.

Once dissolute, the disharmonious elements should not re-emerge; neither would they re-interact with the harmonious elements (which function to reinforce their own energies).

Correctly, all branches ofphysics attempt to catalogue phenomena according to harmonious principles.

Why should there be such a thing as a 'black hole?" The mathematical construct of the phenomena is there, but mathematics itself relies on an ancient idea of "self evidence," which is abandoned as soon as one suggests a "singularity." This logical progression is ridiculous. No, it is more; it is the epitome of all impotence, just as the entire current attempt to consolidate disharmonious elements with the harmony that has allowed science, over several thousand years, to become what it is in its current state.

Sorry,

Didn't mean to interrupt the train. Accidently posted the previous message the departure-point of the previous page of this topic (it has obviously expanded). Please continue.