Black Hole: Take Two, once again: how the hell do you get 0-R?

sooo how do you compress something to a sphere with a radeus of 0?

(yes I know that technically matter is just waves, but still; 0 R?!?

http://www.ptep-online.com/index_files/2008/PP-12-11.PDF

You don't!

The common gravity formula, g(m1)(m2)/r^2 is only an approximation.

It's based on the assumption of continuous (not discrete) distribution of matter within an object.

The calculations for a sphere reduce to equivalent results, as if the mass was concentrated at the center (a property of the sphere).

The formula only applies outside the object!

In general, the gravitational effect depends on the distribution of matter.

Check the web for topics on gravity, shell theorem, etc.

You will discover that the gravitational effect in the center of mass is zero!

The paper you reference is just another example of how assumptions can be wrong.

Actually, I'm the one that referenced the paper. What exactly is "wrong" with it in your opinion?

A sphere of radius zero is a point.

x² = R²

x² = 0 is just a particular case of this and reduces to the same geometric entity in all number of dimensions.

The boundary of an object with spherical symmetry about the origin of the coordinate system is given by that real-valued vector equation: x² = R²

And for a spherically symmetric object of size, s, smaller than any real number, x, can only be satisfied by s = 0. Because if 0 < s, then x = s/2 would mean 0 < x (x is positive) and x < s in violation of the assumption that s is smaller than any positive number.

So x² = 0² correctly describes a spherically symmetric object of size 0, which is a generalization of the concept of a sphere of finite size. Objects of size zero happen all the time in physics when the actual size is unimportant to the question or we are experimentally ignorant about the size being different than zero, or in the case of total gravitational collapse, where we can show that certain spherically symmetric configurations of matter require infinite pressure to maintain hydrostatic equilibrium. Smaller configurations of the same matter would require more than infinite pressure to remain static. Even in total ignorance of the inter-particle forces, we are forced to believe that such an object must collapse to ever smaller sizes. Thus, eventually it must become a spherically symmetric object of a size smaller than any real number, size = 0.

x² = -1 is another generalization of the sphere equation, but one that doesn't have a solution in real-valued vector spaces. While it has a solution in complex vector spaces, the equation x² = R² does not have very "sphere-like" in complex vector spaces and what is wanted is <x|x> = <R|R> in Dirac's Bra-Ket notation, or ∑|x_i|² = |R|² in component notation.

This post has been edited by rpenner on Feb 6 2008, 09:36 PM

Michael Mozina;

Sorry, just too much concentration on the first post.

I don't find anything wrong with it. The author is pointing out a case of equating a mathematical model with reality, i.e. the assumptions.

After 100+ years, and people are still debating the theory!

rpenner;

In reality, isn't that the same thing as no object?

For the math buffs, calculate the gravitational effect for a rod parallel and perpendicular to the earth's center.

I'd like to see your results, but only if the center of force matches the center of mass.