KRAB got to one of the essential points about the "hollow sphere" problem when he showed the relation between the distance the test particle is from the sides of the sphere versus the attraction on the particle due to the effective mass. Basically the lack of attraction inside a hollow...
Golly - we need another 2 cents worth here for sure --- but I did not see anyone mention that without the complex solutions to Schroedinger you don't get "amplitudes" and you don't get the marvelous predictive power of QED. Adding amplitudes when indistinguishable outcomes are in the stew is...
I am not sure what you are looking for, but the google scholar engine produced this on the first page:
http://www.iop.org/EJ/abstract/0959-7174/11/2/301
"Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band"
This is really the essence of the answer and I have little to add; I would observe that the current cosmological models (by current I mean circa 2000, 2001 popularizations) seem to have "space" expanding faster than c (Lawrence Krauss, "Quintescence") -- an interpretation that was confirmed by...
I apologize in advance for making an assumption --- but in another thread the writer seemed to be understandably confused by the famous balloon model where the galaxies are spots on the expanding balloon. You can get the impression that the universe IS the balloon and the center is the center...
If you are in frame O and you measure your v compared to O' as (say) 0.99999c then one meter as measured in O' in the direction of v will seem (and the emphasis is on "seem") to be .0044 meter in the O frame. Since the universe has many frames -- some galaxies are moving away at high fractions...
Am I insane? I've read many cosmology books, most popularizations but some that are somewhat academic and as near as I can see the following is stated as the overwhelming scientific opinion (of course, it could change):
1) The universe (at least the one we can observe) is the finite product...
OK - I know that you can get to SR from several directions; but, really, what is a null geodisic other than a path where (ct)^2 - x^2 - y^2 - z^2= 0 --- i.e., where something is traveling the (constant) speed of light. Again, all the formulations of SR end up equavalent to "c is constant"...
I think that the question is a bit more profound than may be immediately apparent. I am intrigued that Special Rel is basically determined by the behavior of a quantum entity (the photon, of course)-- the disconnect between GR and quantum may ultimately hinge on the fact that there is a subtle...
The internet is great of course (if you are careful of the sites you pick) but anyone who want to know Special and General Relativity via carelfully designed text and problems needs to get
SpaceTime Physics - J.A. Wheeler and E.F. Taylor, isbn 0716723271 (Special rel)
and
Exploring...
How high iis the cannon above the ground? Is that stated in the problem? If the height is H then the answer that many are getting should be incremented by H. The basic Newtonian setup has to be right.
Exploring Black Holes
If you are not a Physicist and want to REALLY understand the math of a non-rotating, non-magnetic black hole (i.e., Schwarzschild black hole) you really should read Wheeler and Taylor's "Exploring Black Holes". It answers multitudes of difficult questions.
:biggrin:
Let me copy/paste a section of Wheeler and Taylor to see if it helps --"wristwatch time" is the observed time of the person in the GR space. I use "tau", "phi" etc. to keep from using weird fonts. phi is the angle around the plane of rotation about the black hole. I see that my superscript...