Would an inverse-cube law obey Newton's shell theorem?

Good, you shouldn't gloat since you didn't and couldn't do any calculations (excepting the trivial one for dimension 0), other people did all the heavy lifting, you couldn't even form the integrand. Moreover, the conjecture still fails for dimensions larger than 3 (actually , it makes no sense for dimensions larger than 3).

 

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If that's what you think then you've learned nothing. The generalization holds for n-dimensions of arbitary n. See, I can continue to sharpen my math skills but you're stuck with your lack of vision until you learn some humility.

 

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Can someone explain why there are pages after pages of complex math when the question was answered with proof in post 13 and easily generalized to other than 3D?

 

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They have the urge to dig. When they see molehills, they make mountains.

 

Not everyone speaks "logic". Hell if I'd known of all these online symbolic integrators I would've had a much easier time on this...

 

I imagine it's because people aren't convinced that it's a proof!

 

You couldn't (and you didn't) even form the integrand if your life depended on it.
You continuously mixed up 1-balls and 1-spheres, circles and discs, etc.

 

I'll assume this is for all the general relativity threads as well! You always seem to skulk away before remembering to thank people for their efforts.

 

Try 4D. You have a 4D hypersphere shell and a force that has 4 components (not a 4-D force, that is something else). You do not have any law of cosines to work with, so you can't use the methodology I outlined for constructing the integrand.

 

Quite possible true; but fortunately the post 13 proof does not require any trig functions. For example, from that proof generalized, these 4D hollow spheres have no force inside IFF the force law is inverse cube. When that force law is not inverse cube, that proof also tell to what part of the 4D hypersphere´s 3D surface the net interal force is directed. What more could you want? Perhaps the magnitude of the interal force at point A when there is force inside? OK here is how to get it:

In post 61 I told where the net force, if it exist, is pointed to. Calculating its magnitude is a little tougher but method was descrived in post 109. To do than in N dimentions you do need the N-D dot product law but, that is surely just a generalization of the the 3-D one, not a complex trig functions as it can be expressed in terms of the vector´s direction coordinates components. You will need to integrate over the surface, even in 3-D, to add up all the differential forces.

Again: What more could you want?

 

I appreciate anyone's contribution when they are providing valuable information.

 

I don't see any proof of that. Can you write down the math?

 

The only heavy lifting I've seen you do is misuse Wolfram's online integrator to come to the wrong conclusion. No wonder you claimed it would only take you 15 minutes...
I thought I smelled a bluff and I was right.

 

I did not misuse it, Wolfram happens to come up with the wrong answer. Other symbolic integrators came up with the same answer as Wolfram. With some coaxing, I got Wolfram to come up with the right answer. So,I'll file up a bug report with them <shrug>.

Yes, it took only 15 minutes to frame the problem in physics terms and to come up with the correct symbolic integral form. Something that you couldn't do even after 9 days.

Listen, clown, you took 9 days and you couldn't even come up with the integrand. 9 days AFTER I posted it for you.

 

Dig up all your "black holes don't exist and I don't understand coordinates in GR" threads and appreciate away! Perhaps you were about to do that, with your last one? Or perhaps you were hoping we'd all forget you made a bit of a whoopsie of yourself, again?

Anyway, I think this is the wrong thread to talk about this. It would be super if you'd like to reserect an appropriate thread.

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Tach: you didn't get the correct integrand until today either, and that was using a cheat. Even then you gave yourself credit with

Tool.

Guest254: this may frustrate you but I still question the existence of black holes. I'm investigating the physical significance of the time parameter in various coordinates. Holding on to my convictions until *I* am satisfied that they must change has gotten me far and this thread is a shining example of it. Of his many character flaws I never thought Tach would've put on such a mathematical sham and as you can see I was prepared to admit I was wrong when I thought I was.

 

Not easily. I used the same method Newton used in the Principles - I.e. geometric proof, not the modern more mathematical form of proof.

In Newton´s day only geometic proofs were considered valid proofs. Today some mathematicians do not consider computer proofs by exhaustion of all possibilites as "valid proofs."

BTW, if you have never read or at least skimmed, Newton´s Principles you should. It shows the power of geometry in the hands of a genius! I think more modern math would have great difficulty proving some of his limas that that take a couple of pages in the Principles. Perhaps no one could give a modern math proof of some.

 

Bzzt, wrong, see here for a reminder. So, we are finding out that you don't understand the difference between integrand and integral. One more "feather" in your crackpot cap.

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LOL. Getting hot under the collar, aren't you?

 

So, what is the proof for 4 dimensions? I don't see you posting any.

 

Your threads don't frustrate people, they just serve as platform for you to demonstrate your ignorance. The fact you keep making the same threads and displaying the same basic misunderstandings indicates you're not a very quick learner! I will remind you of what I said in the previous thread:

Fight the power, and so on!