by Crazyguy 280 Replies latest watchtower bible
Do we agree I have just demonstrated the gravitational field of a hollow shell vanish at all interior points of the shell? Do we agree this mean the acceleration of an object inside the shell will be zero?
I have now done the math in the newtonian case.
This is a newtonian problem yes, The gravitational field doesn't vanish at all interior points, no. Yes the acceleration of an object inside the shell would be zero.
Oy vey; this is still going on?
Yes, we are having fun!
As I have made clear many times we should distinguish between the GR treatment of this subject and the newtonian treatment.
You keep saying that, you've no said why. You're acting as if Newtonian physics means "net effect = nothing there".
Now, to say there is no gravity in some area of space is not to deny that mass warp space in general. This ought be self-evident.
As predicted, you're agreeing with me.
Do we agree I have just demonstrated the gravitational field of a hollow shell vanish at all interior points of the shell? Do we agree this mean the acceleration of an object inside the shell will be zero?
No. You didn't show that at all. You showed the net effect is zero, not that there is no gravitational field.
Care to do the math in the relativistic case? (hint, use Birkhoffs theorem I wrote about on the previous page)
Nope, I have better things to do and, frankly, that math is beyond my skills. How long did it take you to find Birkhoff's theorem with google? There's also no need to suggest I need a hint from you. Anyone that knows what Birkhoff's theorem is absolutely would know shell theorem. Don't pretend like you aren't googling stuff.
Anyway, I WAS incorrect in something I said earlier. The net gravitational effect of any point inside the hollow sphere is zero. However, that does not, by ANY definition of gravitation or gravity, mean there is no gravity. I thank you sincerely for showing me that error in my understanding. An analogy would be to say that because you made $100 and had $100 in bills means you didn't earn any money.
ou are free to insist there is still "gravity" inside it. I am free to insist there is an invisible dragon. From a newtonian POW both are equally undetectable.
Of course you are. You're wrong, but free to be so.
Caedes:
I feel quite confident on this point:
I think you are confusing the derivation of the shell theorem by the physics; the shell theorem can be derived from geometric considerations (cancellation of forces), but the physical statement is the gravitational field is zero, fullstop.
We can perhaps agree you are correct under a newtonian formulation of physics and I am correct under laplaces more modern formulation.
Perhap as an example think of a ping pong ball hovering in a jet of air. The ping pong ball has two forces acting on it one from the gravity and one from the jet of air.
Is it correct to say there are no forces acting on that ball?
Caedes: The gravitational field doesn't vanish at all interior points, no.
This is what I have shown in my above derivation. The gravitational field is a function that maps points in space to vectors in space. What is the gravitational field if not zero?
Disclaimer: I have a degree in physics
Caedes: No, you are correct to say there are two forces on the ping-pong ball. However when we are talking about the gravitational field we have to keep in mind what the gravitational field IS.
To compare to the ping-poing ball, the "field" would be an "effective field" composed of the force of air and gravity. That field would be zero at the ball, hence no field.
Caedes: I do not insist you are wrong under all definitions of the word "gravity", but I think you are wrong under the simplest. It is at any rate completely accurate to say there is no gravitational field inside the sphere (it is zero).
This is what I have shown in my above derivation. The gravitational field is a function that maps points in space to vectors in space. What is the gravitational field if not zero?
What you have shown is the net effect is zero, not "no gravitational field".
Disclaimer: I have a degree in physics
That only furthers my surpise at your struggle to understand this.
