# Are these statements correct?

Someone raised the question: what if the force of gravity varried or fluctuated?

This was the response. Is it correct?

If the gravitational law varied with space, linear momentum could not be conserved. If it varied with time, energy could not be conserved. Since both momentum and energy are indeed conserved, the fact that gravity does not vary with space or time is not surprising in the least. Noether's First Theorem.

The form of the gravitational law is restricted to be invariant by the time- and space-translation symmetries of the universe, which result in the observation that all physical action conserves linear momentum and energy. Gravity simply could not be at times strong and other times weaker in the universe we live in.

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I don't think that answer is necessarily correct, nor a rigorous proof.... but at the same time, it is good reasoning and thus most likely true, and a good motivation for its unlikeliness.

The main problem is that Noether's theorem only works in the other direction, i.e. such a constant force leads to a conservation law. But not necessarily the other way around.

In a laboratory you can create a varying field... it simply requires work to be done. It seems as though this 'could' happen in nature.

Interesting question. Seems to me that if I was a stupid rock zooming through the solar system, I would sense gravitational fields that varied in space and time as I passed the various planets, but I could not detect or reason if gravity per se was varying, or if this was simply due to my proximity to nearby masses. So I'll guess there is no reason for a conservation problem here.

Drakkith
Staff Emeritus
Seems to me that IF gravity wasn't constant, but varied in strength, energy and momentum would still be conserved. It's just that the force of gravity would vary. This changes the amount of potential energy something might have because of gravity, but you aren't losing it since the amount of potential energy depends on the strength of the gravity. Once something was moving, changing gravity would only change the strength of the force acting on it, not the energy itself. Inertia and Mass wouldn't change.

I don't think that answer is necessarily correct, nor a rigorous proof.... but at the same time, it is good reasoning and thus most likely true, and a good motivation for its unlikeliness.

The main problem is that Noether's theorem only works in the other direction, i.e. such a constant force leads to a conservation law. But not necessarily the other way around.

In a laboratory you can create a varying field... it simply requires work to be done. It seems as though this 'could' happen in nature.
How would you get the varrying field?

Does anyone know how a varrying field could be created?

Pythagorean
Gold Member
a non-uniform distribution of mass, spinning?

Does anyone know how a varrying field could be created?
By moving a magnet, mass, or charge.