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Quoting him from: Published in "The Beamline" 27, 14 (1997)

"Although it has not been widely appreciated, Newtonian physics unambiguously implies that the energy of a gravitational field is always negative a fact which holds also in general relativity."

Why can't the zero value of gravitational potential energy be set at a different point instead of infinite distance within Newtonian gravity?

I am not asking why is gravitational potential energy considered negative. I am asking why does it necessarily need to be negative in Newtonian gravity according to Guth.

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  • $\begingroup$ Does he mean that the total gravitational energy of a mass configuration is negative? That follows from the fact that we always have to add external energy to the system to move its individual constituents to infinity. In other words... a rocket payload never launches itself. We always have to expend chemical energy to get it into orbit or to a hyperbolic trajectory. $\endgroup$
    – FlatterMann
    Commented Aug 11 at 9:08
  • $\begingroup$ The 'energy of the gravitational field' should be distinguished the gravitational interaction energy. It appears the latter is meant here, namely that gravitation is always attractive. $\endgroup$
    – my2cts
    Commented Aug 11 at 10:48

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There is probably an implicit assumption that the energy goes to $0$ at infinity.

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You could set the zero of gravitational potential energy to zero wherever you wanted in Newtonian physics, but it wouldn't make a lot of sense. Suppose if we computed the gravitational potential energy integral for two masses and separated them infinitely and decided that the constant of integration should be 1 joule instead of 0 joules. There's no way to access that energy; it's part of the bookkeeping in that system's setup and nothing more. Could you do the extra math and keep that 1 joule hanging around? Sure, but it complicates things without any benefit.

I'm not a general relativity expert by any stretch of the imagination, but I believe that if you wanted the potential energy to be something other than zero at infinity using GR, you would have to increase the mass of the system by that additional mass-energy, which would be problematic, I should think. (I'm more than happy to be corrected if wrong).

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