# I Does spacetime have potential energy?

1. Oct 28, 2016

### IvicaPhysics

Does spacetime have potential energy, and does an object with more potential energy have more mass? (E=mc^2)

2. Oct 28, 2016

### phinds

What do you think potential energy is and how do you think spacetime would have any of it? Regardless of spacetime, how would potential energy lead to more mass?

EDIT: and by the way, I do not mean my questions to be a comment one way or the other on the answer to your questions, I'm just asking you to clarify your understanding of your terms.

3. Oct 28, 2016

### Jonathan Scott

One way to model gravity in many cases is to extend the Newtonian view and say that there is positive energy density $g^2/(8 \pi G)$ in the gravitational field, in a similar way to the energy in an electric or magnetic field, and that an object with more potential energy has its mass adjusted accordingly (usually by some negative amount relative to some reference potential at infinite distance from the source). This then gives a global conservation law similar to Poynting's Theorem in electromagnetism. In that sense, both of your questions could be answered with "Yes".

A more accurate and general model is to use General Relativity. In that model, potential energy as a concept doesn't really work, although in simple cases it gives similar predictions to the Newtonian model. The energy of a gravitational field in GR is not "energy" in the normal sense but there are ways of allowing for it and expressing a conservation law for something like the Newtonian "energy" using a pseudotensor quantity, although there are varying opinions about which is the right expression to use, as the conservation law does not uniquely select a particular pseudotensor.

4. Oct 28, 2016

### Chronos

This looks suspiciously like a vacuum energy [aka zero point energy] question. In which case it would imply this potential energy could somehow be extracted and put to use. In principle ZPE is the ground state of the universe, or the lowest possible energy at which empty space can remain stable. If it were any higher it would spontaneously bleed off into lower energy regions with which it was causally connected. Were it any lower it would leech energy from connected higher energy regions. The consequences of this could be highly undesirable [inimical with life as we know it]. Given that empty space is at least as ancient as the universe, this appears to be a highly unlikely scenario. The universe was in a higher energy state in its infancy, but, that excess energy was exhausted by various processes [e.g., inflation and freeze out into matter] until it reached its current stable zero point value.