# I On gravity and the conservation of energy

1. May 10, 2018

### Monsterboy

"non-stationary" means in an expanding universe ?

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

I didn't get this part. For the system in my example of two massive particles, can we not say that the density of gravitational energy decreases as the particles move away from each other ? maybe I didn't get what "density" of gravitational energy means.

I didn't get what "matter field" actually means, is it like saying (with respect to my example) kinetic energy is positive and gravitational potential energy is negative so they cancel each other out and so energy is conserved ?

2. May 11, 2018

### Staff: Mentor

That is an example of a non-stationary spacetime, yes.

No. You can say that the potential energy increases (not decreases) as the particles move apart, but you can't convert that potential energy to an energy density, because it isn't localized. It's a property of the global configuration of the two particles. It doesn't "belong" to any particular point in space.

It means anything that isn't spacetime/gravity.

3. May 11, 2018

### Staff: Mentor

It's similar in some respects, but not the same, because, as already noted, an expanding universe is not a stationary spacetime, so the concept of gravitational potential energy is not well-defined. The "energy in the gravitational field" that Carroll is talking about in the expanding universe case isn't the same as the gravitational potential energy in the case of the two masses.

4. May 11, 2018

### JMz

From you: You started the two particles off with that potential energy, because of where you placed them. They were "born" with it. Whatever energy you gave them in the beginning, they will keep forever (in this two-particle universe). The energy you gave them is indeed conserved, and there is no other energy in this universe.

5. May 11, 2018

### Monsterboy

Yea, the potential energy is because of the presence of a gravity field right ?

Where does the gravity field originate from ? does it originate from the masses or is it present everywhere even before there were any particles with mass ?

6. May 11, 2018

### JMz

Yes, from the gravitational field.

"Originate" is either a deep philosophical question (Why does gravity exist at all?) or a simple one: Because the Einstein field equations, or something like them (even Newton's), hold, and they say that mass creates gravity.

7. May 11, 2018

### jbriggs444

One can adopt a less causal interpretation. They say that mass (or, more generally, the stress energy tensor) is associated with gravity. Not necessarily that it creates gravity.

Correlation is not the same as causation.

8. May 11, 2018

### JMz

Quite so, but I'm not sure that bringing the semantics of cause into an I-level thread is philosophically simpler. ;-) And the "creates" verb is at least consonant with MTW's "[mass] generates [gravity]".

9. May 14, 2018

### nikkkom

The behavior of bodies moving in gravitational fields like these are very similar to how electrically charged objects interact. A very light negatively charged "asteroid" will swing by a very light, positively charged "Earth" exactly the same (the attractive forces will have the same form, 1/r^2, and magnetic interactions due to the fact that charges are not stationary will be very small).

But somehow that interaction would not look strange to you:

"The others all have a fairly limited range, they're many times stronger than gravity, and they each have a defined carrier particle (or two) that we're aware of. Conservation of energy is pretty straightforward with these, so no big deal."

Why gravity looks stranger that electromagnetism to you?

10. May 14, 2018

### JMz

BTW, this seemed an odd thing to say: Electromagnetism has exactly the same range as gravity. This is usually stated to be "infinite", but the point is that both drop off as 1/r^2 (cosmological corrections aside), so their ratio is constant. As @nikkkom points out, you seem to be asking, for gravity, about something you already accept for electromagnetism.

11. May 15, 2018

### Demystifier

In the Newtonian limit all gravity is encoded in $g_{00}(x)$, which is more like "compression" (of time) than like curvature.