Gravity is different - infinite energy stored

[Lapidus]

Around time 33:40 min in this video, Prof. Paul Steinhardt says the following about gravity:

There is something special about gravity that we all should have learned school, but never did. It is a very basic fact, which is that all the other energies we know have a bottom to them. If you draw the energy down, you eventually hit zero or a minimum where you can't get go below it. It is not true for gravity. Gravity is a unique form of energy which is bottomless.(...) The gravity potential curve goes to negative infinity when two objects are brought arbitrarly close to one another.

This argument is often brought forward, as in this case here, when inflationary cosmology is explained. The energy of the inflating universe comes from gravity or energy of the inflating universe is conserved since the energy of the inflation field is set off by the energy of gravity.

I also know from introductory QFT courses that gravity is special. When computing the vacuum energy, it is pointed out that for gravity not the potential energy difference but the total potential energy matters.

1. But where do I find this "bottomless feature" of gravity in the gravity and GR textbooks? Which chapter or formula in, say, Sean Carroll or in Bernard Schutz book explains it?

2. What makes gravity "bottomless"? Why does the same explanation does not apply for two opposite electric charges brought arbitrarly close to one another?


thank you in advance

 

[mfb]

That is nothing special in gravity, you get the same potential for opposite electric charges. It is a mathematical artifact, however, he tries to apply a formula in a region where it is not valid. You cannot bringt two objects as close to each other as you like, and black holes have a finite energy as well.

 

[Naty1]

I did not watch the video yet, but had the same reaction as was posted...

As far as I have learned, the only 'unique' thing about gravity is that it tilts light cones...
that and the related fact that it has not yet been included in the Standard Model because it stands alone from the other forces...

I'll be interested to hear what Steinhardt has to say. Thanks for the link.

edit: "When computing the vacuum energy, it is pointed out that for gravity not the potential energy difference but the total potential energy matters..."

Can anyone expand on this a bit??

 

[Bill_K]

What makes gravity "bottomless"?

Au contraire, there's a well-known theorem in GR, "For asymptotically flat gravitating systems
the total energy is well defined and must be non-negative."

 

[backward]

gravity is different-infinite energy stored

I did not watch the video yet, but had the same reaction as was posted...

As far as I have learned, the only 'unique' thing about gravity is that it tilts light cones...
that and the related fact that it has not yet been included in the Standard Model because it stands alone from the other forces...


I think there is something else also unique about gravity. Motion is a gravitational field (in the absence of other forces) is a "free fall". If you are in a opaque spaceship (cannot see ouside), you cannot tell whether you are sitting on a planet, moving with a constant velocity, orbiting a planet or a star, or moving along a complex curved path in a gravitational field. You will feel no jerks at all. This is so even when falling in a black hole, until tidal forces become appreciable (if a point mass is falling into a black hole, it will be a free fall). This is because gravitational force is proportional to inertial mass. Hence, acceleration is constant for all the parts of your body as well as the spaceship. This will not happen in any other field-force, because other forces are not proportional to inertial mass.