Does Gravity Gravitate? - Comments

[PeterDonis]

PeterDonis submitted a new PF Insights post

Does Gravity Gravitate?

Continue reading the Original PF Insights Post.

 

[Drakkith]

Nice article, Peter!

 

[Buzz Bloom]

I have a question about the notation in the following equation:
SG = (1/16π) ∫d4x (√−g) R.
Does ∫d4x mean that the integrand (√−g) R is being integrated over all of the 4D spacetime?

 

[PeterDonis]

Does ∫d4x mean that the integrand (√−g) R is being integrated over all of the 4D spacetime?

Yes.

 

[BiGyElLoWhAt]

Intriguing!

 

[exponent137]

How to explain, that moon is a little lighter because of its gravitational energy? It is understandable that Einstein equation is enough for explaining this.

 

[PeterDonis]

How to explain, that moon is a little lighter because of its gravitational energy?

I have a follow-up Insights article that should appear shortly that goes into this. You are right that the Einstein equation can be used to explain it.

 

[PeterDonis]

a follow-up Insights article

The follow-up article is now visible here:

https://www.physicsforums.com/insights/gravity-gravitate-part-2-sequel/#toggle-id-1

 

[samalkhaiat]

I’m afraid you have not made a case for a “No” answer. We know of well defined mathematical criteria for self-interacting fields which works both classically and quantum mechanically: a field theory is said to be self-interacting if, in the absence of sources, the fields satisfy non-linear (can be coupled) second order partial differential equations. And this applies to all self-interacting theories known to us:
(1) In the \Phi^{4} theory, we have \partial_{\mu}(\partial^{\mu}\Phi ) \sim - \lambda \Phi (\Phi^{2}).
(2) For Yang-mills field, you have \partial_{\nu}F_{a}^{\nu}{}_{\mu} = - f_{abc}A^{\nu}_{b} (F_{c \nu \mu}).
And (3) in free space, the gravitational field satisfies \partial_{\nu}(\sqrt{-g}G^{\nu}{}_{\mu}) = - (1/2)\partial_{\mu}g^{\nu \rho} \ (\sqrt{-g} G_{\nu \rho}).
So, why should (1) and (2) but not (3) be self-interacting?

 

[PeterDonis]

I’m afraid you have not made a case for a “No” answer.

My case for the "no" answer was based on putting a particular interpretation on the words "does gravity gravitate?", which is different from the interpretation you are implicitly putting on them here. See below.

why should (1) and (2) but not (3) be self-interacting?

I agree that (3) is self-interacting; that's the "yes" answer. If you interpret "does gravity gravitate?" as meaning "is the field describing gravity self-interacting", the answer is "yes". The article says that.

The "no" answer is based on interpreting "does gravity gravitate?" as "does the RHS of the EFE include gravity?" The answer to that is "no".

In other words, the answer to the question "does gravity gravitate?" depends on how you translate that ordinary language question into physics. Once the translation is done, there is no dispute at all about the physics.