Exploring Gravity: The Mathematical Explanation Behind Expansion and Gravity

[amaruq]

Could somebody show me mathematically why/why not gravity could/couldn't directly be caused by expansion -everything pulling/moving away from each other? When you are in a car, and you are accelerating, your body wants to stay where it was a moment before... Thus your head gets thrown back into the seat until you stop accelerating... Is this why we have gravity? Say a planets particles are moving away from each other, and that this is happening at an ever increasing rate... Is that why we have "gravity"? I wouldn't mind seeing it mathematically.

PS this time i am NOT posing a theory... I am just asking to see this mathematically. ;)

 

[tiny-tim]

Hi amaruq!

Well, yes it could, but the Earth would have to be expanding really fast for that to work, while the Moon would have to be expanding less fast …

so we'd notice that the Moon was getting smaller!

 

[amaruq]

Thank you for going easy on me lol

 

[Ich]

Ok, the Earth obviously isn't exploding. But it's in fact the GR viewpoint that the surface of the Earth is accelerating, and that gravity is the effect of that acceleration. This is realized by curving space and time appropriately, so that there is acceleration without relative motion.

 

[tiny-tim]

… there is acceleration without relative motion.

That doesn't make any sense …

how can we define acceleration without motion?

 

[Ich]

how can we define acceleration without motion?

Operationally, by using an accelerometer (e.g. force or displacement of a test mass). Theoretically, by defining a suitable "proper acceleration", i.e. the covariant derivative of the world line (not sure about the wording).

 

[yogi]

You can derive the inertial reaction of local matter to the acceleration of the universe (best estimates based upon a c velocity recession at the putative Hubble sphere of radius R and a flat universe, yields the isotropic acceleration is (c^2)/R (Smolin). With a little manipulation, G turns out to be (Hc/4(pi))(meters^2)/kgm

There have been several derivations on these boards - One chap did it using the acceleration from Hubbles law - i.e., equate the acceleration of gravity to the acceleration from the derivative of v= HR, and therefore dv/dt = H(dr/dt) = (H^2)R
I think he got it published in an electronics magazine. I have it around here somewhere. His derivation gave the result in perms of the density which is the same as what you get if you solve for G in the equation for critical density that comes out of the Einstein - de Sitter universe That is G =(3H^2)/8(pi)rho

Cheers

 

[amaruq]

beautiful!