B Is the effect of gravity limited by distance?

1. Dec 8, 2016

lifeonmercury

Assume the universe is flat and neither expanding nor contracting whatsoever, and the only matter in it are two marbles separated from each other by a distance of 10 million light years. Would the marbles eventually begin pulling toward each other (after 10 million years)?

2. Dec 8, 2016

Bandersnatch

What do YOU think would happen, and why?

3. Dec 8, 2016

lifeonmercury

I would guess they would pull toward each other because the effect of gravity never truly tapers off to zero. Now will you please tell me what YOU think would happen?

4. Dec 8, 2016

Bandersnatch

Your intuition was good here, as it should be if one's ever seen the gravitational force equation: $F=GmM/R^2$ - no matter how large a distance you substitute for R, the resultant force never equals 0.

5. Dec 9, 2016

Mechanic

Interestingly enough, according to Chernin, et al. (https://arxiv.org/abs/0706.4068) the marbles will recede away from each other if they are beyond a certain distance apart. Per Chernin, gravity and antigravity balance each other out at what they refer to as the “zero gravity surface” and they refer to the distance to this surface as Rv. At distances less than Rv the marbles would accelerate towards one another. At distances greater then Rv they would accelerate away from each other. A smooth transition from the tendency to accelerate towards one another at relatively short distance to the tendency to accelerate away from each other over relatively large distances has been proposed.

6. Dec 9, 2016

Bandersnatch

Not in the setup as stated in the OP, i.e. in a flat, static universe.

7. Dec 9, 2016

Staff Emeritus
Mechanic, this is a B-level thread. And, as Bandersnatch points out, it's for a different setup.

8. Dec 11, 2016

grauitate

By the way, there is an answer of this interesting question from another aspect, too: in an universe filled with only two marbles of some kg, regardless in which distance they are located, the gravitational constant G (6.674e-11 m3/(kg s2)) would not have this value but would be nearly exactly zero instead. Regard that the estimate mass (matter and energy) of the real universe is approx. 1052 kg and that the gravitational interaction of all this stuff still results in this small number of G.
So, the gravitational attraction of these two 1 kg-marbles would be theoretically F = Gm1m2/R2 = G/9*1045 = 7.5e-57 N
and now assuming G as nearly zero as e.g. ≅10-40 m3/kgs2 F would reach 10-100 N, a number which reliably is at least in the vicinity of 0 with some confidence. Or spoken the other way round: these tiny force of 10-100 N would be much lower than any quantum fluctuations which might be present and within this bias of vibrating froth nothing (i.e. 0) could be detected.

9. Dec 11, 2016

Bandersnatch

Can you provide a reliable source for the claim that the value of G is dependent on the energy content of the universe?

10. Dec 12, 2016

grauitate

All comes from the foundation of Einstein's General Relativity, which is fundamentally based on the phenomenon that heavy mass is exactly equal inertial mass and the Mach's statement that the inertia comes from the gravitational effect of the sum of all masses in the universe.
The inertial movement of the Foucault pendulum simply shows the rotation of the earth, because it does not follow the earth's rotation but its polarisation plane stands still against the masses of the universe.
Or citing a joke from H. Pfister, M. King: Inertia and Gravitation, Lecture Notes in Physics 897, Springer Switzerland 2015, p. 137 (fine print), where E. Schucking is quoted as "When one of Mach's principle promotors, Dennis Sciama, slammed on the brakes of his car, propelling his girlfriend, seated next to him, towards the windshield, she was said to be heard moaning, `All those distant galaxies´."
Its just a logical and axiomatic reason that e.g. the gravitational acceleration around a heavy mass is a = GM/R2 (still non-relativistic) where G is the proportional constant determined by the gravitational (= inertial) effects of all masses of the universe, arriving locally at every moment simultaneously from all cosmic distances (i.e. from all past times). Reading Einstein's papers of 1915...1922 and todays experimental verifications e.g. of the frame dragging effect confirms this reason.
So, for the first, I'd recommend this source (among uncountable others):
H. Pfister, M. King: Inertia and Gravitation, Lecture Notes in Physics 897, Springer Switzerland 2015, p133 ff, Chapter 4.3 "Realisation of Machian Ideas in Cosmology and in Nature"
Or answering with a counter-question: What other than the mass and inertia of the world shall determine the value of G? Just a number by accident?

11. Dec 12, 2016

Staff: Mentor

No, it doesn't. In GR, G is a constant and can't change. There are alternate theories of gravity in which the equivalent of G can vary, but all of them are either ruled out by experiment or confined by experiment to a range of parameter values which makes them indistinguishable from GR and G effectively constant. (Brans-Dicke theory is an example of the latter.)

This is not correct. The pendulum's plane is affected by the Earth's rotation; the effect is just very small. Gravity Probe B tested for the same effect (frame dragging) and found it.

It confirms it in the sense that it shows that the distribution of stress-energy in the universe affects the spacetime geometry (in this case the Earth's rotation affects the curvature of spacetime around the Earth), but we already knew that.

It does not say anything about whether G is constant, because frame dragging occurs in both GR, where G is constant, and alternate theories of gravity where the equivalent of G varies.

In GR, nothing does; it's a constant that can't be predicted by the theory and has to be given a value from experimental measurements.

12. Dec 13, 2016

nikkkom

Mach principle is just an idea, it's not an established fact. It is neither confirmed not disproved by current experimental data.
For one, General Relativity is not a machian theory.

13. Dec 13, 2016

Staff: Mentor

I think this depends on your definition of "Machian". Cuifolini & Wheeler wrote a whole textbook, Gravitation and Inertia, arguing that GR is a Machian theory, using their definition of "Machian". Others have said it isn't, using their (different) definition of "Machian". So one really needs to explicitly say, mathematically, what they mean by "Machian" or "not Machian" in order to make a claim like this.

14. Dec 13, 2016

john george pa

would not quantum effects come into play also ?

15. Dec 13, 2016

Staff: Mentor

Not in the problem posed here. They're well and thoroughly negligible when you're dealing with marble-sized masses in free-fall in otherwise empty space.

16. Dec 13, 2016

ProfChuck

Yes, quantum effects must be included to complete the model. There are two (that come to mind); photon pressure and uncertainty when the space time curvature is on the order of the Planck length.

17. Dec 14, 2016

Staff: Mentor

Both of which are irrelevant for the problem posed in this thread.

18. Dec 14, 2016

nikkkom

My definition of "machian" is that the math of the theory in question should include effects of distant masses/objects on the local conditions. IIRC math of GR doesn't. Also, there are valid global GR metrics where entire Universe rotates, which shouldn't be possible if Mach principle is true.

https://en.wikipedia.org/wiki/Gödel_metric
https://en.wikipedia.org/wiki/Van_Stockum_dust

19. Dec 14, 2016

ProfChuck

I'm not so sure about that. In this wildly hypothetical scenario any effect whose value can be calculated should be included in the model. It may be that the problem is insufficiently constrained by the question. If each marble radiates photons, which it would do unless it was at zero Kelvin, they will exert photon pressure on each other. Also if space-time is quantized then gravitation becomes uncertain at a calculable distance.

20. Dec 14, 2016

Staff: Mentor

If the marbles are alone in the universe (no CMBR, no other radiation), then they would be at zero Kelvin, since there is no radiation around for them to establish a thermal equilibrium at finite temperature. Of course this is highly idealized, but so is the scenario as a whole.

Which is a speculative hypothesis that has nothing to do with this scenario, which, as I understand it, assumes classical gravity.