Gravitational Pull Limit Across Distance?

[serp777]

I was wondering if a gravitic field has a limit, where after a certain distance, determined by the properties of the structure creating the gravity field, the force felt by the 1kg masses becomes 0N. For example, will two 1 kg masses, separated by an arbitrarily super large value (I.E. 50 billion light years), eventually make contact given an infinite amount of time? Assume that the expansion of the universe is not involved. My initial guess is that there is a limit, and that given an infinite amount of time, the objects will never make contact. My reasoning is that after the first second the rate of change of distance is less that the Planck constant, and so since an object cannot move distances smaller than the Planck length, the objects will never move.

 

[michael879]

It is very dependent on what theory you are talking about. There is no Planck-scale theory that has been experimentally verified, so we can't really speculate on Planck-scale interactions least of all gravitational ones. According to general relativity, the answer to this question lies on the value of the cosmological constant (acceleration of the universe). If its 0, there is no limit to the distance you can separate 2 objects and have them eventually meet. However if it is negative, as experiments suggest, there is a threshold distance after which gravity actually becomes repulsive.

If you add a little bit of quantum mechanics into the mix, then even with a 0 cosmological constant there should be a threshold distance. $\Delta{x}\Delta{p} \geq \hbar/2$, so the answer really depends on how well you know the distance between the 2 objects. Assuming nonrelativistic speeds, $\Delta{v} \geq \hbar/(2\Delta{x})$. The escape velocity of each object is approximately $\sqrt{GM/x}$, and when the uncertainty of the velocity becomes close to the escape velocity you will see a noticeable decrease in the probability of the object meeting. So $x_{thres} \leq 2GM\Delta{x}/\hbar^2$