Version of Olber's Paradox for gravity [closed]

Question

Olber's Paradox is a famous problem in cosmology.

In astrophysics and physical cosmology, Olbers' paradox, named after the German astronomer Heinrich Wilhelm Olbers (1758–1840), also known as the "dark night sky paradox", is the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. In the hypothetical case that the universe is static, homogeneous at a large scale, and populated by an infinite number of stars, any line of sight from Earth must end at the surface of a star and hence the night sky should be completely illuminated and very bright. This contradicts the observed darkness and non-uniformity of the night.1

The darkness of the night sky is one of the pieces of evidence for a dynamic universe, such as the Big Bang model. That model explains the observed non-uniformity of brightness by invoking spacetime's expansion, which lengthens the light originating from the Big Bang to microwave levels via a process known as redshift; this microwave radiation background has wavelengths much longer than those of visible light, and so appears dark to the naked eye. Other explanations for the paradox have been offered, but none have wide acceptance in cosmology.

https://en.wikipedia.org/wiki/Olbers%27_paradox[1]

So what about gravity? In Newtonian physics gravity is a force emitted by matter. Since the universe has an uniform distrubtion of matter on a large enough scale, and is believed to be many times as large as the observable universe, the force of gravity on any object should be a very strong force coming from all directions.

If the gravitational force coming from all directions is infinitely strong, it would rip apart every object. If it was not infinite, but still strong enough, it would rip apart every object which depends on its internal gravity to hold together, and may even rip apart objectw which are held together by other forces.

Or maybe the equal gravitational forces coming from long distances in opposite directions cancel each other out, and thus only the gravity from randonly positioned nearby objects affects an object.

And of course in relativity grvity is caused by objects with mass bending, and curving space. The curvature of space causes the trajectories of objects to be different from what they would be in uncurved or "flat" space. And in most situations the curvature of space caused by masses causes passing objects to change trajectoriesin exactly the same way as those trajectories would be modified by the Newtonian gravity force that would be emitted by those mosses.

Only extreme situations cause Newtonian gravity and Relatvistic gravity to have different effects and allow for tests to be made.

So if the universe is infinite, there should be equal infinite gravity everywhere according to both Newtonian and relativistic theories. And if the universe is finite but very, very large, there should be equal finite but very, very large gravity everywhere in the universe according to both Newtonian and relativistic theories.

Unless, of course, this is one of the situations where there is a difference between Newtonian and relativistic theories of gravity.

And if gravity is a relativistic curvature of space, and equal masses at equal vast distances and from the equal and opposite directions A and B curve space at point C, would point C have zero space curvature from the distant A and B, they ir balances curvatue cancelling out,and only experience space curvature from unbalaneced randomly placed nearer objects?

Or would the equal and opposite space curvature from A and B cancel each other in direction of space curvature but add to each other in amount of space curvature, so that every spot in the universe would have a very large but non directional amount of space curvature, and onlyhthe lesser amount of curvature caused by relatively nearby unbalanced objects would cause directional space curvature and change the trajectories of objects?

So I wonder if there have been any calculations of the minimum and/or maximum amounts of Newtonian gravitational attraction and/or Einsteinian space curvature there should be in a random location in the universe, and how strong those nondirectional effects from the distant universe would be compared to the directional effects of nearby objects.

Answer 1

OP is correct, this “gravitational Olbers' paradox” is definitely a problem for Newtonian theory of gravity, but this is more of mathematical problem with the usual formalism employed for its formulation rather than with the physical content of such theory.

If the gravitational force coming from all directions is infinitely strong, it would rip apart every object. If the gravitational force coming from all directions is infinitely strong, it would rip apart every object which depends on its internal gravity to hold together, and may even rip apart objectw which are held together by other forces.

This is wrong. In the usual formulation of Newtonian gravity theory the gravitational force is defined by the gravitational acceleration, $\mathbf{g}$. But even if in some region of space this acceleration is arbitrarily large it would not “rip apart” an object because the same large gravitational acceleration would be present in each part of this object, and as a result the object as a whole would be free falling under this acceleration without disintegrating. This is known as “universality of free fall” and it makes impossible to detect the magnitude of homogeneous gravitational acceleration without some external reference.

What is responsible for the “ripping apart” effects is the inhomogeneities of gravitational field, that are given by derivatives of gravitational acceleration, $\mathbf{\nabla g }$. But this derivatives are much more “localized” in character. So if the universe has on large scales approximately constant mass density everywhere, this derivatives would remain bounded on average. Larger objects, such as galaxies, could still be ripped apart, but due to local gravitational effects, such as gravitational field of a nearby galaxy, and not from combined influence of all the matter in the universe.

So the resolution of gravitational Olbers' paradox lies in the formulation of theory of Newtonian gravity that emphasizes its local character and removes all the explicit references to all the masses in the universe from calculations. This is achieved by Newton–Cartan theory of gravity, which is largely modeled after general relativity.

General relativity is a local theory from the start, its equations the Einstein field equations (EFEs) do not depend explicitly on global properties of matter distribution in the universe, so no version of this gravitational Olbers' paradox arises. The solutions of EFEs for homogeneous and isotropic universes filled with matter are the Friedmann–Lemaître–Robertson–Walker metrics which form the starting point of relativistic cosmology.

Answer 2

The gravity that can reach us is not coming from parts behind the horizon of the observable universe. Only light emitted by mass behind the horizon can't reach us. If they could reach us, and the universe was infinite, we would see light from every direction that orginated in all places. In that case the speed of light and gravity would be infinite. This wouldn't give a different result for the gravity felt here (as contributions from all directions would cancel), so the fact we don't see a bright sky is good eveidence that the speed of light is finite!