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Dr. Christopher S. Baird

Does the influence of gravity extend out forever?

Category: Space      Published: June 9, 2015

star warping spacetime
Gravitational effects are the result of spacetime curvature. Public Domain Image, source: Christopher S. Baird.

No. The attractive force called gravity does not extend beyond galaxy groups. If you look at Newton's Law of Universal Gravitation, you see that the force of gravity on one mass due to another mass depends on their separation r according to the dependence 1/r2. As you get farther away from a gravitational body such as the sun or the earth (i.e. as your distance r increases), its gravitational effect on you weakens but never goes completely away; at least according to Newton's law of gravity. However, Newton's law of gravity is wrong.

The most correct theory of gravity is currently not Newton's law, but is Einstein's General Theory of Relativity with the cosmological constant included. General Relativity describes how gravity is not really a direct, classical force. Rather, the effect we call gravity is simply how objects move in a spacetime that is itself curved. A mass such as the sun does not shoot out gravitational force field lines. Rather, mass warps space and time, and when an object travels in a straight line through a warped spacetime, the object seems to be acted on by a force. General Relativity does more than explain traditional gravitational attraction. It also explains other ways in which spacetime behaves. The behavior of spacetime depends on how much mass and energy is present, how it is distributed, and how it is moving.

On the scale of groups of galaxies and smaller, there is enough localized mass present to make spacetime act like traditional gravity. In other words, on the scales of ants, waterfalls, humans, planets, solar systems, galaxies, and galaxy groups, spacetime behaves in such a way that one mass seems to gravitationally attract another mass. On these scales, General Relativity almost exactly reproduces the older and less accurate Newtonian law of gravity. (Even on these scales, there are measurable differences between the incorrect predictions of Newton's law and the correct predictions of General Relativity, but the differences are usually so small that you need sensitive equipment to detect them.) Put in rough terms, on all of the scales that we care about in everyday life, spacetime acts mostly like good old-fashioned gravity.

On scales larger than galaxy groups, the mass of stars, planets, moons, and space dust gets too sparse and too non-localized on average to make spacetime continue acting like traditional gravity. On these scales, spacetime looks mostly empty, mostly uniform, and mostly flat. According to General Relativity with the cosmological constant included, two distant galaxies in such a spacetime no longer move towards each other. They move away from each other. It's not that the two galaxies are actively repelling each other. Rather, the nature of spacetime is such that when it is mostly empty, uniform and flat, it expands. New space is continually created between distant galaxies, so that the distance between galaxies in different galaxy groups is continually growing. Furthermore, the nature of spacetime is such that, on large scales, this expansion is accelerating in time. Galaxies in different groups are not only moving farther apart, they are also moving farther apart at an increasing rate. Scientists call this behavior of spacetime on larges scale by the names "cosmic expansion" or "metric expansion". Cosmic expansion has been confirmed experimentally many times using many different approaches. The key concept for our discussion here is that the accelerating expansion of the universe is an innate property of spacetime itself on scales where spacetime no longer acts like traditional gravity.

In summary, the influence of gravity only extends to the edge of each gravity group. Beyond that, spacetime no longer behaves like gravity. It's not that the gravitational attraction of a star simply gets too weak to notice when you leave its galaxy group. Rather, the gravitational attraction goes completely away outside of the galaxy group. A hammer in the solar system that is let go at rest relative to the sun falls towards the sun. A hammer released at rest in a different galaxy but in the same galaxy group as our sun would also move towards the sun (in addition to moving towards the other, closer masses). In contrast, a hammer in a different galaxy group does not move towards our sun at all. It moves away from our sun, and it moves away at an accelerating rate. In fact, the hypothetical distant hammer moves away from our entire galaxy group at an increasing rate. Spacetime simply does not behave at all like attractive gravity on cosmic scales. For this reason, gravity fundamentally does not extend beyond gravitationally-bound groups of galaxies.

Topics: cosmic expansion, cosmological constant, dark energy, expansion of the universe, general relativity, gravity, metric expansion, spacetime