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Rongqing Dai
戴榕菁
In Newton’s model of gravity, there is no time delay for gravitational forces to act, which means if two massive bodies are formed at a distance D apart, no matter how big D is, their gravitational attraction can be calculated by the famous Newton’s law of gravity without the need of considering any time delay.
However, later scientists did not like the instantaneous action model because they craved to find the mechanism behind the gravitational action. In order to do so, they introduced the speed of gravity S, meaning if two bodies are formed at a distance D apart, their gravitational interaction will reach each other after a time interval t. Now the problem is how big S should be. Some supposed that S should be the same as the speed of light c. Unfortunately, if that is the case, then even the solar system that we live in cannot hold up itself (Dai 2025a, b) [[1],[2]].
Then what if we assume an extremely large speed of gravity? Will that make us safe to assume that the gravity can hold the whole universe together as we humans know today?
The answer is this: we will not be able to put the abstract concept of “extremely large” into any concrete number or any number with a clear order of magnitude if we do not know how big the universe is, which so far no one knows. This is because there must be a maximum time interval τ that is allowed for the gravity to propagate across the whole universe. If τ is too large, then a big part of the universe will not be able to sense the change of the gravitational configuration of some other part of the universe. For example, whatever S we assume, if the real size L of the universe is 100 times larger than what is calculated by S and τ, then 99% of the universe can sense the change of the gravitational configuration of some 1% of the universe, which will definitely troublesome and the universe cannot hold by the gravitational model.
To make the reasoning here less abstract so that more readers can easily grasp this important fundamental issue for physics, no matter how big the universe really is, for the sake of our discussion here we might reasonably imagine it as an enlarged solar system. As we might see from the previous discussion of Dai (2025a), based on the assumption that the speed of gravity the same as the speed of light, the earth will spin violently because at any moment the gravitational pull by the sun on earth will point to the position of the earth at 8 minutes ago. By the same logic, if the speed of gravity is too small compared to the scale of the universe, the consequences of applying this model to the universe will be catastrophic, even if that speed is much faster than the speed of light.
Final Remark
As long as we do not know the actual size of the universe, it does not practically make sense to assume a finite speed of gravity. Even if one day we do know the size of the universe, given the fact that the speed of gravity has to match the scale of the universe, for any hypothetically selected value of the speed of gravity, as long as it allows the universe to be held together by gravity, we should expect that the order of the difference (or error) in calculations at any local scale that is much smaller than the universe between using a finite speed of gravity and using the instant gravity model should be ignorable.
[[1]]Dai, R. (2025a). Speed of Gravity Cannot Equal To Speed of Light. Retrieved from: https://www.academia.edu/127280320/Speed_of_Gravity_Cannot_Equal_To_Speed_of_Light
[[2]]Dai, R. (2025b). Violation of Newton's Third Law of Motion by GTR and the Consequence. Retrieved from: https://www.academia.edu/130264166/Violation_of_Newtons_Third_Law_of_Motion_by_GTR_and_the_Consequence
