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By (my limited knowledge of) Einstein’s theory of General Relativity, as gravity is not a force but rather the effect of an object’s inertial path following a geodesic through curved spacetime due to the mass of another object, would Newton’s Third Law still ‘apply’? Although gravity is not a force, does there exist a ‘reaction’ to it analogous to that of Newtonian gravity?

Qmechanic
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BlueBearBro
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  • A geodesic is the trajectory of a "particle" in a particular spacetime. The definition of a particle (much like dynamics of masses and charges in Newtonian mechanics or electrostatics) is an object that doesn't influence the existing field. So, by definition, a particle exerts no influence on the spacetime. But particles do not exist. To get the actual spacetime dynamics, each object must be accounted for in Einstein's equation: each object changes the curvature of space. In a Newtonian approximation to GR dynamics, these interactions could be seen as arising from Newton II, III and FG. – Ben H Dec 02 '23 at 15:47
  • Does this answer your question? Is Newton's Law of Gravity consistent with General Relativity? – anna v Dec 02 '23 at 16:01
  • this question and answers discuss this, but it needs some mathematical knowledge to understand how Newtons law is consistent with general relativity https://physics.stackexchange.com/q/89/ – anna v Dec 02 '23 at 16:04
  • TLDR: Yes. It works both ways. If you toss a marble into the air, the segment of its world line that represents its flight is a geodesic that bends toward the Earth because of the Earth's mass/energy. At the same time, the Earth's world line bends towards the marble—Just not quite as much. – Solomon Slow Dec 02 '23 at 16:16
  • @SolomonSlow Actually, nobody has ever been able to demonstrate that particles in a two-body problem actually follow geodesics. Approximately they do, sure, particularly when the mass ratio is very large. But exactly, we don't know for sure. – Buzz Dec 02 '23 at 16:44
  • @Buzz, OK, So, I used "geodesic" in an inappropriate way. But all I really wanted to say was that the marble's world line bends toward the Earth, and the Earth's world line bends toward the marble. Did I get that bit right? – Solomon Slow Dec 02 '23 at 16:56
  • Possible duplicates: https://physics.stackexchange.com/q/360930/2451 and links therein. – Qmechanic Dec 02 '23 at 17:05
  • This was closed before I could post the answer I was working on. So I posted it to the linked question. – mmesser314 Dec 02 '23 at 17:10
  • @SolomonSlow Physically, what you said is certainly just about right. I just wanted to mention the mathematically interesting fact that the geodesic nature of particle motion for anything other than a test particle moving in a fixed background spacetime is actually a longstanding open problem. – Buzz Dec 03 '23 at 02:00

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