Comment by db48x | Hacker News Reader

Comment by db48x | Hacker News Reader

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Particles in orbit do accelerate. They accelerate continuously, from our perspective, as they go around the orbit. But seen from the perspective of GR, that orbit is really just a straight line through a curved spacetime. It might be easier to visualize though if you think of it as the bottom of a valley. The walls of the valley rise away from the floor as you get closer to the planet you are orbiting, or further away. You can’t climb those walls without energy, so if you have no energy will you stay in the valley forever.

> it also does not explain momentum, because when that particle accelerate it exchanges momentum with another particle - it does not give momentum to the "geodesic".

No one has said that it should. The geodesic is merely the straight path that the particle must follow when it _isn’t_ exchanging momentum with other particles.

> And explain please what information is not captured by saying "Gravity is a force that acts on energy". What nuance is lost by saying that?

You can’t explain time dilation that way, or length contraction.

A charged particle on a straight line does not emit synchrotron radiation. What happens if it is on a geodesic? Do electrons that circle around a black hole emit synchrotron radiation?

That’s beyond my level of expertise, but yes.

Quoting from the abstract of The Motion of Point Particles in Curved Spacetime <https://web.archive.org/web/20151203142700/http://relativity...>

> This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle.

Note especially that the charged particle won’t actually follow the geodesic. Because the synchrotron radiation carries away some energy, the particle will be continually pushed off of the geodesic; it will spiral inwards instead of orbiting forever.

Does this mean that when the geodesic is a straight line then the particle stays on the geodesic, but when the geodesic is curved the particle interacts with its own e.m. field and deviates from the geodesic because it feels a deflecting force?

Then there would be a fundamental difference between curved and straight geodesics which would be a contradiction to the Einstein Equivalence Principle. How do physicists explain that contradiction?

The equivalence principle only applies to uniform fields and uniform motion. A charged particle in orbit is not in a uniform field and is not experiencing uniform motion.

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