3 ms·

> one path through spacetime that takes no energy to follow. Again, this if fine for an orbit for example, it does not explain how a particle will accelerate,

by ars 2y ago

> one path through spacetime that takes no energy to follow. Again, this if fine for an orbit for example, it does not explain how a particle will accelerate, 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". 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?

AlexandrB 2y ago
Hmm, if you look at another comment here: https://news.ycombinator.com/item?id=41971973 https://news.ycombinator.com/item?id=41971973 It seems like the point is that the particle is actually not accelerating when it follows the one path through spacetime. It only accelerates when it's stopped by something (e.g. the surface of the earth).
- wrs 2y ago
  Another angle that might help: Newton was correct when he said a particle with no forces on it would keep going in a straight line. He was just missing a dimension in his coordinate system. The geodesic is the straight line in spacetime. And mass distorts the spacetime metric (mostly time) in a nonlinear way, so when you project that straight line back into 3D space, it’s not linear, it’s a curve. An “acceleration” curve.
db48x 2y ago
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.
- fxj 2y ago
  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?
  - db48x 2y ago
    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.livingreviews.org/Articles/lrr-2011-7/download/lrr-2011-7Color.pdf 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.
    - fxj 2y ago
      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?
      - db48x 2y ago
        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.

by ars 2y ago

AlexandrB 2y ago

Hmm, if you look at another comment here: https://news.ycombinator.com/item?id=41971973 https://news.ycombinator.com/item?id=41971973 It seems like the point is that the particle is actually not accelerating when it follows the one path through spacetime. It only accelerates when it's stopped by something (e.g. the surface of the earth).

wrs 2y ago
Another angle that might help: Newton was correct when he said a particle with no forces on it would keep going in a straight line. He was just missing a dimension in his coordinate system. The geodesic is the straight line in spacetime. And mass distorts the spacetime metric (mostly time) in a nonlinear way, so when you project that straight line back into 3D space, it’s not linear, it’s a curve. An “acceleration” curve.

db48x 2y ago

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.

fxj 2y ago
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?
- db48x 2y ago
  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.livingreviews.org/Articles/lrr-2011-7/download/lrr-2011-7Color.pdf 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.
  - fxj 2y ago
    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?
    - db48x 2y ago
      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.