4 ms·

Except that the radius of curvature in that case depends on the charge and mass of the particle, but all particles follow the same trajectory in a gravitational

Except that the radius of curvature in that case depends on the charge and mass of the particle, but all particles follow the same trajectory in a gravitational field. The trajectory is a geodesic, a non-Euclidean generalization of a straight line. All objects travel on straight lines unless acted upon by forces: inertia.

ars 3y ago
> but all particles follow the same trajectory in a gravitational field That's not true. The "all masses fall at the same speed" thing is only true when one mass is much larger than the other. (Well, it's never actually true, it's more "is only a useful approximation".) So heavier masses follow different trajectories in a gravitational field, just like more charged particles do.
- akdor1154 3y ago
  Er what? This is outright false.
  - ars 3y ago
    You forget that both particles attract each other. A heavier particle falling toward the sun will cause the sun to move which will in turn influence the path of the particle.
    - evanb 3y ago
      But this is not what anybody means when they talk about the equivalence principle.
      - ars 3y ago
        Sure, but I wasn't talking about the equivalence principle. We were comparing the motion of a charged particle and a mass particle. The equivalence principal was never mentioned.
- raattgift 3y ago
  Some reading on the universality of free fall version of the strong equivalent principle, tested in a manifestly relativistic regime: "Even Phenomenally Dense Neutron Stars Fall like a Feather -- Einstein Gets It Right Again" https://public.nrao.edu/news/neutron-stars-fall/ https://public.nrao.edu/news/neutron-stars-fall/ More detail, Archibald et al. 2018, "Testing the universality of free fall by tracking a pulsar in a stellar triple system" (Nature volume 559, pages 73--76 (2018)) preprint: <https://arxiv.org/abs/1807.02059 https://arxiv.org/abs/1807.02059>. If universality of free fall fails, so does the single metric / purely geometrical theory of General Relativity. That would be very exciting, so it has been looked for a lot. https://duckduckgo.com/?q=tests+of+universality+of+free+fall&ia=web https://duckduckgo.com/?q=tests+of+universality+of+free+fall... You can recover a bit from your statement by considering that solutions of the geodesic equations can be a bit messy in manifestly relativistic or multi-body systems, and the equations of motion of components can be even messier. Nobody would disagree with that (it's why there's e.g. the (gravitational) Self-Force methods and the like; see e.g. <https://arxiv.org/abs/1501.07322v3 https://arxiv.org/abs/1501.07322v3>, which (cf. your second sentence) is useful when a compact mass (e.g. a neutron star) is in a close orbit around a 50x+ more massive black hole, bottom right corner of <https://en.wikipedia.org/wiki/Post-Newtonian_expansion#/media/File:GR2bodyparameterspace.png https://en.wikipedia.org/wiki/Post-Newtonian_expansion#/medi...>).

ars 3y ago

> but all particles follow the same trajectory in a gravitational field That's not true. The "all masses fall at the same speed" thing is only true when one mass is much larger than the other. (Well, it's never actually true, it's more "is only a useful approximation".) So heavier masses follow different trajectories in a gravitational field, just like more charged particles do.

akdor1154 3y ago
Er what? This is outright false.
- ars 3y ago
  You forget that both particles attract each other. A heavier particle falling toward the sun will cause the sun to move which will in turn influence the path of the particle.
  - evanb 3y ago
    But this is not what anybody means when they talk about the equivalence principle.
    - ars 3y ago
      Sure, but I wasn't talking about the equivalence principle. We were comparing the motion of a charged particle and a mass particle. The equivalence principal was never mentioned.
raattgift 3y ago
Some reading on the universality of free fall version of the strong equivalent principle, tested in a manifestly relativistic regime: "Even Phenomenally Dense Neutron Stars Fall like a Feather -- Einstein Gets It Right Again" https://public.nrao.edu/news/neutron-stars-fall/ https://public.nrao.edu/news/neutron-stars-fall/ More detail, Archibald et al. 2018, "Testing the universality of free fall by tracking a pulsar in a stellar triple system" (Nature volume 559, pages 73--76 (2018)) preprint: <https://arxiv.org/abs/1807.02059 https://arxiv.org/abs/1807.02059>. If universality of free fall fails, so does the single metric / purely geometrical theory of General Relativity. That would be very exciting, so it has been looked for a lot. https://duckduckgo.com/?q=tests+of+universality+of+free+fall&ia=web https://duckduckgo.com/?q=tests+of+universality+of+free+fall... You can recover a bit from your statement by considering that solutions of the geodesic equations can be a bit messy in manifestly relativistic or multi-body systems, and the equations of motion of components can be even messier. Nobody would disagree with that (it's why there's e.g. the (gravitational) Self-Force methods and the like; see e.g. <https://arxiv.org/abs/1501.07322v3 https://arxiv.org/abs/1501.07322v3>, which (cf. your second sentence) is useful when a compact mass (e.g. a neutron star) is in a close orbit around a 50x+ more massive black hole, bottom right corner of <https://en.wikipedia.org/wiki/Post-Newtonian_expansion#/media/File:GR2bodyparameterspace.png https://en.wikipedia.org/wiki/Post-Newtonian_expansion#/medi...>).