3 ms·

"is to say that when no force acts on a test particle in curved space, it should move along a geodesic" Every single author who calls gravity not a force, just

by ars 2y ago

"is to say that when no force acts on a test particle in curved space, it should move along a geodesic" Every single author who calls gravity not a force, just hand waves right past this: why should the particle move at all? Sure if the particle is moving it will follow a curved path thinking the path is straight. But if the particle just sits there, okay the path is curved, but it just sits there. I've heard explanations having to do with the fact that particles move through time, that doesn't really answer the question because it can continue moving through time while just sitting there. "in the absence of being pushed or pulled, test particles in a curved spacetime will free fall" Really? Why exactly will they free fall? Why can't they just stay exactly where they are? I've also never heard anyone explain what the issue is with calling gravity a force. One person said it can't be a force because it makes light move, and light is massless. However gravity does not act on mass it acts on energy, and mass is just a form of energy. Since photons have energy obviously they gravitate.

zmgsabst 2y ago
You’re moving in the time direction — and when spacetime is curved, you end up moving in the space direction as well, to follow the geodesic.
- AlexandrB 2y ago
  Not arguing for or against this explanation, but it's hard enough (impossible for me) to visualize a curved 3d space, once you try to think of what curved 4d space might be like any intuitive sense of what should happen goes out the window. Classic diagrams of curved spacetime portray space as a 2d sheet with divots in it. I wonder what a similar visualization of curved 1d time + 1d space would look like. Long valleys for gravitational wells and everything moving along the sheet in the direction of positive time?
- ars 2y ago
  > and when spacetime is curved, you end up moving You did the same as everyone else: You hard waved right past "end up moving". Why do I end up moving instead of just sitting there? And if I "end up moving" that means I exchange momentum, if it's just bent space that magically makes me move, what did I exchange momentum with, if not via a force toward another particle? Gravity is a force that acts on energy. If you disagree please give me a counter example.
  - Filligree 2y ago
    You do just sit there. In the GR-realism view, the only thing particles _ever_ do is self-propagate forwards in time. The problem is, this means the particle’s definition of “time”. Spacetime is 4D, and this can be any timelike direction. That’s what causes it to appear to move, from the perspective of someone whose time vector is pointed differently. Then time can be curved, which reorients said vector as the particle propagates through it. That’s gravity.
- jumping_frog 2y ago
  The river model of general relativity. https://www.youtube.com/watch?v=hFlzQvAyH7g&list=PL__fY7tXwodn7_NGVJxnX1joL_eQJCR-4&index=3 https://www.youtube.com/watch?v=hFlzQvAyH7g&list=PL__fY7tXwo...
db48x 2y ago
> Really? Why exactly will they free fall? Why can't they just stay exactly where they are? Absent any forces, they can only stay on a geodesic. It’s like the arrow that springs from the bow. No hesitation, no doubts. The path is clear. There’s only ever one geodesic, one path through spacetime that takes no energy to follow. This is true even if you ignore general relativity and just focus on classical mechanics, as formulated by Lagrange. In Lagrangian mechanics, you must compute a number called the “action” for every path through space that your system could possibly take. Then your system will take the path that minimizes the action. If your system is a particle in space, then it will stay still if that has the minimum action, or it will follow some path through space if that has the minimum action. It can’t ever do both. Only one of them will minimize the action.
- 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.
tomp 2y ago
what do you mean by "just sits there"? Sits where? In the same position relative to the sun? Relative to the center of the Galaxy? Relative to the local galaxy supercluster? A particle does not just sit still!
- ars 2y ago
  Site there relative to that other mass that wants to accelerate it toward each other.
mecsred 2y ago
I think the missing piece in your puzzle is adding the "time" to space-time. A particle moving through time is "falling" in the time dimension. The curvature of the 4d space makes this movement through time also move through space due to the warping effect of a gravity well.
ImHereToVote 2y ago
There is also the asymmetry of time dilation. Someone moving in a rocket ship will be younger than the person staying behind. Isn't their relative acceleration the same though? Why is the rocket man privileged in staying young? This kinda works if you imagine a grid of sand particles being acted upon by either gravity or traversed by the rocket. The rocket traverses many more grids than the person standing on Earth. The person floating in naked space will traverse the fewest grids. The kicker is that there is no place in space with zero grid traversal. Accounting for all grid traversals becomes a nightmare.

by ars 2y ago

zmgsabst 2y ago

You’re moving in the time direction — and when spacetime is curved, you end up moving in the space direction as well, to follow the geodesic.

AlexandrB 2y ago
Not arguing for or against this explanation, but it's hard enough (impossible for me) to visualize a curved 3d space, once you try to think of what curved 4d space might be like any intuitive sense of what should happen goes out the window. Classic diagrams of curved spacetime portray space as a 2d sheet with divots in it. I wonder what a similar visualization of curved 1d time + 1d space would look like. Long valleys for gravitational wells and everything moving along the sheet in the direction of positive time?
ars 2y ago
> and when spacetime is curved, you end up moving You did the same as everyone else: You hard waved right past "end up moving". Why do I end up moving instead of just sitting there? And if I "end up moving" that means I exchange momentum, if it's just bent space that magically makes me move, what did I exchange momentum with, if not via a force toward another particle? Gravity is a force that acts on energy. If you disagree please give me a counter example.
- Filligree 2y ago
  You do just sit there. In the GR-realism view, the only thing particles _ever_ do is self-propagate forwards in time. The problem is, this means the particle’s definition of “time”. Spacetime is 4D, and this can be any timelike direction. That’s what causes it to appear to move, from the perspective of someone whose time vector is pointed differently. Then time can be curved, which reorients said vector as the particle propagates through it. That’s gravity.
jumping_frog 2y ago
The river model of general relativity. https://www.youtube.com/watch?v=hFlzQvAyH7g&list=PL__fY7tXwodn7_NGVJxnX1joL_eQJCR-4&index=3 https://www.youtube.com/watch?v=hFlzQvAyH7g&list=PL__fY7tXwo...

db48x 2y ago

> Really? Why exactly will they free fall? Why can't they just stay exactly where they are? Absent any forces, they can only stay on a geodesic. It’s like the arrow that springs from the bow. No hesitation, no doubts. The path is clear. There’s only ever one geodesic, one path through spacetime that takes no energy to follow. This is true even if you ignore general relativity and just focus on classical mechanics, as formulated by Lagrange. In Lagrangian mechanics, you must compute a number called the “action” for every path through space that your system could possibly take. Then your system will take the path that minimizes the action. If your system is a particle in space, then it will stay still if that has the minimum action, or it will follow some path through space if that has the minimum action. It can’t ever do both. Only one of them will minimize the action.

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.

tomp 2y ago

what do you mean by "just sits there"? Sits where? In the same position relative to the sun? Relative to the center of the Galaxy? Relative to the local galaxy supercluster? A particle does not just sit still!

ars 2y ago
Site there relative to that other mass that wants to accelerate it toward each other.

mecsred 2y ago

I think the missing piece in your puzzle is adding the "time" to space-time. A particle moving through time is "falling" in the time dimension. The curvature of the 4d space makes this movement through time also move through space due to the warping effect of a gravity well.

ImHereToVote 2y ago

There is also the asymmetry of time dilation. Someone moving in a rocket ship will be younger than the person staying behind. Isn't their relative acceleration the same though? Why is the rocket man privileged in staying young? This kinda works if you imagine a grid of sand particles being acted upon by either gravity or traversed by the rocket. The rocket traverses many more grids than the person standing on Earth. The person floating in naked space will traverse the fewest grids. The kicker is that there is no place in space with zero grid traversal. Accounting for all grid traversals becomes a nightmare.