On Monday, June 16, 2025 at 6:26:36 AM UTC-6 John Clark wrote:
On Sun, Jun 15, 2025 at 10:32 PM Alan Grayson <[email protected]> wrote: *> I fail to see how the EP implies geodesic motion. If true, the proof must be exceedingly subtle.* *I'll try one more time. If you are in freefall then you experience no gravity, so from your perspective your local spacetime is flat and things move in a path that is the shortest distance between two points, a Euclidean straight line. But from my perspective standing on the Earth's surface you are being affected by gravity and are moving through spacetime that is curved and non-Euclidean. The Equivalence Principle says both points of view are equally valid, but the only way that could be true is if I see you moving in a path that is the shortest distance between two points in 4D non-Euclidean space, and that is a geodesic.* *Thank you. I have some questions about your "proof". First, why is the shortest distance between two point on a curved manifold a geodesic, and second, perhaps more important, how can your proof depend on a principle, the EP, which depends on an imprecise measuremen of tidal forces? AG * *> If we assume mass/energy somehow causes a distortion in spacetime gemetry, and we hold a test mass spatially at rest in a gravity field, the question "why does it move"* *If you are holding an object and standing motionless on the Earth's surface then you and the object are still following a path through 4D non-Euclidean spacetime because both of you are still moving through time, but that path is NOT a geodesic because a force is being applied to the bottom of your feet. When you release the object its spacetime path suddenly changes to that of a geodesic while your path remains non-geodesic. * *The logical necessity of that sudden change to a geodesic is not yet convincing. You claim it's related or caused by the EP, but the object suddenly shifting to that geodesic motion "knows" nothing about the EP and free fall in a gravity field. I prefer to reach that conclusion via a postulate, but I could be wrong. AG* *And things on different spacetime paths is the definition of "movement".* *As I wrote, and I think you agree, time doesn't exist because clocks do, but because there are things HAPPENING in the universe; for example, the motion of objects. The "movement" you describe above is caused by a gravitional mass in GR, so cannot be a vacuous universe within which time doesn't exist. AG * *>>My problem is I don't know what sort of explanation would satisfy you. * *>A possible answer to my question might be the form of the equations of a geodesic path.* *But that's what General Relativity's field equations do! They told Einstein what the geodesic would be in the curved non-Euclidean 4D spacetime 34 million miles from the sun, and it produced an orbit that was slightly different than the orbit Newton said it should have. * * > I'm not sure, but space and time (here proper time) might be intertwinded in such a way that the spatial coordinates are forced to change because time continues to advance.* *But that's what a spacetime map is, it shows the relationship between space and time. If gravity is not involved then the map is flat and the relationship is simple; but if gravity is involved then that relationship changes and becomes more complicated because the map is curved, and the more gravity there is the more curvature there is. * * John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* 6hr -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/4d36f093-fb8e-4082-bbc6-66400d0adaben%40googlegroups.com.
