On 5/28/2025 5:38 PM, Alan Grayson wrote:
Then you have to specify the starting point AND an initial velocity...just like in Newtonian mechanics, which can also be written as an extremal principle.On Wednesday, May 28, 2025 at 5:13:43 PM UTC-6 Alan Grayson wrote: On Wednesday, May 28, 2025 at 5:02:16 PM UTC-6 Brent Meeker wrote: On 5/28/2025 2:09 PM, Alan Grayson wrote:On Wednesday, May 28, 2025 at 2:26:25 PM UTC-6 Alan Grayson wrote: On Wednesday, May 28, 2025 at 1:56:51 PM UTC-6 John Clark wrote: On Wed, May 28, 2025 at 3:45 PM Alan Grayson <[email protected]> wrote: /> Why does it "want" to fall when you cease applying the upward force?/ *Because if no force is applied the apple wants to take the shortest path possible through 4D space-time; or to put another way, it wants to take the longest possible proper time to get from your hand to the ground. Remember that unlike the formula for calculating the distance in space, the formula for calculating the spacetime distance between two events contains a minus sign, that's why space is different from time. * But before it starts to move, how does it know which path satisfies the requirement you allege? AG I don't think it knows or wants anything. And I don't think GR can answer my question. It must be a postulate of GR, that geodesic paths maximize proper time and consequently this is the path a test particle will take in free fall. In other words, we don't actually KNOW why it takes the path it does. AGIt's just a definition of "geodesic" that geodesic paths maximize proper time. No, it's not just a defintion. You can calculate proper time along different paths, and find a path which maximizes proper time. But why a particle takes that path, AFAICT, is unknown. It must be a postulate of GR. I was hoping for more. AG Did you KNOW why massive bodies attracted one another in Newtonian physics? Do you know why like charges repel and opposite charges attract, instead of the other way around? If I told you it was God's will that test particles fall along geodesics would you then KNOW why? There are never answers to "why" questions at a fundamental level...otherwise they wouldn't be fundamental. The "why" questions change as we go down the rabbit hole. Some get answered. Asking such questions motivates deeper theories. It's just that I had higher hopes for GR. AGAnother problem is this; starting from some point in spacetime, we can find the geodesic path to some other point in spacetime. But since the particle doesn't know beforehand, the endpoint of its path, how is the motion determined? AG
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