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. AG On Wednesday, May 28, 2025 at 11:49:49 AM UTC-6 John Clark wrote: On Wed, May 28, 2025 at 6:25 AM Alan Grayson <[email protected]> wrote: *>>What physicists call "Proper Time" is a specific clock reading, it's what you see when you look at your wristwatch. And if no force has been applied to enhance your motion then the path you are following through 4D spacetime is a geodesic. And the amount of time it took you to travel through space from point A to point B, as determined by your wristwatch, will be longer than the proper time of anybody else, as determined by their wristwatch, who HAS had an external force applied to them and thus are not on a geodesic path through 4D spacetime.* *> So, if a test particle is spatially at rest, which presumably is non-geodesic motion in spacetime, what causes it to move spatially when the force holding it spatially at rest, is released? AG * *If you're holding an apple above the ground then that apple is on a non-geodesic path because you must apply a force to prevent it from hitting the ground. From the viewpoint of General Relativity and the equivalence principle you're accelerating the apple upward at about 10 m/s^2, but curved 4D spacetime "wants" the apple to fall downward at the same rate, so the spatial distance between the apple and the ground remains the same. But when you drop the apple the force drops to zero and the apple is then able to follow a geodesic path which leads to the ground.* -- 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/7ec3c65b-ce3c-4ec3-9cb8-925f84947463n%40googlegroups.com.
