On Tuesday, June 17, 2025 at 1:27:51 PM UTC-6 John Clark wrote:
On Tue, Jun 17, 2025 at 2:13 PM Alan Grayson <[email protected]> wrote: *>>>No force is being applied to the space station but it is not following a Euclidean straight line because it is not in flat Euclidean space, it is in curved 4D non-Euclidean spacetime and is following a geodesic path. In curved 4D non-Euclidean spacetime the shortest path between any two points along the space station's orbit is the space station's orbit itself. * *>> OK, but then your previous comment, to which I responded, is false. AG * *> Earlier you wrote that free falling in a gravity is like falling, or moving along a straight line as in a flat Euclidean space, but the SS is free falling in a gravity field and traveling in a curved path around the Earth. Can't you just acknowledge your error?* *I'm perfectly capable of making an error but I don't know what I said, or what you think I said, that you're referring to. * You were very clear, two messages back, that a body in free fall will experience straight line motion as in a flat Euclidean space. We know this is false, and I gave the example of the SS orbiting the Earth. AG *But I do know that the Equivalence Principle says if you have no contact with anything that is not in your local space then you can't tell if you're in the gravitational field in curved non-Euclidean spacetime or if you're accelerating in a straight line in flat Euclidean space.* But with sufficiently sensitive instruments one can tell the difference. For this reason I don't like to base arguments on the EP. AG * Spacetime has to be non-Euclidean if time is involved because when it comes to defining a distance the Pythagorean Theorem must be modified, you need to throw in a minus into the equation, D^2=X^2+Y^2+Z^2 - (cT)^2.* This fall far short of an argument. The definition above is certainly non-Euclidean insofar as the Pythogorean theorem is violated, but how does this fact imply geodesic motion, specifically from an initial state of being spatially at rest? AG *And intuitively it sort of makes sense that when it comes to distance the spatial and temporal coordinates should have opposite signs because the larger the spatial distance between 2 points the harder it would be to travel between them, but the larger the time you had to make that journey the easier it would be. * *And the speed of light "c" is just a conversion factor between space and time. * *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* dd0 -- 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/68eb6ba5-b177-4a53-9a6c-145f874298afn%40googlegroups.com.
