On Sunday, June 15, 2025 at 5:48:50 AM UTC-6 John Clark wrote:
On Sat, Jun 14, 2025 at 11:42 PM Alan Grayson <[email protected]> wrote: *>> General Relativity only has 3 postulates:* *1) The speed of light is constant for all observers.* *2) Gravitational mass and inertial mass are equivalent.* *3) Equations expressing physical laws should say the same thing regardless of what coordinate system is used to describe 4D spacetime, even accelerating or rotating ones. * *> bodies in free fall, move along geodesic paths;* *>> That fact is a logical consequence of the Equivalence Principle, which is the third postulate in the above. So no additional postulate is required. * *I fail to see how the EP implies geodesic motion. If true, the proof must be exceedingly subtle. You're just asserting something you believe is true, as distinguished from actually proving it. AG * *> Logical consequence? How so? AG * *The Equivalence Principle says an observer cannot distinguish between being in freefall near the surface of the Earth and being in intergalactic space far from any source of gravitation, if you release an object it will not move relative to your hand. If you are floating in intergalactic space then, because of the laws of geometry, that fact is represented by a straight line in flat Euclidean 4D spacetime. If you are falling to the Earth then, because of the laws of geometry, that fact is represented by a geodesic in curved non-Euclidean 4D spacetime. And Einstein's field equations can tell you precisely how much or how little spacetime needs to be curved.* *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" when released, cannot be answered by an appeal to the "laws of geometry". You really have to be more specific to answer this question. When motion resumes, why does it take the path it does, a geodesic, and not some other path? AG * *>> The Equivalence Principle (postulate #3) says in effect that gravity is the curvature of 4D spacetime, and if gravitational mass and inertial mass are equivalent (postulate #2) then the logical conclusion is that matter causes spacetime to curve. **So no additional postulate is required.* *> See above comment. Can you prove your logical conclusion? AG* *The Equivalence Principle says gravity is the curvature of 4D spacetime, and if gravitational mass and inertial mass are equivalent but mass doesn't cause 4D spacetime to curve, then how in the world could gravitational mass and inertial mass be equivalent?!* *>> do you have a better definition of time than "what a clock measures"? I don't. * *> Sure; time is caused by the existence of observed events. No events. No time. Nothing to do with clocks, AG * *An event is defined as a specific space in 4D spacetime and a specific TIME. So if you use time in a definition of time you get into an infinite regress. * *I shouldn't have used the word "event" since it confused the issue. Earlier you wrote that time is what one reads on a clock, as if the existence of time depends on a clock. I was just trying to indicate that if, say, the universe had no mass and nothing was happening, then time wouldn't exist. The existence of time depends on things happening. Also, you've seen non-periodic clocks, say in the rollover from year 1999 to year 2000. It consisted of a set of numbers for year, month, day of year, and then hours, minutes, seconds elapsed in that day. Such a clock could have continued its time keeping for as long as anyone wanted. AG* *>> If it was impossible to make a clock, if nothing occurred in a periodic manner, then the concept of time would be meaningless.* *To repeat; clocks do not have to be periodic, and this in no makes the concept of time meaningless. AG * *> A clock doesn't have to be periodic. It can be linear. It just needs to assign a unique real number to each event being observed. AG* *So you think a clock could be made by making a list of the position of every particle in the universe with respect to time, but without a clock how do you know what time it is? And even if you could somehow manage to make such a list, how could you know which way to read it? We can tell which way the arrow time is pointing because tomorrow will have more entropy than today, but that would no longer be true when the universe has reached heat death and entropy has risen to a maximum. * *>> The 4D shape of the resulting spacetime is determined by how the matter/energy is distributed, and its precise shape can be calculated with Einstein Field Equations, which uses 4D non-Euclidean tensor calculus. * *> What's obviously lacking is a physical mechanism to get to your conclusion. 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. 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. In such case, the test particle would have move spatially, having been released in a gravity field. The movement itself would be geodesic since that's a postulate of GR. I don't see geodesic motion as following from the Equivalence Principle or the equivalence of inertial and gravitational mass. That is, IMO, your claim that geodesic motion follows from those facts is not convincing. AG* *Give me an example of a phenomenon, ANY phenomenon physical or otherwise, that you feel has a satisfactory explanation and doesn't generate additional questions that are very obvious. * *> Insofar as you defend the Gospel, and vehemently I might add, although at some level you don't think GR is the end of the road, but emotionally you do. AG * *Thanks for that very deep psychoanalysis Dr. Freud.* *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* *tsd* -- 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/856b8e1a-365e-41da-9a4c-1f3739cb6890n%40googlegroups.com.
