On Mon, Dec 31, 2018 at 11:22 PM Brent Meeker <[email protected]> wrote:
>> I hope you know the path yielding the longest proper time duration is >> not the same as having the longest distance through spacetime as time is >> just one dimension and spacetime involves 4. > > > * > Proper time is the distance thru spacetime. * > No it is not. I gave the formula for the spacetime distance between 2 events in my previous post, unless you intend to dispute this well established and uncontroversial formula the only logical conclusion one can make is that to calculate the spacetime distance between 2 events occurring at different times AND different places you must make use of both time and space information. And because in that formula the distance in space is a positive term but the duration in time is a NEGATIVE term the larger the duration in time the smaller the spacetime distance. That is also why the geometry of spacetime is Non-Euclidean, because of that negative value the Pythagorean theorem is not valid in spacetime. Euclid says the hypotenuse of a right triangle (h) is h^2=a^2 + b^2, but in spacetime h^2 = s^2 - (ct)^2 if s is the space distance and t is the time duration and c the speed of light. The minus sign in there means the larger the t is the smaller the h is, and h is the spacetime distance. And proper time doesn't even give you the correct units for spacetime distance. Time is in units of seconds but the formula makes it clear that the spacetime distance (h) is in meters; s is in meters and ct is in meters because c (the speed of light) is in meters/sec and t is in seconds. > > *A distance is always just one number* > Yes, and that number had better be in the correct units! You can never find a distance between anything by subtracting seconds from meters, that would be gibberish, but you can subtract meters from meters. > *(not dimension) however many dimensions the space has.* > And you can not have a shortest distance between 2 points on a curved surface with just one dimension because you can't have a curved surface with just one dimension. And that's why Google was NOT wrong as you claimed when it said a geodesic was "*relating to or denoting the shortest possible line between two points on a sphere or other curved surface*". If the surface is Non-Euclidean the larger the proper time the smaller the spacetime distance. > *> Gravity doesn't "slow down a clock" it just changes the proper > distance. Relativity always talks in terms of ideal clocks that measure > proper time and never "slow down".* > Doesn't slow a clock down relative to what? There is no absolute time in Relativity, a clock never slows down relative to an observer in the same reference frame but to an observer that is moving at a constant speed close to the speed of light your clock is running slow, and to an observer accelerating in a rocket at 10g (or equivalently standing on the surface of a planet with a 10g gravitational field) your clock is running fast. John K Clark -- 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 post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
