On 12/31/2018 7:17 PM, John Clark wrote:
On Mon, Dec 31, 2018 at 2:46 PM Brent Meeker <[email protected]
<mailto:[email protected]>> wrote:
> /But you do know that the straightest path between events in
Minkowski spacetime
/
//
You do know don't you that Minkowski spaceis non-Euclidean because it
treats time differently than the other 3 dimensions but it is not
curved so it is useful in Special Relativity but not in General
Relativity or anything involving gravity.
/> is the longest duration path don't you. /
And 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. A distance is always just
one number (not dimension) however many dimensions the space has.
If r is the distance in space and c the speed of light then the square
of the distance in spacetime between two events is r^2-(ct)^2, so the
largest possible t (proper time) will give smallest possible distance
through spacetime.
> The Google definition seems not to consider mixed signature metrics.
Google said a geodesic is the shortest distance between 2 points on a
curves surface, time is just one dimension and you can't have a curved
surface with just one dimension.
Non sequitur. I said the definition didn't consider spaces with
signatures like (+ - - -). I didn't say anything about limiting it to
one dimension.
> in Minkowski space there is only one time-like geodesic that
connects any given pair of time-like separated events,
True but curved spacetime is not Minkowski space and you can have more
than one one time-like geodesic connecting them.
You are just repeating what I wrote after the above, but you
clipped:/This is not true in curved spacetime. For example two
different orbits of the Earth, both geodesics, can coincide at a pair of
events. /
/> Even a twin paradox can be constructed this way by having the
traveling twin's velocity reversed by the gravity of massive body
far from the stay-home twin; which in GR is not a force./
Then one twin would encounter a intense gravitational field that the
other twin did not and gravity will slow down a clock just like moving
fast will.
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".
> /What "Feynman's example"?/
I posted it a few days ago. it comes from "Surely you're joking Mr.
Feynman" he posed this puzzle to an assistant of Einstein:
"Y/ou blast off in a rocket which has a clock on board, and there's a
clock on the ground. The idea is that you have to be back when the
clock on the ground says one hour has passed. Now you want it so
that//when you come back, your clock is as far ahead as possible.
According to Einstein, if you go very high, your clock will go faster,
because the higher something is in a gravitational field, the faster
its clock goes. But if you try to go too high, since you've only got
an hour, you have to go so fast to get there that the speed slows
yourclock down. So you can't go too high. The question is, exactly
what program of speed and height should you make so that you get the
maximum time on your clock?"/
/
/
/"This assistant of Einstein worked on it for quite a bit before he
realized that the answer is the real motion of matter. If you shoot
something up in a normal way, so that the time it takes the shell to
go up and come down is an hour, that's the correct motion. It's the
fundamental principle of Einstein's gravity--that is, what's called
the "proper time" is at a maximum for the actual curve."/
OK. I already replied to that: "It's an example of a geodesic being the
longest path (in interval) between two events in 4-space."
Brent
/
/
John K Clark
/
/
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