On 1/1/2019 9:04 AM, John Clark wrote:
On Mon, Dec 31, 2018 at 11:22 PM Brent Meeker <[email protected]
<mailto:[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 for two spacelike events (as I specified) h^2 < 0 so you have made
the interval along a world line, the proper time, imaginary. Several
times I pointed out that proper time uses a metric with signature (+ - -
-). You're making a big distinction between spacelike 'distance' and
'proper time'. But it's just muddling the point that the geodesic
followed by a body is the longest interval. Because of the (+ - - -)
signature the extremal path is the longest, not the shortest.
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.
That's why the speed of light is now just a conversion factor.
>///(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?
It's a negative, John! It doesn't slow down realtive to anything. Ideal
clocks in relativity are assumed to accurately measure proper time along
their world line. They never run slow or fast...they just follow
different paths. You're one that referred to the clock being slowed
down. /"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.* "/
Brent
--
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.
