On 1/3/2019 12:05 PM, John Clark wrote:
On Thu, Jan 3, 2019 at 3:58 AM Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
/> The 't' in your formula above is the coordinate time, not the
proper time. /
What the hell are you talking about? If I travel from event A to event
B and use the formula x^2 + y^2 + z^2 -(ct)^2
You can only travel between A and B if they are timelike, in which case
your formula will yield an negative squared distance.
where x,y,and z are the differences in spatial coordinates I observe
and *t is the proper time* it took for me to make the trip I will get
an invariant.
No. To make that work you have to put in the difference in time
coordinate for t. THEN you get the invariant interval (in flat
spacetime) also known at the proper interval, or the proper time when A
and B are timelike. When spactime isn't flat, or the path isn't the
extremal path you have to integrate the proper time intervals along the
path.
If you also travel between event A and B but use a different path you
will get entirely different numbers for x, y and z and you will get a
different number for *the proper time t,* but when you plug in your
numbers into x^2 + y^2 + z^2 -(ct)^2 you will get the exact same
value I do.
/> The proper time is defined as the time kept by a perfect clock
travelling on a geodesic./
No it is not! The proper time is defined as the time measured by a
clock along ANY line through spacetime and it doesn't matter a hoot in
hell if that line is a geodesic or not.
That's right.
And you said "/Proper time is the distance through spacetime/" but
every book on physics on the planet will tell you that the distance
through spacetime is an invariant; but proper time is NOT a invariant,
different observers can have different proper times,
No. Different paths between two events have different proper times
between the same two events. All observers will agree on the length
(proper time duration) of those paths because that is what a clock
measures along the path...it is not observer dependent. You are using
the word "observer" as though it referred to a traveler, but in
relativity it usually means someone measuring a physical process from a
different state of motion. So an observer of a path through spacetime
may measure it to have different coordinate time changes and different
spacial distance changes, but still the same path length or proper time.
even you know this because you said "/two different orbits of the
Earth, both geodesics, can coincide at a pair of events. They will
measure different proper times between those events/".
Actually I wrote that, not Bruce.
So your ideas are not self consistent but then they had to be,
spacetime distance and proper time aren't even in the same units.
You keep a harping on units. That has not more significance than the
fact that we measure the length of highways in miles and widths in
feet. In practice, all distance measurements are made with clocks. If
someone wants the answer in meters they use the conversion factor
299792458 meter/second.
Brent
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