On 1/4/2019 9:43 AM, John Clark wrote:
On Thu, Jan 3, 2019 at 5:59 PM Brent Meeker <[email protected]
<mailto:[email protected]>> wrote:
>>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./
So what? The entire point of looking at things from a spacetime
perspective is to find a invariant that everybody can agree on, and d
provides it. If you don't like imaginary numbers then use d^2, if you
don't like negative numbers then use d^4 and get an old
fashioned positive Real Number; use whichever one that strikes your
fancy it doesn't matter because they're all invariants.
>>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./
Yes.
> /To make that work you have to put in the difference in time
coordinate for t. /
Yes, what else could t mean?
You said *t was the proper time for me to take the trip*. But the
proper time is what a clock measures and so it depends on the path you
took in making the trip.
In the formula for spacetime distance x^2 + y^2 + z^2 -(ct)^2 t is the
difference between what a clock was reading when it started its
journey from what it is reading when it ended its journey between the
2 events; and c is the all important speed of light, the only thing
that prevents the formula from being Monty Python level silly.
>>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./
OK.
>>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. /
No? What the hell do you mean "No"?!
> /Different paths between two events have different proper times
between the same two events./
Exactly true, and that is exactly why I said "proper time is *NOT* an
invariant"!
You apparently use "invariant" in a strange way. Proper time is an
invariant length of a path in 4-space. Just as the length of interstate
10 from L.A. to S.F. is an invariant. Invariant means that all
different observers agree on it. It doesn't mean the length of a path
is independent of the path.
> /All observers will agree on the length (proper time duration) of
those paths/
No observer agrees on that because no observer knows what the hell
meters minus seconds means. But you did agree above that proper time
is the time measured by a clock along any line through spacetime, so
for my twin that was on a rocket at near light speed and then returned
the proper time is one year, but for me who stayed on Earth the proper
time was 10 years. Therefore proper time can not be a invariant,
therefore the length of the path through spacetime can NOT be the
proper time because the length of the path through spacetime *IS *an
invariant.
The length of which path? Every observer can read the clock as it moves
along the path and they will all agree on the length of the path. They
don't agree on the spacial interval or the time interval, but they
argree on the proper time the clock measures along the path. THAT's
what "invariant" means.
> /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. /
Proper Time is defined as the amount of change an observer has seen a
clock make that is in the same reference frame as the observer.
NO. The definition doesn't require the observer to be moving with the
clock.
>> 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. /
Yes, apart from confusion of units your ideas are great. And other
than that how did you like the play Mrs. Lincoln?
Tell it to the SI committee.
/>That has not more significance than the fact that we measure the
length of highways in miles and widths in feet. /
*Bullshit*. We're not talking about confusing miles and feet we're
talking about something far dumber, confusing meters and seconds. The
first thing they teach you on day one of high school physics is YOU'VE
GOT TO GET THE UNITS RIGHT, otherwise you're talking nonsense. And it
doesn't get any more nonsensical than subtracting seconds from meters.
The fact that you're STILL defending this ridiculous notion speaks
volumes.
The first thing they teach you in graduate school is c=G=h=1 is the best
set of units.
/> In practice, all distance measurements are made with clocks. /
Not unless the speed you're moving at is known.
The clock doesn't have to move. All precise distance measurements are
really radar distance measured by EM interference (c.f. LIGO).
> /If someone wants the answer in meters they use the conversion
factor 299792458 meter/second.
/
And you may be uncertain about how fast you're moving but one thing is
absolutely certain, it is *NOT* 299792458 meter/second.
Pay attention. Nobody said I was moving that fast. I said it was a
conversion factor. That's why we talk about spacetime, not space and time.
Brent
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