SNIP
> thus two observers who are in relative
> motion measure different values for the same interval.
Yes.
Harald
> suppose an observer in the experiment below placed one marker at the
> location of the pion's formation and another at the location of its decay.
[quoted text clipped - 17 lines]
> limitations of classical physics and serve as a test of einstein's special
> theory of relativity
xxein: Given that the production of pions at a lab-measured velocity
of .913c covers a decay distance of ~17.4 m, the ~63.7 ns is correct.
That is a lab distance and a lab time.
For the "lab-observed" pion, that does translate to a longer lifetime.
If you attach a clock to the pion, though, it will indicate a shorter
time because the clock is moving at .913c (the ~26 ns in the pion's
rest frame). Iow, the pion will always measure its own lifetime as 26
ns.
But the moving pion also measures a meter that is ~.408x the size of
the lab meter so that instead of ~17.4 meters between its creation and
demise, it will measure it as ~42.65 m.
What?? ~42.65 m / ~26e-9 secs = ~5.5c! Well, yes, unless you correct
for relativity (time and meters).
~.408^2 x ~5.5 = v/c (.913 if you calculate everything by using 17.4
as an exact measure).
It means that we define a meter with TWLS, not OWLS. Let's suppose you
have a spaceship of length L; it will contract with velocity. But two
separate spaceships traveling at the same velocity will not contract L
except by a false synchronicity of acceleration (wrought by Einstein's
own notion of Relativity-math).
But since v/c is relatively small where we live, such velocities as
.913c are good examples for thought applications. As such, we can
calculate, from our rest frame, how long light takes to get from one
ship to another, right? Let's space them 1 ltsec apart. 1 / (1 +
.913) secs one way and 1 / (1 - .913) secs the other way. That totals
more than ~12 secs for a distance of 1 ltsec. Take half of that for an
Einstein one-way time (~6 secs).
We can rectify with time dilation and reduce that time by a factor of
~.408, but that still leaves another identical factor of ~.408 to to
reduce it to a unit 1 sec. It cannot happen.
What you can measure is that all common activities aboard the 'other'
ship appear to happen at your rate of time. You can even measure a
subjective distance to correspond to the delay of signal time using the
2nd postulate of SR. But that is not really the distance you started
with. It is off by a factor of ~.408 (mathematically equal to timerate
or length contraction).
Look at it this way. If you were transversely passing by Earth (if it
were a rest frame), your observation would have nothing at all to do
with a Doppler shift. It is all timerate (v/c wrt rest). You would
see all activity on the Earth moving at 1 / ~.408. Iow, it would look
fast to you because your clock is slow. The easy part of this
explanation is to consider the right opposite. The Earth (and all the
rest of this universe) is traveling at .913c.
Now why wouldn't it look slow? That's what Einstein implies when he
says that all velocity is relative, doesn't he? Well he is confused
with a math that describes Doppler related effects where there is no
Doppler effect. He confused a math that was obscure enough even
further. I can't write a book here, but a little proper physical
thought, in place of Einstein's rote cannot go wrong.
Back to the spaceships: if it were a single ship that was 1 ltsec in
length, you would have the missing ~.408 because of a physical length
contraction. Do you see why a physical length contraction doesn't
imply space contraction?
This and all the other considerations that I have undertaken, lead to a
sense of an absolute. Can we measure it? You bet, as long as we keep
our socks from flopping. Is that gravity? No problem to me.
We need to reinterpret this universe with an empiricism that is NOT
interpreted by old thoughts and theories bent to accommodate it. As I
have shown above, it would take an act of faith, and no independent
physical reasoning, to adopt the Einsteinian.
But, as I always say, SR-GR seems to serve our immediate needs
(although only subjectively and maybe not tomorrow). WAIT A MINUTE.
This is tomorrow. We go outside the theory to see how empirical things
work.
Ah, well. When will we learn to identify an hierarchy of things
physical? Not too soon I suspect.