Re: Incorrect mathematical integration

Den 20.07.2024 23:55, skrev Richard Hachel:

Le 20/07/2024 à 22:05, "Paul.B.Andersen" a écrit :
 

So please show the equation for the proper time as a function of
the velocity and the time in the inertial system, which is
correct physically and mathematically according to your theory.

 I've already given all that away for a long time.
 I take the main equations again.
 To: time in the laboratory (or terrestrial), observable time.
Tr: proper time, tau.
a: acceleration
 x=(1/2)a.Tr²
x=(c²/a)[sqrt(1+a²To²/c²) -1]
 To=(x/c)sqrt(1+2c²/ax)
Tr=sqrt(2x/a)
 To=Tr.sqrt(1+(1/4)a².Tr²/c²)
 R.H.

You didn't answer my question, but as you know,
I am very confused about your different kind
of times and speeds, so please explain what kind of times
and speeds there are in my scenario below.
Since the protons in the LHC  are moving at a pretty constant
speed, I will first like you to consider the case when  a = 0.
A word about synchronisation of clocks.
---------------------------------------
You have said strange statements about synchronisation of clocks.
But you know of course that all clocks in the same time zone
are synchronous. In France and Norway clocks are currently
showing GMT + 2 hour, so my clock and your clock are actually
synchronous. Of course common wristwatches are not very precise
and may be seconds or even minutes off sync. But clocks can
be synchronised via GPS, and atomic clocks can via GPS be synchronised
to GMT+2h within 1 ns.
So: in an inertial system K, a clock C is in inertial motion.
t is the time in K.
A and B are two stationary, synchronous clocks in K.
At t = t₁
   C
   A                     B
--|---------------------|------> x
   0                     L
Clock A is showing t₁, clock C is adjacent to A and is set to zero.
At t = t₂
                         C
   A                     B
--|---------------------|------> x
   0                     L
Clock B is showing t₂, clock C is adjacent to B and is showing τ
Let L = 0.0001 light second = 29979 m
Let (t₂ - t₁) = T = 125 μs
v = L/T = 239833966.4 m/s = 0.8c
w = L/τ
What kind of time is T ?
What kind of speed is v ?
What is τ ? (equation, value and type of time)
What kind of speed is w ?
What is the physical significance of w?
Can it say anything about the position of C at the time τ ?
--
Paul
https://paulba.no/