Re: Incorrect mathematical integration

Den 22.07.2024 23:55, skrev Richard Hachel:

Den 22.07.2024 21:37, skrev Paul.B.Andersen:

 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.
 Please explain why our clocks are NOT synchronous.
(To within few seconds)

 But I keep explaining it to you.
 This is a property of space that can be called universal anisochrony.
 This does not translate into the idea that the “plan of present time” so dear to physicists does not exist, it is a thought that seems logical to them, but it is an abstract thought.
 

I interpret this to mean that watches in Norway and France are
not synchronous even if they both show GMT+2h
I leave Oslo Airport (Gardemoen Airport) when the watch on the airport
shows 12.00.00
I arrive at Paris Airport (Charles De Gaulle Airport) when the watch
on the airport shows 13.30.32.
The difference is T = 1h 30m 32s
Is this a real time, or is it impossible to know the real time
because of the universal anisochrony?
The distance in the ground frame between the airports is L = 1358.03 km.
Is the real speed of the plane in the ground frame v = L/T = 900 km/h,
or is it impossible to know the real speed of the plane because
of the universal anisochrony?

 What do you call the phenomenon that when you look at the clocks
on your table and on your mantelpiece, they always show the same?
(to within the precision with which you have set the clocks.)
 

  If I place myself equidistant from the two watches, and they are correctly adjusted, that is to say that they beat at the same time, with great precision, I will notice that FOR ME (I beg you to do the (effort to understand myself, and this is why I write in capital letters), FOR ME, they always mark the same time at the same moment.
This means that they are perfectly regulated, and that they have an identical chronotropy (because they are in the same stationary frame of reference).
 

So your watches are synchronous because they both are stationary in
the ground frame, but the watches in Oslo and Paris are not synchronous
even if they are stationary in the ground frame?
Or have I misunderstood something?
Are your clocks synchronous for YOU because they are stationary
in the ground frame, but not for ME even if they are stationary
in the ground frame?

 It is obviously impossible to make two clocks side by side show
the same with infinite precision, there will always be a difference.
For atomic clocks this difference may be less than 1 ns,
for say - wristwatches it will be less than 1 second.
 As long as the difference is less than the precision of your
measurements, the clocks can be considered to be synchronous.
 Practical examples:
 100 m sprint:
Two synchronous clocks at start and finish line.
The precision of the measurements is 0.01 second
So the clocks must be synchronous to within 10 ms.
 Tour de France.
Start and finish line may be ~200 km from each other.
The precision of the measurement is 1 second.
So the clocks at the start and the finish must
be synchronous to within 1 second.
 Do you accept this, or are you still insisting that it
is impossible to have clocks synchronous to within
the precision of the actual measurement?

You don't understand anything I'm saying...
 Pfffff...
 I'm not talking about technical precision, I'm talking about a real problem linked to the nature of space and time.
 This problem is anisochrony, two identical and well-adjusted watches, which we slowly and in the same way separate over a distance of 300,000 km will be irremediably out of tune.
 They will always have the same chronotropy (internal speed of the watch mechanism) and for me, who am at the center, they will always mark the same time.
 But between them, there will be a real time difference due simply to the distance. This gap, absolutely real and unavoidable due to the nature of space and time, will be one second between these two watches. Each sees the other beat at the same speed (they are inertial, stationary) but with a strange delay of 1 second.
 Physicists do not seem to understand this property, and only understand the internal chronotropy when watches are in reciprocal motion, but that is not enough. We must also understand anisochrony, which is a real phenomenon, of the first degree, unavoidable, and which has nothing to do with the speed of light. Information propagates instantly, BUT the present moments did not correspond to the departure.

So what does this mean?
Is it impossible to measure the time the cyclists use to cycle
200 km because the clocks on the start and finish can't be synchronous
because of the nature of space an time?

 All the clocks in the the GPS system (satellite clocks, ground clocks)
are synchronous with the UTC (Coordinated Universal Time)
to within ~1 ns.
 Your clock on your table is synchronous with the UTC+2 hours,
to within the precision you have set the clock.
 The UTC is universal in the sense that it covers the whole Earth
and the space in its vicinity.
It is coordinated in the sense that it is defined at any point
on the Earth and in the space in Earth's vicinity.
It is real even if it is defined by man. It is no illusion.
 All clocks on Earth and in the GPS-, GLONASS- and Galileo-satellites
are synchronous to the UTC or UTC+n hours.
 It is a fact that you can synchronise clocks via the GPS.
The GPS receiver determines four entities, the time, altitude,
latitude and longitude. If the spatial position is within 1 m,
the time must be the UTC to within ~2 ns.
 Yes, your GPS receiver does indeed determine the time to within few ns
of the UTC, it must do that to determine the position to few metres.
It is obviously no point in displaying the time with this precision
on the screen.

No comment to this, Richard?
Are you insisting that the GPS doesn't work because the satellite clocks
can't be synchronous because of the nature of space an time?
--
Paul
https://paulba.no/