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From: "Paul.B.Andersen" <relativity@paulba.no>
Newsgroups: sci.physics.relativity
Subject: Re: Pseudoscience III: Each SR/GR experiment is a FRAUD!
Date: Sat, 28 Sep 2024 21:49:11 +0200
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Den 27.09.2024 22:13, skrev rhertz:
> On Fri, 27 Sep 2024 11:53:42 +0000, Paul B. Andersen wrote:
> 
>> Den 27.09.2024 02:47, skrev rhertz:
>>> Final remarks about why I believe that Paul is a fraudster. Actually, I
>>> think that you are much more stupid than fraudulent.
> 
> <snip all the text that you REPEATED from my post>

So I will have repeat the text which was NOT repeated
from your post.


https://paulba.no/paper/Hafele.pdf
top of page 268:
"For an equatorial circumnavigation with constant ground speed v (m/s)
  and altitude h(m), the predicted relativistic time gain for the flying
  clock over a similar reference clock kept at "rest" on the Earth's
  surface is given by:

          Δτ/τ₀ = (τ - τ₀)/τ₀ = gh/c² - (2RΩv + v²)/2c²    (1)

  where τ and τ₀ are the respective times recorded by the flying
  and ground clocks; R (m) is the Earth's radius and Ω (rad/s) its
  angular speed; g(m/s²) is the surface value of the acceleration
  of gravity; and c(m/sec) is the speed of light.
  In Equation 1, the ground speed is positive for eastward and
  negative for westward circumnavigations."

Note that the point with this equation (with constant speed at equator)
is "for estimating the magnitude of expected relativistic effects."

It was obviously not this equation (with constant speed and altitude)
that was used for the calculation of the prediction for all the flights.

-----

If an aeroplane is flying once around the Earth along equator
with a constant ground speed and altitude, and the duration of
the trip is 65.42 hours as measured by UTC clocks which are
stationary on the ground at the geoid, then the kinematic term
of equation (1) will give the following result:

>>> Paul.B.Andersen wrote:
>>>>
>>>> The USNO clocks advances τ₀ = 65.42 hours during the 65.42 hours trip,
>>>>
>>>> I put the values:
>>>> τ₀ = 65.42 h = 235512 s
>>>> R = 6378137 m
>>>> Ω = 7.2921159e-5 rad/s
>>>> c = 299792458 m/s
>>>> v = 2πR/τ₀ = +170.16 m/s
>>>>
>>>> into THE FORMULA  Δτₖ = (-(2RΩv + v²)/2c²)τ₀
>>>> and get Δτₖ = -245.32 ns.
>>>>
>>>>
>>>> This is the kinematic term, so it is only part of the difference
>>>> between the USNO clock and the "flying" clock.
>>>>
>>>>
>>>> But can you please explain why doing what I did made me a fraudster?

It is obviously idiotic to say that to put numbers
into this theoretical flight is fraudulent.

-----------------------

Your real blunder is to insist that that H&K used equation (1)
to calculate the predictions for the trips. They did not.

https://paulba.no/paper/Hafele.pdf
I quote from page 271:
"Commercial around-the-world flights do not, of course,
  maintain constant altitude, latitude, or ground speed.
  In this case, it is necessary to perform a numerical integration
  of the relativistic equations. The necessary calculation is given by

   Δτ = ∫ [gh(τ)/c² - (2RΩ⋅cosλ(τ)⋅cosθ(τ)⋅v(τ) + v²(τ))/2c²]dτ  (2)

  where, for each interval of the summation, λ is the latitude, θ is
  the azimuth or bearing of the plane's velocity relative to east,
  and the rest of the symbols have the same meaning as for Equation (1)
  (v is the unsigned magnitude of the ground speed in Equation 2;
  the azimuth θ accounts for the direction).
"

The eastward trip consisted of 14 flights, and equation (2)
was used for all the flights. When the the clocks were stationary
on the ground Δτ didn't change.


> 
> I´LL REPEAT ONE MORE TIME:
> 
> YOU CAN'T, UNDER ANY DECENT ASSUMPTION, DARE TO ESTIMATE WHAT WAS THE
> ELAPSED TIME AT THE USNO CLOCKS IN WASHINGTON, IF YOU ARE 15,000 MILES
> FAR AWAY AND HAVE NOT ANY MEANS (NOT EVEN AS OF TODAY) TO ESTIMATE THE
> TIME VALUE OF SUCH REFERENCE CLOCK.

Yes, you can ESTIMATE WHAT IS THE TIME AT THE USNO CLOCKS
IN WASHINGTON, IF YOU ARE 15,000 MILES FAR AWAY.
I keep my wristwatch to within 1 second from UTC +2h, so I can at
any time estimate the time at the USNO clocks within 1 second.

Remember that all clocks showing UTC+n hours are synchronous
in the ECI-frame, even if the precision will vary.

> 
> WHEN YOU ASSUME THAT IT'S CORRECT TO ESTIMATE SUCH ELAPSED TIME AS THE
> REMOTE FLIGHT TIME PLUS TIME SPENT AT AIRPORTS (65.42 HOURS), YOU ARE
> BEYOND CRETINISM, BECAUSE OVER THAT RESULT YOU DARE TO ESTIMATE A 200
> NSEC DIFFERENCE WITH THE HAFELE'S CLOCKS.

For estimating the _prediction_ H&K used equation (2) for each flight.
The τ in the equation is the time shown by 'ordinary' clocks on
airport and in planes. When the clocks were stationary on the ground
Δτ didn't change and nothing had to be done.

The point is that the measurement of the duration of each flight
isn't critical, and does not have to be done by an atomic clock.
There are many other parameters (speed,heights etc.) which
are less well known than the time.

In our theoretical flight above, 1 second error in τ₀ would
only give 1 ps error in Δτₖ. So 1 second precision in τ₀
would give Δτₖ = -245.323 ± 0.001 ns

But when H&K _measured_ Δτ the trips were timed with the clocks
at USNO. The start of the trip was when the 4 clocks for the last
time were compared to the USNO clocks before the trip,
the end of the trip was when the 4 clocks for the first time
were compared to the USNO clocks after the trip.
The Δτ was then the difference between the corrected time of
the four clocks and the USNO clock.

> 
> WHEN YOU ACCEPT THAT OVER A THEORETICAL VALUE OF 235,512,000,000,000
> NSEC ELAPSED AT USNO CLOCKS (VALUE PULLED OUT OF YOUR ASS),
> THEORETICALLY CAN ESTIMATE A DIFFERENCE OF 200 NSEC, YOU ARE A LIAR, A
> DECEIVER AND A FRAUDSTER.

The _theoretical_ trip with constant speed along equator
lasts 65.42 hours per definition, and  Δτₖ = -245.323 ns

> 
> CAPITO?
> 
> YOUR REPUTATION AS AN IMBECILE IS WRITTEN ALL OVER THE GOOGLE FORUM FOR
> MORE THAN 20 YEARS. YOU CAN'T ESCAPE FROM SUCH HISTORY OF YOUR
> ADVENTURES HERE. I DON'T KNOW HOW A FRAUDSTER FEEL ABOUT HIMSELF OR HOW
> CAN HE LIVE WITH SUCH SHAME, BECAUSE I'M AN HONEST PERSON AND ALWAYS
> HAVE BEEN. SOMETHING THAT YOUR PARENTS TEACH, BUT THEY FAILED ON YOU.

:-D

Richard, do you remember this blunder of yours?

> Den 16.09.2024 18:32, skrev rhertz:
>>
>> 2) The satellite clock is PERCEIVED to be ticking slower (from the
>> Earth's ground) by a factor: Δf/f = Φ/c² =  GMe/c² (1/Re - 1/Rs)
>> with respect to a TWIN CLOCK, located on the Earth's surface. 

------------
Or this?

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