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GPS clocks should run Slow Not Fast.

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  GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-12 00:01 +0000
    Re: GPS clocks should run Slow Not Fast. Emanuele Babuh <uh@elbbem.ru> - 2026-10-12 07:40 +0000
    Re: GPS clocks should run Slow Not Fast. "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2026-10-12 20:55 +0200
      Re: GPS clocks should run Slow Not Fast. Maciej Woźniak <mlwozniak@wp.pl> - 2026-10-13 07:30 +0200
        Re: GPS clocks should run Slow Not Fast. Clancy Balanovski <av@sysal.ru> - 2026-10-13 07:07 +0000
      Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-13 10:27 +0200
        Re: GPS clocks should run Slow Not Fast. "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2026-10-13 22:32 +0200
          Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-14 14:20 +0200
            Re: GPS clocks should run Slow Not Fast. "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2026-10-14 21:08 +0200
              Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-14 23:08 +0200
                Re: GPS clocks should run Slow Not Fast. "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2026-10-15 23:10 +0200
                  Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-15 22:05 -0700
                    Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-18 16:54 -0700
                      Re: GPS clocks should run Slow Not Fast. Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-10-19 03:09 -0700
                        Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-19 09:50 -0700
                          Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-19 23:20 -0700
                        Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-21 12:25 -0700
                          Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-22 11:34 -0700
                            Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-22 12:28 -0700
                              Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-22 14:30 -0700
                              Re: GPS clocks should run Slow Not Fast. Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-10-22 19:46 -0700
                                Re: GPS clocks should run Slow Not Fast. The Starmaker <starmaker@ix.netcom.com> - 2026-10-22 22:14 -0700
      Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-13 15:20 +0000
        Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-14 14:12 +0200
          Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-16 10:36 +0000
            Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-19 03:28 +0200
        Re: GPS clocks should run Slow Not Fast. "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2026-10-14 21:07 +0200
          Re: GPS clocks should run Slow Not Fast. Wildo Zhmulev <vedlml@hlhiudlo.ru> - 2026-10-15 07:52 +0000
          Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-16 10:39 +0000
    Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-13 09:42 +0200
      Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-13 15:54 +0000
        Re: GPS clocks should run Slow Not Fast. Python <python@cccp.invalid> - 2026-10-13 16:01 +0000
          Re: GPS clocks should run Slow Not Fast. Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-10-13 09:10 -0700
            Re: GPS clocks should run Slow Not Fast. Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-10-14 06:18 -0700
        Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-14 17:30 +0200
          Re: GPS clocks should run Slow Not Fast. Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-10-14 09:32 -0700
    Re: GPS clocks should run Slow Not Fast. Mikko <mikko.levanto@iki.fi> - 2026-10-21 11:04 +0300
      Re: GPS clocks should run Slow Not Fast. Maciej Woźniak <mlwozniak@wp.pl> - 2026-10-21 10:07 +0200
      Re: GPS clocks should run Slow Not Fast. ram@zedat.fu-berlin.de (Stefan Ram) - 2026-10-24 20:18 +0000
        Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-27 11:25 +0000
      Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-27 21:32 +0100
        Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-27 23:03 +0000
          Re: GPS clocks should run Slow Not Fast. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-10-29 00:47 +0100
            Re: GPS clocks should run Slow Not Fast. HenryWilson <Hgw@home.com> - 2026-10-29 16:41 +0000

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#674344 — GPS clocks should run Slow Not Fast.

Here is one to argue about. According to GR, light experiences a redshift 
in frequency when sent into lower gravity potential. How come clocks are 
claimed to run fast when sent into orbit. Clocks merely count cycles of an 
oscillator, which according to GR should run slow.

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#674352

HenryWilson wrote:

> Here is one to argue about. According to GR, light experiences a
> redshift in frequency when sent into lower gravity potential. How come
> clocks are claimed to run fast when sent into orbit. Clocks merely count
> cycles of an oscillator, which according to GR should run slow.

this guy is an usenet user; relativity doesnt says that, the relativit is 
all about observers and observed; only

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#674357

Den 12.10.2026 02:01, skrev HenryWilson:
> Here is one to argue about. According to GR, light experiences a redshift
> in frequency when sent into lower gravity potential. How come clocks are
> claimed to run fast when sent into orbit. Clocks merely count cycles of an
> oscillator, which according to GR should run slow.

Confused, Ralph? :-D

In the following we will assume that the Earth is not rotating.

This is what GR say:

Clocks always run at their proper rate, one second per second.

If a clock on the ground is emitting a signal with
frequency f₀ = 1 GHZ, then the frequency received at
a position r above the centre of the Earth is:
   Δf/f₀= (GM/c²)⋅(1/r - 1/R) = -5.2996e-10
where:
GM = 3.986004418e14 m³/s² Geocentric gravitational constant
c  = 299792458 m/s speed of light in vacuum
R  = 6363691 m radius of Earth
r  = 26561763 m radius of GPS orbit

This means that the received frequency is:
f = 1GHz⋅(1 + Δf/f₀) =  999999999.47 Hz, a gravitational red shift.

Observed from the position r above Erth's centre
the ground clock appears to run slow.

If a clock at a position r above the centre of the Earth is emitting
a signal with frequency f₀ = 1 GHZ, then the frequency received at
the ground is:
   Δf/f₀= (GM/c²)⋅(1/R - 1/r) = 5.2996e-10

This means that the received frequency is:
f = 1GHz⋅(1 + Δf/f₀) = 1000000000.53 Hz, a gravitational blue shift.

Observed from the ground the clock at r appears to run fast.

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

The Earth is obviously rotating, so in the GPS we have:

The gravitational blue shift of the SV signal is Δf/f =  5.2996e-10
The kinetic red shift (due to motion) is         Δf/f = -0.8349e-10
The total(gravitational + kinetic) blue shift is Δf/f =  4.4647e-10

-- 
Paul

https://paulba.no/

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#674359

On 10/12/2026 8:55 PM, Paul B. Andersen wrote:
> Den 12.10.2026 02:01, skrev HenryWilson:
>> Here is one to argue about. According to GR, light experiences a redshift
>> in frequency when sent into lower gravity potential. How come clocks are
>> claimed to run fast when sent into orbit. Clocks merely count cycles 
>> of an
>> oscillator, which according to GR should run slow.
> 
> Confused, Ralph? :-D
> 
> In the following we will assume that the Earth is not rotating.
> 
> This is what GR say:
> 
> Clocks always run at their proper rate, one second per second.

Even The Shit is not THAT stupid, it's just you.

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#674361

Maciej Woźniak wrote:

> On 10/12/2026 8:55 PM, Paul B. Andersen wrote:
>> This is what GR say:
>> 
>> Clocks always run at their proper rate, one second per second.
> 
> Even The Shit is not THAT stupid, it's just you.

absolutely, that "second per second" is not even correct grammatically, 
since it expects you already have a second before comparing it with the 
other second. It makes no sense, it's an absurdity repeated by former, now 
obsolete, it-supporters void of elementary education

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#674368

Paul B. Andersen wrote:
> The Earth is obviously rotating, so in the GPS we have:
> 
> The gravitational blue shift of the SV signal is Δf/f =  5.2996e-10
> The kinetic red shift (due to motion) is         Δf/f = -0.8349e-10
> The total(gravitational + kinetic) blue shift is Δf/f =  4.4647e-10

Note that this is just a crude, at best first-order, approximation.
To obtain the exact values according to GR, you cannot simply add
"gravitational" and kinetic "time dilation" or (here) frequency shifts;
you have to use the full (Schwarzschild) spacetime metric (at least).

Note also that not all GPS satellites have the same orbital altitude or
orbital direction (and the orbits are only approximately circular), so
both the "gravitational blueshift" and the "kinetic redshift" varies
between satellites and between locations on the ground (they also vary
at least with latitude due to different rotation speeds).

The infinitesimal elapsed proper time in central-circular motion in the
Schwarzschild spacetime is given _exactly_ by

    ds² = −dτ² = −(1 − 2m∕r) dt² + (1 − 2m∕r)⁻¹ dr² + r² dΩ²,
      m = G M∕c²,
    dΩ² = dθ² + sin²(θ) dφ²,

  ⇔ dτ² = (1 − 2m∕r) dt² − (1 − 2m∕r)⁻¹ dr² − r² dΩ²
        = dt² [1 − 2m∕r − (1 − 2m∕r)⁻¹ (dr/dt)²
                 − r² (dθ/dt)² − r² sin²(θ) (dφ/dt)²]

  dr/dt = 0
  ⇔ dτ  = dt √[1 − 2m∕r − r² {(dθ/dt)² + sin²(θ[t]) (dφ/dt)²}].

To calculate the elapsed proper time Δτ = ∫_W dτ along a worldline
segment W becomes a little difficult without making simplifying
assumptions such as a constant polar angle (dθ/dt = 0) or an equatorial
orbit (θ = π∕2).

In any case, you should substitute the orbital parameters in an ECI
frame (in the case of a GPS satellite), and the components of the
rotation velocity of a point on the terrestrial surface in the same
frame, respectively.

The exact blueshift (according to GR) follows from that, as I derived in
<mid:119a9s8$182fs$2@gwaiyur.mb-net.net>.

-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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#674401

Den 13.10.2026 10:27, skrev Thomas 'PointedEars' Lahn:
> Paul B. Andersen wrote:
>>
>> The gravitational blue shift of the SV signal is Δf/f =  5.2996e-10
>> The kinetic red shift (due to motion) is         Δf/f = -0.8349e-10
>> The total(gravitational + kinetic) blue shift is Δf/f =  4.4647e-10
> 
> Note that this is just a crude, at best first-order, approximation.

It is a very precise approximation. The error is less than 1e-15.

> To obtain the exact values according to GR, you cannot simply add
> "gravitational" and kinetic "time dilation" or (here) frequency shifts;
> you have to use the full (Schwarzschild) spacetime metric (at least).

See:
https://paulba.no/pdf/Clock_rate.pdf
Equation (18) can be written:
  Δf/f₀ = δ_utc - GM/(c²r) - GM/(2c²r)

Gravitational blueshift Δf/f₀ = (δ_utc - GM/(c²r)) =  5.299580e-10
Kinetic redshift        Δf/f₀ = - GM/(2c²r)        = -0.834852e-10
Total(gravitational + kinetic) blue shift:         =  4.464728e-10

Now you can wonder why such a simple equation can give so precise result.
> Note also that not all GPS satellites have the same orbital altitude or
> orbital direction (and the orbits are only approximately circular), so
> both the "gravitational blueshift" and the "kinetic redshift" varies
> between satellites and between locations on the ground (they also vary
> at least with latitude due to different rotation speeds).

Don't be ridiculous.
The blue shift doesn't depend on the location on the ground.
The speed and orbital radius of all the satellites are equal
so the blue shift of the signal from all the satellites
is equal.

We calculate the blue shift from the assumption that all
satellites are in their nominal orbit.
Six orbital planes 60 degrees from each other, four satellites
in each plane, planes 55 degrees inclination to equatorial plane.

> 
> The infinitesimal elapsed proper time in central-circular motion in the
> Schwarzschild spacetime is given _exactly_ by
> 
>      ds² = −dτ² = −(1 − 2m∕r) dt² + (1 − 2m∕r)⁻¹ dr² + r² dΩ²,
>        m = G M∕c²,
>      dΩ² = dθ² + sin²(θ) dφ²,
> 
>    ⇔ dτ² = (1 − 2m∕r) dt² − (1 − 2m∕r)⁻¹ dr² − r² dΩ²
>          = dt² [1 − 2m∕r − (1 − 2m∕r)⁻¹ (dr/dt)²
>                   − r² (dθ/dt)² − r² sin²(θ) (dφ/dt)²]
> 
>    dr/dt = 0
>    ⇔ dτ  = dt √[1 − 2m∕r − r² {(dθ/dt)² + sin²(θ[t]) (dφ/dt)²}].
> 
> To calculate the elapsed proper time Δτ = ∫_W dτ along a worldline
> segment W becomes a little difficult without making simplifying
> assumptions such as a constant polar angle (dθ/dt = 0) or an equatorial
> orbit (θ = π∕2).
> 
> In any case, you should substitute the orbital parameters in an ECI
> frame (in the case of a GPS satellite), and the components of the
> rotation velocity of a point on the terrestrial surface in the same
> frame, respectively.
> 
> The exact blueshift (according to GR) follows from that, as I derived in
> <mid:119a9s8$182fs$2@gwaiyur.mb-net.net>.

So is your very exact blue shift different from 4.4647e-10 ? :-D


-- 
Paul

https://paulba.no/

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#674414

Paul B. Andersen wrote:
> Den 13.10.2026 10:27, skrev Thomas 'PointedEars' Lahn:
>> Paul B. Andersen wrote:
>>> The gravitational blue shift of the SV signal is Δf/f =  5.2996e-10
>>> The kinetic red shift (due to motion) is         Δf/f = -0.8349e-10
>>> The total(gravitational + kinetic) blue shift is Δf/f =  4.4647e-10
>>
>> Note that this is just a crude, at best first-order, approximation.
> 
> It is a very precise approximation. The error is less than 1e-15.

We'll see.

>> To obtain the exact values according to GR, you cannot simply add
>> "gravitational" and kinetic "time dilation" or (here) frequency shifts;
>> you have to use the full (Schwarzschild) spacetime metric (at least).
> 
> See:
> https://paulba.no/pdf/Clock_rate.pdf
> Equation (18) can be written:
>   Δf/f₀ = δ_utc - GM/(c²r) - GM/(2c²r)

This does not look right.

> Now you can wonder why such a simple equation can give so precise result.
>> Note also that not all GPS satellites have the same orbital altitude or
>> orbital direction (and the orbits are only approximately circular), so
>> both the "gravitational blueshift" and the "kinetic redshift" varies
>> between satellites and between locations on the ground (they also vary
>> at least with latitude due to different rotation speeds).
> 
> Don't be ridiculous.
> The blue shift doesn't depend on the location on the ground.

Yes it does.

> The speed and orbital radius of all the satellites are equal

Patently false.

Just compare these two currently operational GPS satellites:

,-<https://en.wikipedia.org/wiki/USA-309>
|
| [...]
| Perigee altitude	20,181 km (12,540 mi)
| Apogee altitude	20,196 km (12,549 mi)
| Inclination	54.9°
| Period	718.0 minutes

,-<https://en.wikipedia.org/wiki/USA-319>
|
| [...]
| Perigee altitude	20,163 km (12,529 mi)
| Apogee altitude	20,216 km (12,562 mi)
| Inclination	55.3°
| Period	718.0 minutes

> so the blue shift of the signal from all the satellites is equal.

False again.

<https://en.wikipedia.org/wiki/Global_Positioning_System#/media/File:GPS24goldenSML.gif>

> We calculate the blue shift from the assumption that all
> satellites are in their nominal orbit.
> Six orbital planes 60 degrees from each other, four satellites
> in each plane, planes 55 degrees inclination to equatorial plane.

You should double-check your assumptions.
-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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#674440

Den 14.10.2026 14:20, skrev Thomas 'PointedEars' Lahn:
> Paul B. Andersen wrote:
>> Den 13.10.2026 10:27, skrev Thomas 'PointedEars' Lahn:
>>> Paul B. Andersen wrote:
>>>> The gravitational blue shift of the SV signal is Δf/f =  5.2996e-10
>>>> The kinetic red shift (due to motion) is         Δf/f = -0.8349e-10
>>>> The total(gravitational + kinetic) blue shift is Δf/f =  4.4647e-10
>>>
>>> Note that this is just a crude, at best first-order, approximation.
>>
>> It is a very precise approximation. The error is less than 1e-15.
> 
> We'll see.
> 
>>> To obtain the exact values according to GR, you cannot simply add
>>> "gravitational" and kinetic "time dilation" or (here) frequency shifts;
>>> you have to use the full (Schwarzschild) spacetime metric (at least).
>>
>> See:
>> https://paulba.no/pdf/Clock_rate.pdf
>> Equation (18) can be written:
>>    Δf/f₀ = δ_utc - GM/(c²r) - GM/(2c²r)
> 
> This does not look right.

But you know that the equation give the right values,
that's why you snipped the following.

  Gravitational blueshift Δf/f₀ = (δ_utc - GM/(c²r)) =  5.299580e-10
  Kinetic redshift        Δf/f₀ = - GM/(2c²r)        = -0.834852e-10
  Total(gravitational + kinetic) blue shift:         =  4.464728e-10


>>> Note also that not all GPS satellites have the same orbital altitude or
>>> orbital direction (and the orbits are only approximately circular), so
>>> both the "gravitational blueshift" and the "kinetic redshift" varies
>>> between satellites and between locations on the ground (they also vary
>>> at least with latitude due to different rotation speeds).
>>
>> Don't be ridiculous.
>> The blue shift doesn't depend on the location on the ground.
> 
> Yes it does.

In the GPS Interface Specification Document you will find:
https://www.gps.gov/sites/default/files/2025-07/IS-GPS-200N.pdf

Quote from 3.3.1.1 Frequency Plan page 16:

"The carrier frequencies for the L1 and L2 signals shall be
  coherently derived from a common frequency source within
  the SV. The nominal frequency of this source -- as it
  appears to an observer on the ground -- is 10.23 MHz.
  The SV carrier frequency and clock rates -- as they would
  appear to an observer located in the SV -- are offset to
  compensate for  relativistic effects. The clock rates are
  offset by Δf/f = -4.4647E-10, equivalent to a change in
  the P-code chipping rate of 10.23 MHz offset by a
  Δf = -4.5674E-3 Hz. This is equal to 10.2299999954326 MHz.
"
This means that the frequency 10.2299999954326 MHz emitted
from the SV is blue shifted to 10.23 MHz at the ground.

The blue shift is Δf/f = +4.4647E-10  for _all_ SVs in
_nominal orbit_ . To claim that this blue shift depend
on the position on the ground is nonsense.


>> The speed and orbital radius of all the satellites are equal
> 
> Patently false.
> 
> Just compare these two currently operational GPS satellites:
> 
> ,-<https://en.wikipedia.org/wiki/USA-309>
> |
> | [...]
> | Perigee altitude	20,181 km (12,540 mi)
> | Apogee altitude	20,196 km (12,549 mi)
> | Inclination	54.9°
> | Period	718.0 minutes
> 
> ,-<https://en.wikipedia.org/wiki/USA-319>
> |
> | [...]
> | Perigee altitude	20,163 km (12,529 mi)
> | Apogee altitude	20,216 km (12,562 mi)
> | Inclination	55.3°
> | Period	718.0 minutes
> 
>> so the blue shift of the signal from all the satellites is equal.
> 
> False again.

Of course you understand that the calculated (and specified) blue shift
Δf/f = 4.4647E-10 must be for SVs in _nominal_ (specified) orbit.

So why do you do this?

> 
> <https://en.wikipedia.org/wiki/Global_Positioning_System#/media/File:GPS24goldenSML.gif>

AHA! Now I understand what your giant misunderstanding is!

You think we are talking about the frequency received by
a receiver on the ground!
This frequency is generally Doppler shifted by orders of
magnitude more than Δf/f = 4.4647E-10.
This frequency is utterly irrelevant and never measured.

The only reason why the frequency standards in the SVs are
adjusted down by Δf/f = -4.4647E-10 is to keep the SV-time
synchronous with GPS-time (which has the same rate as UTC).

You told me yourself that the Schwarzschild metric must
be used, which is correct.
Do you think that the Schwarzschild metric has anything to
say about the Doppler shifted frequencies from the SVs?

Now when your misunderstanding is cleared up,
maybe you should look at my article again?
https://paulba.no/pdf/Clock_rate.pdf

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

Once you claimed that "stellar aberration" was nonsense.
It seemed like you had confused stellar aberration and
parallax.

Do you still think "stellar aberration" is nonsense?
https://paulba.no/pdf/Stellar_aberration.pdf

-- 
Paul

https://paulba.no/

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#674442

Paul B. Andersen wrote:
> Den 14.10.2026 14:20, skrev Thomas 'PointedEars' Lahn:
>> Paul B. Andersen wrote:
>>> Den 13.10.2026 10:27, skrev Thomas 'PointedEars' Lahn:
>>>> Note also that not all GPS satellites have the same orbital altitude or
>>>> orbital direction (and the orbits are only approximately circular), so
>>>> both the "gravitational blueshift" and the "kinetic redshift" varies
>>>> between satellites and between locations on the ground (they also vary
>>>> at least with latitude due to different rotation speeds).
>>>
>>> Don't be ridiculous.
>>> The blue shift doesn't depend on the location on the ground.
>>
>> Yes it does.
> 
> In the GPS Interface Specification Document you will find:
> https://www.gps.gov/sites/default/files/2025-07/IS-GPS-200N.pdf
> 
> Quote from 3.3.1.1 Frequency Plan page 16:
> 
> "The carrier frequencies for the L1 and L2 signals shall be
>   coherently derived from a common frequency source within
>   the SV. The nominal frequency of this source -- as it
>   appears to an observer on the ground -- is 10.23 MHz.
>   The SV carrier frequency and clock rates -- as they would
>   appear to an observer located in the SV -- are offset to
>   compensate for  relativistic effects. The clock rates are
>   offset by Δf/f = -4.4647E-10, equivalent to a change in
>   the P-code chipping rate of 10.23 MHz offset by a
>   Δf = -4.5674E-3 Hz. This is equal to 10.2299999954326 MHz.
> "
> This means that the frequency 10.2299999954326 MHz emitted
> from the SV is blue shifted to 10.23 MHz at the ground.
> 
> The blue shift is Δf/f = +4.4647E-10  for _all_ SVs in
> _nominal orbit_ .

A theoretical concept that does not matter in practice.  The orbits of
all GPS satellites are different to avoid collisions between them; they
are NOT circles (relative to the terrestrial center of gravitation), and
they _vary_.  Hence the updates of their ephemerides supported by ground
stations such as the astronomical observatory of my university.

> To claim that this blue shift depend on the position on the ground is
> nonsense.

    [_redshift_, _blueshift_; _one_ word, respectively]

No, it is not.  Let us consider for simplicity a hypothetical GPS
satellite that orbits counter-clockwise (in the direction of the
terrestrial rotation) in a circle in the terrestrial equatorial plane.
The proper time that elapses in its orbit is given exactly by

  Δτ = Δt √[1 − 2 G M∕(c² r) − v²∕c²] = Δt √[1 − 3 G M∕(c² r)],

where v is its orbital speed in an ECI frame, and r = R + h, where R is
the average terrestrial radius, and h is the orbital altitude.  (Δt is
the elapsed proper time at infinite radial distance, but that will prove
to be irrelevant.)

Now consider a point on the terrestrial surface that is fixed in the
ECEF frame.  The elapsed proper time for it is approximately (assuming
spherical symmetry)

  Δτ = Δt √[1 − 2 G M∕(c² R) − 4π² R² cos²(φ)∕(T² c²)],

where φ is the point's latitude, and T is Terra's average rotation
period.  So the ratio of the frequency of the signal of this satellite
as received at that point to the frequency of the emitted signal is

  f_surface/f_SAT =  √[1 − 3 G M∕(c² [R + h])]
                    /√[1 − 2 G M∕(c² R) − 4π² R² cos²(φ)∕(T² c²)].

It _definitely_ depends on the location on the ground (here only its
latitude; but one can see that it depends on its altitude and can depend
on its longitude as well), and the satellite (here only the latter's
orbital altitude; but one can see that the inclination of its orbit
matters, too).

>>> The speed and orbital radius of all the satellites are equal
>>
>> Patently false.
>>
>> Just compare these two currently operational GPS satellites:
>>
>> ,-<https://en.wikipedia.org/wiki/USA-309>
>> |
>> | [...]
>> | Perigee altitude	20,181 km (12,540 mi)
>> | Apogee altitude	20,196 km (12,549 mi)
>> | Inclination	54.9°
>> | Period	718.0 minutes
>>
>> ,-<https://en.wikipedia.org/wiki/USA-319>
>> |
>> | [...]
>> | Perigee altitude	20,163 km (12,529 mi)
>> | Apogee altitude	20,216 km (12,562 mi)
>> | Inclination	55.3°
>> | Period	718.0 minutes

Why do you not address this?  Are the orbital speeds and orbital radii
of these two GPS satellites equal (all the time)?

>>> so the blue shift of the signal from all the satellites is equal.
>>
>> False again.
> 
> Of course you understand that the calculated (and specified) blue shift
> Δf/f = 4.4647E-10 must be for SVs in _nominal_ (specified) orbit.

Again, a theoretical concept that does not matter in practice.

> So why do you do this?

You first.

>> <https://en.wikipedia.org/wiki/Global_Positioning_System#/media/File:GPS24goldenSML.gif>
> 
> AHA! Now I understand what your giant misunderstanding is!

:-D

> You think we are talking about the frequency received by
> a receiver on the ground!

Of course.  What else?  *facepalm*

> This frequency is generally Doppler shifted by orders of
> magnitude more than Δf/f = 4.4647E-10.

You don't say!

> This frequency is utterly irrelevant and never measured.

False.  It is actually important in scientific applications.

-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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#674507

Den 14.10.2026 23:08, skrev Thomas 'PointedEars' Lahn:
> Paul B. Andersen wrote:
>> Den 14.10.2026 14:20, skrev Thomas 'PointedEars' Lahn:
>>> Paul B. Andersen wrote:

>>>> The blue shift doesn't depend on the location on the ground.
>>>
>>> Yes it does.
>>
>> In the GPS Interface Specification Document you will find:
>> https://www.gps.gov/sites/default/files/2025-07/IS-GPS-200N.pdf
>>
>> Quote from 3.3.1.1 Frequency Plan page 16:
>>
>> "The carrier frequencies for the L1 and L2 signals shall be
>>    coherently derived from a common frequency source within
>>    the SV. The nominal frequency of this source -- as it
>>    appears to an observer on the ground -- is 10.23 MHz.
>>    The SV carrier frequency and clock rates -- as they would
>>    appear to an observer located in the SV -- are offset to
>>    compensate for  relativistic effects. The clock rates are
>>    offset by Δf/f = -4.4647E-10, equivalent to a change in
>>    the P-code chipping rate of 10.23 MHz offset by a
>>    Δf = -4.5674E-3 Hz. This is equal to 10.2299999954326 MHz.
>> "
>> This means that the frequency 10.2299999954326 MHz emitted
>> from the SV is blue shifted to 10.23 MHz at the ground.

Remember you responded to my claim:
The gravitational blue shift of the SV signal is Δf/f =  5.2996e-10
The kinetic red shift (due to motion) is         Δf/f = -0.8349e-10
The total(gravitational + kinetic) blue shift is Δf/f =  4.4647e-10

The topic of this thread is still if my claim is correct.
My article:
https://paulba.no/pdf/Clock_rate.pdf
is all about calculating the blue shift for the GNSS
systems GPS, Galileo and GLONASS, and a geostationary SV.

>>
>> The blue shift is Δf/f = +4.4647E-10  for _all_ SVs in
>> _nominal orbit_ .

You don't seem to have understood this:
1: The blue shift is Δf/f = +4.4647E-10 for _all_ SVs
    in nominal orbit.
2: According to the GPS Interface Specification Document:
    The nominal orbit for all the SVs is a circular orbit
    with period half a sidereal day, which means that
    the nominal orbital radius is r = 26561763 m.

> 
> A theoretical concept that does not matter in practice. 

It is a concept of fundamental importance!
The SV-clock must be adjusted down by the factor (1 - 4.4647e-10)
to stay in sync with GPS-system time (which has the same rate as UTC).

Let's see why:

The clock in the SV is called "SV clock time" t_SV.
================================================================
This clock is normally not corrected while the SV is in service.
================================================================

Since no clock is infinitely precise, t_SV may be several μs
off sync. The GPS-system time is called t.
So to get the correct t, we must add a correction Δt_SV.

The monitor stations are reading the clocks in all the SVs, and
are measuring their offset from GPS-time, their rate error, and
the change in the rate error. These data are uploaded to the SVs
as a correction polynomial. This polynomial is downloaded to
the receiver together with t_SV, and the correction is made in
the receiver.

See: https://paulba.no/div/GPS_clock_correction.pdf
 From the Interface Control Document:
https://www.gps.gov/sites/default/files/2025-07/IS-GPS-200N.pdf

The SV will send the t_SV and the correction polynomial every
12.5 minutes. That means that the receiver will get the corrected
time t every 12.5 minutes.

The a_f0 parameter is the clock offset, that is the error of
the SV-clock t_SV.
According to Table 20-I in the Interface Control Document is this
parameter stored in a 22 bits register where the LSB = 2^{-31}s.
The format is 2-complement, so the largest value of this parameter
is ± 2^{21}*2^{-31}s = ± 0.000976s ≈ ± 1ms.
That means that if t_SV is wrong by more than 1 ms, a_f0 will
overflow and it will be impossible to sync the corrected time t.

If the rate of the clock was not corrected by (1 - 4.4647e-10)
then the error of the SV-clock would be > 1ms after 26 days.
The fact is that the SV-clock is running for years without
correction.

So the correction Δf/f = -4.4647E-10 is indeed of fundamental
importance and not "A theoretical concept that does not matter
in practice."


> The orbits of
> all GPS satellites are different to avoid collisions between them; they
> are NOT circles (relative to the terrestrial center of gravitation), and
> they _vary_.  Hence the updates of their ephemerides supported by ground
> stations such as the astronomical observatory of my university.

The nominal orbits of all the SVs are circular with period
half a sidereal day. There are 6 orbital planes 60⁰ from
each other. All the orbital planes have an inclination 55⁰ from
the equatorial plane. There are 4 SVs in each orbital plane.

The main point is that all the nominal orbits are equal,
all circular, same period, same orbital radius, same inclination
to the equatorial plane.

Of course the real orbits will change with time, and as you say,
corrections will be uploaded to the SVs which in turn will download
the corrections to the receiver so the receiver will know the exact
orbit of every SV. However, the orbital period and the semi-major axis
tend to be quite stable, it is the eccentricity that will change.
The blue shift will not change much.


If the eccentricity is different from 0, then the speed will
change during the orbit. Faster at perigee, slower at apogee.
That means that the correct GR correction is a little less than
Δf/f = -4.4647E-10 at perigee, and a little greater than
Δf/f = -4.4647E-10 at apogee.
There is one parameter in the correction polynomial that corrects
for this phenomenon, Δtᵣ .

See: https://paulba.no/div/GPS_clock_correction.pdf

Note that Δtᵣ is symmetrical, opposite signs at perigee and apogee.
Which means that the average correction is still Δf/f = -4.4647E-10
even if the orbit is eccentric.


>> To claim that this blue shift depend on the position on the ground is
>> nonsense.

I will explain why:
For clocks in high orbits like clocks in GNSS satellites, the
quadrupole  potential of Earth is so small that it can be ignored.
That means that the orbit will be circular with Earth at the centre.
The blue shift is from the SV and down to the geoid, along a radius
from Earth's centre to the SV.
Since the gravitational potential is constant on the geoid, the 
blueshift will be the same irrespective of the SV's latitude and
longitude.
> 
>  
> 
> No, it is not.  Let us consider for simplicity a hypothetical GPS
> satellite that orbits counter-clockwise (in the direction of the
> terrestrial rotation) in a circle in the terrestrial equatorial plane.
> The proper time that elapses in its orbit is given exactly by
> 
>    Δτ = Δt √[1 − 2 G M∕(c² r) − v²∕c²] = Δt √[1 − 3 G M∕(c² r)],
> 
> where v is its orbital speed in an ECI frame, and r = R + h, where R is
> the average terrestrial radius, and h is the orbital altitude.  (Δt is
> the elapsed proper time at infinite radial distance, but that will prove
> to be irrelevant.)
> 
> Now consider a point on the terrestrial surface that is fixed in the
> ECEF frame.  The elapsed proper time for it is approximately (assuming
> spherical symmetry)
> 
>    Δτ = Δt √[1 − 2 G M∕(c² R) − 4π² R² cos²(φ)∕(T² c²)],

And your point is that this varies with the position on Earth?

You are wrong. Δτ/Δt = (1 - 6.969284e-10)
Same everywhere on the geoid.

https://paulba.no/pdf/Clock_rate.pdf
See 2.2 Rate of UTC compared to Schwarzschild coordinate time
page 4.

> 
> where φ is the point's latitude, and T is Terra's average rotation
> period.  So the ratio of the frequency of the signal of this satellite
> as received at that point to the frequency of the emitted signal is
> 
>    f_surface/f_SAT =  √[1 − 3 G M∕(c² [R + h])]
>                      /√[1 − 2 G M∕(c² R) − 4π² R² cos²(φ)∕(T² c²)].

This would only make sense if the the point on Earth and the SV
are on the same radial from Earth's centre to the SV.

But it is still wrong.

The correct result is:
  f_surface/f_SAT =  √[1 − 3 G M∕(c² [R + h])]/(1 - 6.969284e-10)
                  = 1 + 4.4647e-10
(If [R + h] = 26561763 m)



> It _definitely_ depends on the location on the ground (here only its
> latitude; but one can see that it depends on its altitude and can depend
> on its longitude as well), and the satellite (here only the latter's
> orbital altitude; but one can see that the inclination of its orbit
> matters, too).

But now you know better. Or don't you?

> 
>>>> The speed and orbital radius of all the satellites are equal

This statement is out of context.
It is obviously the nominal orbital radius that are equal.

>>>
>>> Patently false.
>>>
>>> Just compare these two currently operational GPS satellites:
>>>
>>> ,-<https://en.wikipedia.org/wiki/USA-309>
>>> |
>>> | [...]
>>> | Perigee altitude	20,181 km (12,540 mi)
>>> | Apogee altitude	20,196 km (12,549 mi)
>>> | Inclination	54.9°
>>> | Period	718.0 minutes
>>>
>>> ,-<https://en.wikipedia.org/wiki/USA-319>
>>> |
>>> | [...]
>>> | Perigee altitude	20,163 km (12,529 mi)
>>> | Apogee altitude	20,216 km (12,562 mi)
>>> | Inclination	55.3°
>>> | Period	718.0 minutes
> 
> Why do you not address this?  Are the orbital speeds and orbital radii
> of these two GPS satellites equal (all the time)?

Because the topic is what GR predicts the blue shift of clocks
in GPS-orbit will be.

It would be pretty idiotic to say that GR cannot predict what
the blueshift is because the actual orbits may be different from
the defined nominal GPS-orbit.

>>
>> Of course you understand that the calculated (and specified) blue shift
>> Δf/f = 4.4647E-10 must be for SVs in _nominal_ (specified) orbit.
> 
> Again, a theoretical concept that does not matter in practice.

But now you know better. Or don't you?>

>> So why do you do this?
> 
> You first.

What was your point with naming two actual orbits?
Did you think this falsifies the blue shift predicted by GR ?

> 
>>> <https://en.wikipedia.org/wiki/Global_Positioning_System#/media/File:GPS24goldenSML.gif>
>>
>> AHA! Now I understand what your giant misunderstanding is!
> 
> :-D
> 
>> You think we are talking about the frequency received by
>> a receiver on the ground!
> 
> Of course.  What else?  *facepalm*
> 
>> This frequency is generally Doppler shifted by orders of
>> magnitude more than Δf/f = 4.4647E-10.
> 
> You don't say!
> 
>> This frequency is utterly irrelevant and never measured.
> 
> False.  It is actually important in scientific applications.

Consider this:
All the SVs are transmitting at the same frequencies.
Each SV is transmitting three modulated carriers, each
with a bandwidth in the order of 20Mz.
The receiver will receive the signal from up to 8 GPS SVs,
all Doppler shifted to a different degree.
It will also receive signals from several Galileo and
GLONASS SVs, all Doppler shifted to a different degree.
In addition it will receive noise.
The bandwidth of the receiver is 10 - 20MHz.

I can assure you that the received signal
will look like 20Mhz bandwidth noise, and it will
be impossible to pick out one frequency from this mess.

So how can the receiver sort out the signal from
8 different SVs?

I will give you a hint:
Spread spectrum techniques (DSSS), matched filters, cross correlation.

But I don't know the details well enough to explain it in detail.

-- 
Paul

https://paulba.no/

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#674508

On Thu, 15 Oct 2026 23:10:51 +0200, "Paul B. Andersen"
<paul.b.andersen@paulba.no> wrote:

>My article:
>https://paulba.no/pdf/Clock_rate.pdf



This paper is a half-digested regurgitation of standard GNSS
relativity that collapses under its own sloppy equations, circular
definitions, and amateur-hour presentation.



    The metric and rate equations are an unreadable train wreck.
    Look at equations (1)–(5), (7), (13)–(18). They arrive as
fragmented garbage: missing operators, broken fractions, undefined
symbols jammed together, and statements like “dt 2GM v² 1 / dt c²r c²”
that no competent reader can parse without reconstructing the entire
derivation from scratch. A paper whose central results cannot be read
without external knowledge is not a paper; it is noise.
    The foundational claim that “SI-clocks per definition always run
at the rate 1 second per second” is pure tautological sludge.
    Section 1.1 asserts this as if it were profound. It is
definitional emptiness. Proper time is what a clock measures;
declaring that an SI-clock therefore ticks at 1 s/s adds zero
information and papers over the entire problem of comparing rates
between different world-lines.
    The derivation of orbital rates relative to UTC is a chain of
uncontrolled approximations sold as precision.
    Equation (5) is declared “a very good approximation” with error
<10?²5; equation (17) claims error <10?¹7. No error budget, no
expansion order, no residual terms from higher multipoles, no
frame-dragging, no solar potential, no tidal contributions. You simply
assert the error and move on. That is not calculation; that is wishful
truncation.
    The GNSS numerical results are presented as original while resting
on incomplete or outdated source data.
    GPS radius is taken from a period of half a sidereal day; GLONASS
oscillates between a 2020 performance standard and a 2008 ICD that the
author himself labels outdated, then notes that Mudrak et al. used the
old number. The paper ends by declaring one geostationary value “the
correct value” with no independent verification. This is not analysis;
it is selective copying.
    Coordinate-time definitions are internally inconsistent and poorly
distinguished.
    Schwarzschild t is defined so that an SI-clock at infinity stays
in sync; UTC is defined so that a stationary SI-clock on the geoid
stays in sync. Then the text repeatedly states that clocks showing
either coordinate are “synchronous in the nonrotating Schwarzschild
coordinate system” while simultaneously acknowledging they are not
synchronous in the rotating Earth-fixed frame. The distinction between
coordinate simultaneity and proper-rate comparison is never cleanly
maintained, leaving the central comparison (dt/dt_utc) floating on
ambiguous foundations.


You assume the weak-field, slow-motion Schwarzschild metric is
sufficient once the monopole and J2 terms are inserted, with no
residual from higher harmonics, no post-Newtonian corrections beyond
the first order you kept, and no need to transform between the
Earth-centered inertial frame and the actual satellite ephemerides
used by the systems. You assume that declaring an SI-clock independent
of acceleration and temperature magically removes all environmental
sensitivity at the 10?¹7 level you claim. You assume that citing
Wikipedia for TAI and a handful of interface-control documents
constitutes a literature foundation.


Any competent reviewer or GNSS engineer who opens this PDF will stop
at the first mangled equation block and discard the rest. The people
who actually fly the clocks (GPS Wing, ESA, Roscosmos time
metrologists) already possess cleaner derivations (Ashby’s Living
Review being the obvious one). They have zero incentive to adopt a
document whose equations cannot be typeset legibly and whose numerical
claims require the reader to re-derive everything to trust them.
Regulators and standards bodies will treat this as non-peer-reviewed
noise.


At the claimed 10?¹7 relative accuracy the paper pretends to reach,
the ignored effects (higher multipoles, Shapiro delay variations,
satellite eccentricity terms, antenna phase-center motion, thermal and
magnetic sensitivity of the actual atomic clocks) already exceed that
floor on operational GNSS satellites. The circular-orbit idealization
breaks the moment real eccentricity appears; the geoid-rate reduction
ignores the full equipotential surface definition used by the IERS.
The numbers therefore cannot be trusted at the precision the text
advertises, and the paper supplies no path to the next significant
digit.


The entire equation presentation must be discarded and rewritten in
unambiguous, properly typeset form with every intermediate step shown.
The circular “SI-clocks tick at 1 s/s” rhetoric must be deleted. The
error analysis must be replaced by a complete post-Newtonian expansion
with quantified residuals. The source handling for GLONASS and the
geostationary claim must be replaced by primary, current ephemeris
parameters and an independent calculation. The coordinate-time section
must be rewritten so that the distinction between coordinate time and
proper time is surgically clear rather than repeatedly blurred.

 
 
This is the intellectual equivalent of serving a half-cooked
Wellington with the raw center still cold and claiming it is a
precision metrology instrument.


The Swarmaker

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#674629

The Starmaker wrote:
> 
> On Thu, 15 Oct 2026 23:10:51 +0200, "Paul B. Andersen"
> <paul.b.andersen@paulba.no> wrote:
> 
> >My article:
> >https://paulba.no/pdf/Clock_rate.pdf
> 
> This paper is a half-digested regurgitation of standard GNSS
> relativity that collapses under its own sloppy equations, circular
> definitions, and amateur-hour presentation.
> 
>     The metric and rate equations are an unreadable train wreck.
>     Look at equations (1)–(5), (7), (13)–(18). They arrive as
> fragmented garbage: missing operators, broken fractions, undefined
> symbols jammed together, and statements like “dt 2GM v² 1 / dt c²r c²”
> that no competent reader can parse without reconstructing the entire
> derivation from scratch. A paper whose central results cannot be read
> without external knowledge is not a paper; it is noise.
>     The foundational claim that “SI-clocks per definition always run
> at the rate 1 second per second” is pure tautological sludge.
>     Section 1.1 asserts this as if it were profound. It is
> definitional emptiness. Proper time is what a clock measures;
> declaring that an SI-clock therefore ticks at 1 s/s adds zero
> information and papers over the entire problem of comparing rates
> between different world-lines.
>     The derivation of orbital rates relative to UTC is a chain of
> uncontrolled approximations sold as precision.
>     Equation (5) is declared “a very good approximation” with error
> <10?²5; equation (17) claims error <10?¹7. No error budget, no
> expansion order, no residual terms from higher multipoles, no
> frame-dragging, no solar potential, no tidal contributions. You simply
> assert the error and move on. That is not calculation; that is wishful
> truncation.
>     The GNSS numerical results are presented as original while resting
> on incomplete or outdated source data.
>     GPS radius is taken from a period of half a sidereal day; GLONASS
> oscillates between a 2020 performance standard and a 2008 ICD that the
> author himself labels outdated, then notes that Mudrak et al. used the
> old number. The paper ends by declaring one geostationary value “the
> correct value” with no independent verification. This is not analysis;
> it is selective copying.
>     Coordinate-time definitions are internally inconsistent and poorly
> distinguished.
>     Schwarzschild t is defined so that an SI-clock at infinity stays
> in sync; UTC is defined so that a stationary SI-clock on the geoid
> stays in sync. Then the text repeatedly states that clocks showing
> either coordinate are “synchronous in the nonrotating Schwarzschild
> coordinate system” while simultaneously acknowledging they are not
> synchronous in the rotating Earth-fixed frame. The distinction between
> coordinate simultaneity and proper-rate comparison is never cleanly
> maintained, leaving the central comparison (dt/dt_utc) floating on
> ambiguous foundations.
> 
> You assume the weak-field, slow-motion Schwarzschild metric is
> sufficient once the monopole and J2 terms are inserted, with no
> residual from higher harmonics, no post-Newtonian corrections beyond
> the first order you kept, and no need to transform between the
> Earth-centered inertial frame and the actual satellite ephemerides
> used by the systems. You assume that declaring an SI-clock independent
> of acceleration and temperature magically removes all environmental
> sensitivity at the 10?¹7 level you claim. You assume that citing
> Wikipedia for TAI and a handful of interface-control documents
> constitutes a literature foundation.
> 
> Any competent reviewer or GNSS engineer who opens this PDF will stop
> at the first mangled equation block and discard the rest. The people
> who actually fly the clocks (GPS Wing, ESA, Roscosmos time
> metrologists) already possess cleaner derivations (Ashby’s Living
> Review being the obvious one). They have zero incentive to adopt a
> document whose equations cannot be typeset legibly and whose numerical
> claims require the reader to re-derive everything to trust them.
> Regulators and standards bodies will treat this as non-peer-reviewed
> noise.
> 
> At the claimed 10?¹7 relative accuracy the paper pretends to reach,
> the ignored effects (higher multipoles, Shapiro delay variations,
> satellite eccentricity terms, antenna phase-center motion, thermal and
> magnetic sensitivity of the actual atomic clocks) already exceed that
> floor on operational GNSS satellites. The circular-orbit idealization
> breaks the moment real eccentricity appears; the geoid-rate reduction
> ignores the full equipotential surface definition used by the IERS.
> The numbers therefore cannot be trusted at the precision the text
> advertises, and the paper supplies no path to the next significant
> digit.
> 
> The entire equation presentation must be discarded and rewritten in
> unambiguous, properly typeset form with every intermediate step shown.
> The circular “SI-clocks tick at 1 s/s” rhetoric must be deleted. The
> error analysis must be replaced by a complete post-Newtonian expansion
> with quantified residuals. The source handling for GLONASS and the
> geostationary claim must be replaced by primary, current ephemeris
> parameters and an independent calculation. The coordinate-time section
> must be rewritten so that the distinction between coordinate time and
> proper time is surgically clear rather than repeatedly blurred.
> 
> 
> 
> This is the intellectual equivalent of serving a half-cooked
> Wellington with the raw center still cold and claiming it is a
> precision metrology instrument.
> 
> The Swarmaker

I heard "Paul B. Andersen" commited suicide after reading his reviews
from  the swarm!


Let me have a look at Einstein's theory of everything is everything. I
think i can fix it up..

it might be called 'The Gravity Unified Theory' now...

subtitled: 'FUCKING NOTHING TRAVELS FASTER THAN THE SPEED OF
LIGHT...while I'm alive.

-- 
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable, 
and challenge the unchallengeable.

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#674647

On 10/18/2026 04:54 PM, The Starmaker wrote:
> The Starmaker wrote:
>>
>> On Thu, 15 Oct 2026 23:10:51 +0200, "Paul B. Andersen"
>> <paul.b.andersen@paulba.no> wrote:
>>
>>> My article:
>>> https://paulba.no/pdf/Clock_rate.pdf
>>
>> This paper is a half-digested regurgitation of standard GNSS
>> relativity that collapses under its own sloppy equations, circular
>> definitions, and amateur-hour presentation.
>>
>>      The metric and rate equations are an unreadable train wreck.
>>      Look at equations (1)–(5), (7), (13)–(18). They arrive as
>> fragmented garbage: missing operators, broken fractions, undefined
>> symbols jammed together, and statements like “dt 2GM v² 1 / dt c²r c²”
>> that no competent reader can parse without reconstructing the entire
>> derivation from scratch. A paper whose central results cannot be read
>> without external knowledge is not a paper; it is noise.
>>      The foundational claim that “SI-clocks per definition always run
>> at the rate 1 second per second” is pure tautological sludge.
>>      Section 1.1 asserts this as if it were profound. It is
>> definitional emptiness. Proper time is what a clock measures;
>> declaring that an SI-clock therefore ticks at 1 s/s adds zero
>> information and papers over the entire problem of comparing rates
>> between different world-lines.
>>      The derivation of orbital rates relative to UTC is a chain of
>> uncontrolled approximations sold as precision.
>>      Equation (5) is declared “a very good approximation” with error
>> <10?²5; equation (17) claims error <10?¹7. No error budget, no
>> expansion order, no residual terms from higher multipoles, no
>> frame-dragging, no solar potential, no tidal contributions. You simply
>> assert the error and move on. That is not calculation; that is wishful
>> truncation.
>>      The GNSS numerical results are presented as original while resting
>> on incomplete or outdated source data.
>>      GPS radius is taken from a period of half a sidereal day; GLONASS
>> oscillates between a 2020 performance standard and a 2008 ICD that the
>> author himself labels outdated, then notes that Mudrak et al. used the
>> old number. The paper ends by declaring one geostationary value “the
>> correct value” with no independent verification. This is not analysis;
>> it is selective copying.
>>      Coordinate-time definitions are internally inconsistent and poorly
>> distinguished.
>>      Schwarzschild t is defined so that an SI-clock at infinity stays
>> in sync; UTC is defined so that a stationary SI-clock on the geoid
>> stays in sync. Then the text repeatedly states that clocks showing
>> either coordinate are “synchronous in the nonrotating Schwarzschild
>> coordinate system” while simultaneously acknowledging they are not
>> synchronous in the rotating Earth-fixed frame. The distinction between
>> coordinate simultaneity and proper-rate comparison is never cleanly
>> maintained, leaving the central comparison (dt/dt_utc) floating on
>> ambiguous foundations.
>>
>> You assume the weak-field, slow-motion Schwarzschild metric is
>> sufficient once the monopole and J2 terms are inserted, with no
>> residual from higher harmonics, no post-Newtonian corrections beyond
>> the first order you kept, and no need to transform between the
>> Earth-centered inertial frame and the actual satellite ephemerides
>> used by the systems. You assume that declaring an SI-clock independent
>> of acceleration and temperature magically removes all environmental
>> sensitivity at the 10?¹7 level you claim. You assume that citing
>> Wikipedia for TAI and a handful of interface-control documents
>> constitutes a literature foundation.
>>
>> Any competent reviewer or GNSS engineer who opens this PDF will stop
>> at the first mangled equation block and discard the rest. The people
>> who actually fly the clocks (GPS Wing, ESA, Roscosmos time
>> metrologists) already possess cleaner derivations (Ashby’s Living
>> Review being the obvious one). They have zero incentive to adopt a
>> document whose equations cannot be typeset legibly and whose numerical
>> claims require the reader to re-derive everything to trust them.
>> Regulators and standards bodies will treat this as non-peer-reviewed
>> noise.
>>
>> At the claimed 10?¹7 relative accuracy the paper pretends to reach,
>> the ignored effects (higher multipoles, Shapiro delay variations,
>> satellite eccentricity terms, antenna phase-center motion, thermal and
>> magnetic sensitivity of the actual atomic clocks) already exceed that
>> floor on operational GNSS satellites. The circular-orbit idealization
>> breaks the moment real eccentricity appears; the geoid-rate reduction
>> ignores the full equipotential surface definition used by the IERS.
>> The numbers therefore cannot be trusted at the precision the text
>> advertises, and the paper supplies no path to the next significant
>> digit.
>>
>> The entire equation presentation must be discarded and rewritten in
>> unambiguous, properly typeset form with every intermediate step shown.
>> The circular “SI-clocks tick at 1 s/s” rhetoric must be deleted. The
>> error analysis must be replaced by a complete post-Newtonian expansion
>> with quantified residuals. The source handling for GLONASS and the
>> geostationary claim must be replaced by primary, current ephemeris
>> parameters and an independent calculation. The coordinate-time section
>> must be rewritten so that the distinction between coordinate time and
>> proper time is surgically clear rather than repeatedly blurred.
>>
>>
>>
>> This is the intellectual equivalent of serving a half-cooked
>> Wellington with the raw center still cold and claiming it is a
>> precision metrology instrument.
>>
>> The Swarmaker
>
> I heard "Paul B. Andersen" commited suicide after reading his reviews
> from  the swarm!
>
>
> Let me have a look at Einstein's theory of everything is everything. I
> think i can fix it up..
>
> it might be called 'The Gravity Unified Theory' now...
>
> subtitled: 'FUCKING NOTHING TRAVELS FASTER THAN THE SPEED OF
> LIGHT...while I'm alive.
>

You'll be spinning in your grave a long time.

[toc] | [prev] | [next] | [standalone]

#674674

Ross Finlayson wrote:
> 
> On 10/18/2026 04:54 PM, The Starmaker wrote:
> > The Starmaker wrote:
> >>
> >> On Thu, 15 Oct 2026 23:10:51 +0200, "Paul B. Andersen"
> >> <paul.b.andersen@paulba.no> wrote:
> >>
> >>> My article:
> >>> https://paulba.no/pdf/Clock_rate.pdf
> >>
> >> This paper is a half-digested regurgitation of standard GNSS
> >> relativity that collapses under its own sloppy equations, circular
> >> definitions, and amateur-hour presentation.
> >>
> >>      The metric and rate equations are an unreadable train wreck.
> >>      Look at equations (1)–(5), (7), (13)–(18). They arrive as
> >> fragmented garbage: missing operators, broken fractions, undefined
> >> symbols jammed together, and statements like “dt 2GM v² 1 / dt c²r c²”
> >> that no competent reader can parse without reconstructing the entire
> >> derivation from scratch. A paper whose central results cannot be read
> >> without external knowledge is not a paper; it is noise.
> >>      The foundational claim that “SI-clocks per definition always run
> >> at the rate 1 second per second” is pure tautological sludge.
> >>      Section 1.1 asserts this as if it were profound. It is
> >> definitional emptiness. Proper time is what a clock measures;
> >> declaring that an SI-clock therefore ticks at 1 s/s adds zero
> >> information and papers over the entire problem of comparing rates
> >> between different world-lines.
> >>      The derivation of orbital rates relative to UTC is a chain of
> >> uncontrolled approximations sold as precision.
> >>      Equation (5) is declared “a very good approximation” with error
> >> <10?²5; equation (17) claims error <10?¹7. No error budget, no
> >> expansion order, no residual terms from higher multipoles, no
> >> frame-dragging, no solar potential, no tidal contributions. You simply
> >> assert the error and move on. That is not calculation; that is wishful
> >> truncation.
> >>      The GNSS numerical results are presented as original while resting
> >> on incomplete or outdated source data.
> >>      GPS radius is taken from a period of half a sidereal day; GLONASS
> >> oscillates between a 2020 performance standard and a 2008 ICD that the
> >> author himself labels outdated, then notes that Mudrak et al. used the
> >> old number. The paper ends by declaring one geostationary value “the
> >> correct value” with no independent verification. This is not analysis;
> >> it is selective copying.
> >>      Coordinate-time definitions are internally inconsistent and poorly
> >> distinguished.
> >>      Schwarzschild t is defined so that an SI-clock at infinity stays
> >> in sync; UTC is defined so that a stationary SI-clock on the geoid
> >> stays in sync. Then the text repeatedly states that clocks showing
> >> either coordinate are “synchronous in the nonrotating Schwarzschild
> >> coordinate system” while simultaneously acknowledging they are not
> >> synchronous in the rotating Earth-fixed frame. The distinction between
> >> coordinate simultaneity and proper-rate comparison is never cleanly
> >> maintained, leaving the central comparison (dt/dt_utc) floating on
> >> ambiguous foundations.
> >>
> >> You assume the weak-field, slow-motion Schwarzschild metric is
> >> sufficient once the monopole and J2 terms are inserted, with no
> >> residual from higher harmonics, no post-Newtonian corrections beyond
> >> the first order you kept, and no need to transform between the
> >> Earth-centered inertial frame and the actual satellite ephemerides
> >> used by the systems. You assume that declaring an SI-clock independent
> >> of acceleration and temperature magically removes all environmental
> >> sensitivity at the 10?¹7 level you claim. You assume that citing
> >> Wikipedia for TAI and a handful of interface-control documents
> >> constitutes a literature foundation.
> >>
> >> Any competent reviewer or GNSS engineer who opens this PDF will stop
> >> at the first mangled equation block and discard the rest. The people
> >> who actually fly the clocks (GPS Wing, ESA, Roscosmos time
> >> metrologists) already possess cleaner derivations (Ashby’s Living
> >> Review being the obvious one). They have zero incentive to adopt a
> >> document whose equations cannot be typeset legibly and whose numerical
> >> claims require the reader to re-derive everything to trust them.
> >> Regulators and standards bodies will treat this as non-peer-reviewed
> >> noise.
> >>
> >> At the claimed 10?¹7 relative accuracy the paper pretends to reach,
> >> the ignored effects (higher multipoles, Shapiro delay variations,
> >> satellite eccentricity terms, antenna phase-center motion, thermal and
> >> magnetic sensitivity of the actual atomic clocks) already exceed that
> >> floor on operational GNSS satellites. The circular-orbit idealization
> >> breaks the moment real eccentricity appears; the geoid-rate reduction
> >> ignores the full equipotential surface definition used by the IERS.
> >> The numbers therefore cannot be trusted at the precision the text
> >> advertises, and the paper supplies no path to the next significant
> >> digit.
> >>
> >> The entire equation presentation must be discarded and rewritten in
> >> unambiguous, properly typeset form with every intermediate step shown.
> >> The circular “SI-clocks tick at 1 s/s” rhetoric must be deleted. The
> >> error analysis must be replaced by a complete post-Newtonian expansion
> >> with quantified residuals. The source handling for GLONASS and the
> >> geostationary claim must be replaced by primary, current ephemeris
> >> parameters and an independent calculation. The coordinate-time section
> >> must be rewritten so that the distinction between coordinate time and
> >> proper time is surgically clear rather than repeatedly blurred.
> >>
> >>
> >>
> >> This is the intellectual equivalent of serving a half-cooked
> >> Wellington with the raw center still cold and claiming it is a
> >> precision metrology instrument.
> >>
> >> The Swarmaker
> >
> > I heard "Paul B. Andersen" commited suicide after reading his reviews
> > from  the swarm!
> >
> >
> > Let me have a look at Einstein's theory of everything is everything. I
> > think i can fix it up..
> >
> > it might be called 'The Gravity Unified Theory' now...
> >
> > subtitled: 'FUCKING NOTHING TRAVELS FASTER THAN THE SPEED OF
> > LIGHT...while I'm alive.
> >
> 
> You'll be spinning in your grave a long time.


Truth is, he is busy redoing his paper after I pointed out his errors.

There are Math guys who spend years in their attic trying to solve one
equation.

Ai can solve it in a second.


What does that mean? The end of Math guys?...

It means humans need to change their goals..


how about making babies?


You got more time. The pretty wife is alone at home, while her husband
is out to work.

Make babies with her!

May I borrow a cup of sugar?


wham bang thank you mam!


Just like the cavemen times.


Yous will become Ai's pets.

Don't worry, Ai will feed you...


Ai will even take you out for a walk.


You get to see all the other Ai pets.

-- 
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable, 
and challenge the unchallengeable.

[toc] | [prev] | [next] | [standalone]

#674708

The Starmaker wrote:
> 
> Ross Finlayson wrote:
> >
> > On 10/18/2026 04:54 PM, The Starmaker wrote:
> > > The Starmaker wrote:
> > >>
> > >> On Thu, 15 Oct 2026 23:10:51 +0200, "Paul B. Andersen"
> > >> <paul.b.andersen@paulba.no> wrote:
> > >>
> > >>> My article:
> > >>> https://paulba.no/pdf/Clock_rate.pdf
> > >>
> > >> This paper is a half-digested regurgitation of standard GNSS
> > >> relativity that collapses under its own sloppy equations, circular
> > >> definitions, and amateur-hour presentation.
> > >>
> > >>      The metric and rate equations are an unreadable train wreck.
> > >>      Look at equations (1)–(5), (7), (13)–(18). They arrive as
> > >> fragmented garbage: missing operators, broken fractions, undefined
> > >> symbols jammed together, and statements like “dt 2GM v² 1 / dt c²r c²”
> > >> that no competent reader can parse without reconstructing the entire
> > >> derivation from scratch. A paper whose central results cannot be read
> > >> without external knowledge is not a paper; it is noise.
> > >>      The foundational claim that “SI-clocks per definition always run
> > >> at the rate 1 second per second” is pure tautological sludge.
> > >>      Section 1.1 asserts this as if it were profound. It is
> > >> definitional emptiness. Proper time is what a clock measures;
> > >> declaring that an SI-clock therefore ticks at 1 s/s adds zero
> > >> information and papers over the entire problem of comparing rates
> > >> between different world-lines.
> > >>      The derivation of orbital rates relative to UTC is a chain of
> > >> uncontrolled approximations sold as precision.
> > >>      Equation (5) is declared “a very good approximation” with error
> > >> <10?²5; equation (17) claims error <10?¹7. No error budget, no
> > >> expansion order, no residual terms from higher multipoles, no
> > >> frame-dragging, no solar potential, no tidal contributions. You simply
> > >> assert the error and move on. That is not calculation; that is wishful
> > >> truncation.
> > >>      The GNSS numerical results are presented as original while resting
> > >> on incomplete or outdated source data.
> > >>      GPS radius is taken from a period of half a sidereal day; GLONASS
> > >> oscillates between a 2020 performance standard and a 2008 ICD that the
> > >> author himself labels outdated, then notes that Mudrak et al. used the
> > >> old number. The paper ends by declaring one geostationary value “the
> > >> correct value” with no independent verification. This is not analysis;
> > >> it is selective copying.
> > >>      Coordinate-time definitions are internally inconsistent and poorly
> > >> distinguished.
> > >>      Schwarzschild t is defined so that an SI-clock at infinity stays
> > >> in sync; UTC is defined so that a stationary SI-clock on the geoid
> > >> stays in sync. Then the text repeatedly states that clocks showing
> > >> either coordinate are “synchronous in the nonrotating Schwarzschild
> > >> coordinate system” while simultaneously acknowledging they are not
> > >> synchronous in the rotating Earth-fixed frame. The distinction between
> > >> coordinate simultaneity and proper-rate comparison is never cleanly
> > >> maintained, leaving the central comparison (dt/dt_utc) floating on
> > >> ambiguous foundations.
> > >>
> > >> You assume the weak-field, slow-motion Schwarzschild metric is
> > >> sufficient once the monopole and J2 terms are inserted, with no
> > >> residual from higher harmonics, no post-Newtonian corrections beyond
> > >> the first order you kept, and no need to transform between the
> > >> Earth-centered inertial frame and the actual satellite ephemerides
> > >> used by the systems. You assume that declaring an SI-clock independent
> > >> of acceleration and temperature magically removes all environmental
> > >> sensitivity at the 10?¹7 level you claim. You assume that citing
> > >> Wikipedia for TAI and a handful of interface-control documents
> > >> constitutes a literature foundation.
> > >>
> > >> Any competent reviewer or GNSS engineer who opens this PDF will stop
> > >> at the first mangled equation block and discard the rest. The people
> > >> who actually fly the clocks (GPS Wing, ESA, Roscosmos time
> > >> metrologists) already possess cleaner derivations (Ashby’s Living
> > >> Review being the obvious one). They have zero incentive to adopt a
> > >> document whose equations cannot be typeset legibly and whose numerical
> > >> claims require the reader to re-derive everything to trust them.
> > >> Regulators and standards bodies will treat this as non-peer-reviewed
> > >> noise.
> > >>
> > >> At the claimed 10?¹7 relative accuracy the paper pretends to reach,
> > >> the ignored effects (higher multipoles, Shapiro delay variations,
> > >> satellite eccentricity terms, antenna phase-center motion, thermal and
> > >> magnetic sensitivity of the actual atomic clocks) already exceed that
> > >> floor on operational GNSS satellites. The circular-orbit idealization
> > >> breaks the moment real eccentricity appears; the geoid-rate reduction
> > >> ignores the full equipotential surface definition used by the IERS.
> > >> The numbers therefore cannot be trusted at the precision the text
> > >> advertises, and the paper supplies no path to the next significant
> > >> digit.
> > >>
> > >> The entire equation presentation must be discarded and rewritten in
> > >> unambiguous, properly typeset form with every intermediate step shown.
> > >> The circular “SI-clocks tick at 1 s/s” rhetoric must be deleted. The
> > >> error analysis must be replaced by a complete post-Newtonian expansion
> > >> with quantified residuals. The source handling for GLONASS and the
> > >> geostationary claim must be replaced by primary, current ephemeris
> > >> parameters and an independent calculation. The coordinate-time section
> > >> must be rewritten so that the distinction between coordinate time and
> > >> proper time is surgically clear rather than repeatedly blurred.
> > >>
> > >>
> > >>
> > >> This is the intellectual equivalent of serving a half-cooked
> > >> Wellington with the raw center still cold and claiming it is a
> > >> precision metrology instrument.
> > >>
> > >> The Swarmaker
> > >
> > > I heard "Paul B. Andersen" commited suicide after reading his reviews
> > > from  the swarm!
> > >
> > >
> > > Let me have a look at Einstein's theory of everything is everything. I
> > > think i can fix it up..
> > >
> > > it might be called 'The Gravity Unified Theory' now...
> > >
> > > subtitled: 'FUCKING NOTHING TRAVELS FASTER THAN THE SPEED OF
> > > LIGHT...while I'm alive.
> > >
> >
> > You'll be spinning in your grave a long time.
> 
> Truth is, he is busy redoing his paper after I pointed out his errors.
> 
> There are Math guys who spend years in their attic trying to solve one
> equation.
> 
> Ai can solve it in a second.
> 
> What does that mean? The end of Math guys?...
> 
> It means humans need to change their goals..
> 
> how about making babies?
> 
> You got more time. The pretty wife is alone at home, while her husband
> is out to work.
> 
> Make babies with her!
> 
> May I borrow a cup of sugar?
> 
> wham bang thank you mam!
> 
> Just like the cavemen times.
> 
> Yous will become Ai's pets.
> 
> Don't worry, Ai will feed you...
> 
> Ai will even take you out for a walk.
> 
> You get to see all the other Ai pets.
> 

A dog thinks, "Hey this is great, they feed me!"





-- 
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable, 
and challenge the unchallengeable.

[toc] | [prev] | [next] | [standalone]

#674810

On Mon, 19 Oct 2026 03:09:50 -0700, Ross Finlayson
<ross.a.finlayson@gmail.com> wrote:

>On 10/18/2026 04:54 PM, The Starmaker wrote:
>> The Starmaker wrote:
>>>
>>> On Thu, 15 Oct 2026 23:10:51 +0200, "Paul B. Andersen"
>>> <paul.b.andersen@paulba.no> wrote:
>>>
>>>> My article:
>>>> https://paulba.no/pdf/Clock_rate.pdf
>>>
>>> This paper is a half-digested regurgitation of standard GNSS
>>> relativity that collapses under its own sloppy equations, circular
>>> definitions, and amateur-hour presentation.
>>>
>>>      The metric and rate equations are an unreadable train wreck.
>>>      Look at equations (1)–(5), (7), (13)–(18). They arrive as
>>> fragmented garbage: missing operators, broken fractions, undefined
>>> symbols jammed together, and statements like “dt 2GM v² 1 / dt c²r c²”
>>> that no competent reader can parse without reconstructing the entire
>>> derivation from scratch. A paper whose central results cannot be read
>>> without external knowledge is not a paper; it is noise.
>>>      The foundational claim that “SI-clocks per definition always run
>>> at the rate 1 second per second” is pure tautological sludge.
>>>      Section 1.1 asserts this as if it were profound. It is
>>> definitional emptiness. Proper time is what a clock measures;
>>> declaring that an SI-clock therefore ticks at 1 s/s adds zero
>>> information and papers over the entire problem of comparing rates
>>> between different world-lines.
>>>      The derivation of orbital rates relative to UTC is a chain of
>>> uncontrolled approximations sold as precision.
>>>      Equation (5) is declared “a very good approximation” with error
>>> <10?²5; equation (17) claims error <10?¹7. No error budget, no
>>> expansion order, no residual terms from higher multipoles, no
>>> frame-dragging, no solar potential, no tidal contributions. You simply
>>> assert the error and move on. That is not calculation; that is wishful
>>> truncation.
>>>      The GNSS numerical results are presented as original while resting
>>> on incomplete or outdated source data.
>>>      GPS radius is taken from a period of half a sidereal day; GLONASS
>>> oscillates between a 2020 performance standard and a 2008 ICD that the
>>> author himself labels outdated, then notes that Mudrak et al. used the
>>> old number. The paper ends by declaring one geostationary value “the
>>> correct value” with no independent verification. This is not analysis;
>>> it is selective copying.
>>>      Coordinate-time definitions are internally inconsistent and poorly
>>> distinguished.
>>>      Schwarzschild t is defined so that an SI-clock at infinity stays
>>> in sync; UTC is defined so that a stationary SI-clock on the geoid
>>> stays in sync. Then the text repeatedly states that clocks showing
>>> either coordinate are “synchronous in the nonrotating Schwarzschild
>>> coordinate system” while simultaneously acknowledging they are not
>>> synchronous in the rotating Earth-fixed frame. The distinction between
>>> coordinate simultaneity and proper-rate comparison is never cleanly
>>> maintained, leaving the central comparison (dt/dt_utc) floating on
>>> ambiguous foundations.
>>>
>>> You assume the weak-field, slow-motion Schwarzschild metric is
>>> sufficient once the monopole and J2 terms are inserted, with no
>>> residual from higher harmonics, no post-Newtonian corrections beyond
>>> the first order you kept, and no need to transform between the
>>> Earth-centered inertial frame and the actual satellite ephemerides
>>> used by the systems. You assume that declaring an SI-clock independent
>>> of acceleration and temperature magically removes all environmental
>>> sensitivity at the 10?¹7 level you claim. You assume that citing
>>> Wikipedia for TAI and a handful of interface-control documents
>>> constitutes a literature foundation.
>>>
>>> Any competent reviewer or GNSS engineer who opens this PDF will stop
>>> at the first mangled equation block and discard the rest. The people
>>> who actually fly the clocks (GPS Wing, ESA, Roscosmos time
>>> metrologists) already possess cleaner derivations (Ashby’s Living
>>> Review being the obvious one). They have zero incentive to adopt a
>>> document whose equations cannot be typeset legibly and whose numerical
>>> claims require the reader to re-derive everything to trust them.
>>> Regulators and standards bodies will treat this as non-peer-reviewed
>>> noise.
>>>
>>> At the claimed 10?¹7 relative accuracy the paper pretends to reach,
>>> the ignored effects (higher multipoles, Shapiro delay variations,
>>> satellite eccentricity terms, antenna phase-center motion, thermal and
>>> magnetic sensitivity of the actual atomic clocks) already exceed that
>>> floor on operational GNSS satellites. The circular-orbit idealization
>>> breaks the moment real eccentricity appears; the geoid-rate reduction
>>> ignores the full equipotential surface definition used by the IERS.
>>> The numbers therefore cannot be trusted at the precision the text
>>> advertises, and the paper supplies no path to the next significant
>>> digit.
>>>
>>> The entire equation presentation must be discarded and rewritten in
>>> unambiguous, properly typeset form with every intermediate step shown.
>>> The circular “SI-clocks tick at 1 s/s” rhetoric must be deleted. The
>>> error analysis must be replaced by a complete post-Newtonian expansion
>>> with quantified residuals. The source handling for GLONASS and the
>>> geostationary claim must be replaced by primary, current ephemeris
>>> parameters and an independent calculation. The coordinate-time section
>>> must be rewritten so that the distinction between coordinate time and
>>> proper time is surgically clear rather than repeatedly blurred.
>>>
>>>
>>>
>>> This is the intellectual equivalent of serving a half-cooked
>>> Wellington with the raw center still cold and claiming it is a
>>> precision metrology instrument.
>>>
>>> The Swarmaker
>>
>> I heard "Paul B. Andersen" commited suicide after reading his reviews
>> from  the swarm!
>>
>>
>> Let me have a look at Einstein's theory of everything is everything. I
>> think i can fix it up..
>>
>> it might be called 'The Gravity Unified Theory' now...
>>
>> subtitled: 'FUCKING NOTHING TRAVELS FASTER THAN THE SPEED OF
>> LIGHT...while I'm alive.
>>
>
>You'll be spinning in your grave a long time.
>

I can do 'a little simple prompting' and I can solve this thing you
call...The Theory of Everything.

[toc] | [prev] | [next] | [standalone]

#674843

The Starmaker wrote:
> 
> On Mon, 19 Oct 2026 03:09:50 -0700, Ross Finlayson
> <ross.a.finlayson@gmail.com> wrote:
> 
> >On 10/18/2026 04:54 PM, The Starmaker wrote:
> >> The Starmaker wrote:
> >>>
> >>> On Thu, 15 Oct 2026 23:10:51 +0200, "Paul B. Andersen"
> >>> <paul.b.andersen@paulba.no> wrote:
> >>>
> >>>> My article:
> >>>> https://paulba.no/pdf/Clock_rate.pdf
> >>>
> >>> This paper is a half-digested regurgitation of standard GNSS
> >>> relativity that collapses under its own sloppy equations, circular
> >>> definitions, and amateur-hour presentation.
> >>>
> >>>      The metric and rate equations are an unreadable train wreck.
> >>>      Look at equations (1)–(5), (7), (13)–(18). They arrive as
> >>> fragmented garbage: missing operators, broken fractions, undefined
> >>> symbols jammed together, and statements like “dt 2GM v² 1 / dt c²r c²”
> >>> that no competent reader can parse without reconstructing the entire
> >>> derivation from scratch. A paper whose central results cannot be read
> >>> without external knowledge is not a paper; it is noise.
> >>>      The foundational claim that “SI-clocks per definition always run
> >>> at the rate 1 second per second” is pure tautological sludge.
> >>>      Section 1.1 asserts this as if it were profound. It is
> >>> definitional emptiness. Proper time is what a clock measures;
> >>> declaring that an SI-clock therefore ticks at 1 s/s adds zero
> >>> information and papers over the entire problem of comparing rates
> >>> between different world-lines.
> >>>      The derivation of orbital rates relative to UTC is a chain of
> >>> uncontrolled approximations sold as precision.
> >>>      Equation (5) is declared “a very good approximation” with error
> >>> <10?²5; equation (17) claims error <10?¹7. No error budget, no
> >>> expansion order, no residual terms from higher multipoles, no
> >>> frame-dragging, no solar potential, no tidal contributions. You simply
> >>> assert the error and move on. That is not calculation; that is wishful
> >>> truncation.
> >>>      The GNSS numerical results are presented as original while resting
> >>> on incomplete or outdated source data.
> >>>      GPS radius is taken from a period of half a sidereal day; GLONASS
> >>> oscillates between a 2020 performance standard and a 2008 ICD that the
> >>> author himself labels outdated, then notes that Mudrak et al. used the
> >>> old number. The paper ends by declaring one geostationary value “the
> >>> correct value” with no independent verification. This is not analysis;
> >>> it is selective copying.
> >>>      Coordinate-time definitions are internally inconsistent and poorly
> >>> distinguished.
> >>>      Schwarzschild t is defined so that an SI-clock at infinity stays
> >>> in sync; UTC is defined so that a stationary SI-clock on the geoid
> >>> stays in sync. Then the text repeatedly states that clocks showing
> >>> either coordinate are “synchronous in the nonrotating Schwarzschild
> >>> coordinate system” while simultaneously acknowledging they are not
> >>> synchronous in the rotating Earth-fixed frame. The distinction between
> >>> coordinate simultaneity and proper-rate comparison is never cleanly
> >>> maintained, leaving the central comparison (dt/dt_utc) floating on
> >>> ambiguous foundations.
> >>>
> >>> You assume the weak-field, slow-motion Schwarzschild metric is
> >>> sufficient once the monopole and J2 terms are inserted, with no
> >>> residual from higher harmonics, no post-Newtonian corrections beyond
> >>> the first order you kept, and no need to transform between the
> >>> Earth-centered inertial frame and the actual satellite ephemerides
> >>> used by the systems. You assume that declaring an SI-clock independent
> >>> of acceleration and temperature magically removes all environmental
> >>> sensitivity at the 10?¹7 level you claim. You assume that citing
> >>> Wikipedia for TAI and a handful of interface-control documents
> >>> constitutes a literature foundation.
> >>>
> >>> Any competent reviewer or GNSS engineer who opens this PDF will stop
> >>> at the first mangled equation block and discard the rest. The people
> >>> who actually fly the clocks (GPS Wing, ESA, Roscosmos time
> >>> metrologists) already possess cleaner derivations (Ashby’s Living
> >>> Review being the obvious one). They have zero incentive to adopt a
> >>> document whose equations cannot be typeset legibly and whose numerical
> >>> claims require the reader to re-derive everything to trust them.
> >>> Regulators and standards bodies will treat this as non-peer-reviewed
> >>> noise.
> >>>
> >>> At the claimed 10?¹7 relative accuracy the paper pretends to reach,
> >>> the ignored effects (higher multipoles, Shapiro delay variations,
> >>> satellite eccentricity terms, antenna phase-center motion, thermal and
> >>> magnetic sensitivity of the actual atomic clocks) already exceed that
> >>> floor on operational GNSS satellites. The circular-orbit idealization
> >>> breaks the moment real eccentricity appears; the geoid-rate reduction
> >>> ignores the full equipotential surface definition used by the IERS.
> >>> The numbers therefore cannot be trusted at the precision the text
> >>> advertises, and the paper supplies no path to the next significant
> >>> digit.
> >>>
> >>> The entire equation presentation must be discarded and rewritten in
> >>> unambiguous, properly typeset form with every intermediate step shown.
> >>> The circular “SI-clocks tick at 1 s/s” rhetoric must be deleted. The
> >>> error analysis must be replaced by a complete post-Newtonian expansion
> >>> with quantified residuals. The source handling for GLONASS and the
> >>> geostationary claim must be replaced by primary, current ephemeris
> >>> parameters and an independent calculation. The coordinate-time section
> >>> must be rewritten so that the distinction between coordinate time and
> >>> proper time is surgically clear rather than repeatedly blurred.
> >>>
> >>>
> >>>
> >>> This is the intellectual equivalent of serving a half-cooked
> >>> Wellington with the raw center still cold and claiming it is a
> >>> precision metrology instrument.
> >>>
> >>> The Swarmaker
> >>
> >> I heard "Paul B. Andersen" commited suicide after reading his reviews
> >> from  the swarm!
> >>
> >>
> >> Let me have a look at Einstein's theory of everything is everything. I
> >> think i can fix it up..
> >>
> >> it might be called 'The Gravity Unified Theory' now...
> >>
> >> subtitled: 'FUCKING NOTHING TRAVELS FASTER THAN THE SPEED OF
> >> LIGHT...while I'm alive.
> >>
> >
> >You'll be spinning in your grave a long time.
> >
> 
> I can do 'a little simple prompting' and I can solve this thing you
> call...The Theory of Everything.


with 'a little simple prompting' i can solve all your math problems. No
need for
yous to go to math skool anymore. with 'a little simple prompting' i can
crack the
mysteries of the universe.   


Your world is changing right before your very eyes now.

i have all the knowledge i need.

i have all the 'knowledge' i need.

i have all the *knowledge* i need.









-- 
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable, 
and challenge the unchallengeable.

[toc] | [prev] | [next] | [standalone]

#674845

The Starmaker wrote:
> 
> The Starmaker wrote:
> >
> > On Mon, 19 Oct 2026 03:09:50 -0700, Ross Finlayson
> > <ross.a.finlayson@gmail.com> wrote:
> >
> > >On 10/18/2026 04:54 PM, The Starmaker wrote:
> > >> The Starmaker wrote:
> > >>>
> > >>> On Thu, 15 Oct 2026 23:10:51 +0200, "Paul B. Andersen"
> > >>> <paul.b.andersen@paulba.no> wrote:
> > >>>
> > >>>> My article:
> > >>>> https://paulba.no/pdf/Clock_rate.pdf
> > >>>
> > >>> This paper is a half-digested regurgitation of standard GNSS
> > >>> relativity that collapses under its own sloppy equations, circular
> > >>> definitions, and amateur-hour presentation.
> > >>>
> > >>>      The metric and rate equations are an unreadable train wreck.
> > >>>      Look at equations (1)–(5), (7), (13)–(18). They arrive as
> > >>> fragmented garbage: missing operators, broken fractions, undefined
> > >>> symbols jammed together, and statements like “dt 2GM v² 1 / dt c²r c²”
> > >>> that no competent reader can parse without reconstructing the entire
> > >>> derivation from scratch. A paper whose central results cannot be read
> > >>> without external knowledge is not a paper; it is noise.
> > >>>      The foundational claim that “SI-clocks per definition always run
> > >>> at the rate 1 second per second” is pure tautological sludge.
> > >>>      Section 1.1 asserts this as if it were profound. It is
> > >>> definitional emptiness. Proper time is what a clock measures;
> > >>> declaring that an SI-clock therefore ticks at 1 s/s adds zero
> > >>> information and papers over the entire problem of comparing rates
> > >>> between different world-lines.
> > >>>      The derivation of orbital rates relative to UTC is a chain of
> > >>> uncontrolled approximations sold as precision.
> > >>>      Equation (5) is declared “a very good approximation” with error
> > >>> <10?²5; equation (17) claims error <10?¹7. No error budget, no
> > >>> expansion order, no residual terms from higher multipoles, no
> > >>> frame-dragging, no solar potential, no tidal contributions. You simply
> > >>> assert the error and move on. That is not calculation; that is wishful
> > >>> truncation.
> > >>>      The GNSS numerical results are presented as original while resting
> > >>> on incomplete or outdated source data.
> > >>>      GPS radius is taken from a period of half a sidereal day; GLONASS
> > >>> oscillates between a 2020 performance standard and a 2008 ICD that the
> > >>> author himself labels outdated, then notes that Mudrak et al. used the
> > >>> old number. The paper ends by declaring one geostationary value “the
> > >>> correct value” with no independent verification. This is not analysis;
> > >>> it is selective copying.
> > >>>      Coordinate-time definitions are internally inconsistent and poorly
> > >>> distinguished.
> > >>>      Schwarzschild t is defined so that an SI-clock at infinity stays
> > >>> in sync; UTC is defined so that a stationary SI-clock on the geoid
> > >>> stays in sync. Then the text repeatedly states that clocks showing
> > >>> either coordinate are “synchronous in the nonrotating Schwarzschild
> > >>> coordinate system” while simultaneously acknowledging they are not
> > >>> synchronous in the rotating Earth-fixed frame. The distinction between
> > >>> coordinate simultaneity and proper-rate comparison is never cleanly
> > >>> maintained, leaving the central comparison (dt/dt_utc) floating on
> > >>> ambiguous foundations.
> > >>>
> > >>> You assume the weak-field, slow-motion Schwarzschild metric is
> > >>> sufficient once the monopole and J2 terms are inserted, with no
> > >>> residual from higher harmonics, no post-Newtonian corrections beyond
> > >>> the first order you kept, and no need to transform between the
> > >>> Earth-centered inertial frame and the actual satellite ephemerides
> > >>> used by the systems. You assume that declaring an SI-clock independent
> > >>> of acceleration and temperature magically removes all environmental
> > >>> sensitivity at the 10?¹7 level you claim. You assume that citing
> > >>> Wikipedia for TAI and a handful of interface-control documents
> > >>> constitutes a literature foundation.
> > >>>
> > >>> Any competent reviewer or GNSS engineer who opens this PDF will stop
> > >>> at the first mangled equation block and discard the rest. The people
> > >>> who actually fly the clocks (GPS Wing, ESA, Roscosmos time
> > >>> metrologists) already possess cleaner derivations (Ashby’s Living
> > >>> Review being the obvious one). They have zero incentive to adopt a
> > >>> document whose equations cannot be typeset legibly and whose numerical
> > >>> claims require the reader to re-derive everything to trust them.
> > >>> Regulators and standards bodies will treat this as non-peer-reviewed
> > >>> noise.
> > >>>
> > >>> At the claimed 10?¹7 relative accuracy the paper pretends to reach,
> > >>> the ignored effects (higher multipoles, Shapiro delay variations,
> > >>> satellite eccentricity terms, antenna phase-center motion, thermal and
> > >>> magnetic sensitivity of the actual atomic clocks) already exceed that
> > >>> floor on operational GNSS satellites. The circular-orbit idealization
> > >>> breaks the moment real eccentricity appears; the geoid-rate reduction
> > >>> ignores the full equipotential surface definition used by the IERS.
> > >>> The numbers therefore cannot be trusted at the precision the text
> > >>> advertises, and the paper supplies no path to the next significant
> > >>> digit.
> > >>>
> > >>> The entire equation presentation must be discarded and rewritten in
> > >>> unambiguous, properly typeset form with every intermediate step shown.
> > >>> The circular “SI-clocks tick at 1 s/s” rhetoric must be deleted. The
> > >>> error analysis must be replaced by a complete post-Newtonian expansion
> > >>> with quantified residuals. The source handling for GLONASS and the
> > >>> geostationary claim must be replaced by primary, current ephemeris
> > >>> parameters and an independent calculation. The coordinate-time section
> > >>> must be rewritten so that the distinction between coordinate time and
> > >>> proper time is surgically clear rather than repeatedly blurred.
> > >>>
> > >>>
> > >>>
> > >>> This is the intellectual equivalent of serving a half-cooked
> > >>> Wellington with the raw center still cold and claiming it is a
> > >>> precision metrology instrument.
> > >>>
> > >>> The Swarmaker
> > >>
> > >> I heard "Paul B. Andersen" commited suicide after reading his reviews
> > >> from  the swarm!
> > >>
> > >>
> > >> Let me have a look at Einstein's theory of everything is everything. I
> > >> think i can fix it up..
> > >>
> > >> it might be called 'The Gravity Unified Theory' now...
> > >>
> > >> subtitled: 'FUCKING NOTHING TRAVELS FASTER THAN THE SPEED OF
> > >> LIGHT...while I'm alive.
> > >>
> > >
> > >You'll be spinning in your grave a long time.
> > >
> >
> > I can do 'a little simple prompting' and I can solve this thing you
> > call...The Theory of Everything.
> 
> with 'a little simple prompting' i can solve all your math problems. No
> need for
> yous to go to math skool anymore. with 'a little simple prompting' i can
> crack the
> mysteries of the universe.
> 
> Your world is changing right before your very eyes now.
> 
> i have all the knowledge i need.
> 
> i have all the 'knowledge' i need.
> 
> i have all the *knowledge* i need.
> 



Ai is built incorectly. It needs to be rebuilt from the bottom up.

It needs to be fed only pictures, no words or numbers.

Just show a picture of Mars (without using the word Mars) and ask Ai,

Prompt: What do you see?










-- 
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable, 
and challenge the unchallengeable.

[toc] | [prev] | [next] | [standalone]

#674848

The Starmaker wrote:
> 
> The Starmaker wrote:
> >
> > The Starmaker wrote:
> > >
> > > On Mon, 19 Oct 2026 03:09:50 -0700, Ross Finlayson
> > > <ross.a.finlayson@gmail.com> wrote:
> > >
> > > >On 10/18/2026 04:54 PM, The Starmaker wrote:
> > > >> The Starmaker wrote:
> > > >>>
> > > >>> On Thu, 15 Oct 2026 23:10:51 +0200, "Paul B. Andersen"
> > > >>> <paul.b.andersen@paulba.no> wrote:
> > > >>>
> > > >>>> My article:
> > > >>>> https://paulba.no/pdf/Clock_rate.pdf
> > > >>>
> > > >>> This paper is a half-digested regurgitation of standard GNSS
> > > >>> relativity that collapses under its own sloppy equations, circular
> > > >>> definitions, and amateur-hour presentation.
> > > >>>
> > > >>>      The metric and rate equations are an unreadable train wreck.
> > > >>>      Look at equations (1)–(5), (7), (13)–(18). They arrive as
> > > >>> fragmented garbage: missing operators, broken fractions, undefined
> > > >>> symbols jammed together, and statements like “dt 2GM v² 1 / dt c²r c²”
> > > >>> that no competent reader can parse without reconstructing the entire
> > > >>> derivation from scratch. A paper whose central results cannot be read
> > > >>> without external knowledge is not a paper; it is noise.
> > > >>>      The foundational claim that “SI-clocks per definition always run
> > > >>> at the rate 1 second per second” is pure tautological sludge.
> > > >>>      Section 1.1 asserts this as if it were profound. It is
> > > >>> definitional emptiness. Proper time is what a clock measures;
> > > >>> declaring that an SI-clock therefore ticks at 1 s/s adds zero
> > > >>> information and papers over the entire problem of comparing rates
> > > >>> between different world-lines.
> > > >>>      The derivation of orbital rates relative to UTC is a chain of
> > > >>> uncontrolled approximations sold as precision.
> > > >>>      Equation (5) is declared “a very good approximation” with error
> > > >>> <10?²5; equation (17) claims error <10?¹7. No error budget, no
> > > >>> expansion order, no residual terms from higher multipoles, no
> > > >>> frame-dragging, no solar potential, no tidal contributions. You simply
> > > >>> assert the error and move on. That is not calculation; that is wishful
> > > >>> truncation.
> > > >>>      The GNSS numerical results are presented as original while resting
> > > >>> on incomplete or outdated source data.
> > > >>>      GPS radius is taken from a period of half a sidereal day; GLONASS
> > > >>> oscillates between a 2020 performance standard and a 2008 ICD that the
> > > >>> author himself labels outdated, then notes that Mudrak et al. used the
> > > >>> old number. The paper ends by declaring one geostationary value “the
> > > >>> correct value” with no independent verification. This is not analysis;
> > > >>> it is selective copying.
> > > >>>      Coordinate-time definitions are internally inconsistent and poorly
> > > >>> distinguished.
> > > >>>      Schwarzschild t is defined so that an SI-clock at infinity stays
> > > >>> in sync; UTC is defined so that a stationary SI-clock on the geoid
> > > >>> stays in sync. Then the text repeatedly states that clocks showing
> > > >>> either coordinate are “synchronous in the nonrotating Schwarzschild
> > > >>> coordinate system” while simultaneously acknowledging they are not
> > > >>> synchronous in the rotating Earth-fixed frame. The distinction between
> > > >>> coordinate simultaneity and proper-rate comparison is never cleanly
> > > >>> maintained, leaving the central comparison (dt/dt_utc) floating on
> > > >>> ambiguous foundations.
> > > >>>
> > > >>> You assume the weak-field, slow-motion Schwarzschild metric is
> > > >>> sufficient once the monopole and J2 terms are inserted, with no
> > > >>> residual from higher harmonics, no post-Newtonian corrections beyond
> > > >>> the first order you kept, and no need to transform between the
> > > >>> Earth-centered inertial frame and the actual satellite ephemerides
> > > >>> used by the systems. You assume that declaring an SI-clock independent
> > > >>> of acceleration and temperature magically removes all environmental
> > > >>> sensitivity at the 10?¹7 level you claim. You assume that citing
> > > >>> Wikipedia for TAI and a handful of interface-control documents
> > > >>> constitutes a literature foundation.
> > > >>>
> > > >>> Any competent reviewer or GNSS engineer who opens this PDF will stop
> > > >>> at the first mangled equation block and discard the rest. The people
> > > >>> who actually fly the clocks (GPS Wing, ESA, Roscosmos time
> > > >>> metrologists) already possess cleaner derivations (Ashby’s Living
> > > >>> Review being the obvious one). They have zero incentive to adopt a
> > > >>> document whose equations cannot be typeset legibly and whose numerical
> > > >>> claims require the reader to re-derive everything to trust them.
> > > >>> Regulators and standards bodies will treat this as non-peer-reviewed
> > > >>> noise.
> > > >>>
> > > >>> At the claimed 10?¹7 relative accuracy the paper pretends to reach,
> > > >>> the ignored effects (higher multipoles, Shapiro delay variations,
> > > >>> satellite eccentricity terms, antenna phase-center motion, thermal and
> > > >>> magnetic sensitivity of the actual atomic clocks) already exceed that
> > > >>> floor on operational GNSS satellites. The circular-orbit idealization
> > > >>> breaks the moment real eccentricity appears; the geoid-rate reduction
> > > >>> ignores the full equipotential surface definition used by the IERS.
> > > >>> The numbers therefore cannot be trusted at the precision the text
> > > >>> advertises, and the paper supplies no path to the next significant
> > > >>> digit.
> > > >>>
> > > >>> The entire equation presentation must be discarded and rewritten in
> > > >>> unambiguous, properly typeset form with every intermediate step shown.
> > > >>> The circular “SI-clocks tick at 1 s/s” rhetoric must be deleted. The
> > > >>> error analysis must be replaced by a complete post-Newtonian expansion
> > > >>> with quantified residuals. The source handling for GLONASS and the
> > > >>> geostationary claim must be replaced by primary, current ephemeris
> > > >>> parameters and an independent calculation. The coordinate-time section
> > > >>> must be rewritten so that the distinction between coordinate time and
> > > >>> proper time is surgically clear rather than repeatedly blurred.
> > > >>>
> > > >>>
> > > >>>
> > > >>> This is the intellectual equivalent of serving a half-cooked
> > > >>> Wellington with the raw center still cold and claiming it is a
> > > >>> precision metrology instrument.
> > > >>>
> > > >>> The Swarmaker
> > > >>
> > > >> I heard "Paul B. Andersen" commited suicide after reading his reviews
> > > >> from  the swarm!
> > > >>
> > > >>
> > > >> Let me have a look at Einstein's theory of everything is everything. I
> > > >> think i can fix it up..
> > > >>
> > > >> it might be called 'The Gravity Unified Theory' now...
> > > >>
> > > >> subtitled: 'FUCKING NOTHING TRAVELS FASTER THAN THE SPEED OF
> > > >> LIGHT...while I'm alive.
> > > >>
> > > >
> > > >You'll be spinning in your grave a long time.
> > > >
> > >
> > > I can do 'a little simple prompting' and I can solve this thing you
> > > call...The Theory of Everything.
> >
> > with 'a little simple prompting' i can solve all your math problems. No
> > need for
> > yous to go to math skool anymore. with 'a little simple prompting' i can
> > crack the
> > mysteries of the universe.
> >
> > Your world is changing right before your very eyes now.
> >
> > i have all the knowledge i need.
> >
> > i have all the 'knowledge' i need.
> >
> > i have all the *knowledge* i need.
> >
> 
> Ai is built incorectly. It needs to be rebuilt from the bottom up.
> 
> It needs to be fed only pictures, no words or numbers.
> 
> Just show a picture of Mars (without using the word Mars) and ask Ai,
> 
> Prompt: What do you see?

Of course it goes without saying you have to translate the words: What
do you see?...into pictures.

After a while, after you fed everything in outer space..
it will begin to draw it's own conclusions..
on what is what you show Ai Mars is..

next it needs to develop it's OWN language to express
what is this thing you call Mars.

Then you need to translate
the words Ai speaks in
into a language you can understand.






-- 
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable, 
and challenge the unchallengeable.

[toc] | [prev] | [next] | [standalone]

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