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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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#674853

On 10/22/2026 12:28 PM, 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?
>
>
>
>
>
>
>
>
>
>


Don't be quoting me and not quoting me.


Though, I guess after Starmaker had the "over my dead body"
there was my "You'll be spinning in your grave a long time."



Clocks either slow or meet, there are a variety of
natural clocks, micro and macro and macro again and meso, scales,
that's what Einstein needs is more timebases for clocks and
less inaccurate pocketwatches.

Einstein is pretty remarkable as a grandiose hedge,
meaning that his summary or final word from
"Out of My Later Years" says quite a bit less
than usual given accounts, while distinguishing
the linear and rotational after distinguishing
the "spatial" and "spacial" and making for the
L-principle that RoS is non-local, that SR is local.

Most people don't get that, yet, many do.

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#674859

Ross Finlayson wrote:
> 
> On 10/22/2026 12:28 PM, 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?
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> 
> Don't be quoting me and not quoting me.
> 
> Though, I guess after Starmaker had the "over my dead body"
> there was my "You'll be spinning in your grave a long time."
> 
> Clocks either slow or meet, there are a variety of
> natural clocks, micro and macro and macro again and meso, scales,
> that's what Einstein needs is more timebases for clocks and
> less inaccurate pocketwatches.
> 
> Einstein is pretty remarkable as a grandiose hedge,
> meaning that his summary or final word from
> "Out of My Later Years" says quite a bit less
> than usual given accounts, while distinguishing
> the linear and rotational after distinguishing
> the "spatial" and "spacial" and making for the
> L-principle that RoS is non-local, that SR is local.
> 
> Most people don't get that, yet, many do.


You seem to say everything and nothing at the same time...





-- 
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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#674381

On Mon, 12 Oct 2026 20:55:22 +0200, 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.

Clocks don't 'RUN'. They COUNT.

> 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

Not so! The rate at which waves are received must equal their rate of 
emission. 

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

That idea was concocted because Einstein prohibited the signal from 
changing speed.    

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

Rubbish. wavelengths cannot disappear. For any two objects that are MAR 
the WER must equal the WAR no matter what gravity does to the signal.

> 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

That was Einstein's way of balancing the energy equation without admitting 
that the signal had changed speed and kinetic energy in exactly the same 
proportion, 5.2996e-10
> 
> This means that the received frequency is:
> f = 1GHz⋅(1 + Δf/f₀) = 1000000000.53 Hz, a gravitational blue shift.

...but it does not actually happen. Einstein had to concoct the idea that 
Time itself changed in the different gravity potentials.
 
> Observed from the ground the clock at r appears to run fast.

That is not what the GR redshift says. Clocks count oscillator cycles. If 
the oscillator was redshifted, its frequency would have slowed...and so 
would the clock. 

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

How can the fact that the Earth is rotating affect something that happens 
26000 kms away? Are the Norwegian fairies playing tricks again?

> 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

SR got it all back to front...but it doesn't matter because the clocks are 
empirically adjusted anyway. Their actual rate is not important so long as 
they are al in absolute synch..

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#674413

HenryWilson wrote:
> On Mon, 12 Oct 2026 20:55:22 +0200, Paul B. Andersen wrote:
>> This is what GR say:
>>
>> Clocks always run at their proper rate, one second per second.
> 
> Clocks don't 'RUN'. They COUNT.

Semantic fallacy.  This means the same thing.  "Running" in English
refers to the operation of a clock, a device which measures/counts time.

>> 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
> 
> Not so! The rate at which waves are received must equal their rate of 
> emission. 

That is already not so for sound waves where there is the Doppler
effect, you wannabe physicist and actual _non_-physicist.

>> This means that the received frequency is:
>> f = 1GHz⋅(1 + Δf/f₀) =  999999999.47 Hz, a gravitational red shift.
> 
> That idea was concocted because Einstein prohibited the signal from 
> changing speed.    

It was not "concocted".  It is a logically inevitable, mathematical
conclusion of that assumption; and if you would read what Einstein
wrote, and what I wrote so far, you might be able to understand that.

Einstein made that assumption because the speed of light in vacuum _did_
not change if the source moved relative to the observer.  It was and is
an experimental fact.

In general relativity where spacetime is curved, this has to be modified
(or clarified), though: only the _local_ speed of light in vacuum is
constant.  But that suffices to calculate this effect, as I have showed.

>> Observed from the position r above Earth's centre the ground clock
>> appears to run slow.
> 
> Rubbish. wavelengths cannot disappear.

Nobody said that they would disappear.  "Appear" is NOT used here in the
sense of "suddenly showing up".  Learn comprehensive reading.

> For any two objects that are MAR the WER must equal the WAR no matter what
> gravity does to the signal.

Whatever those acronyms that you just invented are supposed to mean.

>> 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
> 
> That was Einstein's way of balancing the energy equation 

No, this has nothing to do with energy or "balancing an 'energy
equation'", whatever you mean by that.

In general, energy is NOT conserved.  That is already so in Newtonian
mechanics where the kinetic energy of a massive object depends on the
choice of the inertial frame of reference.

>> This means that the received frequency is:
>> f = 1GHz⋅(1 + Δf/f₀) = 1000000000.53 Hz, a gravitational blue shift.
> 
> ...but it does not actually happen.

Yes, it does.  Measurably, and _measured_.  Read the NAVSTAR GPS NTS-2
report.  Read the GPS Specification.

>> Observed from the ground the clock at r appears to run fast.
> 
> That is not what the GR redshift says.

There is "gravitational" redshift observed at a larger radius (farther
away from the surface of a planet, for examplefor a signal emitted at a
smaller radius, and there is "gravitational" blueshift observed at a
smaller radius for signal emitted at a larger radius.

Blueshift means that the clock at the source appears to have larger
frequency, that the light wave that the source emits appears to have a
shorter wavelength, than at the receiver's; so that clock _appears_ to
run faster than a clock at the receiver's.

If only you could read comprehensively.

>> The Earth is obviously rotating, so in the GPS we have:
> 
> How can the fact that the Earth is rotating affect something that happens 
> 26000 kms away? 

Because Earth is rotating, the source (each GPS satellite) is moving
relative to the (GPS) receiver.  But the GPS satellites are also
orbiting Earth; so the relative motion between each satellite and a
receiver is a combination of those two motions.  Put simply, "moving
clocks run slower than stationary ones" (an effect predicted and
described by special relativity):

<https://en.wikipedia.org/wiki/Global_Positioning_System#Space_segment>

In particular:

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

>> 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
> 
> SR got it all back to front...

This is a calculation that includes an effect predicted by _GR_,
therefore called "/gravitational/ blueshift".  However, it is at best
only a crude approximation because you cannot simply add quantities that
are consequences of special-relativistic effects and effects that can
only occur in GR where spacetime is curved, respectively:

  √(1 − x − y) ≠ √(1 − x) + √(1 − y).

-- 
PointedEars

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

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#674518

On Wed, 14 Oct 2026 14:12:23 +0200, Thomas 'PointedEars' Lahn wrote:

> HenryWilson wrote:
>> On Mon, 12 Oct 2026 20:55:22 +0200, Paul B. Andersen wrote:
>>> This is what GR say:
>>>
>>> Clocks always run at their proper rate, one second per second.
>> 
>> Clocks don't 'RUN'. They COUNT.
> 
> Semantic fallacy.  This means the same thing.  "Running" in English
> refers to the operation of a clock, a device which measures/counts time.
> 
>>> 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
>> 
>> Not so! The rate at which waves are received must equal their rate of
>> emission.
> 
> That is already not so for sound waves where there is the Doppler
> effect, you wannabe physicist and actual _non_-physicist.

Hey dopey, sound travels in a medium...are you a closet Aetherist by any 
chance?

>>> This means that the received frequency is:
>>> f = 1GHz⋅(1 + Δf/f₀) =  999999999.47 Hz, a gravitational red shift.
>> 
>> That idea was concocted because Einstein prohibited the signal from
>> changing speed.
> 
> It was not "concocted".  It is a logically inevitable, mathematical
> conclusion of that assumption; and if you would read what Einstein
> wrote, and what I wrote so far, you might be able to understand that.

How can its 'frequency' shift when it doesn't exist? Are you talking about 
'wave arrival rate? If so, it is obviously frame dependent.

> Einstein made that assumption because the speed of light in vacuum _did_
> not change if the source moved relative to the observer.  It was and is
> an experimental fact.

HAHAHAAHAHAHA! YOU ARE just a silly AETHERIST.
 
> In general relativity where spacetime is curved, this has to be modified
> (or clarified), though: only the _local_ speed of light in vacuum is
> constant.  But that suffices to calculate this effect, as I have showed.

Einstein's use of transforms never actually implied that the speed of 
light was constant. He only derived a mathematical way to make MEASURED 
speed independent of source speed for a particular observer. Different 
observers apply different transforms to the same moving object (light 
source) but the observers are not all moving at the same speed.
 
>>> Observed from the position r above Earth's centre the ground clock
>>> appears to run slow.
>> 
>> Rubbish. wavelengths cannot disappear.
> 
> Nobody said that they would disappear.  "Appear" is NOT used here in the
> sense of "suddenly showing up".  Learn comprehensive reading.

If the WAR does not equal the WER, waves must have disappeared.

>> For any two objects that are MAR the WER must equal the WAR no matter
>> what gravity does to the signal.
> 
> Whatever those acronyms that you just invented are supposed to mean.

mutually at rest, wave arrival rate , wave emission rate.

>>> 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
>> 
>> That was Einstein's way of balancing the energy equation
> 
> No, this has nothing to do with energy or "balancing an 'energy
> equation'", whatever you mean by that.

A vertical beam of Light slows due to gravity, (proof: it is bent 
downwards by the sun). Therefore, on reaching a fixed object, its 
wavelengths must have shrunk because the have all travelled the same 
distance in the same time.     
 
> In general, energy is NOT conserved.  That is already so in Newtonian
> mechanics where the kinetic energy of a massive object depends on the
> choice of the inertial frame of reference.

Gawd! here we go again. like all Einstein worshippers, you know nothing 
about physics. Kinetic energy is NOT frame dependent. No form of energy 
can be ... except is the eyes of an perpetual motion fanatics! The term 
1/2mv^2 is obviously frame dependent but at least two objects are involved 
in the creation or change of KE and the total energy involved is a;ways 
FRAME DEPENDENT. Work that out yourself if you can. 
> 
>>> This means that the received frequency is:
>>> f = 1GHz⋅(1 + Δf/f₀) = 1000000000.53 Hz, a gravitational blue shift.
>> 
>> ...but it does not actually happen.
> 
> Yes, it does.  Measurably, and _measured_.  Read the NAVSTAR GPS NTS-2
> report.  Read the GPS Specification.
> 
>>> Observed from the ground the clock at r appears to run fast.
>> 
>> That is not what the GR redshift says.
> 
> There is "gravitational" redshift observed at a larger radius (farther
> away from the surface of a planet, for examplefor a signal emitted at a
> smaller radius, and there is "gravitational" blueshift observed at a
> smaller radius for signal emitted at a larger radius.

You have finally seen my point. If there is a redshift, at the top, the 
clock should run slow, not fast. 'Fast' means a blue shift. So what can 
you say about that?
> 
> Blueshift means that the clock at the source appears to have larger
> frequency, that the light wave that the source emits appears to have a
> shorter wavelength, than at the receiver's; so that clock _appears_ to
> run faster than a clock at the receiver's.

So a clock sent into orbit runs fast but its oscillator is redshifted, 
ie., runs slow. Let's say the clock integrates the WAR of that slowed 
signal..but GR just said the opposite.
 
> If only you could read comprehensively

..if you could comprehend what you read....

>>> The Earth is obviously rotating, so in the GPS we have:
>> 
>> How can the fact that the Earth is rotating affect something that
>> happens 26000 kms away?
> 
> Because Earth is rotating, the source (each GPS satellite) is moving
> relative to the (GPS) receiver.  But the GPS satellites are also
> orbiting Earth; so the relative motion between each satellite and a
> receiver is a combination of those two motions.  Put simply, "moving
> clocks run slower than stationary ones" (an effect predicted and
> described by special relativity):
> 
> <https://en.wikipedia.org/wiki/Global_Positioning_System#Space_segment>
> 
> In particular:
> 
> <https://en.wikipedia.org/wiki/Global_Positioning_System#/media/
File:GPS24goldenSML.gif>

OK, explain this. Imagine is a very large digital clock in the sky, a 
light year away from Earth,. It is moving towards Earth at v. According to 
Newton, an aearthly observer would see it running fast by (c+v)/c. If it 
was moving away, that would be (c-v)/c. According to Einstein it slows in 
both directions by gamma.     

>>> 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
>> 
>> SR got it all back to front...
> 
> This is a calculation that includes an effect predicted by _GR_,
> therefore called "/gravitational/ blueshift".  However, it is at best
> only a crude approximation because you cannot simply add quantities that
> are consequences of special-relativistic effects and effects that can
> only occur in GR where spacetime is curved, respectively:
> 
>   √(1 − x − y) ≠ √(1 − x) + √(1 − y).

GR predicts a clock's 'oscillator' will run fast but light's 'oscillator' 
will run slow when sent into space. How do you explain that?

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#674636

HenryWilson wrote:
> On Wed, 14 Oct 2026 14:12:23 +0200, Thomas 'PointedEars' Lahn wrote:
>> HenryWilson wrote:
>>> On Mon, 12 Oct 2026 20:55:22 +0200, Paul B. Andersen wrote:
>>>> 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
>>>
>>> Not so! The rate at which waves are received must equal their rate of
>>> emission.
>>
>> That is already not so for sound waves where there is the Doppler
>> effect, you wannabe physicist and actual _non_-physicist.
> 
> [...] sound travels in a medium... [...]

Irrelevant.

>>>> This means that the received frequency is:
>>>> f = 1GHz⋅(1 + Δf/f₀) =  999999999.47 Hz, a gravitational red shift.
>>>
>>> That idea was concocted because Einstein prohibited the signal from
>>> changing speed.
>>
>> It was not "concocted".  It is a logically inevitable, mathematical
>> conclusion of that assumption; and if you would read what Einstein
>> wrote, and what I wrote so far, you might be able to understand that.
> 
> How can its 'frequency' shift when it doesn't exist?

That it would not exist is merely your fantasy and your fallacy.

> Are you talking about 'wave arrival rate?

There is no such thing.  A wave is everywhere in space(time).

>> Einstein made that assumption because the speed of light in vacuum _did_
>> not change if the source moved relative to the observer.  It was and is
>> an experimental fact.
> 
> HAHAHAAHAHAHA! YOU ARE just a silly AETHERIST.

Nonsense.

>> In general relativity where spacetime is curved, this has to be modified
>> (or clarified), though: only the _local_ speed of light in vacuum is
>> constant.  But that suffices to calculate this effect, as I have showed.
> 
> Einstein's use of transforms never actually implied that the speed of 
> light was constant.

False.  Read his paper; I already gave you the reference to the official
translation into English in case your German is not good enough.

>>>> Observed from the position r above Earth's centre the ground clock
>>>> appears to run slow.
>>> Rubbish. wavelengths cannot disappear.
>> Nobody said that they would disappear.  "Appear" is NOT used here in the
>> sense of "suddenly showing up".  Learn comprehensive reading.
> 
> If the WAR does not equal the WER, waves must have disappeared.

*facepalm*

>>> For any two objects that are MAR the WER must equal the WAR no matter
>>> what gravity does to the signal.
>>
>> Whatever those acronyms that you just invented are supposed to mean.
> 
> mutually at rest, wave arrival rate , wave emission rate.

The latter two are merely fantasies of yours.  In the actual physics, we
speak of the frequency of the wave at the source or "emitted frequency"
for short, and the frequency at the receiver or the "received frequency"
for short.  That aside, your statement is correct in a _flat spacetime_;
 but that is precisely what the Doppler effect and the relativistic
Doppler effect are about: source and receiver/observer are /in motion/
relative to each other.

In a curved spacetime your statement no longer holds as (proper) time
elapses differently at different locations, especially at points that
have a different distance from the center of mass.  (As I already proved
to you.)  And /regardless/ whether you accept this theory that is
accepted throughout the scientific community, it does not change the
fact of the observations; for example:

Atomic clocks at the top of a building are ahead of atomic clocks in its
basement (tested at the University of Colorado Boulder, for example); a
GPS signal from orbit _is_ blueshifted when it is received on the
ground, and the light of the star S2 _is_ redshifted when it passes
close to the black hole Sagittarius A*, for example.

<https://www.npr.org/2014/11/03/361069820/new-clock-may-end-time-as-we-know-it>

    [The statement "speed at which time passes depends on the strength
     of gravity" there is wrong.  But the article also offers
     the correct statement "this isn't some effect of gravity on the
     clock's machinery. Time itself is flowing more quickly on the wall
     than on the floor."]

<https://www.gps.gov/sites/default/files/2025-07/IS-GPS-200N.pdf#page=32>

| 3.3.1.1 Frequency Plan
|
| [...] 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 rate of 10.23 MHz offset by Δf∕f = −4.4647E−10,
| equivalent to a change in the P-code chipping rate Delta
| f = −4.5674E−3 Hz.  This is equal to 10.2299999954326 MHz.

(referred from
<https://www.gps.gov/interface-control-documents-icds-interface-specifications-iss>)

<https://en.wikipedia.org/wiki/Sagittarius_A*#Central_black_hole#:~:text=gravitational%20redshift>

>>>> 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
>>>
>>> That was Einstein's way of balancing the energy equation
>> No, this has nothing to do with energy or "balancing an 'energy
>> equation'", whatever you mean by that.
> 
> A vertical beam of Light slows due to gravity,

No.  The coordinate speed of light in vacuum decreases when it _passes
by_ an object because of the curvature of spacetime due to that object,
compared to a flat spacetime.  This is called *Shapiro delay*.

> (proof: it is bent downwards by the sun).

There is no "down" in outer space.

The light path is temporarily curved towards the center of Sol because
spacetime in the vicinity of Sol is curved due to her presence and
corresponding to the energy-momentum density of spacetime thus produced,
and light paths are described by null geodesics of spacetime.

> Therefore, on reaching a fixed object, its wavelengths must have shrunk 
> [...]

/Ex falso quodlibet./

>> In general, energy is NOT conserved.  That is already so in Newtonian
>> mechanics where the kinetic energy of a massive object depends on the
>> choice of the inertial frame of reference.
> 
> Gawd! here we go again. like all Einstein worshippers, you know nothing 
> about physics.

:-D

I have /studied/ Astrophysics /at university/, you poor lunatic.

> Kinetic energy is NOT frame dependent.

Yes it is because speed is, and kinetic energy is a function of speed.

> No form of energy can be ...

Wrong.

> except is the eyes of an perpetual motion fanatics!

Energy is merely a calculational quantity.  It depends on coordinates,
and so in general it depends on the choice of rest frame.  The only
energy that does not depend on the choice of rest frame is the rest
energy E₀ = m c² because mass m is (provably, and proven by me several
times here and elsewhere) frame-invariant.

> The term 1/2mv^2 is obviously frame dependent

So you are contradicting yourself just a few paragraphs later :-D

> but at least two objects are involved in the creation or change of KE

Wrong.

> and the total energy involved is a;ways FRAME DEPENDENT.

AISB.

>>>> Observed from the ground the clock at r appears to run fast.
>>>
>>> That is not what the GR redshift says.
>>
>> There is "gravitational" redshift observed at a larger radius (farther
>> away from the surface of a planet, for examplefor a signal emitted at a
>> smaller radius, and there is "gravitational" blueshift observed at a
>> smaller radius for signal emitted at a larger radius.
> 
> You have finally seen my point.

You do not have a point, just one big misconception out of many.

> If there is a redshift, at the top, the clock should run slow, not fast.

No, the clock "at the top", i.e. on the satellite, is observed "from
below", i.e. from the ground.  It does not run faster because it is in
orbit; it just measures more time there because more proper time elapses
there.  But from the ground it _appears as if_ it would run faster than
on the ground when clocks are compared.

> 'Fast' means a blue shift.

Which we observe for the signal of a GPS satellite, for example.

> So what can you say about that?

The *direction of the signal* matters: where it is emitted from, and
where it is received at.  Which I already explained to you.  Learn
comprehensive reading.

>> Blueshift means that the clock at the source appears to have larger
>> frequency, that the light wave that the source emits appears to have a
>> shorter wavelength, than at the receiver's; so that clock _appears_ to
>> run faster than a clock at the receiver's.
> 
> So a clock sent into orbit runs fast

It runs fast _compared to a clock of the same design on the ground_.

> but its oscillator is redshifted, [...]

No.  It _would_ be observed "redshifted" (this term does not really make
sense for an oscillator; first think, then post!) _from an even higher
orbit_.
>> If only you could read comprehensively
> 
> ..if you could comprehend what you read....

You are mirroring well.

*facepalm*

> OK, explain this. Imagine is a very large digital clock in the sky, a 
> light year away from Earth,. It is moving towards Earth at v. According to 
> Newton, an aearthly observer would see it running fast by (c+v)/c.

Nonsense.  That quantity is dimensionless.  What is it supposed to mean?

> If it was moving away, that would be (c-v)/c.

Nonsense, again.

> According to Einstein it slows in both directions by gamma.     

No.  What this clock would show in each case, i.e. how it would be
/observed from a distance/ (according to special relativity) is rather
complicated because the light-travel times vary, too.  But it can be
shown approximately relatively easy with a spacetime diagram and
lightlike worldlines emanating in regular intervals of proper time
towards a location at relative rest; I have done so here before when
discussing the twin effect.  Bottom line: the clock would appear to tick
slower when it is receding, and faster when it is approaching but NOT by
the Lorentz factor.  And it would also exhibit Doppler
redshift/blueshift, respectively.

>>>> 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
>>>
>>> SR got it all back to front...
>>
>> This is a calculation that includes an effect predicted by _GR_,
>> therefore called "/gravitational/ blueshift".  However, it is at best
>> only a crude approximation because you cannot simply add quantities that
>> are consequences of special-relativistic effects and effects that can
>> only occur in GR where spacetime is curved, respectively:
>>
>>   √(1 − x − y) ≠ √(1 − x) + √(1 − y).
> 
> GR predicts a clock's 'oscillator' will run fast but light's 'oscillator' 
> will run slow when sent into space. How do you explain that?

You don't know what you are talking about.

-- 
PointedEars

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

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#674439

Den 13.10.2026 17:20, skrev HenryWilson:
> On Mon, 12 Oct 2026 20:55:22 +0200, 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.
> 
> Clocks don't 'RUN'. They COUNT.
> 
>> 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
> 
> Not so! The rate at which waves are received must equal their rate of
> emission.

This weird misconception explains a lot.


-- 
Paul

https://paulba.no/

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#674445

Paul B. Andersen wrote:

> Den 13.10.2026 17:20, skrev HenryWilson:
>> Not so! The rate at which waves are received must equal their rate of
>> emission.
> 
> This weird misconception explains a lot.

so true indeed; this wanker must be a half german illegally occupying the 
australian continent

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#674519

On Wed, 14 Oct 2026 21:07:53 +0200, Paul B. Andersen wrote:

> Den 13.10.2026 17:20, skrev HenryWilson:
>> On Mon, 12 Oct 2026 20:55:22 +0200, 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.
>> 
>> Clocks don't 'RUN'. They COUNT.
>> 
>>> 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
>> 
>> Not so! The rate at which waves are received must equal their rate of
>> emission.
> 
> This weird misconception explains a lot.

don't change you name Paul, so you can support your own drivel.

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#674366

HenryWilson wrote:
> Here is one to argue about. According to GR, light experiences a redshift 
> in frequency when sent into lower gravity potential.

No, _blueshift_, in a sense.  But in GR there is no _gravitational_
potential in the Newtonian sense because gravitation is not explained as
the consequence of the gravitational force.

[In GR, the gravitational potential is represented by the components of
the metric tensor, but I think that this is way over your head.]

> How come clocks are claimed to run fast when sent into orbit.

From ground to orbit it is the opposite direction.

You appear to have a misconception as to how to calculate the
gravitational potential according to Newton's theory of gravitation.
To first approximation, it is given by

  Φ(r) ≈ −G M∕r,

where r is the radial coordinate, approximately the distance from the
center of mass of the body with mass M.  Note the minus sign: the
gravitational potential is _larger_ at _greater_ distance from the
center of mass.  This makes sense because you need _more_ energy to be
there.

> Clocks merely count cycles of an oscillator,

Correct.

> which according to GR should run slow.
No; according to GR, _more_ proper time should elapse in the GPS orbit
than on the ground:

The elapsed proper time is given by (I already derived it here from the
Schwarzschild metric many times)

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

where r is the radial coordinate.  For a circular orbit we may use
Kepler's Third Law/Newton's Law of Universal Gravitation to substitute
the orbital speed

  v = √(G M∕r),

and to obtain

  Δτ = Δt √[1 − 3 G M∕(c² r)].

You can see that (for constant Δt) Δτ increases as r increases.  [And it
is equal to zero at r = 3 G M∕c² (1.5 Schwarzschild radii), which is how
light orbits a black hole in a circle there, producing its photon sphere.]

And that is indeed the case, as confirmed first (but not last) in 1977:

Easton, Roger L. et al. (1978) "Initial Results of the NAVSTAR GPS NTS-2
Satellite". "Frequency Determination".  Archived on 2025-12-06
(presumably PST) from the original
<https://apps.dtic.mil/sti/tr/pdf/ADA058591.pdf#page=15> (currently
offline due to maintenance)
<https://web.archive.org/web/20251206154234/https://apps.dtic.mil/sti/tr/pdf/ADA058591.pdf#page=15>
(retrieved: 2026-10-13 CEST)

So the clock aboard a GPS satellite counts (/would/ count) more cycles
there than it does on the ground.

If you then compare its time with the time on the ground (provided the
two clocks had been properly synchronized before), it appears as if the
clock on a GPS satellite would run faster than a clock of the same
design on the ground.

Thus a GPS satellite's clock is "slowed" (you cannot slow an atomic
clock, you can only count less cycles of its "ticking"; nowadays the
sending frequency is decreased instead), so that it appears as if it
runs as fast as the USNO Master Clock on the ground (so that the
received frequency is the same as written in the GPS Specification, and
not the blueshifted value).

See also:

Ashby, Neil (2003). "Relativity in the Global Positioning System."
In: "Living Reviews in Relativity". Springer.
<https://link.springer.com/article/10.12942/lrr-2003-1>

-- 
PointedEars

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

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#674382

On Tue, 13 Oct 2026 09:42:00 +0200, Thomas 'PointedEars' Lahn wrote:

> HenryWilson wrote:
>> Here is one to argue about. According to GR, light experiences a
>> redshift in frequency when sent into lower gravity potential.
> 
> No, _blueshift_, in a sense.  

AHAHAAAHAAHAHA! So you have changed the rules because you know I'm right.

> But in GR there is no _gravitational_
> potential in the Newtonian sense because gravitation is not explained as
> the consequence of the gravitational force.
> 
> [In GR, the gravitational potential is represented by the components of
> the metric tensor, but I think that this is way over your head.

The whole idea of Metric tensors and Schwarzschild radii are just 
unnecessary complications consequent of Eisntein's silly idea. If the 
whole GPS system used Newton throughout, everything would fall neatly into 
place, The orbits and clocks would not need so much continuous 
correcting.. 


>> How come clocks are claimed to run fast when sent into orbit.
> 
> From ground to orbit it is the opposite direction.
> 
> You appear to have a misconception as to how to calculate the
> gravitational potential according to Newton's theory of gravitation.
> To first approximation, it is given by
> 
>   Φ(r) ≈ −G M∕r,
> 
> where r is the radial coordinate, approximately the distance from the
> center of mass of the body with mass M.  Note the minus sign: 

Yes. It shouldn't be there. Integrating Newton's force equation removes 
the minus. .but that's way above your head.

>the
> gravitational potential is _larger_ at _greater_ distance from the
> center of mass.  This makes sense because you need _more_ energy to be
> there.

It makes no sense. It is just a concoction used to avoid the fact that 
light has mass.

>> Clocks merely count cycles of an oscillator,
> 
> Correct.
> 
>> which according to GR should run slow.
> No; according to GR, _more_ proper time should elapse in the GPS orbit
> than on the ground:

Again, another concoction used to avoid accepting that it slows down. 
 
> The elapsed proper time is given by (I already derived it here from the
> Schwarzschild metric many times)
> 
>   Δτ = Δt √[1 − 2 G M∕(c² r) − v²∕c²],
> 
> where r is the radial coordinate.  For a circular orbit we may use
> Kepler's Third Law/Newton's Law of Universal Gravitation to substitute
> the orbital speed
> 
>   v = √(G M∕r),

There is no square root. There is a fractional speed change of GM/rc^2 (at 
infinity)

> and to obtain
> 
>   Δτ = Δt √[1 − 3 G M∕(c² r)].
> 
> You can see that (for constant Δt) Δτ increases as r increases.  [And it
> is equal to zero at r = 3 G M∕c² (1.5 Schwarzschild radii), which is how
> light orbits a black hole in a circle there, producing its photon
> sphere.

Black holes are simple Newtonian phenomena..Their escape velocity is 
greater than c.

Time doesn't move or change. Everything in the universe moves along the 
same time axis at the same rate (relative to a second time axis)
 
> And that is indeed the case, as confirmed first (but not last) in 1977:
> 
> Easton, Roger L. et al. (1978) "Initial Results of the NAVSTAR GPS NTS-2
> Satellite". "Frequency Determination".  Archived on 2025-12-06
> (presumably PST) from the original
> <https://apps.dtic.mil/sti/tr/pdf/ADA058591.pdf#page=15> (currently
> offline due to maintenance)
> <https://web.archive.org/web/20251206154234/https://apps.dtic.mil/sti/
tr/pdf/ADA058591.pdf#page=15>
> (retrieved: 2026-10-13 CEST)
> 
> So the clock aboard a GPS satellite counts (/would/ count) more cycles
> there than it does on the ground.
> 
> If you then compare its time with the time on the ground (provided the
> two clocks had been properly synchronized before), it appears as if the
> clock on a GPS satellite would run faster than a clock of the same
> design on the ground.

Yes. like anything else, the clocks change slightly after losing 
gravitational self compression.

> Thus a GPS satellite's clock is "slowed" (you cannot slow an atomic
> clock, you can only count less cycles of its "ticking"; nowadays the
> sending frequency is decreased instead), so that it appears as if it
> runs as fast as the USNO Master Clock on the ground (so that the
> received frequency is the same as written in the GPS Specification, and
> not the blueshifted value).

Yes. Accepting Einstein has made the GPS system ridiculously and 
unnecessarily complicated. 

> See also:
> 
> Ashby, Neil (2003). "Relativity in the Global Positioning System."
> In: "Living Reviews in Relativity". Springer.
> <https://link.springer.com/article/10.12942/lrr-2003-1>

It is infintely easier if based on Newton.

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#674383

Ralph,

> It is infintely easier if based on Newton.

Excellent. Then actually do it.

Give us the Newtonian GPS model which you say makes everything "fall
neatly into place".

For a GPS satellite, derive from Newton alone:

    1. the gravitational clock-rate correction;
    2. the kinematic clock-rate correction;
    3. their signs;
    4. their numerical magnitudes;
    5. the resulting net correction;
    6. the signal propagation time used by the receiver.

Not "something changes because gravitational self compression is lost."

An equation.

Your "self compression" explanation is particularly interesting. GPS
uses atomic clocks. So please derive from Newtonian gravity how changing
the Earth's potential changes the relevant atomic transition frequency
by the observed amount.

What physical quantity in the atom changes?

How much?

Why exactly that much?

You also write:

> There is no square root.

Unfortunately Newton himself disagrees with you.

For a circular orbit Newton gives

    GMm/r² = mv²/r

hence

    v² = GM/r

and therefore

    v = sqrt(GM/r).

That square root isn't an Einsteinian conspiracy. It falls straight out
of Newton's equations.

Likewise,

    Phi = -GM/r

is not a "concoction". Since

    F/m = -GM/r²,

the potential satisfies

    -dPhi/dr = -GM/r²,

hence

    dPhi/dr = GM/r²

and, choosing Phi(infinity)=0,

    Phi = -GM/r.

Changing the arbitrary zero of potential cannot remove the physics.

And finally:

> Black holes are simple Newtonian phenomena..Their escape velocity is
> greater than c.

The old Newtonian escape-speed coincidence gives

    r = 2GM/c²

when v_escape=c.

It does not give you a GR black hole.

It gives no event horizon, no Schwarzschild geometry, no causal
structure, no gravitational time dilation, and no photon sphere at

    r = 3GM/c².

Indeed, your Newtonian "light has mass and gravity changes its speed"
model must now tell us what light actually does near that object.

This is the recurring problem.

You keep saying Newton is "infinitely easier" because you don't actually
carry the Newtonian model far enough to calculate the observables.

Newton is wonderfully easy if you stop immediately before the part where
it has to predict anything that distinguishes it from GR.

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#674385

On 10/13/2026 09:01 AM, Python wrote:
> Ralph,
>
>> It is infintely easier if based on Newton.
>
> Excellent. Then actually do it.
>
> Give us the Newtonian GPS model which you say makes everything "fall
> neatly into place".
>
> For a GPS satellite, derive from Newton alone:
>
>     1. the gravitational clock-rate correction;
>     2. the kinematic clock-rate correction;
>     3. their signs;
>     4. their numerical magnitudes;
>     5. the resulting net correction;
>     6. the signal propagation time used by the receiver.
>
> Not "something changes because gravitational self compression is lost."
>
> An equation.
>
> Your "self compression" explanation is particularly interesting. GPS
> uses atomic clocks. So please derive from Newtonian gravity how changing
> the Earth's potential changes the relevant atomic transition frequency
> by the observed amount.
>
> What physical quantity in the atom changes?
>
> How much?
>
> Why exactly that much?
>
> You also write:
>
>> There is no square root.
>
> Unfortunately Newton himself disagrees with you.
>
> For a circular orbit Newton gives
>
>     GMm/r² = mv²/r
>
> hence
>
>     v² = GM/r
>
> and therefore
>
>     v = sqrt(GM/r).
>
> That square root isn't an Einsteinian conspiracy. It falls straight out
> of Newton's equations.
>
> Likewise,
>
>     Phi = -GM/r
>
> is not a "concoction". Since
>
>     F/m = -GM/r²,
>
> the potential satisfies
>
>     -dPhi/dr = -GM/r²,
>
> hence
>
>     dPhi/dr = GM/r²
>
> and, choosing Phi(infinity)=0,
>
>     Phi = -GM/r.
>
> Changing the arbitrary zero of potential cannot remove the physics.
>
> And finally:
>
>> Black holes are simple Newtonian phenomena..Their escape velocity is
>> greater than c.
>
> The old Newtonian escape-speed coincidence gives
>
>     r = 2GM/c²
>
> when v_escape=c.
>
> It does not give you a GR black hole.
>
> It gives no event horizon, no Schwarzschild geometry, no causal
> structure, no gravitational time dilation, and no photon sphere at
>
>     r = 3GM/c².
>
> Indeed, your Newtonian "light has mass and gravity changes its speed"
> model must now tell us what light actually does near that object.
>
> This is the recurring problem.
>
> You keep saying Newton is "infinitely easier" because you don't actually
> carry the Newtonian model far enough to calculate the observables.
>
> Newton is wonderfully easy if you stop immediately before the part where
> it has to predict anything that distinguishes it from GR.


Real space-contraction
with distinct space-contraction-linear
and space-contraction-rotational.

Not exactly Newtonian, not even exactly Galilean,
since Galileo says nothing about spinning bodies,
where it is well-known that accounts of kinetics
the linear and kinematics the rotational have
effects of the rotational not explained by Magnus
and Coriolis, "Newton's zero-eth" laws, that would
automatically equip "the laws of motion" and classical
mechanics.

Then, with "Newtonian" in that, it's Newtonian.

And Euclidean, ....

Derivations of the Newtonian can simply have added
"spurious 2's" to give accounts what otherwise
would be explained with precession after nutation.



Einstein makes a distinction linear and rotational,
calls it his "second mass/energy equivalency formula",
which most people don't know, though "E = mc^2" is
the only formula of physics anybody knows, which is
a truncation, anyways.


About "The System of the World", perhaps
you better ask Kepler than Newton.



Anyways the real space-contraction then makes the
settings for length-contraction and time-dilation
together, explaining all the effects.


Dark Matter and Dark Energy have falsified, violated
the naive accounts you have, yet, tossing the ball
around already does, classical mechanics.

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#674415

On 10/13/2026 09:10 AM, Ross Finlayson wrote:
> On 10/13/2026 09:01 AM, Python wrote:
>> Ralph,
>>
>>> It is infintely easier if based on Newton.
>>
>> Excellent. Then actually do it.
>>
>> Give us the Newtonian GPS model which you say makes everything "fall
>> neatly into place".
>>
>> For a GPS satellite, derive from Newton alone:
>>
>>     1. the gravitational clock-rate correction;
>>     2. the kinematic clock-rate correction;
>>     3. their signs;
>>     4. their numerical magnitudes;
>>     5. the resulting net correction;
>>     6. the signal propagation time used by the receiver.
>>
>> Not "something changes because gravitational self compression is lost."
>>
>> An equation.
>>
>> Your "self compression" explanation is particularly interesting. GPS
>> uses atomic clocks. So please derive from Newtonian gravity how changing
>> the Earth's potential changes the relevant atomic transition frequency
>> by the observed amount.
>>
>> What physical quantity in the atom changes?
>>
>> How much?
>>
>> Why exactly that much?
>>
>> You also write:
>>
>>> There is no square root.
>>
>> Unfortunately Newton himself disagrees with you.
>>
>> For a circular orbit Newton gives
>>
>>     GMm/r² = mv²/r
>>
>> hence
>>
>>     v² = GM/r
>>
>> and therefore
>>
>>     v = sqrt(GM/r).
>>
>> That square root isn't an Einsteinian conspiracy. It falls straight out
>> of Newton's equations.
>>
>> Likewise,
>>
>>     Phi = -GM/r
>>
>> is not a "concoction". Since
>>
>>     F/m = -GM/r²,
>>
>> the potential satisfies
>>
>>     -dPhi/dr = -GM/r²,
>>
>> hence
>>
>>     dPhi/dr = GM/r²
>>
>> and, choosing Phi(infinity)=0,
>>
>>     Phi = -GM/r.
>>
>> Changing the arbitrary zero of potential cannot remove the physics.
>>
>> And finally:
>>
>>> Black holes are simple Newtonian phenomena..Their escape velocity is
>>> greater than c.
>>
>> The old Newtonian escape-speed coincidence gives
>>
>>     r = 2GM/c²
>>
>> when v_escape=c.
>>
>> It does not give you a GR black hole.
>>
>> It gives no event horizon, no Schwarzschild geometry, no causal
>> structure, no gravitational time dilation, and no photon sphere at
>>
>>     r = 3GM/c².
>>
>> Indeed, your Newtonian "light has mass and gravity changes its speed"
>> model must now tell us what light actually does near that object.
>>
>> This is the recurring problem.
>>
>> You keep saying Newton is "infinitely easier" because you don't actually
>> carry the Newtonian model far enough to calculate the observables.
>>
>> Newton is wonderfully easy if you stop immediately before the part where
>> it has to predict anything that distinguishes it from GR.
>
>
> Real space-contraction
> with distinct space-contraction-linear
> and space-contraction-rotational.
>
> Not exactly Newtonian, not even exactly Galilean,
> since Galileo says nothing about spinning bodies,
> where it is well-known that accounts of kinetics
> the linear and kinematics the rotational have
> effects of the rotational not explained by Magnus
> and Coriolis, "Newton's zero-eth" laws, that would
> automatically equip "the laws of motion" and classical
> mechanics.
>
> Then, with "Newtonian" in that, it's Newtonian.
>
> And Euclidean, ....
>
> Derivations of the Newtonian can simply have added
> "spurious 2's" to give accounts what otherwise
> would be explained with precession after nutation.
>
>
>
> Einstein makes a distinction linear and rotational,
> calls it his "second mass/energy equivalency formula",
> which most people don't know, though "E = mc^2" is
> the only formula of physics anybody knows, which is
> a truncation, anyways.
>
>
> About "The System of the World", perhaps
> you better ask Kepler than Newton.
>
>
>
> Anyways the real space-contraction then makes the
> settings for length-contraction and time-dilation
> together, explaining all the effects.
>
>
> Dark Matter and Dark Energy have falsified, violated
> the naive accounts you have, yet, tossing the ball
> around already does, classical mechanics.
>
>


See, these sorts of accounts are not readily disputable.

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#674419

HenryWilson wrote:
> On Tue, 13 Oct 2026 09:42:00 +0200, Thomas 'PointedEars' Lahn wrote:
>> HenryWilson wrote:
>>> Here is one to argue about. According to GR, light experiences a
>>> redshift in frequency when sent into lower gravity potential.
>>
>> No, _blueshift_, in a sense.  
> 
> AHAHAAAHAAHAHA! So you have changed the rules because you know I'm right.

No, I have explained your misconception to you.

>> But in GR there is no _gravitational_
>> potential in the Newtonian sense because gravitation is not explained as
>> the consequence of the gravitational force.
>>
>> [In GR, the gravitational potential is represented by the components of
>> the metric tensor, but I think that this is way over your head.
> 
> The whole idea of Metric tensors and Schwarzschild radii are just 
> unnecessary complications consequent of Eisntein's silly idea.
                                          ^^^^^^^^ aggravated? :-D

No, they describe very precisely what is going on.  Black holes have
been observed, too, and they are (at least from the outside) as GR
predicts, and NOT as Newtonian mechanics predicts:

<https://en.wikipedia.org/wiki/Sagittarius_A*>

<https://en.wikipedia.org/wiki/Astrophysical_jet#Relativistic_jet>

> If the whole GPS system used Newton throughout, everything would fall
> neatly into place,

No, it would simply not work as the satellite clock would be ahead of
the ground clocks by 38.2752 μs per standard day.  How do we /know/
that?  We /tried/ it _before_ with an atomic clock that was in all
aspects the same as a clock on the ground.  Read page 11 of the NAVSTAR
GPS NTS-2 report (page 15 in the PDF document).

Also, if the speed of light in vacuum would not be finite and constant,
the distance to a satellite could not even be calculated, and so the
location of the receiver could not be calculated.

>>> How come clocks are claimed to run fast when sent into orbit.
>>
>> From ground to orbit it is the opposite direction.
>>
>> You appear to have a misconception as to how to calculate the
>> gravitational potential according to Newton's theory of gravitation.
>> To first approximation, it is given by
>>
>>   Φ(r) ≈ −G M∕r,
>>
>> where r is the radial coordinate, approximately the distance from the
>> center of mass of the body with mass M.  Note the minus sign: 
> 
> Yes. It shouldn't be there.

It should be.

> Integrating Newton's force equation removes the minus.

Wrong.

In Newtonian mechanics, the gravitational force is an _attractive_,
therefore _centripetal_ force, so it acts _opposite_ to the direction of
the radius vector r⃗ (which is anchored at the center of mass, pointing
outwards) whose magnitude (Euclidean norm) is r:

     F⃗(r⃗ ) = −G M m∕r² (r⃗∕r).

The gravitational force is by definition the _negative_ of the gradient
of the gravitational potential energy U, and the gravitational potential
Φ is by definition the gravitational potential energy per unit (test)
mass m, Φ = U/m.  So U = m Φ, and

     F⃗(r⃗ ) = −∇U(r⃗ ) = −m ∇Φ(r⃗ )≈ −m ∇(−G M∕r) = G M m ∇(1∕r).

       1∕r = 1∕√(r²)
           = 1∕√(x² + y² + z²),  r⃗ = [x, y, z]ᵀ
           = 1∕(x² + y² + z²)^{1∕2}
           =   (x² + y² + z²)^{−1∕2}

  ⇒ ∇(1∕r) = [∂_x (x² + y² + z²)^{−1∕2},
              ∂_y (x² + y² + z²)^{−1∕2},
              ∂_z (x² + y² + z²)^{−1∕2}]ᵀ

           = [−1∕2 (x² + y² + z²)^{−3∕2} ∂_x (x² + y² + z²),
              −1∕2 (x² + y² + z²)^{−3∕2} ∂_y (x² + y² + z²),
              −1∕2 (x² + y² + z²)^{−3∕2} ∂_z (x² + y² + z²)]ᵀ

           = [−1∕2 (r²)^{−3∕2} 2x,
              −1∕2 (r²)^{−3∕2} 2y,
              −1∕2 (r²)^{−3∕2} 2z]ᵀ

           = [−r⁻³ x,
              −r⁻³ y,
              −r⁻³ z]ᵀ

           = [−x∕r³, −y∕r³, −z∕r³]ᵀ
           = −1/r³ [x, y, z]ᵀ
           = −r⃗∕r³

  ⇒  F⃗(r⃗ ) = G M m ∇(1∕r) = −G M m r⃗∕r³ = −G M m∕r² (r⃗∕r).

Therefore, in order to obtain an _attractive_, _centripetal_
gravitational force, the gravitational potential MUST have that minus
sign (too). ∎

Alternatively, instead of simply assuming the form of the *gravitational
potential energy*, we /find/ it by calculating the negative line
integral of the (measured) gravitational force over a path from a point
at "infinite distance" to a point of reference at a finite distance r
from the center of mass.  Because the gravitational potential energy at
the latter point is the negative of the work that needs to be done to
bring an object from infinity to the reference point.

Because the potential energy must not depend on the shape of the path,
only its end points (there is only a potential energy if the force is
conservative), and the force (field) is spherically symmetric, so must
be the associated potential energy (field), we can choose a path that is
easy to integrate over.  The easiest path to integrate over is a radial
one (i.e. in spherical coordinates at constant polar angle and azimuth):

  U(r) =  W_{r⃗ → ∞ }
       = −W_{∞ → r⃗ }
       = −∫_{∞ → r⃗ } dr⃗' ⋅ F⃗(r⃗')
       = −∫_∞^r ‖dr⃗'‖ ‖−G M m/(r')² (r⃗'∕r')‖ cos(∠[dr⃗', F⃗(r⃗')])
       = −∫_∞^r  dr'  ‖−G M m/(r')² (r⃗'∕r')‖ cos(π)
       = −∫_∞^r  dr'  ‖−G M m/(r')² (r⃗'∕r')‖ (−1)
       = |−G M m| ∫_∞^r dr' |1/(r')²| ‖r⃗'∕r'‖
       =   G M m  ∫_∞^r dr'  1/(r')²
       =  −G M m  1/r'|_∞^r
       =  −G M m  (1/r − lim{r' → ∞} 1/r')
       =  −G M m/r,

where ‖⋅‖ means the Euclidean norm of a 3-vector, and r' = ‖r⃗'‖.

The gravitational potential is the gravitational potential energy per
unit (test) mass m:

  Φ(r) = U(r)/m = (−G M m/r)/m = −G M∕r. ∎

> .but that's way above your head.

No, vector calculus is way over _your_ head, wannabe physicist, wannabe
physics teacher.  Both calculations above are already taught in
_freshman_ (first- and second-semester) Physics classes (BTDT).

>> the gravitational potential is _larger_ at _greater_ distance from the
>> center of mass.  This makes sense because you need _more_ energy to be
>> there.
> 
> It makes no sense. It is just a concoction used to avoid the fact that 
> light has mass.

Light does NOT have (non-zero) mass.  Effects that are communicated by
objects that have non-zero mass cannot and do not propagate at the speed
of light in vacuum (c).

>>> which according to GR should run slow.
>> No; according to GR, _more_ proper time should elapse in the GPS orbit
>> than on the ground:
> 
> Again, another concoction used to avoid accepting that it slows down. 

It does not slow down.  Can't you read?  How could it have measured
_more_ time than atomic clocks on the ground by slowing down?  *facepalm*

>> The elapsed proper time is given by (I already derived it here from the
>> Schwarzschild metric many times)
>>
>>   Δτ = Δt √[1 − 2 G M∕(c² r) − v²∕c²],
>>
>> where r is the radial coordinate.  For a circular orbit we may use
>> Kepler's Third Law/Newton's Law of Universal Gravitation to substitute
>> the orbital speed
>>
>>   v = √(G M∕r),
> 
> There is no square root. 

False.  If for simplicity we consider just the magnitude of the
gravitational force, we find for the orbital speed v (assuming the
experimentally confirmed equivalence of inertial and gravitational mass):

    F_centripetal = m a = m v²∕r =    G M m∕r² = F_gravitational

  ⇔                         v²∕r =    G M∕r²
  ⇔                         v²   =    G M∕r

  ⇔                         v    = √(G M∕r). ∎

Or from Kepler's Third Law we find for circular orbits around the same
object with mass M (where the radius of the orbit is equal to its
semi-major axis; and the orbital speed is constant, considering Kepler's
Second Law), we find for the orbital speed of one object (with Kepler it
was a planet, but we found [not least thanks to Galilei and Newton] that
this works for all celestial objects):

        T₁²    ∕    T₂²     = r₁³∕r₂²

  ⇔  4π T₁²    ∕(4π T₂²)    = r₁³∕r₂³
  ⇔ (2π T₁)²   ∕(2π T₂)²    = r₁³∕r₂³
  ⇔ (2π T₁)²   ∕(2π T₂)²    = r₁³∕r₂³
  ⇔ (2π T₂)²   ∕(2π T₁)²    = r₂³∕r₁³
  ⇔ (2π∕T₁)²   ∕(2π/T₂)²    = r₂³∕r₁³
  ⇔ (2π r₁∕T₁)²∕(2π r₂∕T₂)² = r₂ ∕r₁
  ⇔ (2π r₁∕T₁)²∕(2π r₂∕T₂)² = r₂ ∕r₁
  ⇔         v₁²∕v₂²         =     r₂∕r₁
  ⇔         v₁²∕v₂²         = G M r₂∕(G M r₁)
  ⇒                     v₁² = G M∕r₁

  ⇔                     v₁  = √(G M∕r₁). ∎

Again, /freshman/ (astro)physics.

> There is a fractional speed change of GM/rc^2 (at infinity)

What is "c" supposed to mean there? :-D

>> and to obtain
>>
>>   Δτ = Δt √[1 − 3 G M∕(c² r)].
>>
>> You can see that (for constant Δt) Δτ increases as r increases.  [And it
>> is equal to zero at r = 3 G M∕c² (1.5 Schwarzschild radii), which is how
>> light orbits a black hole in a circle there, producing its photon
>> sphere.
> 
> Black holes are simple Newtonian phenomena..Their escape velocity is 
> greater than c.

False twice.

> Time doesn't move or change.

Time does change, obviously (even in Newtonian mechanics).
Nobody except you has /ever/ said that "time moves".

> Everything in the universe moves along the same time axis at the same
> rate (relative to a second time axis)
False again; falsified by observational evidence (not just GPS).

>> If you then compare its time with the time on the ground (provided the
>> two clocks had been properly synchronized before), it appears as if the
>> clock on a GPS satellite would run faster than a clock of the same
>> design on the ground.
> 
> Yes. like anything else, the clocks change slightly after losing 
> gravitational self compression.

Such a nonsense, it's not even wrong.

>> Thus a GPS satellite's clock is "slowed" (you cannot slow an atomic
>> clock, you can only count less cycles of its "ticking"; nowadays the
>> sending frequency is decreased instead), so that it appears as if it
>> runs as fast as the USNO Master Clock on the ground (so that the
>> received frequency is the same as written in the GPS Specification, and
>> not the blueshifted value).
> 
> Yes. Accepting Einstein has made the GPS system ridiculously and 
> unnecessarily complicated. 

No, it makes it _work_.

>> See also:
>>
>> Ashby, Neil (2003). "Relativity in the Global Positioning System."
>> In: "Living Reviews in Relativity". Springer.
>> <https://link.springer.com/article/10.12942/lrr-2003-1>
> 
> It is infintely easier if based on Newton.

It would simply not work.  We have _tested_ that, and in fact it is
being tested and confirmed every nanosecond by the fact that it _works_
based on what GR predicts.  It would NOT work if GR's predictions were
wrong.  So they /are/ NOT wrong, and GR is NOT wrong, no matter how
often you in your (blissful?) ignorance claim the opposite.

-- 
PointedEars

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

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#674428

On 10/14/2026 08:30 AM, Thomas 'PointedEars' Lahn wrote:
> HenryWilson wrote:
>> On Tue, 13 Oct 2026 09:42:00 +0200, Thomas 'PointedEars' Lahn wrote:
>>> HenryWilson wrote:
>>>> Here is one to argue about. According to GR, light experiences a
>>>> redshift in frequency when sent into lower gravity potential.
>>>
>>> No, _blueshift_, in a sense.
>>
>> AHAHAAAHAAHAHA! So you have changed the rules because you know I'm right.
>
> No, I have explained your misconception to you.
>
>>> But in GR there is no _gravitational_
>>> potential in the Newtonian sense because gravitation is not explained as
>>> the consequence of the gravitational force.
>>>
>>> [In GR, the gravitational potential is represented by the components of
>>> the metric tensor, but I think that this is way over your head.
>>
>> The whole idea of Metric tensors and Schwarzschild radii are just
>> unnecessary complications consequent of Eisntein's silly idea.
>                                            ^^^^^^^^ aggravated? :-D
>
> No, they describe very precisely what is going on.  Black holes have
> been observed, too, and they are (at least from the outside) as GR
> predicts, and NOT as Newtonian mechanics predicts:
>
> <https://en.wikipedia.org/wiki/Sagittarius_A*>
>
> <https://en.wikipedia.org/wiki/Astrophysical_jet#Relativistic_jet>
>
>> If the whole GPS system used Newton throughout, everything would fall
>> neatly into place,
>
> No, it would simply not work as the satellite clock would be ahead of
> the ground clocks by 38.2752 μs per standard day.  How do we /know/
> that?  We /tried/ it _before_ with an atomic clock that was in all
> aspects the same as a clock on the ground.  Read page 11 of the NAVSTAR
> GPS NTS-2 report (page 15 in the PDF document).
>
> Also, if the speed of light in vacuum would not be finite and constant,
> the distance to a satellite could not even be calculated, and so the
> location of the receiver could not be calculated.
>
>>>> How come clocks are claimed to run fast when sent into orbit.
>>>
>>>  From ground to orbit it is the opposite direction.
>>>
>>> You appear to have a misconception as to how to calculate the
>>> gravitational potential according to Newton's theory of gravitation.
>>> To first approximation, it is given by
>>>
>>>    Φ(r) ≈ −G M∕r,
>>>
>>> where r is the radial coordinate, approximately the distance from the
>>> center of mass of the body with mass M.  Note the minus sign:
>>
>> Yes. It shouldn't be there.
>
> It should be.
>
>> Integrating Newton's force equation removes the minus.
>
> Wrong.
>
> In Newtonian mechanics, the gravitational force is an _attractive_,
> therefore _centripetal_ force, so it acts _opposite_ to the direction of
> the radius vector r⃗ (which is anchored at the center of mass, pointing
> outwards) whose magnitude (Euclidean norm) is r:
>
>       F⃗(r⃗ ) = −G M m∕r² (r⃗∕r).
>
> The gravitational force is by definition the _negative_ of the gradient
> of the gravitational potential energy U, and the gravitational potential
> Φ is by definition the gravitational potential energy per unit (test)
> mass m, Φ = U/m.  So U = m Φ, and
>
>       F⃗(r⃗ ) = −∇U(r⃗ ) = −m ∇Φ(r⃗ )≈ −m ∇(−G M∕r) = G M m ∇(1∕r).
>
>         1∕r = 1∕√(r²)
>             = 1∕√(x² + y² + z²),  r⃗ = [x, y, z]ᵀ
>             = 1∕(x² + y² + z²)^{1∕2}
>             =   (x² + y² + z²)^{−1∕2}
>
>    ⇒ ∇(1∕r) = [∂_x (x² + y² + z²)^{−1∕2},
>                ∂_y (x² + y² + z²)^{−1∕2},
>                ∂_z (x² + y² + z²)^{−1∕2}]ᵀ
>
>             = [−1∕2 (x² + y² + z²)^{−3∕2} ∂_x (x² + y² + z²),
>                −1∕2 (x² + y² + z²)^{−3∕2} ∂_y (x² + y² + z²),
>                −1∕2 (x² + y² + z²)^{−3∕2} ∂_z (x² + y² + z²)]ᵀ
>
>             = [−1∕2 (r²)^{−3∕2} 2x,
>                −1∕2 (r²)^{−3∕2} 2y,
>                −1∕2 (r²)^{−3∕2} 2z]ᵀ
>
>             = [−r⁻³ x,
>                −r⁻³ y,
>                −r⁻³ z]ᵀ
>
>             = [−x∕r³, −y∕r³, −z∕r³]ᵀ
>             = −1/r³ [x, y, z]ᵀ
>             = −r⃗∕r³
>
>    ⇒  F⃗(r⃗ ) = G M m ∇(1∕r) = −G M m r⃗∕r³ = −G M m∕r² (r⃗∕r).
>
> Therefore, in order to obtain an _attractive_, _centripetal_
> gravitational force, the gravitational potential MUST have that minus
> sign (too). ∎
>
> Alternatively, instead of simply assuming the form of the *gravitational
> potential energy*, we /find/ it by calculating the negative line
> integral of the (measured) gravitational force over a path from a point
> at "infinite distance" to a point of reference at a finite distance r
> from the center of mass.  Because the gravitational potential energy at
> the latter point is the negative of the work that needs to be done to
> bring an object from infinity to the reference point.
>
> Because the potential energy must not depend on the shape of the path,
> only its end points (there is only a potential energy if the force is
> conservative), and the force (field) is spherically symmetric, so must
> be the associated potential energy (field), we can choose a path that is
> easy to integrate over.  The easiest path to integrate over is a radial
> one (i.e. in spherical coordinates at constant polar angle and azimuth):
>
>    U(r) =  W_{r⃗ → ∞ }
>         = −W_{∞ → r⃗ }
>         = −∫_{∞ → r⃗ } dr⃗' ⋅ F⃗(r⃗')
>         = −∫_∞^r ‖dr⃗'‖ ‖−G M m/(r')² (r⃗'∕r')‖ cos(∠[dr⃗', F⃗(r⃗')])
>         = −∫_∞^r  dr'  ‖−G M m/(r')² (r⃗'∕r')‖ cos(π)
>         = −∫_∞^r  dr'  ‖−G M m/(r')² (r⃗'∕r')‖ (−1)
>         = |−G M m| ∫_∞^r dr' |1/(r')²| ‖r⃗'∕r'‖
>         =   G M m  ∫_∞^r dr'  1/(r')²
>         =  −G M m  1/r'|_∞^r
>         =  −G M m  (1/r − lim{r' → ∞} 1/r')
>         =  −G M m/r,
>
> where ‖⋅‖ means the Euclidean norm of a 3-vector, and r' = ‖r⃗'‖.
>
> The gravitational potential is the gravitational potential energy per
> unit (test) mass m:
>
>    Φ(r) = U(r)/m = (−G M m/r)/m = −G M∕r. ∎
>
>> .but that's way above your head.
>
> No, vector calculus is way over _your_ head, wannabe physicist, wannabe
> physics teacher.  Both calculations above are already taught in
> _freshman_ (first- and second-semester) Physics classes (BTDT).
>
>>> the gravitational potential is _larger_ at _greater_ distance from the
>>> center of mass.  This makes sense because you need _more_ energy to be
>>> there.
>>
>> It makes no sense. It is just a concoction used to avoid the fact that
>> light has mass.
>
> Light does NOT have (non-zero) mass.  Effects that are communicated by
> objects that have non-zero mass cannot and do not propagate at the speed
> of light in vacuum (c).
>
>>>> which according to GR should run slow.
>>> No; according to GR, _more_ proper time should elapse in the GPS orbit
>>> than on the ground:
>>
>> Again, another concoction used to avoid accepting that it slows down.
>
> It does not slow down.  Can't you read?  How could it have measured
> _more_ time than atomic clocks on the ground by slowing down?  *facepalm*
>
>>> The elapsed proper time is given by (I already derived it here from the
>>> Schwarzschild metric many times)
>>>
>>>    Δτ = Δt √[1 − 2 G M∕(c² r) − v²∕c²],
>>>
>>> where r is the radial coordinate.  For a circular orbit we may use
>>> Kepler's Third Law/Newton's Law of Universal Gravitation to substitute
>>> the orbital speed
>>>
>>>    v = √(G M∕r),
>>
>> There is no square root.
>
> False.  If for simplicity we consider just the magnitude of the
> gravitational force, we find for the orbital speed v (assuming the
> experimentally confirmed equivalence of inertial and gravitational mass):
>
>      F_centripetal = m a = m v²∕r =    G M m∕r² = F_gravitational
>
>    ⇔                         v²∕r =    G M∕r²
>    ⇔                         v²   =    G M∕r
>
>    ⇔                         v    = √(G M∕r). ∎
>
> Or from Kepler's Third Law we find for circular orbits around the same
> object with mass M (where the radius of the orbit is equal to its
> semi-major axis; and the orbital speed is constant, considering Kepler's
> Second Law), we find for the orbital speed of one object (with Kepler it
> was a planet, but we found [not least thanks to Galilei and Newton] that
> this works for all celestial objects):
>
>          T₁²    ∕    T₂²     = r₁³∕r₂²
>
>    ⇔  4π T₁²    ∕(4π T₂²)    = r₁³∕r₂³
>    ⇔ (2π T₁)²   ∕(2π T₂)²    = r₁³∕r₂³
>    ⇔ (2π T₁)²   ∕(2π T₂)²    = r₁³∕r₂³
>    ⇔ (2π T₂)²   ∕(2π T₁)²    = r₂³∕r₁³
>    ⇔ (2π∕T₁)²   ∕(2π/T₂)²    = r₂³∕r₁³
>    ⇔ (2π r₁∕T₁)²∕(2π r₂∕T₂)² = r₂ ∕r₁
>    ⇔ (2π r₁∕T₁)²∕(2π r₂∕T₂)² = r₂ ∕r₁
>    ⇔         v₁²∕v₂²         =     r₂∕r₁
>    ⇔         v₁²∕v₂²         = G M r₂∕(G M r₁)
>    ⇒                     v₁² = G M∕r₁
>
>    ⇔                     v₁  = √(G M∕r₁). ∎
>
> Again, /freshman/ (astro)physics.
>
>> There is a fractional speed change of GM/rc^2 (at infinity)
>
> What is "c" supposed to mean there? :-D
>
>>> and to obtain
>>>
>>>    Δτ = Δt √[1 − 3 G M∕(c² r)].
>>>
>>> You can see that (for constant Δt) Δτ increases as r increases.  [And it
>>> is equal to zero at r = 3 G M∕c² (1.5 Schwarzschild radii), which is how
>>> light orbits a black hole in a circle there, producing its photon
>>> sphere.
>>
>> Black holes are simple Newtonian phenomena..Their escape velocity is
>> greater than c.
>
> False twice.
>
>> Time doesn't move or change.
>
> Time does change, obviously (even in Newtonian mechanics).
> Nobody except you has /ever/ said that "time moves".
>
>> Everything in the universe moves along the same time axis at the same
>> rate (relative to a second time axis)
> False again; falsified by observational evidence (not just GPS).
>
>>> If you then compare its time with the time on the ground (provided the
>>> two clocks had been properly synchronized before), it appears as if the
>>> clock on a GPS satellite would run faster than a clock of the same
>>> design on the ground.
>>
>> Yes. like anything else, the clocks change slightly after losing
>> gravitational self compression.
>
> Such a nonsense, it's not even wrong.
>
>>> Thus a GPS satellite's clock is "slowed" (you cannot slow an atomic
>>> clock, you can only count less cycles of its "ticking"; nowadays the
>>> sending frequency is decreased instead), so that it appears as if it
>>> runs as fast as the USNO Master Clock on the ground (so that the
>>> received frequency is the same as written in the GPS Specification, and
>>> not the blueshifted value).
>>
>> Yes. Accepting Einstein has made the GPS system ridiculously and
>> unnecessarily complicated.
>
> No, it makes it _work_.
>
>>> See also:
>>>
>>> Ashby, Neil (2003). "Relativity in the Global Positioning System."
>>> In: "Living Reviews in Relativity". Springer.
>>> <https://link.springer.com/article/10.12942/lrr-2003-1>
>>
>> It is infintely easier if based on Newton.
>
> It would simply not work.  We have _tested_ that, and in fact it is
> being tested and confirmed every nanosecond by the fact that it _works_
> based on what GR predicts.  It would NOT work if GR's predictions were
> wrong.  So they /are/ NOT wrong, and GR is NOT wrong, no matter how
> often you in your (blissful?) ignorance claim the opposite.
>


For "the true centrifugal" vis-a-vis the "centripetal", with
regards to which is "real" and which is "fictitious" (yet,
applies and is real), is that the centripetal is an account
of classical forces, yet, in a potentialistic setting where
the potential fields are the real fields, is room for a
"true centrifugal".

Yes, we all sat the standard linear curriculum, where it was
introduced first the concept of the centrifgual, then the
formalism of the centripetal.

It's not dis-similar the pre-calculus to introduce the limit
and after Zeno's arguments to dis-suade from the clock arithmetic
for the field arithmetic, or similarly for .999 vis-a-vis 1,
about the notation, and the implicits, with two definite and different
mechanisms, about the same thing.

So, space-contraction as real, and sc-linear and sc-rotational
as distinct, and potential fields as real, is a very usual
account, that reason arrives at must be so (and experiment
does not falsify).

So, for "room in the theory" as both "room in the formalism"
(deriving as via different implicits) and "room in the data"
(not being falsified) then has that automatically more so.

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#674781

On 12/10/2026 03:01, HenryWilson wrote:

> Here is one to argue about. According to GR, light experiences a redshift
> in frequency when sent into lower gravity potential.

According to GR light from higher to deeper potiential is blue shifted.
More generally, the period of any wave or any periodic signal or
duration of any process is seen longer at lower altitude.

-- 
Mikko

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#674782

On 10/21/2026 10:04 AM, Mikko wrote:
> On 12/10/2026 03:01, HenryWilson wrote:
> 
>> Here is one to argue about. According to GR, light experiences a redshift
>> in frequency when sent into lower gravity potential.
> 
> According to GR light from higher to deeper potiential is blue shifted.
> More generally, the period of any wave or any periodic signal or
> duration of any process is seen longer at lower altitude.

Another thing your mad religion is asserting
is that perfect clocks are desynchronizing clocks.
The idiot you're worshiping could as well
imagine that perfect bridges are collapsing
bridges.



> 

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#674961

Mikko <mikko.levanto@iki.fi> wrote or quoted:
>According to GR light from higher to deeper potiential is blue shifted.

  Ok. "Blueshifted" means the frequency increases and the
  period gets shorter.

>More generally, the period of any wave or any periodic signal or
>duration of any process is seen longer at lower altitude.

  "Longer" applied to light means "redshifted". And some
  inattentive readers now might read your sentence to say,
  "The period of light is redshifted at lower altitude."
  and see a contradiction to the first sentence.

  So, one should clarify that light at a lower altitude is
  redshifted /when seen from above/.

  In other words:

  Let's say there is a source SH of monochromatic light resting 40
  Mm above the surface of the Earth together with an observer OH.
  ("H"="high")

  Let's say there is a source SL of monochromatic light on the
  surface of the Earth together with an observer OL. ("L"="low")

  Let's call the frequency of the light of SH as observed by OH "fHH".
  Let's call the frequency of the light of SL as observed by OH "fLH".
  Let's call the frequency of the light of SH as observed by OL "fHL".
  Let's call the frequency of the light of SL as observed by OL "fLL".

  Then, fHH < fHL and fLH < fLL.
  

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#675066

On 24 Oct 2026 20:18:36 GMT, Stefan Ram wrote:

> Mikko <mikko.levanto@iki.fi> wrote or quoted:
>>According to GR light from higher to deeper potiential is blue shifted.
> 
>   Ok. "Blueshifted" means the frequency increases and the period gets
>   shorter.
> 
>>More generally, the period of any wave or any periodic signal or
>>duration of any process is seen longer at lower altitude.
> 
>   "Longer" applied to light means "redshifted". And some inattentive
>   readers now might read your sentence to say,
>   "The period of light is redshifted at lower altitude."
>   and see a contradiction to the first sentence.
> 
>   So, one should clarify that light at a lower altitude is redshifted
>   /when seen from above/.
> 
>   In other words:
> 
>   Let's say there is a source SH of monochromatic light resting 40 Mm
>   above the surface of the Earth together with an observer OH.
>   ("H"="high")
> 
>   Let's say there is a source SL of monochromatic light on the surface
>   of the Earth together with an observer OL. ("L"="low")
> 
>   Let's call the frequency of the light of SH as observed by OH "fHH".
>   Let's call the frequency of the light of SL as observed by OH "fLH".
>   Let's call the frequency of the light of SH as observed by OL "fHL".
>   Let's call the frequency of the light of SL as observed by OL "fLL".
> 
>   Then, fHH < fHL and fLH < fLL.

Define 'frequency' please.

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