2021-09-13 05:53:18 UTC
The approximation used by the GPS Directoriate to explain the part of
gravitational blue shifting (45 usec) since it was made public by 1989, and
that plagues the web in any article dealing with the 38.5 μsec/day clock's
shift was INVENTED by Einstein and published on In June 1911 in the Annalen
der Physik as "Uber den Einfluβ der Schwerkraft auf die Ausbreitung des Lichtes" ("On the Influence of Gravitation on the Propagation of Light").
Here is a link to the 1923 translation of that paper, so you can fact-check it:
This old and forgotten paper was not related in any way to the mathematics
of his GR, presented to the Prussian Academy of Science on Nov. 25, 1915.
It anticipates results that come out from complex and non-linear set
of equations that form "his" gravitational field equation by 54 months,
and the formulae into it is exclusively based on his 1905 SR plus E=mc²,
plus a lot of fallacies to hide the use of Planck's quanta of energy and
to justify his assertion of equality between inertial and gravitational
I'll only copy here excerpts from such 1911 paper, what can be verified by
anyone by just clicking on the link and read it. It's EXTREMELY simple, but
fallacious as hell.
Maybe you'll wonder how such extremely elemental but fallacious
invention of concepts out of thin air survived not only 54 months to
be embedded into the complexity of GR. You also might wonder how
come the "exact analytical solution" given by Schwarzschild and later
corrected by Hilbert (1917) can be TUNED to match such simplicity.
Also, you might wonder how come such 1911 fallacies survived until
today and has been spread to any article or paper (as approximation)
to justify the Schwarzschild's effect on the 38.5 μsec/day.
Now, the excerpts from the 1911 paper:
§ 2. On the Gravitation of Energy
The theory of relativity shows that the inertial mass of a body increases
with the energy it contains; if the increase of energy amounts to E, the
increase in inertial mass is equal to E/c², where c denotes the velocity of
light. Now, is there an increase of gravitational mass corresponding to
this increase of inertial mass?
We consider the process of transmission of energy by radiation from S2
to S1 from a system K0, which is free of acceleration. At the moment
when the radiation energy E2 is emitted from S2 toward S1, let the velocity
of K′ relative to K0 be ZERO. The radiation will arrive at S1 when the time
h/c has elapsed (to a first approximation).
But at this moment the velocity of S1 relative to K0 is γh/c = v. Therefore
by the ordinary theory of relativity the radiation arriving at S1 does not possess the energy E2, but a greater energy E1, which is related to E2, to
a first approximation, by the equation:
(1) E1 = E2 . (1+ v/c) = E2 . (1+γh/c²)
By our ASSUMPTION exactly the same relation HOLDS if the same
process takes place in the system K, which is NOT ACCELERATED, but
is provided with a GRAVITATIONAL FIELD.
In this case we may replace γh by the potential Φ of the gravitation vector in S2, if the arbitrary constant of Φ in S1 is set to zero. We then have the
(1a) E1 = E2 + E2/c² . Φ
This equation expresses the energy law for the process under
observation. The energy E1 arriving at S1 is greater than the energy E2,
measured by the same means, which was emitted from S2, the EXCESS
BEING THE POTENTIAL ENERGY of the mass E2/c² in the gravitational
(1b) M' - M = E/c²
The increase in GRAVITATIONAL mass is thus equal to E/c2, and therefore
equal to the increase in INERTIAL mass as given by the theory of relativity.
§ 3. Time and the Velocity of Light in the Gravitational Field
f the radiation emitted in the uniformly accelerated system K′ in S2 toward
S1 had the frequency f2 relative to the clock at S2, then, relative to S1, at
its arrival at S1 it no longer has the frequency f2 relative to an identical
clock at S1, but a greater frequency f1, such that, to a first approximation
(2) f1 = f2 . (1+γh/c²)
(2a) f1 = f2 . (1+Φ/c²)
NOTE: Using Planck's E = hf (for a photon), he applied it to (1a)
This result (which by our derivation is valid to a first approximation)
permits, first, the following application. Let f0 be the oscillation-number
of an ELEMENTARY LIGHT-GENERATOR, measured by a CLOCK U at the
same location. This oscillation-number is then independent of the
locations of the LIGHT-GENERATOR and the CLOCK.
If we measure time at S1 with the clock U, then we must measure time
at S2 with a clock which goes 1 + Φ/c² times more slowly than the clock
U when compared with U at one at the same location. For when measured
by such a clock, the frequency of the light-ray which is considered above
is at its emission from S2
f2 . (1+Φ/c²)
and is therefore, by (2a), equal to the frequency ν1 of the same light-ray
on its arrival at S1.
If we call the velocity of light at the origin of co-ordinates c0, then the
velocity of light c at a location with the gravitation potential Φ will be
given by the relation
(3) c= c0 . (1+Φ/c²)
------------------------------------- End of excerpts --------------------------------------------------
Now, fast forward 104 years to 2015, in order to read the paper from
Dr. A. Mudrak et. all: "Relativistic Corrections in the European GNSS
Galileo", working at the European Space Agency - The Netherlands.
This paper criticizes the decision to NOT USE relativistic corrections
in the Galileo satellites. I posted an analysis of this paper here:
New thread for GPS, Galileo satellites and relativistic corrections.
I quote this excerpt from the Mudrak's paper:
3.1. Gravitational Frequency Shift
As shown in , the relative frequency shift between a clock experiencing
the gravitational potential Φ+ΔΦ and the one at the gravitational potential
Δf/f = ΔΦ/c² (1)
For an unperturbed circular Keplerian orbit, the gravitational potential omitting the higher-order harmonics in line with the approach taken in
 and  is given by
Φsat = −G.Me/r (2)
where r is the radius of the satellite orbit.
And this EXACTLY what can be directly derived from the 1911 equation:
(2a) f1 = f2 . (1+Φ/c²)
If the elementary formula adopted by Mudrak (without questions) is
applied to Galileo satellites, as he did using for ΔΦ:
Δf/f = −G.Me/c². (1/Re - 1/Rs) , for gravitational shift.
Δf/f = + 5.3146 . 10^-10 , which gives clock differences of
47.1982 μsec/day, using:
G.ME = 3.986004418×10^14 m³/s²
c = 299792458 m/s
Rs = 26936715 m (Galileo satellite orbit radius)
Re = 6378136.55 m (Earth radius)
So, if 120 years ago, Einstein had imagined his "light-generator" located
about 26.5 Km over his head and emitting microwaves at about 2 Ghz
(I wonder why he didn't), he could have forecast future by 75 years, and
left to the future GPS enterprise a sheer warning about to take him
Hell! He could even had invented GPS, with trilateration math and else.
After all, it is far less complex than GR, and he "invented" the laser
in 1917, when meddling with Bohr's theory, as fanatics like to point out.
BUT, and THIS is very important to HIGHLIGHT: He did all of this without
messing with non-linear, mass sensitive, space-time and tensors.
He just used the OLD LINEAR AND EUCLIDEAN SR, plus E=mc², plus
E = h.f, plus Eotvos (1885 - 1909) results for inertial and gravitational masses, plus a lot of fallacies to make you believe it.
Now, as the topic of the Schwarzschild Effect is open to many
interpretations (GR is that flexible, with more than 20 parameters to
fit into anything that appears), I left to you to wonder if this effect is
real or not.
What are the answers for:
1) t ≠ t' or t = t'?
2) Δf/f = 0 or Δf/f = −G.Me/c². (1/Re - 1/Rs) , for gravitational shift.
3) GR is correct or is a mathematical expression brought to the
4) What are the consequences in the real life and technologies if all of
this shit is ABSOLUTELY FALSE?