Figure
1 Scaled Comparison of the logarithmic 1/Ln(D)
Shapiro Delay
and
the 1/D
Effect of the Gravitational Light Bending of Relativity
Note here again that at a
distance of 100 solar radii the value of the Shapiro delay
has been recorded to be at least 21% of its maximum effect. One speaks of a ‘longrange effect’, as the 1 /
ln(D)
effect does not reach zero for large values of D. The solar wind of
dense electrons apparently has a profound effect on the microwave signals
used by the researchers to record the Shapiro delay effects, chiefly because of the
chosen wavelengths in the order of cm's. These effects engulf most
of the planets of the solar system.
The theoretical solar light
bending effect of General Relativity is predicted to vary
proportional to 1 / D, essentially a 1/R effect from the
gravitational light bending equation of General Relativity
as illustrated in Figure
2.
Figure
2 An Animated Illustration of the Predicted 1/R
Gravitational Lensing Effect of General Relativity
Recorded history
of solar light bending for wavelengths in the nm region has indicated a rapid drop off to a nearly zero
light bending effect only slightly above the rim. This drop off is faster than the predicted 1/D
effect of General Relativity, at distances of a fraction of a solar radius, in the
empty vacuum space above the plasma rim of the sun. It is important
to note that the solar wind
electrons from all observational evidence to date have virtually no effect at all
on the optical wavelength astronomy.
Shapiro measured a time delay that had a
maximum value of 180 µs during which time the impact parameter of the microwave beam was at
a minimum. This occurred during which time the planet Venus was at opposition
on January 25, 1970. This delay referred to as "Excess Delay" by
Shapiro is depicted in Figure
3. Details on these results are given in Reference 1).
Figure
3 Shapiro Delay of 180 µs
during the Venus
Opposition
As previously stated, the Shapiro
effect appears to increase for smaller impact parameters of the
probing beam of microwave signals and decreases only slowly (never going
to zero) with
increasing distance D from the sun. Figure 4 shows how the Shapiro
delay slowly varies essentially proportional to 1 / ln(D),
a logarithmic function. The graph clearly shows how the Shapiro
effect never goes to zero or vanishes entirely. A clear
detail discussion on this and Figure 4 is found in Reference 3).
Figure 4 Contribution of the Shapiro
effect to the EarthMarsEarth delay
It is therefore clearly seen that the
Shapiro delay is essentially a transittime effect
which is due to the physical characteristics of a space of an electron
density profile that governs the propagation of
microwaves. The gravitational light
bending rule of General Relativity is a theoretical
explanation for the path
of the electromagnetic waves due either to a direct or an indirect
interaction between the gravitational field of the sun and the bent light
rays. The
Shapiro delay and the gravitational light
bending rule of General Relativity are two
entirely different physical phenomena, requiring very different theoretical
explanations.
On November 26, 1976, Shapiro calculated a time delay of
247.36 µs for the EarthMarsEarth
roundtrip. As depicted in Figure 5, the microwave signal that is
transmitted from a satellite orbiting Mercury, during which time the
planets Mercury and Earth are at opposition to one another, must
pass by the limb of the sun before reaching Earth. It is well known that,
due to the vast quantities of solar winds that are ejected for the sun,
the microwave signals must pass through a space of highly dense electrons.
Figure
5 All Microwave Signals propagate with a Frequency Dependent Transit
Time Delay
due
to a Plasma Resonance of Microwaves with the Varying Impact Parameter
Dependent
Electron
Density Profile N_{e}(r)
∝
r^{2}
with
an Index of Refraction n(r) > 1.000000.
As a consequence of the
solar winds, the radial expanding supersonic atmosphere of the sun, the
propagation velocity of the microwave signals vary as the waves must pass
through space of varying electron densities. N_{e}(r) is the
density of the electrons present in the solar wind at a radial distance r
from the center of the sun. The solar winds move with supersonic
velocities up to 500 km per sec and expand out to beyond Jupiter and the
outer most planets and eventually falls back as recombined matter and
dust. It is easily shown that the electron densities, as observed and
measured using the Viking, Mariner 6 and 7 spacecraft in references 1 thru
6, which is very prevalent throughout the solar winds, with values of N_{e}(r)
up to 10^{4} electrons per cm^{3}, can be used to
calculate the index of refraction as a function of N_{e}(r) and N_{c}
given by the following equation.
(2)
N_{c} is the
frequency dependent the critical density given by N_{c}
= 1.240x10^{4} f^{2} (MHz)cm^{3};
where f
is the frequency of the microwave link. The index of refraction is given
by the following equations.
(3)
Unfortunately, the
mainstream of the Physical science community seems to view the Shapiro
delay as a spacetime effect of General Relativity. It is easily shown
here that this is not at all the case and that, due to the very
slow drop off trend of the Shapiro delay as shown in Figure
4, or the ‘longrange effect' described by 1 / ln(D) and even described
by Shapiro himself, an effect which never seems to go to zero, this
characteristics does not fit the theoretical predictions of the spacetime
effect of General Relativity. The Shapiro delay has simple,
clear classical explanations, not requiring any of the rigorous treatments
of spacetime or time dilations. It is easily seen that the vacuum space
around the sun that includes Mercury, Venus, Earth and Mars has to have a refractive
index n > 1.000000 from more that a
century of astrophysical observations of the comets and the electron
density profile of the solar winds. An estimate the refractive index of
microwaves of frequencies 2.2 and 8.8GHz propagating in the
vacuum space near the sun is given in Table 1.
SOLAR PLASMA INDEX
OF REFRACTION 
r(R_{sun})

N_{e}(
cm^3)

N_{e }/ N_{c} 
N_{e }/ N_{c} 
n=1½N_{e}/N_{c} 
n=1½N_{e}/N_{c} 
1 / n 
1 / n 
1 / n 
2.2GHz

8.8GHz 
2.2GHz

8.8GHz 
2.2GHz

8.8GHz 
Optical 
200

5.4606E+00

9.0985E11

5.6866E12 
1.0000000000

1.0000000000 
1.0000000000

1.0000000000

1.0000000000 
150

1.0124E+01

1.6869E10

1.0543E11 
0.9999999999

1.0000000000 
1.0000000001

1.0000000000

1.0000000000 
100

2.4386E+01

4.0632E10

2.5395E11 
0.9999999998

1.0000000000 
1.0000000002

1.0000000000

1.0000000000 
50

1.1282E+02

1.8798E09

1.1749E10 
0.9999999991

0.9999999999 
1.0000000009

1.0000000001

1.0000000000 
40

1.8640E+02

3.1059E09

1.9412E10 
0.9999999984

0.9999999999 
1.0000000016

1.0000000001

1.0000000000 
30

3.5868E+02

5.9763E09

3.7352E10 
0.9999999970

0.9999999998 
1.0000000030

1.0000000002

1.0000000000 
20

9.1538E+02

1.5252E08

9.5327E10 
0.9999999924

0.9999999995 
1.0000000076

1.0000000005

1.0000000000 
15

1.7986E+03

2.9968E08

1.8730E09 
0.9999999850

0.9999999991 
1.0000000150

1.0000000009

1.0000000000 
12

3.0559E+03

5.0919E08

3.1824E09 
0.9999999745

0.9999999984 
1.0000000255

1.0000000016

1.0000000000 
11

3.7631E+03

6.2702E08

3.9189E09 
0.9999999686

0.9999999980 
1.0000000314

1.0000000020

1.0000000000 
3

9.2431E+04

1.5401E06

9.6257E08 
0.9999992299

0.9999999519 
1.0000007701

1.0000000481

1.0000000000 

Table
1 Index of refraction calculated from the electron density N_{e}(r), and
the critical density N_{c}, given by equation 2, for 2.2GHz and
8.8GHz. The Table shows the reciprocal (1/n), since theoretically for
Plasma n < 1. For
all optical frequencies of nm wavelengths n = 1.000000000.
Note that as the impact
parameter r(R_{sun})
in units of solar radii decreases, the electron density N_{e}(r)
increases rapidly and the frequency
dependent values for N_{e}(r)/N_{c}
also increases. For increased
microwave frequencies above the resonance frequency of the electron
plasma, the values for N_{e}(r)/N_{c}
and thus for the plasma index of refraction
decreases. For optical frequencies, the plasma index of refraction is
practically n = 1.000000000.
Planet 
Distance from Sun (m) 
Transit Time (sec) 
Mercury 
57.9x10^{9} 
193.13 
Venus 
108.2x10^{9} 
360.92 
Earth 
149.6x10^{9} 
498.01 
Mars 
227.9x10^{9} 
760.19 
Table
2 Transit Times (sec) assuming
n = 1.000000000
Using the information given
in Table 2, the roundtriptime required for the
microwave signal to propagate for the path EarthMarsEarth, assuming an
index of refraction of n = 1, is 2x(499.01+760.19) = 2516.40 sec.
The measured roundtriptime delay for
path EarthMarsEarth found by
Shapiro is 247.36x10^{6}^{
}sec.
Equating the ratio
between the time delay and the transit time of the microwave signal, we
have a time delay of 9.822x10^{08}, an additional amount to be
added onto the propagation time required for the microwave signal, ignoring other effects. One can equate the mean refractive index
of the vacuum space for the entire path to be equal to the vacuum index of
refraction n
= 1.000000 plus an additional factor due to refraction giving a
slightly larger refractive index, i.e., a larger n
> 1.000000. This yields a mean index of refraction of n_{mean}
= 1+9.822x10^{8 }or 1.00000009822.
This is the mean refractive index that will slow down the propagation
velocity of the microwave signal so that it would arrive at a time delay
of exactly 247.36x10^{6}^{
}sec. Assuming the refractive index
n(r) varied as a function of the radial distance from the sun, moving from
the Earth to Mars and back to Earth, passing by the rim of the sun for a
minimum value of r and a maximum value of n(r), and if the function f =
n(r) were of the form of a triangle as given in Figures 3 and 4, or even as near
trapezoid shape that is narrow at the top, where the maximum value of n(r) would be at the impact parameter of
the microwave beam (a
minimum r). A good approximation for n(r) at the impact parameter (a
minimum r) could be a value of 1 plus 1.9644x10^{08}
or roughly n(r_{min}) = 1.00000019644.
In light of the fact that vast quantities of solar winds
with this electron density profile are prevalent throughout the
solar system, this index of refraction profile illustrated for 2.2GHz may be
a reasonable estimate. Note again, the propagation delay is frequency
dependent and thus cannot have anything to due with an effect of General
Relativity or a Space Time effect which are both independent of frequency.
In Reference 4, the data
for the electron density profile collected by the Viking spacecraft and
analyzed for the radial distances from 4 solar radii (R_{sun})
to 200 R_{sun}. The equation that was fitted to the data in
Reference 4 and graphically displayed as the "Equatorial electron
density profile" was plotted on a linear scale in Figure 6 from 0 to
250 R_{sun}, a scale of from 0
to nearly 1.4 astronomical units (AU's).
Figure
6 N_{e} behaves
nearly as r^{2}
for distances beyond 1 AU or
200 R_{sun}
Independent researchers
consistently show that the electron density profile behaves very nearly as
an inverse square of r, namely as r^{2}.
In reference 6 for Mariner6, the electron density N_{e}(r)(cm^{3})
falls off as r^{2.05}
and for Mariner7 as r^{2.08}.
In this same reference, a density at 1 AU of 9.1+/2.6
electrons cm^{3} is sited for a 6 month period of the experiment.
Figure
7 The Experimental Facts pertaining to the
Propagation of Microwaves in the Solar System: 
 Microwaves are always deflected by the angle 1.75 arsecs only at the thin plasma
limb of the sun
 Microwaves are subjected to both a frequency
and impact parameter
dependent transit time delay
due to the resonance
of microwaves with the solar wind electrons and the solar plasma

Conclusion
The Shapiro delay is merely a very
good fit to the data dealing with the transit times of the microwave
signals as function of the selected microwave frequencies of the
transmitted link and as affected by the space properties of the solar wind
that govern the propagation of
microwaves signals in space. The Shapiro delay is the determination of
the transittime delay (usually expressed in microseconds) due to the influence
of the expanding solar atmosphere (solar wind) of a measurable electron
profile. The Shapiro delay
has nothing at all to
do with spacetime or the gravitational solar light bending effect of General
Relativity (usually expressed in radians
or seconds of arc).
References
1)
Shapiro
Delay, a Frequency Dependent Transit Time Effect, Shahin
Ghanzanshahi (1), Edward H. Dowdye, Jr.(2), SPIE (International
Society for Optics & Photonics 2011), (1) California State University,
Fullerton, California 92834, (2) Pure Classical Physics Research, (to be
published in upcoming Proceedings of SPIE Volume 8121 The Nature of Light:
What are Photons? IV)
2)
The Shapiro Experiment:
http://www.relativity.li/en/epstein2/read/i0_en/i3_en/
3)
SolarSystem
Dynamics and Tests of General Relativity with Planetary Laser Ranging,
J.
F.Chandler (1), M. R. Pearlman (1), R. D. Reasenberg (1), J. J. Degnan (2)
, (1) SAO, HarvardSmithsonian Center for Astrophysics. (2) Sigma Space
Corporation
4)
Solar Wind Electron Densities From
Viking DualFrequency Radio Measurements, Duane
O Muhleman, Division of Geological and Planetary
Science California Institute of Technology John D. Anderson, Jet
Propulsion Laboratory, California Institute of Technology, Received
1980 December 1: accepted 1981 February 11, The Astrophysical Journal,
247:10931101 August 1, 1981. pp. 10941100
5)
Experiment Test of General
Relativity Using TimeDelay Data From Mariner 6 and Mariner 7, John
D. Anderson, Paquale B Esposito, Warren Martin and Catherine L. Thornton, Jet
Propulsion Laboratory, California Institute of Technology and
Duane O. Muhleman, Division of Geological and Planetary Science
California Institute of Technology, Received 1974 December 19; Revised
1975 February 10, The Astrophysical Journal, 200:221233 August
15, 1975. pp. 221, 222, 224 6)
The Electron Density Profile of the
Outer Corona and the Interplanetary Medium from Mariner6 and Mariner7
TimeDelay Measurements, Muhleman, D.
O.; Esposito, P. B.; Anderson, J.D., Astrophysical Journal, Part 1 vol.
211, Feb. 1, 1977, p. 943957.
SUMMARIZING in a PICTURE
Summary
The electron density profile of solar
wind is found to behave very nearly as an inverse square of r, namely as
r^{2}, with electron density profile models ranging from r^{2.05}
to r^{2.08}, and with effects that engulf the outmost planets
of the solar system. The bulk of all the Shapiro delay measurements were
done using microwave frequencies from 500 MHz to 8.8GHz (with
wavelengths from 80cm to 3.5cm). Significant findings of this research
reveal that, for all microwave signals propagating in the solar wind
atmosphere of the solar system, the waves are subjected to a frequency
dependent plasma index of refraction n(r) that exceeds unity, i.e., n >
1.0000000000. For optical, IR and UV wavelengths, the plasma index of
refraction is practically n = 1.0000000000 and these wavelengths are
virtually unaffected by the widespread atmosphere of the expanding solar
wind described by the electron density profile. As a consequence, the
Shapiro delay is only a very good measurement of a frequency dependent
transittime effect and can not be or have anything to do with a spacetime effect of General
Relativity which is independent of frequency. 