Significant Findings

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Abstract:

First noticed by Irvin L. Shapiro in 1964, the transit time required for a microwave signal to propagate through space, arrive at a satellite orbiting Venus or Mercury, required a measurable time delay for the reply signal to propagate back to the earth to be received at the antenna of the observatory. The time delay was noticeably affected by the relative position of the sun. Controlled measurements conducted by Shapiro determined that the time-tagged microwave signals had measurable effects that varied as a function of the impact parameter of the microwave beam relative to the sun. The delays were observed to be in the 100's of microseconds when the impact parameter of the microwave beam was at a minimum. After repeated measurements, varying time delays were recorded and were referred to as the Shapiro delay. These measurements permitted a precise determination of the electron density profile of the solar wind as a function of the radial distance r from the sun. 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 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 a very good measurement of a frequency dependent transit-time effect and can not be a space-time effect of General Relativity that is independent of frequency.

 

What is the Shapiro effect or Shapiro delay?

 

The transit time for a microwave signal transmitted into deep space, beamed at and bounced off Venus and Mercury, required a noticeable time delay to propagate back to the earth and be received at the antennas of the observatory. The time delay was noticeably affected by the relative position of the sun. Shapiro proposed to conduct a controlled observational test to measure the round-trip transit time that would be required by a time-tagged microwave signal. In 1964 careful measurements were made by Shapiro, while recording the relative positions of the sun and the impact parameter of beams of microwave signals bounced off the planets. After repeated measurements, varying delays in the transit time requirements of up to 200 microseconds, well within the limitations of the technology at that time in the 1960s were recorded. The noticeable transit time delay as a function of the impact parameter of the beam relative to the sun is referred to as the Shapiro delay

It is important to note that historically the bulk of these measurements were made using microwave bands of frequencies from 500Mz up to 8.5 GHz (wavelengths from 80cm to 3.5cm). Also note that the beams of a microwave signal, once leaving the transmitting antenna, will spread considerably when propagating over large astronomical distances. The microwave probes are therefore not suitable at all for any investigation of a light bending effect at the very thin plasma rim of the sun. 

It is also important to note that the observed gravitationally lensed light of the stars have wavelengths in the optical region of from 400nm to 700nm. The light in this spectral region is apparently not affected at all by the electrons in the solar wind, that vacuum space belonging to the expanding solar atmosphere of the sun containing the dense electrons in the space just above the thin plasma rim of the sun. It will be seen later that the index of refraction of the electron atmosphere of the solar wind for optical frequencies does not deviate from 1.0000000000.

 

Transit Time Delay as opposed to Light Bending

Gravitational light bending effects have been observed to be in the range of very small angles of seconds of arc, requiring high resolving powers of precision optical instruments to properly observe the extremely narrow regions of the solar plasma rim. All electromagnetic radiation, be it optical, infrared (IR), ultraviolet (UV) or microwave will propagate along a well defined minimum energy path in the narrow solar plasma rim exposed to the gradient gravitational field of the sun. The microwave radiation, however, has been found to be very sensitive to the electron density profile of the solar winds for virtually all space with a transit time effect engulfing the outermost planets of the solar system.

IMPORTANT NOTE The electron density profile has virtually no effect at all on the optical, IR or UV waves, thereby presenting to these waves an index of refraction for these frequencies of practically 1.0000000000. Moreover, there is no evidence of a light bending effect due to the solar winds.  

Historically, the microwave probes have had only the capability of investigating the propagation delays or the times-of-arrival of time tagged microwave beams that tend to spread considerably after having been transmitted from the antennas of the microwave instruments. Moreover, the Shapiro delay is merely a very good fit to the data dealing with the transit times of the microwave signals affected by the space properties of the electron density profile that govern the propagation of microwaves signals in the space local to the solar system. The surrounding space properties have been observed to vary and are governed by the vast quantities of solar ions injected into the space around the sun. This applies directly to the space around all other sun-like stellar systems. Hence, radio astronomy in the microwave spectrum is subject to time-delays in the signals from radio pulsars located near stellar systems that produce stellar winds.

The Details

It is noteworthy to mention that the Shapiro delays were successfully measured from the signals arriving from radio pulsars that are emitting in the microwave regions, belonging to a double pulsar or a system involving a pulsar and a companion which is a stellar system. From the observational evidence, the space properties governed by the expanding solar atmosphere of electrons at various positions in the solar system obviously transmit effects that are inversely proportionally to the radial distance from the sun. Historically, the recorded Shapiro delays appears to be greater for smaller impact parameters of the probing beams of microwave signals and decreases only slowly with increasing distances D from the sun. The Shapiro delay, however, varies proportionally to 1 / ln(D), a logarithmic function, two entirely different theoretical functions as depicted in Figure 1, describing different physical phenomena requiring entirely different theoretical explanations.

 

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 ‘long-range 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 Earth-Mars-Earth delay

It is therefore clearly seen that the Shapiro delay is essentially a transit-time 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 Earth-Mars-Earth 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 Ne(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. Ne(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 Ne(r) up to 104 electrons per cm3, can be used to calculate the index of refraction as a function of Ne(r) and Nc given by the following equation.

  (2)

Nc is the frequency dependent the critical density given by Nc = 1.240x104 f2 (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 space-time 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 ‘long-range 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 space-time effect of General Relativity. The Shapiro delay has simple, clear classical explanations, not requiring any of the rigorous treatments of space-time 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(Rsun)

Ne( cm^-3)

  Ne / Nc

  Ne / Nc

n=1-˝Ne/Nc

n=1-˝Ne/Nc

1 / n

1 / n 1 / n

2.2GHz

8.8GHz

   2.2GHz

8.8GHz

   2.2GHz

8.8GHz Optical

200

5.4606E+00

9.0985E-11

5.6866E-12

1.0000000000

1.0000000000

1.0000000000

1.0000000000

1.0000000000

150

1.0124E+01

1.6869E-10

1.0543E-11

0.9999999999

1.0000000000

1.0000000001

1.0000000000

1.0000000000

100

2.4386E+01

4.0632E-10

2.5395E-11

0.9999999998

1.0000000000

1.0000000002

1.0000000000

1.0000000000

50

1.1282E+02

1.8798E-09

1.1749E-10

0.9999999991

0.9999999999

1.0000000009

1.0000000001

1.0000000000

40

1.8640E+02

3.1059E-09

1.9412E-10

0.9999999984

0.9999999999

1.0000000016

1.0000000001

1.0000000000

30

3.5868E+02

5.9763E-09

3.7352E-10

0.9999999970

0.9999999998

1.0000000030

1.0000000002

1.0000000000

20

9.1538E+02

1.5252E-08

9.5327E-10

0.9999999924

0.9999999995

1.0000000076

1.0000000005

1.0000000000

15

1.7986E+03

2.9968E-08

1.8730E-09

0.9999999850

0.9999999991

1.0000000150

1.0000000009

1.0000000000

12

3.0559E+03

5.0919E-08

3.1824E-09

0.9999999745

0.9999999984

1.0000000255

1.0000000016

1.0000000000

11

3.7631E+03

6.2702E-08

3.9189E-09

0.9999999686

0.9999999980

1.0000000314

1.0000000020

1.0000000000

3

9.2431E+04

1.5401E-06

9.6257E-08

0.9999992299

0.9999999519

1.0000007701

1.0000000481

1.0000000000

Table 1  Index of refraction calculated from the electron density Ne(r), and the critical density Nc, 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(Rsun) in units of solar radii decreases, the electron density Ne(r) increases rapidly and the frequency dependent values for  Ne(r)/Nc also increases. For increased microwave frequencies above the resonance frequency of the electron plasma, the values for Ne(r)/Nc 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 57.9x109

193.13

Venus 108.2x109

360.92

Earth 149.6x109

498.01

Mars 227.9x109

760.19

Table 2  Transit Times (sec) assuming n = 1.000000000

Using the information given in Table 2, the round-trip-time required for the microwave signal to propagate for the path Earth-Mars-Earth, assuming an index of refraction of n = 1, is 2x(499.01+760.19) = 2516.40 sec.

The measured round-trip-time delay for path Earth-Mars-Earth 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 nmean = 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(rmin) = 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 (Rsun) to 200 Rsun. 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 Rsun, a scale of from 0 to nearly 1.4 astronomical units (AU's).  

Figure 6 Ne behaves nearly as r-2 for distances beyond 1 AU or 200 Rsun

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 Mariner-6, the electron density Ne(r)(cm-3) falls off as r-2.05 and for Mariner-7 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 transit-time 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 space-time 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) Solar-System 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, Harvard-Smithsonian Center for Astrophysics. (2) Sigma Space Corporation

4) Solar Wind Electron Densities From Viking Dual-Frequency Radio Measurements, Duane O MuhlemanDivision 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, 247:1093-1101 August 1, 1981.   pp. 1094-1100  

5) Experiment Test of General Relativity Using Time-Delay 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, 200:221-233 August 15, 1975. pp. 221, 222, 224

6) The Electron Density Profile of the Outer Corona and the Interplanetary Medium from Mariner-6 and Mariner-7 Time-Delay Measurements, Muhleman, D. O.; Esposito, P. B.; Anderson, J.D., Astrophysical Journal, Part 1 vol. 211, Feb. 1, 1977, p. 943-957.

 

 

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 transit-time effect and can not be or have anything to do with a space-time effect of General Relativity which is independent of frequency.

 

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