What is the Shapiro effect or 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.

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 �s 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 �s 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 �s 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 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 10⁴ electrons per cm³, 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 = 1.240x10⁴ 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.