The Shapiro Effect

You may not have heard of the Shapiro effect before, but you are about to find out that it is the explanation for the distance-redshift effect discovered by Edwin Hubble, and it has been proven experimentally many times!

It all started with a short letter in the Journal of Astrophysics in 1964 by Dr. Irwin I. Shapiro of the Lincoln Labs of the Massachusetts Institute of Technology, which stated in part:

"...according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path."

He was speaking, of course, of Einstein’s General Theory of Relativity. Dr. Shapiro, it seems, was the first to make use of a previously forgotten facet of relativity theory -- that the speed of light is reduced when it passes through a gravitational field.

Another major quote by Einstein is as follows:

“So, it is absolutely true that the speed of light is not constant in a gravitational field [which, by the equivalence principle, applies as well to accelerating (non-inertial) frames of reference]. If this were not so, there would be no bending of light by the gravitational field of stars. One can do a simple Huyghens reconstruction of a wave front, taking into account the different speed of advance of the wavefront at different distances from the star (variation of speed of light), to derive the deflection of the light by the star”.

In this landmark letter, Dr. Shapiro went on to suggest that this new test of relativity theory could be verified by observing the time delay of radar signals returned from the surface of the planets Venus and Mercury. He estimated that the effect of the sun’s gravitational field on the radar beam would be to cause a delay of as much as two hundred microseconds (0.0002 seconds) in the round trip travel time of a radar signal returned from a distant planet. The maximum delay would occur at the beam’s closest approach to the sun. He went on to explain how, with the knowledge and technology available (in the mid 1960’s), such a test could be successfully made to within five to ten percent accuracy using the MIT Haystack radar.

His idea was to bounce radar beams off the surface of the planets Venus and Mercury, and measure the total time it took for the beams to go from the earth to these planets and return. Since the relative positions of the planets and earth are known quite accurately, the expected travel time of the radar beam could be computed with great accuracy as well. His solution of Einstein’s equations of relativity indicated that as the radar beam passed closer and closer to the sun, there would be a small time delay. The total time for the radar beam to go from the earth to the planets and back, at the closest approach of the radar beam to the sun, would be increased by 200 microseconds compared to what would be expected if the sun were not there. This is a relatively easy time difference to measure.

Shapiro.gif (71024 bytes)


Dr. Shapiro was right! The first test of this new aspect of Einstein’s theory was resoundingly successful, matching not only the predicted amount of time delay, but also the relationship predicted by Einstein as well. That relationship is very important, as we shall soon see.

Further Tests of the Shapiro Effect

The first experiments with the MIT Haystack radar and the distant planets were highly successful, but relatively crude by modern standards. The experiments have been repeated many times since, with increasing accuracy, until today the deviation between the experimental results and solutions to Einstein’s equations is less than one percent. Thus the measurement of the predicted time delay is one more verification that Einstein’s general theory of relativity is correct.

One of the modern set of experiments measured time differences from signals returned by transponders on the Mariner 6 and Mariner 7 spacecraft as they orbited the planet Mars. This is a far more accurate test than simply bouncing radar beams off the surface of a planet, since surface irregularities introduce an element of error which cannot be controlled. The use of highly accurate and controlled transponders aboard these satellites significantly reduced the errors present. These experiments, coupled with numerous data collected during the Mariner program, led to refinements in many of the variables involved in the test, such as planetary motion, solar corona effects, etc., further reducing the potential error sources.

Perhaps the most accurate experiments of the Shapiro effect have been conducted as a result of NASA’s Viking project. This program placed unmanned landing craft on the surface of the planet Mars to explore its characteristics. One of the wonderful results of this program, you may recall, was to return color photographs of the Martian surface. A lesser known part of this program was to leave transponders on the surface of Mars. These transponders respond to radio signals from earth and return, or echo" these signals back to earth, ideal for testing the gravitational time delay. Such controlled signal response from fixed positions eliminates both the random nature of raw radar returns from a planetary surface, and possible orbital variations present when returning signals from the Mariner spacecraft.

The following figure illustrates a typical experiment to measure the gravitationally induced time delay. In these experiments, radio signals were sent to satellites Mariner 6 and Mariner 7 as they orbited the planet Mars. When the radio signal passed far from the sun, the signal and its return from transponders on the satellites experienced a travel time which could be easily calculated based on the known distance between the earth and the satellites, considering that radio waves travel approximately at the speed of light. Total transit times were typically 30-40 minutes.

Shapiro effect and mariner.gif (12558 bytes)

Typical test of the gravitational time delay (Shapiro effect), using transponders on the Mariner 6 spacecraft as it orbited the planet Mars.

shapiro effect

The results match Dr. Shapiro’s predictions very well, which were based on Einstein’s General Theory of Relativity

As the line of sight between Earth and Mars drew closer and closer to the sun, a measurable excess time delay began to occur. When the line of sight came nearest to the Sun (called superior conjunction), the maximum excess time delay occurred -- about 200 microseconds as predicted by Shapiro’s equations.

Dr. Shapiro’s discovery, which has now been named The Shapiro effect or gravitational time dilation, is extremely important from two aspects -- it proves that light rays lose velocity (and thus energy) when passing through a gravitational field, resulting in a redshift, and that the effect is a long-range one!

A Long-Range Effect

Let me explain the importance of this long-range aspect. The bending of light by the sun or any other massive object, as well as the attractive force of gravity, are short-range effects — they die off very quickly with distance. The deflection of light just grazing the surface of the sun is 1.75" (arc-seconds), or about 1 / 2000th of a degree. At one hundred times the sun’s radius the effect has dropped to one percent of this value. This is a short-range effect.

The Shapiro effect, on the other hand, is a long-range effect. Instead of the time delay effect decreasing with the inverse of the distance from the center of the sun ( 1/d ), as does the bending of light, the Shapiro effect decreases with the inverse of the logarithm of distance ( 1 / ln (d) ). If the time delay at closest approach to the Sun is 200 microseconds, at one hundred times the sun’s radius the effect has dropped to 44 microseconds, or twenty-two percent of its maximum. In contrast, at this distance the bending of light has dropped to one percent of its value at the surface of the sun. The time delay is still 14% of its maximum value when the radio beam passes at 1,000 times the solar radius. At this distance the bending of light is insignificant. Thus the Shapiro effect is a long-range effect! The importance of this logarithmic aspect of a gravitational effect is major, and has been totally ignored.

Further Evidence that Gravity Reduces the Velocity of Light!

The Pioneer 10 and Pioneer 11 spacecraft were launched into space in January, 1987, and were the first spacecraft to exit the solar system. Their trajectories were followed for many years with extreme precision until they were too weak to respond. Detailed analysis showed a strange anomaly in their positions. It appears they were drawn slowly toward the Sun beyond anything predicted by the Theory of Gravity.

A detailed 55 page analysis was conducted to attempt to explain this anomaly, but failed to do so. The only plausible explanation is that the velocity of light in the vicinity of the Sun is slightly less than expected. This is in complete agreement with what would be expected from Gravity Drag (i.e. the Shapiro effect)!  (Study of the anomalous acceleration of Pioneer 10 and 11, Anderson, et al. 11 April, 2007).

This team investigated every possible cause for this anomaly. In the end, they could find no cause, and the question was left unanswered. However, one of the team members, David Crawford, provided a clue. He postulated that if the frequency of light was affected by the Sun’s gravitational field, appearing as a Doppler shift, it would explain the anomaly. However, his input was not included in the conclusions by the team.

In spite of the lack of conclusions by the team, I believe that the results show that the velocity of light in the vicinity of the Sun is less than previously thought, due to the influence of the gravitational field of the Sun. The effect is extremely small, but the cumulative effect on the trajectories of the Pioneer spacecraft over many years clearly demonstrates this effect.  The paths of Pioneer 10 and 11 seem to show that the velocity of light in the vicinity of the Sun is ever so slightly lower than thought, due to the influence of the Sun’s gravity field. This suggests that the velocity reduction of light by gravitational fields is real, and is the cause of the redshift of distant galaxies, and not the Doppler effect. And without the Doppler effect there is no reason to believe there ever was a Big Bang.

Overcoming Objections

In online forums I have seen several objections to what has been presented above.  The following addresses these concerns:

Objection #1 – The measured time delay is because the radar paths are longer due to bending the path by the sun’s gravitational field.

The time delay because of a longer path has been studied by Michael Berry, Principles of cosmology and gravitation, Cambridge University Press.  He states:

‘…this differs from unity by only 10-8, which corresponds to a few microseconds in experiments involving Mercury and Venus. The relativistic time-delay excess amounts to about 100 microseconds…”

The measured time delay is real, and not due to a longer ray path!

Objection #2 – After the velocity of a photon is reduced by a gravitational field it will accelerate back to its original value.

I used to think that too, but after much thought, I realized there was no known mechanism for accelerating a photon.  Einstein only discusses velocity reduction, never acceleration.  Some have suggested that photons will be accelerated toward a distant gravitational field, as if they were attracted to an object such as the sun, earth or perhaps a galaxy.  But this would require that photons have mass.  As discussed by Laura Whitlock:

“And try as we might, we can measure no mass for the photon. We can just put upper limits on what mass it can have. These upper limits are determined by the sensitivity of the experiment we are using to try to "weigh the photon". The last number I saw was that a photon, if it has any mass at all, must be less than 4 x 10-48 grams. For comparison, the electron has a mass of 9 x 10-28 grams. “

 There is simply no mechanism for accelerating a photon once its velocity has been reduced by a gravitational force! With every gravitational force it encounters, no matter how small, a photon will continue to decelerate and lose energy. I call this “gravity drag”, which was also named by famous astronomer Fritz Zwicky many years ago.


·        Light loses velocity as it passes through a gravitational field and never returns to its original velocity

·        The reduction in velocity results in a redshift when observed through our telescopes (if the reduction is large enough to be detected).



Return to the Main Page