h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: shapiro effect - A3900430
Author: johninf - U1421776

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.

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.



(Click here for an full-sized view of this geometry)

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 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 seconds.





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



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.

The Shapiro Effect and Redshift of Distant Galaxies

So what does this mean? Imagine light being emitted from a distant galaxy one hundred million light years away (meaning the light has to travel a hundred million years to reach us). As that light wends its way tirelessly toward earth, it passes continually through the extremely small but ever-present gravitational field present in outer space -- the cumulative gravitational field of every star and galaxy along its path. As we now know from Dr. Shapiro’s experiments, that light will experience a small, cumulative deceleration from the forces of this gravitational field acting at long range. This is not an interaction of the light photon with interstellar matter, which would smear the light and provide a visible signature, but simply a gravitationally induced time delay. The photon’s interaction with gravity does not alter its path, nor change its characteristic, except by gradually decreasing its velocity and energy.

By the time light from a distant galaxy reaches Earth and our telescopes, it has less velocity than when it left its host star, and thus less energy than when it started. In a word, it is redshifted! And not because the distant source galaxy is receding, but because the inter-galactic gravitational field has reduced its energy. The Shapiro effect has shown us that a redshift is to be expected, which increases with distance! That is just what Hubble observed, but with an explanation which does not require the Doppler effect, an expanding universe, or a Big Bang.

Hello and welcome to H2G2.

This entry appears to be cut and pasted directly from
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Is this your own writing? If not, could you please remove it as soon as possible, as it could be regarding as plagiarism.

If it is your site and you'd like this information to form part of the edited guide, it would be well worth re-editing to make it a bit more accessible for the general reader.

The entry is copied and pasted from another site,
I do not claim any authrship. But will rewrite it as soon as I can.
Because there is no other entry for this important document.

You can't post other people's work on this website - it's against the house rules. If you want to write a guide entry on the Shapiro effect that would be excellent , but you can't just re-write someone else's work. Of course it's okay to draw from various sources as part of your research, but just rephrasing won't be enough. If you want to write an edited guide entry, it should have your structure and your words.

Ok I'm working on it now.