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Relativity Experimental verification of the predictions of General Relativity The predictions of general relativity have been (and are being) tested against direct observations. Eddington’s total eclipse measurements (1919) For the laws of physics to be the same in all reference frames, Einstein realised that light must be affected by gravitational fields in a similar way to bodies with rest mass. In other words, light should "fall" under the influence of gravity. This means that the path of a beam of light should be curved when it passes near a massive body like the sun. During a total eclipse of the sun Eddington measured the apparent change in the position of a star due to "bending" of the light from the star as it passed very close to the sun (see diagram below). The diagram greatly exaggerates the "bending"; in reality it is only a few seconds of arc.
...... The results agreed very closely with Einstein’s calculated values for the apparent displacement of the star. On the next diagram (which is a magnified view of the part of the diagram in the dotted "box"), by considering different parts of the same light beam as it passes close to a massive body we can see why we should expect time to be "slowed down" by a gravitational field.
As we see, some of the light goes from a to b and some of it goes from c to d. The light at the "top" of the beam has further to go than the light at the "bottom". If the beam is to stay together (which it does) then this implies that the light at the "top" goes faster! The whole theory of relativity is based on the constancy of the speed of light. Einstein was forced to conclude that time was modified by the presence of the mass just enough to make the speed of light the same. The Gravitational "Red Shift" This is another effect due to "slow time" in a gravitational field. Suppose radiation is produced at a point in a gravitational field but observed by someone outside the field. Let’s put in some simple figures. If the radiation has a frequency of 1×109Hz, this means that one oscillation takes 1ns. But, this is 1ns at a place where clocks run slowly. Suppose the observer is at a place where clocks runs 10% faster. The observer’s clock will register (about) 1·1ns for an oscillation. In other words, the observer will measure the frequency of the radiation to be (about) 9×108Hz. A lower frequency corresponds to a longer wavelength. If we were talking about light (these figures correspond to radio waves) we would see the radiation shifted towards the red end of the spectrum. This effect has been observed using gamma rays and the results of the experiment agreed very closely with the predictions of general relativity. It can be shown that, if we consider a
source of radiation and an observer separated by a height
where f is the emitted frequency and
Example Considering again radio waves emitted with
frequency 1×109Hz and observed to have a frequency
of 9×108Hz. Let
= (about) 9×109Nkg-1 (!) Remembering that the gravitational field strength near the surface of the sun is about 280Nkg-1 you can see why gravitational red shifts are (usually) very small. Gravitational Waves General relativity predicts the existence of gravitational waves. If a system of bodies emits gravitational waves, it must lose energy. Many stars exist in pairs, orbiting around their common centre of gravity. It has been suggested that the orbital time periods of double stars should gradually decrease as they emit energy in the form of gravitational waves. This effect has been observed in a pair of orbiting neutron stars. The rate of change of the time period is in agreement with the value predicted by general relativity (to within ±1%). This is therefore strong indirect evidence in support of gravitational waves. Other, more direct methods have also been employed in the search for gravitational waves but at the time of writing (18/03/2002 at about half past ten), these methods have not yet been successful. |
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h, in a gravitational field of
strength g, then the red shift can be calculated from
