### THE THEORY OF RELATIVITY

This is a brief account of the theory of relativity and how it impacts on the problems of modern science. The Theory of Relativity is basically philosophical in nature and this part of it is not at all difficult to understand, requiring no more than high school algebra.

Albert Einstein published the Special theory of Relativity in 1905. The theory was an answer to the problem which arose when Michelson and Morley published their famous experiment in 1885, though no one realized this at the time. This established the constancy of the velocity of light, irrespective of the velocity of the measuring platform. See Figure #17. This was already implicit in Maxwell's equations.

At first sight this might not appear to be very remarkable. When one considers that the platform might be moving at a very high speed v, relative to the earth, just a touch below the speed of light (Which is c) it appears to be very weird. Under these circumstances one would expect that a light beam from earth would take a considerable time to catch up with the space ship and that the measured speed of the beam of light would be considerably less, i.e. c - v. In fact it measures exactly the same as on a platform on the earth.

This certainly does not happen with sound, where the measured velocity would be s - v (Where "s" is the velocity of sound). The problem of relative motion had been well understood by the early Greeks who understood the theory of motion in such circumstances as a person walking along the deck of a moving boat. They naturally referred the resultant speed to a reference point on the supposedly fixed earth. When one becomes aware of the earth's motion through space, one has some difficulty in determining a fixed reference point. Even the sun or the whole galaxy itself cannot be regarded as fixed. At one time it was thought that there had to be a fixed "Ether" which was a substance which could carry the undulations of light waves. The Michelson and Morley experiment was designed to determine the velocity of the earth as it moved through the ether, but it failed to detect any motion whatsoever. This resulted in the abandonment of the idea of the ether, though it was still being referred to as existing right up to the 1930s.

Einstein performed a further thought experiment trying to determine whether anyone inside a closed vehicle traveling at a uniform speed could determine his absolute velocity in any way. Measuring the speed of light inside the vehicle was no good as it was always constant. Even a beam of light coming from outside was of no help. Einstein realized that if there was no way that absolute motion could be measured, it did not exist. Therefore anybody on any platform, irrespective of their state of motion was entitled to their own view of the world from the point of view of moving objects and they could measure all velocities relative to their own platform. He then performed another thought experiment which is illustrated in Figure 16.

Since both points of view are correct, we need a mathematical transformation in order to relate them.

Two vehicles are moving apart at high speed. One shines a light, and the other carries a mirror which reflects the light back. Figure 16, part A, shows the interpretation of events from the point of view of vehicle A. Figure 16, part B, shows the interpretation of vehicle B. Each are entitled to their own view and each must be correct and consistent according to a correct body of physical law.

According to the conventional interpretation of physical law these two views are inconsistent. The observers on one vehicle interpret the moment of impact of a flash of light on the mirror to be midway between the events of sending and receiving. The observers on the other one do not. The problem arises because light always travels at the same speed. If it were allowed to vary there would be no problem.

Einstein realized that a consequence of the constancy of the velocity of light there had to be a complete revolution of our mode of thinking with regard to such fundamentals as the flow of time, the constancy of length etc.

It turned out that the rate of flow of time is not constant. We do not have such a thing as absolute simultaneity in two systems which are moving relative to one another. Nor do we have constancy of length from two observers, one of which is moving relative to the other. Another thing which had been thought to be constant and which is not so, is mass. Einstein published a further paper in 1915 which brought in accelerations and gravity, in which he predicted that atomic clocks would run more slowly in a strong gravitational field. This was the general theory of relativity. Although at first it was thought that this was all very remote and unimportant at any of the speeds we would be likely to encounter in practice, this has turned out not to be the case. It has already entered everyday life. In the type of machine used in the radiotherapy of cancer, the linear accelerator, we have high energy electrons which are traveling at velocities comparable to the speed of light and they do get heavier. In Lawrence's cyclotron the increase in the mass of the particles (Such as protons) which are being accelerated by a high frequency alternating electric field, causes them to get out of synchrony with the alternating field. This imposes a limit on the maximum energy which can be achieved. This can be overcome to some extent by changing the frequency cyclically. Another example of relativistic effects is the fact that one can detect mesons at sea level. Mesons can be created in high energy machines so we can measure their half life. As this is very short one would not expect a cosmic ray shower, which creates mesons in the upper atmosphere, to produce measurable mesons at sea level. They should not exist for long enough to get there, as they should all have decayed away by that time. In fact they do appear because their internal clock is slowed by their high velocity travel. All of these effects occur at very high energies and high velocities and none of it is relevant to the brain. However there is one aspect of relativity which could have a bearing on the problem. Einstein ultimately solved the time problem by realizing the four dimensional system of geometry proposed by Riemann or that of Minkowski would allow the proper relationship between space and time. These were combined together under the dimension of "Space-Time". He proposed that a four dimensional geometry truly represented the real world in which we live. The possibility that the locality problem, which we have with quantum theory could be solved by invoking an extra dimension therefore exists. This only has a very indirect relevance to the integrative problem of the mind.