Albert Einstein is somebody we have all heard about, but of his earth shaking theories we know little; how could we, -- Einstein thought in another dimension, unknown and practicably unknowable to most of us. Most of us rest our case on our senses; so, to the average layman, Einstein's theories (never mind that they have checked out in reality) are incredible: space is curved; the shortest distance between two points is not a straight line; the universe is finite but unbounded; parallel lines eventually meet; light rays are curved; time is relative and cannot be measured in exactly the same way everywhere; measurements of length vary with speed; the universe is cylindrical instead of spherical in shape; a body in motion will contract in size but increase in mass; and a fourth dimension - time - is added to the familiar three of height, length, and width. Most of us can only shake our head and base our belief in all of this very strange stuff, simply on the basis of what Einstein has said.
Einstein was the first to improve upon the theories of Newton; and so Einstein ranks with Newton. I am not in a position to speculate who else we might rank in this pinnacle group of scientists; but, I will venture to comment on what the individual must accomplish in order to become part of this timeless and select group. Each will have had to announce to the world a complete and novel proposition on how things in our universe work; and, further, that these propositions, within their sphere, were tested in a practical manner over and over again; and further, these propositions have passed every test and are now taken as working truths on which our very existence depends.
Einstein was born into a middle-class Jewish family located in a Bavarian city called Ulm situated on the upper reaches of the Danube River. As a student he was not especially outstanding except when it came to mathematics where he definitely showed signs of genius at an early age. Einstein emigrated to Switzerland to attend Polytechnic Academy at Zurich. He married a fellow student and became a Swiss citizen. His course of study was designed to lead him into a professorship, but no openings arose. He made a living as a young man shaping up inventors' applications for the patent office; all along Einstein read the works of the philosophers, the scientists and mathematicians. In 1905, at the age of 26, Einstein wrote a paper wherein he set forth the Special Theory of Relativity. Einstein observed that one can only gage the motion of one body in comparison to another. If a body next to you appears to be in motion, it could be you are still (in the larger picture this is rather a remote possibility) and the other is moving, or it is still and you are moving, or (the usual case) you are both in motion; thus, all motion is relative. Another of Einstein's observations (hypothesis) is that "the velocity of light is independent of the motion of its source. .... No force can make it go faster or slower." Nothing can go faster than light and that "Light is, in fact, the only constant, unvarying factor in all nature." As for time: it does not in absolute terms, exist; it is "relative to the position and speed of the observer ..." He further observed that as speed increases, time slows down. By Einstein's theory: if one shot a yard stick through space at 161,000 miles per second, it would shrink to a half yard. That, in fact, the rotation of the earth has the effect of diminishing the circumference of the earth by about three inches. However, as the velocity increases of any object (except light) its mass increases.
I belong to a group, I suspect a rather vast group, who, while fairly adept at every day merchant mathematics, cannot do or understand the mathematics in which Einstein expressed his theories. At any rate, his theories, initially, in 1905, were worked out only to the extent that it applied, mathematically speaking, in one or two dimensional space; his theory, in 1905, so to speak, could only be worked out in straight lines. What Einstein longed to do was to present the proofs that his theories also worked in three dimensional space, the place where most of us live. In 1915 he achieved his hearts desire and published his General Theory of Relativity, being a full exposition of his theories in three dimensional space. In his 1915 work Einstein advanced a new concept of gravitation: so powerful, Einstein concluded, were the galactic gravitational fields, that they could and did bend light. It was in this manner that Einstein laid the foundation to his theory that all space was curved. Accepting Einstein's theory of curved space then one could logically proceed to deduce that space is finite. Because light is curved due to these galactic gravitational fields, it only need be ever so slightly so, then light, say a light ray from a star, eventually returns to the point from which it originated. It's Einstein's theory that everything must come around again, like a model train. And though no boundaries can be established, at least any person might recognize, the universe does not extend forever into space it has a finite limitation.
Electromagnetic Theory of Light:-
The electromagnetic theory of light, is, that visual light is a form of electromagnetic radiation. With the acceptance of this theory of light there remained however a mystery. What was the medium through which these waves traveled? It was assumed that a massless medium, the ether, was the carrier of light waves, just as air or water carries sound waves. All this work was thrown into question, when, during the period of 1881-87, experiments were carried out by Michelson and others showing that no such thing as ether existed. With the theory of relativity, as developed by him, Einstein showed that the idea of an ether was unnecessary to the electromagnetic theory. Though the matter is beyond my comprehension, what Einstein in 1905 explained, was, that light is one effect of any number of photoelectric effects that come about as a result of electromagnetic radiation, which "travel as tiny bundles of energy, called light quanta, or photons, that behave as particles." And so, the scientific minds came back to a theory that Christian Hymens (1629-93), a Dutch physicist, had proposed four hundred and fifty years back, -- light might be explained as a wave phenomenon. Beginning there with Hymens and leading through the work of Michelson, Einstein came up with the best definition of light to his time: "Light behaves as a wave, as in diffraction and interference phenomena, or as a stream of particles, as in the photoelectric effect. The theory of relativity predicts that the speed of light in a vacuum (186,282 mi/sec = 299,792.458 km/sec) is the limiting velocity for material particles." (The two theories were combined into what we now know as quantum theory.)
"In spite of the astonishing and dramatic verifications of the theory [Theory of Relativity], many people find its four-dimensional, non-Euclidean, universe totally unpalatable. No one can visualize a four-dimensional, non-Euclidean world, but those who insist on visualizing the concepts with which science and mathematics now deal are still in the dark ages of their intellectual development. Almost since the beginning of work with numbers, mathematicians have carried on algebraic reasoning that is independent of sense experience. Today they consciously construct and apply geometries that exist only in human brains and that were never meant to be visualized. Of course, all contact with sense perception has not been abandoned. The conclusions about the physical world predicted by geometrical and algebraic cognitions must be in accord with observation and experimentation if the logical structure is to be useful for science. However, to insist that each step in a chain, even of geometrical reasoning, be meaningful to the senses is to rob mathematics and science of two thousand years of development. We should recall how people reacted to the fact that the earth is spherical and later that the Earth is moving around the sun. Certainly our perception did not agree with these facts. We should be more receptive to the relativistic concepts of time, simultaneity, space, and mass. The theory of relativity warns us against taking appearances, which hold only for a particular reference system, as the truth in any absolute sense. Here as in other physical areas mathematical laws tell us what is truth and really objective. Nature does not care much about our impressions. She continues on her course whether or not we are there.Einstein never could accept the randomness of quantum theory: "God does not play dice." Reality does not lie within our grasp; our senses and our mathematical knowledge gives us a grasp of only some parts of reality.
"The union of space and time and the influence of matter on space-time proposed by the theory of relativity, ideas that would have seemed outlandish to philosophers of the early 1900's, have now become embodied in a philosophy of nature more and more widely held. Nature presents herself to us as an organic whole, with space, time, and matter commingled. Humans have in the past analyzed nature, selected certain properties that they regarded as most important, forgotten they were abstracted aspects of a whole, and regarded them thereafter as entirely distinct entities. They are now surprised to learn that they must reunite these supposedly separate concepts to obtain a consistent, satisfactory synthesis of knowledge.
"Aristotle first formulated the philosophical doctrine that space, time, and matter are distinct components of experience. This view was subsequently adopted by scientists and used by Newton. We, following him, have become so accustomed to thinking of space and time as fundamental and distinct components of our physical world, and separate from matter, that we no longer recognize this view of nature as manmade and as only one of a number of possible views. Of course, the philosophers of the contemporary scene, among them the late Alfred North Whitehead, do not argue that this analysis of nature is useless. On the contrary, it has proved quite valuable and even essential. However, we should be aware that it is artificial, and we should not mistake our analysis for nature itself any more than we should mistake the organs observed by dissection of the human body for the living body itself.
It is now possible to appreciate how much of science has become mathematized in the form of geometry. Since the days of Euclid the laws of physical space had been no more than theorems of this geometry. Hipparchus, Ptolemy, Copernicus, and Kepler summarized the motions of the heavenly bodies in geometrical terms. With his telescope Galileo extended the application of geometry to infinite space and to many millions of heavenly bodies. When Lobatchevsky, Bolyai, and Riemann showed us how to construct different geometrical worlds [non-Euclidian geometry], Einstein seized the idea in order to fit our physical world into a four-dimensional, mathematical one. Thereby gravity, time, and matter became, along with space, merely part of the structure of geometry. Thus the belief of the classical Greeks that reality can be best understood in terms of geometrical properties and the Renaissance doctrine of Descartes that the phenomena of matter and motion can be explained in terms of the geometry of space have received sweeping affirmation."1
"Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavour to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears it ticking, but he has no way of opening the case. If he is ingenious he may form some picture of the mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility of the meaning of such a comparison."2Einstein's reputation cannot be said to rest on any one theory such as his, Theory of Relativity. He worked indefatigably all his life on many theories (in 1921 he won the Nobel prize in physics). All his life's work, Einstein felt, could be tied into a single statement, a single theory which he called the Unified Field Theory. In 1950, the 71 year old Einstein, just five years before his death presented his Unified Field Theory to the world. The only problem is, --as right, as many scientists think Einstein may be in respect to his last and all encompassing theory -- is that no one, as far as I know, has been able to figure out just how we might go about testing it. Einstein predicted that others would have difficulties to test his final theory: "... the years of searching in the dark for a truth that one feels, but cannot express; the intense desire and the alternations of confidence and misgiving, until one breaks through to clarity and understanding, are only known to him who has himself experienced them."3
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^{1} Morris Kline, Mathematics and the Search for Knowledge (Oxford University Press, 1985) at p. 219.
^{2} Ibid.
^{3} Einstein in an address at the University of Glasgow in 1933.
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2015