It stands alone
It stands alone
Abstract and Keywords
The theory of relativity is unique and is based on very simple ideas. In fact, it has only one fundamental premise and one physical fact. The premise is that the laws of physics must be the same everywhere. It does not matter where we are or how we are moving, the laws must be the same. This is just an article of faith in the unity of nature. The physical fact is that the speed of light in a vacuum is the same no matter what. If the light source is stationary, or moving towards us, or moving away from us, we always measure the same speed. This is counterintuitive, but experiment shows it to be true and it must be accepted. Relativity then follows by inexorable logic. This minimalist foundation is part of the beauty of relativity. The structure of the theory is also so beautiful that it compels belief.
Classical mechanics and relativity are unlike many other physical theories in that they are not based on any ideas of what the constituents of the world are like or what they are made of. They do not depend on whether or not matter is made of atoms, or on whether light consists of particles or waves, or on the kind of forces acting between atoms, or on any other information about the nature of matter and energy. The only other theory with such simplicity is thermodynamics, which is also independent of material constitution and of time and place. In fact, some scientists were so impressed by its universality that an entire school of scientific thought rose up in the nineteenth century, called Energetics, that tried to base all science on thermodynamics without any reference to atoms. But mechanics is different in several respects. First, it includes the crucial concept of time; second, it connects widely different regions of space, whereas thermodynamics is essentially local; and third, it encompasses a description of dynamics. In many ways, thermodynamics is a flawless logical construct that exposes the relations among physical quantities. But if any significant numerical results that relate to real physical systems are to be obtained, the underlying theory of statistical mechanics that relates thermodynamic quantities to the nature of atoms and molecules is required. Classical and relativistic mechanics, on the other hand, gave many new results, and continues to give new results, without reference to the nature of matter.
Elasticity theory is based on assumptions about the forces acting between elementary parts of solid bodies; theories of chemistry are (p.215) based on the nature of the fundamental interactions among atoms; electrodynamic theory is an expression of the nature of electrical forces; hydrodynamics arises from the properties of fluids. And quantum mechanics, the other great scientific achievement of the twentieth century is, from top to bottom, a study of the ultimate composition of matter and the properties of its constituents.
But relativity is quite different than classical mechanics. It is nothing more than the study of what it means to make scientific measurements of distance and of time. It grew out of an analysis of the actual physical operations of making a measurement of distance with a real physical ruler and of measuring time with an actual physical clock. It is true that many of the physical results depend on specific laws that do arise from applying relativity to theories of the nature of matter and radiation, but this is not the essential point. Relativity is, fundamentally, nothing more than a theory of the simplest of all experiments: the measurement of macroscopic distances and times.
The foundation of relativity is incredibly basic and incredibly simple, and yet it took men of genius to discover it and to develop it. It took genius to accept the results of experiments, even when they ran counter to conventional wisdom and established beliefs, and it took genius to follow the logic based on these experiments rigorously and without deviation no matter how strange the consequences.
Human intelligence did not evolve for the purpose of discovering the truths of nature, but in response to the requirements of survival. Manipulation of matter on a human scale was important; time intervals of minutes, hours, and months were important; speeds of rivers, running animals, and visible projectiles were important. Human-scale times, distances, and speeds were the experiences that fed intelligence and created the physical intuition that allowed human beings to survive and prosper. This intuition even predated the emergence of human consciousness, because animals also had to deal with a world governed by the same scale. So when scientific studies showed that these concepts had to be changed in ways that made them completely different (p.216) from common experience, the mind strongly resisted the new concepts. They were at variance with ideas that had served people well throughout their existence, and only genius could break through the conditioning of millennia.
Field theories are intrinsically beautiful because they start with a few assumptions from which all else follows by the application of elegant differential equations. Relativity is the most elegant example of a field theory.
All who have studied the theory of relativity have found it hugely attractive and called it beautiful. It is so compelling and carries such an aura of truth that its verification by observation and experiment is indeed fortunate. If relativity were not true, then there would be something wrong with our perception of the world, because it feels as if it surely should be true. Of course, experimental fact is the ultimate arbiter, but what a loss it would be if relativity were shown to be false! The basic concepts of relativity have the feeling of always being right.
The elegance of relativity theory starts with the simplicity of its assumptions. Let's restate them here and stress that they apply to general relativity, of which special relativity is a limiting case. The first is that the speed of light in a vacuum is the same in every local inertial system. The second is that the laws of nature are the same in every coordinate system. The first assumption is the theory's experimental content and the second is its philosophical foundation. It's hard to argue with these statements. Every measurement ever made supports them and no violation has ever been found.
There is a profound difference in the nature of the two assumptions even though they are both empirically based, and I have tried to recognize the difference by calling one of them “philosophical”. The constancy of the velocity of light is a straightforward fact and readily verified by specific measurements.
The second postulate is called the “principle of covariance”. It is not immediately established by any single type of experiment. To the modern scientific mind it is a natural assumption because it seems ridiculous to think that the laws of nature should depend (p.217) on which coordinate system is used to describe them. But this was not always so, and science had to evolve for centuries before such an idea could be accepted.
Aristotle and Ptolemy thought that the Earth gave a special point of view for all natural phenomena, celestial as well as terrestrial. This was first adopted on scientific grounds but was later given the force of religious dogma. Copernicus revived Aristarchus' ancient idea of a heliocentric solar system, and this was confirmed by Galileo's observations, so the center of the world moved to the Sun, but there was still a special set of coordinates for describing nature. It was not until Faraday and Maxwell forced Einstein to carefully analyze the measurement of distance and time that it became clear that no coordinate system was special. The history leading to covariance is the story of a continual march away from anthropomorphism: from man being the center of all things, to every point in the universe being equally valid for describing nature.
Only logic is used to work out the consequences of relativity. No other data or assumptions are needed. The mathematical structure is so general that it does not even refer to any particular geometry or set of coordinates, but is valid for all of them. Furthermore, the theory is fully deterministic, in the sense that it ties together causes and effects in a tight temporal chain, and all quantities can be defined and computed to any degree of precision required. Also it is a field theory, which means that any event at a particular point in place and time is determined only by the conditions of the space very near to that place and that time. There is no action-at-a-distance, an idea that was always troublesome.
A measurement of time or distance is well defined in relativity theory and always gives a unique answer. The limitations of the theory arise from the fact that these are macroscopic measurements that ignore the atomic constitution of matter. It is assumed that measurements of distance or of time can be made to any degree of accuracy desired. But we know that such accuracy is impossible, even in principle, because experimental devices are made of atoms. We know, from quantum mechanics, that any (p.218) measurement at atomic distances disturbs the system, so that precise measurements are impossible. The process of measurement transfers energy to the atom that kicks it around, so position cannot be measured precisely, and distance is indeterminate. This is true for all measurements. At the atomic level, measurements are subject to Heisenberg's uncertainty principle, which states that simultaneous measurements of physical quantities can be determined only within certain limits. This is not because devices cannot be made accurately enough; it is an inherent property of nature.
General relativity is a macroscopic theory, and it breaks down for the description of nature at atomic scales. Normally, this is not a problem because gravitational forces are very weak compared to other forces. Intermolecular, interatomic, and internuclear forces are so much stronger that gravity can be completely ignored when one studies molecules, atoms, or fundamental particles. And gravitational effects normally involve such large distances and massive objects that interactions at the atomic and nuclear scale are irrelevant. Usually, then, relativity, which is a theory of measurement of macroscopic objects, and quantum mechanics, which is a theory of measurement of microscopic objects, are well separated and work well within their respective domains. But there are important exceptions, and these are very important exceptions. When a region of space is very small, so that it is of the order of atomic dimensions, and its mass is so high that its density approaches infinity, then a theory that simultaneously describes quantum-sized distances and very large gravitational forces is needed. The interior of a black hole and the Big Bang origin of the universe are two such instances, so there are astrophysical and cosmological phenomena that cannot be understood unless relativity and quantum theory can be combined into a single, unified whole. The search for such a theory has been going on for decades without success. The fundamental difficulty is that the two theories are based on radically different concepts of that most important issue, the meaning of a measurement.
Yet relativity is unparalleled. The stark simplicity of its assumptions, its striking mathematical structure, its universality, its (p.219) deterministic field theory character, and its total success in its own domain make it unlike any other scientific theory.
The search for its unification with quantum mechanics is just another expression of Einstein's belief in the unity of nature and his confidence that the ultimate answers could be found by human reason.