Much of the remainder of this book will concern itself with those aspects of theoretical physics which seek to understand the nature of matter. Such understanding as we have has mainly been achieved by probing the structure of successively smaller constituents and, at least on the face of things, the regions of space and time we need to consider are far too small for spacetime curvature to be of any signicance. Many of our considerations will therefore be restricted to Minkowski or, as in the present chapter, Galilean spacetime. Paradoxically, however, it seems that gravity and the structure of space and time may have a vital role to play in our understanding of matter on the very smallest scales, and we shall see something of the ways in which this comes about in later chapters.
Much of the remainder of this book will concern itself with those aspects of theoretical physics which seek to understand the nature of matter. Such understanding as we have has mainly been achieved by probing the structure of successively smaller constituents and, at least on the face of things, the regions of space and time we need to consider are far too small for spacetime curvature to be of any signicance. Many of our considerations will therefore be restricted to Minkowski or, as in the present chapter, Galilean spacetime. Paradoxically, however, it seems that gravity and the structure of space and time may have a vital role to play in our understanding of matter on the very smallest scales, and we shall see something of the ways in which this comes about in later chapters.
Much of the remainder of this book will concern itself with those aspects of theoretical physics which seek to understand the nature of matter. Such understanding as we have has mainly been achieved by probing the structure of successively smaller constituents and, at least on the face of things, the regions of space and time we need to consider are far too small for spacetime curvature to be of any significance. Many of our considerations will therefore be restricted to Minkowski or, as in the present chapter, Galilean spacetime. Paradoxically, however, it seems that gravity and the structure of space and time may have a vital role to play in our understanding of matter on the very smallest scales, and we shall see something of the ways in which this comes about in later chapters.
Up to this point, our study of quantum mechanics has concerned itself with the behaviour of particles that inhabit a Galilean spacetime. For many purposes, in atomic, molecular and condensed matter physics, this theory is quite adequate. We saw in earlier chapters, however, that our actual spacetime has a structure which is much closer to that of the Minkowski spacetime of special relativity and that more general structures must be considered when gravitational phenomena are signicant. From a purely theoretical point of view, it is therefore important to formulate quantum theory in a way which is consistent with these more general spacetimes. The benets of constructing a relativistic quantum theory actually go far beyond the aesthetic satisfaction of making our geometrical and quantum-mechanical reasoning compatible. For one thing, we shall discover that the relativistic theory provides a deeper understanding of spin and the distinction between fermions and bosons, which in the non-relativistic theory appear simply as facts of life that we must strive to accommodate. Also, of course, there are many situations in which relativistic eects become observable, for which non-relativistic theory provides no explanation. The most obvious are high-energy scattering experiments, in which particles acquire kinetic energies comparable with or greater than their rest energies mc2, and the correct 4-momentum (3.33) must be used. There are, however, more subtle eects, such as the spin-orbit coupling that is essential for interpreting atomic spectra, which are also of relativistic origin.
Up to this point, our study of quantum mechanics has concerned itself with the behaviour of particles that inhabit a Galilean spacetime. For many purposes, in atomic, molecular and condensed matter physics, this theory is quite adequate. We saw in earlier chapters, however, that our actual spacetime has a structure which is much closer to that of the Minkowski spacetime of special relativity and that more general structures must be considered when gravitational phenomena are significant. From a purely theoretical point of view, it is therefore important to formulate quantum theory in a way which is consistent with these more general spacetimes. The benefits of constructing a relativistic quantum theory actually go far beyond the aesthetic satisfaction of making our geometrical and quantummechanical reasoning compatible. For one thing, we shall discover that the relativistic theory provides a deeper understanding of spin and the distinction between fermions and bosons, which in the non-relativistic theory appear simply as facts of life that we must strive to accommodate. Also, of course, there are many situations in which relativistic effects become observable, for which nonrelativistic theory provides no explanation. The most obvious are high-energy scattering experiments, in which particles acquire kinetic energies comparable with or greater than their rest energies mc2, and the correct 4-momentum (3.34) must be used. There are, however, more subtle effects, such as the spin-orbit coupling that is essential for interpreting atomic spectra, which are also of relativistic origin.
Abstract Quantum theory has presented scientists and philosophers of science with a series of perplexing questions. It seems to many that any attempt to comprehend a world described by quantum theory will require revision in our understanding of the nature of things far more radical than the revision in our understanding of the nature of space and time demanded by the theories of relativity. It has been claimed that to comprehend quantum theory we must revise our very understanding of such matters as the objective nature of reality and its independence from our perception of it, the nature of a complex system and its relation to its components, and the nature of causal and other kinds of determination in the world.
It has become ever more clear over the past 70 years that reality is best described by a theory that no one fully understands and which cannot be applied to most everyday phenomena. Quantum theory has been subjected to many stringent tests and all of its predictions, however strange, have always been borne out. Originally developed to account for why atoms do not collapse and why they radiate and absorb energy in discrete amounts (quanta), it has now gone far beyond these rather simple beginnings. It is essentially a mathematical theory, so trying to describe it in words is analogous to transforming a picture into a poem. Inaccuracies, distortions and over-simplifications inevitably creep in. Nevertheless, one can convey the essence of the picture, and that is what is attempted here. Some grasp of what the material world is really like, and of the unfamiliar ways in which it can behave, is probably necessary to reaching an understanding of awareness and is certainly needed to comprehend the experimental evidence set out in Chapter 5.
A few days later, while finishing his dinner, Mr Tompkins remembered that it was the night of the professor's lecture on the structure of the atom, which he had promised to attend. But he was so fed up with his father-in-law's interminable expositions that he decided to forget the lecture and spend a comfortable evening at home. However, just as he was getting settled with his book, Maud cut off this avenue of escape by looking at the clock and remarking, gently but firmly, that it was almost time for him to leave. So, half an hour later, he found himself on a hard wooden bench in the university auditorium together with a crowd of eager young students. ‘Ladies and gentlemen,’ began the professor, looking at them gravely over his spectacles, ‘In my last lecture I promised to give you more details concerning the internal structure of the atom, and to explain how the peculiar features of this structure account for its physical and chemical properties. You know, of course, that atoms are no longer considered as elementary indivisible constituent parts of matter, and that this role has passed now to much smaller particles such as electrons, protons, etc. ‘The idea of elementary constituent particles of matter, representing the last possible step in divisibility of material bodies, dates back to the ancient Greek philosopher DEMOCRITUS who lived in the fourth century B.C. Meditating about the hidden nature of things, Democritus came to the problem of the structure of matter and was faced with the question whether or not it can exist in infinitely small portions.