@As a way of honoring Professor Wheeler on his sixtieth birthday, I propose to take this opportunity to elaborate upon certain somewhat speculative ideas which I have tried to hint at on occasion, concerning the possible nature of a quantized space-time. The reader will not need to be too discerning to recognize some substantial dierences between the ideas I am proposing here and those which Professor Wheeler has on many occasions so eloquently and forcefully put forward. Nonetheless, there is little doubt in my own mind as to the very great inspirational inuence that Professor Wheeler’s own views have had in the development of several of the thoughts which I am expressing here. To begin with, let me make clear that I do not necessarily mean by \quantized space-time something which could be obtained by applying standard (or even non-standard) techniques of quantization to Einstein’s general theory of relativity. What I wish to say has its roots in something which is really more primitive than either quantum theory or relativity as such. This is the question of the fundamental role played by the mathematical concept of continuum in virtually the whole of accepted present-day physical theory. Not only does the continuum occupy a basic position in our mathematical models of space and time (with the concomitant implication of a continuous nature for many related physical concepts such as velocity, energy, momentum, temperature, etc.), but so also does present-day quantum theory rest crucially on a continuum concept, namely on the two-dimensional complex continuum of probability amplitudes, this being the continuum which also occurs in the superposition law. Let me say at the outset that I am not happy with this state of aairs in physical theory. The mathematical continuum has always seemed to me to contain many features which are really very foreign to physics. This point = @ @
@As a way of honoring Professor Wheeler on his sixtieth birthday, I propose to take this opportunity to elaborate upon certain somewhat speculative ideas which I have tried to hint at on occasion, concerning the possible nature of a quantized space-time. The reader will not need to be too discerning to recognize some substantial dierences between the ideas I am proposing here and those which Professor Wheeler has on many occasions so eloquently and forcefully put forward. Nonetheless, there is little doubt in my own mind as to the very great inspirational inuence that Professor Wheeler’s own views have had in the development of several of the thoughts which I am expressing here. To begin with, let me make clear that I do not necessarily mean by \quantized space-time something which could be obtained by applying standard (or even non-standard) techniques of quantization to Einstein’s general theory of relativity. What I wish to say has its roots in something which is really more primitive than either quantum theory or relativity as such. This is the question of the fundamental role played by the mathematical concept of continuum in virtually the whole of accepted present-day physical theory. Not only does the continuum occupy a basic position in our mathematical models of space and time (with the concomitant implication of a continuous nature for many related physical concepts such as velocity, energy, momentum, temperature, etc.), but so also does present-day quantum theory rest crucially on a continuum concept, namely on the two-dimensional complex continuum of probability amplitudes, this being the continuum which also occurs in the superposition law. Let me say at the outset that I am not happy with this state of aairs in physical theory. The mathematical continuum has always seemed to me to contain many features which are really very foreign to physics. This point = @ @
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
I conclude the first part of this book by carrying the story up to 1928, to the lightning flash in Eddington's mind produced by Dirac's paper on the wave equation of the electron. Setting out the context and Eddington's thinking about it is a very different matter for quantum mechanics and relativity. Both theories are commonly expressed in austere mathematical language. In the case of relativity the basic ideas behind the mathematics are now well understood and can be set out with little complication. These ideas were mostly already clear to Eddington. But for quantum mechanics the mathematics, yoked to the wealth of experimental results, drove the development of the theory at a breakneck speed, mostly without anyone pausing for deeper understanding. It is indeed only in the last decade that it has become generally accepted that quantum mechanics still lacks any coherent interpretation. To explain Eddington's context it is therefore necessary to say something about the mathematical formalism. It is true, as will become clear, that Eddington was a little more sceptical than most, but by and large the mathematics drove him as it did those directly working in the theory. I begin, then, with a description of that part of the early (pre-1925) history of quantum mechanics that was in Eddington's mind in 1923. Then I explain what happened in 1925–6 and Eddington's reaction to it. The chapter concludes with Dirac's relativistic wave equation of 1928 and Eddington's further reaction to that. The old quantum theory What is now called the old quantum theory arose at the turn of the century. Two related experimental contradictions with classical physics played important roles in this.
It was with some trepidation that I agreed to speak today, because of a strong doubt that I could say anything substantial not already to be found in the literature of the subject. I cannot say that this trepidation has been subsequently relieved: all I can claim to offer in this paper is a review of certain basic characteristics or themes in the quantum-mechanical situation (which by now should, I think, be thoroughly understood by everyone engaged with the matter), supplemented by some rather general reflections on our philosophical predicament. In aid of these more general reflections, I shall indulge a proclivity for calling on historical matters—some fairly recent, some older, some ancient—which I hope may serve to place current issues in a useful perspective; and I ask your forgiveness for allowing myself to quote certain previous, but hitherto unpublished, remarks of my own.
There can be few physicists who have delved as deeply into the philosophical implications of their subject as has David Bohm. It is therefore with some trepidation that I am paying my respects to him on the occasion of his retirement with an attempt of my own to relate questions of philosophy to those of the foundations of physics. The viewpoint that I am putting forward here attempts to relate questions that have been two of Bohm's major interests over the years; namely, a possible breakdown of quantum mechanics on a macroscopic scale and the physical basis of conscious thought. It must be evident to the reader that in both these topics I am venturing into dangerously speculative territory. Moreover others more expert that I (such as Wigner 1, as well as Bohm 2 himself) have put forward strongly-reasoned views which relate these topics. Yet I do feel that my own viewpoint is both well worth describing and sufficiently different from these others that the reader may find something of value here. But my account must necessarily be somewhat truncated, for reasons of space and of time. It is my intention to expand these thoughts at much greater length elsewhere.
June 1997, “Painting My Stripes” I am just returning from the library, where – completely by accident – I ran into and read an entertaining little article: A Peres, “Einstein, Gödel, Bohr,” Foundations of Physics 15 (2), 1985, 201–205. I was especially entertained by your closing line, “Any attempt to inject realism in physical theory is bound to lead to inconsistencies.” Do you have any other writings (beside the AJP paper with Zurek) where you expand upon the ideas presented in this? In connection to this, I have another question. If I recall correctly, you once told me that you finally came to grips (“interpretationally,” that is) with quantum mechanics in 1986. (Perhaps I have the year wrong, but that's part of the question.) Would you be willing to expand upon that point? In particular, was your arrived-at comfort founded upon the line I quote above? I suppose I ask these questions for several reasons, perhaps the strongest of which is a renewed dilettante interest in the foundations of quantum theory. Among other things, I am trying to plan (or dream up!) a talk for the Hull conference in September to be titled something like: “Quantum Information Theory's Implications for the Foundations of the Quantum as a Whole.” My own pet “idea for an idea” (as Wheeler would say) is that the quantum theoretical description – along with its Hilbert-space structure – is forced upon us when the information we have about a physical situation/system is of a certain variety.