Surely, after 62 years, we should have an exact formulation of some serious part of quantum mechanics? By ‘exact’ I do not of course mean ‘exactly true’. I mean only that the theory should be fully formulated in mathematical terms, with nothing left to the discretion of the theoretical physicist...until workable approximations are needed in applications. By ‘serious’ I mean that some substantial fragment of physics should be covered. Nonrelativistic ‘particle’ quantum mechanics, perhaps with the inclusion of the electromagnetic field and cut-off interaction, is serious enough. For it covers ‘a large part of physics and the whole of chemistry’ (P A M Dirac 1929 Proc. R. Soc.A 123 714). I mean too, by ‘serious’, that ‘apparatus’ should not be separated off from the rest of the world into black boxes, as if it were not made of atoms and not ruled by quantum mechanics.
Surely, after 62 years, we should have an exact formulation of some serious part of quantum mechanics? By ‘exact’ I do not of course mean ‘exactly true’. I mean only that the theory should be fully formulated in mathematical terms, with nothing left to the discretion of the theoretical physicist...until workable approximations are needed in applications. By ‘serious’ I mean that some substantial fragment of physics should be covered. Nonrelativistic ‘particle’ quantum mechanics, perhaps with the inclusion of the electromagnetic field and cut-off interaction, is serious enough. For it covers ‘a large part of physics and the whole of chemistry’ (P A M Dirac 1929 Proc. R. Soc.A 123 714). I mean too, by ‘serious’, that ‘apparatus’ should not be separated off from the rest of the world into black boxes, as if it were not made of atoms and not ruled by quantum mechanics.
Surely, after 62 years, we should have an exact formulation of some serious part of quantum mechanics? By ‘exact’ I do not of course mean ‘exactly true’. I mean only that the theory should be fully formulated in mathematical terms, with nothing left to the discretion of the theoretical physicist … until workable approximations are needed in applications. By ‘serious’ I mean that some substantial fragment of physics should be covered. Non-relativistic ‘particle’ quantum mechanics, perhaps with the inclusion of the electromagnetic field and a cut-off interaction, is serious enough. For it covers ‘a large part of physics and the whole of chemistry’. I mean too, by ‘serious’, that ‘apparatus’ should not be separated off from the rest of the world into black boxes, as if it were not made of atoms and not ruled by quantum mechanics. The question, ‘… should we not have an exact formulation …?’, is often answered by one or both of two others. I will try to reply to them: Why bother? Why not look it up in a good book ? Why bother? Perhaps the most distinguished of ‘why bother?’ers has been Dirac. He divided the difficulties of quantum mechanics into two classes, those of the first class and those of the second. The second-class difficulties were essentially the infinities of relativistic quantum field theory. Dirac was very disturbed by these, and was not impressed by the ‘renormalisation’ procedures by which they are circumvented. Dirac tried hard to eliminate these second-class difficulties, and urged others to do likewise.
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.
Abstract Chemistry is about the atom and molecule, motion of which follows quantum mechanics established 100 years ago by Werner Heisenberg, inspired by a number of milestone findings including Max Planck’s first quanta concept for black body radiation, Albert Einstein’s photon concept for photoelectric effect and oscillator quanta for heat capacity of solid, and Niels Bohr’s quantum model for atomic structure. Independently, inspired by Louis de Broglie’s particle-wave duality, Erwin Schrödinger established wave mechanics, which is shown to be equivalent to Heisenberg’s mechanics by Paul Dirac. The latter further established the relativistic quantum mechanics, and then claimed that the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws lead to equations much too complicated to be soluble. In the occasion of celebrating The International Year of Quantum Science and Technology (IYQ 2025, quantum2025.org), we will present a heuristic review of the development of quantum theory and its application to chemistry, namely, quantum chemistry (QC). Then, we will discuss some of the current challenges and the future developments, especially on the quantum computing for quantum chemistry (QCQC).
Bohr is said to have remarked that anybody who is not shocked by quantum theory has not understood it. No physicist, however, challenges its practical usefulness in predicting experimental results and providing an explanatory framework for an enormous range of study. Nevertheless, more thoughtful physicists have been astonished and disturbed by what is implied when attempts are made to interpret its meaning. As a result a variety of ingenious, and sometimes bizarre, schemes have been devised since its inception in order to make these implications more acceptable to the scientific mind. Some of these schemes have resulted in proposals which appear stranger than the problems they have been designed to resolve. After some sixty years there is no consensus of opinion upon the solution of the epistemological problems posed. Indeed the debate keeps on resurfacing in the scientific literature and continues to generate library shelves of books. Some progress, however, has been made and the late John Bell himself and the experimental work of Alain Aspect have demonstrated that some epistemological positions cannot be sustained.
The basic thesis of this book is that there is no quantum measurement problem. I do not mean by this that the apparent paradoxes of quantum mechanics arise because we fail to recognize ‘that quantum theory does not describe physical reality’ (Fuchs and Peres 2000a). Quantum theory describes reality just fine, like any other scientific theory worth taking seriously: describing (and explaining) reality is what the scientific enterprise is about. Nor do I mean that we have found solutions to the problem, ways to modify or supplement quantum mechanics so that the paradoxes are removed. I don’t actually think that we have found any very satisfactory solutions in this sense (at least not in the relativistic domain) but that isn’t my theme: even if we did have these modifications, they would be ways of changing from quantum physics, which supposedly does have a measurement problem, to some other theory, which supposedly doesn’t.