The principles of quantum mechanics are discussed in two of the other books in The Physical World series Quantum physics: an introduction and some of its applications are described in Quantum physics of matter

The basic working philosophy of most scientists, including those who say they have no philosophy, is a kind of realism. (Philosophers recognize many shades of realism.) The three main points of this creed are: Our senses allow us to observe a physical world, and our bodies allow us to interact with that world. Although our perceptions may differ, we all share the same physical world, which exists independently of our observations, e.g. the same Moon is really out there for all of us, even if none of us is looking at it. Although our actions may cause disturbances, it is possible to investigate the physical world without destroying its essential structure. We may therefore try to deduce the essential features of the physical world by combining experiment and observation with rational speculation. One of the many astonishing features of quantum mechanics is that it calls into question some of the central ideas of this kind of realist philosophy. When speaking about the nature of the microscopic entities that are described by quantum mechanics one of the subject's pioneers said: '...they form a world of potentialities or possibilities rather than one of things or facts.'
Werner Heisenberg Another of the quantum pioneers put it even more simply: 'There is no quantum world.'
Niels Bohr Let's see how such statements came to be made.
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By 1925 it was clear that atoms consisted of positively charged cores, called nuclei, around which swarmed negatively charged electrons. It was also clear that conventional classical mechanics was incapable of correctly describing the behaviour of those electrons, and the search was on for a new mechanics that could be applied to particles in the atomic domain. The (limited) success of Bohr's model of the atom indicated that the new mechanics would involve Planck's constant, so Max Born, a leading atomic researcher at the University of Göttingen in Germany, named the new mechanics quantum mechanics, even though he had no real idea of its basic rules at the time. It was supposed that quantum mechanics would be more fundamental than classical mechanics, so that once the rules of quantum mechanics were uncovered it would be possible to deduce the laws of classical mechanics from them. Those basic rules of quantum mechanics were actually brought to light over a period of about a year, starting in the summer of 1925. The first breakthrough was made by Werner Heisenberg, a 24-year-old researcher at Göttingen, who had been working closely with Born. Heisenberg's first paper on the subject sketched out his basic ideas, but it was far from being a systematic formulation of quantum mechanics; neither the mathematical basis of quantum mechanics (its formalism) nor its physical meaning (its interpretation) was at all clear. Intensive work by Heisenberg, Born and others over the next six months did much to clarify the formalism (which turned out to involve mathematical objects called matrices), and to show that quantum mechanics was at least as successful as Bohr's rather unsatisfactory atomic theory, but it did not clarify the interpretation. At that stage, early in 1926, Erwin Schrödinger (1887-1961), an Austrian working at the University of Zurich, published a different and somewhat simpler formulation of quantum mechanics. Schrödinger's approach was based on de Broglie's idea that matter has a wave-like aspect. Schrödinger himself soon showed that his approach was mathematically equivalent to that of Heisenberg, but he too had difficulty working out what it all meant. The key step in the interpretation of quantum mechanics was first put into print by Born in June 1926. Imagine that you could arrange a collision between a particle and a target and that, after the collision, the particle was deflected to the left. If you could repeat the collision under exactly the same conditions, you would naturally expect to see the particle deflected to the left again. If the particle were unexpectedly deflected to the right you would probably assume that the second collision had been set up in a slightly different way to the first, in spite of your best efforts to make the conditions identical. Born used the new formalism of quantum mechanics to study collisions and realized that, in utter contrast to classical expectations, quantum mechanics allows identical experiments to have different outcomes. Two collisions could be set up in exactly the same way (the discreteness of quantum mechanics helps to enable this). Yet, in spite of starting out in the same way, a particle may be deflected to the left in one collision and to the right in the other. In any single collision it is impossible to predict which way the particle will go. You might wonder whether science is possible at all if Nature behaves so capriciously. Fortunately, quantum mechanics does allow us to make predictions, but with some uncertainty. In any experiment, the formalism of quantum mechanics can, in principle, predict: the possible outcomes; the probability (i.e. the relative likelihood or chance) of each of those possible outcomes. However, what quantum mechanics cannot do, and what Born was convinced it would never do, was to go beyond probabilities and predict a definite outcome for a particular experiment that might have more than one outcome. Returning to the example of collisions, quantum mechanics can predict that particles colliding in a certain way might be deflected to the left or to the right; it can also predict the probability of deflection to the left or the right and hence the relative numbers deflected left or right in a large number of identical collisions; but it cannot predict whether a particular particle in a particular collision will be deflected right or left. Dealing with probabilities is an intrinsic part of quantum physics that cannot be avoided.
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The use of probability in physics was not new. But the suggestion that probability was intrinsic and unavoidable was shocking. In classical physics, probability was used when something which could be known in principle (such as the exact path of a particle) was not known; probability filled the gap left by ignorance. Statistical mechanics, for example, used probabilities to estimate likely pressures and entropies, compensating for ignorance about detailed molecular motions. It was not doubted however, that such details existed, and could be determined in principle. In quantum mechanics the situation was completely different; a probabilistic statement along the lines of 'this has a 30% chance of happening' might well be the most that could be said in a certain situation, even in principle.

Figure 1.30 A quantum mechanical model of a hydrogen atom, which has one electron, in its state of lowest energy. The varying density of the spots indicates the relative likelihood of finding the electron in any particular region. Click here for larger image (11.88kb)

Niels Bohr, whose atomic theory was overthrown by quantum mechanics, was a keen supporter of the new mechanics. He had partly inspired Heisenberg to undertake its development in the first place, and in May 1926 he welcomed Heisenberg to his institute in Copenhagen where a great deal of effort went into formulating a complete interpretation of quantum mechanics that included the idea of intrinsic probabilities. The Copenhagen interpretation that emerged from this work is now regarded as the conventional interpretation of quantum mechanics, though there have always been those who have questioned its correctness. Some of the features of this interpretation are: The measurable properties of objects (position, velocity, etc.) do not generally have values except just after a measurement. Measurement causes potentiality to become actuality. The measured values occur at frequencies determined by probabilistic rules. The probabilities are intrinsic and fundamental, and can be predicted by quantum mechanics. The last of these points represents a substantial shift from classical determinism. In classical mechanics the past uniquely determines the present and hence the future. In quantum mechanics this is not so. Even the most complete possible knowledge of the past would only permit the calculation of the probability of future events. Some, perhaps a little naively, saw in this a scientific basis for free will: there was an element of freedom, or at least of chance, in the Universe. The Copenhagen interpretation calls simple realism into question. If the most that you can say about a position measurement you are about to perform is that various values may be obtained, with various probabilities, then it may well mean that the object has no position until it is measured. Note that this is quite different from saying that the object has a position which you don't happen to know - it is as if the object had not made up its mind where to appear until the position measurement has been made. Clearly if you say that the object has no position, you call into question its independent reality, and hence the philosophy of realism, at least in its simplest form. This emphasizes the enormous importance of measurement in quantum physics and the motivation for making statements such as '...they form a world of potentialities or possibilities rather than one of things or facts' and 'there is no quantum world'. An alternative stance is to assume that there is a real world out there, but to admit that it cannot be adequately described in terms of classical concepts such as position or velocity. This is plausible. We have no right to expect microscopic physics to be just a scaled-down version of everyday experience. Given that quantum mechanics deals with a microscopic world well beyond the immediate reach of our senses and intuitions, perhaps the most surprising thing is that we can make predictions at all. From this perspective, the price that must be paid for the mismatch between our classical concepts and the quantum world is astonishingly small, and is reflected mainly in the appearance of probabilities. In philosophical terms, the concept of a real world can be preserved by admitting that certain aspects of it are inaccessible to us, clumsy giants that we are. But in practical, or scientific, terms this makes no difference. It is hard to see how we could ever develop an understanding that was not based on classical concepts, so probabilities seem destined to remain intrinsic and unavoidable, offering the only gateway through which we can glimpse the microscopic world. Question 1.6 Answer In Section 1 it was said that the notion of scientific law was based on the fact that identical situations produced identical outcomes. To what extent does this remain true in quantum physics where identical experiments may produce different outcomes?
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From its inception, quantum physics was concerned not just with particles such as electrons, but also with light and other forms of electromagnetic radiation. In 1900 Planck discovered the quantum in the transfer of energy from matter to radiation, and in 1905, Einstein's explanation of the photoelectric effect assumed that the transfer of energy from radiation to matter occurred in a similarly quantized fashion. It is therefore hardly surprising that the development of quantum mechanics was soon followed by an attempt to formulate a quantum theory of electromagnetic radiation. That meant, of course, combining quantum ideas such as Planck's constant and intrinsic probabilities with the field theory of electromagnetism. The result would be a quantum field theory. The quantum field theory of electromagnetism is called quantum electrodynamics, or QED for short. Its formulation proved to be very difficult. The first steps were taken by the British physicist Paul Dirac in 1927, but the theory was not really sorted out until the late 1940s. During the lengthy development of QED the following important features of quantum field theory became apparent. Quantum field theory provides the natural way of combining special relativity and quantum physics. Quantum mechanics, as originally formulated by Heisenberg and Schrödinger was inconsistent with the principle of relativity. Attempts were made to rectify this problem and significant progress was made by Dirac with his relativistic electron equation. However, despite many successes it became increasingly clear that relativistic quantum mechanics was ultimately self-contradictory and that quantum field theory provided the natural way of producing a relativistic quantum physics. Quantum fields may be regarded as collections of particles.In the case of the quantized electromagnetic field these particles are called photons. Each photon of a particular colour carries a characteristic amount of energy: the quantum of energy used by Planck and Einstein. Emission and absorption of radiation corresponds to the creation and destruction of photons and therefore inevitably involves the transfer of complete quanta of energy. (Interestingly, Einstein realized as early as 1905 that the quantized transfer of energy would be explained if radiation actually consisted of particles, but the idea was not well received and he did not press it. Photons only became an accepted part of physics in the 1920s.) Quantum field theory can be used to describe all fundamental particles. Electrons and positrons are normally regarded as examples of fundamental particles of matter. In quantum field theory all such particles are associated with quantum fields in much the same way that photons are associated with the electromagnetic field. The number of particles of a given type reflects the state of excitation of the field, and the particles are said to be 'quanta of excitation' of the field. Thus, although quantum field theory describes particles and the forces between them, it does so entirely in terms of quantum fields. Quantum field theory describes processes in which particles are created or destroyed. When a quantum field becomes more excited, the number of quanta of excitation increases. This occurs because new particle-antiparticle pairs are created from radiation. When a quantum field becomes less excited, the number of quanta of excitation decreases. This is achieved by processes in which particles and antiparticles collide and annihilate one another to produce radiation. (Both of these processes are permitted by Einstein'sE=mc²and were explicitly predicted by Dirac.) These were all very attractive features of quantum field theory and raised the hope that it might be a truly fundamental theory capable of providing a new world-view. However there were serious problems within quantum electrodynamics that had to be overcome before such hopes stood any chance of being realized. Using QED to predict the value of a physically measurable quantity involved, in practice, working out the contribution made by several different sub-processes. Making sure that these sub-processes were fully identified was a problem in itself, working out their individual contributions was even worse. Even in the simplest cases determining the contributions was difficult, and in the more complicated cases the result was usually a meaningless infinity showing that something was wrong.
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It was the problem of infinities that really delayed the completion of QED until the late 1940s. At that time, in a burst of post-war activity, a technique called renormalization was developed that made it possible to get at the physical result hidden behind the unphysical infinity. At the same time a simple diagrammatic method was devised that made it much easier to identify and perform the necessary calculations. The problem of infinities was solved by Julian Schwinger (1918-1994), Sin-itiro Tomonaga (1906-1979) and Richard P. Feynman. The last of these was also responsible for the diagrams, which have become known as Feynman diagrams (Figure 1.33).

Figure 1.33 Feynman diagrams of some of the processes that contribute to the scattering of colliding electrons. Each diagram represents a complicated mathematical expression. The wavy lines represent photons. Click here for larger image (7.20kb)

The completion of QED presented physicists with the most precise theory of Nature they had ever possessed. However, by the time that completion had been achieved it was already clear that electromagnetism and gravitation were not the only forces at work in the world. The familiar contact forces you feel when pressing on a surface had long been understood to be nothing more than manifestations of electromagnetism - atoms repelling other atoms that got too close - but the 1930s and 1940s had provided clear evidence of the existence of two other fundamental forces. These new forces were quite powerful, but both were of such short range that they mainly operated within atoms rather than between them. The new forces were called the strong and weak nuclear forces since their effects were most clearly seen in the behaviour of atomic nuclei. The major properties of all four of the fundamental forces are listed in Table 1.1

Force	Strength	Range	Force Carrier
strong	10-1	10-15m	gluon
electromagnetic	10-2	infinite	photon
weak	10-2	10-17m	W and Z bosons
gravitational	10-45	infinite	graviton(?)

Table 1.1 The four fundamental forces. The strengths are roughly those found at high collision energies, and the force carriers are the particles most closely associated with each force. The graviton is followed by a question mark because its existence is still in doubt.

Formulating quantum field theories of each of the four fundamental forces was an obvious goal, and remains so to this day. Three of the forces - the strong, the weak and the electromagnetic - have been treated with great success; and have been combined to form a so-called standard model of fundamental forces. However, gravity has resisted all attempts to fit it into the same kind of theoretical strait-jacket and seems to require very special treatment if it is to be treated as a quantum field theory at all. If it were not for the problem of gravity we would be able to say that the physicist's current world-view is that the Universe consists of a set of mutually interacting quantum fields that fill the space-time described by special relativity. But it seems that this will not do. A way forward may be indicated by the standard model itself. The standard model is actually something more than a description of three of the four fundamental forces; it is also to some extent a prototype for their union. Within the standard model the electromagnetic and weak forces appear as a unified electroweak force. The exact meaning of unification in this context is too technical to go into here, but suffice it to say that, under unification, the quantum fields responsible for the weak and electromagnetic forces combine in a way that is slightly reminiscent of Einstein's fusion of space and time to form space-time.
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The success of electroweak unification has been one of the motivations for suggesting that all three of the forces that appear in the standard model might be unified within a grand unified theory, and that a further step of unification might also incorporate gravity, thus bringing all four fundamental forces within a single superunified theory. The form that such a superunified theory might take is far from clear. Would it involve quantum fields in a curved space-time, or would something altogether more radical be required?

Figure 1.35 A possible route to superunification of the four fundamental forces. At low energies we have laboratory evidence of four forces, but the weak and electromagnetic forces are known to acquire a common strength at high energies. Perhaps this process continues. Click here for larger image (11.88kb)

For some time many hoped that an approach called string theory might provide a solution to the problem of superunification. The idea of this approach was that the basic entities were not quantized fields that filled the points of four-dimensional space-time, but rather extended objects called strings that vibrated in ten or more dimensions. There was never any experimental evidence to support this idea, but what really caused theorists to lose faith in it was the discovery that string theory is not unique. There is a strong prejudice amongst those searching for a unified theory of everything that there should only be one such theory, not a whole class of them. String theory fails to satisfy this uniqueness criterion. However, hope of string-based superunification has not been entirely lost. A new subject called M-theory is being investigated in which all of the plausible string theories appear as different aspects of a single theory - perhaps. At the present time, the quest to find the ultimate constituents of the Universe and the laws that regulate their behaviour ends not with an answer, but with a set of loose ends. Perhaps this is as it should be in a healthy science, or perhaps it is a sign that we are heading towards a dead end. Perhaps there is no single world-view for physics to uncover, or perhaps it is not the function of physics to do so. Question 1.7 Answer Does quantum field theory suffer from the same kind of conflict with simple realism that arose in quantum mechanics? Continue on to 5.3 The end of physics?
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Suppose for the moment that quantum field theory, or string theory or M-theory, or some other theory no one has yet heard of, does turn out to be the much sought-after superunified theory.

so wonderfully compact that it can be printed on the front of a teeshirt

Suppose it is unique and is so wonderfully compact that it can be printed on the front of a teeshirt. What would such a theory really tell us about the world? Looking on the positive side, the theory should indicate the fundamental entities of which the world is composed, whether they are particles, strings, quantum fields, or whatever. The theory should also indicate the truly fundamental constants of Nature (it may be that Planck's constant, the speed of light and so on are not really as fundamental as we think), and it should certainly indicate all the fundamental processes that can occur - the elementary processes from which all other processes are composed. This would be the ultimate realization of reductionism, the view that every phenomenon can be reduced to some more elementary set of phenomena, all the way back to a set of truly fundamental entities and interactions. Being rather more negative, a fundamental theory of everything might not really tell us very much at all. It is hard to believe, for example, that even a supremely intelligent scientist equipped with as much computing power as he or she could desire could set to work from the theory of everything and predict the existence of the Earth, let alone something like my choice of breakfast today. They might show that the existence of an Earth-like planet, or an egg-like breakfast was consistent with the theory of everything, but that's a long way from predicting particular cases. There are several reasons why a theory of everything will probably not really be a theory of all that much. Here are some: The problem of initial conditions. In a fully deterministic theory, such as Newtonian mechanics, the present is determined by the past. To predict particular eventualities in the present Universe we would therefore need to know the initial state of our Universe. It may not be impossible to determine these cosmic initial conditions, but it's not clear, and it is hard to believe we will ever know for sure. The problem of indeterminacy. We have seen that when it comes to predicting particular events quantum physics is limited to making probabilistic predictions. It seems certain that quantum physics will be an underlying principle of any conceivable theory of everything, so the predictions may always be limited to possibilities rather than particular eventualities. Some might hope, as Einstein did, that quantum physics will eventually be shown to be incomplete and that a full theory will replace +y by certainty, but all current indications are that this is not going to be the case and the one thing that's certain is that uncertainty is here to stay. The problem of emergence. Reductionism was originally a biological doctrine which aimed to reduce biology to more fundamental sciences such as chemistry and physics. It was opposed by the doctrine of emergence which claimed that even if all physical and chemical phenomena were known it would not be possible to predict biological phenomena because new properties emerged at the level of biology that were not contained in any of its parts. These doctrines are now used generally in discussions of science, including physics. To give a physical example; water is wet and it is made of molecules, yet no molecule is wet; the wetness is a property of the water that emerges when large numbers of molecules come together.
Most physicists would expect a satisfactory explanation of the wetness of water to make contact with fundamental principles (somehow, the wetness of water must be implicit in the electrical interactions of its molecules) and, in this sense, they are reductionists.

complex phenomena require explanations on many different levels

But it often happens that complex phenomena require explanations on many different levels, and it would be wrong to dismiss the higher levels as being unimportant, or uninteresting to the physicist. The interactions of atoms and molecules are now understood - at least in terms of the fundamental laws that operate. Yet a wealth of unexpected phenomena continues to emerge in the physics of atoms, molecules, solids and liquids, showing that there is much to explore in physics above the most fundamental level. The challenges are as much to do with understanding the consequences of known laws as with discovering new ones. Perhaps the ultimate challenge will be to provide a chain of understanding that links fundamental principles to truly complex phenomena, such as how a brain works. For all of these reasons, and others you can discover for yourself, it seems safe to conclude that physics has a healthy future that might well include a theory of everything, but which is very unlikely to be ended by such a theory.
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