5 The uncertain Universe An introduction to the uncertain UniverseDespite the impact of relativity, the greatest source of change in the scientific world-view in the twentieth century has undoubtedly been the development of quantum physics. This is the branch of physics that is mainly concerned with microscopic entities such as atoms and molecules, and their constituents.
quantum physics and classical physics, where, by classical physics, we mean anything that is not quantum physics. To be fair, it should be noted that some authors prefer to define classical physics as consisting of those subjects that were already well-defined by the year 1900, together with their direct developments in the twentieth century. In this way they include mechanics, thermodynamics and electromagnetism, but they exclude special and general relativity. Most physicists, however, would not hesitate to say that general relativity was a classical theory of gravity, and would regard relativity as the culmination of classical physics rather than a step beyond it. In any event, there can be no doubt that the development of quantum physics has demanded a fundamental change in outlook by physicists. Quantum physics was born in 1900, but it took about twenty five years to reach maturity. During the first quarter of the twentieth century it had a rather rickety feel; there was not really any coherent theory of quantum physics, just assorted quantum ideas that were so successful in solving certain outstanding puzzles that it seemed there had to be something behind it all. The strongest characteristic of quantum physics during this early period was an emphasis on graininess or discreteness. Indeed, the word quantum actually comes from the Latin for 'unit of quantity' or 'amount' and was introduced into physics by the German scientist Max Planck (1858-1947), in the course of his investigations into the emission of electromagnetic radiation from hot surfaces.Crudely speaking, Planck was looking into why hot things glow. He knew that the light given off by a heated object is a mixture of all the possible colours of light and he wanted to predict the relative brightness with which each colour would be emitted from an object at a given temperature. It was changes in these relative brightnesses as temperature increased that explained why objects went from being red-hot at fairly low temperatures to white-hot or blue-hot at fairly high temperatures.
An introduction to the uncertain UniversePlanck found that, in order to account for the observed pattern of emission from hot bodies, he had to assume that energy was transferred from the heated surface to the emitted radiation in a 'grainy' way. Corresponding to each particular colour of light there was a minimum amount of energy - a quantum of energy - that could be carried away from the surface by the light. The size of this quantum of energy depended on the colour of the light; an energy quantum of violet light was almost twice as energetic as an energy quantum of red light, and every other colour had its own charac-teristic quantum. Planck was able to write down a law that related the quantum of energy corresponding to any particular colour to the physical property (frequency) which determined that colour. In doing so he introduced a new fundamental constant of Nature - now called Planck's constant (h = 6.626 * 10^{-34} 1 joule seconds). The appearance of Planck's constant in a calculation can be taken as a clear indication that quantum physics is involved.
5.1 Quantum mechanics and chance 5 The uncertain Universe 5.1 Quantum mechanics and chance Part 1 of 3 | Part 2 | Part 3 For a printable version of 'The uncertain Universe' click here The real quantum revolution dates from the formulation of quantum mechanics by Werner Heisenberg (1901-1976) and others in 1925, and its physical interpretation by Max Born (1882-1970) in 1926. However, before attempting even the most basic sketch of quantum mechanics let's take a small diversion into the realm of philosophy. An introduction to the uncertain Universe
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. Continue on to Quantum mechanics and chance, part 2 of 3 5 The uncertain Universe 5.1 Quantum mechanics and chance Part 1 of 3 | Part 2 | Part 3 For a printable version of 'The uncertain Universe' click hereBy 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 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 probability (i.e. the relative likelihood or chance) of each of those possible outcomes. 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.Continue on to Quantum mechanics and chance, part 2 of 3 5 The uncertain Universe 5.1 Quantum mechanics and chance Part 1 of 3 | Part 2 | Part 3 For a printable version of 'The uncertain Universe' click hereThe 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.
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?Continue on to 5.2 Quantum fields and unification 5 The uncertain Universe 5.2 Quantum fields and unification Part 1 of 3 | Part 2 | Part 3 For a printable version of 'The uncertain Universe' click hereFrom 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 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 field theory provides the natural way of combining special relativity and quantum physics.In the case of the quantized electromagnetic field these particles are called Quantum fields may be regarded as collections of particles.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.) 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 can be used to describe all fundamental particles. 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'sQuantum field theory describes processes in which particles are created or destroyed.^{2}Continue on to Quantum fields and unification, part 2 of 3 5 The uncertain Universe 5.2 Quantum fields and unification Part 1 of 3 | Part 2 | Part 3 For a printable version of 'The uncertain Universe' click hereIt 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).
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
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.Continue on to Quantum fields and unification, part 3 of 3 5 The uncertain Universe 5.2 Quantum fields and unification Part 1 of 3 | Part 2 | Part 3 For a printable version of 'The uncertain Universe' click hereThe 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?
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?5 The uncertain Universe 5.3 The end of physics? Part 1 of 1 For a printable version of 'The uncertain Universe' click hereSuppose 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.
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: 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 initial conditions. 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 indeterminacy. 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 The problem of emergence.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.
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. Continue on to 6 Closing Items |