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Quantum Mechanics

John C. Polkinghorne

I. History - II. Uncertainty and complementarity - III. Double slit experiment and superposition - IV. Measurement in quantum mechanics. 1. Large measuring apparatus. 2. Consciousness. 3. Many Worlds. 4. Deterministic theory. - V. Non-locality - VI. Wider lessons.

I. History

The two great discoveries of 19th century physics were the nature of light as waves of electromagnetic radiation and the use of statistical mechanics to understand the energetic properties of complex systems. When these two insights were combined to discuss the properties of radiation contained in a perfectly absorbing and emitting cavity (black body radiation), the disastrous conclusion emerged that there would be infinite amounts of energy present at the very highest frequencies. In 1900, Max Planck found a way to circumvent this “ultraviolet catastrophe”. He did so by the radical proposal that radiation was not emitted or absorbed continuously, as had hitherto been supposed, but in discrete packets (quanta).

Planck's idea contradicted the concept of smooth change on which the classical physics of Newton and Maxwell had been based and replaced it by something altogether more discontinuous. It was not clear, however, whether these discrete quantum properties applied only to the emission and absorption process itself – like individual drips from a tap which merge into a single body of fluid in the basin – or whether there was an abiding character to the packets of energy. In 1905, Albert Einstein showed that the emission of electrons from a metal induced by incident light (the photoelectric effect) could only be understood on the basis of the continuing identity of the light quanta (subsequently called photons). Physicists were now faced by the paradox that light sometimes showed wavelike properties (as in classical diffraction experiments) and sometimes particlelike properties (as in the quantum account of the photoelectric effect). No immediate resolution of this dilemma could be found.

In 1912, Niels Bohr made a brilliant new use of Planck's idea to explain the stability of atoms and the structure of atomic spectra. This was achieved by mixing quantum and classical concepts in a way that was empirically successful but where their mutual consistency was far from evident.

It was not until 1925 that a fully consistent quantum mechanics was discovered, almost simultaneously by Werner Heisenberg and Erwin Schrödinger. Their formulations appeared very different and it took a little while to see that both had discovered the same theory, differently expressed. The fundamental principles of quantum mechanics were then clearly formulated by Paul Dirac. Max Born clarified the intrinsically probabilistic character of the theory: in general there is not a determinate outcome of a quantum process but one can only assign probabilities for a variety of possible outcomes, one of whieh will be realised on any one particular occasion. Later Dirac discovered quantum field theory. This proved to be the resolution of the paradox of wave/particle duality, for a field is a spatially extended entity, and so has wavelike properties, but the presence of quanta also endow it with particlelike behaviour.

II. Uncertainty and complementarity

Heisenberg realised that the new quantum theory implied limits on what can be measured. All measurement involves an interference with the system being measured (for example, bouncing light off an electron to see where it is), but in classical physics this interference can be made as little as one pleases. The existence of quanta, however, forbids such infinitesimal intervention. A beam of light must include at least one photon. This means that there is an irreducible degree of uncontrollable disturbance involved in a quantum measurement (see below, IV). For a quantum entity such as an electron, Heisenberg showed that this implied, that one could not know exactly both where it was (position) and also how it was moving (momentum). This limitation was expressed in the famous uncertainty principle. Since it was derived from consideration of measurement procedures, it is clear that the uncertainty principle is primarily an epistemological principle of ignorance. Almost immediately, however, the vast majority of physicists, Heisenberg himself included, began to interpret it as an ontological principle of indeterminacy. On this view, it is not just the case that we cannot know simultaneously the positions and momenta of quantum entities, but such entities do not possess definite positions and momenta unless one or other of these quantities is actually measured. As we shall see, this interpretation is a metaphysical extension of the theory that is not entailed by the physics alone.

In classical physics, systems are described by giving the positions and momenta of their constituents. In quantum theory, this is not possible and instead there are two alternative forms of description, each complete and distinct, one framed in terms of positions and the other in terms of momenta. Bohr emphasised the complementary character of these two points of view. The same concept of complete but mutually exclusive accounts can be used to think about the dual aspect of light, an entity that can be thought of in wave terms or in particle terms. (It had also been discovered that electrons, and in fact all quantum entities, have this wave/particle character.) No contradiction is involved in these complementary pictures, since they correspond to different forms of experimental investigation and so apply in mutually exclusive circumstances. If experimentally one asks a wavelike question about light (a diffraction experiment), then one gets a wavelike answer, if one asks a particlelike question (the photoelectric effect), one gets a particle like answer. The two empirical questions cannot both be put at the same time, for they correspond to different experimental arrangements.

These properties imply that the quantum world is altogether more veiled and elusive in its character than one would expect on the basis of intuition grounded in everyday experience. There has been much discussion of the philosophical consequences of this. Bohr himself wrote extensively, and cloudily, on these issues. He once said that there is no quantum world, only quantum physical description. By itself the remark sounds instrumentalist (antirealist), as if quantum mechanics was only concerned with empirical adequacy and not with what the physical world is actually like. However, many commentators on Bohr believe that he held to some form of the realist stance that is so natural to the scientist. Einstein certainly did. He believed that quantum mechanics was in some way incomplete, but his enmity towards his. intellectual grandchild was partly motivated by a mistaken equation of reality with objectivity of the kind that classical physics affords. Heisenberg took a more measured view, believing that a revival of the Aristotelian concept of potentia would be helpful. For him, quantum entities did not possess positions and momenta but rather the potentiality for such properties when they were actually measured.

Another consequence of the veiled character of the quantum world relates to what physicists call statistics, that is to say, the behaviour of collections of identical particles. In classical physics identical particles are nevertheless distinguishable, because the trajectory of each one of them can be followed, so that we always know which is which. In this way, a specific particle at the beginning of a process can be identified with a specific particle at the end of the process. Quantum mechanics does not permit this detailed account, so that identical particles are indistinguishable. One can only say that one has two electrons initially and two finally, but it is not possible to make a linkage of the way the two pairs relate to each other. It turns out that this implies two different types of behaviour for collections of identical particles in quantum mechanics: either they are what are called “bosons”, in which case there is a strong tendency for them to associate in the same state of motion, or they are “fermions”, in which case no two of them can ever be in the same state ( MATTER, III.4). Electrons are fermions and this property plays an essential role in the understanding of the structure of atoms.

III. Double slit experiment and superposition

A highly instructive system to consider is the double slit experiment. A source of quantum entities (for definiteness, let us consider electrons) is separated from a detecting screen by a second interposed screen in which there are two slits permitting the passage of the electrons.

The electrons arrive at the detecting screen one by one, manifesting their particlelike property. If they were simply behaving like little bullets, one would expect most of them to arrive opposite one or other of the open slits. However, this does not prove to be the case. In fact most arrive at a midway point on the detecting screen, with alternating bands of arrival and non-arrival on either side of this peak. This is precisely the effect that physicists identify with wavelike behaviour (a diffraction pattern). If waves were spreading out from the two slits, they would arrive at the midpoint in step with each other, crest reinforcing crest to give maximum total effect. A little to one side, however, the waves would be out of step, trough cancelling crest. As one moves further to one side there is a succession of bands of alternate reinforcement and cancellation.

The experiment neatly illustrates wave/particle duality. A critical question to consider concerning the phenomenon is, Which slit did one of the arriving electrons pass through on its way? Suppose it was the top slit. Then the bottom slit was irrelevant for this electron and could as well have been closed as open. But one needs two open slits to generate a diffraction pattern. Therefore, the electron could not just have gone through the top slit. A similar argument disposes of the possibility of its traversing the bottom slit alone. One is driven to the strange conclusion that the indivisible electron went through both sits!

Perplexing as that conclusion seems to everyday thinking, it is readily accommodated within a quantum mode of thought. This is because quantum mechanics is based on what Dirac called “the superposition principle”, which encapsulates the essential difference between the formulations of classical physics and quantum physics. In classical physics an electron always has a definite position, it is either “here” or “there”. In quantum mechanics, an electron does not have a definite position, it can be “here” or “there” or a variety of mixtures of these possibilities. The defining feature of the quantum formalism is that it permits the adding together of possibilities that classical physics (and commonsense) hold rigidly separate from each other. Thus, in the double slit experiment, the electron is in a state which is a mixture of (going through the top slit) and (going through the bottom slit).

The superposition principle illustrates two fundamental properties of the quantum world: its unpicturability and its probabilistic character. We certainly cannot envisage what a state of “going through both slits” would look like. If we were to investigate the state by putting detectors at the two slits, we would sometimes find the electron at the top slit and sometimes at the bottom slit, in this case with equal probabilities for either result. (It turns out that this intervention would also destroy the diffraction pattern at the detecting screen).

Another interesting consequence of the superposition principle is that a different kind of logic applies to the quantum world than applies in the world of everyday. Aristotelian logic is based on the “principle of the excluded middle”: there is no third possibility between “here” and “not here”. In quantum mechanics, on the contrary, there is an infinite range of middle possibilities, corresponding to adding together some amount of “here” and some amount of “not here”.

IV. Measurement in quantum mechanics

An electron may be in a state which is a mixture of “here” and “there”, but if we actually measure its position we always get a definite answer (though not always the same answer on each occasion). This implies that a discontinuous change takes place on measurement. Probability, which had been spread out over a range of possible positions, is suddenly all concentrated on the actual result obtained (“here”). This phenomenon is called “the collapse of the wavepacket”. It has to be imposed on the formalism as an additional rule, for it does not follow from any other aspect of quantum mechanics. The issue of understanding the physical origin and character of this collapse is called “the measurement problem”. How does it come about that measurement always results in a definite result?

Quantum mechanics has been a highly successful physical theory. Originally developed to understand the behaviour of atoms, it is now applied with equal success to understand the behaviour of quarks, the current candidates for the basic constituents of matter, which are at least one hundred million times smaller than atoms, A necessary part of this success has been that quantum mechanics recapitulates the successful predictions of Newtonian mechanics for the behaviour of large entities ( MECHANICS, III). This is, in fact, the case and it is well understood in terms of what are called “correspondence principles”.

What is not well understood, even after more than seventy years successful exploitation of the theory, is the measurement problem. It is concerned with the relationship between a microscopic system (the quantum entity being measured) and a macroscopic system (the measuring apparatus). Measurement may be thought of as an event in which there is irreversible registration on the macroscopic scale of a state of affairs on the microscopic scale. (It is important to recognise that this does not necessarily involve the participation of a conscious observer). It is necessary to survey a number of proposals that have been made about how one should understand the process of measurement:

1. Large measuring apparatus. The problem was discussed in the early days of quantum mechanics and Bohr proposed a way of understanding that has come to be called “the Copenhagen interpretation”. He insisted that entity and apparatus must be considered as a single phenomenon and that it was the role of “large” classical measuring instruments that brought about a definite result. There is a certain initial plausibility to this view, since laboratories clearly contain much apparatus of this kind. However, the proposal has a serious flaw. Essentially, it supposes a dualistic picture of the physical world in which there are both indeterminate quantum entities and also determinating classical instruments, even if the precise division between them is made somewhat flexible by their being paired in a single phenomenon. In reality, however, there is but one physical world, in “which apparatus” is itself composed of quantum constituents.

A modification of this approach, which may be termed neo-Copenhagen, is to acknowledge the unity of the physical world but to assert that it is the “largeness” of the instruments that induces their determinating role. The problem then is to understand how this comes about, and no fully articulated account has so far been given. Yet, there is one hopeful sign that this might prove in the end to be the right approach. The fundamental laws of physics are time-reversible. That is to say, they contain no intrinsic distinction between past and future, which they treat symmetrically. The behaviour of large classical systems, on the other hand, displays obvious irreversibility, corresponding to an arrow of time pointing from the past into the future. Although the emergence of this arrow is also not well understood, it is widely believed that it arises from the thermodynamic behaviour of large systems, which in isolation always develop in the direction of increasing entropy (increasing disorderliness). Measurement is also an irreversible process, with a “before”, when the result is not known, and an “after”, when it is. There may well be a connection between these two irreversibilities associated with large and complex systems.

2. Consciousness. While the presence of a conscious observer is not part of the definition of measurement, it is obviously the case for any measurement whose result is actually known. The nature of consciousness, that experienced interface between the material and the mental, is not understood, but there are clearly effects of the material on the mental, as the consequences of drug taking or brain damage make plain. May there not also be effects of the mental on the material, including the determination of otherwise indeterminate quantum measurements? A number of distinguished physicists have espoused this view. However, it leads to a number of surprising conclusions.

Consciousness is a late arrival on the cosmic scene. Are we to suppose that, for billions of years, no quantum process ever had a definite outcome? If a measurement is made and recorded on a computer printout, which is not read by anyone for many months, are we to conclude that until that time of reading there was no definite imprint on the paper?

There is the further question of whose consciousness can do it? Schrödinger posed this vividly with his famous thought experiment involving a cat. The animal is incarcerated in a box in which there is a radioactive source with a 50-50 chance of decaying in the next hour. If the decay takes place, it will trigger the breaking of a vial of poison gas that will kill the cat. If it does not take place, the cat, of course, is unharmed at the end of the hour. Are we to suppose that, before the lid is opened and a human looks inside, the cat is a superposition of alive/dead? It surely does not need a human to enforce its demise, so feline consciousness should suffice. Where do we stop? Would a worm be “aware” that it was dead, and so collapse the wavepacket?

3. Many Worlds. Some physicists have urged that the principles of quantum mechanics should be treated absolutely seriously. The formalism does not express the collapse of the wavepacket, which we have seen has to be imposed upon it as a further postulate. It has therefore been suggested that there is no such collapse; everything that can happen, does happen. There is a world in which Schrödinger’s cat dies and one in which it lives. Our impression that we see a definite outcome (either a cooling corpse or a frisking feline) is due to the fact that the universe has divided into two, and ourselves as observers with it, one clone in the world of the dead cat, the other in the world of the live cat.

It is clear that this is a proposal of immense prodigality, resulting in a vast and continuing proliferation of worlds with their different outcomes. Only one group of physicists has shown a decided attraction to this point of view. They are the quantum cosmologists, seeking to apply quantum mechanics to the whole universe ( COSMOLOGY, III; MANY-WORLDS MODELS, III). It is not at all clear how feasible this ambitious project actually is, but if it is to be pursued, the many worlds option seems the way to do so. When the cosmos is the system under consideration, there is no room for appeal to large measuring apparatus, or to observers, lying outside it.

4. Deterministic theory. It had been supposed, on the basis of an argument given by John von Neumann, that it was impossible to interpret quantum mechanics in such a way that it would be deterministic, with its probabilistic character arising simply from an ignorance of some of the causes at work (just as the tossing of a coin appears random because we are not aware of the fine detail of its actual propulsion). It was therefore a considerable surprise when David Bohm produced a theory of just this kind, with identical empirical consequences to those of “conventional quantum” mechanics but with the probabilities due to the presence of veiled effects (usually called “hidden variables”). (The flaw in von Neumann's argument was subsequently identified). In Bohm's theory there are both particles and a wave, appearing as separate entities. The particles are directly observable in as unproblematically objective a way as Newton himself could have wished. Their motion, however, is influenced by the wave, which is not directly observable and which encodes information about the whole environment. It is sometimes called a “guiding wave”.

For Bohm, the uncertainty principle is simply a principle of ignorance and not of indeterminacy, illustrating the fact, already noted (see above, III), that this latter interpretation is metaphysical and not physical in its character. In Bohm's theory, the electron in the double slit experiment has to go through a specific slit, but the existence of the other slit is not an irrelevancy, because whether it is open or shut affects the form of the wave, and so indirectly the way in which the electron moves.

No empirical test can decide between Bohm's theory and conventional quantum mechanics. Yet the vast majority of physicists hold the conventional view. Their reasons are necessarily metaphysical and relate to the detection of a degree of contrivance in Bohm's ideas, which consequently can be admired for their ingenuity but not found to be persuasively plausible.

V. Non-locality

Einstein remained opposed to quantum mechanics and he spent much time trying to show that it was in some way incomplete, In 1935, with two young collaborators, Boris Podolsky and Nathan Rosen, he drew attention to a property that seemed to be so counterintuitive (“spooky” was his word for it) that he felt it must indicate that something was lacking. This property, usually called “the EPR effect”, implies that once two quantum entities have interacted with each other, they remain mutually entangled however far they may separate spatially, so that a measurement made on one of them will produce an instantaneous effect also on the other. This unexpected non- locality (togetherness-in-separation) has subsequently been demonstrated to be an actual property of nature. The relevant experiments were done by Alain Aspect in the 1980s, making use of an empirically accessible test (the Bell inequalities) which had been formulated by John Bell. In other words, it was discovered that the subatomic world cannot be treated atomistically, because it has an intrinsic holism built into its structure ( REDUCTIONISM, II-III).

Two comments may be made. The first is that it is important to recognise that the EPR effect is an ontological effect, of causal efficacy, and not merely an epistemological result. The latter would present no surprise to commonsense. If there are two balls in an urn, one white, one black, and two people each take out one ball hidden in their clenched fists, when one opens his fist to see a white ball, he immediately knows that the other person has the black ball, however far away that person may then be. This is unproblematic, because this was always the case, all that has happened is that it has become known that this is so. The EPR effect is totally different. Making different measurements on one of the entities will have different (and mutually incompatible) consequences for the other. There is a genuine causal effect involved.

The second point is to consider whether this instantaneous effect would not contradict special relativity, with its prohibition of propagation faster than the velocity of light. In fact it is the propagation of information (a message) that relativity constrains ( RELATIVITY, THEORY OF, I). The EPR effect, however, cannot be used to transmit information, and so escapes the ban. This is because it produces correlations of behaviour between the two separated entities, the unravelling of whose significance requires knowledge of what is happening at both ends, and so it cannot be used to transmit a message from one to the other. A musical analogy may prove helpful. Suppose two singers each sing what appears to be random sequences of notes. Only someone able to hear both simultaneously would be able to perceive that they were in harmony with each other. This harmony would be the analogue of EPR correlations.

VI. Wider Lessons

The strange quantum world illustrates a number of epistemological and metaphysical features that may be of wider relevance for other forms of human encounter with reality, including theological enquiry:

(i) There is an important distinction between explanation (an account of a phenomenon) and understanding (the attainment of profound intellectual adequacy and satisfaction). Quantum mechanics is explanatorily extremely successful, enabling the calculation of a vast range of physical effects. However, until an agreed resolution of the measurement problem has been attained, it would not be possible to claim that full understanding has been gained. Those who think of physics as the paradigm of rational enquiry, should note that it has lived for more than seventy years in this state of partial achievement,

(ii) There is to be no undue tyranny of commonsense. Everyday intuitions cannot be extended indefinitely into other realms of encounter with reality. The existence of quantum logic, with its re-evaluation of the meanings of “and” and “or”, makes the point most clearly. There is no universal epistemology, but entities can only be known in ways that accord with their nature. If the quantum world is to be known, it must be accepted in its Heisenbergian uncertainty, for it is not possible to know it with Newtonian clarity. (Even Bohm's theory has hidden variables).

(iii) Empirical adequacy, though essential to a successful scientific theory, is not the sole ground for theory choice. The choice between Bohr and Bohm cannot be made on these grounds alone but it must appeal to metaphysical considerations such as simplicity, economy and naturalness (lack of contrivance).

(iv) Although the character of the quantum world is veiled and counterintuitive, almost all physicists believe in the reality of quantum entities, such as electrons and photons. The fundamental ground for this belief is that the assumption of their existence makes sense of great swathes of physical experience. In other words, it is intelligibility which supports belief in the existence of unseen realities.

(v) Although quantum mechanics is strange, of itself it by no means licences the acceptance of other forms of Strangeness. Popular books sometimes indulge in an illegitimate kind of “quantum hype”. The EPR effect does not explain telepathy (after all, it cannot be used to transmit messages). Wave/particle duality is a well-understood physical phenomenon, but the complementarity involved cannot be appealed to simply and unproblematically to resolve the theological problem of the duality of the human and the divine in Christ.

(vi) The quantum world is interconnected and veiled, but it is not all-dissolving, so that parallels sometimes claimed with the experiences of Eastern mystics are highly questionable when looked at carefully. For instance, quantum mechanics also explains the persisting stability of atoms and, in its applications to elementary particle physics, it makes much use of symmetry principles, which are systems of structured order.

(vii) Although it is often asserted that talk of “observer-created reality” is authorised by quantum mechanics, it will be clear that this is by no means the case. Exactly what should be said will depend upon which solution of the measurement problem proves eventually to prevail. Bohm's interpretation is purely objective. The consciousness interpretation is the one that lies closest to this point of view, but even then the range of possibility is confined to possible outcomes of the process, so that “observer-influenced reality” would be the more judicious phrase to use.

(viii) Some have speculated (starting with William Pollard, 1959) that God might act in the world by determining the outcomes of quantum events. For such action to have discernible effects, it would have to be amplified in some way to produce macroscopic consequences. In large systems, quantum uncertainties usually tend to cancel each other out to produce reliable, quasi-deterministic behaviour, but this is not inevitably the case so that there might be limited possibilities for divine action of this kind. However, the discontinuities in physical process that this view seeks to exploit are limited to measurements (not necessarily conscious observations, but certainly macroscopic registrations). Such events only happen from time to time, so that divine action in this mode would be curiously episodic.

These wider considerations relating to quantum mechanics may well have analogical value for theology in its search for understanding of divine reality.

John C. Polkinghorne

See also: DETERMINISM/INDETERMINISM; IDEALISM; MATTER; MECHANICS; RELATIVITY, THEORY OF.

Bibliography

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