Quantum Reality

by Jim Baggott

  * He tended to avoid the word ‘wavefunction’, presumably as this is closely associated with Schrödinger’s wave mechanics. He preferred to think of the description of quantum systems in terms of rather more abstract ‘state functions’ in a mathematical ‘Hilbert space’. And, with some modifications, this is the description commonly taught to students today.

  * They have also been found in some simple prokaryotic cells.

  10

  Quantum Mechanics is Incomplete

  Because….Okay, I Give Up

  The View from Charybdis: Everett, Many Worlds, and the Multiverse

  You will gather from the title I’ve chosen for this final chapter that I’m not particularly enamoured of the interpretations we will consider here. Whilst this is certainly true, my ambition is nevertheless to make the case both in favour and against these interpretations, as best I can, so that you can judge for yourself. I’ll explain my problems with them as we go.

  Irrespective of what I think, it has never ceased to amaze me that one of the simplest solutions to the problem of the collapse of the wavefunction leads to one of the most bizarre conclusions in all of quantum mechanics, if not all of physics. This solution involves first recognizing that we have absolutely no evidence for the collapse. It was introduced by von Neumann as a postulate. We have seen quantum systems in various stages of coherence, and we can create superpositions of objects that are intermediate between quantum and classical, but we have to date never seen a system undergo collapse, nor have we seen superpositions of large, cat-sized objects. In any realistic interpretation of the wavefunction, the notion of collapse has always been nothing more than a rather ad hoc device to get us from a system we are obliged to describe as a superposition of possible measurement outcomes to a system with a single outcome.

  There’s another reason to question the need for the collapse, as I already mentioned in passing in Chapter 6. This is related to the relationship between quantum theory and the spacetime described by Einstein’s general theory of relativity.

  Einstein presented the general theory in a series of lectures delivered to the Prussian Academy of Sciences in Berlin, culminating in a final, triumphant lecture on 25 November 1915. Yet within a few short months he was back, advising the Academy that his new theory of gravitation might need to be modified: ‘the quantum theory should, it seems, modify not only Maxwell’s electrodynamics but also the new theory of gravitation’.1

  Attempts to construct a quantum theory of gravity were begun in 1930 by Bohr’s protégé, Leon Rosenfeld. As I explained in Chapter 5, there are three ‘roads’ that can be taken, one of which involves the quantization of spacetime in general relativity and leads to structures such as loop quantum gravity. The result is a quantum theory of the gravitational field, a quantum theory of spacetime itself.

  The difficulties are not to be underestimated. Quantum mechanics is formulated against an assumed background spacetime, conceived not much differently from the absolute space and time of Newton’s classical mechanics. Quantum mechanics is ‘background-dependent’. In contrast, the spacetime of general relativity is dynamic. The geometry of spacetime is variable: it emerges as a consequence of physical interactions involving mass–energy. General relativity is ‘background-independent’.

  In any realistic interpretation of the wavefunction, these different ways of conceiving of space and time give us a real headache. In quantum mechanics, we routinely treat a quantum system as though it is sitting in a box, isolated from an outside world that, for the sake of simplicity, we prefer not to consider. Inside this box, we apply the Schrödinger equation and the wavefunction of the system evolves smoothly and continuously as it moves in time in a distributed, non-local fashion from place to place. This is Axiom #5, or von Neumann’s process 2. Satisfied, we now turn our attention to the classical measuring device, which is located in the world outside the box. When this interacts with the quantum system we suppose that the wavefunction collapses according to process 1.

  Just how are we meant to apply this logic to a quantum spacetime? Aside from some ‘spooky’ non-local effects, we can regard a quantum system formed from a material particle or ensemble of particles as being broadly ‘here’, in this place in the Universe, and therefore inside this box. The box is clearly defined by boundaries imagined in spacetime. But if we consider the entirety of spacetime itself, no such boundaries can be imagined. A quantum theory of spacetime is, kind of by definition, a quantum theory of the entire Universe, or a quantum cosmology.

  In any realistic interpretation of the wavefunction, the need to invoke a separate process for ‘measurement’ really makes quite a mess of things, as this necessarily assumes a perspective that is outside of the system being measured and, so far as we know, there can be nothing outside the Universe. This dilemma caught the attention of Hugh Everett III, a chemical engineering graduate who had migrated first to mathematics (including military game theory) at Princeton University, and then in 1955 to studies for a PhD in physics under the supervision of John Wheeler. In a 1957 paper based on his dissertation, he wrote:2

  No way is it evident to apply the conventional formulation of quantum mechanics to a system that is not subject to external observation. The whole interpretative scheme of that formalism rests upon the notion of external observation.

  Given the problems that the collapse creates and the lack of any direct evidence for it, why not simply get rid of it? I’ve already explained that scientists down the centuries have made a useful habit of eliminating from their theories all the unnecessary baggage and frills, typically introduced to satisfy certain metaphysical preconceptions but ultimately unsupported by the empirical facts. This is what Everett chose to do. In his dissertation, he followed von Neumann’s logic in assuming that the quantum mechanics of process 2 applies equally to large-scale, classical objects, and offered the following alternative interpretation:3

  To assume the universal validity of the quantum description, by the complete abandonment of Process 1. The general validity of pure wave mechanics, without any statistical assertions, is assumed for all physical systems, including observers and measuring apparata. Observation processes are to be described completely by the [wave]function of the composite system which includes the observer and his object-system, and which at all times obeys the [Schrödinger] wave equation (Process 2).

  At first sight, this suggestion seems somewhat counterproductive. If it is indeed our experience that pointers point in only one direction at a time and cats are either alive or dead, then giving up the collapse would seem to be taking us in the wrong direction. Surely, we are confronted by Schrödinger’s infinite regress, with an endless complexity of superpositions of measuring devices, cats, and ultimately human observers?

  But, of course, we never experience superpositions of large-scale, classical objects. Everett argued that the only way out of this contradiction is to suppose that all possible measurement outcomes are realized.

  How can this be? Once again, it’s easier to follow Everett’s logic using an example so, for the last time, let’s return to our quantum particle A prepared in a superposition of ↑ and ↓ spin states. The total wavefunction encounters a measuring device, and the larger system evolves smoothly into a superposition of the outcomes A↑ and A↓. These trigger a response from a gauge attached to the measuring device, entangling the outcomes with the ‘pointer states’ of the gauge, as before, resulting in a superposition of the product states A↑ and A↓. But this is no longer the kind of superposition we’ve been considering thus far. In his dissertation, Everett wrote:4

  Whereas before the observation we had a single observer state afterwards there were a number of different states for the observer, all occurring in a superposition. Each of these separate states is a state for an observer, so that we can speak of the different observers described by the different states. On the other hand, the same physical system is involved, and from this viewpoint it is the same observer, which is in di
fferent states for different elements of the superposition (i.e. has had different experiences in the separate elements of the superposition).

  Everett was not proposing that the observer enters some kind of conscious superposition, in which both outcomes are experienced simultaneously, but rather that the observer ‘splits’ between different states. In our example, one of these observer states corresponds to the experience of A↑ and another corresponds to the experience of A↓:

  Everett was not clear on the nature or cause of the ‘split’, but there is evidence in his writings that he interpreted it quite literally as a physical phenomenon acting on (or promoted by) a real wavefunction. Wheeler was much more cautious, annotating one of Everett’s manuscripts with the comment ‘Split? Better words needed’, and recommending that Everett rephrase his arguments to avoid ‘mystical misinterpretations by too many unskilled readers’.5

  This is Everett’s ‘relative state’ interpretation, the use of the word ‘relative’ deriving from the correlations established between the components of the superposition in the total wavefunction and the different experiences of the observer following the split. One observer state corresponds to A↑ and the other to A↓ relative to the first. Everett argued that quantum probability is then nothing more than a subjective probability imposed by an observer who, in a succession of observations on identically prepared A particles, notes that the outcomes are random, with a 50:50 probability of observing ↑ or ↓. Everett wrote: ‘We are then led to the novel situation in which the formal theory is objectively continuous and causal, while subjectively discontinuous and probabilistic.’6

  Despite his concern about some of Everett’s phraseology, Wheeler sent his dissertation to Bohr and later visited Bohr in Copenhagen in an effort to drum up support for what he judged to be a promising approach. These efforts culminated in a visit by Everett himself in March 1959. But all was in vain. Bohr, ever mindful of the use and misuse of language in physical descriptions, had no wish even to discuss ‘any new (strange) upstart theory’.7 Everett’s approach challenged too many elements of the Copenhagen orthodoxy, such as the complementarity of waves and particles and the interpretation of quantum probability. The Copenhagen school rejected outright any suggestion that quantum mechanics could be applied to classical objects.

  Everett was dismayed. By this time he had already been working for two and a half years with the Pentagon’s Weapons Systems Evaluation Group, and he rebuffed Wheeler’s attempts to lure him back to academia. He was invited to present his relative state interpretation at a conference in 1962, but his ideas were largely ignored by the physics community at the time.

  With one notable exception.

  Bryce DeWitt had been intrigued by Everett’s analysis and had written to him in 1957 with a lengthy critique. If the observer state splits every time an observation is made then why, DeWitt wondered, is the observer not aware of this? Everett responded with an analogy. We have no reason to question the conclusions of astronomy and classical physics which tell us that the Earth spins on its axis as it orbits the Sun. And yet because of our own inertia, we don’t directly experience this motion. Likewise, an observer maintains a sense of a single identity and a single history that can be reconstructed from memories, unaware that there exist multiple versions of him or herself, all with different recollections of the sequence of events. Everett slipped this argument into the proofs of his 1957 paper as a footnote.

  DeWitt was convinced. Struggling to come to terms with a quantum cosmology seemingly at odds with a formalism that appeared to place far too much emphasis on external ‘measurement’, DeWitt sought to raise the profile of Everett’s interpretation in a paper published by Physics Today in September 1970. Bohr had died in 1962, and there might have been signs that the Copenhagen interpretation was starting to lose its stranglehold. DeWitt may have judged that the time for pussyfooting around with politically correct language was over, and he chose to describe the interpretation using words that the old guard (including Wheeler) would never have approved.

  He wrote: ‘I shall focus on one [interpretation] that pictures the universe as continuously splitting into a multiplicity of mutually unobservable but equally real worlds, in each one of which a measurement does give a definite result.’8 Thus Everett’s relative state formulation became the many-worlds interpretation of quantum mechanics. Almost overnight, Everett’s interpretation transformed from being one of the most obscure to one of the most controversial.

  Everett appears to have been pleased with DeWitt’s choice of words.* Wheeler once advised him that, whilst he ‘mostly’ believed in the interpretation, he reserved Tuesdays once a month to disbelieve it. But his reservations were stronger than this anecdote would imply, and in time he withdrew his support, such as it had been, later accepting that the interpretation ‘carried too much metaphysical baggage along with it’, and made ‘science into a kind of mysticism’.9 But even as he distanced himself he acknowledged Everett’s contribution as one of the most original and important in decades.10

  DeWitt secured a copy of Everett’s original dissertation from his wife Nancy. With Everett’s blessing and the help of his student Neill Graham, DeWitt published this in 1973, together with Everett’s 1957 paper, an ‘assessment’ of this paper published back to back in the same journal by Wheeler, DeWitt’s Physics Today article, and a couple of further supportive articles by DeWitt, Graham, and Leon Cooper and Deborah van Vechten. The book is titled The Many Worlds Interpretation of Quantum Mechanics.

  Schrödinger’s cat is no longer simultaneously alive and dead in one and the same world, it is alive in one world and dead in another. With repeated measurements, the number of worlds splitting off from each other multiplies rapidly. The act of measurement has no special place in the many-worlds interpretation, so there is no reason to define measurement to be distinct from any process involving a quantum superposition. We can suppose that a great many such processes have occurred since the Big Bang origin of the Universe, some 13.8 billion years ago. Each will have split the world into as many branches as there have been components in the various superpositions that have formed since.

  In his Physics Today article, DeWitt estimated that by now there must be more than 10100+ different branches, or distinct worlds. Each of these worlds contain ‘slightly imperfect copies of oneself all splitting into further copies, which ultimately become unrecognizable…. Here is schizophrenia with a vengeance.’11

  Because it assumes only the continuous mechanics described by the Schrödinger equation, and nothing more, the many-worlds interpretation is often advertised as satisfying the demand that quantum mechanics be regarded as a complete theory. If that’s the case, then the title I’ve chosen for this chapter is incorrect. Needless to say, I don’t agree. Whilst the theory might be mathematically complete (and there are more arguments to come on this score), I think completing the theory by invoking an enormous multiplicity of mutually unobservable real worlds is rather costly, and certainly not ‘nothing’. It has been observed that the many-worlds interpretation is ‘cheap on assumptions, but expensive on universes’.12

  Caught in a strong trade wind, the Ship of Science is hurtling relentlessly towards Charybdis, that dangerous whirlpool of metaphysical nonsense about the nature of reality.

  There have been many efforts at rehabilitation in the years that have followed. It’s not clear what splitting the world implies for the interference terms in the superposition, and one of Dieter Zeh’s motivations for developing ideas about decoherence was to replace the notion of ‘many worlds’ with that of ‘multiconsciousness’, or what is now known as the ‘many minds’ interpretation.13 The splitting or branching of worlds or universes is replaced by the splitting or branching of the observer’s consciousness. The observer is never consciously aware of the superposition, since environmental decoherence destroys (or, more correctly, suppresses) the interference terms. The observer is only ever consciously aware of one outcome, but the other outc
omes nevertheless exist in the observer’s mind, although these alternative states of consciousness are inaccessible. In short, the observer does not possess a single mind but rather a multiplicity (or even a continuous infinity) of minds, each weighted according to the amplitude of the wavefunction such that one is dominant.

  Space precludes a more detailed discussion of the many minds interpretation, a term coined by philosophers David Albert and Barry Loewer in 1988. The relationship between the mind–body problem and quantum mechanics was independently explored by philosopher Michael Lockwood, in his 1989 book Mind, Brain & the Quantum: The Compound ‘I’.14 The many minds interpretation is presented in Albert’s popular book Quantum Mechanics and Experience, first published in 1992.15

  John Bell saw close similarities between many worlds and de Broglie–Bohm theory, arguing that Everett’s original interpretation could be rationalized as the pilot wave theory but without particle paths. In this sense, the splitting or ‘branching’ implied by many worlds is no more or less extravagant than the ‘empty waves’ of de Broglie–Bohm theory. Like Wheeler, Bell regarded the endless multiplication of worlds to be rather over the top, arguing that it serves no real purpose and so can be safely eliminated. The novel element that Everett had introduced was ‘a repudiation of the concept of the “past” ’.16 Instead of a branching system of worlds sprouting like the limbs of a tree, Bell suggested instead that the various particle ‘histories’ run in parallel, sometimes coalescing to produce interference effects. The outcomes are then determined by summing over these histories, with no association discernible between any particular present and any particular past.