Quantum Reality

by Jim Baggott

  Our rationalist tendency is to put a probability on each action and choose the action with the highest probability of delivering the expected utility. We don’t necessarily calculate these probabilities: we might look at bank interest rates, study the stock market, and try to form a rational, though qualitative, view. Or we might run with some largely subjective opinions about these different choices taking into account our perceptions and appetite for financial risk. Of course, we might shift the burden of responsibility for these choices to a financial adviser, if we can afford one, but we’re still going to want to hear the rationale behind them before we commit.

  This notion of probability as a measure of our subjective degree of belief or uncertainty is credited to the eighteenth-century statistician, philosopher, and Presbyterian minister Thomas Bayes. Bayes’ approach was given its modern mathematical formulation by Pierre Simon Laplace in 1812.

  Suppose you form a hypothesis that some statement might be true or valid. In Bayesian probability theory, you assign this hypothesis a probability of being valid, or as a measure of the extent of your belief in it. This is called a prior probability. Now look at it again in the light of some factual evidence. The probability that your hypothesis is valid in the light of the evidence is then called a posterior probability.

  You’re now faced with a simple question. Is the posterior probability larger or smaller than the prior probability? In other words, does the evidence confirm or at least support your hypothesis, does it disconfirm or serve to undermine it? Or is it neutral? Bayesian probability theory is used extensively in science, and especially in the philosophy of science as a way of thinking about how we use empirical evidence to confirm or disconfirm scientific theories.

  But if we think about this for a while, we will conclude that these probabilities are really all rather subjective. I might come to believe one thing, but you might look at the same evidence and come to believe something completely different. Who is to say which of us is right? We are able to get away with this kind of subjectivity in daily life, but surely this has no place in theories of physics based on objective facts about an objective reality (Proposition #1).*

  Perhaps this is a good point to provide a more extended version of this quote from Heisenberg:9

  Our actual situation in research work in atomic physics is usually this: we wish to understand a certain phenomenon, we wish to recognise how this phenomenon follows from the general laws of nature. Therefore, that part of matter or radiation which takes part in the phenomenon is the natural ‘object’ in the theoretical treatment and should be separated in this respect from the tools used to study the phenomenon. This again emphasises a subjective element in the description of atomic events, since the measuring device has been constructed by the observer, and we have to remember that what we observe is not nature in itself but nature exposed to our method of questioning.

  When scientists go about their business—observing, experimenting, theorizing, predicting, testing, and so on—they tend to do so with a certain fixed attitude or mindset. Scientists tend to assume that there is, in fact, nothing particularly special about ‘us’. We are not uniquely privileged observers of the Universe we inhabit. We are not at the centre of everything. This is the ‘Copernican Principle’: science strives for a description in which our existence is a natural consequence of reality rather than the reason for it.

  Remember that one consequence of Einstein’s theories of relativity is that the observer is put back into the reality that is being observed. So, shouldn’t we at least accept the need to put the experimenter back into the quantum reality that is being experimented on? We don’t have to go so far as to suggest a causal connection—we don’t need to reject Proposition #1 and argue that the Moon ceases to exist when nobody looks at it or thinks about it. Perhaps we just need to accept that our scientific description isn’t really complete unless we place ourselves firmly in the thick of it.

  In 2002, Carlton Caves, Christopher Fuchs, and Rüdiger Schack proposed to do just this. Instead of denying the subjective element in quantum mechanics they embraced it. They argued that quantum probabilities computed using the Born rule are not objective probabilities related in a mechanical way to the underlying quantum physics. They are Bayesian probabilities reflecting the personal, subjective degree of belief of the individual experimenter, related only to the experimenter’s experience of the physics.

  Your first instinct might be to reject this idea out of hand. Surely, there’s a world of difference between my subjective beliefs about the stock market and the unassailably objective facts of physics? But think about it. My ability to predict movements in the stock market are limited by my lack of experience and knowledge. If I took the time to expand my experience, build my knowledge, and codify this in a couple of useful algorithms, there’s a good chance I’d be able to make more realistic predictions (just ask Warren Buffet).

  How is quantum physics different? For the past hundred years or so, physicists have taken the time to expand their experience, building a body of knowledge about quantum systems which is codified in the set of equations we call quantum mechanics. Why believe in the Born rule? Because this is what any rational physicist with access to the experience, knowledge, and algorithms of quantum mechanics will choose to do. ‘The physical law that prescribes quantum probabilities is indeed fundamental, but the reason is that it is a fundamental rule of inference—a law of thought—for Bayesian probabilities.’10

  This is an interpretation known as Quantum Bayesianism, abbreviated as QBism (pronounced ‘cubism’). It is entirely subjective. QBists view quantum mechanics as ‘an intellectual tool for helping its users interact with the world to predict, control and understand their experiences of it’.11 Despite the exhortations of his professors, Mermin converted to QBism following six weeks in the company of Fuchs and Schack at the Stellenbosch Institute for Advanced Study in South Africa in 2012, where he ‘finally began to understand what they had been trying to tell me for the past ten years’.12

  The approach reaches beyond the Born rule to the quantum states themselves, and the wavefunctions we use to represent them. The Schrödinger equation simply constrains the way any rational physicist will choose to describe their experience, until such time as they become aware of the outcome of a measurement. And this is unproblematic, for the same reason that Rovelli argued that his knowledge about China changes instantaneously whenever he chooses to read an article about China in the newspaper.

  As the gauge pointer moves to the left, the rational Alice chooses to describe this experience of the outcome of a measurement in terms of the quantum state A+. She expresses her degree of belief in this outcome by entering a ‘+’ in her laboratory notebook. The rational Bob, stuck outside in the corridor with his research supervisor, chooses to describe his experiences in terms of a macroscopic quantum superposition involving the quantum system, measuring device, gauge, Alice, and her notebook. When Bob finally enters the laboratory, Alice shows him her notebook and Bob’s experience and beliefs change. This is Bob’s ‘measurement’. It doesn’t involve any quantum systems, detection devices, or gauges. Bob makes his measurement just by looking at Alice’s notebook, or simply by asking her a question. Of course, Bob wasn’t present when Alice made her measurement, but he trusts Alice implicitly and his degree of belief in the outcome is unshaken.

  By making this all about subjective experiences, once again all the problems associated with a realist interpretation of the wavefunction evaporate. Quantum probability is a personal judgement about the physics; it says nothing about the physics itself.13 There is no collapse of the wavefunction, for the simple reason that there are no outcomes before the act of measurement (however this is defined): experiences can’t exist before they are experienced. There is no such thing as non-locality, and no spooky action at a distance: ‘QBist quantum mechanics is local because its entire purpose is to enable any single agent to organize her own degrees of belief about the contents of he
r own personal experience. No agent can move faster than light.’14

  This is a ‘single-user’ interpretation. The experiences and degrees of belief are unique to the individual—the Bayesian probabilities make no sense when applied to many individuals at once. We have to face up to the fact that the subjective nature of our individual experiences means that we all necessarily carry different versions of reality around with us in our own minds. If this is really the case, how is science of any kind even possible?

  Calm down. The versions of reality that we all carry in our minds are still shaped by our experiences of a single, external, Empirical Reality. As a result of all our experiences, learning, and communicating with our fellow humans we develop what the philosopher John Searle calls the background, which I mentioned briefly in Chapter 2. This is an enormously wide and varied backdrop against which we interact with external reality. It is everything we learn from experience and come to take for granted, social and physical, as we live out our daily lives. The background is where we find all the regularities and the continuity, the expectation that the Sun will rise tomorrow, that things will be found where we left them, that cars won’t turn into trees, that this $20 bill really is worth $20, and that when you turn the next page it will be covered by profoundly interesting text, and not pictures of sausages.

  We each form the background by accumulating a set of mental impressions. But these have great similarity, derived from a broad set of common experiences (including experiences of quantum physics), a common body of knowledge, commonly accessible forms of communication, and human empathy. It is the close similarity of these individual backgrounds that makes human interaction possible.

  Similar, but not the same. Within my mind is the reality with which I have learned to interact. You have no access to this reality, because you have no access to my mind. Within your mind is the reality with which you have learned to interact. I have no access to this reality, because I have no access to your mind. My reality is not your reality. But these individual realities possess many common features, such as the recognition that a $20 bill is money, or that if I perform this experiment I’ll get the result A↑ 50% of the time. Through the extraordinary complexity of our everyday interactions, we perceive these separate realities as one.

  Clearly, QBism rejects Proposition #3 and in this regard is unashamedly anti-realist at the level of representation. It has nothing meaningful to say about the physics underlying the experiences. Once more, there’s nothing to see here.

  The Copenhagen interpretation seeks to place the blame for the inaccessibility of the quantum world on our classical language and apparatus. Rovelli’s relational interpretation shifts the blame to the need to establish relationships with quantum states if they are to acquire any physical significance. Interpretations based on information do much the same. In the consistent or decoherent histories interpretation, the blame resides in the fundamentally probabilistic nature of all quantum events, and the lack of a rule to determine the ‘right’ framework.

  In QBism, all of physics beyond our experience is in principle inaccessible. This kind of subjectivism applies equally well to classical mechanics, in which we codify our experience in equations that represent the behaviour of classical objects in terms of things such as mass, velocity, momentum, and acceleration.15 Arguably, we are forced to acknowledge this subjectivism only in quantum mechanics, when we’re finally confronted with the bizarre consequences of adopting a realist perspective.

  But Fuchs argues that QBism is not instrumentalist. Inspired by many of John Wheeler’s arguments, he prefers to think of the interpretation as involving a kind of ‘participatory realism’ (more on this to follow). This is participatory not in the sense of human perception and experience being necessary to conjure something from nothing and ‘make it real’, which would involve rejecting Propositions #1 and #2. Instead QBism simply argues that, in quantum mechanics, we can no longer ignore the fact that we are very much part of the reality we’re trying so desperately hard to describe:16

  QBism breaks into a territory the vast majority of those declaring they have a scientific worldview would be loath to enter. And that is that the agents (observers) matter as much as electrons and atoms in the construction of the actual world—the agents using quantum theory are not incidental to it.

  Hardy’s axiomatic reconstruction, consistent histories, and QBism all require some substantial trade-offs. Yes, all the problems go away and we can forget about them. But we are left to contemplate a reality made of probabilities, and nothing more, or the abandonment of a single version of the historical truth, or a reality that is inherently subjective and participatory. It’s clear that none of these attempts can provide us with any new insights or understanding of the underlying physics. In the context of Proposition #4 they are passive, not active, reconstructions or interpretations.

  It seems that even if we’re not still trapped by Scylla, mercilessly exposed to her brutally monstrous charms, then we haven’t managed to sail the ship very far.

  * |On further reflection, Hardy realized he could drop the demand for continuous transformation. The assumption of reversibility, when combined with his third axiom, is sufficient to necessitate continuity.

  * The ‘space’ in question happens to be an abstract mathematical space called Hilbert space, named for David Hilbert.

  * 42.

  * These realist propositions are handily summarized in the Appendix if you need to refer back to them.

  7

  Quantum Mechanics is Incomplete

  So We Need to Add Some Things

  Statistical Interpretations Based on Local and Crypto Non-local Hidden Variables

  Chapters 5 and 6 summarize interpretations of quantum mechanics that follow from the legacy of Copenhagen. They are based on a set of metaphysical preconceptions that tend to side with the anti-realism of Bohr and (especially) Heisenberg, based on the premise that quantum mechanics is complete. In the inaccessible quantum world we’ve finally run up against the boundary between things-in-themselves and things-as-they-appear that philosophers have been warning us about for centuries. We have to come to terms with the fact that there’s nothing to see here, and we’ve reached the end of the road.

  But this anti-realist perspective is not to everybody’s taste, as theorist John Bell made all too clear in 1981:1

  Making a virtue of necessity, and influenced by positivistic and instrumentalist philosophies, many came to hold not only that it is difficult to find a coherent picture but that it is wrong to look for one—if not actually immoral then certainly unprofessional.

  If we make the philosophical choice to side with Einstein, Schrödinger, and Popper and adopt a more realist position, this means we can’t help but indulge our inner metaphysician. We can’t help speculating about a reality beyond the empirical data, a reality lying beneath the things-as-they-appear. We must admit that quantum mechanics is incomplete, and be ready to make frequent visits to the shores of Metaphysical Reality in the hope of finding something—anything—that might help us to complete it.

  In doing this we might be led astray, but I honestly think that it goes against the grain of human nature not to try.

  Opening the door to realism immediately puts us right back in a fine mess. Any realist interpretation, reformulation, or extension of quantum mechanics necessarily drags along with it all the associated metaphysical preconceptions about how reality ought to be. It must address all the bizarre things that quantum physics appears to allow, such as superpositions now involving real physical states (rather than coded information), the instantaneous collapse of the wavefunction, and the spooky action at a distance this would seem to imply. It has to explain away or eliminate the randomness and discontinuity inherent in quantum mechanics and restore some sense of continuity and cause-and-effect, presided over by a God free of a gambling addiction. It has to find a way to make the quantum world compatible with the classical world, explaining or avoiding an arbitrary ‘s
hifty split’ between the two.

  Where do we start?

  In his debate with Bohr and his correspondence with Schrödinger, Einstein had hinted at a statistical interpretation. In his opinion, quantum probabilities, derived as the squares of the wavefunctions,* actually represent statistical probabilities, averaged over large numbers of physically real particles. We resort to probabilities because we’re ignorant of the properties and behaviours of the physically real quantum things. This is very different from anti-realist interpretations which resort to probabilities based on previous experience because we can say nothing meaningful about any of the underlying physics.

  Einstein toyed with just such an approach in May 1927. This was a modification of quantum mechanics that combined classical wave and particle descriptions, with the wavefunction taking the role of a ‘guiding field’ (in German, a Führungsfeld), guiding or ‘piloting’ the physically real particles. In this kind of scheme, the wavefunction is responsible for all the wave-like effects, such as diffraction and interference, but the particles maintain their integrity as localized, physically real entities. Instead of waves or particles, as complementarity and the Copenhagen interpretation demands, Einstein’s adaptation of quantum mechanics was constructed from waves and particles.