by Jim Baggott
* To be clear, because the wavefunction might contain i, the square root of –1, we multiply it by its complex conjugate, in which i is replaced by –i (since –i × i = –i2 = +1), so we always get a positive result. This is called modulus square of the wavefunction. It is actually the two locked boxes facing off against each other.
* We’ll see how this can be done in practice in later chapters.
* The sign ≥ means ‘is greater than or equal to’. This works in the same way as an equals sign. For example, we could divide both sides by the uncertainty in momentum to give: uncertainty in position ≥ h/(4π × uncertainty in momentum). This shows straight away that if the uncertainty in momentum is zero, then the uncertainty in position would be infinite.
2
Just What is This Thing Called ‘Reality’, Anyway?
The Philosopher and the Scientist: Metaphysical Preconceptions and Empirical Data
It’s a cliché, but as I’ve grown older I’ve definitely become more impatient, more of an old curmudgeon. I’ve grown increasingly exasperated with our species’ seeming inability to learn anything at all from the past. This is certainly not an exasperation born of a nostalgia for the ‘good old days’. As anyone who grew up in the shadow of the Cold War and the threat of mutual assured destruction will tell you, there is no fondness for those times among those who survived them. Rather, this is an exasperation born from watching helplessly as the seemingly common sense and virtuous victories of decades of peaceful, liberal democracy are unravelled by a new breed of aggressive, opportunistic populists, intent on exploiting the legacy of a decade of economic hardship inflicted in 2008 by the greed of a few bankers. We seem to be at great risk of forgetting everything we’ve learned from modern humanity’s great successes and its horrific past mistakes.
My impatience knows no bounds. Much the same goes for our understanding of ‘reality’. I can’t begin to count the number of books and research papers I’ve read, the number of television documentaries I’ve watched, which purport to tell us how this or that scientific theory describes something new and unusually bizarre about reality, without ever being clear on the kind of reality that is supposedly being described.
Hang on. ‘Kind of reality’? What on Earth is that supposed to mean?
If you pick up an introductory text on philosophy, there’s a good chance that this will have sections on things like epistemology (the study of knowledge and justified belief), metaphysics (the study of the fundamental nature of being and existence, encompassing ontology and cosmology), logical reasoning, the philosophy of mind, moral philosophy, ethics and aesthetics, and the philosophy of science. If you look up ‘reality’ in the index, you’ll find that this is a subject discussed extensively under the heading of metaphysics.
So, to a philosopher, reality is metaphysics (meaning, literally, ‘beyond physics’). And yet, to a physicist, reality is something described by theories that are unquestionably scientific, such as quantum mechanics. What’s going on?
Now, there have been some well-known and very well-respected scientists who have publicly disparaged philosophy, ‘which at its best seems to me a pleasing gloss on the history and discoveries of science’, writes Nobel laureate Steven Weinberg.1 This kind of negativity is born from a judgement that philosophy appears to offer little or no guide to the inception, development, and evolution of a scientific theory, or even what it really means when we talk about the ‘scientific method’. ‘Let’s not put the cart before the horse,’ says Stanford University theorist Leonard Susskind, ‘Science is the horse that pulls the cart of philosophy.’2 ‘Of course, philosophy is the field that hasn’t progressed in two thousand years, whereas science has,’ says astrophysicist Lawrence Krauss, in a talk about his book A Universe from Nothing, an example of rather poor quality philosophy masquerading as science.3
Rather like the fractious members of the People’s Front of Judea in Monty Python’s Life of Brian, such scientists demand to know: ‘What has philosophy ever done for us?’
I confess I don’t really understand this kind of argument, or the attitudes that lie beneath it. So let’s be absolutely clear. Philosophy is not science. Philosophy does make progress, but this is not the same kind of progress that we tend to associate with science. It’s likely true that we can’t use philosophy to tell us how to develop a scientific theory, though I believe it holds some useful lessons, as we’ll see in the next chapter. This is, after all, what science is supposed to be for. But, as I hope to be able to show in what follows, when we look closely we find that it’s not actually possible to do science of any kind without metaphysics, interpreted broadly as the assumption of things we can’t prove. And the moment we accept this is the moment we open the door to philosophy.
As we’ve seen in the opening chapter, quantum mechanics forces us to confront some uncomfortable truths about what we can and cannot hope to fathom about the nature of reality. I firmly believe that if we want to understand how to interpret what quantum mechanics is telling us, then appreciation of a few lessons from philosophy is absolutely essential.4
So, let’s get back to reality. We’ll start by trying to discover what—if any—difference exists between the realities of the philosopher and the scientist.
Fans of the 1999 movie The Matrix will recall the scene in which Morpheus instructs Neo: ‘How do you define real? If you’re talking about what you can feel, what you can smell, what you can taste and see, then real is simply electrical signals interpreted by your brain.’5 Spend a few minutes pondering on this, and you should have no real difficulty in accepting its basic truth. You rely on your body’s sensory apparatus to deliver a complex set of sense impressions (converted into electrical signals) to your brain. As a result of some processes we do not yet fully understand, these impressions are synthesized in your conscious mind to deliver a set of perceptions and experiences (what some philosophers refer to as ‘qualia’) which combine to form a representation of the world around you. The result is what you call your reality. It is very specifically—and uniquely—yours.
You take this at face value because you have no real choice. If you went around questioning everything you perceive, then you wouldn’t get much done. Is this rose really red? Just what is ‘red’ anyway? Such questions concern your conscious experience, but what if you’re not around to experience things? If a tree falls in a forest, and there’s nobody around to hear, does it still make a sound? Is the Moon still there if you’re not looking at it, or thinking about it? And there goes another missed deadline.
You might want to argue that, after all, you are a highly intelligent life form, the result of about four billion years of evolution by natural selection on planet Earth, punctuated by at least five mass extinctions. Does it make any sense for Homo sapiens to have evolved a way of perceiving a reality that is in some way fundamentally different from, or inconsistent with, how it really is?
But then in another moment of quiet reflection you will realize that there is no evolutionary law you can point to that would guarantee this. One of the factors that contributes to the survival of a species in the hectic scramble we call life is that certain genetic mutations bring with them survival advantages that are then selected for. With any luck, you live long enough to procreate, hopefully passing these advantages to a new generation. All we can be sure of is that we’ve evolved a finely tuned mental representation of those aspects of reality necessary to ensure our survival. There is no evolutionary selection pressure to develop a mind to represent reality as it really is.
Unsure? Ponder the evidence from synesthesia, a condition in which those who experience it* report perceptions that have become ‘mixed up’, with stimulation of one sense triggering involuntary responses from one or more other senses. One fairly common form is known as grapheme-colour synesthesia, in which letters and numbers are perceived to be coloured: ‘Wednesday is indigo blue’.6 It’s easy to dismiss this as incorrect wiring or ‘cross-talk’ in the brain, giving ris
e to an incorrect representation of reality, but with a prevalence estimated to be about four per cent of the population, those affected do not always see it this way. Who’s to say whose perceptions are the ‘right’ ones?
And, before you ask, it’s no good trying to corroborate what you perceive by sharing your experiences with a friend. Unless they’re a synesthete (and you’re not), your friend will doubtless confirm that they perceive precisely the same things that you perceive: ‘Yes, that rose is red.’ But, even if we presume that your friend has a mind that works in much the same way as yours (and he or she is not a philosophical zombie), all this tells us is that both your minds have developed in a similar fashion. You learned about the colour red as a small child, perhaps from pictures in a book that your parents would point to whilst saying ‘red’ out loud. You can be pretty sure that your friend’s knowledge and understanding of colour is derived from a set of very similar experiences. All this tells us is that your minds have undergone much the same conditioning, producing what philosopher John Searle refers to as the ‘background’.
This problem with reality has been recognized by philosophers since the ancient Greeks. In The Republic, which was written nearly two and a half thousand years ago, Plato devised an allegory which we can re-purpose to explore the situation a little more deeply. This is Plato’s famous allegory of the cave.
Deep in the cave is a number of prisoners, chained to a wall. They have lived their entire lives in the cave, and have no experience of a world outside. They’re not even aware that they are prisoners.
It is dark, but the prisoners are nevertheless aware of men and women passing continually along the wall in front of them, carrying all sorts of vessels, and statues and figures of animals. Some are talking among themselves. But, in truth, there is a fire constantly burning at the back of the cave, filling it with a dim light. The fire is out of sight and the prisoners are completely unaware of it. The men and women that the prisoners can see against the far wall are, in fact, the shadows cast by real people passing in front of the fire. The reality that the prisoners experience is made up of the crude appearances of things—people and objects—which they have mistaken for the things themselves.
Plato’s allegory was intended to illustrate his three-tier theory of knowledge. The shadows represent common belief or popular opinion (doxa) based merely on appearances. The objects themselves represent a deeper form of understanding derived, for example, from science (episteme, from which we get ‘epistemology’). The topmost tier is noesis (or ‘nous’), knowledge that goes beyond the superficial facts of the objects and concerns their form and nature.7 But the allegory serves our purpose here as an illustration of the fact that, as human beings, we rely on our senses to deliver a representation of reality that we have learned to take at face value, if not for granted. In our everyday lives, it’s simply a waste of time to question everything we experience.
We should nevertheless acknowledge a simple truth. Our reality is made up of shadows, of things-as-they-appear, and we have no real way of knowing to what extent the representation shaped by our perceptions reflects reality as it really is, a reality of things-in-themselves.
So how then can we be sure that a reality of things-in-themselves even exists? Well, we can’t, but let’s fast-forward a couple of thousand years to 1781, and the great philosopher Immanuel Kant. In the Critique of Pure Reason, Kant distinguished between what he called noumena, the metaphysical objects of reality or things-in-themselves that we can conceive only in our minds, and the empirical phenomena, the shadows or the things-as-they-appear in our perception and experience.*
Don’t take this to mean that noumena are merely figments of a fertile imagination. I can imagine all kinds of entertaining things—such as Gandalf, unicorns, or Westeros—but these obviously don’t connect with phenomena; they don’t manifest themselves as things we can directly perceive, except in works of fiction.
More practically, we can point to lots of ways in which what we call ‘electrons’ manifest themselves in our empirical reality. These are electrons-as-they-appear. But an electron-in-itself without any kind of interaction through which it can make itself manifest exists, kind of by definition, only in our imaginations.
Kant claimed that it makes no sense to deny the existence of the things-in-themselves, as there must be some things that cause appearances in the form of sensory perceptions: there can be no appearances without anything that appears.* Just because we can’t perceive reality as it really is doesn’t mean that it has ceased to exist. The great science-fiction writer Philip K. Dick was surely paraphrasing Kant when he observed: ‘Reality is that which, when you stop believing in it, doesn’t go away.’8
But we have to accept a trade-off. Whilst we might happily conclude that the things-in-themselves must exist, we must grumpily accept that we can in principle gain no knowledge of these. When judged in terms of Plato’s three tiers, Kant denies that noesis is possible—we can never have knowledge of the form and nature of the things-in-themselves.
Now, in the last chapter we encountered another big disconnect, of a very different kind but no less profound. This is the disconnect between the quantum world of molecular, atomic, and subnuclear dimensions and the classical world of everyday experience. It is the disconnect created by the locked box of the wavefunction, measurement operators, and the collapse of the wavefunction. What we will discover is that our anxiety over the relationship between reality and perception carries over to that between reality and measurement. We will find that we can no longer assume that what we measure necessarily reflects reality as it really is, and that there is also a difference between things-in-themselves and things-as-they-are-measured.
The contemporary physicist and philosopher Bernard d’Espagnat called it ‘veiled reality’, and commented that ‘we must conclude that physical realism is an “ideal” from which we remain distant. Indeed, a comparison with conditions that ruled in the past suggests that we are a great deal more distant from it than our predecessors thought they were a century ago.’9
So, this is why philosophers consider any kind of speculation, any conception, discussion, dissection, or thesis on the nature of a reality of things-in-themselves, to be metaphysics.*
It’s probably about here that more pragmatic readers might be starting to lose patience. Philosophers are known for their tendency to argue, obfuscate, and confuse, to see problems where they don’t exist and make mountains out of molehills. This stuff about noumena and phenomena is all very well, but scientists don’t want to waste their precious time nitpicking over the meanings of words. ‘Physics’, the philosopher(!) Karl Popper once said in an interview, ‘is that!’, as he slammed a book down hard on the table in front of him.10
Science is surely different. It proceeds through the painstaking gathering of hard, reproducible, and verifiable facts. Scientists develop theories that can accommodate these facts and explain the patterns that they form in terms of some underlying laws of nature. These theories make predictions that can be tested by reference to new observations or experiments which generate new facts. Sometimes the new facts don’t fit, so the theory is either tweaked in some way or thrown out and replaced by a new theory. This is how science makes progress in ways that (at least according to Krauss) philosophy doesn’t.
Except that it’s not quite as simple as this, as we’ll see in the next chapter.
Okay, so we can never be sure that the reality that we perceive or measure reflects or represents the things-in-themselves, but this quite obviously doesn’t prevent us from making observations, doing experiments, and developing and testing scientific theories. We can still determine that if we do this then that will happen. We can still establish hard facts about the shadows—the projections of whatever we think reality might be into our world of perception and measurement—and we can compare these with similar facts that have been derived by others. If these facts agree, then surely we have learned something about the nature of reality?
And this is indeed the bargain we make. The philosophers tell us that reality-in-itself is metaphysics. Although scientists don’t often openly acknowledge it up front, the reality that they study is inherently an empirical reality deduced from their studies of the shadows. It is an empirical reality of observation, experiment, measurement, and perception; an empirical reality of things-as-they-appear and of things-as-they-are-measured. As Heisenberg once explained: ‘we have to remember that what we observe is not nature in itself but nature exposed to our method of questioning.’11
We’re not quite done yet. Scientists work best within a framework based on laws or rules. They need parameters. Even though we might not be able to gain knowledge of a metaphysical reality-in-itself, we can follow Kant (and Philip K. Dick) and assume that such a reality must exist. There can be no appearances without something that appears. What’s more, it must surely exist objectively and independently of our ability to perceive or measure it. We would expect that the shadows would continue to be cast on the wall whether or not there were any prisoners in the cave to observe them.
We might also agree that, whatever reality is, it does seem to be rational and predictable, at least within limits. It appears to be logically consistent. The shadows that we perceive and measure are surely not completely independent of the things-in-themselves that cause them; otherwise, anything goes and science of any kind would be impossible. Even though we can never have knowledge of the things-in-themselves, as Kant argued, we can assume that the properties and behaviour of the shadows they cast are somehow determined by the things that cast them.
The truth is that empirical reality is a pretty dull place. It is a reality consisting only of numbers, of effects, a reality of doing this and getting that. Imagine a research paper that says: ‘We did these things and we got these results.’ Full stop, end of story. The numbers and the effects are meaningless until we try to interpret them. To do this we construct a theory that tries to explain what’s going on, with the broad aim of improving our understanding. And I would argue that any kind of scientific theorizing is simply impossible without first assuming the independent existence and the rational, logical consistency of the reality that lies beneath all the bald empirical experiences.