3
Sailing on the Sea of Representation
How Scientific Theories Work (and Sometimes Don’t)
We all tend to use the word ‘theory’ rather loosely. I have a theory about the reasons why British citizens voted by a narrow margin to leave the European Union in the referendum that was held in June 2016. I also have a theory about Donald Trump’s outrageous success in the race to become the 45th President of the United States later that year. We can all agree that no matter how well reasoned they might be, these are ‘just theories’.
But successful scientific theories are much more than this. They appear to tell us something deeply meaningful about how nature works. Theories such as Newton’s system of mechanics, Darwin’s theory of evolution, Einstein’s special and general theories of relativity, and, of course, quantum mechanics are broadly accepted as contingently ‘true’ representations of reality and form the foundations on which we seek to understand how the Universe came to be and how we come to find ourselves here, able to theorize about it. Much of what we take for granted in our complex, Western scientific-technical culture depends on the reliable application of a number of scientific theories. We have good reasons to believe in them.
In a recent New York Times online article, cell biologist Kenneth R. Miller explained that a scientific theory ‘doesn’t mean a hunch or a guess. A theory is a system of explanations that ties together a whole bunch of facts. It not only explains those facts, but predicts what you ought to find from other observations and experiments.’1
This is all well and good, but how does that happen? Where does a scientific theory come from and how is it shaped through the confrontation of metaphysical preconceptions with the empirical facts? How does it gain acceptance and trust in the scientific community? And, most importantly for our purposes here, how should we interpret what the theory represents?
In other words, what exactly is involved in sailing the Ship of Science across the Sea of Representation?
Your first instinct might be to reach for a fairly conventional understanding of what’s generally referred to as the ‘scientific method’. You might think that scientists start out by gathering lots of empirical data, and then they look for patterns. The patterns might suggest the possibility that there is a cause-and-effect relationship or even a law of nature sitting beneath the surface which guides or governs what we observe.
Drawing on our metaphor, the scientists arm themselves with a cargo of empirical data and set sail for the shores of Metaphysical Reality. Here they collect those preconceptions about reality that are relevant to the data they want to understand, perhaps involving familiar concepts, such as space and time, and familiar (but invisible) entities such as photons or electrons, and what we already think we know about their behaviours and their properties.
If these are patterns in physical data, the scientists will typically use mathematics to assemble their preconceptions into a formal theoretical structure, involving space and time, mass and energy, and maybe further properties such as charge, spin, flavour, or colour. To be worthy of consideration, the new structure will provide the scientists with the connections they need. The theory will say that when we do this, we get that pattern, and this is consistent with what is observed. The scientists then go further. Trusting the veracity of the structure, they figure out that when instead we choose to do that, then something we’ve never before observed (or thought to look for) should happen. They sail back across the Sea to the shores of Empirical Reality to make more observations or do some more experiments. When this something is indeed observed to happen, the theory gains greater credibility and acceptance.
Credit for this version of the scientific method, based on the principle of induction, is usually given to Francis Bacon who, after an illustrious career (and public disgrace), died of pneumonia caught whilst trying to preserve a chicken by stuffing it with snow. Now, we might feel pretty comfortable with this version of the scientific method, which remained unquestioned for several hundred years, but we should probably acknowledge that science doesn’t actually work this way.
If the eternal, immutable laws of nature are to be built through inductive inference substantiated or suitably modified as a result of experiment or observation, then, philosophers of the early twentieth century argued, we must accept that these laws can never be certain.
Suppose we make a long series of observations on ravens all around the world. We observe that all ravens are black. We make use of induction to generalize this pattern into a ‘law of black ravens’.* This would lead us to predict that the next raven observed (and any number of ravens that might be observed in the future) should also be black.
But then we have to admit that no matter how many observations we make, there would always remain the possibility of observing an exception, a raven of different colour, contradicting the law and necessitating its abandonment or revision. The probability of finding a non-black raven might be considered vanishingly small, but it could never be regarded to be zero and so we could never be certain that the law of black ravens would hold for all future observations. This is a conclusion reinforced by the experiences of European explorers—who might have formulated a similar ‘law of white swans’—until they observed black swans (Cygnus atratus) on the lakes and rivers of Australia and New Zealand.
The philosopher Bertrand Russell put it this way: ‘The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken.’2
Karl Popper argued that these problems are insurmountable, and so rejected induction altogether as a basis on which to build a scientific method. In two key works, The Logic of Scientific Discovery (first published in German in 1934) and Conjectures and Refutations (published in 1963), he argued that science instead proceeds through the invention of creative hypotheses, from which empirical consequences are then deduced. Conscious of some outstanding problems or gaps in our understanding of nature, scientists start out not with lots of empirical data, but by paying a visit to the shores of Metaphysical Reality. They conjure some bold (and, sometimes, outrageous) ideas for how nature might be, and then deduce the consequences on the voyage back across the Sea of Representation. The result is a formal theory.
What then happens when we reach the shores of Empirical Reality? This is easy: the theory is tested. It is exposed to the hard, brutal, and unforgiving facts. If the theory is not falsified by the data, by even just a single instance (observation of a single black swan will falsify the ‘law of white swans’), then Popper argued that it remains a relevant and useful scientific theory.
We can go a bit further than Popper and suggest that if the test is based on existing data, on empirical facts we already know, then the theory will be tentatively accepted if it provides a better explanation of these facts than any available alternative. Better still, if the theory makes predictions that can be tested, and which are then upheld by data from new observations or experiments, then the theory is likely to be more widely embraced.*
I honestly doubt that many practising scientists would want to take issue with any of this. I could provide you with many, many examples from the history of science which show that this is, more or less, how it has worked out. This isn’t a book about history, however, so I’ll restrict myself to just one very pertinent example.
We saw in Chapter 1 that the real quantum revolutionary was Einstein, who published his light-quantum hypothesis in his ‘miracle year’ of 1905. It’s important to note that Einstein didn’t induct this hypothesis from any available data. He simply perceived a problem with the way that science was coming to understand matter—in terms of discrete atoms and molecules—and electromagnetic radiation, which was understood exclusively in terms of continuous waves. The prevailing scientific description of matter and light didn’t fit with Einstein’s metaphysical preconceptions about how nature ought to be. Whilst on his visit to the shores of Metaphysical Reality, he conjectured that Planck’s conclusions should be interpreted as though light itself is composed of discrete quanta.
Einstein then sailed across the sea, representing his light-quanta in a theory that predicted some consequences for the photoelectric effect. The rest, as they say, is history.
The light-quantum hypothesis passed the test, but as we’ve seen, it still remained controversial (scientists can be very stubborn). Just a few years after the experiments on the photoelectric effect, Arthur Compton and Pieter Debye showed that light could be ‘bounced’ off electrons, with a predictable change in the frequency (and hence the energy) of the light. These experiments demonstrated that light does indeed consist of particles moving like small projectiles. Gradually, light-quanta became less controversial and more acceptable.
Popper’s take on science is known as the ‘hypothetico-deductive’ method. This is a bit of a clumsy term, but essentially it means that scientists draw on all their metaphysical preconceptions to hypothesize (or ‘make a guess’) about how nature works, and then deduce a formal theory which tells what we might expect to find in empirical observations or experiments. Science then proceeds through the confrontation between theory and the facts, as the ship sails between the shores. This is not a one-way journey—the ship makes many journeys back and forth, and those relevant metaphysical preconceptions that survive become tightly and inextricably bound into the theory (and, as we’ve seen, into the empirical observations, too). In this way the relevant metaphysics becomes ‘naturalized’ or ‘habitual’, justified through the success of the resulting theory.3
It’s worth mentioning in passing that the preconceptions, data, and indeed the ship itself is conditioned by their historical and cultural contexts, or perspectives. There are passages in Newton’s Principles of Natural Philosophy, published in 1687, that refer to God’s role in keeping the stars apart, a metaphysical preconception that would be unusual in today’s science. ‘Journeys are always perspectival,’ contemporary philosopher Michela Massimi told me in a discussion based on my metaphor, ‘we sail our ship using the only instruments (compass and whatever else) that our current technology, theories, and experimental resources afford. So any back and forth between the shores of Empirical Reality and metaphysical posits is guided and channelled by who we are, and most importantly, by our scientific history.’4 Compare a seventeenth-century tall ship in full sail with a modern ocean liner.
There is in principle no constraint on the nature of the hypotheses that scientists might come up with during their frequent visits to the shores of Metaphysical Reality. How, you might then ask, is science any different from any other kind of wild speculation? If I propose that some mysterious force of nature governs our daily lives depending on our birth signs, surely we would all agree that this is not science? What if I propose that similia similibus curentur—like cures like—and that when diluted by a factor of 1012 (or 1060), the substances that cause human diseases provide effective cures for them? Is this science? Or is it snake oil? What if I reach for the ultimate metaphysical preconception and theorize that God is the intelligent cause of all life on planet Earth, and all that we erroneously claim to be the result of evolution by natural selection is actually God’s grand design?
Your instinct might be to dismiss astrology, homeopathy, and intelligent design as pseudoscience, at best. But why? After all, they involve hypotheses based on metaphysics, from which certain theoretical principles are deduced, and they arguably make predictions which can be subjected to empirical test. We can see immediately that, given the fundamental role of metaphysics in scientific theorizing, if we are to draw a line between theories that we regard to be scientific and pseudoscience or pure metaphysics, then we need something more. We need a demarcation criterion.
The logical positivists proposed to use ‘verification’ to serve this purpose. If a theory is capable in principle of being verified through observational or experimental tests, then it can be considered to be scientific. But the principle of induction was also central to the positivists’ programme and, in rejecting induction, Popper had no alternative but to reject verification as well. Logically, if induction gives no guarantees about the uniformity of nature (as Russell’s chicken can attest), then the continued verification of theories gives none either. Theories tend to be verified until, one day, they’re not.
As we saw earlier, Popper argued that what distinguishes a scientific theory from pseudoscience and pure metaphysics is the potential for it to be falsified on exposure to the empirical data. In other words, a theory is scientific if it has the potential to be proved wrong.
This shift is rather subtle, but it is very effective. Astrology makes predictions, but these are intentionally general, and wide open to interpretation. Popper wrote: ‘It is a typical soothsayers’ trick to predict things so vaguely that the predictions can hardly fail: that they become irrefutable.’5 If, when confronted with contrary and potentially falsifying evidence, the astrologer can simply reinterpret the prediction, then this is not scientific. We can find many ways to criticize the premises of homeopathy and dismiss it as pseudoscience, as it has little or no foundation in our current understanding of Western, evidence-based medicine—as a theory it doesn’t stand up to scrutiny. But even if we take it at face value we should admit that it fails all the tests—there is no evidence from clinical trials for the effectiveness of homeopathic remedies beyond a placebo effect. Those who stubbornly argue for its efficacy are not doing science.
And, no matter how much we might want to believe that God designed all life on Earth, we must accept that intelligent design makes no testable predictions of its own. It is simply a conceptual alternative to evolution as the cause of life’s incredible complexity. Intelligent design cannot be falsified, just as nobody can prove the existence or non-existence of God. Intelligent design is not a scientific theory: it is simply overwhelmed by its metaphysical content.
Alas, this is still not the whole story. This was perhaps always going to be a little too good to be true. The lessons from history teach us that science is profoundly messier than a simple demarcation criterion can admit. Science is, after all, a fundamentally human endeavour, and humans can be rather unpredictable things. Although there are many examples of falsified or failed scientific theories through history, science doesn’t progress through an endless process of falsification. To take one example: when Newton’s classical mechanics and theory of universal gravitation were used to predict the orbit of a newly discovered planet called Uranus in 1781, the prediction was found to be wrong. But this was not taken as a sign that the structures of classical mechanics and gravitation had failed.
Remember that it’s actually impossible to do science without metaphysics, without some things we’re obliged to accept at face value without proof. Scientific theories are constructed from abstract mathematical concepts, such as point-particles or gravitating bodies treated as though all their mass is concentrated at their centres. If we think about how Newton’s laws are actually applied to practical situations, such as the calculation of planetary orbits, then we are forced to admit that no application is possible without a whole series of so-called auxiliary assumptions or hypotheses.
Some of these assumptions are stated, but most are implied. Obviously, if we apply Newton’s mechanics to planets in the Solar System then, among other things, we assume our knowledge of the Solar System is complete and there is no interference from the rest of the Universe. In his recent book Time Reborn, contemporary theorist Lee Smolin wrote: ‘The method of restricting attention to a small part of the universe has enabled the success of physics from the time of Galileo. I call it doing physics in a box.’6
One of the consequences of doing physics in a box is that when predictions are falsified by the empirical evidence, it’s never clear why. It might be that the theory is false, but it could simply be that one or more of the auxiliary assumptions is invalid. The evidence doesn’t tell us which. This is the Duhem–Quine thesis, named for physicist and philosopher Pierre Duhem and philosopher Willard Van Orman Quine.
And, indeed, the problem with the orbit of Uranus was traced to one of the auxiliary assumptions. It was solved simply by making the box a little bigger. John Adams and Urbain Le Verrier independently proposed that there was an as-yet unobserved eighth planet in the Solar System that was perturbing the orbit of Uranus. In 1846 Johann Galle discovered the new planet, subsequently called Neptune, less than one degree from its predicted position.
Emboldened by his success, in 1859 Le Verrier attempted to use the same logic to solve another astronomical problem. The planetary orbits are not exact ellipses. If they were, each planet’s point of closest approach to the Sun (called the perihelion) would be fixed, the planet always passing through the same point in each and every orbit. But astronomical observations had shown that with each orbit the perihelion shifts slightly, or precesses. It was understood that much of the observed precession is caused by the cumulative gravitational pull of all the other planets in the Solar System, effects which can be predicted using Newton’s gravitation.
But, for the planet Mercury, lying closest to the Sun, this ‘Newtonian precession’ is predicted to be 532 arc-seconds per century.* The observed precession is rather more, about 575 arc-seconds per century, a difference of 43 arc-seconds. Though small, this difference accumulates and is equivalent to one ‘extra’ orbit every three million years or so.
Le Verrier proposed the existence of another planet, closer to the Sun than Mercury, which became known as Vulcan. Astronomers searched for it in vain. Einstein was delighted to discover that his general theory of relativity predicts a further ‘relativistic’ contribution of 43 arc-seconds per century, due to the curvature of spacetime around the Sun in the vicinity of Mercury.† This discovery gave Einstein the strongest emotional experience of his life in science: ‘I was beside myself with joy and excitement for days.’7
It seems from this story that a theory is only going to be abandoned when a demonstrably better theory is available to replace it. We could conclude from this that scientific theories are never falsified, as such, they are just eventually shown to be inferior when compared with competing alternatives. Even then, demonstrably falsified theories can live on. We know that Newton’s laws of motion are inferior to quantum mechanics in the microscopic realm of molecules, atoms, and subatomic particles, and they break down when stuff of any size moves at or close to the speed of light. We know that Newton’s law of universal gravitation is inferior to Einstein’s general theory of relativity. And yet Newton’s laws remain perfectly satisfactory when applied to ‘everyday’ objects and situations and physicists and engineers will happily make use of them, even though we know they’re ‘not true’.
Problems like these were judged by philosophers of science to be insurmountable, and consequently Popper’s falsifiability criterion was abandoned (though, curiously, it still lives on in the minds of many practising scientists). Its demise led Paul Feyerabend—something of a Loki among philosophers of science—to reject the notion of the scientific method altogether and promote an anarchistic interpretation of scientific progress. In science, he argued, anything goes. He encouraged scientists8
to step outside the circle and either to invent a new conceptual system, for example a new theory, that clashes with the most carefully established observational results and confounds the most plausible theoretical principles, or to import such a system from outside science, from religion, from mythology, from the ideas of incompetents, or the ramblings of madmen.
According to Feyerabend, science progresses in an entirely subjective manner, and scientists should be afforded no special authority: in terms of its application of logic and reasoning, science is no different from any other form of rational inquiry. He argued that a demarcation criterion is all about putting science on a pedestal, and ultimately stifles progress as science becomes more ideological and dogmatic.
In 1983, philosopher Larry Laudan declared that the demarcation problem is intractable, and therefore a pseudo-problem.* He argued that the real distinction is between knowledge that is reliable and that which is unreliable, irrespective of its provenance. Terms like ‘pseudoscience’ and ‘unscientific’ are ‘just hollow phrases which only do emotive work for us’.9
Okay—time for some confessions. I don’t buy the idea that science is fundamentally anarchic, and that it has no rules. I can accept that there are no rules associated with the creative processes that take place along the shores of Metaphysical Reality. You prefer induction? Go for it. You think it’s better to deduce hypotheses and then test them? Great. Although I would personally draw the line at seeking new ideas from religion, mythology, incompetents, and madmen,* at the end of the day nobody cares overmuch how new theoretical concepts or structures are arrived at if they result in a theory that works.
But, for me at least, there has to be a difference between science and pseudoscience, and between science and pure metaphysics. As evolutionary-biologist-turned-philosopher Massimo Pigliucci has argued, ‘it is high time that philosophers get their hands dirty and join the fray to make their own distinctive contributions to the all-important—and sometimes vital—distinction between sense and nonsense.’10
So, if we can’t make use of falsifiability as a demarcation criterion, what do we use instead? I don’t think we have any real alternative but to adopt what I might call the empirical criterion. Demarcation is not some kind of binary yes-or-no, right-or-wrong, black-or-white judgement. We have to admit shades of grey. Popper himself (who was no slouch, by the way) was more than happy to accept this:11
the criterion of demarcation cannot be an absolutely sharp one but will itself have degrees. There will be well-testable theories, hardly testable theories, and non-testable theories. Those which are non-testable are of no interest to empirical scientists. They may be described as metaphysical.
Some scientists and philosophers have argued that ‘testability’ is to all intents and purposes equivalent to falsifiability, but I disagree. Testability implies only that the theory either make contact or, at the very least, hold some promise of making contact, with empirical evidence. It makes absolutely no presumptions about what we might actually do in light of the evidence. If the evidence verifies the theory, that’s great—we celebrate and then start looking for another test. If the evidence fails to support the theory, then we might ponder for a while or tinker with the auxiliary assumptions. Either way, we have something to work with. This is science.
Returning to my grand metaphor, a well-testable theory is one for which the passage back across the sea to Empirical Reality is relatively straightforward. A hardly testable theory is one for which the passage is for whatever reason more fraught. Some theories take time to develop properly, and may even be perceived to fail if subjected to tests before their concepts and limits of applicability are fully understood. Sometimes a theory will require an all-important piece of evidence which may take time to uncover. Peter Higgs proposed the mechanism that would be named for him in a paper published in 1964, and the Higgs mechanism went on to become an essential ingredient in the standard model of particle physics, the currently accepted quantum description of all known elementary particles. But the mechanism wasn’t accepted as ‘true’ until the tell-tale Higgs boson was discovered at the Large Hadron Collider, nearly fifty years later.
Make no mistake, if the theory fails to provide even the promise of passage across the sea—if it is trapped in the tidal forces of the whirlpool of Charybdis—then this is a non-testable theory. No matter how hard we try, we simply can’t bring it back to Empirical Reality. This implies that the theory makes no predictions, or makes predictions that are vague and endlessly adjustable, more typical of the soothsayer or the snake oil salesman. This is pure metaphysics, not science, and brings me to my second-favourite Einstein quote: ‘Time and again the passion for understanding has led to the illusion that man is able to comprehend the objective world rationally by pure thought without any empirical foundations—in short, by metaphysics.’12
I want to be absolutely clear. I’ve argued that it is impossible to do science of any kind without involving metaphysics in some form. The scientists’ metaphysical preconceptions are essential, undeniable components in the construction of any scientific theory. But there must be some kind of connection with empirical evidence. There must be a tension between the ideas and the facts. The problem is not metaphysics per se but rather the nature and extent of the metaphysical content of a theory. Problems arise when the metaphysics is all there is.
Of course, this is just my opinion. If we accept the need for a demarcation criterion, then we should probably ask who should be responsible for using it in making judgements. Philosophers Don Ross, James Ladyman, and David Spurrett argue that individuals (like me, or them) are not best placed to make such judgements, and we should instead rely on the institutions of modern science.13 These institutions impose norms and standards and provide sense-checks and error filters that should, in principle, exclude claims to objective knowledge derived from pure metaphysics. They do this simply by not funding research proposals that don’t meet the criteria, or by not publishing papers in recognized scientific journals.
But, I would argue, even institutions are fallible and, like all communities, the scientific community can fall prey to groupthink.14 We happen to be living in a time characterized by a veritable cornucopia of metaphysical preconceptions coupled with a dearth of empirical facts. We are ideas-rich, but data-poor. As we will see in Chapter 10, I personally believe the demarcation line has been crossed by a few theorists, some with strong public profiles, and I’m not entirely alone in this belief. But, at least for now, the institutions of science appear to be paying no attention.
So I encourage you to form your own opinions.
An accepted scientific theory serves at least two purposes. If it is a theory expressed in the form of one or more mathematical equations, then these equations allow us to calculate what will happen given a specific set of circumstances or inputs. We plug some numbers in, crank the handle, and we get more numbers out. The outputs might represent predictions for observations or experiments that we can then design and carry out. Or they might be useful in making a forecast, or designing a new electronic device, building a skyscraper, or planning a town’s electricity network. Used in this way, our principal concerns rest with the inputs and the outputs, and we might not need to think too much about what the theory actually says. Provided we can trust its accuracy and precision, we can quite happily use the theory as a ‘black box’, as an instrument.
The second purpose is concerned with how the theory should be interpreted. The equations are expressed using a collection of concepts represented by sometimes rather abstract symbols. These concepts and symbols may represent the properties and behaviours of invisible entities such as electrons, and the strengths of forces that act on them or that they produce or carry. Most likely, the equations are structured such that everything we’re interested in takes place within a three-dimensional space and in a time interval stretching from then until now, or from now until sometime in the future. The interpretation of these symbols then tells us something meaningful about the things we find in nature. This is no longer about our ability to use the theory; it is about how the theory informs our understanding of the world.
You might think I’m labouring this point. After all, isn’t it rather obvious how a physical theory should be interpreted? What’s the big deal? If we’re prepared to accept the existence of objective reality (Realist Proposition #1), and the reality of invisible entities such as photons and electrons (Realist Proposition #2), it surely doesn’t require a great leap of imagination to accept:
Realist Proposition #3: The base concepts appearing in scientific theories represent the real properties and behaviours of real physical things.
By ‘base concepts’ I mean the familiar terms we use to describe the properties and behaviours of the objects of our theories. These are concepts such as mass, momentum, energy, spin, and electric charge, with events unfolding in space and time. It’s important to distinguish these from other, more abstract mathematical constructions that scientists use to manipulate the base concepts in order to perform certain types of calculations. For example, in classical mechanics it is possible to represent the complex motions of a large collection of objects more conveniently as the motion of a single point in something called configuration space or phase space. Nobody is suggesting that such abstractions should be interpreted realistically, just the base concepts that underpin them. We’ll soon see that arguments about the interpretation of quantum mechanics essentially hinge on the interpretation of the wavefunction. Is the wavefunction a base concept, with real properties and real behaviours? Or is it an abstract construction?
Proposition #3 appears straightforward, but then I feel obliged to point out that the conjunction of everyday experience and familiarity with classical mechanics has blinded us to the difference between the physical world and the ways in which we choose to represent it.
Let’s use Newton’s second law of motion as a case in point. We know this law today by the rather simple equation:
This says that accelerated motion will result if we apply a force (or an ‘action’ of some kind) on an object with a certain mass. Now, whilst it is certainly true to say that the notion of mechanical force still has much relevance today, as I explained in Chapter 1 the attentions of eighteenth- and nineteenth-century physicists switched from force to energy as the more fundamental concept. My foot connects with a stone, this action impressing a force on the stone. But a better way of thinking about this is to see the action as transferring energy to the stone.
The term ‘energy’ was first introduced in the early nineteenth century and it gradually became clear that this is a conserved quantity—energy can be neither created nor destroyed and is simply moved around a physical system, shifting from one object to another or converting from one form to another. It was realized that kinetic energy—the energy associated with motion—is not in itself conserved. Physicists recognized that a system might also possess potential energy by virtue of its physical characteristics and situation. Once this was understood it became possible to formulate a law of conservation of the total energy—kinetic plus potential—and this was achieved largely through the efforts of physicists concerned with the principles of thermodynamics.
Today, we replace Newton’s force with the rate of change of potential energy in space. Think about it this way. Sisyphus, the king of Ephyra, is condemned for all eternity to push an enormous boulder to the top of a hill, only for it roll back to the bottom (Figure 8). As he pushes the boulder upwards, he expends kinetic energy on the way, determined by the mass of the boulder and the speed with which he rolls or carries it. If we neglect any losses due to friction, all this kinetic energy is transferred into potential energy, held by the boulder, perched at the top. This potential energy is represented by the way the hill slopes downwards. As the boulder rolls back down the slope, the potential energy is converted back into the kinetic energy of motion. For a given mass, the steeper the slope (the greater the force), the greater the resulting acceleration.
Figure 8 The myth of Sisyphus (painting by Titian, 1549) demonstrates the relationship between kinetic and potential energy.
With this in mind, why would we hesitate, even for an instant, to accept Realist Proposition #3? Sisyphus is a figure from Greek mythology, but there are many real hills, and many real boulders, and we don’t doubt what will happen as the boulder rolls down. Acceleration is something we’ve experienced many thousands of times—there is no doubting its reality.
But force = mass × acceleration is an equation of a classical scientific theory, and we must remember that it is impossible to do science without metaphysics, without assuming some things for which we can’t contrive any evidence. And, lest we forget, remember that to apply this equation we must also do physics in a box.
The first thing we can acknowledge is that the slope of the hill represents the rate of change of potential energy in space. Acceleration is the rate of change of velocity with time. And, for that matter, velocity itself is the rate of change of the boulder’s position in space with time. That Newton’s second law requires space and time should come as no real surprise—it’s about motion, after all.
But, as I explained in Chapter 2, Newton’s absolute space and time are entirely metaphysical. Despite superficial appearances, we only ever perceive objects to be moving towards or away from each other, changing their relative positions. This is relative motion, occurring in a space and time that are in principle defined only by the relationships between the objects themselves. Newton’s arch-rival, the philosopher Gottfried Wilhelm Leibniz, argued: ‘the fiction of a finite material universe, the whole of which moves about in an infinite empty space, cannot be admitted. It is altogether unreasonable and impracticable.’15
Newton understood very well what he was getting himself into. So why, then, did he insist on a system of absolute space and time? Because by adopting this metaphysical preconception he found that he could formulate some very highly successful laws of motion. Success breeds a certain degree of comfort, and a willingness to suspend disbelief in the grand but sometimes rather questionable foundations on which theoretical descriptions are constructed.
Then there’s the question of Newton’s definition of mass. Here it is: ‘The quantity of matter is the measure of the same, arising from its density and bulk conjunctly…. It is this that I mean hereafter everywhere under the name body or mass.’16 If we interpret Newton’s use of the term ‘bulk’ to mean volume, then the mass of an object is simply its density (say in grams per cubic centimetre) multiplied by its volume (in cubic centimetres). It doesn’t take long to figure out that this definition is entirely circular, as Mach pointed out many years later: ‘As we can only define density as the mass of a unit of volume, the circle is manifest.’17
I don’t want to alarm you unduly, but no matter how real the concept of mass might seem, the truth is that we’ve never really understood it. Einstein messed things up considerably with his famous equation E = mc2, which is more deeply meaningful when written as m = E/c2: ‘The mass of a body is a measure of its energy content.’18 In the standard model of particle physics, elementary particles such as electrons are assumed to ‘gain mass’ through their interactions with the Higgs field (this is the Higgs mechanism). The masses of protons and neutrons (and hence the masses of all the atoms in your body) are actually derived in large part from the energy of the colour force (carried by gluons) that binds the up and down quarks inside them.19
See what I mean? If an equation as simple and familiar as force = mass × acceleration is rife with conceptual problems and difficulties of interpretation, why would we assume that we can understand anything at all?
Once again we should remember that we don’t actually have to understand it completely in order to use it. We know that it works (within the limits of its applicability) and we can certainly use it to calculate lots of really useful things. But the second law of motion is much more than a black box. There is a sense in which it provides genuine understanding, even though we might be unsure about the meaning of some of its principal concepts.
Of course, we know that Newton’s laws have been superseded by Einstein’s special and general theories of relativity, which change the way we think about space, time, and mass. But these are still classical theories (in the sense that they’re not quantum theories). Take it from me that there’s nothing in relativity that should shake our confidence about Realist Proposition #3. Though they’re still very much on the surface, we have to accept that even the base concepts in our theories sometimes need to be understood at a somewhat deeper level. Space, time, and mass are real but our understanding of them in Newton’s second law of motion is only approximate. After all, scientific theories are provisional. They’re only approximately or contingently true, valid for as long as they continue to provide descriptions that are judged to be in agreement with the evidence.
Nevertheless, if I’ve managed to sow a few seeds of doubt then I’ve done my job. As we’ve already seen in Chapter 1, in quantum mechanics these doubts return with a startlingly cruel vengeance.
Now, I’ve tended to find that discussions about the interpretation of quantum mechanics can quickly get bogged down and confused on the subject of ‘reality’. There’s a tendency to conflate objective reality (Realist Proposition #1), the reality of ‘invisible’ entities like electrons (Proposition #2), and the reality of the representation of the properties and behaviour of these entities in scientific theories (Proposition #3). I’d be the first to admit that these propositions are not so cleanly separable, but I’d argue that there’s much to be gained by considering them as such.
It would seem that Proposition #3 is contingent on the acceptance of #1 and #2. It’s surely pointless to argue for a realist interpretation of a scientific representation whilst at the same time denying that stuff is real when we’re not looking at it or thinking about it, and when our only evidence for it is indirect.* But, of course, acceptance of Propositions #1 and #2 doesn’t imply acceptance of #3. We can accept #1 and #2 but still choose to reject #3. I’ve come to believe that the best way to appreciate the debate about the interpretation of quantum mechanics is to view this not as a debate about the ‘nature of reality’, as such, but as a debate about the realism (or otherwise) of our representation of reality. In essence, it’s a debate about Proposition #3.
For the sake of completeness, I want to be clear that there’s a little more to scientific realism than this.20 We need to propose further that scientific theories, interpreted realistically according to #3, meet the empirical criterion: they can be tested and either confirmed as approximately or contingently true (for now) or their predictions can be shown to be false by comparison with empirical evidence. We also need to agree that when we talk about ‘progress’ in science, we understand that this is based on successively more accurate representations, the result of sailing the Ship of Science back and forth across the sea over time, refining and tightening the relationship between our metaphysical preconceptions and the empirical data. The philosopher Hilary Putnam wrote: ‘The positive argument for realism is that it is the only philosophy that doesn’t make the success of science a miracle.’21 This is sometimes referred to as the no miracles argument.
This would seem to make for a relatively straightforward distinction between realism and empiricism (or anti-realism) at the level of representation, but let’s not be too hasty. In seeking to resolve some of the contradictions between realism and anti-realism, the philosopher John Worrall developed a philosophy derived from a position first described by mathematician Henri Poincaré. This is called structural realism. According to Worrall, scientific theories tell us only about the form or structure of reality, but they tell us nothing about the underlying nature of this reality.*
As one theory displaces another, the mathematics might change and even the interpretation of the base concepts might change, but the structure or network of relationships between physical things is preserved. In general, a better theory will accommodate all the relationships between phenomena established through the theory it has replaced. For example, the quantum mechanical description of photons preserves all the structural relationships associated with the phenomena of diffraction and interference previously described by the wave theory of light, despite the fact that the mathematical formulations of these theories are so very different.
Structural realism comes in two flavours. There’s a Kantian flavour which suggests that scientific theories are about things-as-they-appear in the form of a structure of empirical relationships. But there are, nevertheless, metaphysical things-in-themselves that are presumed to exist because, as Kant argued, there can be no appearances without anything that appears. This was largely Poincaré’s position. In another, more empiricist flavour, the structural relationships are all there is and there are no things-in-themselves. This might lead us to wonder how it is possible to establish relationships if there’s nothing to relate to, but perhaps this is really rather moot. Even if the things-in-themselves exist, we can still say nothing meaningful about them.
This kind of approach makes the realist/anti-realist distinction much less straightforward. The philosopher Ian Hacking anticipated this dilemma, and reminded us that there is more to science than theoretical representation. Science has two principal aims: theory and experiment. Theories represent, says Hacking, and experiments intervene. We represent in order to intervene, and we intervene in the light of our representations. He wrote:22
I suspect there can be no final argument for or against realism at the level of representation. When we turn from representation to intervention, to spraying niobium balls with positrons, anti-realism has less of a grip…. The final arbitrator in philosophy is not how we think but what we do.
Theories come and go and, Hacking argues, intervention—experiment—is the final arbitrator on vexed questions concerning reality. As we will see in what follows, deciding whether a representation conforms to Proposition #3 can be a bit of a tricky business. In such situations, we will find it helpful to reach for a further proposition to help bring us to a conclusion. Therefore, at risk of blurring Hacking’s distinction between representation and intervention, I propose to paraphrase his arguments as follows:
Realist Proposition #4: Scientific theories provide insight and understanding, enabling us to do some things that we might otherwise not have considered or thought possible.
I think of this as the ‘active’ proposition. Only by taking the representation seriously do we have a firm basis on which to act. This might take the form of a search for new empirical data, by designing, building, and performing new experiments or making new observations. This doesn’t mean that it’s impossible for a ‘passive’, anti-realist representation to engage and motivate experimentalists. But, as we will see, this happens most often because those experimentalists who care about these things tend to favour realist representations, and are generally uncomfortable with anti-realism.
I want to contrast this with the views of the anti-realist philosopher Bas van Fraassen, who in the 1970s developed a philosophy known as constructive empiricism, a less dogmatic descendant of logical positivism. Van Fraassen argues that scientific theories need only be ‘empirically adequate’. It is sufficient that the representation accommodates all the empirical data and enables some prediction, but we should avoid getting tangled up in too much metaphysics. The representation is an instrument. It passively represents, nothing more.
This, then, is the proposition of last resort. If there are arguments both ways at the level of Proposition #3, we will seek judgement based on what the representation encourages us to do. If it actively represents, then we might be inclined to accept that this is a realist representation. If it passively represents, then we might consider it to be anti-realist.
Okay. That’s enough of that.* Now, where were we?