Erwin Schrödinger Didn't Have a Cat

image: Erwin Schrödinger

"Science is the belief in the ignorance of experts."
Richard Feynman. "What is Science?"
The Physics Teacher Vol. 7, issue 6 (1969)

"I think I can safely say that
nobody understands quantum mechanics."
Richard Feynman. The Character of Physical Law (1965)

~~~~

SCHRÖDINGER'S CAT is one of the most famous thought experiments in the history of science. Erwin Schrödinger (left) used it to try to argue against adopting one approach Quantum Mechanics. Most people seem unaware that he was trying to highlight a problem with what was, in 1935, a controversial theory, but which has become the orthodoxy: namely the Copenhagen Interpretation of Quantum Mechanics . These days when we say Quantum Mechanics we usually mean the Copenhagen Interpretation of Quantum Mechanics (hereafter QM). Many people who know next to nothing about science, or about Schrödinger, have tried to co-opt Schrödinger's cat to show how there is a relationship between physics and Buddhism. Let me say at the beginning that I don't believe that there is any significant cross-over between physics and Buddhism, and that I hope to explain why in the rest of this post. Granted my degree is in chemistry and it was a long time ago; but I also studied physics, and I'm an ordained Buddhist, so I feel at least not-overly-unqualified to comment.

To begin with we need to be clear on scale. An atom is between 32 picometres and 225 picometres in diameter. A picometer is 1×10⁻¹² m, i.e. a trillionth of a metre, or 0.000000000001 m. By contrast a human hair is around 50 µm or 0.000005 m. So a single hair is about about 1.5 million helium atoms in diameter. Basically this scale is unimaginable, so let's put it another way: if the diameter an atom was the thickness of a single sheet of copier paper (0.08mm) then a human hair would be 120 metres in diameter. Amedeo Avogadro showed that 12g of carbon contains approximately 6 x 10²³ atoms of carbon. That is 600,000,000,000,000,000,000,000 (600 sextillion) atoms. If each carbon atom was 1 mm³ then the 12g of carbon would fill the Western Mediterranean Ocean (from Gibraltar to Sicily), with plenty to spare. In fact 12g of carbon (in the form of powdered soot) is about 2 teaspoons. In QM we're dealing with the subatomic world, with the protons, neutrons and elections, and the weirder particles which make up atoms. A proton is about 1/50th of the diameter of the smallest atom; while an electron is thought to be in the region of 10⁻²²m, which is one 10-billionth the diameter of a proton. Don't be fooled by our ability to write these properties down in numbers: they are highly abstract, unimaginable, incomprehensible, and none of us can draw on experience to get a sense of them. If you are still confident that any of this is relevant to human existence then read on.

Those with an interest in this subject will know that QM conceives of subatomic particles as waves (which can behave like particles under some conditions) that are described not in terms of physical properties, but in mathematical formulas. QM is the first theory of science to not be based on observations of physical properties, but to emerge from abstract mathematical speculation. [ 1 ] Though of course QM makes testable predictions about the behaviour of matter on the picometer scale. This description of sub-atomic particles as waves has some interesting consequences. One is that the particle is not a point in space, but is smeared out over space. Another is that all we can know about the particles in atoms are the odds of the particle being in any one place in space at any given time. What's more, as Heisenberg showed, if we know precisely where a particle is, then we can't simultaneously know how fast it is going - this is called the Uncertainty Principle.

Schrödinger's thought experiment related to a curious prediction arising out of the mathematics of waves (subsequently experimentally confirmed). Under certain circumstances two wavy particles can become 'entangled' which means that their waves combine into a single system, though they retain their identities. (Don't worry if you don't quite understand how this works - Feynman was not being ironic when he said that no one understands QM.) Schrödinger's problem was that this meant that observing some of the properties of one of the particles, meant having certain knowledge about the other particle because the two must be in opposition. The main property we are concerned with is called 'spin' - which relates to the magnetic properties of charged particles.

The two entangled particles can be in one of two spin states, but cannot both occupy the same state. With regard to the spin state of any single particle we can only talk about the probability that they will be in a given state at any time until we observe it. However, observing the spin of one entangled particle, determines which state the other will be in with 100% certainty without observing it, no matter where it is in the universe. This appears to contradict the limit introduced by Einstein's Special Theory of Relativity (1905) that nothing, not even information, can travel faster than the speed of light. But also, and even more weirdly, before an observation we can only think about spin states in terms of probabilities and the the maths tells us that the combined probabilities of the two particles being in any given state always equals one. The Copenhagen Interpretation says that this effectively means that the two entangled particles are both in both states simultaneously - the two states are superimposed as the jargon goes.

This is quite counter-intuitive, but it has been a boon for science-fiction because the spin states of the entangled particles are linked no matter how far apart they are - "spooky action at a distance" as Einstein facetiously referred to it - which if you aren't too fussy about details gives you an excellent medium for instantaneous communications across the vastness of space.

However, it begs the question: how can something be in two states at once until observed? It was in order to highlight these paradoxical aspects of QM that Schrödinger put his imaginary cat in the imaginary box. With it he placed a mechanism which would release cyanide gas, with a switch triggered by the decay of an atom of Uranium, the timing of which we cannot predict from theory. Close the lid of the box, prime the switch and think: is the cat alive at this moment, or is it dead? If the atom has not decayed the cat will be alive, and if it has decayed the cat will be dead. We can't know until we open the box and observe. Schrödinger invited us to think of the cat as a metaphor for the infinitesimal sub-atomic particle, whose wave was metaphorically entangled with the Uranium atom. If the cat truly was like a sub-atomic particle, then it was both alive and dead until the box was opened, and it was observed to be one or the other. He was trying to show that this is a ridiculous conclusion, and that therefore the Copenhagen Interpretation must be flawed. He lost that particular argument.

A lot of people jump from the picometre scale to the metre scale without any thought for the consequences of a trillion-fold change in scale - even though we know, for example, that our bath water doesn't really behave like an ocean! Or though we know that those pre-CGI movie special effects with models are totally unconvincing. The problem is that in a real cat there are several thousand sextillions of atoms, made up of many particles. Although each infinitesimal particle is a wave and subject to QM effects, these are averaged out over some tens or hundreds of thousands of sextillions of particles. The behaviour of any one particle, or even any million or billion particles, is not going to change the average properties of the cat. Unlike sub-atomic particles, cats simply do not wink in and out of existence; they are not smeared out over space (except perhaps when run over); and we can in fact know quite precisely (compared to the size of the cat) where a cat is and how fast it is moving at the same time. The Uncertainty Principle doesn't apply on the macro level. QM has almost no relevance to the macro world, to a world where objects are made up of septillions of atoms because of the averaging effect of so many particles - if weird stuff was happening we'd never know because a human hair is millions of atoms in diameter. And this is partly why Schrödinger was unable to undermine the Copenhagen Interpretation with this thought experiment, and why it has been co-opted by the targets of his critique, not to mention Buddhists! Actually sub-atomic particles are not alive and it is not ridiculous to argue that they can be in two superimposed states at once, even though it is ridiculous to argue it for a cat. In effect, Schrödinger's Cat proved nothing.

One of the unfinished tasks of modern physics is finding some way to marry QM with Relativity (E=mc² yadda yadda again we don't really understand this). This has proved elusive, though work is going on at both the empirical and the theoretical ends of the problem. So far no one has unequivocal evidence for, say, quantum gravity; and no one has been able to make the maths add up. It may in fact turn out that the two theories are not adequate to the task and that both will be subsumed into some larger construct (some people claim that String Theory will do it, if anyone can ever solve the equations; Stephen Hawking barracks for M-Theory if anyone can both figure out what equations are and how to solve them). Certainly dark matter and dark energy are causing a scramble to rework the Standard Model of Cosmology to account for the observations that gave rise to those terms. Often theories don't survive being scaled up by a dozen orders of magnitude, and this is the case for QM (so far).

It's pretty clear that QM, a mathematical abstraction, doesn't apply to our macro world. However it does have indirect consequences for us as QM issues have to be taken into account in designing new micro-processors which pack millions of transistors into square millimetres; and in nascent nano-technology. But in terms of our daily lives none of the observations of sub-atomic particles apply. None. The similarity of vocabulary is superficial and coincidental, just as the similarity of ethical jargon in various religions is largely superficial and coincidental! well, perhaps not entirely coincidental because like Schopenhauer, both Schrödinger and Niels Bohr were interested in so-called 'Eastern philosophy' and built some of it into the narrative.

Some weeks ago now, in the comments to my post on Rebirth and the Scientific Method Elisa and Krishna were asking: "why do Buddhists feel the need to justify their beliefs by appealing to science?" Part of my answer related to the way the scientific paradigm has dominated our lives for roughly 150 years. Science is incredibly successful in describing the physical world, and predicting new observations and properties of matter. Just look at the recent crop of Nobel Prizes to see the contribution that science makes. In a way it's obvious that we'd want to participate in that. It is a bit ironic that so few Buddhists are educated in the sciences, and tend to approach science with a mixture of abhorrence for perceived materialism, and credulous wonder at its success and authoritativeness.

I don't see much advantage in invoking the talisman of science in defence of religion, especially when on the whole we religieux are so ignorant of science (one of my teachers recently mentioned the way "larger bodies attract smaller ones" in a public talk. He's not an idiot, nor spiritually shallow, but he is clearly, painfully ignorant of science!). It so happens that Buddhists avoid some of the pitfalls of the modern world view (we don't have creation stories for instance), but though monotheism more obviously runs foul of science, I don't think we can sustain our traditional eschatologies, nor claims of ESP powers, nor to know the nature of 'reality', if we are working in a scientific paradigm. It's a minefield.

I don't think Buddhism on its own terms needs any scientific apologetic. Buddhism is originally the product of Iron Age India, and has adapted to many different cultural environments and world-views because, in my opinion, it is not so concerned with the realm of physics, it is concerned with the realm of the mind. Physics provides us with a far superior description of the physical world; but equally in the domain of the mind, and especially the problem of suffering, that Buddhism is far superior descriptively and practically (in terms of practices for working on the mind). This superiority in its own field is not a consequence of levels of technology or an understanding of physics. It's to do with observing our own minds. We don't need a Large Hadron Collider for this. We just need to sit quietly and observe our minds. It is a kind of empiricism, but we don't need to get caught up in making a 'science' out of it.

~~ oOo ~~

Notes

1. This feature of QM not deriving from observations of physical properties was recently the subject of an article in the New Scientist: Webb, Richard. 'Reality Gap' 21 August 2010, p.32-6. NS apparently subscribes to another uncertainty principle as the article title is quite changeable:
   • on the cover - The Ultimate Quantum Paradox
   • contents page - The Ultimate Paradox
   • printed article - Reality Gap
   • online article - Is quantum theory weird enough for the real world? [login required]
   • ScienceDirect article database - Quantum Mechanics: The Reality Gap [login required].
   (return to article)

(Note: Though I gather that Schrödinger loved women and a good party, I confess I'm not really sure whether he owned a cat. Some people claim that Schrödinger was a cat lover, and some that he was a cat hater, but I thought my title was catchy and ran with it. I hope my readers will allow me some poetic licence.)

image: Erwin Schrödinger (internet endemic, i.e. copied so many times that there is no longer a discernible source).

Feynman quotes from Wikiquote.

If you want to learn about Quantum Theory from one of the men who helped to develop it, then I can recommend these three lectures by Hans Bethe: Quantum Physics Made Relatively Simple. As the site says, the Prof is 93 years old and lecturing to the other residents at his retirement home.


Updates to this post

Am I a materialist?

Recently on the Buddhist Geeks website my enthusiastic endorsement of the scientific method was referred to as "dry", "reductionist", and (shock horror) "materialistic". I thought the terms of the discussion were a bit limited. I'm not really much of a philosopher, and have not studied much Western philosophy, but I don't think of myself as a materialist. I understand my philosophical position to be this:

I'm a sceptical epistemological realist; and more vaguely, a transcendental idealist. Though I'm also a pragmatic Popperian empiricist.

The basic position of an epistemological realist is that objects exist independently of your mind. Many Buddhists take the position that objects do not exist independently of your mind, but only exist in conjunction with your mind, or indeed only in your mind. I think this takes the Buddhist argument on the nature of experience too far. I go back to the basic Buddhist teachings and base myself on the idea that consciousness is always specific to the sense associated with it, and arises in dependence on contact between sense equipment, and sense object.

Since all the information we have about objects comes through the senses there are limitations on what we can say about them. But certain consistencies occur. For instance objects are recognisable, and memorable. With reference to any particular object, people agree (more often than not) that there is an object, and also agree on its general characteristics, even though specifics may be disputed. If you could see me writing this you'd probably agree that I'm sitting at a desk, in a room, in a house, in a town, etc; or you'd be open to the charge of madness. If someone else sees an object and communicates to me about it in a way that suggests that they see the same object as I see, then I take that as evidence pointing towards the independence of the object from either of our minds. When everyone laughs at the same time in a movie then it suggests the movie is external to all of us. Explaining observations like these becomes very difficult if objects only exist in our minds.

The view that objects only exist when I observe them at best is egocentric. But consider - when I leave my room and go downstairs to make a cup of coffee, it seems nonsensical to me that my room and all of the hundreds of objects which fill it cease to be because I'm not there to see them. And what about when I blink? In that fraction of a second when I do not see the things, do they disappear? And do they then reappear when my eyes are open again? What happens to them during my blink? Trying to explain this is much more difficult, much more cumbersome, than assuming than that the objects simply exist. However I don't think we can say much about that existence, which is why I am a sceptical empirical realist.

It is my view that the Buddha was unconcerned with the nature of existence, or reality. That is to say he was not concerned with the nature of the objective pole of experience. This lack of concern with existence (and non-existence) is clear in, for instance, the Kaccānagotta Sutta, and strongly re-emphasised in Nāgārjuna's Mūlamadhyamakakārikā. The duality between subject and object is uncontentious in the Pāli Canon, it is simply a given. The conceptualisation of the problem of suffering, all of the analysis, and all of the practices, focus on the subjective side of experience. The nature of the object is simply irrelevant, it has to be there of course, but the arising of suffering is to do with our internal relationship to our perceptions, not with the objects of perception.

I've also said that I'm a transcendental realist, which in a way flows out of the previous paragraph. I must say I'm not a very sophisticated transcendental realist, and not very well versed in Kant or other philosophers of that ilk. Kant began with a problem. Hume had showed that a purely empirical approach to knowledge denied the possibility of metaphysical concepts like causality, time, and space. On the other hand empirical scientists, exemplified by Newton, had shown that we can say very definite things about causality, time, and space. Newton's well-known laws of motion are example. Kant's solution to this was to propose that the human mind interpreted sense experience in terms of inbuilt, or a-priori, categories of knowledge. The very usefulness of Newton's laws showed that a-priori categories had, to some extent, to reflect reality. Kant showed that the subject was involved in the creation of all knowledge, but that knowledge thereby created was valid. We can know useful things about the universe and how it works. Things are more or less as they appear to us.

In terms of my approach to Buddhism what this comes down to is, again, a focus on understanding the subjective side of experience, trying to understand the a-priori, what we bring to our interpretations of experience. This comes out of a study and practice of Buddhism, but in terms of relating it to the categories of Western philosophy this is as close as I've come. The fundamental problem is that we interpret experience in ways that cause us misery. Experience arises out of contact between objects and our sensory apparatus - but it is not the experience per se that is problematic, not the raw experience anyway. It what we make of experience, and how we relate to experience, the stories we tell ourselves about experience that cause us suffering. In other words it is not pleasure per se that is evil, only the pursuit of pleasure with the thought that it will make us happy. Hence the knowledge we need is knowledge of our relationship to experience; knowledge of the way we process experience into views and reactions. It is this kind of knowledge that will be liberating.

The last label I referred to was "pragmatic Popperian empiricist". Karl Popper was to some extent reacting against a trend in European thought which sought to evaluate all knowledge by the criteria of 'verifiability'. That is to say some philosophers were not prepared to accept knowledge as valid unless it could be verified. Sadly, although this philosophical position has long been superseded, it is more or less the popular view that science operates along these lines. But any living scientist will acknowledge the contribution of Karl Popper. At one time it was axiomatic that all Swans were white, because no European had ever seen a Swan that was any other colour. The statement "all swans are white" had become a standard in textbooks of logic even. However when Europeans got to Australia they discovered black swans. One can never anticipate when one might find a black swan which falsifies the statement that all swans are white. And this is the essence of Karl Popper's theory of knowledge, which informs my own understanding, and all of modern science. Facts and laws are only ever provisional because at any time a counter-example may disprove them. Theories might prove to be useful, but they can never be proved once and for all.

I said I'm also a pragmatist and this is because though they cannot be falsified, let alone proved, some forms of knowledge and some forms of practice are useful, or better helpful (I'm not a utilitarian). Some forms of knowledge which have been falsified on one level, even retain their usefulness on another. It is a fact that Newton's Laws remain useful in some contexts - say landing a human on the moon, or designing an aeroplane - even though observations have shown them to be inaccurate, for instance, when considering objects moving close to the speed of light. Then there is the placebo effect, the phenomena that we heal better, if we believe that we have had an effective treatment - even though it may be false to state that we have actually had an effective treatment, still we fair better than if we had no treatment at all. I argued this in the case of karma, which cannot be either verified or disproved, but is still useful as a view in helping to determine how we should behave. That is, I believe the theory of karma is morally helpful, even though it has doubtful truth value, if only in a provisional sense. (see Hierarchies of Values). Despite my definite preference for the rational, factual truth is not the only criteria that I apply when assessing the value of an idea. I may also form an opinion on the basis of helpfulness, or more aesthetic qualities such as elegance or beauty.

I don't feel entirely comfortable with this kind of discussion, or with these kinds of labels, I'm all too aware of the extent of my ignorance of Western philosophy. But when someone calls me a materialist because I'm educated in, and enthusiastic about, the scientific method, I need a way to respond which doesn't buy in to the simplistic duality being proposed: either one is a materialist, or a non-materialist. This simple opposition is not very helpful. People don't really hold views that are either one or the other, but have a far more sophisticated relationship to the objective pole of experience. One simply cannot be a practising Buddhist, as I have been for 16 years, and maintain a purely materialist view of the world. Clearly I do have a view about the material world, and I do think science can tell us far more about the material world than can Buddhism, but my focus is very much on the subjective, on the relationship to perception, on the nature of experience. Traditional Buddhist approaches to knowledge are rooted in pre-technological world-views that are frequently little better than superstition - the Buddha has a magical ability to know ultimate reality through super-powers - which just doesn't chime with my own experience of Buddhists and Buddhism. I see the European Enlightenment as a good thing (unlike some of my colleagues).

The other aspect of the criticism was that scientific investigation is reductionist. Reductionism by definition is the attempt to "explain a complex set of facts, entities, phenomena, or structures by another, simpler set" (the free dictionary). Which means of course that Buddhist doctrine is on the whole reductionist, because at its heart are explanations of phenomena in terms of short lists of mental states and events; and simplified models of dependent arising. By contrast some people try to explain phenomena in terms of more complex, often metaphysical or even mystical, ideas; they go against Occam and invent new entities to explain what they experience. What to call this kind of approach? Inflationist? The inflationist critique of science is that it tries to explain the unknown in terms of the known; whereas inflationists try to explain things in terms of the unknown, and the more mysterious the better. Apparently no one likes to admit that they simply don't know the cause of some experiences, nor the nature of them. If someone claims to remember a past life and I express doubt then I am, apparently, a materialist. But I don't see why an experience should be interpreted in terms of mysterious entities and processes as opposed to known entities and processes, if the truth is that we just don't know.

The charge is that experience is reduced only to that which can be measured. I would turn this around: it seems to me that inflationistists tend to project their subjectivity onto the world, and assign it an objective status which it does not deserve. There are many examples of inflationism stemming from interpretations of Indian religious ideas. Despite all evidence to the contrary people treat cakras, for instance, as really existent rather than symbolic or at best subjective; similarly they insist that the mysterious 'third eye' has some physical manifestation in the body (a past acquaintance assured me that it was connected to the pineal gland!) . I know many people who have seen or felt ghosts, because the house up the road (which is occupied by members of my order and community) is haunted. In fact it is supposedly one of the most haunted houses in the UK. I do not doubt that people have had uncanny, strange, unnerving, and inexplicable experiences. However I also do not necessarily accept that ghosts are the best explanation for those experiences. Some experiences do not have external objects, as anyone who has ever meditated, dreamed, taken psychedelic drugs, or gone mad will confirm. Actually anyone who ever thought, or remembered, or imagined anything is not (necessarily) working with external objects. A ghost certainly has more mystique, than a hallucination, but is it more likely? I'd have to say no. Plus at least half of the weird experiences are obviously caused by sleep paralysis. [See also today's xkcd cartoon]

So, am I a materialist? No. I'm a sceptical epistemological realist, a transcendental idealist, and a pragmatic Popperian empiricist (or something like that - actually I usually just say Buddhist). As such I don't have much to say about the nature of existence or reality (or any of that material stuff). Although I really enjoyed those Brian Cox documentaries and read Stephen Hawking, these days I'm mostly interested in the nature of experience. I do see an empirical approach to investigating it as the most useful; though I'm prepared to be pragmatic about what is helpful for that investigation. The main point is that I reject the dumbing down of religious discussions, especially in the area of the interaction between religion and science. If anything is dry and reductionist, and frankly boring, it is the idea that everyone interested in science is necessarily a materialist.

Next week [22 Oct 2010] I attempt to demolish the idea that Buddhism and Quantum Mechanics have anything in common. See Erwin Schrödinger Didn't Have a Cat.