Friday, March 25, 2016

Schrödinger’s Kittens

     John Gribbin. Schrödinger’s Kittens (1995) Gribbin’s follow-up to his In Search of Schrödinger’s Cat, an earlier attempt to explain quantum mechanics. Here, he begins with an overview of the weird results of experiments inspired by various interpretations of QM, and an overview of several attempts to explain the weirdness. He focusses on non-locality, as evidenced in entanglement for example. Non-locality appears to require an instantaneous exchange of information: If you determine the polarisation of one electron, the other instantly “collapses” into the complementary polarisation.
     And so on.
     I’ll note in passing that Gribbin spends a lot of time debunking the Copenhagen Interpretation (CI), which he claims requires a conscious observer. I don’t think it does, but let that pass. Either way, the CI interpretation relies on the metaphor of collapsing probability waves.
     Gribbin’s first insight, with which I agree, is that interpretations are metaphors or analogies. The question is of what? Gribbin says “Models!”, by which he means theories. And fails to see that Models is another metaphor. But he does say a couple of useful things about the relationship between theories (or models) and what they purport to explain, in particular that they are stories that we make up in order to make sense of our observations. I don’t think he emphasises enough that these stories are told in mathematics.
     His second insight follows from the fact that all experiments, and hence the theories that explain them, deal with a limited set of variables. Hence the models based on them are limited. An experiment is a deliberate reduction of degrees of freedom, aka variables. Hold as many variables as possible constant, and see what happens when you mess with the rest, preferably just one if you can manage it. You will create a model of just one aspect of reality (whatever it is). E.g., the laws of motion don’t concern themselves with the chemical properties of the objects whose motion they describe.
     So which of the many models of reality embodied in QM and its interpretations is “true”? They all are, says Gribbin, as far as they go. Which one goes farthest?
     Gribbin plumps for string theory, which was fairly new in 1995, and Cramer’s transaction interpretation, which hasn’t gained as much traction as string theory has. Cramer points out that a key equation in QM has two solutions, one of which implies that “waves” propagate backwards in time. Cramer argues that both forward and backward propagating waves are real. They cancel out, so to speak, so the experiments that reveal them show non-locality. Gribbin claims that this “myth for our time” resolves the paradoxes and weirdnesses of QM.
     Well, it made sense while I was reading it.
     Throughout his book, Gribbin, like other scientists who’ve offered interpretations of QM, talks as if theories are descriptions of reality. He does this even when he reminds us that any theory that works is true only as far as it goes. Thus the Rutherford atom works just fine in chemistry, which deals with the interactions of the electrons that surround the atom. Newton’s equations work just fine for small jaunts into space. The notion of a photon as a wave works for certain experiments, and not for others.
     By “works”, I infer that Gribbin means “predicts observations accurately to the desired degree of precision”. Gribbin neither states this concept explicitly nor examines what it might mean. I think he doesn’t think about what a model is. I’ve built models, so I’m acutely aware that a model is not a replica of its prototype. You can get close, as with a model steam locomotive that operates on steam. But its boiler will have thicker than scale-size walls because otherwise it would be too weak to hold the necessary steam pressure. Its control handles must be bigger than scale so you can work them. And so on.
     All models compromise, and in doing so they misrepresent what they model. A model is limited to the features that the modeller finds interesting and leaves out everything else. So if we declare that a theory is model, just what does that imply?
     A theory is a collection of intertwined equations that describe the possible states of some natural system and how it may change states. In this sense, a theory is a model of the system. More precisely, if it’s well enough constructed, it’s an algorithm. Input some data (say the present position and velocity of a rocket), turn the crank, and output some data (the position and velocity of the rocket a few minutes or days or weeks from now). The simple model of rocket motion ignores the effects of wind as it rises through the atmosphere, and the effects of gravity as passes by the Moon and Mars. To fix that, more complex models are devised. Divergence between calculated and observed values requires that the model be rerun with new, actually observed values. And so on.
     In short, the model supplies information. It tells us where to look for the rocket. It’s not a description of reality, but a recipe for acquiring knowledge. But it’s limited: The Newtonian model tells us about the rocket’s velocity and location, but it doesn’t tell us how the crew is doing, and whether they will survive. For that, we need a different model (and a rather more complicated one).
     A theory is about how we can know some things about some entities. It is not a description of those entities. Philosophically, it’s epistemological, not ontological.
     So also with QM. It doesn’t tell us what an electron is, or even where it will be. It only tells where it’s been, and where it might be if you look again. The probability wave isn’t a description of all possible states of the electron, it’s a description of all possible states of our knowledge, of how likely we are to know that the electron is in any given state.
     Even if you don’t go as far down the epistemological path as I’ve gone, you still don’t know what an electron is. All we know of the electron is a list of interactions, and some recipes for predicting which interactions will be observed when and where. Those recipes are amazingly accurate. Well, they amaze people who know how difficult it is to make accurate and precise observations, which includes me. I think it’s the success of QM that tempts physicists into thinking they are talking about reality. They aren’t. They’re talking about interactions, of which observation by a human is merely one more, and which I don’t believe is privileged in any way.
     Still, the book is worth a read if you have the time. It’s a good introduction to some of the wonderful strangeness of our universe. Gribbin has continued to publish his ruminations about QM and many other topics, His website
will tell you more. The Wikipedia entry includes a complete bibliography.
     Recommended, but sometimes heavy going. ***
     Minor revisions and corrections 2016-03-29 & 2016-07-13
 

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