Hawking’s hidden dice

Do our actions effect changes in our futures, or is choice a fiction in a universe on a fixed course? Theologians and philosophers have long threaded their way through the implications of the free will question, ending up in the logically numb state which is the usual outcome of applying language to problems for which language allows only inexact expression.

The scientific version of the debate concerns how much we can know about the state of the universe: whether we can measure, at least in principle, all that there is out there to be measured. In other words, can we ever know everything? Or will there always be surprises?

Einstein thought that we could, famously asserting that “God does not play dice.” Today’s most celebrated scientist, Stephen Hawking, co-author of the recent The Grand Design, has determined that not only was Einstein wrong, but that there’s even more uncertainty than previously thought.

Why in the world am I writing about Hawking? This is one of those wordy blogs, isn’t it, with nary a mathematical expression in sight. The first reason is that a certain learned friend refuses to read these postings because they lack scientific content. When invited to check out a particular article, he invariably asks “Is there any science in it?” Well, this time there is — at least a recapitulation of a representation of science.

The second reason: despite the woeful inadequacy of my own science and math education, I have been an avid fan of popularized science — the kind without any math. So I thought that I might try my hand at explaining something scientific to see if I understand it even enough to rephrase it. My scientific friend can adjudicate —  if I can get him to read it.

Let’s start by setting one thing straight. When Einstein used or Hawking uses the word “God,” neither of them means anything like a personal Saviour or designing Creator or any other personified super-Being.

Einstein wrote, “If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it”; and, “I believe in Spinoza’s God who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with the fates and actions of human beings.”

Hawking has written, “The question is: is the way the universe began chosen by God for reasons we can’t understand, or was it determined by a law of science? I believe the second. If you like, you can call the laws of science ‘God’, but it wouldn’t be a personal God that you could meet, and ask questions.”

If “God” means to you “the structure of the world so far as our science can reveal it” or “the laws of science,” then Einstein’s or Hawking’s metaphor is perfect for you. Otherwise, you’re just plain out of luck. Sorry.

But the absence of a manipulating and meddling God doesn’t in and of itself answer the question of whether the universe is, from our point of view, determined or random. To decide that, we look to quantum theory, including strangely-named things like Planck’s constant, Heisenberg’s uncertainty principle, and Schroedinger’s equation. This is all pretty arcane stuff — in fact, it’s the closest science ever gets to traditional metaphysics, requiring frequent thought experiments and metaphors, which is very lucky for me, because if the issue were even a tiny bit less insubstantial it would be much too concrete for someone trained in the ephemera of Jesuitical casuistry.

The founding father of the determinists is Laplace, who claimed that if we were ever able to measure the mass, position, and velocity of every object in the universe at a single moment, it would then be a matter simply of calculation (but not a matter of simple calculation!) to determine the movement of every object in the universe forward in time forever — to predict the future mathematically, and to end the debate over free will philosophically in the bargain.

Laplace was dealing with a Newtonian universe, one with objects large and material enough to understand as “objects” in the same way that we think of tables and ping pong balls as “objects.” Things soon changed, however, and Laplace’s determined universe was undetermined by one with stranger inhabitants: the quantum universe.

Along came Max Planck, who was fooling around with just the kind of problem we all like to toss about on a lazy weekend afternoon: why isn’t everything in the universe the same temperature? If bodies all radiate heat, shouldn’t there have been sufficient time by now for the exchanges all to equal out, leaving everything with the same amount of energy? Since this wasn’t the case, Planck created  a mathematical restriction on energy, such that it could be radiated not in any old bits but only in discrete units, or quanta. Energy could no longer be thought of as the stream of water but rather as the tiny pebbles on the bottom. You could throw as many pebbles as you had strength to throw, but you had to throw pebbles. You couldn’t grind up the pebbles and throw dust.

Planck’s Constant

Planck thought that this was a neat mathematical trick, but he didn’t know at first that his numbers game was the best bet going for describing the universe at the level of the very small. When his quantum packet idea proved to be good at predicting real events, like the actions of elementary particles, the science of quantum mechanics was born. But Laplace’s determinism wasn’t completely dead yet — that would wait for another, even more counter-intuitive idea.

In 1926, Werner Heisenberg explained the notion that would make him infamous, the Uncertainty Principle. In order to do Laplace’s measurements, you had to observe the position and the speed of the particles you encountered. Heisenberg realized that, according to Planck’s math, you could observe very small objects with no less than one quantum of light. That is, you couldn’t scale the observation down to any old arbitrary and convenient value. But the energy in even a single quantum of light is enough to disturb the particle you’re trying to measure.

Worse, to measure position very accurately, you need very powerful light, like x-rays or gamma rays, which are even more disturbing to little particles than normal light is. So the more precisely you try to measure position, the more you disturb speed. And vice versa, it turns out. Hawking puts it more clearly — or less, depending on your comfort level with the jargon: “the uncertainty in the position of a particle, times the uncertainty in its speed, is always greater than a quantity called Planck’s constant, divided by the mass of the particle.”

Heisenberg’s Uncertainty Principle


So we can’t know the position and the speed accurately at the same time, but we can measure their combined probability — the”wave function” of a particle. This means that, thanks to Schroedinger’s equation, we can predict the future wave functions of these particles, which is a kind of low-rent determinism substitute. It doesn’t look like butter, and it tastes a bit like motor oil, but it’ll go on your pancakes if you can’t get your hands on anything better.

Schroedinger’s Equation

i\hbar\frac{\partial}{\partial t} \Psi = \hat H \Psi

Einstein didn’t like this newfangled notion at all. Even if the quantum characteristic of light meant that we couldn’t see precisely, the precision was still sure to be in there somewhere. You’re not a blur because my glasses are smudged, even if that’s what I see. So Einstein disputed the ultimate reality of the Uncertainty Principle, saying — well, we all know what he said.

Einstein’s insistence that God doesn’t play dice is a version of Laplace’s notion, but Einstein knew that thanks to the curvature of space-time (one of his own little discoveries) there would be things we couldn’t see. Still, he was convinced — by his sense of the inherent orderliness of the universe if not by his mathematics  — that there was an underlying order, even if “only God can know it.” So his was a “hidden-variable” theory.

Unfortunately for Einstein, later experiments showed that “hidden-variable” theories are incorrect. And then along came Hawking, with his work on black holes, and the last little shreds of determinism blew away in the breeze.

It seems that space-time can be distorted so strongly that it develops regions which we cannot observe at all, regions which we call “black holes.” Imagine a round piece of putty. If you stick your finger into it, the putty depresses and you have to look at a sharper angle to see your fingernail. Now push further and harder than that, and the putty deforms so much that your fingertip “disappears” into the centre of the mass. You can’t see it at all, although it’s still there. Distorting space-time is something like that. Well, no, it isn’t, but we can think of it more easily if we pretend that it is.

The more massive and more compact an object is — the more dense it is — the stronger this distortion becomes. The “hole” in the putty ball becomes effectively bottomless, to the point that a fingertip that goes in can no longer come back out. Neither can even light itself, which is why it’s called a “black hole” in the first place. So we can’t “see” anything that’s in a black hole, meaning that there are parts of the universe which remain ever closed to us.

It gets worse. Hawking has shown that very small black holes do, in fact, spit out random bits of particles and radiation. The reason has something to do with the Uncertainty Principle, with the fact that you can’t have truly empty space, since it would then have completely determined position (0) and completely determined speed (0). This “0,0” state is impossible, so even “empty” space is occupied by pairs of particles and anti-particles, called “virtual particles,” which do a little dance before annihilating each other in the physics version of a high energy mosh pit. This whole process is known as “vacuum fluctuation,” which doesn’t sound as sexy as “slam-dancing,” which would have been my term of preference.

Anyway, it seems that sometimes only one of a virtual particle pair is drawn into a black hole, or sometimes only one of a virtual particle pair is spewed back out as part of the “empty” space around the black hole. In either case, there’s a virtual particle with no murder-suicide partner, so it has no choice but to become a real particle, one that we can detect. To us, it would look like the detected particle has been emitted by the black hole. It would also not matter what kind of matter went into the black hole — what came out would appear completely random to an observer. Not a single particle of determinability in sight.

What all this means, Hawking says, is that in the case of black holes, since the wave function of any particle that enters the black hole can’t be determined (that information was lost when the particle entered the putty ball and sank), then the position or speed of any particle that “emerges” (the way it looks to our eyes, anyway) is completely random.

Hawking puts it this way:

But there’s no combination of the position and speed of just one particle that we can definitely predict, because the speed and position will depend on the other particle,
which we don’t observe. Thus it seems Einstein was doubly wrong when he said, God does not play dice. Not only does God definitely play dice, but He sometimes confuses
us by throwing them where they can’t be seen.

He also puts it this way:


Sorry, Laplace. Sorry, Einstein.

Well, that’s it. It’s taken me only 2,000 words to do what a particle physicist can do in a couple of squiggly equations.

Got it now?

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3 thoughts on “Hawking’s hidden dice

  1. In “The Grand Design” Hawking says that we are somewhat like goldfish in a curved fishbowl. Our perceptions are limited and warped by the kind of lenses we see through, “the interpretive structure of our human brains.” Albert Einstein rejected this subjective approach, common to much of quantum mechanics, but did admit that our view of reality is distorted.

    Einstein’s Special Theory of Relativity has the surprising consequences that “the same event, when viewed from inertial systems in motion with respect to each other, will seem to occur at different times, bodies will measure out at different lengths, and clocks will run at different speeds.” Light does travel in a curve, due to the gravity of matter, thereby distorting views from each perspective in this Universe. Similarly, mystics’ experience in divine oneness, which might be considered the same “eternal” event, viewed from various historical, cultural and personal perspectives, have occurred with different frequencies, degrees of realization and durations. This might help to explain the diversity in the expressions or reports of that spiritual awareness. What is seen is the same; it is the “seeing” which differs.

    In some sciences, all existence is described as matter or energy. In some of mysticism, only consciousness exists. Dark matter is 25%, and dark energy about 70%, of the critical density of this Universe. Divine essence, also not visible, emanates and sustains universal matter (mass/energy: visible/dark) and cosmic consciousness (f(x) raised to its greatest power). During suprarational consciousness, and beyond, mystics share in that essence to varying extents. [quoted from my e-book on comparative mysticism]

    Heisenberg, Schroedinger, de Broglie, Jeans, Planck, Pauli, and Eddington were supporters of mysticism. A good reference is “Quantum Questions / Mystical Writings of the World’s Greatest Physicists,” edited by Ken Wilber (Shambhala 1984, 2001). I had read 40 books on physics, biology and psychology while writing my e-book, but am certainly not a scientist.

    • I am certainly no expert in quantum physics, as I hope I acknowledged clearly at the start of the posting. Writing about science is for me an entirely amateur exercise in understanding and composition, which I’m sure the posting’s limitations make clear.

      I know no way of disproving the mystical experience, but I also know no way of “pointing” to it. I think that one has either to limit oneself to the material, whatever that is, or to consider the material as only one manifestation of a larger perception, whatever that is. I don’t see how they can be easily mixed.

      I am superficially familiar with Heisenberg’s “mystical experience” and with Planck’s belief in a divine consciousness behind the physical universe. I remain unconvinced, however, that we can simply assert the metaphysical in the same way that we assert the physical — even if both are considered mental constructs. It seems to me that the sensory interpretation “table” is of quite a different nature than is the internal apprehension “spirit.”

      I can stub my toe on a stone; I can stub only my mind on an angel.

  2. Sensory perceptions and rational conceptions are limited, as we each acknowledge of our experiences in this life. Suprarational consciousness, which is usually fleeting, allows us to transcend our individual limitations to a transpersonal awareness. It is consummate cognition, unmediated discernment, with certainty. It cannot be proven, it can only be lived. Unfortunately, that is an unsatisfactory explanation for most people.

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