Mouse trap universe
The atmosphere is electric. All eyes are on eight-year-old Louise, to whom I have bestowed the momentarily ultimate honour of being master of ceremonies. A countdown worthy of mission-control cuts through the excited murmurs; my inner ten year old boy squirms with excitement. Will it work? Louise flicks the all-important trigger and the ultimate machine kicks into action. In its sixth major iteration of the afternoon, the product of the collective mind of a room of twelve-year-olds (and several overexcited fathers too, who boast wistfully of their Meccano creations of youth) is wacky, hilariously complex and, to my joyful pride, works pretty darn well, maybe with an occasional prod en-route. A (by now, disturbingly leaky) can of spam wobbles toe-curlingly down a ramp, nudging a seesaw whose action pushes a plastic superman down a zip-wire to decapitate a Barbie, whose head tumbles onto a toy car, which rolls majestically down an incline to set off the next table of events. A bewildered mother enters the room with her sprog and asks me what I’m doing. After a brief moment of existential crisis, I welcome them to the Science Festival and explain that we are building a Heath-Robinson contraption, whose ultimate aim is to make a cardboard frown in the corner become happy (obviously…). (I overhear a boy utilising impeccable pre-pubescent logic to explain the same to a pal: “We’re boys, so we don’t like girls, so we are trying to kill as many Barbies as possible.”) I begin to wonder whether our universe is like a big game of mousetrap – whether, in theory, if we had data on the initial states of every fundamental particle, we could predict exactly what were to happen in, say, half an hour’s time. To answer the question, I went to speak to Dr. David Seery, theoretical cosmologist here at Sussex, who would be my guide on a journey into the extraordinarily weird happenings of the very small.
Take an electron and cage it in a box. Now, measure its momentum and its position. The greater your certainty of the momentum, the less certain you can be about its position, and vice-versa. Incredibly, this is not an artefact of poor measurement. If you measure a tomato, and one moment you think that it’s 10cm across, and the next, 10.5cm, you’d have strong words in Smith’s and buy a better rule. But, at the scale of the very small, even the ‘perfect’ ruler isn’t sufficient. The uncertainty is intrinsic to the system. But, it gets weirder.
Now, cage a cat, and in a scheme worthy of Dr. Evil, affix a charge of explosives to the kitty, and set the system to explode upon activation of a Geiger counter. Finally, cackling wildly, place a weak radioactive source next to the Geiger counter, and quickly close up the box. If the source decays, kitty goes to heaven; if not, kitty can claw at your face, when you open the box – this is the famous thought experiment known as Schrödinger’s cat. Either way, you’ll only know when you lift the lid. Quantum mechanics has it that the probability of decay is defined by the wave function, whose evolution through time is defined by the Schrödinger equation, the exponent of this thought experiment. So, once again, the result is uncertain.
But, is it really the case that, if we had more knowledge, we might be absolute whether or not the cat will snuff it? Consider rolling a die. We all know that the probability of rolling a six is 1 in 6. Yet, if we had all the information about the initial state of the dice (its initial trajectory and position and so on), surely we could exactly predict which number would appear? So, what do we mean by ‘probability’ in this case? Empirically, since we do not have this information, if we repeat our dice roll, then, on average, we would expect on in six rolls to land on a six. More theoretically, if we consider all the possible methods of throwing a die to get a sixth, for each of these methods, we may simply rotate the die so that another number is initially in place of the six. Since the die is perfectly symmetrical, the trajectory will not change, so the number of possible trajectories for any two sides is identical. Since there are six sides, and probabilities sum to one, we explain the 1/6. Thus, could it be that we are simply ‘missing’ hidden variables in our discussion of the Schrödinger equation? Might there be hidden information somewhere that, if we had knowledge of it, we could take our discussion out of the context of probability and be exactly sure that an event might occur? Einstein famously thought so: “God does not play dice with the universe.”
To answer the question, let us turn to a curious problem from quantum mechanics and a beautiful resolution from the mathematics of conditional probability. We’ve already heard that knowledge of certain properties of fundamental particles precludes knowledge of other properties. However, Einstein, Poldolsky and Rosen gave a thought experiment to suggest how this assertion might be violated. When pairs of particles are produced as a result of decay of certain particles, they necessarily have linked and opposite properties. ‘Spin’, a fundamental property of elementary particles (and most politicians), provides us with an enlightening example. A pion, for instance, may decay to an electron and its antiparticle, the positron; these decay particles necessarily have opposite spin about the x- and y-axes. Suppose that we measure the spin for the first particle about the x-axis; then, the other particle must have the opposite spin. In addition, since by uncertainty we cannot have knowledge of spin in both axes, we now know nothing about the spin of the second particle about the y-axis. Thus, the crucial question is, did the second particle take the deduced spin value before we measured that of the first, or did it somehow ‘know’ that the other particle had been measured and therefore which x-spin value to take on and to know to ‘obscure’ the y-spin? In the first case, there must be the aforementioned hidden variables (and God does not play dice); in the second, particles must instantaneously ‘communicate’ (which upon first glance, would appear to contradict a central tenet of relativity, that no information can be passed faster than the speed of light but this is not the case, since it can be shown that it is logically impossible to pass information with this method). To exclude hidden variables, we turn to Bell’s inequality – whose derivation wholly lies on hard mathematical logic.
Let’s take an analogy from hotdogs – always good fun! Bell’s inequality would state that if we added together the number hotdogs that are smothered in ketchup but not mustard to those adorned with mustard but not mayo, then their number would equal or exceed the number of hotdogs with ketchup without mayo. Taking analogous discrete measurements at the quantum level (like spin) and applying the logic, we find that if we introduce hidden variables, Bell’s inequality is violated! Thus, either the universe is not amenable to our brand of logic, or at some fundamental level, things are essentially ‘random’.
So, what happened to Schrödinger’s cat? If you subscribe to the Copenhagen interpretation – the interpretation of quantum mechanics proposed by Niels Bohr in 1927 – as Dr. Seery tells me most do, you believe that at the moment of measurement, the wavefunction collapses and takes on a particular value: the cat will live, or will die. Until then, the cat is both alive and dead! The suggestion that the universe is only defined upon conscious observation is perhaps a little unsettling (not least that the observer themselves, as part of the universe, has his own wavefunction! – a wavefunction being a mathematical equation which describes the state of what is usually a subatomic particle, such as an electron). As Einstein was supposed to have said, “Is the moon there when nobody looks?” Under the ‘many-worlds’ interpretation, with every such event, the universe splits off, so that everything that could have happened happens in some universe. The problem with such interpretations, according to Dr. Seery, is that all subscribers use the same equations, and as yet, there is no experimental basis for differentiating between them.
So, determinism has crashed around us. Or has it? Do indeterministic effects have an observable effect at the macroscopic scale? It seems clear that they can; emission of an alpha particle is indeterministic. To a good first approximation, for large objects and short time scales, the universe does seem to behave as though it is deterministic –which is great, otherwise the universe might seem even weirder than it already is! Dr. Seery provides some comfort: “Do I expect my desk to have vaporised by next week? No.”