Chance and probability surround us (Image: Eugenia Loli)
“OH, I am fortune’s fool,” says Romeo. Rest easy, lover boy; we all are. Or are we?
Romeo, having killed Tybalt and realising he must leave Verona or risk death, was expressing a view common in Shakespeare’s time: that we are all marionettes, with some higher cause pulling the strings. Chance – let alone our own decision-making – plays little part in the unravelling of cosmic designs.
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Even processes that inherently involved chance were pre-determined. Long before dice were used for gaming, they were used for divination. Ancient thinkers thought the gods determined the outcome of a die roll; the apparent randomness resulted from our ignorance of divine intentions.
Oddly, modern science at first did little to change that view. Isaac Newton devised laws of motion and gravitation that connected everything in the cosmos with a mechanism run by a heavenly hand. The motion of the stars and planets followed the same strict laws as a cart pulled by a donkey. In this clockwork universe, every effect had a traceable cause.
If Newton’s universe left little room for randomness, it did at least provide tools to second-guess the Almighty’s intentions. If you had all the relevant facts pertaining to a die roll at your fingertips – trajectory, speed, roughness of the surface and so on – you could, in theory, calculate which face would end up on top. In practice this is far too complex a task. But it showed that randomness was nothing intrinsic; just a reflection of our lack of information.
Confidence in cosmic predictability led the French mathematician and physicist to assert, a century after Newton, that a sufficiently informed intelligence could forecast everything that is going to happen in the universe – and, working backwards, tell you everything that did happen, right back to the cosmic beginnings.
It’s a glorious and rather discomfiting idea. If everything really is predictable, then surely all is pre-determined and free will is an illusion? Romeo, in other words, is right. Perhaps so, says physicist , who studies randomness and its limits at the Centre for Quantum Technologies in Singapore. “One may believe that a single causal chain determines everything – call it God, the big bang or robots-behind-the-matrix,” he says. “Then there is no randomness.”
The connection between a universe that admits randomness and one that admits free will is an old one, . The 13th century Christian philosopher Thomas Aquinas insisted a perfect universe must contain randomness to allow humans their autonomy. But it was also there to limit them. God made humans with less than divine abilities, so there must be a sphere of events beyond our control.
It wasn’t until about two centuries after Newton that anyone began seriously to challenge the notion of a predictable cosmos. In 1859, Scottish physicist James Clerk Maxwell drew attention to the huge disparities in outcome that can stem from tiny factors affecting the collisions of molecules.
This was the beginnings of chaos theory. In its most familiar guise of the butterfly effect – that the flap of a butterfly’s wings in Brazil might set off a tornado in Texas, as the chaos theorist Edward Lorenz put it in 1972 – this seems to restore unpredictability to the world. With a sufficiently complex system, even the tiniest approximation while working at the limits of your clock, barometer or ruler, or the slightest rounding error in a computation, can drastically affect the result. This is what makes the weather so hard to predict (see “Risky business: The weather man“). Its eventual state is highly dependent on the initial measurement – and we can never have a perfect initial measurement.
So, small, human-scale decisions might indeed matter on the wider stage. Romeo’s predicament traces back to the initial conditions that first put him in the same room as Juliet – or further back still. Take that too far, though, and we might trace them back to before our ancestors came down from the trees, which seems to circumvent any sensible notion of human free will.
It’s a head-scratcher, alright – but as yet we are only scratching the surface.
Because while we seem to occupy a reality where causes lead to predictable effects, dig down and that’s apparently not how things work at all. Quantum theory, developed in stages since the early 20th century, is our working theory of reality at its most basic – and it does away with cast-iron certainty entirely. “It appears to us, via quantum experiments, that nature is fundamentally random,” says , a mathematician at the University of Cambridge.
“Probability of 26 consecutive black numbers in roulette: 1 in 136,823,184; This happened in Monte Carlo in 1913”
Fire a single photon of light at a half-silvered mirror, and it might pass through or be reflected: quantum rules give us no way to tell beforehand. Give an electron a choice of two slits in a wall to pass through, and it chooses at random. Wait for a single radioactive atom to emit a particle, and you might wait a millisecond or a century. This rather lackadaisical attitude to classical certainties could even account for why we are here in the first place. A quantum vacuum containing nothing can randomly and spontaneously generate something. Such a careless energy fluctuation might best explain how our universe began.
Explaining the explanation is trickier. We don’t know where the quantum rules came from; all we know is that the mathematics behind them, rooted in uncertainty, corresponds to reality observed up close. That starts with the Schrödinger equation, which describes how a quantum particle’s properties evolve over time. An electron’s position, for example, is given by an “amplitude” smeared over space, and there is a set of mathematical rules you can apply to find the probability that any particular measurement will pinpoint the electron to any particular position.
That’s no guarantee the electron will be in that position at any one time. But by repeatedly doing the same measurement, resetting the system each time, the distribution of results will match the Schrödinger equation’s predictions. The repeated, predictable patterns of the classical world are ultimately the result of many unpredictable processes.
Chance and probability surround us (Image: Michael Zumstein/Agence VU/Camera Press)
The repercussions are interesting. Say you want to walk through a wall; quantum theory says it’s possible. Each one of your atoms has a position that could – randomly – turn out to be on the other side of the wall when it interacts. That event’s probability is exceedingly low, and the probability that all of your atoms will simultaneously locate to the other side of the wall is infinitesimally small. A nasty bruise is the sum of all the other probabilities. Welcome to reality.
Does lightning strike twice? (Image: Steve Marcus/Reuters)
“Globally averaged probability of being killed by lightning: 1 in 300,000”
Einstein was particularly exercised by this probabilistic approach to real-world events, famously complaining it was akin to God playing dice. He conjectured that there must be some missing information that would tell you the measurement’s outcome in advance.
Hidden realities
In 1964, the physicist John Bell laid out a way to test for such “hidden variables”. His idea has since been implemented time and again, mainly using entangled pairs of photons. Entangled particles are a staple feature of the quantum world. They have interacted at some point in the past and now appear to have shared properties, such that a measurement on particle A will instantaneously affect what you get from a measurement on particle B, and vice versa.
What’s behind this? The details of Bell’s tests are complex and subtle, but the principle is akin to a sport in which two groups of experimenters play according to different rules. Team Alpha assumes that the quantum correlations are down to some hidden exchange of information, and make measurements accordingly. Team Beta, on the other hand, assumes the correlations materialise at random on measurement.
And Team Beta wins every time. The weird correlations of the quantum world derive from fundamental randomness.
Or do they? Physicists are still investigating loopholes in the way we do quantum measurements that might skew the results and simulate randomness – the fact that we can’t measure the state of photons with 100 per cent accuracy, for instance, or even the question of whether we have free will in choosing the measurements we make. “I think it’s premature to say we’ve closed all the important Bell loopholes,” says Kent.
It is possible that quantum theory’s vagaries might one day be explained, perhaps by compromising some other cherished principle, such as Einstein’s relativity. Or maybe someone will come up with some more intuitive, non-random theory that reproduces all the predictions of quantum theory and makes some stronger ones as well. “That hypothetical theory would be a new theory – a successor to quantum theory, not a version of it,” Kent says.
, a physicist at Imperial College London, agrees. Quantum theory is our ultimate theory of nature, and it seems to suggest the universe is random, but that is no guarantee it is. “I don’t think we can ever prove it,” he says.
If so, randomness might still prove to be an illusion – and with it, perhaps our free will. “Then quantum physics is just part of the big conspiracy,” says Scarani.
Fortune’s fools? Perhaps we’re not at liberty to decide.
Read more: “Chance: How randomness rules our world“
This article appeared in print under the headline “Random reality”
