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It's 11pm on a Friday night and I'm writing an article on free will. Did I decide to do this freely? Well, I've got a deadline and a tendency to obsession, but on the whole I'd say I did. I could just as well have joined my friends in the pub.

Most people would probably agree with me. Mental disorders aside, most of us think that we have the capacity to act freely. Our sense of morality, our legal system, our whole culture is based on the idea that there is such a thing as free will.

Does the Universe run like a giant clockwork? Image courtesy NASA.

It's embarrassing then that classical physics seems to tell a different story. In 1687 Isaac Newton published his laws of motion, which describe the behaviour of all physical objects, from particles to planets. They tell you exactly how an object will move when it's given a push. And they say that no object will change its path without such a push. There's no effect without a cause and for every cause there's a unique effect.

Newton's remarkable achievement led to the idea, first proposed by Pierre de Laplace, that the Universe runs like a giant clockwork. "The idea is that if you know everything about the state of a system [for example the Universe] at a particular time and you know the forces that are operating on this system, then there is only one future course of events for this system," says Jeremy Butterfield, a philosopher of physics at the University of Cambridge. "It's dictated by the initial state and the forces operating on it." And if you accept that we are part of physical reality, then this means that our future is determined too. This leaves no room for free will or for moral responsibility.

Predestined but unpredictable

This idea of determinism may seem absurd when you first come across it, but it has become deeply rooted in science. It had, and still has, prominent defenders. Einstein was one of them and he put the idea very elegantly: "Everything is determined, the beginning as well as the end, by forces over which we have no control. It is determined for the insect as well as the star. Human beings, vegetables, or cosmic dust, we all dance to a mysterious tune, intoned in the distance by an invisible piper."

The idea of a clockwork Universe goes back to Isaac's Newton's laws of motion.

But determinism is not quite as sinister an idea as it first appears. In practice it will never be possible for anyone to calculate the future of the Universe with any degree of accuracy. To do this, you'd need to know absolutely everything about its current state. But even the smallest inaccuracy in a measurement of these starting conditions would soon snowball into a massive error in the predictions. That's the famous butterfly effect. Even if the entire Universe consisted of only three particles, accurate predictions over any length of time would be impossible.

What's more, any calculated knowledge of the future is hermetically sealed off from us. If I calculated what you are going to do next from a set of initial conditions, then the very act of revealing this information would invalidate my calculations. Telling you that you're about to have a cup of coffee would alter the state of your brain, therefore altering the starting conditions. I'd have to start again and the outcome could be vastly different.

So, if we cannot access any knowledge of the future, does it matter if everything is pre-determined? Nature has equipped us with a strong sense of free will, perhaps because it underlies our impulse to treat others well. Since cooperative societies do better than dog-eat-dog ones, free will may be an illusion bred through natural selection. Stephen Hawking suggests that our concept of free will forms a good "effective theory" (see for example his book Black holes and baby universes). Even if everything is in reality pre-determined, the illusion of free will works well enough for us, so why not leave it at that?

Quantum randomness

If this feels less than satisfactory, you'll be glad to hear that Newton did not have the last word on physics. The early twentieth century produced quantum mechanics, a hugely difficult and counter-intuitive theory. One of its results is that at the level of the fundamental particles there is fundamental indeterminacy. Whether one thing happens or another simply can't be predicted in advance.

"Suppose there's this little particle and you're going to put it in a magnetic field and it's going to come out at A or come out at B," says the mathematician John Conway (interviewed by Rachel Thomas in this Plus article). Conway is imagining an experiment, such as the Stern Gerlach experiment, where a magnetic field diverts an electron's path. "Even if you knew exactly where the particles were and what the magnetic fields were and so on, you could only predict the probabilities. A particle could go along path A or path B, with perhaps 2/3 probability it will arrive at A and 1/3 at B. And if you don't believe me then you could repeat the experiment 1000 times and you'll find that 669 times, say, it will be at A and 331 times it will be at B."

Anton Zeilinger is Professor of Physics at the University of Vienna. Image: Jaqueline Godany.

This randomness of nature seems to put a nail in the coffin of determinism. But does it make room for free will? "One has to be very cautious," says Anton Zeilinger, Professor of Physics at the University of Vienna. "Indeterminacy means that there is not sufficient cause fully explaining an individual event." But events having no cause does not imply that we act freely. Whether you killed someone because you were pre-destined to do so, or as a result of some random blip in your brain, you're still not free and you are just as exonerated from responsibility. This is assuming that random quantum blips can actually impact on your brain, which is highly debatable.

But the absence of a physical cause does not preclude a hidden un-physical cause. Could a human mind that's entirely separate from physical reality, as described by René Descartes and later Karl Popper, be behind the seemingly random outcome? "One could argue that indeterminacy and the fact that we can only make predictions [on average] means that for a small fraction of individual events there could be a cause that we don't know about," says Zeilinger. "This is pure speculation, but it is logically possible."

However, the freedom afforded the disembodied mind in this way would be highly limited: it may be able to nudge the outcome of an individual event this way or that, but it cannot change the overall probabilities without violating the laws of physics. If you perform many experiments as described above, 2/3 of your particles would still have to end up at A and 1/3 at B.

The role of the observer

However, randomness isn't all there is to quantum physics. It also suggests a mysterious link between the observer, or at least the observation, and physical reality. Heisenberg's famous uncertainty principle states that certain physical features of a particle can correspond to mutually exclusive aspects of reality. Position and momentum are an example. While no-one is looking, a particle simply does not have a well-defined position and momentum. Rather it exists in some ghost-like state of superposition, having a broad range of momentums and positions at the same time. It is only when you measure either position or momentum that the range of possibilities collapses into one definite reality. If you measure where a particle is, it will come up with a precise answer. If you measure its momentum, you will also get a precise answer. Only you can't do both at the same time.

Werner Heisenberg in 1933 (photo: German Federal Archive)

This suggests that if there is freedom in the world, in the sense that neither your or the particle's actions are pre-determined by the past history of the Universe, then this freedom is of two kinds. "One is my freedom to choose which experiment to do [measuring position or momentum] and the other is nature's freedom to give me the answer it wants to give — this is the randomness of nature," explains Zeilinger. "And the two go together in a sense. That's a fascinating feature of the world."

However, it's entirely unclear how the measuring process causes a system in superposition to collapse into a definite reality — that's the famous measurement problem of quantum mechanics. Some physicists, for example Eugene Wigner and John von Neumann, have proposed that conscious minds existing outside the boundaries of physics cause the collapse, harking back to the mind-body dualism proposed by Descartes. But this is highly controversial. According to Butterfield, these theories are "delightfully vague and mystical, but wholly unbelievable." And exactly what they mean for free will is even harder to determine.

Many worlds?

There is however another interpretation of quantum mechanics which does not require the catastrophic collapse into one reality. According to the many worlds view, first proposed by Hugh Everett in the 1950s, the world splits into several branches whenever a measurement is made. Each of these parallel worlds corresponds to one possible outcome.

This can be extended to human choices. When you make a decision about whether to turn right or left, the Universe immediately splits into two. In one version you've turned right and in another you've turned left. Looking at this as the you just before the decision, this means that there's no choice at all involved. You'll end up doing both things. But looking at it as one of the yous just after the decision, your choice was made and for all you care it was made freely. As Paul Davies writes in his book God and the new physics, "saying that you have [turned left] in preference to [turning right] amounts to no more than a definition of 'you'."

So is there free will?

For all the progress physics has made in the last 100 or so years, it has not provided an answer to the free will question. Even quantum indeterminacy does not entirely kill off determinism. Quantum effects take place at tiny scales and whether they can affect the macroscopic world in a meaningful way is debatable.

And as Conway has pointed out, there's always the possibility that we live in a "second time around Universe". The first time around, quantum events may have been random and peoples' choices may have been free, but if we live in a replay, then everything happens in a totally determined fashion. "In the end a completely deterministic world is not incompatible with quantum mechanics," says Zeilinger. "I would say either way is basically speculation, the claim that things are deterministic is speculation and the rest too. This simply is a wide open question."

But Zeilinger also points out that people who claim that there is no free will usually don't practice what they preach. "When I was younger and less cautious I was at a conference where somebody claimed there was no free will and that everything was determined. So I got up and insulted him in front of 300 people. He got upset and I said in a very quiet voice: why do you get upset, I had no choice!"

And Zeilinger has a point. Hardened scientists excepted, most of us find determinism a very hard pill to swallow. The question then is if we can explain how the will of a human being can possibly effect change in the physical world without violating the laws of physics. And this is what we'll look at in the next article.

About the author

Marianne Freiberger is co-editor of Plus.