Free will - you only think you have it
04 May 2006
Exclusive from New Scientist Print Edition.
Zeeya Merali

      "WE MUST believe in free will, we have no choice," the novelist Isaac Bashevis Singer once said. He might as well have said, "We must believe in quantum mechanics, we have no choice," if two new studies are anything to go by.
Early last month, a Nobel laureate physicist finished polishing up his theory that a deeper, deterministic reality underlies the apparent uncertainty of quantum mechanics. A week after he announced it, two eminent mathematicians showed that the theory has profound implications beyond physics: abandoning the uncertainty of quantum physics means we must give up the cherished notion that we have free will. The mathematicians believe the physicist is wrong.

      "It's striking that we have one of the greatest scientists of our generation pitted against two of the world's greatest mathematicians," says Hans Halvorson, a philosopher of physics at Princeton University.

      Quantum mechanics is widely accepted by physicists, but is full of apparent paradoxes, which made Einstein deeply uncomfortable and have never been resolved. For instance, you cannot ask what the spin of a particle was before you made an observation of it - quantum mechanics says the spin was undetermined. And you cannot predict the outcome of an experiment; you can only estimate the probability of getting a certain result.

      "Quantum mechanics works wonderfully well, but it's not complete," says Gerard 't Hooft of Utrecht University in the Netherlands, who won the Nobel prize for physics in 1999 for laying the mathematical foundations for the standard model of particle physics. One major reason why many physicists, including 't Hooft, yearn for a deeper view of reality than quantum mechanics can offer is their failure so far to unite quantum theory with general relativity and its description of gravity, despite enormous effort. "A radical change is needed," says 't Hooft.

       For more than a decade now, 't Hooft has been working on the idea that there is a hidden layer of reality at scales smaller than the so-called Planck length of 10^-35 metres. 't Hooft has developed a mathematical model to support this notion. At this deeper level, he says, we cannot talk of particles or waves to describe reality, so he defines entities called "states" that have energy. In his model, these states behave predictably according to deterministic laws, so it is theoretically possible to keep tabs on them.

       However, the calculations show that individual states can be tracked for only about 10^-43 seconds, after which many states coalesce into one final state, which is what creates the quantum mechanical uncertainty. Our measurements illuminate these final states, but because the prior information is lost, we can't recreate their precise history.

       While 't Hooft's initial theory explained most quantum mechanical oddities, such as the impossibility of precisely measuring both the location and momentum of a particle, it had a major stumbling block - the states could end up with negative energy, which is physically impossible. Now, 't Hooft has worked out a solution that overcomes this problem, preventing the states from having negative energy (www.arxiv.org/quant-ph/0604008). "It was an obnoxious difficulty," he says. "But having solved it I am more and more convinced that this is the right approach."

        Essentially, 't Hooft is saying that while particles in Quantum mechanics seem to behave unpredictably, if we could track the underlying states, we can predict the behaviour of particles.

       Others are impressed. "This is a very beautiful theory that tells us about the world on the smallest scales," says physicist Willem de Muynck at Eindhoven University of Technology in the Netherlands. "But these are scales that current experiments cannot reach, so if anything the theory is before its time."

       As enticing as 't Hooft's theory may be to physicists, it has an unexpected and potentially frightful consequence for the rest of us. Mathematicians John Conway and Simon Kochen, both at Princeton University, say that any deterministic theory underlying quantum mechanics robs us of our free will.

      "When you choose to eat the chocolate cake or the plain one, are you really free to decide?" asks Conway. In other words, could someone who has been tracking all the particle interactions in the universe predict with perfect accuracy the cake you will pick? The answer, it seems, depends on whether Quantum mechanics' inherent uncertainty is the correct description of reality or 't Hooft is right in saying that beneath that uncertainty there is a deterministic order.

       Conway and Kochen explored the implications of 't Hooft's theory by looking at what happens when you measure the spin of a particle. Spin is always measured along three perpendicular axes. For a spherical particle, the particular axes that you choose and the order in which you carry out the measurements are up to you. But are your choices a matter of free will, or are they predetermined?
       What the mathematicians proved is this: if you have the slightest freedom to choose the axes and order of measurement, then particles everywhere must also have the same degree of freedom. That means they can behave unpredictably. However, if particles have no freedom, as implied by 't Hooft's theory, the mathematicians proved that you have no real say in the choice of axes and order of measurement. In other words, deterministic particles put an end to free will (www.arxiv.org/quant-ph/0604079).

       Arguments about free will are as old as philosophy itself, and ever since quantum mechanics was proposed people have attempted to connect free will to the indeterminacy at the heart of this theory. "We're proud because this is the first solid proof relating these issues," says Conway.

       Kochen and Conway stress that their theorem doesn't disprove 't Hooft's theory. It simply states that if his theory is true, our actions cannot be free. And they admit that there's no way for us to tell. "Our lives could be like the second showing of a movie - all actions play out as though they are free, but that freedom is an illusion," says Kochen.

       Since the mathematicians believe that we have free will, it follows for them that 't Hooft's theory must be wrong. "We have to believe in free will to do anything," says Conway. "I believe I am free to drink this cup of coffee, or throw it across the room. I believe I am free in choosing to have this conversation."

       Halvorson says the debate really boils down to a matter of personal taste. "Kochen and Conway can't tolerate the idea that our future may already be settled," he says, "but people like 't Hooft and Einstein find the notion that the universe can't be completely described by physics just as disturbing."

       For philosophers, both arguments can be troubling. "Quantum randomness as the basis of free will doesn't really give us control over our actions," says Tim Maudlin, a philosopher of physics at Rutgers University in New Brunswick, New Jersey.      "We're either deterministic machines, or we're random machines. That's not much of a choice."

      Halvorson, however, welcomes the work by 't Hooft, Conway and Kochen. "Philosophy has separated itself from science for far too long," he says. "There are very important questions to be asked about free will, and maybe physics can answer them."

Printed on Mon May 22 07:21:21 BST 2006