The common definition of free will often has problems when relating to desire and power to choose. An alternative definition that ties free will to different outcomes for life despite one's past is supported by the probabilistic nature of quantum physics. This definition is compatible with the Many Worlds Interpretation of quantum physics, which refutes the conclusion that randomness does not imply free will, writes Tim Andersen.

Free will is one of those things where people tend to be very attached to its being true or false and yet most people implicitly treat it as true. Consider that we hold people accountable for their actions as if they decided to carry out those actions of their own free will. We reward people for their successes and discoveries likewise. If Albert Einstein didn’t really make his discoveries but it was, instead, inevitable that his brain would do so, does he really deserve his Nobel Prize?

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Some argue that we should accept that free will is a myth and change our society accordingly. Our justice system (especially in the United States) is heavily invested in the free will hypothesis. We punish people for crimes. We do no treat them like broken machines that need to be fixed. Other nations like Norway, however, take exactly this approach.

Many physicists believe that free will in incompatible with modern physics.

The argument goes like this:

(1) Classical (non-quantum) mechanics is deterministic. Given any initial conditions to a classical system, and the entire future and past state of the system can be determined. There is no free will in determinism.

(2) Quantum mechanics allows for randomness in the outcomes of experiments, but we have no control over those outcomes. There is no free will in randomness.

(3) Human will is a product of the brain which is a physical object. All physical objects are subject to physics and the sum total of physics is contained in classical and quantum mechanics (technically, classical is an approximation of quantum).

Ergo, humans have no free will. Our brains are simply carrying out a program that, while appearing to be making free choices, is in fact just a very complex algorithm.

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As Schopenhauer said, ‘Man can will what he wants but cannot will what he wills.’

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The logic seems sound and in any philosophical discourse we need to look at the logic and decide (whether freely or not). There are quite a few ways to counter this argument. The first is to object to #3. This is the approach many religions take. Human will is not necessarily reducible to physical causation. Therefore, it is beyond physical law. The brain simply interacts with the will and carries out its commands.

Another is to question the reductionist assumption of the conclusion, i.e., that everything is reducible to the properties of its constituent parts, no matter how complex. If the individual parts are deterministic, so must the whole. Science has not proven that yet. Perhaps if we could model a human brain in a computer in its entirety, we might know better.

Another approach is to question what the scientist means by free will. Most scientists aren’t philosophers and don’t necessarily define their philosophical terms as clearly as their scientific ones. The common definition of free will is that it is the freedom to choose, the ability to decide to choose or do otherwise, to be the source of one’s actions. Philosophers largely tie free will to the concept of moral responsibility. Am I morally responsible for my actions?

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To put is precisely, an agent S is morally accountable for performing an action ϕ =df. S deserves praise if ϕ goes beyond what can be reasonably expected of S and S deserves blame if ϕ is morally wrong. The key then is whether an agent has the ability or power to do otherwise.

Now, what does it mean to have the ability to choose or do otherwise? It can’t simply mean to have the power because one must have both the power and the desire. But what if one does not have the power to change what one desires? Then you are stuck with no free will or only a pseudo-free will in which you can change your actions but not your desires.

As Schopenhauer said, ‘Man can will what he wants but cannot will what he wills.’ Consider, if I have a choice to practice my cello or lift weights, I choose to practice my cello. Now, I seem to have had the power to choose to lift weights but I did not have the desire to do so. Did I have the power to desire differently?

From the argument of physics, the brain’s desires are either fixed results of classical laws or random results of quantum effects. A random quantum fluctuation creates voltage bias in one of my neurons which cascades to other neurons and suddenly I want to lift weights. According to the physicist, I did not choose. It just appeared as if I did. And certainly if I had chosen differently I would have done differently, and yet in reality quantum physics chose for me by rolling a cosmic die.

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You have to see free will as having the power to have different outcomes for your life despite your past.

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This kind of free will definition, which is the one most people think of and the one that most scientists seem to assume, has a lot of problems. It’s hard to even understand what we really mean by freedom because it gets all muddled with desire.

Without a good definition, it is impossible to argue that something exists or not. Another definition of free will avoids this problem and throws a monkey wrench into the scientist on the street’s knee-jerk attitude that free will is impossible in a quantum world.

This alternative is called the categorical analysis and is stated as follows: An agent S has the ability to choose or do otherwise than ϕ at time t if and only if it was possible, holding fixed everything up to t, that S choose or do otherwise than ϕ at t.

What this means is that we have to take into account the state of the agent up until the time the choice is made and given that state ask if there is a possible world where the agent makes a choice other than the one he or she made. That, then, is what freedom of choice is.

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Oxford physicist David Deutsch favours this definition of free will because it is compatible with his Many Worlds Interpretation (MWI) of quantum physics. But even if you don’t accept MWI, what it says is that there are probable states that have the same past up until a point t and then a choice is made and a non-deterministic path is followed. It doesn’t matter if those paths are all “real worlds” as Deutsch believes. What matters is that they have different futures, and all interpretations of quantum physics as-is support this idea.

If that is true, and this is the most important point, then you can say that freedom of choice exists because the agent made different choices in different probable realities. Thus, the agent had the power to choose and exercised it.

This definition of free will is interesting from a physics perspective because it is not true in a classical, deterministic world in which all pasts have the same future, but it is true in a quantum world where all pasts do not share the same future. Thus, it refutes the conclusion from #2 above that randomness does not imply free will. It only does so if you define free will in the way that people commonly understand it which is, frankly, not a defensible definition.

Rather, you have to see free will as having the power to have different outcomes for your life despite your past. Whether you can affect those outcomes by changing your actions or desires is a meaningless statement.

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Freedom of choice exists because the agent made different choices in different probable realities.

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Thus if I made the choice to practice in 60% of quantum futures and lift weights in 40%, then that proves I had the power to do otherwise. If I practiced in 100% of futures, then I did not have that power. Whether science can prove this is an open question, but it does not require any modification to quantum theory. Indeed, some modifications attempt to remove this possibility, incorrectly I believe.

While it may seem that this is sleight of hand in changing definitions, it is in reality making the definition of free will precise by saying that it is exactly the power to do otherwise. This is evidenced by quantum physics, i.e., because more than one outcome of a choice can occur from a single state of the universe, an agent does have “the power to do otherwise” which is what free will is.