If you’ve browsed the web sometime in the last three decades, especially if you visit any New Age or philosophy websites, you’ve probably come across the argument that quantum mechanics proves the existence of free will. Superficially, this seems somewhat plausible, in that quantum mechanics blows away our traditional idea that we can fully understand the future behavior of the universe based on observable properties of its particles and forces. Free will seems like a nice way to fill in the gap. But when you think about it in slightly more detail, there seems to be a fatal flaw in this argument. So let’s take a closer look.

To start with, what is so special about quantum mechanics? This is the area of physics, developed in the 20th century, that tries to explain the behaviors we observe in subatomic particles. What’s bizarre about it is that according to its calculations, as Einstein stated, God is playing dice with the universe: we can calculate probabilities of the position and momentum of particles, but not the exact values until we observe them. For example, suppose I am throwing a toy mouse for my cat to catch. Since this is a macroscopic object, classical physics works fine: my cat can take out a calculator, and based on the force I throw with, the mass of the mouse, and the effects of gravity, he will be able to figure out exactly where to pounce. But now suppose I am throwing a photon for him to catch. Even if he knows everything that is theoretically knowable about my throw, he will not be able to calculate exactly where it will land— he can only calculate a set of probabilities, and then figure out where the photon went by observing it. Of course, my cat uses the observation technique even with macroscopic mice, so no doubt he has read a few books on quantum physics and is trying to use the most generally applicable hunting method.

But how does this lead to free will? The most common argument is that since things happen in the universe that cannot be precisely calculated from all the known properties of its particles and energies, there must be another factor that determines what is happening. Many physicists seem to believe that a hidden physical factor has been largely ruled out. That means the missing piece, according to the free will argument, is likely to be human consciousness. When the activities of the particles in our brain could determine multiple possible outcomes, it is our consciousness that chooses which one will actually happen. The quantum events in my brain, for instance, could lead with equal probability to me recording a podcast this afternoon, or playing video games. My free will is needed to make the final choice.

Now time for the fundamental flaw in this argument. Suppose the quantum activities in my brain do ultimately give me a 50% chance of recording a podcast this afternoon, and a 50% chance of playing videogames. The implicit assumption in the free will argument is that if the properties of my brain determined completely that I would make a podcast this afternoon, then I would not have free will. Since there are two alternatives and I have to choose one, there is free will. However, remember that the quantum calculations provided an exact probability for each event, not just a vague uncertainty, and these probabilities have been well-confirmed in the lab. If I’m required to roll a 6-sided die, and record the podcast if numbers 1-3 come up, or play videogames if 4-6 comes up, aren’t I just as constrained as if I were only allowed one of those options? I still don’t get any freedom here. Either way, it’s not a question of my consciousness, it’s just another calculation, though one whose result cannot be predicted. If I’m forced to do certain things with known probabilities, that’s the opposite of free will.

There is one more wrinkle here though, which may rescue the free will argument. Suppose we interpret the quantum calculation slightly differently. Yes, there is a 50% chance of me recording the podcast, and 50% of playing a videogame. But maybe this isn’t the universe rolling a die— maybe it’s a measure of the type of personality created by the sum total of quantum interactions in my brain. So rather than being forced to roll a virtual die and decide, the universe has just built me into the kind of guy who, given a choice, would have a 50-50 chance of podcasting or gaming this afternoon. All the quantum calculations about my brain activity are just figuring out the type of personality that has been created by its construction. That argument rescues free will in the presence of quantum probabilities. Though it does put us in the odd position of wanting to ascribe some kind of conscious will to subatomic particles observed in a physics lab, or to assume some hidden spirits in the room are making decisions for them.

So what’s the answer here? Well, I’m afraid that as often happens with these types of questions, we will not resolve it in a 5-minute podcast. You can also find some more subtle arguments that incorporate other aspects of quantum physics, though those don’t look too convincing to me either. If humanity truly doesn’t have free will, I’ll look forward to the day when someone writes a treatise on how a large Big Bang of hydrogen atoms fundamentally leads to Math Mutation podcasts a few billion years later.

And this has been your math mutation for today.

References:

- https://bigthink.com/experts-corner/quantum-mechanics-supports-free-will
- https://conscienceandconsciousness.com/2020/12/11/does-quantum-mechanics-allow-for-free-will/