As best we know, every particle in our universe follows the exact same physical laws.

These laws are not “deterministic.” We wouldn’t know what would happen next even if we could somehow measure everything about the state of our universe right now. But the unpredictable parts of each particle’s motion – due to each particle possessing a probabilistic mix of perhaps contradictory properties, which sounds strange in metaphorical languages (like English, Spanish, Mandarin, etc.) but not when expressed in mathematics – are totally outside of our control.

As best we know, humans shouldn’t have free will. Our future behaviors will unfold from the present positions and momenta of all the particles in our brains and bodies and the environments around us. Our thoughts will result from cascades of salt atoms crossing neuronal membranes. These salt atoms – like all other particles – are simply following physical laws that are, ahem, totally outside our control.

As best we know, we can make no choices.

As best we know, it’s still totally reasonable for the collections of particles inside our brains and bodies to experience an emergent phenomenon like consciousness. The particles inside of us collaboratively form neurons which collaboratively form minds. These minds can feel. But these minds still follow physical laws.

We can experience choices, not make them.

As best we know, we should experience our lives only passively, as though watching extremely immersive television shows. At times our minds would feel as though they had made choices, but that would just be a plot device. Cinematographic trickery! The choices are actually made by the positions and momentums of particles inside of us, which always result from their positions and momentums a moment before, and so on.

The math all works out.

So, for people who understand the math and the underlying physics, there’s a choice to be made (or perhaps I should say, “the person will passively feel as though they have made a choice”): should they believe in the laws of physics, or should they believe in free will?

Free will certainly feels real. But the sun also feels like it revolves around our planet. Our feelings have been wrong before.


In Existential Physics, Sabine Hossenfelder professes not to believe in free will. But Hossenfelder’s disbelief feels unconvincing. For instance, in describing how we can react to immoral behavior without referencing free will, Hossenfelder writes that:

We evaluate which actions are most likely to improve our lives in the future.

This is nonsense, of course. Without free will, there is nothing to evaluate – “evaluate” is an active verb that implies choice. Without free will, we would have no way to “improve our lives,” because this phrasing also implies action and choice. If the entire course of the future depends solely on the current positions and momenta of particles, then our lives will simply happen. The future isn’t predetermined – the mathematics of quantum mechanics injects randomness into the future – but we have no way to influence it. The future course of our lives is not up to us.

The particles will act as they must. Our minds will only watch.

As best we know, the laws of physics tell us that each and every moment in which we feel like an active participant in our lives is simply an illusion.

Personally, I believe the laws of physics are wrong. So does Hossenfelder, most of the time. In her day to day life, she contemplates cognitive biases – for example, the “sunk cost fallacy,” that makes it easy for people to continue making a bad choice so that they don’t feel bad about the bad choices they’ve already made, like when Hossenfelder further delays enrolling in a frequent flier program because she has already missed out on some benefits – and in her better moments, Hossenfelder chooses to overcome them. Hossenfelder also believes that she chose to study physics (and she believes that more people would make a similar choice if introductory physics were taught with a different mathematically formulation).

Hossenfelder discusses the ways that poverty and childhood trauma can influence the choices that we make as adults – some decisions feel easier than others because we are always sailing through a headwind of our past experiences – but in every passage of the book, Hossenfelder conveys her belief in free will.

And for good reason! We do have free will. Everyone agrees – even people who, for professional reasons, claim that free will can’t exist.

Honestly, there’d be no other way to live. Human brains couldn’t fathom existence without choice.

So, where does that leave us?

Either our belief in free will is wrong, or our current understanding of physics is wrong. As Hossenfelder meticulously explains, the two belief systems are incompatible.


Personally, I think our current understanding of physics is wrong. And I felt surprised that Hossenfelder never even mentions a major assumption that underlies her work. Occasionally, her chapters will include descriptions of theories that she doesn’t favor (usually followed by a curt dismissal), but the entire text of Existential Physics ignores the most glaring flaw in Hossenfelder’s arguments.

For instance, Hossenfelder writes that “We are all ultimately made of particles, and these particles follow computable equations.” And maybe this is true! But we have no evidence to suggest that it is.

All computation is digital. We can perform digital calculations at various levels of precision – for instance, if we’re trying to predict the behavior of a marble inside a pinball machine, we might measure the marble’s position down to the nearest inch, or tenth of an inch, or hundredth of an inch – but computation can never handle infinite precision. You can’t write the exact square root of two in decimal notation. You can’t write down the exact solution for the behavior of particles in any system with three or more – we can perform excellent calculations for the electronic structure of a hydrogen atom floating in an otherwise empty universe, but for atoms like helium, or for anything more complicated, we couldn’t come up with exact solutions even if we found empty universes for them to exist inside.

Possibly, our universe is digital, too. The mathematics of contemporary physics works best if we believe that our universe exists on a lattice of positions spaced approximately a Planck length apart: this would be a bit like a digital picture, where you can zoom in so far that eventually you’ll see that a red pixel can be either here or there but not anywhere in between.

Many of Hossenfelder’s claims presuppose that our universe is digital. In a digital universe, the amount of information in any particular volume of space would be finite. Decimal mathematics could correctly express everything. We could solve three-body problems, and the chaotic glitches** caused by rounding errors in our computations would be mirrored by chaotic glitches caused by rounding errors in the universe itself!

Wouldn’t that be grand!

But the only “evidence” we have so far that our universe might be digitized – pixelated, voxelated – is that it makes computation easier. That’s not compelling evidence.

It is testable. Consider a hydrogen atom held at a specific location with its electron in an excited orbital. When its electron collapses back to the ground state, the atom emits a photon that zooms off in a random direction. We might then kick the hydrogen’s electron back into an excited state, let it relax to the ground state again, and send another photon zooming off in another random direction. Again and again, photons zoom away!

If physical space were continuous, then the photons produced by this experiment could hit every possible location on detectors placed at any distance away – the probability distribution for photon collisions would be smooth over a sphere. But if physical space were digital, then photons could fly off in straight paths starting only at lattice points adjacent to the hydrogen atom (after accounting for the superposition of possible hydrogen positions). A graph of the probability distribution of photon strikes over a large sphere would show dark regions where photons couldn’t reach – locations where a photon’s path would’ve needed to pass between two lattice points to get there.

As best we know, the spacing between lattice points – if our universe were digital – would be ten to the minus thirty-fifth meters, which is like taking a yardstick and slicing it into a billion pieces, then slicing that piece into a billion pieces, and slicing that into a billion pieces, and slicing that into a billion, until you’ve taken just one billionth part four times over. This is very tiny! Which means that we wouldn’t notice a dark region unless our detector was very far away, and we would have to repeat this experiment with many photons to reveal it.

But – unlike several theories in contemporary physics – this is testable. It’s just an excruciating engineering problem.

Until we test this, though, Hossenfelder’s ardent claims – such as her claim that we can’t have free will – are a matter of belief. Although Hossenfelder doesn’t address this in her text, her worldview presupposes a digitized universe. There simply isn’t any evidence for this.

Until then, I’m perfectly content believing in free will. Even if my belief presupposes that our universe is continuous and is therefore not computable. I mean, computers are fun and all. But the way they work might not mirror our world. Even if that would make the math look prettier.





** Note: often, numerical approximations of a solution will approach the real answer. If we were working on a problem that involved the number pi, we might treat pi as being equal to 3.14 and we’d get an answer, and then we could go through the math again while setting pi equal to 3.14159, and we’d often get an answer that was very similar and slightly more accurate. But certain systems exist at the cusp of very different behaviors – for example, if we were studying a neuron that was close to the threshold of either firing or not, small changes in our understanding of the present would lead to large changes in our predictions for the future. Sometimes rounding errors don’t matter much; sometimes they do.