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The Physics of Free Will


Image used with permission under Creative Commons.

You’re playing a game of pool. You line up your cue stick behind the cue ball. You practice your stroke…one…two…three… On the fourth stroke, you follow through and the cue stick makes contact. If we could stop time in this moment, we could predict with reasonable certainty the outcome of your shot. The cue stick determines the path of the cue ball. The path of the cue ball determines if and how it will hit the target ball. How it hits the target ball determines the path of both, and whether either will reach a pocket.

But is this moment the earliest we could make our prediction? Wasn’t the path of the cue stick determined by the motion of your arm? And wasn’t that determined by an electrical signal from your brain? If we could monitor the state of your brain, could we predict the future of the pool table as you decide to make your shot?

And why stop there? Your brain is composed of neurons, white matter, and signaling molecules that must also obey the laws of physics – reacting to forces, conserving momentum, etc. Using brain-monitoring equipment and the same principles that applied to the pool table, could we predict your decision before you’re aware of making one?

Perhaps you, as a reader, can sense that things are starting to get philosophical. Using the laws of physics to ascertain what will happen – what must happen – on a pool table is all well and good. Now, though, we’re talking about using physics to anticipate what pool shot you will attempt. And if physics determines that decision, does it determine all of your decisions?

When we are deciding between aiming for the red ball or the yellow ball, we believe that we could choose either one. Thus, when we line up for the red ball, we believe that we have exerted agency, exercised our free will. But now it appears that someone monitoring our brain could have known, before we did, that we would choose the red ball. The idea that we could choose the yellow ball was just an illusion. In light of modern science, is free will merely an illusion?


I first delved into the free-will debate in a philosophy course during my freshman year of college, Introduction to Metaphysics. At the same time, I was taking a physics course in electricity and magnetism and a mathematics course in differential equations. Unsurprisingly, my physics course relied on lessons from my mathematics course. But I was fascinated to discover the degree to which metaphysics relies on fine, technical lessons from physics. This was especially true in the debate on free will.

In this debate, the pool table reasoning outlined above embodies an argument known as determinism. In the most general terms, determinism argues against free will (bear with me now) as follows: the state of the universe at a given time plus the physical laws – which determine how each part of the universe will react to its current state – precisely determine all past and future states of all parts of the universe (including humans). As an equation, determinism looks as such:

State of the universe at a given time + Physical laws = State of the universe at any time

 Under this reasoning, there is no room for free will.

Determinism drew my attention not only for its use of physics but also for the significance of its consequences. The question of free will is relevant on a societal level – impacting how we mete out justice and whether we care for others. More often, though, I think, the question wracks a person’s conscience for its personal implications. What does my life mean if I don’t have free will to choose my future? What do I do with this illusion of agency? Why can I even ask these questions?

However, determinism rests on a branch of physics known as Newtonian physics. Newtonian physics does a very good job of predicting events at the right scale – not too small (protons) and not too big (planetary systems) – e.g., human scale. But in the last century, it has been usurped as a description of the universe by newer theories: relativity and quantum mechanics. These two pillars of modern physics supersede Newtonian physics in ways which are important to this debate. And which might save us from the paralyzing effects of the questions above.


Relativity arose from Einstein’s posit that space and time are uniquely intertwined. Without relativity, our intuition tells us that a given moment in time is, in Newton’s words, “diffused throughout space.” In other words, we believe that position and movement within the three dimensions of space are independent of position and movement through the dimension of time.

But relativity says otherwise. Relativity says we live in a four-dimensional ‘space-time’, and movement through time is relative to movement through space.

Imagine that we have a train at rest. On top of each train car, there are analog clocks which have been very precisely tuned to the same time. Now the train begins to move. We stand on a station platform and the train passes us at nearly the speed of light.

Our intuition is that the clocks on each car should all read the same time. Relativity, though, dictates otherwise. As the train goes by, to those of us on the platform, the clocks on the train appear to be ticking slowly compared to our own wristwatches and, moreover, each clock reads a different time. From the platform, the farther back a clock is on the train, the further ahead in time it is.

On the train, however, these strange effects are not experienced. To a passenger in any car, all clocks read the same time. Thus, a moment of simultaneity for a passenger is multiple, temporally-separated moments for those of us on the platform.

This experience of relativity is critical because it counters the underlying assumption of determinism. The power of determinism lies in how straightforward it seems to our gut, a feeling that philosophers call ‘intuition.’ We intuit we have free will. Determinism overrides this initial intuition by appealing to our other intuitions about nature. But relativity shows “the state of the universe at a given time” – a necessary element in our Newtonian determinism equation above – is not a concept which actually exists. This new understanding of temporal relativity undermines the baseline assumptions of determinism and, therefore, its ability to oppose free will.

Quantum Mechanics

Relativity is only part of the story. What can quantum mechanics tell us about free will?

Quantum mechanics was born, in part, from the discovery that some subatomic particles do not exist in a single location, leading us to question whether they are ‘particles’ at all. Electrons are a key example. Before the 1900s, we understood electrons as particles with a defined charge and mass. But when scientists put electrons through a test known as the double-slit experiment, they found reason to question that assumption.

In the experiment, we have a screen with two parallel and identical slits cut in its surface. We then fire an object – say a paintball or a laser – through the screen, where a canvas on the other side records where (or how) the object emerged. Particles (like paintballs) and waves (like laser light) leave different types of marks on the canvas. Electrons, despite having charge and mass like a particle, behave in this test like a wave, seeming to travel through both slits at once.

So we now think of electrons as having some properties, like charge and mass, that are determinate and some properties, like position, that are normally indeterminate. We think of an undisturbed electron’s position as a superposition of all the places it could inhabit.

Now, we might wonder, as earlier scientists did, what electrons ‘look like’ in this superposition. We can try to answer this question by modifying our double-slit experiment, placing a ‘camera’ at one of the slits to watch the electrons as they pass through the screen.

But either the camera sees the electron or it does not see the electron. It cannot exist in a superposition of both seeing and not seeing. Thus, in the presence of the camera, the electron adopts a definite position and is either seen or not seen in a specific location.

Well then, what has quantum mechanics got to do with free will? If cameras can’t meaningfully interact with the uncertainty of quantum indeterminacy, humans certainly can’t either. Therefore, we cannot say that quantum indeterminacy directly frees us from philosophical determinism.

However, quantum particles can sometimes cross paths with our macroscopic world. Whether the electron will travel through the slit with the camera or the slit without is unknowable, and therefore the camera’s future – of either seeing or not seeing the electron – is unpredictable.

Philosophical determinism argues that physical laws precisely predict the future. For quantum particles, though, the law is unpredictability. So if a creature made and carried out decisions through the flow of electrically charged particles (such as the signals within or between neurons, perhaps...), this level of uncertainty would make it awfully difficult to argue their future can be precisely pre-determined.

Do We Have Free Will?

I must admit that I do not have a satisfying answer. But I do claim that progress has been made. While Newtonian determinism appeared to (unsatisfactorily) close the question of free will, modern physics has introduced uncertainty, and therefore a reason to continue searching for an answer. And now you, the reader, are primed to do just that. To learn more about these topics, the classic works A Brief History of Time, by Stephen Hawking and Relativity, by Albert Einstein are surprisingly accessible (though not ‘light reading’). You could also dig deeper into the debate (which is far from over) with recent articles and blog posts) – and perhaps even consider the connections between free will and a wider range of physics topics, like entropy.

One idea, known as compatibilism, attempts to develop a definition of freedom that is compatible with both determinism and free will. The argument does not quite satisfy me but I am interested in how making clear definitions might be helpful. Determinism still chafes me because it portrays people as passive entities, defined by outside influence. My sense of free will is my sense of agency in my life. As I continue to ponder this debate I have begun to think about how this agency might lead to a functional definition of free will.

I left my philosophy class without answers to these questions but with the thought that physics would be critical to finding answers. Who knows? We may yet discover the Free-Will particle.



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