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Free will is hard to define but it exists

Sabine Hossenfelder wrote an essay arguing that the free will doesn't exist even though she can't quite define the concept. To decide whether the free will "exists", I think it's almost necessary to define what this concept means. Wikipedia says:

Free will is the ability of agents to make choices unconstrained by certain factors. Factors of historical concern have included metaphysical constraints (such as logical, nomological, or theological determinism), physical constraints (such as chains or imprisonment), social constraints (such as threat of punishment or censure), and mental constraints (such as compulsions or phobias, neurological disorders, or genetic predispositions). The principle of free will has religious, legal, ethical, and scientific implications.
So the free will is the ability to make choices so that the choice wouldn't be done by "someone else". What we mean is that other, alternative spacetimes with the same past but different future seem to be compatible with all the knowledge (there are options!) but the choice of one particular possibility or another isn't determined by factors that we consider "external" relatively to the agent whose free will we are discussing. The term "free will" has many levels that differ by the inclusiveness of the factors that we consider "external".

For example, we talk about the "free will" in the political sense. Citizens of free countries and/or honest scientists have (and need) the free will – the freedom to make decisions about their life and about their experiments that are not determined by others. Citizens of North Korea are mindless screws in a squeaking machine so they don't have the free will. Alarmed climate scientists don't have the free will, either; their decisions are dictated by the external "cause" so regardless of the evidence and their personal views, they behave in a way that has the potential to maximize the climate panic and to please Al Gore and his accomplices.

But in the philosophical context, we want to view these political considerations as trivial. A person's decision may be determined by other people's desires and rules. In that case, we want to ask about the free will of these more powerful people. Do they really have the ability to make the choices? Where does the ability come from?

These questions may look well-defined to a philosopher (and to Sabine Hossenfelder) but they still fail to be well-defined according to a careful physicist. A careful physicist insists that at least in principle, there has to exist an operational definition of the free will – a procedure that decides about the answers to these questions operationally. And it's a problem. At most, in physics, you are allowed to decide whether some outcomes are determined/affected by or correlated with some other factors. You don't want to personify these factors or assign them with a thick layer of emotions and political labels because those are unphysical.

Moreover, if we don't want our thoughts about the free will to become vacuous, we must stop asking "why" at some moment. Arthur Schopenhauer has famously said "Man can indeed do what he wants, but he cannot will what he wants" (Einstein has loved that quote since he was a kid, and so did I). We might say that I went inline skating yesterday because I wanted – a manifestation of the free will – but one could still ask "who" or "what" determined that I wanted to go inline skating. Was it me or something else? Or something external? For the purposes here, it's enough for the free will to be able to "do what we want" even though we can't "will what we want". ;-)

In the framework that is close enough to the physical reasoning, we may define the free will by various correlations between the phenomena. For example, we may define the free will as the
"ability to circumvent or violate the laws of Nature – both the strict deterministic laws we knew in classical physics and the probabilistic laws provided by quantum mechanics".
Sabine seems to have adopted this definition. I agree with her that the free will defined in this way doesn't exist. No one and nothing can violate the laws of physics. In classical physics, this sentence had the obvious strict meaning. In quantum physics, it means that phenomena (and, importantly, ensembles of phenomena) don't happen if quantum mechanics implies that their probability is a sufficiently insanely tiny number.

I can't really prove that her definition is a "wrong one" or an inconsistent one. But it still seems like an unwise, redundant one. The laws of physics have always applied in the Universe and most of the sensible people realized that they did. These people have still talked about the "free will". So I think that meaningful definitions of the free will shouldn't be in direct contradiction with the validity of the laws of physics.

(Let me mention that Sabine's opinion that the free will doesn't exist isn't just an innocent implication of her unwise definition of the term. She is a proponent of the superdeterminism, the ultimate conspiracy theory that envisions a cosmic dictatorship that really prevents experimenters from deciding to measure one quantity or another if the result could be an inconvenient truth for the cosmic dictator. I won't discuss this lunacy in this blog post.)

It seems much wiser to me to define the free will of a human or an object as
"the ability to pick one outcome from the list of at least two a priori possible outcomes so that the choice isn't a function of the whole past of the whole Universe with the object removed."
I think that this is pretty much the definition adopted by Conway and Kochen in their free-will theorem: Wiki, TRF, arXiv. These thinkers have proven that if the experimenters enjoy the free will in this innocent sense, and sensible people think that they do (and this free will is necessary for science to be possible: see the point 10 at the very bottom of this blog entry), so do the elementary particles. This theorem doesn't imply that elementary particles are intelligent agents who should be treated just like humans, enjoy human rights, and/or be held accountable for their acts. But it means that the "random generator" choosing the outcome from a list of possible outcomes is "owned" by these particles. The outcomes are not determined elsewhere, in the rest of the Universe. The elementary particles contain whatever is needed to produce the outcome. The generation of the outcome may be associated with the region occupied by these particles.

Classical physics

Was there the free will according to classical physics? Well, it depends on what you mean by the word "external" that I discussed at the beginning. If you view all atoms of your body and your brain as "external stuff" that doesn't belong to you – and you want to define yourself as some kind of a "pure soul" – then indeed, there was no free will in classical physics. There were no souls, either. The atoms behaved (well, they were believed to behave) according to some deterministic laws.

These dust particles and small objects levitate not because they have the free will but because they are carried by the acoustic standing waves. Thanks to Gordon.

But you could also agree that the atoms in your brain "were" you. Then you had the free will according to classical physics because of some "locality": the motion of your mouth was indeed decided by the coordinates and momenta of particles that make up your brain. And these particles "were you" which is why "it was you who made the decisions". The decisions were done according to the values of the coordinates and momenta of the atoms – lots of numbers – but those numbers were what "defined what you were". You were these numbers. So if these numbers implied something, it was you who decided.

Some people can't swallow that "they are the numbers" which is the reason why they would say that they didn't have the free will according to classical physics. But the proposition "my identity isn't given by these numbers" is just an additional assumption, one that is in tension if not a direct conflict with the scientific thinking. I don't want to discuss the problem of the "free will" from the viewpoint of those who believe that the evolution of the Universe has nothing to do with any numbers because I think that these people are too stupid to deserve their spot on this blog.

Quantum mechanics

In quantum mechanics, the outcomes of the measurements are only determined probabilistically which apparently "extends" the room for the free will. The random decisions are made by someone – a random generator (or a really, really good quasirandom one, but there is no known way how to replace the genuinely random numbers in quantum physics by quasirandom ones that wouldn't contradict other insights we have about Nature).

The free will theorem guarantees that these decisions are really made in the spacetime region where we observe them – the measured values can't be functions of some hidden variable that would live in the rest of the Universe. So the decision which keys I press (on the PB EasyNote keyboard whose keys A,C,F,N,alt seem to become insensitive at random moments) may be associated with processes inside my brain. In this sense, I have the free will. And electrons' whose spin turns out to be "down" and not "up" decided to have this spin themselves, too. The free will theorem is another theorem claiming that hidden variables cannot exist – but it selectively focuses on hypothetical hidden variables that would live in a particular region of the space (outside the subject or particle with the free will).

You see that according to the diagram above, your humble correspondent believes that physical determinism is false (well, the classical one is false: I mean that the right quantum theory is probabilistic) and the free will is possible which makes me a "libertarian". I don't quite see why these metaphysical views are correlated with the political ones but the result works pretty well, so it's OK. ;-)

Sabine discusses "ten misconceptions".
1. If you do not have free will you cannot or do not have to make decisions.
Sabine disagrees with that because you can't avoid making decisions. Well, I think that the ability to make decisions is what should be called the free will – so I disagree with her view. They're just two ways to describe the same thing – both ways have the same additional ambiguities in their definition. A definition of the "free will" that can be non-existent even for objects that can make decisions seems meaningless to me.
2. If you do not have free will you have no responsibility for your actions.
I don't know what to do with such things. The problem is that the term "responsibility for your actions" is a political phrase that is meant to be applied to human beings. It implicitly assumes all the human characteristics that people have, including the free will. If someone or something – like a mindless germ or a robot – does something that kills many people but if this killing was hardwired to them, we may say that the objects that caused the death didn't have the free will. Does it mean that they have no responsibility for the actions? Well, we may still better destroy the germ or the robot because it's dangerous. We do so regardless of these subjects' or objects' being animate or inanimate. The words about "responsibility" are just some extra emotions that we add to the comments, words that we sometimes say to the culprits because we assume that they're able to listen. But we usually don't chastise germs or robots. We think it's a waste of time. But their having done a bad thing may still have consequences. Operationally, the differences may be very small. Using the term "responsibility" only means that we think of the culprits as being human and similar to ourselves but there's no "objective" criterion that would say how much similar they have to be.
3. People should not be told they don’t have free will because that would undermine the rules of morally just societies.
I partly agree with her. The society may work in pretty much the same way even if people say that they don't have the free will. After all, most people don't give a damn about these philosophical discussions, anyway. But those who do care may change their behavior. If someone suppresses the instincts and decides that everything is determined etc., he may become a nihilist or something else. Of course that such a change of the behavior is "irrational" in some sense. But the behavior dictated by the biological instincts (their previous behavior?) is arguably "irrational", too. So in practice, these changing collective beliefs about metaphysics may have social implications even though every individual can convince himself that the metaphysical debates may be disentangled from his behavior and goals.
4. If you do not have free will your actions can be predicted.
Well, I defined the free will so that its absence means that the "choices apparently made by an agent" are functions of some external data which means that they can in principle be predicted. Of course, if one defines the free will in her way, the quote above is invalid. Things can't be predicted – the quantum randomness is genuinely random and lots of complex classical processes are unpredictable in practice, anyway, even though she defines the free will as something that cannot exist.
5. If you do not have free will the future is determined by the past.
It's pretty much the same thing as the previous point and the same comments apply here, too.
6. If we do not have free will we can derive human morals.
Pretty much independently of the free will, science cannot answer moral questions.
7. Free will is impossible.
Her impossible "free will" is claimed to be possible now with the help of a preprint claiming that the laws of physics may belong to a "third group" which is neither deterministic nor probabilistic/random. I don't believe that there can exist any "third way" when it comes to the laws of physics so I disagree with her assertion here, too. The free will – if defined by a conflict with both deterministic and probabilistic laws of physics – is impossible.
8. You need to be a neuroscientist to talk about free will.
Well, I mostly disagree with her in this point, too. Yes, neuroscience is just an application of physics etc. but it is also exactly the right level of science to discuss operationally meaningful yet nontrivial questions about the decisions and their origin. So the sentence above is largely true. You will be becoming a neuroscientist if you will be increasingly able to trace the origin of decisions etc.
9. You need to be a philosopher to be allowed to talk about free will.
Well, I mostly agree: you don't have to be a philosopher to participate in these debates. But I would add that you have to be a philosopher of a sort not to realize that such talking about metaphysics is largely ill-defined and a waste of time.
10. If we do not have free will we cannot do science.
I disagree with her, mostly. An experimenter must have a free will to decide what to measure in order for his conclusions to be undistorted. A researcher (a natural scientist or a crime investigator or anyone who was assigned similar tasks) whose investigation was controlled by some "external factors" that could have affected where the investigator looked and where he didn't (or where he looked more carefully or more often) is a corrupt researcher – much like researchers into "global warming" – and he cannot be trusted. One can't build any science out of this research. The results of the scientific research are only trustworthy if we assume that the experimenters are "independent" in the sense of the free will – and all the evidence we have is supporting the opinion that this assumption is valid.

P.S. While I don't think that Michio Kaku has answered all conceivable questions on the free will in this Big Think video (with half a million views), I would probably endorse this one in its entirety – which doesn't mean that I would endorse all of his videos, of course. ;-)

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reader ppnl said...

As I said over there I think the free will question is the wrong question. We believe we have free will or a soul or whatever simply because we experience our thoughts. Without that raw ability to experience, the question of free will would never come up.

reader BobSykes said...

Your diagram requires a cross reference to the standard libertarian classification card.

reader John H. said...

Benjamin Libet famous experiments led to the idea that it is not so much "free will" as free NOT to do, an interpretation consistent with his experimental results. For myself I don't care much about free will because it teaches me nothing about behavior. In that sense it is an empty concept. In any event we are clearly to some extent constrained in the choices we make so I think the very use of the word "free" is misleading. It is limited choices at best. As ppnl stated, it is the wrong question. It probably has its origins in the Arminian - Pelagian-Calvinist debates concerning predestination, sin, etc etc.

reader Luboš Motl said...

Do you mean this one?

reader Bob Felts said...

If a definition of "free will" as defined for humans doesn't equally apply to computers, then it's a bogus definition.

reader Uncle Al said...

If reality is fundamentally determined, events can launch into existing trajectories rather than create them from scratch. Chosen events will have anomalously small empirical basis. Entanglement comes to mind, as does the violently shrinking information content of the human genome. 2 million genes estimated are now marked down to a paltry 19,000.

reader Alexander Ač said...

As usually I dont agree with this, not that it matters what you or I think, what matters is reality.

"...doing something truly significant about mitigating climate change is and will remain impossible because the instinctual drive to grow (in numbers or consumption) would have to be overridden at the level of human populations. (Some individuals can exercise "free will" in this matter, choosing to downsize, but only a very few.)" --

reader Honza said...

Of course free will discussion depends very much on definition. I think that it is almost impossible to define free will which people would have, and which would be any useful. So far I like most the views of Sam Harris, as expressed for example here (free will is just an illusion our mind creates for us)

reader Luboš Motl said...

Dear Alexander, did you suffer an injury today, one that made your serious mental condition even worse?

What does "mitigating climate change" and the related conspiracy theories you wrote down have to do with the discussion about the free will?

reader Alexander Ač said...


the link is simple - we DON'T have the collective "free will" to do anything meaningful about climate change (or carbon emissions in other words) -- nor have the humans the "free will" in regulating the global population, etc.

Even in other words, there are limits to "free will",


reader lucretius said...

They want to "save us" the same as the Muslims want to "save" the infidels by dragging them to Paradise in chains.
(The Prophet said, "Allah wonders at those people who will enter Paradise in chains.")

reader Jack Fox said...

It's worth noting that under Set Theory "choice" is an axiom. In Homotopy Type Theory,, (and I believe some of the lessor Type Theories) "choice" is a theorem. Some proponents say HoTT is a better foundational Math theory than ZFC Set Theory. (I'm not qualified to judge.) HoTT has in large part been driven by Computer Science researchers. I may be reaching too far, but seems like there is a connection between choice in math and free will in physics and philosophy.

reader Luboš Motl said...

LOL, interesting but I prefer the Axiom of Choice to be considered false.

reader Eugene S said...

One Cerberus? I've got 120 slavering bloodhounds... and they haven't been fed in five days!

The reference was to Edie Brickell's song What I Am:

I'm not aware of too many things

I know what I know if you know what I mean

Choke me in the shallow water

Before I get too deep

So you like Kodály, that's nice. He earned a footnote in the history of music and his merits were chiefly for collecting and preserving folk music (and also for his teaching methodology). As a composer, he was decidedly second fiddle to his compatriot and collaborator Béla Bártok. That piece on Youtube is barely one step above gypsy schmaltz, I'm sorry to say. But that's why you like it, right? Nothing disturbing about it, just perfect as acoustic wallpaper for your Sunday morning snooze after reading the funnies.

I can't give you a primer in 20th-century "modern classical" music in the space of this comment. Some of it, it is true, requires some real effort to understand and appreciate. Most of Schönberg, Berg, Webern is not accessible upon first hearing. (That is why performances of their music often feature a free introductory talk an hour before the start.) For you, of course, even Mahler is too "modern", it makes you uncomfortable. Western music ended with Brahms, right? You get your pre-chewed morsels from your favorite FM "classical greatest hits" station, which is guaranteed never to disrupt your routine as you move through your day. (Occasionally the presenter will throw out Charles Ives' "Unanswered Question" or Stravinsky's "Sacre" as something really, really risqué.)

Unfortunately I can't strap you down like Alex in Clockwork Orange and force-feed you good, serious modern classical music, it wouldn't work. You can like what you like and live your Babbitt-like life, it's none of my concern. What irks me is your moronic claim that "most modern music (and modern art) is degraded (the talent component is lacking)". Dear Gordon, you wouldn't know musical originality if it bit you in the ass. Of course most of the new music produced every year is rightly forgotten soon after it is premiered. It's been like that since the first cavemen got together to play their nose flutes! Top-flight talent is rare and always has been. The Vienna classic period that you adore -- in fact there were dozens, nay, hundreds of composers working then. We still perform Haydn and Mozart but Salieri (actually his music isn't half bad) and the many lesser lights are forgotten. While you listen to your safe, non-challenging Kodály and Andrew Lloyd Webber like millions of your contemporaries, a few hardy enthusiasts scattered across the gllobe are spreading the word about twelve-tone and serial music, about musique concréte, microtonal experiments, minimal music, neoclassical and folk-inspired, experimental jazz and fusion, electronic and hybrid, and I could go on for pages but it's just gibberish to you, like Woodstock's speech bubbles in the Peanuts cartoon.

reader Alexander Ač said...

Well, you write:

"...who would love to destroy the freedom of the remaining people on Earth."

Then I am wondering, what exactly does the destroying of living environment....

reader Gordon said...

Yes, I love that quote. I remember it used by a sceptic in a debate.

reader Gordon said...

Hmmm, re the youtube song Prinz Eugen---I don't speak much German, but wrt Eugene, "dummer pobel" springs to mind.

reader lucretius said...

Well, I think I was right : "
Prinz Eugen, der edle Ritter" - in the "culture wars" naturally ;-)

I have nothing to add except a link to another performance of

I have never been able to find an English translation but non-Russian speakers can get the idea from here:

reader lucretius said...

Actually prince Eugene was one of history's greatest patrons of the arts and a man of great refinement. The fact that he drove the Turks out of the Balkans was a bonus.

reader Shannon said...

Alexander wants to force "free will" on the global population :-).

reader Alexander Ač said...


you are wrong. I dont want anything (anymore).


reader Shannon said...

Awh... Don't be sad Alexander. It makes me sad too. OK,just tell me what to do so I can lower my carbon emissions. I'll do it just for you.

reader Alexander Ač said...


It is ok, I am not sad, I just dont give a shit about important issues, just as 99 % of population. I am just like them. I dont give a shit about climate change or resource depletion, I believe in humant brilliant ingenuity (but not mine, you know), so I can enjoy my life and fuck up with everyone else. That a a trully good life.

And sorry, I cant give you relevant advice on lowering your carbon footprint. You would not do a damn thing.



reader lukelea said...

Some layman! No offense but I thought this debate was supposed to be about bridging the gulf between the two cultures of the arts and the sciences.

reader lukelea said...

The Philistine Philharmonic.

reader lemiere said...

the experiment is quite easy to make, you let somebody on an island alone without any constraints...
hey where do the constraints come from?
from my point of view the very existence of constraints proves the very existence of free will.

And what is the meaning of freedom, am i either free or constrained? ot am i x% free...

such ideas made the success ot psychoanalysis..".it is not your fault"... god... the whose fault is it?

reader lukelea said...

I don't think he looked uncomfortable. Quite relaxed actually.

reader lucretius said...

I have found a more "eventful" performance of the Rayok from 2005. You can actually see Boris Yeltsin the audience and there are other goings on ;-)

reader Rehbock said...

That is just it, though. What distinguishes us from a purely deterministic system is that we think we can choose to cause or not cause something that physics does not preclude.
I am not sure a computer cannot do that but it is hard to see how or why such a universe would have creatures that believed they were choosing to build machines. It seems somewhat strange given that if there is no free will consciousness seems superfluous.

reader Werdna said...

With regard to the diagram, it's kind of interesting, but I think that many people assume, *given* that determinism is true, free will would then not be possible. While I agree that we don't live in a deterministic universe, my personal view is that, even if we *did* live in a deterministic universe (or, in hypothetical universes where determinism is absolute and true) it would *not* preclude free will. I guess that makes me a compatiblist-libertarian.

reader nobody said...

you might want to read this:

reader John H. said...

*Arthur Schopenhauer

A man can surely do what he wills to do, but he cannot determine what he wills.

reader Eugene S said...

Wonderful, thank you! Makes me sad that I never learned Russian though I recognized several of the songs in the satirical pastiche.

Have to hand it to Yeltsin, he was a good sport. Can't imagine ole stoneface Vladimir sticking around in his box seat until the final curtain.

reader Eugene S said...

It's probably a typo, but I think you hit on a new emoticon, the duck:

: "

reader Sage Basil said...

Choice is false, but close enough to suggest many theorems which can later be proven.

There are two nontrivial arguments in set theory, Cantor's first diagonalization and Cantor's second diagonalization. The rest exists to provide jobs for autistics.

reader John H. said...

There are thousands of studies on human decision making. To discuss free will without first becoming acquainted with a fraction of these is to make the philosopher's error. Thinking without evidence doesn't work.

reader lucretius said...

So Paul Cohen must have been the first autistic Fields medalist.

reader CentralCharge15 said...

Thanks for this post!

Many people oftren claim that "free will means that the laws of physics are denied", and other such meaningless rubbish, which had drawn me too into believing that free will does not exist. But after reading this post, I am convinced that disbelieving in free will is like being an anti-quantum person,.

Very nice post!

reader kashyap vasavada said...

Interesting comment Giotis. So if I understand SUSY is the only consistent extension of Lorentz group. There is "absolutely" no other choice. I think Lubos may have said similar thing in some past blog.

reader Giotis said...

In the presence of massive particles in Minkowski space-time
yes; with the clarification of course that when I say additional I mean in
addition to the Poincare group which is the Lorentz group + translations. These
are the most general space-time symmetries. We have also internal symmetries of the various gauge groups but these transform trivially (i.e. as scalars) under the above symmetries i.e. they don’t mix. So in terms of conserved charges you have the Pμ, Mμν and the conserved
charges of the internal symmetries.

If you want to see it in another way SUSY extends space-time
to superspace by including fermionic coordinates.

When there are no masses present we can have conformal
symmetry too and by adding SUSY to it you get super-conformal symmetry.

reader kashyap vasavada said...

Ok. Thanks. Your last sentence "When there are no masses present we can have conformal symmetry too". But conformal symmetry is assumed routinely and there are always massive particles around. So it must be approximate and broken (?).

reader Luboš Motl said...

The existence of any particular masses is incompatible with the conformal symmetry. So yes, the symmetry must be broken if there are masses around.