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Cristi Stoica: on 7/14/09 at 14:48pm UTC, wrote Dear Zeeya, You say “Some have argued that certain deterministic...

Ryan Westafer: on 1/21/09 at 6:28am UTC, wrote Much like the 20-questions game a poster mentioned, let's play another...

Dave King: on 8/24/08 at 19:11pm UTC, wrote Goodness, what well read commenters you have - I think I'll just leave a...

John Merryman: on 8/5/08 at 10:43am UTC, wrote Jack B. alludes to it above, that "Free will" is something of a misnomer,...

William Orem: on 8/4/08 at 19:49pm UTC, wrote Zeeya, Great post! Your last point is the one I always came to when...

Guenther Greindl: on 7/28/08 at 20:29pm UTC, wrote Physicists are often hopelessly naive about free will. But then again, much...

Jesse: on 7/25/08 at 17:24pm UTC, wrote I wonder if the problem of determinism as you describe it is rooted in a...

Crikey: on 7/25/08 at 13:35pm UTC, wrote Zeeya, I came to your piece via a very convoluted and protracted path. If...


Thomas Ray: "The speed of light isn't a theoretical limit. Neither are the 19 or so..." in Bohemian Reality:...

Anonymous: "The Fact? The only 'fact' of the Big Bang is the math behind the measures,..." in Bohemian Reality:...

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Jason Wolfe: "Mystical religious beliefs are completely justified. it is the scientific..." in Wandering Towards a Goal:...

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Our Place in the Multiverse
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Sounding the Drums to Listen for Gravity’s Effect on Quantum Phenomena
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TOPIC: Do we really have free will? [refresh]
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FQXi Administrator Zeeya Merali wrote on Jul. 24, 2008 @ 19:40 GMT

I may have been predestined to write this.

There is a new paper this week by John Conway and Simon Kochen that reconsiders what physics has to tell us about free will.

I’ve written about an earlier version of Conway and Kochen’s “Free Will Theorem” in the past, for New Scientist magazine. This, of course, predisposes me towards covering the mathematicians’ new thoughts on the subject. But at a deeper level, do I have any real choice about whether not or not I write this? Or am I inevitably driven to do so by chemical reactions in my brain that were predetermined to occur via a long causal chain of reactions set up billions of years ago by the peculiar way that the particles were created after the Big Bang? It’s this deeper question that Conway and Kochen tackle.

For them, the answer is no, my actions are not predetermined. Their theorem, which was originally set out in 2006, purports to be the first logical proof demonstrating that if humans have free will, then the laws that govern the behaviour of subatomic particles cannot be deterministic. That’s not a problem for Conway and Kochen, since standard interpretations of quantum mechanics happily embrace indeterminism. Before measurement, conventional wisdom goes, a quantum particle exists in a superposition of many mutually contradictory states; only after measurement does the particle settle into one of these options. Prior to measurement it is impossible to know for certain what the outcome of the measurement will be. That indeterminacy is good news, say Conway and Kochen. It means that free will survives.

But what if this standard interpretation of quantum mechanics is wrong and the world is governed by deterministic laws? There are physicists who are currently investigating this possibility, for example, FQXi’s Antony Valentini of Imperial College London, who is looking into whether the random outcomes of quantum experiments are determined in advance by “hidden variables”—subatomic blueprints to which we do not currently have access.

If a hidden-variables theory is correct, then Conway and Kochen’s theorem tells us that we cannot truly have free will. The thought was so alarming that it caused Nobel Laureate Gerard ’t Hooft, who is developing his own deterministic theory, to attempt to redefine “free will” in a way that isn’t in conflict with determinism.

(Image: Frank Foreman)

Conway and Kochen’s proof is based on the ways that you can poke a particle to determine the value of its spin along a certain axis. Measuring a particle's spin is a lot like playing the game "twenty questions", where one player tries to guess what their opponent is thinking of by asking them yes/no questions. If you play honestly, you think of an object before the game starts and stick with it. This corresponds to a deterministic theory—a particle has definite predetermined spin values before you look at it, and when you probe it along three axes, it simply yields these set values.

The crux of the proof rests on the fact that if you measure the square of the spin of so-called “spin 1” particles along three perpendicular axes, you always uncover the same three values—1,0,1—in various orders. Just over 40 years ago, Kochen and his colleague Ernst Specker showed that with this restriction in place, it's impossible for the particle to have consistently defined spins along every direction you might choose to measure, before the game begins. Even if you just look at 33 possible directions, the particle can't set spin values along each of the 33 direction such that you get you 1, 0, 1, no matter which three perpendicular directions you choose to poke. You can set consistent spins for 30 directions, but the final three must paradoxically be both 1 and 0.

That's fine for quantum mechanics, where the particle sets its spin on-the-fly. This corresponds to cheating at "twenty questions", where you can keep changing the object in mind, as the questions are being asked.

But if we want a deterministic theory to hold, there seems to be only one way to avoid hitting a paradox. Nature must somehow restrict the experimenter’s choice, so that she only chooses to measure along three axes chosen from the 30 directions along which spin is completely defined. But, if that’s the case, Conway and Kochen argue, then she cannot have had the free will to set up her experiment as she desired; her choice wasn’t under her control, but predetermined by nature to stop her from running into the paradox.

Conclusion: If the experimenter is truly free to choose the directions along which to make her measurement, then the particle’s response cannot have been predetermined.

Some have argued that certain deterministic theories could still survive the free-will trap. For example, there may be more complicated ways of setting spin values, in which the measurement order influences the values of spin returned upon measurement. Although Conway and Kochen addressed this point in their original theorem, they have now tightened their axioms in an attempt to close this loophole completely.

It will be interesting to see if Conway and Kochen have been successful in setting all deterministic theories up against free will. But even if they succeed, is quantum indeterminism really the saviour free will? It may be true that it saves us from simply playing out a predetermined destiny, planned out in advance in a clockwork universe. But in what sense do we have control over our choices in this quantum world? Are we simply replacing a predetermined future over which we have no control, with a future based on random quantum outcomes, again, over which we have no control? Quantum mechanics may *free* us from a future that was set in stone billions of years ago, but it still cannot explain the origin of the *will* that allows us to make choices.

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Liza Rothwell wrote on Jul. 25, 2008 @ 12:59 GMT
Interesting research. I am always struck though (as a historian) by the fact that science is always changing: for many years people completely believed that the Sun went around the Earth. Even if research now shows that as far as we can tell free will is a fallacy, might we not in the future make other discoveries which completely invalidate this idea? And also this concept does not seem to allow for the idea that perhaps some things are in fact immeasurable. Maybe it just comes down to your belief systems, but I'd refer you to the Great Bard: "The fault, dear Brutus, is not in our stars,But in ourselves."

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Jack B. wrote on Jul. 25, 2008 @ 13:22 GMT
It may be worth checking in with Daniel Dennett, who has written about this particular subject at length. He points out, as Zeeya does in the last paragraph, that relying on QM to ground free will physics really only offers a choice of either determinism or randomness, neither of which feels satisfactory. Instead, he talks about analyzing the problem of free will at different levels of complexity As an example, he describes the game of "Life" ( in which pixels are either "on" or "off." But the pixels also operate at a group level, in which "organisms" of pixels "live" or "die" based on interactions with other organisms in complex and (I think) often unpredictable ways. For humans, Dennett appears to say that while particle determinism might invalidate a classical understanding of "free will," it doesn't interfere with a subject's "evitability" -- the ability to pursue goods and avoid harm. I think you can find good argument for this (I can't do it justice) in "Freedom Evolves"

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Crikey wrote on Jul. 25, 2008 @ 13:35 GMT

I came to your piece via a very convoluted and protracted path. If that path was predestined, and time and the universe were simply turning the handle, I'm impressed.

I confess that I am no physicist, and have only a tenuous knowledge of what is now refered to as "popular science", i.e. the coffee table books such as "a brief history of time". However, this all seems to be leading on from the concept of shroedinger's (probably spelt wrong) cat (more likely to be spelt correctly), which is all well and good.

My science doesn't go much further than Aristotle, (or was it Plato, or perhaps Socrates). Anyway one of these chaps made a fairly pertinent comment, which was more or less "let us start from what we know". From that, science has progressed thoughout the ages, making hypothesis after hypothesis, and testing these to see if they adequately explained the world around us. In that sense Conway and Kochen seem justified in changing their hypothese to explain whatever they're investigating, if old hypothese did not answer all the questions. If I understand you correctly, however, it seems they have merely changed the goalposts and are ignoring inconvenient parameters, which doesn't sound scientific at all. Comments such as "oh, that just a rogue data point," or "oh, that mark is just a feducial scratch" has never cut it with me, unless there is justification.

In any event, it is interesting and startling that science, as unemotioinal as it is, remains obsessed by these areas of research, which seem to me purely designed to find God, and explain why we are here. I thought science killed god years ago. In any event I hope our protagonists don't wander off down some blind ally and find some arbitary talisman as our god, but then, they may have no choice.

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Jesse wrote on Jul. 25, 2008 @ 17:24 GMT
I wonder if the problem of determinism as you describe it is rooted in a philosophical assumption we would do well to examine. The position assumes a fundamental materialism. To me, the only possibility of escaping some form of determinism is to entertain the possibility of the will and some feature of our conscientiousness arising from outside of physical phenomenon.

As the names Plato and Aristotle have already been mentioned, we could begin with their theories of form and reality, neither of which would conform to the ardent materialism which has grown into the modern assumption. I don't find materialism an especially intuitive or plausible account for the nature and structure of the universe, and I think that the human experience and the nature of human consciousness provides a fairly compelling witness to its lack of intuitive appeal.

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Guenther Greindl wrote on Jul. 28, 2008 @ 20:29 GMT
Physicists are often hopelessly naive about free will. But then again, much philosophy written on the subject is bogus too. Everything written by Daniel Dennett (mentioned above), though, can be warmly recommended.

Eli Yudkowsky at has an excellent analysis of the problem here (the article also links to previous posts which might be necessary for understanding his argument):

I wonder why everybody is so keen on having free will? The underlying assumption is that free will is something to be desired. But actually it is only a ploy by religion to get around the theodicy problem, a psychological mechanism to justify retributive anger and punishment, and a persistent cognitive illusion from a brain unaware (in principle) of it's underlying physical state.

Buddhism, by the way, does not have the problem in the first place: see the doctrine of Pratītyasamutpāda (at wikipedia for instance): dependent origination. But then again, Buddhist metaphysics was always very "empirical" and thus merges well with science.

Conway and Kochen, before using QM for subjects where it can't deliver, should reconsider if free will is even a coherent (and desirable) concept.



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William Orem wrote on Aug. 4, 2008 @ 19:49 GMT

Great post! Your last point is the one I always came to when considering the "quantum mechanics frees us" move made by popular science writers as far back as the '80's. In what way does inability to determine the exact moment when an atomic nucleus will decay, say, connected to what we mean by "free will"? The suggestion always seemed to be that subatomic nature isn't predictable, so macroscopic things like brains must be similarly unconstrained. But indeterminacy doesn't apply to anything else macroscopic, so why would neurons be different? And even if neuronal firing isn't deterministic, which is a big claim, is it therefore random in the manner of atomic decay? My thoughts don't seem random or merely statistical any more than they seem deterministic.

It seems that if we want indeterminacy to "free" us, we need to suggest that consciousness emerges at the level of protons and neutrons, not at the level of neurons. Without that claim, which is pretty unlikely, we're probably guilty of the critique Daniel Dennett made (I believe it was Dennett) of Penrose's book "The Emperor's New Mind" -- "Consciousness is weird, quantum mechanics is weird, so the two must have something to do with each other."

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John Merryman wrote on Aug. 5, 2008 @ 10:43 GMT
Jack B. alludes to it above, that "Free will" is something of a misnomer, if not outright oxymoron. Contrary to the top down theological assumption that good and bad are a primordial duel between the forces of light and darkness, they are the biological binary code. Even single celled organisms distinguish between beneficial and detrimental. So our entire neurological makeup is constantly weighing all such factors, from the depths of our subconscious and quite literally the pit of our gut. When we make the distinction between good and bad choices, the decision is already made. It is a manifestation of the will to balance all factors and proceed in the direction that is judged beneficial, even if it might be distorted from prevalent views. We don't come to this point and then decide.

I think anther philosophy of physics issue also applies, in that particle physics seems to assume the noun is cause and the verb is effect, yet all we have learned seems to pint in the opposite direction, that form follows function. Consider strings, with all their extra dimensions curled up inside. Wouldn't it be logical to think of them as vortices in some larger pattern? It just seems like physics is caught up in some ancient Greek thought experiment, where we are breaking the rock into smaller and smaller pieces, trying to find the smallest possible unit and that will provide some physical basis to explain what otherwise seems more of a fluctuating vacuum, where if we were to add up all the balancing forces it would cancel out completely.

Given this lack of substantial physical basis, the point of whether it is deterministic or not seems meaningless, since it has bootstrapped itself out of nothing and should all the cherries ever line up, would flatline back into nothing.

The problem with looking for meaning is that meaning is static and reductionistic, while reality is dynamic and wholistic.

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Dave King wrote on Aug. 24, 2008 @ 19:11 GMT
Goodness, what well read commenters you have - I think I'll just leave a note saying that I found it interesting (and in parts somewhat over my head).

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Ryan Westafer wrote on Jan. 21, 2009 @ 06:28 GMT
Much like the 20-questions game a poster mentioned, let's play another thought game. This one is particularly fun (and sneaky).

"My deterministic is your random."

I choose to eat a banana, and I choose to throw the peel near your bus stop. You slip, and I never admit I knew your propensity to walk that path every day. How will you prove I acted in a deterministic way? You must investigate me. You require more information. The perceived randomness is your uninformed state and it is maintained by your continued decision not to question me. Furthermore, your suspicion is due to some sort of history suggesting I might act in such a way.

Observations fall into history and allow correlations and prediction; they thereby thrust light into the random dark.

My argument here is this: determinism and randomness are much like two sides of a coin- they, like so many other observations, align well with our notions of symmetry, balance, and duality.

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Cristi Stoica wrote on Jul. 14, 2009 @ 14:48 GMT
Dear Zeeya,

You say “Some have argued that certain deterministic theories could still survive the free-will trap.”

Here is a solution to eliminate the apparent wavefunction collapse in quantum mechanics. This makes the time development deterministic, but with the initial conditions delayed (undetermined until the measurement is performed). This solution, although deterministic, allows the free-will to the same extent as the standard QM, although, like this one, it doesn’t guarantee it. Therefore, the free-will hypothesis and determinism are independent. But is the free-will hypothesis testable? A briefer exposition of these ideas is here.

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