Talk:Free will theorem

Free will?

Although it's interesting, the theorem this article describes doesn't seem to have much to do with free will. If it's valid, all it demonstrates is that if indeterminacy is involved in human choices, it's involved in the actions of particles at the quantum level too. But indeterminacy isn't free will - to have free will in the sense that's important to us, we need to be able to act ourselves, not to act in an unpredictable way. Cheers, Sam Clark 11:03, 19 August 2006 (UTC)

Agreed. This has to do with information theory and particle physics. It in no way addresses the anthropomorphic issue of free will. --Vector4F 20:23, 15 October 2006 (UTC)

Also agreed. Using "Free Will" in this sense is very 18th Century :) sidd 07:36, 15 March 2007 (UTC)

Not agreed. The theorem makes logical room, within physics, for anthropomorphic consciousness to arise -- it just makes that cocommitant with other forms of consciousness such as "electron consciousness". It fixes the boundary problem that arises when people try to assert that human consciousness just emerges from a jumble of nerves. It predicts that the circuits of the brain produce an entangled functor the state of which integrates a lot of the information content of our perceptive apparatus -- the unity of qualia. Douglas Adams made the joke that "and then God disappeared in a poof of logic" and, interestingly, this theorem is pretty much the opposite -- deniers of a metaphysics beyond determinism disappear when they trace out their best models of determinism. I'm not a theist in the slightest degree but, in this theorem -- well, there's god, the soul, etc. -- if you catch my drift. -t

As stated in this article, the "Min" axiom is not a weakened form of the "Fin" axiom: "Fin" asserts only a finite bound on propagation of information, whereas "Min" states that (spacelike-separated) experimenters can make a "choice" of measurement and thus presupposes human free will. Zoetropo (talk) 11:31, 29 April 2015 (UTC)

This article is just interesting enough to be frustrating. I badly want somebody who understands the theorem to explain the indigestible bits. The first indigestible bit: "The Kochen-Specker theorem shows that the results of probing the particle can't be determined ahead of time, if the questions aren't." What questions? The article on the K-S theorem doesn't mention any "questions". Rick Norwood 18:14, 19 October 2007 (UTC)

The question is "what is your spin?" in a certain direction. Adrionwells (talk) 10:43, 22 January 2010 (UTC) —Preceding unsigned comment added by Adrionwells (talk • contribs) 10:41, 22 January 2010 (UTC)

That's an incredibly naive definition of free will. No philosopher defines free will like that.

In some initial surveys we found that people do not understand the concept ‘determinism’ in the technical way philosophers use it. Rather, they tend to define ‘determinism’ in contrast with free will. This result alone, we suggest, does not bolster the incompatibilist position. It does not suggest that people consider ‘determinism’, as defined in (one of) the technical ways philosophers define it, to be incompatible with free will or moral responsibility. Rather, it seems that many people think ‘determinism’ means the opposite of free will, as suggested by the phrase ‘the problem of free will and determinism’.

— Eddy Nahmias, Stephen Morris, Thomas Nadelhoffer & Jason Turner, Surveying Freedom: Folk Intuitions about free will and moral responsibility, Philosophical Psychology (2005), 18, p. 565

Compatibilism wouldn't even make sense if you defined free will as opposed to determinism. Yet, 59% of philosophers are compatibilists (http://philpapers.org/rec/BOUWDP). That's a clear indication that the definition is contradicting what philosophers understand by "free will".

The views of philosophers on an issue that is empirical has been shown time and time again to not actually matter. Philosophy on observable notions is useless, and where it comes into use we call it Science. This article is surely lacking, but it relates to something called Superdeterminism, which is a resolution to Bell's Theorem that has non-local hidden variables. Superdeterminism is inherently incompatible with free will, and is given the name as determinism isn't typically viewed as incompatible with free will, at least from the scientific point of view. The way you should then view this is just another way of looking at the implications of Bell's theorem. Either everything is superdeterministic and there is no free will (which comes with a lot of strange implications, such as most of statistics becoming meaningless), or indeterminism extends to both people and particles. These were already our options before this, and no amount of philosophical masturbatory criticism over this will change the results of this, but it's another bit of proof that indicates these two outcomes are what we have to choose from. There is no deterministic physics and human free will regardless of what any philosophers would like to believe or how many philosophers believe it. — Preceding unsigned comment added by 144.121.8.162 (talk) 15:59, 12 March 2018 (UTC)

The views of philosophers matter, because they help clarify what the question is. You can't run an empirical experiment to test the outcome to some question until you've figured out what the question is. 67.198.37.16 (talk) 01:27, 24 October 2020 (UTC)

I would argue that the problem is even worse—not even lay people would recognize indeterminacy or "randomness" as free will. --189.122.148.176 (talk) 18:02, 18 February 2015 (UTC)

Conway-Kochen are not claiming that free-will is randomness; that is a mis-reading 67.198.37.16 (talk) 01:30, 24 October 2020 (UTC)

Recent developments and a context

Today searching for free+will in titles from arXiv.org produced 21 items. Some of them are before Conway and Kochen, most are later and include comments, limitations, generalizations and further complications. Some of this could be reported in the article.91.92.179.172 (talk) 09:18, 12 September 2010 (UTC)

Pseudometric space

I'm not sure I get the argument about the universe not necessarily being a metric space. There's a step between the math and the physics that's missing for me; is it really conceivable that the universe has such a nature that a suitable metric could not be supplied to make it a metric space? Probably just as importantly, the only external reference this article gives is Conway and Kochen's article, and that doesn't mention metric spaces as far as I could find. Which means this is probably prohibited original research and should be deleted in whole. Otherwise, this really needs a cite.--Prosfilaes (talk) 01:29, 19 December 2007 (UTC)

Any natural 4-tensor field with (0,2) indices and nondegenerate determinant can serve as a metric field. E.g. the Ricci tensor can be so used. Unified field theorists from around 1940-1960 tended to treat the affine connection as more fundamental, and of course since you can construct the Ricci tensor from the affinity alone, you can get a metric. This affects the constraints when you use a variational principle to produce field equations. I don't think any of this has anything to do with free will. — DAGwyn 71.121.204.138 (talk) 15:13, 6 February 2016 (UTC)

Contrapositive

I attended a talk where Conway also discussed this rule the other way around. "An experimenter has no more 'free will' (what ever we choose to mean by that) than does an electron". —Preceding unsigned comment added by 87.194.171.29 (talk) 04:43, 28 February 2008 (UTC)

Exactly so. I also heard him speak on a different occasion. 1. Consider a simple experiment where the experimenter has two buttons (one red, one green) and must push one of them. The experimenter has no constraint; he can choose based on his "Free Will". 2. The experiment is set up such that, depending on the button, one of two types of quantum measurement is performed. 3. Conway proved that the experimenter's "Free Will" to choose which button to press is exactly equivalent to an electron's quantum "Free will" to be spin-up or spin-down. 87.194.171.29 (talk) 18:31, 12 October 2010 (UTC)

Randomness

As is explained in http://arxiv.org/abs/0807.3286 the following statement from the section "Problems and Limitations" is incorrect:

'The definition of "free will" used in the proof of this theorem is simply that an outcome is "not determined" by prior conditions, and may therefore be equivalent to the possibility that the outcome is simply random.'

My reading of the papers on this theorem is that the theorem is actually much more radical and interesting than is generally believed, but of course this article isn't the place to go into that. However, Conway and Kochen do argue (persuasively) that "randomness" is not adequate to explain the particular nondeterminism involved. "simply random," in any reasonable interpretation of the phrase, is factually incorrect, so I'll remove it. Misterbailey (talk) 00:00, 6 February 2009 (UTC)

I'm doing some more editing of the page. I'm uncomfortable with the fact that section "The theorem" seems to pretend to give an outline of the proof. Viewed by that standard, it's not quite right and not very clear. I'm cleaning it up. Misterbailey (talk) 00:25, 6 February 2009 (UTC)

Okay, still editing. In addition to what I think are some stylistic changes, I'm making one more "correction." The theorem does not suppose that two particles can be "quantum entangled." Only that they produce the same spin-squared measurements when measured in parallel directions. This is a consequence of quantum entanglement. It would be an overburdened theorem indeed if it needed to invoke a notion called "quantum entanglement." Misterbailey (talk) 00:52, 6 February 2009 (UTC)

Layman's Terms

This article is like a science report in a newspaper. As an encyclopedia, Wikipedia should introduce the technical material involved. This fails to. It can and should contain the proof. Phrases like "seems to" appear throughout it, as if the article is making guesses about the contents of this ineffable proof. It is not ineffable. It is a proof. 24.58.158.27 (talk) 03:47, 26 May 2009 (UTC)

what axioms?

In the article it says: " Since the theorem applies to any arbitrary physical theory consistent with the axioms..." This is too ambiguous and leading to misunderstanding. I think more should be said about what is meant by arbitrary physical theory and what does it mean to be consistent with the axioms in this case. When that is done it comes to light that a sea of other axioms are being assumed. Options that I see are: (1) Not mentioning that at all (although part of the beauty of the result is its formal nature, leading to this kind of statements), (2) explaining in more detail what is meant here by "arbitrary physical theory consistent with the axioms" (it is not so arbitrary), (3) just adding a warning about what the problem is. To notice what I mean take for example the incidence axioms of Euclid together with the inference laws of logic. The way in which the statement "Desargues theorem is true in any arbitrary model in which these axioms hold" is true is very different from the mentioned statement in this article.  franklin  21:06, 12 February 2010 (UTC)

The last reference: "Probing Free Will ..." is by J.H.Conway. 66.130.86.141 (talk) 05:51, 15 February 2010 (UTC) John McKay

Hidden variables

How is this theorem any different from the theorems that are well known in the Quantum Physics literature, which assert that the outcome of measurements on a quantum system cannot be predicted and cannot even have been foredetermined by the configuration of some classical (but experimentally hidden) variables?

Because from a physics perspective, Conway's result as presented in this article seems:

• Unexciting. It was already so well known that at the microscopic scale particles appear not to behave deterministically. Where is the novelty added in the theorem?
• Philosophically overstated. Since anyway nobody equates "deliberate willed choice" (like consciousness) with "selection completely at random" (like rolling dice) - yet the departure from determinism in QM is only to thoroughly Gaussian (e.g., as opposed to unpredictable black swan) randomness.
• Potentially false. Since although the projection into classical macroscopic measurement results cannot be determined beforehand from prior classical state data, the evolution of the system is unitary, which is to say that nonetheless the future quantum state of the universe as a whole is deterministically specified by the previous quantum state thereof.

I don't see how it advances on the thinking of Laplace and so on (who were already aware that mechanistic interactions of the atomic constituents implies the behaviour of people, consisting of atoms, is equally mechanistic).

Can someone better explain Conway's theorem in the context of what was already known in physics? Cesiumfrog (talk) 04:19, 29 October 2010 (UTC)

Agree with the above, especially the "philosophically overstated". This seems to be just an illustration of EPR. Since nobody would equate "free will" with "violation of causality" to begin with, claiming that this is a theorem about "free will" is basically just semantic obfuscation. --dab (𒁳) 18:35, 23 May 2011 (UTC)

It relates to free will in the sense that we're talking about a choice between non-deterministic behavior between both particles and humans and super determinism. It removes the middle ground of having determinism and free will. Super determinism is mutually exclusive with free will, so this necessarily relates. It's certainly a bit lofty to frame it as particles having "free will", but that's the wording they chose to relate these things. And to OP's point, there really isn't much difference, but this is essentially Bell's statement about super determinism being a solution to the "problem" of Bell's theorem in rigorous form.

Boy

Boy, this is vague.84.226.177.139 (talk) 20:04, 22 March 2014 (UTC)

A definition of free will is needed

This article should include the definition of free will the authors have in mind. Is it just determinism vs randomness? —Preceding unsigned comment added by 66.49.224.196 (talk) 00:05, 20 October 2010 (UTC)

That seems clear from the article. Is an experimenter free to make measurement A or measurement B, or is he or she constrained to make measurement A, not matter what.Rick Norwood (talk) 23:29, 22 March 2014 (UTC)

They define "being free" as "not being a function of the past" and conflate "being free" with "having free will", and so in a sense they do define "free will". Of course, this does lead it to open to equivocation (which I think the authors are guilty of), being that "free will" is usually understood to mean "making free choices", with "being free" and "making choices" meaning different things – and nowhere have they shown that particles make choices. — Preceding unsigned comment added by 81.168.40.68 (talk) 15:26, 22 December 2016 (UTC)

User-generated content

The editor Ghrom (Piotr Farbiszewski) seems to be promoting his own views on this subject at the end of the Reception section. The source on Quora is written by the editor himself and appears to be an original work. I don't think this belongs on Wikipedia. This source was also used on Change_(philosophy) 95.97.239.172 (talk) 23:18, 17 January 2017 (UTC)

speed of information

How can the speed of information be different than speed of light? I wish there was a footnote in that statement to show why that comment is there. — Preceding unsigned comment added by 96.65.204.149 (talk) 19:57, 30 March 2018 (UTC)

(1) it can be slower; it just can't be faster. (2) In some theories of entanglement, the resolution of wave function collapse happens via propagation of phases into the past, e.g. the two-state vector formalism. Now, it is not information that is travelling backwards in time, but rather the geometric phase (aka the holonomy). Put differently, one has a U(1)-connection relating the phase of the quantum-mechanical particle (taken to be the phase of the spinor on a spin manifold); that phase has to be consistent across time (and not just space, as it is in the Aharonov–Bohm effect); to describe this consistency, one has to use the holonomy of the connection (mathematics). If the phase in the future, after wave function collapse, is going to be consistent with the past, then you have to propagate it "all the way around", "into the past" as well as "into the future" -- to close the loop -- the holonomic loop (aka the "Wilson loop"). That's what makes the two state-vector formalism work. It is not "information" in the sense of "classical bits", that propagates into the past, its qubits. Anyway, that's the general idea, as I understand it. The article on Aharonov–Bohm effect has a tortured, painful explanation of the space-like only version of this; I've seen far more elegant explanations elsewhere; however, they require understanding what a spin connection is, etc. Search-engine "U(1) Holonomy" for details. Anyway, that is my understanding of wave-function collapse. There's no speed-limit in this. Basically, you can think of the past as being "not yet fully frozen" or "not yet fully determined" until the future forces those holonomic loops to close; when they finally freeze up, that wave-front of "freezing up" is what necessarily propagates at the speed of light. (I suppose if you are bold, you can claim its exactly the U(1) of electromagnetism; which is why its the "speed of light" and not some other speed. I don't know if one can be that bold, or not.) It is also what is carrying the "classical bits" of information, the classical bit being "is this loop closed yet, or not?" I have no clue at all how this Conway-Kochen theory accounts for any of this, other than it does tip a hat to spin manifolds and entanglement; for whatever reason, it leaves out the holonomy which seems like a critical ingredient to me, and replaces it with the more nebulous idea of "causality", which seems pretty bogus to me. If you wanted to improve on the theory, nuke the causality hypothesis into oblivion, and replace it with the holonomy and you get something that is more believable/realistic. (To rephrase that: 99.8% of algebraic topology is about loops. You can do calculations with that concept, see e.g. spectral sequences or more generally the Postnikov tower. You cannot do comparable calculations with "causality". You can't stick "causality" and "determinism" into some equation and turn the crank. It doesn't work.) 67.198.37.16 (talk) 01:19, 24 October 2020 (UTC)

I forgot to mention; the other problem with the naive concept of the "speed of information" is with what happens at the event horizon at a black hole. My naive, faulty understanding is that, again, this is where the holonomy plays a key role; the holonomy in a certain sense "escapes" the black-hole information paradox. The holonomic loops are free to thread through the event horizon; that is because they are not "physical particles" and have no "speed" and thus no "speed limit". Whatever is entangled inside the horizon must still be phase coherent across the horizon with whatever is going on outside. The evaporation is what "tunnels" the phase from the inside to the outside. Thus, it is not "information" that is being radiated away during during evaporation, it is the end-points of the holonomic loops; when these finally close, the "information" that they are closed is now outside of the BH. For evaporation, the end-points happen to be entangled spinors. ("Evaporation" means Hawking radiation.) They carry no information by themselves, the information is "created" when the wave-functions that they are a part of collapse. That is where "information" comes from. (it is also "why" it looks like information "lives on" the event horizon; the information is a count of the not-yet-closed loops that are waiting for closure. This is consistent with the replica trick (from spin glasses) that is used to resolve the ER=EPR suggestion. The ER's are the places through which the Wilson loops thread through.) In more abstract terms, information is a cobordism, or rather, the content of what is required to specify a specific cobordant arrangement. I'm told that its got something to do with spectral triples, but I don't entirely get it. Something about how the spectral triple entangles what is inside and outside the event horizon or something like that. I dunno, may have that wrong. Anyway, this has not much to do with this Conway-Kochen thing, other than offering the mathematical details for why "causality" and "determinism" are faulty concepts. John Baez explained one aspect of this more elegantly in 2004 where he argued for getting rid of category "Set" and replacing it by category "nBord" and category "Hilb". It gets rid of the stupidities with set theory and functions, which are the same stupidities of "causality" and "determinism", that everyone gets so hung up about, and replaces them with e.g. the infinity category. Presumably, Conway&Kochen have found a way of saying the same thing without having to say infinity groupoid and index theorem. Except they're still ham-strung on "causality". Whatever. I surrender. 67.198.37.16 (talk) 02:48, 24 October 2020 (UTC)

And one more thing: Although modern physics uses the Standard Model to describe particle interactions, lets fall back to a simpler description, which can be used in generic settings (including in curved space-time): this is the resonant interaction. In this case, the conservation of energy becomes a Diophantine equation $\omega _{1}\pm \omega _{2}\pm \cdots \pm \omega _{n}=0$. Hilbert's tenth problem asks for the enumeration of such solutions, and it is now known that this is algorithmically impossible -- there is no computer program that can achieve this. Roger Penrose uses this kind of argument to "explain" free will. That is, "determinism" or "causality" is that thing which results when you use digital algorithms; such systems have no "free will". This is how one builds the bridge from undecidability (Turing incompleteness) to "free will" in physics. To be crystal clear: the outcome of the interaction between physical (quantum mechanical) particles (in a curved space-time background) requires a decision problem to be solved, that cannot be solved using algorithms/Turing machines. Ergo "free will". It is not clear whether or not geometric finite automata, for example, the quantum finite automata can evade these non-computability results. 67.198.37.16 (talk) 17:49, 24 October 2020 (UTC)

Reception

The reception section seems to be drawing conclusion that are the exact opposite of the free will theorem from the free will theorem. The free will theorem says that if we have free will, then particles must have free will. This presumably is counterintuitive. It makes no claim about a world in which we don't have free will (a deterministic world). There's no way to argue for free will on the basis of this theorem - and yet, this is what the section claims, without any exposition.--Rxtreme (talk) 22:33, 30 June 2018 (UTC)

Agreed -- and made an edit which hopefully improves it. The references were good sources but the text of the article vastly misinterpreted them. I didn't look at references [6] and [7] to see if those were accurate, though. In particular the sentence "Some critics argue that the theorem applies only to deterministic models" is a bit vague (though it is a direct quote). Cstanford.math (talk) 23:08, 30 June 2018 (UTC)

Reception: Conclusion is present in the premises of any non-empirical proof

"Others have argued that the indeterminism that Conway and Kochen claim to have established was already assumed in the premises of their proof."

The conclusion is already present in the premises of any proof via deductive logic. Why is this worth mentioning at all? What a proof does is to make that already-present conclusion more clearly visible. The moment we define a right triangle with the various axioms of geometry, our premises already contain the fact of the Pythagorean theorem. Does that makes its proof immaterial? 2601:641:500:11A4:D14B:861:75EA:162 (talk) 06:54, 20 August 2019 (UTC)

Exactly right. Conclusions from premises have no free-will; they are pre-determined by the premises. This is a basic result from proof theory, innit? Anyway, the article no longer seems to say that. 67.198.37.16 (talk) 01:40, 24 October 2020 (UTC)

How would the apparent "solving" of the Wigner's friend paradox effect this theorem?

https://www.scientificamerican.com/article/this-twist-on-schroedingers-cat-paradox-has-major-implications-for-quantum-theory/

Specifically it says that we can either give up locality, Accept that measurements dont have a single result OR allow super determinism, id assume that giving up locality would destroy FIN/MIN/LIN (is FIN/MIN/LIN required in the fist place?) and allowing super determinism would just completely destroy this thing altogether (theres also the option of Objective collapse theory) seems like the only way out would be "accept that measurements do not have a single result that observers must agree" (from the article) — Preceding unsigned comment added by Johannes.Dickenson (talk • contribs) 09:40, 23 February 2021 (UTC)

Emphasis on assumption of free will and experimental verification I'm not totally sure about my analysis of the theorem, but I think I read in a paper that this is not a proof of free will but emphasizes on the assumption of free will ( which is generally taken to be axiomatic in QM). I do agree that the interpretation might vary but I don't at all agree that the theorem is scientifically iffy. The free will theorem, along with the kochen specker theorem are mathematically and scientifically rigorous. The free will theorem was also experimentally proven in 2016 (https://arxiv.org/abs/1603.08254). I do agree that this theorem doesn't help that much in understanding free will from a neuroscience, but irrespective it is a paramount theorem in the history of no-go and indeterministic theorems. I would just state that its okay to attack the question philosophically but I think, from a physics perspective, it's futile to question the validity of a peer-reviewed , mathematically robust and experimentally verified theorem. — Preceding unsigned comment added by TAYLORHEYHEY (talk • contribs) 15:28, 20 March 2021 (UTC)