Talk:Free will theorem

message: 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)
thread_title:  Recent developments and a context 

message: 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)
replies: text: 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)
thread_title:  Pseudometric space 

message: 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)
thread_title:  Contrapositive 

message: 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)
thread_title:  Randomness 

message: 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)
thread_title:  Layman's Terms 

message: 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)
thread_title:  what axioms? 

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

message: 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)
replies: text: 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)

text: 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)
thread_title: A definition of free will is needed

message: 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)
thread_title: User-generated content

message: 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)
replies: text: (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)

text: 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)

text: 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)
thread_title:  speed of information 

message: 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)
thread_title:  Reception 

message: "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)
replies: text: 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)
thread_title:  Reception: Conclusion is present in the premises of any non-empirical proof 

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