(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 9006737, 150176] NotebookOptionsPosition[ 8990053, 149723] NotebookOutlinePosition[ 8992456, 149786] CellTagsIndexPosition[ 8992373, 149781] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell["Slide 1", "Section", FontSize->18], Cell[CellGroupData[{ Cell["\<\ The Conway-Kochen \"Free Will Theorem\" \ \>", "Title", CellChangeTimes->{{3.4567532760102787`*^9, 3.456753309039323*^9}, { 3.468508814566348*^9, 3.468508821339122*^9}, 3.4685089103784857`*^9}, FontFamily->"Marker Felt", FontSize->48], Cell["\<\ Nicholas Wheeler Reed College Physics Seminar 2 December 2009\ \>", "Text", CellChangeTimes->{{3.456753329452243*^9, 3.45675334758354*^9}, { 3.4578237797191133`*^9, 3.457823788050664*^9}, {3.468508943553997*^9, 3.4685089462735662`*^9}}, FontSize->16] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell["Slide 2", "Section", FontSize->18], Cell[CellGroupData[{ Cell["Deep History", "Subtitle", CellChangeTimes->{{3.4685082929743834`*^9, 3.468508297019987*^9}, 3.4685083876895237`*^9, 3.4685089669372787`*^9}, FontFamily->"Marker Felt", FontSize->36, FontWeight->"Bold"], Cell["EINSTEIN, PODOLSKY & ROSEN (EPR)", "Text", CellChangeTimes->{{3.468508421671385*^9, 3.468508510140196*^9}}, FontSize->24, FontWeight->"Bold"], Cell[TextData[{ StyleBox["1935", "Subsection", FontSize->18], StyleBox[": A. 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Rosen (then 23 years old), who had \ acquired prior experience with \"entangled states\"\[LongDash]yet to be given \ their name\[LongDash]from work on the hydrogen molecule.\n\nPaper pointed out \ that if a composite system (comprised of subsystems A and B), is in an \ entangled state, then the results of measurements performed on A and B will \ exhibit correlations, even though the measurement events lie outside each \ other's lightcones. This held by Einstein, a \"local realist,\" to be absurd\ \[LongDash]spoke of a \"", FontSize->18], StyleBox["spukhafte Fernwirkung", FontSize->18, FontSlant->"Italic"], StyleBox["\" (spooky action at a distance), rendered quantum mechanics \ implicitly nonlocal.\n", FontSize->18], "\n", StyleBox["\"", FontSize->18], StyleBox["I find the idea quite intolerable that an electron exposed to \ radiation should choose of its own free will, not only its moment to jump \ off, but also its direction. In that case, I would rather be a cobbler, or \ even an employee in a gaming house, than a physicist", FontSize->18, FontSlant->"Italic"], StyleBox["\". \[LongDash]AE", FontSize->18], "\n" }], "Text", CellChangeTimes->{{3.4567572893204517`*^9, 3.4567573729934072`*^9}, 3.4567574073336143`*^9, {3.4567575479311867`*^9, 3.456757602405839*^9}, { 3.456757702128508*^9, 3.4567577116884003`*^9}, {3.456758070573998*^9, 3.45675811392511*^9}, {3.4567583512225037`*^9, 3.456758377700038*^9}, { 3.456758412316271*^9, 3.4567586229617453`*^9}, {3.4567586570650253`*^9, 3.456758910102386*^9}, {3.456758948743063*^9, 3.4567589708632727`*^9}, { 3.456759002384117*^9, 3.456759090343392*^9}, {3.456759156281845*^9, 3.4567592114591837`*^9}, {3.456759481037359*^9, 3.456759734506884*^9}, { 3.45675976630079*^9, 3.456759791214304*^9}, {3.456759824559148*^9, 3.456759830535391*^9}, {3.456760043825665*^9, 3.456760063906001*^9}, { 3.456760094276205*^9, 3.45676016942237*^9}, {3.4567602070774317`*^9, 3.456760248694229*^9}, {3.4567603259587*^9, 3.456760331127062*^9}, { 3.456760894470685*^9, 3.456760928180818*^9}, 3.4575791533492327`*^9, { 3.457579309221292*^9, 3.4575793197515707`*^9}, {3.457579399158842*^9, 3.457579410587392*^9}, {3.457579794419023*^9, 3.4575798037915983`*^9}, 3.457579914649026*^9, {3.45757996636068*^9, 3.457579983354707*^9}, { 3.4575800729145412`*^9, 3.4575800862703657`*^9}, {3.457580156054688*^9, 3.4575801658590317`*^9}, {3.457580234196052*^9, 3.457580262369014*^9}, { 3.457824220627817*^9, 3.457824225971662*^9}, 3.457824332056876*^9, { 3.457824575087079*^9, 3.457824578898403*^9}}, FontSize->14] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Slide 3", "Section", CellChangeTimes->{{3.468511948489377*^9, 3.468511952700135*^9}}, FontSize->18], Cell["\<\ Problem avoided if particles were endowed with internal \"instruction sets,\" \ written onto \"hidden variables.\" Probabilistic aspects of quantum mechanics \ would then be a reflection of our ignorance of the state of the hidden \ variables\[Ellipsis]and it was that kind of ignorance that in EPR's view \ rendered quantum mechanics \"incomplete.\" Bohr immediatey wrote a strong rebuttal (which Bell later held to be \"almost \ unintelligible\"), and anyway it was widely believed that John von Neumann \ (1932) had shown hidden variable theories to be impossible (by a line of \ argument that Bell later showed to contain a fatal flaw). So Pauli, Born and nearly everybody else was happy to dismiss the whole \ issue. Schr\[ODoubleDot]dinger, however, considered (1935) that EPR had identified \ the most profoundly puzzling/distinctive feature of quantum theory (and gave \ \"entangled states\" their name). \ \>", "Text", CellChangeTimes->{{3.457824440513422*^9, 3.457824486617043*^9}, { 3.457824529161523*^9, 3.457824544870864*^9}, 3.457824675395093*^9, { 3.4578253267763653`*^9, 3.457825347776301*^9}, {3.468621115953309*^9, 3.468621133487142*^9}}, FontSize->18] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Slide 4", "Section", CellChangeTimes->{3.468512596885482*^9}, FontSize->18], Cell["DAVID BOHM, YAKIR AHRANOV", "Text", CellChangeTimes->{{3.468508421671385*^9, 3.468508510140196*^9}, { 3.4685097435803967`*^9, 3.468509747512114*^9}, {3.468512284506689*^9, 3.46851230255075*^9}}, FontSize->24, FontWeight->"Bold"], Cell[TextData[{ StyleBox["1951", FontWeight->"Bold"], ": Publishes ", StyleBox["Quantum Mechanics", 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S. 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Hidden variable analysis leads (as Bell ingeniously \ demonstrates) to an inequality which ordinary quantum theory would in some \ cases violate, the implication being that\n\n\"", FontSize->18], StyleBox["No physical theory of local hidden variables can ever reproduce \ all of the predictions of quantum mechanics", FontSize->18, FontSlant->"Italic"], StyleBox[".\"\n\nBell had identified von Neumann's elementary error, made \ lively again the possibility that hidden variables ", FontSize->18], StyleBox["might", FontSize->18, FontSlant->"Italic"], StyleBox[" exist. Tended intuitively to favor that hypothesis, sought to \ establish that quantum mechanics", FontSize->18], StyleBox[" is", FontSize->18, FontSlant->"Italic"], StyleBox[" a local theory\[LongDash]incomplete as it stands. 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contributions to \ quantum mechanics\"", FontColor->RGBColor[0, 0, 1]], "). Not directly concerned with hidden variable question, but sprang from \ the same von Neumann/Mackey quantum axiomatics that led von Neumann to his \ (fallacious) \"no-hidden variables theorem.\"\n\nBell recognized the \ importance of Gleason's theorem, of which he provided his own alternative \ proof.\n\n" }], "Text", CellChangeTimes->{{3.468515633234192*^9, 3.468515659244912*^9}, { 3.468519340191513*^9, 3.468519422318915*^9}, {3.468621811015841*^9, 3.4686218355144253`*^9}, {3.4686218676383047`*^9, 3.468621869405909*^9}, { 3.468621983849277*^9, 3.46862198909704*^9}, {3.468704278835987*^9, 3.468704294452379*^9}}, FontSize->18] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Slide 7", "Section", CellChangeTimes->{{3.468518759799735*^9, 3.468518763018742*^9}}, FontSize->18], Cell["KOCHEN-SPECKER THEOREM", "Text", CellChangeTimes->{{3.468508421671385*^9, 3.468508510140196*^9}, { 3.4685097435803967`*^9, 3.468509747512114*^9}, {3.468512284506689*^9, 3.46851230255075*^9}, {3.4685184276376534`*^9, 3.468518442539344*^9}, { 3.468518813362533*^9, 3.468518819597662*^9}}, FontSize->24, FontWeight->"Bold"], Cell[TextData[{ StyleBox["1967", "Subsection", FontSize->18], StyleBox[": Simon Kochen & Ernst Specker publish \"The problem of hidden \ variables in quantum mechanics,\" Journal of Mathematics & Mechanics ", FontSize->18], StyleBox["17", FontSize->18, FontWeight->"Bold"], StyleBox[", 59-87. The work had been completed in \ 1963-64\[LongDash]simultaneously with but in ignorance of Bell's work.\n", FontSize->18], "\n\n", Cell[BoxData[ GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJzsvfdaI0n2sDm7eyV7DTvT0+WrKIryBQWF995777333nvvPQgJkEAg773H leme+e33117AnsgQWVkSUFCmx3w9z/ucORlKpUT3jN4TkRGRrokh/3fIX/7y l//rL3/5P/6/v/zl/+xF+cn730jOLuH92WfIxtOzT8DJ6Ud7jk8+kFx4gg34 Uhjqe7+Hy65P/fLUP+Gyv516pv27vp/r/C1Hx+9Jjo8u5uT4w4Vc558Plffv P56cvQcsp2e0HZZvUKjD09f3Hz//9VcH4O7tp7duPbl1y+nvt5xu3Xv+zNmn a2SOqzIL1RaByijWmMVao0yt1xiPeELpOm17dX1jbWMTWN+krayt4xwacfsG bWtzi47ZYmzTt3cYO7vbu0wAEjhEjQzmFn0XgATntK0diIxt1vbOHkRohMhk HeztcwD2Ae/gkM/hCrk8EY8vBiCBQ0j4AgkGt+MWnkAI8IUiKtAiFEsEIrE9 8AJGJJIAYrEUY3MokchQo0QqlSvEcoVEoSSRKjQypVah1pMoNQYCo0prUmuM gEZrsgG3ky9pdWaM3nBEYLkYo8kGnd5Mcum7rrwCxmAyX4jOeAQYCIyGi8FX 1hLg86kYrsRoOgaubrkO+F0/gpN/CSbz6YXYn6knMJhPAb3FlsuuQ8VsOSMx EuCrYYznjRdiviFGy4cbcdl1Lvv+1G/+74D+/F+QDTrj8YVoz/+Po9GbL8Ly bUL/sXb7GaK88OI/UOg/SvQ3Ffpl4v5RQj89fX98egaYT05B6D6BIQ5PX4LQ 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Foundational physics has become a crowded field!!\n\nThe ", StyleBox["simplifications that result from appeal to the quantum physics of \ spin-one particles", FontWeight->"Bold"], " (see below!) were first noted in unpublished work (1969) by Richard \ Friedberg at Columbia University, according to Max Jammer, ", StyleBox["The Philosophy of Quantum Mechanics", FontSlant->"Italic"], " (1974), page 324." }], "Text", CellChangeTimes->{{3.468705576813466*^9, 3.468705659049259*^9}, { 3.468705712395707*^9, 3.468705730845852*^9}, {3.4687141448748817`*^9, 3.468714145713757*^9}}, FontSize->18] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Slide 8", "Section", CellChangeTimes->{{3.468519677878384*^9, 3.468519688188778*^9}}, FontSize->18], Cell["\<\ ASHER PERES' SIMPLIFIED VERSION OF THE KOCHEN-SPECKER NO-GO THEOREM\ \>", "Text", CellChangeTimes->{{3.468508421671385*^9, 3.468508510140196*^9}, { 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Zimba & R. Penrose, \"On Bell non-locality without probabilities: more \ curious geometry,\" Stud. Hist. Phil. Sci. ", StyleBox["24", FontWeight->"Bold"], ", 697, (1993). See also J. E. Massad & P. K. Aravind, \"The Penrose \ dodecahedron revisited,\" AJP ", StyleBox["67", FontWeight->"Bold"], ", 631 (1993). ", StyleBox["It was a Tom Wieting seminar based upon the latter paper that \ first brought Penrose's work to my attention", FontColor->RGBColor[0, 0, 1]], ".\n\nPenrose's theorem exploits properties of 40 rays that live in a \ certain\n 4-dimensional Hilbert space. 20 of those\[LongDash]which Penrose \ calls \"ordinary rays,\" refer to the spin-one-half states that result when \ the spin of a spin-3/2 particle is measured along one or another of the 20 \ directions defined by the vertices of a dodecahedron. 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And it has been shown by Conway/Kochen to \ render the contextual hidden variable hypothesis equally untenable (", StyleBox["at least for twinned spin-one particles, therefore generally?", FontColor->RGBColor[0, 0, 1]], "). Conway/Kochen argue that those two hypotheses exhaust the \ possibilities, that no mechanism for exercising hidden deterministic control \ of quantum processes survives. ", StyleBox["The quantum world has been shown to be ", FontColor->RGBColor[1, 0, 0]], StyleBox["indeterministic", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], ". " }], "Text", CellChangeTimes->{{3.468612485642701*^9, 3.468612722932589*^9}, { 3.468612764450263*^9, 3.468612791720603*^9}, {3.4686129297276173`*^9, 3.468612930887752*^9}, {3.468612963845743*^9, 3.4686130754154263`*^9}, 3.468628545746757*^9}, FontSize->18], Cell[TextData[{ "Therefore \"quantum systems do not know how they will respond to \ measurement until they have done so.\" Which echos Bohr's \"No quantum \ phenomenon is a phenomenon until it is a ", StyleBox["recorded", FontSlant->"Italic"], " phenomenon.\"\n\nAlice/Bob did not know which buttons they were going to \ press until\[LongDash]unforcedly/undeterministically\[LongDash]they did so. \ Which is what we mean when we say they acted from spontaneous exercise of \ free will. Conway & Kochen insist that ", StyleBox["for that same reason, and to that same extent, we must attribute \ \"free will\" to the particles themselves", FontColor->RGBColor[1, 0, 0]], ". Which is the upshot of their ", StyleBox["FREE WILL THEOREM", FontWeight->"Bold"], ".\n\n" }], "Text", CellChangeTimes->{{3.468613215608938*^9, 3.468613268235194*^9}, { 3.468613300308292*^9, 3.468613526955925*^9}, {3.468613645933421*^9, 3.468613650855505*^9}, {3.468615185551889*^9, 3.468615206127459*^9}, { 3.468628594511909*^9, 3.4686286537598248`*^9}}, FontSize->18], Cell["", "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Slide 20", "Section", CellChangeTimes->{{3.468628674174049*^9, 3.468628695442462*^9}}, FontSize->18], Cell["COMMENTARY", "Text", CellChangeTimes->{{3.468628715633997*^9, 3.468628717419159*^9}}, FontWeight->"Bold"], Cell["\<\ Conway & Kochen do not suppose particles to be sentient\[LongDash]they have \ detached \"free will\" from \"mind,\" and therefore from all that \ philosophers have had, over the centuries, to say about \"the free will \ problem.\" \ \>", "Text", CellChangeTimes->{{3.468628753976342*^9, 3.46862883807362*^9}, { 3.468709349019844*^9, 3.468709366091145*^9}, {3.468709398703545*^9, 3.468709425459499*^9}}, FontSize->18], Cell[TextData[{ "Is the traditionally troublesome concept of \"free will\" so \ well-understood that its use by physicists can serve to clarify understanding \ of (say) the quantum mechanical two-slit experiment? Or ", StyleBox["any", FontSlant->"Italic"], " quantum phenomenon? 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Whence the several flavors of \"compatibilism\":\ \>", "Text", CellChangeTimes->{{3.4687095363914223`*^9, 3.468709611278647*^9}, { 3.46870997499275*^9, 3.4687100064358892`*^9}, {3.46871005133926*^9, 3.468710069715789*^9}, {3.468710159354191*^9, 3.468710162709701*^9}, 3.46871040755413*^9}, FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Hyperlink", "[", RowBox[{ "\"\\"", ",", "\"\\""}], "]"}]], "Input", CellChangeTimes->{{3.468710109590108*^9, 3.468710142181387*^9}}, FontSize->16], Cell[BoxData[ TagBox[ ButtonBox[ PaneSelectorBox[{False->"\<\"Compatibilism\"\>", True-> StyleBox["\<\"Compatibilism\"\>", "HyperlinkActive"]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{"Hyperlink"}, BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], BaseStyle->"Hyperlink", ButtonData->{ URL["http://plato.stanford.edu/entries/compatibilism/"], None}, ButtonNote->"http://plato.stanford.edu/entries/compatibilism/"], Annotation[#, "http://plato.stanford.edu/entries/compatibilism/", "Hyperlink"]& ]], "Output", CellChangeTimes->{3.468710147492668*^9}, FontSize->16] }, Open ]], Cell["\<\ Such philosophers, having established that conceptual independence, would \ insist that indeterminism does not imply free will. One cannot, in \ particular, identify free will as a necessarily active agent in a random \ world.\ \>", "Text", CellChangeTimes->{{3.468710210672244*^9, 3.4687103712326393`*^9}}, FontSize->18], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.468709457664282*^9}, FontSize->18], Cell[TextData[{ "Conway & Kochen tacitly dismiss the possibility that Alice/Bob and their \ particles/equipment might be interlinked by ", StyleBox["tachyons", FontColor->RGBColor[0, 0, 1]], ". No problem if tachyons cannot convey information\[Ellipsis]as has been \ argued by those to assert the impossibility of \"tachyonic telephones\" \ (which would enable one to communicate/interact with one's past)." }], "Text", CellChangeTimes->{{3.468629125832596*^9, 3.4686293183285637`*^9}, { 3.4686293585255117`*^9, 3.46862937052509*^9}}, FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Hyperlink", "[", RowBox[{ "\"\\"", ",", "\"\\""}], "]"}]], "Input", CellChangeTimes->{{3.468690178400621*^9, 3.468690226942377*^9}}, FontSize->16], Cell[BoxData[ TagBox[ ButtonBox[ PaneSelectorBox[{False->"\<\"Tachyonic Telephones\"\>", True-> StyleBox["\<\"Tachyonic Telephones\"\>", "HyperlinkActive"]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{"Hyperlink"}, BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], BaseStyle->"Hyperlink", ButtonData->{ URL["http://en.wikipedia.org/wiki/Tachyonic_antitelephone"], None}, ButtonNote->"http://en.wikipedia.org/wiki/Tachyonic_antitelephone"], Annotation[#, "http://en.wikipedia.org/wiki/Tachyonic_antitelephone", "Hyperlink"]& ]], "Output", CellChangeTimes->{3.468690232880711*^9}, FontSize->16] }, Open ]], Cell[TextData[{ "One can imagine a world so deterministic that Alice/Bob are prevented from \ making the choices that would expose results inconsistent with determinism. \ Conway & Kochen dismiss this possibility on grounds that ", StyleBox["in such a conspiratorial world (where the free decisions of \ experimentalists are constrained) science is impossible", FontVariations->{"Underline"->True}], ".\n" }], "Text", CellChangeTimes->{{3.468629393658593*^9, 3.4686295330381193`*^9}, 3.468629634294273*^9, {3.468629684035624*^9, 3.46862987213941*^9}, 3.468713390608848*^9}, FontSize->18], Cell[TextData[{ "\nSince about 1990, Gerard 't Hooft has been cultivating a theory which \ purports to deduce quantum theory from ", StyleBox["a completely deterministic physics at the Planck scale", FontVariations->{"Underline"->True}], ". He claims that the Conway/Kochen argument fails because Alice/Bob \ actually do NOT have free will they imagine themselves to have\[Ellipsis]so \ therefore neither do particles." }], "Text", CellChangeTimes->{{3.46862990967795*^9, 3.468630167129558*^9}, { 3.468630201760935*^9, 3.4686302238072166`*^9}, {3.4686896532618513`*^9, 3.468689658101774*^9}, 3.468710430333459*^9}, FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Hyperlink", "[", RowBox[{ "\"\\"", ",", "\"\\""}], "]"}]], "Input", CellChangeTimes->{{3.468689318195628*^9, 3.4686893700069113`*^9}}, FontSize->16], Cell[BoxData[ TagBox[ ButtonBox[ PaneSelectorBox[{False->"\<\"Determinism Beneath Quantum Mechanics\"\>", True-> StyleBox["\<\"Determinism Beneath Quantum Mechanics\"\>", "HyperlinkActive"]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{"Hyperlink"}, BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], BaseStyle->"Hyperlink", ButtonData->{ URL["http://arxiv.org/pdf/quant-ph/0212095v1"], None}, ButtonNote->"http://arxiv.org/pdf/quant-ph/0212095v1"], Annotation[#, "http://arxiv.org/pdf/quant-ph/0212095v1", "Hyperlink"]& ]], "Output", CellChangeTimes->{3.468689376498337*^9}, FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Hyperlink", "[", RowBox[{ "\"\<'t Hooft's Opinion\>\"", ",", "\"\\""}], "]"}]], "Input", CellChangeTimes->{{3.468689545812913*^9, 3.4686896032620487`*^9}, { 3.468689669147788*^9, 3.468689669553234*^9}}, FontSize->16], Cell[BoxData[ TagBox[ ButtonBox[ PaneSelectorBox[{False->"\<\"'t Hooft's Opinion\"\>", True-> StyleBox["\<\"'t Hooft's Opinion\"\>", "HyperlinkActive"]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{"Hyperlink"}, BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], BaseStyle->"Hyperlink", ButtonData->{ URL["http://www.sciencenews.org/view/generic/id/35391/title/Math_Trek__\ Do_subatomic_particles_have_free_will%3F"], None}, ButtonNote-> "http://www.sciencenews.org/view/generic/id/35391/title/Math_Trek__Do_\ subatomic_particles_have_free_will%3F"], Annotation[#, "http://www.sciencenews.org/view/generic/id/35391/title/Math_Trek__Do_\ subatomic_particles_have_free_will%3F", "Hyperlink"]& ]], "Output", CellChangeTimes->{3.4686896122374*^9, 3.468689673715868*^9}, FontSize->16] }, Open ]], Cell[TextData[{ "Physicists sometimes allow themselves to say \"the system ", StyleBox["wants", FontSlant->"Italic"], " to \[Ellipsis]\", \"Nature might have been that way, or that other way, \ but ", StyleBox["chose", FontSlant->"Italic"], " to be this way\[Ellipsis]\". I try never to use, and always object to \ such anthropocentric language, but not so Conway (& Kochen), who carry it to \ a shameless extreme. It is my own suspicion that ", StyleBox["the laws of Nature cannot self-consistently be other than what \ they are, and that\[LongDash]contrary to the claims of some string theorists\ \[LongDash]no question of \"choice\" is involved", FontWeight->"Bold"], ". Interestingly, Conway and other mathematicians never assert that revealed \ ", StyleBox["mathematical", FontVariations->{"Underline"->True}], " facts \"might\" have been other than what they are found to be, and become \ nervous when mathematical arguments appeal to the Axiom of Choice.\n\n " }], "Text", CellChangeTimes->{{3.468630703727694*^9, 3.468630954328993*^9}, { 3.468630984812377*^9, 3.468631284010867*^9}, {3.468631321784552*^9, 3.46863135804809*^9}, {3.468710476390106*^9, 3.468710536873712*^9}, 3.468713376226843*^9}, FontSize->18], Cell["\<\ Conway and Kochen can properly claim to have driven yet another nail into the \ hidden variables coffin, though some people find loopholes in their argument, \ to which they take technical exception:\ \>", "Text", CellChangeTimes->{{3.468693194569788*^9, 3.468693275532959*^9}, { 3.468713014843843*^9, 3.4687130172602787`*^9}}, FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Hyperlink", "[", RowBox[{ "\"\\"", ",", "\"\\""}], "]"}]], "Input", CellChangeTimes->{{3.468693393005464*^9, 3.4686934229899073`*^9}, 3.468693460607472*^9}, FontSize->16], Cell[BoxData[ TagBox[ ButtonBox[ PaneSelectorBox[{False->"\<\"Tumulka's Critique\"\>", True-> StyleBox["\<\"Tumulka's Critique\"\>", "HyperlinkActive"]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{"Hyperlink"}, BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], BaseStyle->"Hyperlink", ButtonData->{ URL["http://arxiv.org/pdf/quant-ph/0611283"], None}, ButtonNote->"http://arxiv.org/pdf/quant-ph/0611283"], Annotation[#, "http://arxiv.org/pdf/quant-ph/0611283", "Hyperlink"]& ]], "Output", CellChangeTimes->{3.468693466877068*^9}, FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Hyperlink", "[", RowBox[{ "\"\\"", ",", "\"\\""}], "]"}]], "Input", CellChangeTimes->{{3.4686935251148977`*^9, 3.468693580351548*^9}}, FontSize->16], Cell[BoxData[ TagBox[ ButtonBox[ PaneSelectorBox[{ False->"\<\"What Does the Free Will Theorem Actually Prove?\"\>", True-> StyleBox["\<\"What Does the Free Will Theorem Actually Prove?\"\>", "HyperlinkActive"]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{"Hyperlink"}, BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], BaseStyle->"Hyperlink", ButtonData->{ URL["http://arxiv.org/abs/0905.4641"], None}, ButtonNote->"http://arxiv.org/abs/0905.4641"], Annotation[#, "http://arxiv.org/abs/0905.4641", "Hyperlink"]& ]], "Output", CellChangeTimes->{3.468693589197844*^9}, FontSize->16] }, Open ]], Cell[TextData[{ "Conway & Kuchen take their \"discovery\" very seriously, stress that it is \ after all a \"theorem\". Are reportedly writing a book-length account of the \ subject, to be published by Princeton UP. \n\n\nBut in my view ", StyleBox["all they have done is to decorate an old cake with some \ (objectionably anthropomorphic) rhetorical frosting", FontColor->RGBColor[1, 0, 0]], ". Conway's work has been marked by breathtaking originality, a calculated \ capacity to astound. But here he seems to have fallen victim to his own \ sophomoric enthusiasm. His mathematical innovations have taught us useful \ things we didn't already know. But his Free Will Theorem, though it is based \ upon sound/interesting physics, seems NOT to teach us \"useful things we \ didn't already know,\" and to have no useful consequence.\n\n\nMy guess is \ that the Conway/Kochen Free Will Theorem is destined to be kicked around by \ philosophers/kooks\[Ellipsis]and ignored by physicists\[LongDash]except, \ perhaps, in this regard:\n\n" }], "Text", CellChangeTimes->{{3.4686936628759203`*^9, 3.468693755197612*^9}, { 3.468693902633699*^9, 3.468693984535961*^9}, {3.468694058659343*^9, 3.4686941553016*^9}, {3.468694195851112*^9, 3.468694311716151*^9}, { 3.46869435243362*^9, 3.468694415425696*^9}, {3.4686952530442038`*^9, 3.468695253216367*^9}, {3.468696465493677*^9, 3.4686964722336807`*^9}, { 3.4687130457116423`*^9, 3.468713076923238*^9}, {3.4687131284243517`*^9, 3.4687131955813427`*^9}, {3.468713362483087*^9, 3.468713366875555*^9}}, FontSize->18], Cell["\<\ Experimentalists who based their work on Bohm/Ahranov used paired \ spin-one-half particles in a specialized state (the singlet state) to \ extablish violation of Bell's inequality\[LongDash]evidence that \ non-contextual hidden variables cannot exist. Kochen-Specker made no \ state-specializing assumption, and very recently (May 2009) experimentalists \ have provided state-independent verification \ \>", "Text", CellChangeTimes->{{3.468695447979225*^9, 3.4686954963326893`*^9}, { 3.468695547380733*^9, 3.468695599270959*^9}, {3.468695663475522*^9, 3.4686956992803593`*^9}, {3.4686959505769444`*^9, 3.468696002862114*^9}, { 3.46869604862754*^9, 3.4686961037600203`*^9}, {3.468696135950951*^9, 3.4686961788530493`*^9}, {3.46869638501919*^9, 3.4686964356014023`*^9}}, FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Hyperlink", "[", RowBox[{ "\"\\"", ",", "\"\\""}], "]"}]], "Input", CellChangeTimes->{{3.4686962711990223`*^9, 3.468696318886857*^9}, 3.468696357690439*^9}, FontSize->16], Cell[BoxData[ TagBox[ ButtonBox[ PaneSelectorBox[{ False->"\<\"State-independent Experimental Non-contextuality\"\>", True-> StyleBox["\<\"State-independent Experimental Non-contextuality\"\>", "HyperlinkActive"]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{"Hyperlink"}, BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], BaseStyle->"Hyperlink", ButtonData->{ URL["http://arxiv.org/abs/0904.1655"], None}, ButtonNote->"http://arxiv.org/abs/0904.1655"], Annotation[#, "http://arxiv.org/abs/0904.1655", "Hyperlink"]& ]], "Output", CellChangeTimes->{3.4686965774025183`*^9}, FontSize->16] }, Open ]], Cell["\<\ of the correctness of the Kochen-Specker conclusion that non-contextual \ hidden variables cannot account for the quantum mechanical facts. Perhaps a \ state-independent experimental dismissal of contextual hidden varables lies \ not too far in the future.\ \>", "Text", CellChangeTimes->{ 3.4686964419413*^9, {3.46869649157664*^9, 3.468696545669591*^9}}, FontSize->18], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.4686944564992237`*^9}, FontSize->18], Cell["The Conway-Kochen paper can be found at", "Text", CellChangeTimes->{{3.4686944766269503`*^9, 3.468694487393537*^9}}, FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Hyperlink", "[", RowBox[{ "\"\\"", ",", "\"\\""}], " ", "]"}]], "Input", CellChangeTimes->{{3.4686326725828857`*^9, 3.4686327147404633`*^9}}, FontSize->16], Cell[BoxData[ TagBox[ ButtonBox[ PaneSelectorBox[{False->"\<\"Free Will Theorem\"\>", True-> StyleBox["\<\"Free Will Theorem\"\>", "HyperlinkActive"]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{"Hyperlink"}, BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], BaseStyle->"Hyperlink", ButtonData->{ URL["http://arxiv.org/abs/quant-ph/0604079"], None}, ButtonNote->"http://arxiv.org/abs/quant-ph/0604079"], Annotation[#, "http://arxiv.org/abs/quant-ph/0604079", "Hyperlink"]& ]], "Output", CellChangeTimes->{3.468632718758497*^9}, FontSize->16] }, Open ]], Cell["\<\ For videos of six lectures on the subject, presented before non-specialist \ audiences at Princeton (23 March\[Dash]\[Dash]27 April 2009) by Conway \ himself, visit\ \>", "Text", CellChangeTimes->{ 3.468632118430087*^9, {3.468633335899568*^9, 3.468633428747102*^9}, 3.468633460399988*^9, {3.4686945335229692`*^9, 3.468694556966301*^9}}, FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Hyperlink", "[", RowBox[{ "\"\\"", ",", " ", "\"\\""}], "]"}]], "Input", CellChangeTimes->{{3.468633436248763*^9, 3.468633454412053*^9}, 3.4686336723098507`*^9}, FontSize->16], Cell[BoxData[ TagBox[ ButtonBox[ PaneSelectorBox[{False->"\<\"Conway Lectures\"\>", True-> StyleBox["\<\"Conway Lectures\"\>", "HyperlinkActive"]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{"Hyperlink"}, BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], BaseStyle->"Hyperlink", ButtonData->{ URL["http://www.princeton.edu/main/news/archive/S23/75/58A30/index.xml?\ section=featured"], None}, ButtonNote-> "http://www.princeton.edu/main/news/archive/S23/75/58A30/index.xml?\ section=featured"], Annotation[#, "http://www.princeton.edu/main/news/archive/S23/75/58A30/index.xml?section=\ featured", "Hyperlink"]& ]], "Output", CellChangeTimes->{3.4686336785619717`*^9}, FontSize->16] }, Open ]], Cell[TextData[{ "and click on ", StyleBox["viewing online", FontVariations->{"Underline"->True}], "." }], "Text", CellChangeTimes->{{3.468633687418666*^9, 3.468633703597731*^9}}, FontSize->18], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.4686946280886993`*^9, 3.468694628236493*^9}}, FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Hyperlink", "[", RowBox[{"\"\\"", ",", "\"\\""}], "]"}]], "Input", FontSize->16], Cell[BoxData[ TagBox[ ButtonBox[ PaneSelectorBox[{False->"\<\"Google\"\>", True-> StyleBox["\<\"Google\"\>", "HyperlinkActive"]}, Dynamic[ CurrentValue["MouseOver"]], BaseStyle->{"Hyperlink"}, BaselinePosition->Baseline, FrameMargins->0, ImageSize->Automatic], BaseStyle->"Hyperlink", ButtonData->{ URL["http://www.google.com/"], None}, ButtonNote->"http://www.google.com/"], Annotation[#, "http://www.google.com/", "Hyperlink"]& ]], "Output", CellChangeTimes->{3.468631370557928*^9}, FontSize->16] }, Open ]], Cell[TextData[{ "Key word: ", StyleBox["free will", FontWeight->"Bold"], " (\"free willy\" gives 3,910,000 hits, \"free will astrology\" gives \ 9,590,000 )\n\nKey word: ", StyleBox["free will theorem", FontWeight->"Bold"], " (10,300 hits, ~10,000 kooky blogs)" }], "Text", CellChangeTimes->{{3.4686314247342052`*^9, 3.46863144794424*^9}, { 3.468631490498435*^9, 3.468631537474156*^9}, {3.468631583850699*^9, 3.468631829079319*^9}, 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