(* 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[ 1034551, 19355] NotebookOptionsPosition[ 1020875, 18980] NotebookOutlinePosition[ 1022198, 19020] CellTagsIndexPosition[ 1022116, 19015] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Slide 1", "Section", CellChangeTimes->{3.566061659307358*^9}], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.566061670912799*^9, 3.566061671836248*^9}}], Cell["Introduction to the Quantum Theory of", "Text", CellChangeTimes->{{3.566060834630555*^9, 3.5660608368587093`*^9}, { 3.566061039401969*^9, 3.566061061330552*^9}}, TextAlignment->Center, FontSize->36], Cell["OPEN SYSTEMS", "Text", CellChangeTimes->{{3.5660610949915247`*^9, 3.5660611000375967`*^9}}, TextAlignment->Center, FontSize->72], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.566061766524674*^9, 3.566061766721857*^9}}], Cell["\<\ ÌÇÐÄÊÓƵ Physics Seminar 13 February 2013\ \>", "Text", CellChangeTimes->{{3.566061203636999*^9, 3.566061229802677*^9}}, TextAlignment->Center, FontSize->24], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.566061452873996*^9, 3.566061454716961*^9}}], Cell["\<\ Dedecated to the memory of Richard E. 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But recall \ \>", "Text", CellChangeTimes->{{3.566181913347701*^9, 3.566181986167465*^9}, { 3.5661820537501993`*^9, 3.566182202012781*^9}}, FontSize->24], Cell[TextData[{ "\[Bullet] ", StyleBox["NEWTON'S BUCKET", "Subsection", FontSize->18], ": Local inertia coordinated with \"fixed stars.\"\n\n\[Bullet] ", StyleBox["MACH'S PRINCIPLE", "Subsection", FontSize->18], ": Mass/inertia meaningless in one particle universe \[Ellipsis]conjectured \ to arise therefore by mysterious influence of remote \ masses\[Ellipsis]isotropy of mass/inertia implies effect is non-local, must \ be attributed to most remote masses. ", StyleBox["\"When the subway jerks, it's the fixed stars that throw you down.\ \"", FontSlant->"Italic"], "\n\nEinstein partly motivated by Mach's idea. Solution sought now in Higgs \ field? 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FontSlant->"Italic"], " von Neumann sketches a ", StyleBox["dynamical model", FontWeight->"Bold"], " of the hypothetically abrupt & irreversible projective measurement \ process. 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[I discussed \"Quantum measurement with imprefect devices\" \ at a Reed Physics seminar on 16 February 2000.] Here is a representation of \ what such a meter actually accomplishes: \ \>", "Text", CellChangeTimes->{{3.566496208130192*^9, 3.566496282065555*^9}, { 3.566496401891675*^9, 3.5664964561399508`*^9}, {3.566496601429138*^9, 3.566496616763466*^9}, 3.566496698464533*^9}, FontSize->18], Cell[BoxData[ GraphicsBox[{CircleBox[{0, 0}], LineBox[{{0, 0}, {1.2, 0}}], LineBox[{{0, 0}, {0, 1.2}}], {Thickness[Large], ArrowBox[NCache[{{0, 0}, { Rational[1, 2] 3^Rational[1, 2], Rational[1, 2]}}, {{0, 0}, { 0.8660254037844386, 0.5}}]]}, {RGBColor[1, 0, 0], Dashing[{Small, Small}], LineBox[NCache[{{Rational[1, 2] 3^Rational[1, 2], Rational[1, 2]}, { Rational[1, 2] 3^Rational[1, 2], 0}}, {{0.8660254037844386, 0.5}, { 0.8660254037844386, 0}}]]}, {RGBColor[0, 0, 1], Dashing[{Small, Small}], LineBox[NCache[{{Rational[1, 2] 3^Rational[1, 2], Rational[1, 2]}, { 0, Rational[1, 2]}}, {{0.8660254037844386, 0.5}, {0, 0.5}}]]}, {RGBColor[1, 0, 0], Thickness[Large], ArrowBox[{{0, 0}, {1, 0}}]}, {RGBColor[1, 0, 0], ArrowBox[NCache[{{0, 0}, { Cos[Rational[1, 50] Pi], Sin[Rational[1, 50] Pi]}}, {{0, 0}, { 0.9980267284282716, 0.06279051952931337}}]]}, {RGBColor[1, 0, 0], ArrowBox[NCache[{{0, 0}, { Cos[Rational[1, 50] Pi], -Sin[Rational[1, 50] Pi]}}, {{0, 0}, { 0.9980267284282716, -0.06279051952931337}}]]}, {RGBColor[0, 0, 1], Thickness[Large], ArrowBox[{{0, 0}, {0, 1}}]}, {RGBColor[0, 0, 1], ArrowBox[NCache[{{0, 0}, {-Sin[Rational[1, 50] Pi], Cos[Rational[1, 50] Pi]}}, {{0, 0}, {-0.06279051952931337, 0.9980267284282716}}]]}, {RGBColor[0, 0, 1], ArrowBox[NCache[{{0, 0}, { Sin[Rational[1, 50] Pi], Cos[Rational[1, 50] Pi]}}, {{0, 0}, { 0.06279051952931337, 0.9980267284282716}}]]}, InsetBox[ StyleBox["\<\"Measurement with Imperfect Meter\"\>", StripOnInput->False, FontSize->24], {0, 1.3}]}, ImageSize->{477., Automatic}]], "Output", CellChangeTimes->{ 3.5658173815282907`*^9, {3.565817413780546*^9, 3.565817436824066*^9}, { 3.565817703849813*^9, 3.5658177533169317`*^9}, {3.565894393446348*^9, 3.565894435920355*^9}, 3.56597513140772*^9}, TextAlignment->Center], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.566496736455346*^9}], Cell["\<\ The results of A-measurements will be ambiguous if the spectrum of \ \[DoubleStruckCapitalA] is degenerate. 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A. Rozema et al, \"Violation of Heisenberg's \ measurement-disturbance relationship by weak measurements,\" Phys. Rev. \ Letters ", StyleBox["109", FontWeight->"Bold"], ", 100404 -1. 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Y. She & H. Heffner, PR ", StyleBox["152", FontWeight->"Bold"], ", 1103 (1966)) that their results could be obtained from a maximal entropy \ principle. But otherwise, the Arthurs-Kelly paper\[LongDash]now recognized to \ be a classic\[LongDash]was almost totally neglected. Their results have now \ been reproduced by a great many alternative lines of argument." }], "Text", CellChangeTimes->{{3.566598055824479*^9, 3.566598075609907*^9}, { 3.5665981099362383`*^9, 3.566598210247954*^9}, {3.566598527219219*^9, 3.566598581397876*^9}, {3.566609260692614*^9, 3.566609337810575*^9}, { 3.5666093776259117`*^9, 3.5666093851271048`*^9}}, FontSize->24], Cell[CellGroupData[{ Cell["Slide 8", "Section", CellChangeTimes->{{3.56650575860753*^9, 3.566505776076726*^9}}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{3.566505785564724*^9}] }, Open ]], Cell[CellGroupData[{ Cell["Conclusion", "Title", CellChangeTimes->{{3.5665058013130913`*^9, 3.5665058032397213`*^9}}], Cell[TextData[{ "At some early point in my career I dismissed\[LongDash]perhaps too facilely\ \[LongDash]literature relating to foundational matters in physics as \"", StyleBox["so much inconclusive philosophical verbiage that could be safely \ ignored", FontVariations->{"Underline"->True}], ",\" a waste of time to pursue. That is no longer so. It was arguably ", StyleBox["John S. Bell who changed all of that, who rendered the \ foundational studies subject to explicit calculation and experiment", FontColor->RGBColor[0, 0, 1]], ". \n\nInsights have in recent decades been developed and are today being \ cultivated that lie beyond the reach of contemporary textbooks but that\ \[LongDash]after they have been distilled\[LongDash]will, I am convinced, be \ prominent in the quantum texts (and philosophical monographs) of the future. \ I speak of ", StyleBox["developments that have been inspired by recognition of the role \ that i", FontColor->RGBColor[0, 0, 1]], StyleBox["nformation-theoretic notions", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox[" are destined to play, by the expanding importance of ", FontColor->RGBColor[0, 0, 1]], StyleBox["entanglement physics", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox[", by the technical requirements of ", FontColor->RGBColor[0, 0, 1]], StyleBox["quantum computation", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], ". \n\nMy effort here has been to demonstrate that some of those \ developments (many of which have deep historical roots, however exotically \ strange they may at first sight appear) are already quite accessible, even to \ undergraduates. " }], "Text", CellChangeTimes->{{3.5665095622503242`*^9, 3.566509621027866*^9}, { 3.566509654980166*^9, 3.566509703549687*^9}, {3.566509740674127*^9, 3.566509755571827*^9}, {3.56650978572607*^9, 3.566509961054335*^9}, { 3.566509993836282*^9, 3.5665099985319853`*^9}, {3.566510038581978*^9, 3.56651004184595*^9}, {3.5665101657849607`*^9, 3.566510166222816*^9}, { 3.5665101972853403`*^9, 3.566510341198266*^9}, {3.566510414083856*^9, 3.566510446548595*^9}, {3.566510494452567*^9, 3.566510514215794*^9}, { 3.5665105464808903`*^9, 3.566510807156392*^9}, {3.566511615236742*^9, 3.5665116164401827`*^9}}, FontSize->24] }, Open ]], Cell[CellGroupData[{ Cell["Things to Read", "Title", CellChangeTimes->{{3.566505810737602*^9, 3.566505814896924*^9}}], Cell[TextData[{ "Heinz-Peter Breuer & Francesco Petruccione, ", StyleBox["The Theory of Open Quantum Systems", FontSlant->"Italic"], " (Oxford, 2006).\n\nStephen M. Barnett, ", StyleBox["Quantum Information", FontSlant->"Italic"], " (Oxford, 2009).\n\nMaximilian Schlosshauer, ", StyleBox["Decoherence and the Quantum-to-Classical Transition", FontSlant->"Italic"], " (Springer, 2008).\n\nDomenico Guilini, Erich Joos, Claus Kiefer, Joachim \ Kupsch, Ion-Olimpiu Stamatescu & Heinzx-Dieter Zeh, ", StyleBox["Decoherence and the Appearance of a Classical World in Quantum \ Theory", FontSlant->"Italic"], ", Springer (1996).\n\nChristopher Gerry & Peter Knight,", StyleBox[" Introductory Quantum Optics", FontSlant->"Italic"], " (Cambridge, 2005).\n\nMichael A. Nielsen & Isaac L. Chuang, ", StyleBox["Quantum Computation and Quantum Information", FontSlant->"Italic"], " (Cambridge, 2000).\n\nWojciech H. Zurek (editor), ", StyleBox["Complexity, Entropy and the Physics of Information", FontSlant->"Italic"], "; Volume VIII, Santa Fe Institute Studies in the Sciences of Complexity \ (Addison-Wesley, 1990), proceedings of a workshop held \n29 May-10 June 1989 \ to which many of the leading figures in the field made contributions.\n\n\ Wojciech H. Zurek, \"Decoherence and the transition from quantum to classical\ \[LongDash]", StyleBox["Revisited,", FontSlant->"Italic"], "\" Los Alamos Science, Number 27 (2002, available on the web).\n\nE. \ Arthurs & J. L. Kelly Jr, \"On the simultaneous measurement of a pair of \ conjugate observables,\" Bell System Tech. J. ", StyleBox["44", FontWeight->"Bold"], ", 725 (1965).\n\nN. A. Wheeler, \"Simultaneous measurement of noncommuting \ quantum observables\" (October, 2012); pdf file available by request.\n\nN. \ A. Wheeler, \"Harmonic oscillator\[LongDash]revisited: coherent states,\" \n\ (December, 2012); pdf file available by request.\n\nThose books and papers \ provide references to a vast and rapidly growing literature. Consult the web \ for lists of the publications by (for example) \n \[Bullet] Wojciech Zurek\n\ \[Bullet] William Wooters\n \[Bullet] Asher Peres\n \[Bullet] Reinhard \ Werner\n \[Bullet] Anton Zeilinger\n\n\n\n\n\n\n\n\n" }], "Text", CellChangeTimes->CompressedData[" 1:eJwLyk9STGVgYGACYjEQ7fhq0sSPrKrdIPqv+OI+ID2J+USYF4gWtls4AUTL L7V5BqI1vl1hANFGfnVdINoqjqEQRNubZHCBaH/7O2wgOqR7HQeIjp+3DWT+ pOTyh4vAdJ2HBYjOUqrtBNEF63lmgehqU5HLILqjvowPRE+Q+GgLoqeekQCr myv9HGzu4tXZaSD6xc/fv0D0t88qrUB6Mt/lvFUgWvB1lgOItpkUPh9EO7jv MgHRYUc2uYHoIscFTkB6StrBwEVg+priJxCdl3PODkQXhe4EmTOlLPLBUxDd tN87D0T3zjBUANETM9VKQPR03uXsIHqeQa4aiF7f/RTkrikbDvDogOitf7a8 AdG7znL8AgB027nd "], FontSize->24] }, Open ]] }, Open ]] }, ScreenStyleEnvironment->"Working", WindowSize->{868, 932}, WindowMargins->{{8, Automatic}, {Automatic, 11}}, FrontEndVersion->"7.0 for Mac OS X PowerPC (32-bit) (November 11, 2008)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline 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