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What's been done
What's new
What needs to be done\
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Cell["\<\
It is an old dream (or perhaps more accurately, a recurring nightmare) to \
express laws of physics using quaternions.  In these web pages, quaternion \
operators were employed to express central laws of physics:  Newton's second \
law, the Maxwell equations, and the Klein-Gordon equation for relativistic \
quantum mechanics.  Applications of quaternions to special relativity were \
done in detail, with over 50 problems worked out explicitly.  Quaternions do \
not make problem solving easy.  Rather, they help unite the laws themselves.  \
Significantly, an analysis of the length of a quaternion interval if the \
origin is moved establishes a connection to the machinery of general \
relativity, the affine parameter.\
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One might suspect that the reason for the success claimed above is that \
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tensors of rank zero and one, and while used in a new way here, does anything \
genuinely novel appear?\
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Cell["\<\
I believe that a new very powerful idea drives this work, namely, that events \
represented as quaternion are a topological algebraic field.  This implies \
that any collection of events can be generated by an appropriate quaternion \
function.  Scalars and vectors mix under multiplication, so quaternions are a \
mixed representation.\
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A new view of relativistic quantum mechanics was outlined.  The Klein-Gordon \
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identity analogous to the Maxwell equations.  These additional identities are \
also valid by the conventional analysis, but they do not naturally arise, so \
the parallel to the Maxwell equations is less clear.\
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A new link to general relativity has been proposed which is slightly \
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changes, then the first term of the difference between the two event \
quaternions and the origin quaternions squared is similar to the square of \
the affine parameter of general relativity.  The only difference lies in the \
cross term.\
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Every event, every function, every operator used was a member of the field of \
quaternions.  This might strike some as a comic reliance on a solitary tool.  \
I prefer to think of it as a great democratic principle.  Physics is \
impressively democratic, with each photon or electron obeying the same \
collection of laws interchangeably.  The mathematics underlying the laws of \
physics should reflect this interchangeability.\
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Nothing presented was proven rigorously.  There were few references to the \
literature.  This body of work is more like a skeleton of work, a reflection \
of the author's semi-formal training and isolation from the professional \
physics community.  There is a need to flesh these ideas out only if there is \
the potential for new insights.  Although I appreciate the standard approach, \
I feel like I have gained new insight into why Maxwell's equations are \
necessary, have a new way to view relativistic quantum mechanics, and cling \
to a novel toehold on general relativity.  And since each of these is a \
quaternion, it becomes possible to mix and match them to create new areas of \
study.  I hope this work generates interest in the physics community.\
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More problems need to be solved.  My upcoming focus will be the Dirac \
function and Fourier analysis using quaternions.  If I can build these \
functions, it should be possible to approach problems in electromagnetism and \
quantum mechanics.  I won't be easy, it never is, but it might be elegant.  \
And maybe I'll dabble a little with curves...\
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    FontSize->14],
  
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    ImageMargins->{{38, Inherited}, {Inherited, 0}},
    FontFamily->"Courier",
    FontSize->14],
  
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    FontWeight->"Plain",
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    FontTracking->"Plain",
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->False,
    "Outline"->False,
    "Shadow"->False}],
  
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    FontSize->14],
  
  Cell[StyleData["CellLabel", "Condensed"],
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    FontSize->14],
  
  Cell[StyleData["CellLabel", "Printout"],
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    FontSize->14,
    FontColor->GrayLevel[0]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Formulas and Programming"]], "Section"],
  
  Cell[CellGroupData[{
  
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    CellHorizontalScrolling->True,
    ScriptLevel->1,
    SingleLetterItalics->True],
  
  Cell[StyleData["InlineFormula", "Presentation"],
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    LineSpacing->{1, 5}],
  
  Cell[StyleData["InlineFormula", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1}],
  
  Cell[StyleData["InlineFormula", "Printout"],
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    CellHorizontalScrolling->True,
    DefaultFormatType->DefaultInputFormatType,
    ScriptLevel->0,
    SingleLetterItalics->True,
    UnderoverscriptBoxOptions->{LimitsPositioning->True}],
  
  Cell[StyleData["DisplayFormula", "Presentation"],
    LineSpacing->{1, 5}],
  
  Cell[StyleData["DisplayFormula", "Condensed"],
    LineSpacing->{1, 1}],
  
  Cell[StyleData["DisplayFormula", "Printout"]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Styles for Headers and Footers"]], "Section"],
  
  Cell[StyleData["Header"],
    CellMargins->{{7, 0}, {4, 1}},
    Evaluatable->False,
    PageBreakWithin->Automatic,
    AspectRatioFixed->True,
    StyleMenuListing->None,
    FontFamily->"Times",
    FontSize->12,
    FontSlant->"Italic"],
  
  Cell[StyleData["Footer"],
    CellMargins->{{7, 0}, {0, 4}},
    Evaluatable->False,
    PageBreakWithin->Automatic,
    TextAlignment->Center,
    AspectRatioFixed->True,
    StyleMenuListing->None,
    FontFamily->"Times",
    FontSize->12,
    FontSlant->"Italic"],
  
  Cell[StyleData["PageNumber"],
    CellMargins->{{0, 0}, {4, 1}},
    StyleMenuListing->None,
    FontFamily->"Times",
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Palette Styles"]], "Section"],
  
  Cell[TextData[StyleBox[
  "The cells below define styles that define standard ButtonFunctions, for \
use in palette buttons."]], "Text"],
  
  Cell[StyleData["Paste"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
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          FrontEnd`InputNotebook[ ], #, After]}]&)}],
  
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    ButtonStyleMenuListing->Automatic,
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          FrontEnd`InputNotebook[ ], #, All], 
        SelectionEvaluate[ 
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    ButtonStyleMenuListing->Automatic,
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          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionMove[ 
          FrontEnd`InputNotebook[ ], All, Cell, 1], 
        FrontEnd`SelectionEvaluateCreateCell[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
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    ButtonStyleMenuListing->Automatic,
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          FrontEnd`InputNotebook[ ], All], 
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionEvaluate[ 
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  Cell[TextData[StyleBox[
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The \"Hyperlink\" style is for links within the same Notebook, or between \
Notebooks."]], "Text"],
  
  Cell[CellGroupData[{
  
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    ButtonStyleMenuListing->Automatic,
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    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
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    ButtonNote->ButtonData}],
  
  Cell[StyleData["Hyperlink", "Presentation"]],
  
  Cell[StyleData["Hyperlink", "Condensed"]],
  
  Cell[StyleData["Hyperlink", "Printout"],
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    FontVariations->{"Underline"->False}]
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  Cell[TextData[StyleBox[
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system."]], "Text"],
  
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    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
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  Cell[StyleData["MainBookLink", "Condensed"]],
  
  Cell[StyleData["MainBookLink", "Printout"],
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  }, Closed]],
  
  Cell[CellGroupData[{
  
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    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
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    ButtonFrame->"None"}],
  
  Cell[StyleData["AddOnsLink", "Presentation"]],
  
  Cell[StyleData["AddOnsLink", "Condensed"]],
  
  Cell[StyleData["AddOnLink", "Printout"],
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    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
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    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontFamily->"Courier",
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "RefGuideLink", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["RefGuideLink", "Presentation"]],
  
  Cell[StyleData["RefGuideLink", "Condensed"]],
  
  Cell[StyleData["RefGuideLink", "Printout"],
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    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["GettingStartedLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&),
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    ButtonFrame->"None"}],
  
  Cell[StyleData["GettingStartedLink", "Presentation"]],
  
  Cell[StyleData["GettingStartedLink", "Condensed"]],
  
  Cell[StyleData["GettingStartedLink", "Printout"],
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    FontVariations->{"Underline"->False}]
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  Cell[CellGroupData[{
  
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    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["OtherInformationLink", "Presentation"]],
  
  Cell[StyleData["OtherInformationLink", "Condensed"]],
  
  Cell[StyleData["OtherInformationLink", "Printout"],
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    FontVariations->{"Underline"->False}]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Placeholder Styles"]], "Section"],
  
  Cell[TextData[StyleBox[
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palette templates."]], "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Placeholder"],
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    Selectable->False,
    StyleBoxAutoDelete->True,
    Placeholder->True,
    StyleMenuListing->None],
  
  Cell[StyleData["Placeholder", "Presentation"]],
  
  Cell[StyleData["Placeholder", "Condensed"]],
  
  Cell[StyleData["Placeholder", "Printout"]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["SelectionPlaceholder"],
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    Selectable->False,
    StyleBoxAutoDelete->True,
    Placeholder->Primary,
    StyleMenuListing->None,
    DrawHighlighted->True],
  
  Cell[StyleData["SelectionPlaceholder", "Presentation"]],
  
  Cell[StyleData["SelectionPlaceholder", "Condensed"]],
  
  Cell[StyleData["SelectionPlaceholder", "Printout"]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["FormatType Styles"]], "Section"],
  
  Cell[TextData[StyleBox[
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cells.  If a cell's FormatType matches the name of one of the styles defined \
below, then that style is applied between the cell's style and its own \
options."]], "Text"],
  
  Cell[StyleData["CellExpression"],
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    CellMargins->{{6, Inherited}, {Inherited, Inherited}},
    ShowCellLabel->False,
    ShowSpecialCharacters->False,
    AllowInlineCells->False,
    AutoItalicWords->{},
    StyleMenuListing->None,
    FontFamily->"Courier",
    Background->GrayLevel[1]],
  
  Cell[StyleData["InputForm"],
    AllowInlineCells->False,
    StyleMenuListing->None,
    FontFamily->"Courier"],
  
  Cell[StyleData["OutputForm"],
    PageWidth->Infinity,
    TextAlignment->Left,
    LineSpacing->{1, -5},
    StyleMenuListing->None,
    FontFamily->"Courier"],
  
  Cell[StyleData["StandardForm"],
    LineSpacing->{1.25, 0},
    StyleMenuListing->None,
    FontFamily->"Courier"],
  
  Cell[StyleData["TraditionalForm"],
    LineSpacing->{1.25, 0},
    SingleLetterItalics->True,
    TraditionalFunctionNotation->True,
    DelimiterMatching->None,
    StyleMenuListing->None],
  
  Cell[TextData[StyleBox[
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within another."]], "Text"],
  
  Cell[StyleData["InlineCell"],
    TextAlignment->Left,
    ScriptLevel->1,
    StyleMenuListing->None],
  
  Cell[StyleData["InlineCellEditing"],
    StyleMenuListing->None,
    Background->RGBColor[1, 0.749996, 0.8]]
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  }, Open  ]]
  }]
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