GraphingCalculator 3.5;
Window 47 2 643 782;
PaneDivider 263;
SignificantDigits 14;
FontSizes 18 14 10;
BackgroundType 0;
SliderControlValue 33;
2D.BottomLeft -1.71875 -2.9375;
2D.Axes 0;
2D.GraphPaper 0;
Text "Time dilation – light clock.

Version 0.3, 1-29-09
To do:
(i) Dots as wiggly photons?
(ii) Continue photon path for moving ship


Speed of light";
Color 7;
MathPaneSlider 4;
Expr c=slider([0,10,40]);
Text "Separation of light clock mirrors; length of mirrors; thickness of mirrors";
Color 2;
MathPaneSlider 200;
Expr D=slider([0,1]);
Color 3;
MathPaneSlider 107;
Expr L=slider([0,1]);
Color 2;
MathPaneSlider 62;
Expr d=slider([0,0.1]);
Text "Fraction of the speed of light at which the ship (frame P) travels relative to stationary observers (frame O).";
Color 5;
MathPaneSlider 22;
Expr f=slider([0,1,40]);
Text "Speed of ship (frame P) relative to frame O; Lorentz factor.";
Color 6;
Expr V=c*f,g=1/sqrt(1-V^2/c^2);
Text "Horizontal and vertical dimensions of ship; exponent";
Color 4;
MathPaneSlider 96;
Expr a=slider([0,1]);
Color 4;
MathPaneSlider 200;
Expr b=slider([0,1]);
Color 5;
Expr m=6;
Text "Basis vectors";
Expr I=vector(1,0),J=vector(0,1);
Text "Origin of frame O; origin of frame P";
Color 3;
Expr O=vector(0,0),P=O+n*V*I;
Text "Frame with origin O; ship at rest.";
Color 17;
Expr O;
Color 17;
Expr O,I;
Color 17;
Expr O,J;
Color 7;
Expr [x/(D+a)]^m+[y/b]^m<1;
Text "Frame with origin P; ship in motion.";
Color 17;
Expr P;
Color 17;
Expr P,P+I;
Color 17;
Expr P,P+J;
Color 17;
Expr [(x-(n*V))/(D+a)]^m+[y/b]^m<1;
Text "Light clock mirrors in rest frame of ship (O)";
Color 8;
Expr (D-d)/2<abs(y)<(D+d)/2,-L/2<x<L/2;
Text "Time between ticks in rest frame of clock (proper time):";
Color 2;
Expr T=2*D/c;
Text "Bouncing light signal and its path.   (Note 2-D points won't accept conditions [:-(].)";
Color 2;
Expr [x+d/2]^2+[y-[c*mod([n,T])-D/2]]^2<d^2,0<mod([n,T])<T/2;
Color 2;
Expr [x-d/2]^2+[y-[-(c*mod([n,T]))+3*D/2]]^2<d^2,T/2<mod([n,T])<T;
Color 17;
Expr x=-d/2,-D/2<y<min([c*n-D/2,D/2]);
Color 17;
Expr x=d/2,D/2>y>max([3*D/2-(c*n),-D/2]);
Text "Mirrors in moving ship:";
Color 17;
Expr (D-d)/2<abs(y)<(D+d)/2,-L/2<x-(n*V)<L/2;
Color 17;
Expr (D-d)/2<abs(y)<(D+d)/2,-L/2<x<n*V;
Text "Time between ticks in frame O watching ship (clock) fly by at speed V (this is time dilation)";
Color 7;
Expr T_O=g*T;
Text "Light signal in moving ship.   [Note that light moves at speed c along the diagonal; c_x = V, c_y = c/g; the length of the horizontal segment of the triangle is VTO/2=gDV/c; and the length of the diagonal segment (the path of the light) is cTO/2=gD.]";
Color 17;
Expr [x+d/2-(V*n)]^2+[y-[c/g*mod([n,T_O])-D/2]]^2<d^2,0<mod([n,T_O])<T_O/2;
Color 17;
Expr [x-d/2-(V*n)]^2+[y-[-(c/g*mod([n,T_O]))+3*D/2]]^2<d^2,T_O/2<mod([n,T_O])<T_O;
Color 17;
Expr y=c/(g*V)*x-D/2,0<x<min([V*n,g*D*V/c]);
Color 17;
Expr y=-(c/(g*V)*x)+3*D/2,g*D*V/c<x<min([V*n,2*g*D*V/c]);
Text "Note if you show both frames at once you can see directly that the moving clock ""runs slow"" – TO > T (period is longest in rest frame). ";
Text "


<size=14>Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>";