<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field>

<Text-field style="Heading 1" layout="Heading 1">Time Dilation and Contraction Formulas</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Box at rest</Text-field>

We know that

Distance = Speed * Time;

L0kpRGlzdGFuY2VHNiIqJkkmU3BlZWRHRiQiIiJJJVRpbWVHRiRGJw==

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

Light path denoted by dashed yellow line, and L denote the Length.

In This Figure ( Box is shown in a reference frame where it's at rest) You

Will Notice That Light Goes A Round-Trip 2L Between Source, Bouncing

Off The Mirror , And Returning To The Source .

If We Apply Distance = Speed * Time Equation To Obtain The Time (Speed Of Light) We Get:\342\200\262

R1 := (2 * L = C * Tprime);

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkjUjFHRiYvLCQqJiIiIyIiIkkiTEdGJkYwRjAqJjYnSTlzcGVlZF9vZl9saWdodF9pbl92YWN1dW1HUUtDOlxQcm9ncmFtfkZpbGVzXE1hcGxlfjEwL2xpYlxzY2FuZHNlYS5tbGFGJi9JJ3N5bWJvbEclKnByb3RlY3RlZEdJImNHRjUvSSZ2YWx1ZUdGJSIqZUN6KkgvSSx1bmNlcnRhaW50eUdGJiIiIS9JJnVuaXRzR0YmKiZJIm1HRjVGMEkic0dGNSEiIkYwSSdUcHJpbWVHRiZGMDcjRiw=

Where (the time in this reference frame called t' (Tprime), GetConstant (c) = Speed Of Light ).

Dividing both sides of R1 by C:

R2 := Tprime = 2*L / C;

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkjUjJHRiYvSSdUcHJpbWVHRiYsJCooIiIjIiIiSSJMR0YmRjE2J0k5c3BlZWRfb2ZfbGlnaHRfaW5fdmFjdXVtR1FLQzpcUHJvZ3JhbX5GaWxlc1xNYXBsZX4xMC9saWJcc2NhbmRzZWEubWxhRiYvSSdzeW1ib2xHJSpwcm90ZWN0ZWRHSSJjR0Y1L0kmdmFsdWVHRiUiKmVDeipIL0ksdW5jZXJ0YWludHlHRiYiIiEvSSZ1bml0c0dGJiomSSJtR0Y1RjFJInNHRjUhIiJGRUYxNyNGLA==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 2" layout="Heading 2">Box is moving</Text-field>

"Now let's go illustrate the frame in which the box is moving at speed v, and we're calling

t the time between departure and return of the light flash.. So distance = Speed * Time tells

us that the distance the box travels is just vt. While the box goes half this distance, the light

itself takes the diagonal path up to the mirror, where the long of this diagonal is the hypotenuse

of a right triangle with sides 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The pythagorean theorem then gives it's length:

x1 := sqrt(((1/2*v*T)^2)+(L^2));

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkjeDFHRiYsJComIyIiIiIiI0YvKSwmKiYpSSJ2R0YmRjBGLylJIlRHRiZGMEYvRi8qJiIiJUYvKUkiTEdGJkYwRi9GL0YuRi9GLzcjRiw=

The total light path is twice this distance, the time the light takes is T, speed of light is C therefore:

x2 := (2 * x1 = C*T);

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkjeDJHRiYvKiQpLCYqJilJInZHRiYiIiMiIiIpSSJUR0YmRjNGNEY0KiYiIiVGNClJIkxHRiZGM0Y0RjQjRjRGM0Y0KiZJIkNHRiZGNEY2RjQ3I0Ys

Now we want to know the timt T, because it's inside the square root, we need to square both sides:

x3 := (2 * x1)^2 = (C * T)^2;

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkjeDNHRiYvLCYqJilJInZHRiYiIiMiIiIpSSJUR0YmRjFGMkYyKiYiIiVGMilJIkxHRiZGMUYyRjIqJilJIkNHRiZGMUYyRjNGMjcjRiw=

And now by subtractingQyQqJilJInZHNiIiIiMiIiIpSSJUR0YmRidGKEYo from both sides we get:

x4 := (x3-((v^2)*(T^2)));

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkjeDRHRiYvLCQqJiIiJSIiIilJIkxHRiYiIiNGMEYwLCYqJilJIkNHRiZGM0YwKUkiVEdGJkYzRjBGMComKUkidkdGJkYzRjBGOEYwISIiNyNGLA==

Final step: divide both sides by QyQqJClJImNHNiIiIiMiIiJGKA==, and then squared both side:

x5 := (x4)/(C^2);

KiQpSSJjRzYiIiIjIiIi

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkjeDVHRiYvLCQqKCIiJSIiIilJIkNHRiYiIiMhIiIpSSJMR0YmRjNGMEYwKiZGMUY0LCYqJkYxRjApSSJUR0YmRjNGMEYwKiYpSSJ2R0YmRjNGMEY6RjBGNEYwNyNGLA==

Partitionized the x5 statement into two section: x6 := LCQqKCIiJSIiIilJIkxHNiIiIiNGJSlJIkNHRihGKSEiIkYl and x7 := KiYsJiomKUkiQ0c2IiIiIyIiIilJIlRHRidGKEYpRikqJilJInZHRidGKEYpRipGKSEiIkYpRiVGLw==

x6 := sqrt(4*L^2/C^2);

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkjeDZHRiYsJComIiIjIiIiKSomKUkiQ0dGJkYuISIiKUkiTEdGJkYuRi8jRi9GLkYvRi83I0Ys

x7 := sqrt((C^2*T^2-v^2*T^2)/C^2);

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkjeDdHRiYqJCkqJilJIkNHRiYiIiMhIiIsJiomRi8iIiIpSSJUR0YmRjFGNUY1KiYpSSJ2R0YmRjFGNUY2RjVGMkY1I0Y1RjFGNTcjRiw=

x8 := simplify(x6 = x7);

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkjeDhHRiYvLCQqJiIiIyIiIikqJilJIkNHRiZGLyEiIilJIkxHRiZGL0YwI0YwRi9GMEYwKiQpLCQqKClJIlRHRiZGL0YwLCYqJEYzRjBGNSokKUkidkdGJkYvRjBGMEYwRjNGNUY1RjhGMDcjRiw=

x9 := ((2*L/C) = (T*sqrt(1-(v^2)/(C^2))));

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkjeDlHRiYvLCQqKCIiIyIiIkkiQ0dGJiEiIkkiTEdGJkYwRjAqJkkiVEdGJkYwKSwmRjBGMComKUkidkdGJkYvRjApRjFGL0YyRjIjRjBGL0YwNyNGLA==

And we have LCQqKCIiIyIiIkkiTEc2IkYlSSJDR0YnISIiRiU== SSdUcHJpbWVHNiI=in the Box at rest section \342\210\264

x10 := ((Tprime) = (T*sqrt(1-(v^2)/(C^2))));

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkkkeDEwR0YmL0knVHByaW1lR0YmKiZJIlRHRiYiIiIpLCZGMEYwKiYpSSJ2R0YmIiIjRjApSSJDR0YmRjYhIiJGOSNGMEY2RjA3I0Ys

plot3d(T * sqrt(1-v^2) , T=1..15, v=0.1..1, axes=BOXED, lightmodel=light1,title="A Surface Plot" );

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