Time dilation visualized with light clocks

Time dilation visualized with light clocks.
Photon clocks revealing path langth on stationary and moving reference frame.

[vesuvandoppelganger]

It is possible to derive 2 contradictory time dilation equations. Imagine that Sally is in a spaceship and has reflective mirrors on floor and ceiling of her ship and she is moving to the right and is aiming a flashlight straight up and down so that Sally sees the light moving straight up and down and John is outside the spaceship and sees the light forming a triangle with the floor of the spaceship. Now imagine that Sally is aiming a flashlight upwards and towards the left while the spaceship moves to the right. Now the situation is exactly reversed. Sally sees the light forming a triangle with the floor and John sees the light bouncing straight up and down. Here's the details...
Sally is in a moving spaceship. John is outside the spaceship. Sally is moving to the right at .6c. The height of her spaceship is .8 light-seconds. If Sally has a flashlight with the light bouncing straight up and down the light will make a 3-4-5 right triangle from the viewpoint of John. If the change in time for Sally is delta T_o and the change in time for John is delta T then the following equation can be derived:

delta T = delta T_o/((1-.6^2)^.5)

Now Sally has a flashlight but this time she is holding the flashlight at an angle of 53.13 degrees above the horizontal and pointed to the left. Now the leftward movement of the light exactly matches the rightward movement of the spaceship from John's viewpoint. Now the light is bouncing straight up and down from the viewpoint of John and the light is making a 3-4-5 right triangle from viewpoint of Sally. If the change in time for Sally is delta T_o and the change in time for John is delta T then the following equation can be derived:

delta T_o = delta T/((1-.6^2)^.5)

The 2 equations are in direct contradiction to each other.

[franzscheerer]

So schwer ist das eigentlich nicht zu verstehen. Im Raumschiff ist der Lichtweg (auf und ab) kürzer als der Zickzack-Weg. Wenn wir auf der Erde tatsächlich die gleiche Lichtgeschwindigkeit messen bleibt nur eine Erklärung: Die bewegte Uhr geht langsamer.

Etwas müssen wir noch anmerken. Der Abstand der Spiegel senkrecht zur Bewegung ist für beide Beobachter gleich. Dies muss so sein, weil beide Beobachter sich nach dem Relativitätsprinzip mit gleichem Recht als ruhend betrachten dürfen. Dies ist aber nicht so selbstverständlich, denn Strecken in Richtung der Bewegung sind aus Sicht des Raumfahrers kürzer, denn wenn eine Sekunde kürzer ist (zeitlich), dann ist auch eine Lichtsekunde gemessen in Richtung der Relativgeschwindigkeit kürzer.

[ibrenecario]

The light clock hight is not equal size ?! wtf.

[sadev]

its a fun thought experiment but its actually wrong.
now her is the dilemma. if you have 2 mirrors perpendicuar to each other in perfection so the light keeps bouncing inn a straight line.
if its standing still the light bounces between the mirrors (theoreticly as mirrors are not perfect).
einsteins mirror clock then moves and the animation shows the light keeps between the mirrors traveling a longer distance.
in reality if such a clock was possible. when you move the mirror the light should keep bouncing in the same location while you slide the mirrors sideways untill the light isnt in the center anymore and the mirrors move out of the lightbeam.
there is no way a light beam would follow the center of the 2 mirrors. the mirror would just slide out of the way and the beam fies of into infinity.
the only way the light moves with the mirrors as they travel is if the mirror would be slightly adjusted to direct the light ahead to where the opposing mirror will be next time its hit