@maxdancona,
Quote:Delta T is the change in time for John and delta T_o is the change in time for Sally.
So 0.8 seconds for John = 1 second for Sally.
That is what you are misunderstanding.
You're hung up on the variable names and that's why you're not getting it? Ok. I'll fix that.
Let's try this again....
Do you know how the equation delta A = delta B/((1-v^2)^.5) is derived?
If you don't know, this is how...
Imagine 2 people, one of them is inside a spaceship, her name is Sally.
From floor to ceiling of her spaceship it is 0.8 light-seconds.
Imagine Sally is moving to the right at 0.6c.
The other person is named John, he is outside the spaceship.
Sally has light clock with the light source aimed straight up. Sally sees her light go straight up and bounce back and forth between the floor and the ceiling. According to John, because Sally is moving to the right the light forms the hypotenuse of a 3-4-5 right triangle with sides 0.6 light-seconds, height 0.8 light-seconds, and hypotenuse 1 light-second. By applying the Pythagorean theorem and some math we get delta A = delta B/((1-v^2)^.5) so in this specific case it is delta A = delta B/((1-.6^2)^.5).
Delta A is the change in time for John and delta B is the change in time for Sally.
So in this case 1 second for John = 0.8 seconds for Sally.
Now let's forget about that situation for a moment and concentrate on a different situation.
Imagine 2 people, one of them is inside a spaceship, her name is Sally.
From floor to ceiling of her spaceship it is 0.8 light-seconds.
Imagine Sally is moving to the right at 0.6c.
The other person is named John, he is outside the spaceship.
Sally has a flashlight inside her spaceship that is aimed so that it follows the same path upward and to the left as John saw in the first situation.
Sally sees the light form a 3-4-5 right triangle with the floor with sides 0.6 light seconds, 0.8 light seconds, and hypotenuse 1 light-second.
Because Sally is moving to the right at 0.6c and the leftward movement of the light is 0.6c, John sees the light bouncing straight up and down.
By applying the Pythagorean theorem and some math we get delta C = delta D/((1-v^2)^.5) so in this specific case it is delta C = delta D/((1-.6^2)^.5).
Delta D is the change in time for John and delta C is the change in time for Sally.
So 0.8 seconds for John = 1 second for Sally.
So why would moving clocks run fast or slow depending upon how Sally is holding her flashlight?
So did changing the variable names help you to understand?
I can change the variables to w,x,y, and z if you like.