1. Part 2: Time Dilation

2. Time Dilation
In the Train (Proper Time)
Outside the train

3. Time Dilation
Light travels further when viewed outside the train than inside.
The velocity of light is the same in all reference frames.
Therefore if the speed of light is a constant then time and space are not.
To a stationary observer, a moving clock runs slower than a stationary clock. This is time dilation.

4. Time Dilation 𝑡= 𝑡 0 1− 𝑣 2 𝑐 2 =𝛾 𝑡 0
𝑡= 𝑡 − 𝑣 2 𝑐 2 =𝛾 𝑡 0
t = dilated time (measured with two synchronized clocks) to = proper time (measured with a single clock at rest) v = speed of the moving reference frame c = speed of light in a vacuum

5. Example
A certain isotope has a half-life of 5.0 s. What will its new half-life be if it is fired into a particle accelerator and reaches a speed of 0.85c?

6. The Twin Paradox
You and your identical twin are 20 years old. Your twin boards a spaceship and travels to the far reaches of the galaxy close to the speed of light while you stay behind. Sixty years go by on Earth when your twin’s spaceship finally returns home and, due to time dilation, has only aged about 10 years. But was the spaceship moving at close to the speed of light and the earth stationary, or was the spaceship stationary and the earth moving close to the speed of light? Should the space traveller be younger then? No, the earth dweller (in an inertial frame) was not subject to the same forces as was the space traveller and can use special relativity to make predictions while the space traveller cannot.