special relativity

Time versus Velocity

relativity is a geometric effect.

animation

The relationship between your time and spacecraft time is simple. All you need is Pythagoras's theorem.

The following are a list of points to be mindful of when studying the animation.

  • A time interval of 1 second in your frame of reference is represented by the blue line.
  • The orange line is the time interval passed on the spacecraft for 1 of your seconds.
  • With a spacecraft speed of less than 0.1c the difference in the two times is very small.
  • Above 0.9c a small change in velocity results in a big variation in spacecraft time.
  • At 1.0c the time passed on the spacecraft is zero seconds for each of your seconds. Time has stopped on the spacecraft.

animation controls

There are two text boxes

spacecraft elapsed time : enter a time interval less than, or equal, to 1.0. The graph will update to show the corresponding spacecraft velocity.

velocity : enter a spacecraft velocity as a fraction of c. The graph will update to show the elapsed time in the spacecraft.

Origin of Triangle

The triangle originates from the photon path in the time dilation animation.

The triangle in the illustration is for a spacecraft velocity of 0.866c. The same as the example triangle above.

Scale the hypotenuse to 1 and the green length is the velocity of the spacecraft. The length of the orange line is the spacecraft time interval for 1 second of your time.

time dilation equation

Pythagoras to the rescue.

(tc)2 = (vt)2 + (τc)2

(tc)2 - (vt)2 = (τc)2

t2( c2 - v2) = (τc)2

t2( 1 - v2/c2) = τ2

t( 1 - v2/c2)½ = τ

t = τ/( 1 - v2/c2)½