P^2+Σ2P

PN is the space of real null rays in Minkowski space . PT is the projective twistor space. Z is a twistor, and Z2=Z3=0 You see Penrose tiling .

Minkowski space is based on Lorentz transformation . w = i ct This is imaginary time. You can't exceed the speed of light, so you must be inside of red lines. Future ← Past →

You move from S(x,y,z) to S'(x',y',z') by uniform linear motion (v) on x. This is called Galilean transformation. c is the speed of light. This is S'. You see that the speed of light should be stable, so S' is the same. You know Galilean transformation. ∴ Then you see S. ∴ A=E ∴ You know Lorentz factor .

When you move, your light clock is slower about T times. This is called Lorentz factor. c is the speed of light. 2a/c=1 This is the light clock, so you always have 1 second. When you move from A to C, your light clock move slower. T=2L/c T is time, and c is the speed of light. You see Pythagorean theorem . ∴ You see 2a=c from the light clock. This is called Lorentz factor.