A Harvard pole vaulter carries a pole that is just as long as a barn. He encounters a NJ farmer. Overhead view: Is this Nonsense? -- Space & Time are Relative

The farmer gathers 100 witnesses and this is what they see: The pole vaulter then bursts through the second door. The witnesses ALL agree: THE FARMER WON

? According to the Pole Vaulter, the Farmer cheats!! He shuts the front door before the back one! But, alas, not one witness agrees

A New Geometry for Space and Time Space, Time, Simultaneity, Energy, Momentum are all relative Yet, some things, like the speed of light, are absolutes (“invariants”)

ct x SPACE-TIME DIAGRAM WELCOME TO YOUR 4-DIMENSIONAL WORLD Bob’s viewpoint

ct x SPACE-TIME DIAGRAM an event a worldline light

y x SPACE-SPACE DIAGRAM a point

y x SPACE-SPACE DIAGRAM y’y’ x’x’ a point

ct SPACE-TIME DIAGRAM light x Bob’s viewpoint

ct SPACE-TIME DIAGRAM light ct ’ x x’x’ Alice’s viewpoint

ct SPACE-TIME DIAGRAM light ct ’ x x’x’

ct SPACE-TIME DIAGRAM ct ’ x x’x’ an event

ct SPACE-TIME DIAGRAM ct ’ x x’x’ an event

ct TIME & SIMULTANEITY ARE RELATIVE x Farmer’s viewpoint

ct ct ’ x x’x’ TIME & SIMULTANEITY ARE RELATIVE first second Pole vaulter’s viewpoint

Alice Bob people “Twin Paradox” Revisited v Alice Bob v The End ?

t x AT LAST: THE TWIN PARADOX Alice takes off Alice returns

t x SPACE-TIME DIAGRAM Alice takes off Alice returns Bob’s “worldline”

t x SPACE-TIME DIAGRAM Alice takes off Alice returns Alice’s “worldline” Kink: only Alice feels acceleration

y x SPACE-SPACE DIAGRAM Shortest distance between two points is a straight line

t x SPACE-TIME DIAGRAM Alice takes off Alice returns Alice’s “worldline” Longest time between two events is a straight line

E = mc 2 E =  m rest c 2