From Quantum Weirdness to Spacetime Weirdness Relativity ETHER

From Quantum Weirdness to Space-time Weirdness Relativity

ETHER?

Light travels at the same speed (thru vacuum) no matter what direction you move

Maxwell’s Equations (1873) 1831 -1879

A B • Alice is in the Dinky. Bob is by the side of the tracks. • The Dinky has velocity v. AB = 5 m/s to the right. • Alice, travelling in the Dinky, throws the ball with velocity v. A = 5 m/s relative to herself.

A B 12: 00 TIMEX 0 5 10

A B 0 0 5 5 10 12: 00: 01 TIMEX • Alice, standing on the train, sees the ball move 5 m in one sec • Bob, standing on the ground next to the tracks, sees the Alice move 5 m and the ball move 5 m ahead of her • So Bob see balls move 10 m in one second, or 10 m/s VELOCITIES ADD

Imaginary speed-of-light measurement device. incoming pulse of light ruler 0 stopwatch 5 00: 00 ME AC light detectors

flashlight A 5 m/s B A flashlight in the train makes a pulse of light. Alice (in the train) measures light’s speed to be 300, 000 m/s relative to her. Bob (standing still) measures the same pulse of light. What does he get? 300, 000 m/s + 5 m/s = 300, 005 m/s Or so says Newton… Maxwell’s equations: No! speed should be the same.

Special Relativity If the speed of light is the same, then the clocks and rulers used to measure velocities must measure different times and distances!

mirror d mirror Alice is now in a spaceship. Two mirrors are separated by distance d. Time for a pulse of light to go from floor to ceiling and back is 2 d t. A = c

v d • Bob is outside the spaceship, which moves by with speed v. • He sees the light pulse take the path shown above, which is longer than the path seen by Alice. • Einstein/Maxwell: Light moves at same speed; but the clock runs slow, according to Bob’s watch

v d d v t. B/2 L = [ d 2 + (v t. B/2)2]1/2 t. B = 2 L/c = 2 [ d 2 + (v t. B/2)2]1/2 /c t. B 2 = 4 [ d 2 + (v t. B/2)2]/c 2 t. B [1 2 –(v/c)2] =4 d 2 /c 2 t. A t. B = 2 d /c 1 –(v/c)2

Time Dilation time in frame where clock moves (Bob) t. B = t. A = Lorentz factor time in frame where clock is at rest (Alice) 1 2 v 1 - 2 c (lower case greek letter gamma) Note: is always 1, so time measured in rest frame of clock is less than for any other frame