Time Dilation

Relative Time  Special relativity predicts that events seen as simultaneous by one observer are not simultaneous to an observer in motion.  The notion that the passage of time is constant for all observers must not exist.  The speed of light is the true constant of motion.

Light Clock  Einstein’s postulate is that the speed of light is constant in all inertial frames. Light to keep timeLight to keep time

Moving Clock  The light on the moving rocket takes a longer path. Rocket speed v Distance L’ Moving time  t’

Dilation  The apparent time is longer on the moving rocket.

Gamma Factor  The relation between the two times is known as the Lorentz factor.

Proper Time  The clock at rest with an observer keeps proper time. Always shortest timeAlways shortest time  Time dilation has been confirmed experimentally. Particle decayParticle decay

The Twin Paradox  Spedo travels to Planet X and returns. Planet X: 20 light years from earth Rocket speed: 0.95c  This is an example of a thought experiment.  Consider twins Gozlo and Spedo. Gozlo stays on Earth.

The Twins’ Perspectives Gozlo’s view  Spedo traveled 21 years to X and returned. So Gozlo has aged 42 years.  Spedo is time dilated with a slow clock and sees 13 years go by.  Spedo is younger than Gozlo when they meet again. Spedo’s view  Spedo thinks he was at rest.  Gozlo and the Earth raced away and then headed back.  The paradox – which twin is the traveler and which is really older?

Paradox Resolved  Relativity applies to reference frames moving at uniform speeds. Gozlo and the Earth are inertialGozlo and the Earth are inertial Spedo accelerates at X to turn aroundSpedo accelerates at X to turn around  Gozlo gets to make the time measurements. Gozlo proper time of 42 yearsGozlo proper time of 42 years Spedo proper time of 13 yearsSpedo proper time of 13 years  There is no true paradox since Spedo is not in an inertial frame. next