The Metric Equation …putting time and space together.

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The Metric Equation …putting time and space together

Important ideas… Change in Time and Change in Spatial Location are inextricably linked by the metric equation: A moving clock (or one that has been moved) must run slower than any stay-at- home clock!

Spacetime intervals in 3 flavours… events connected by a spacelike interval cannot be causally connected

Proper time…

Gedanken Experiments The Spacetime Interval is invariant – all observers – even in different inertial frames – will agree to this! The metric equation tells us that spacetime is non-Euclidean. Crudely put: “ a longer world-line means shorter proper time” Photon clock applet Space time applet

Sample Questions… Your twin brother leaves for Vega (25 ly away) on your 21 st birthdays. He travels at 0.9c. How old will the two of you be when he arrives? –Draw a spacetime diagram illustrating this –Solve this using the definition of proper time