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Lecture5

# Lecture5 - Summary of Lecture 4 Spacetime interval Doppler...

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Lecture 5 Relativistic momentum • Relativistic energy: kinetic and “rest” energy Summary of Lecture 4 • Spacetime interval • Doppler effect • The “pole-and-barn paradox”: relativity of simultaneity • The “twin paradox”: asymmetric reference frames ! s ( ) 2 = c ! t ( ) 2 " ! x ( ) 2 + ! y ( ) 2 + ! z ( ) 2 { } f observed = ! 1 ± " ( ) f proper

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Newton’s 2nd Law & Special Relativity Special relativity: maximum speed = c. Newton’s 2nd Law ( F = m a ) implies that a force exerted on a mass will eventually result in arbitrarily large speed. Hence, we need to redefine our fundamental concepts of mass, momentum, & energy. Note that conservation laws of momentum & energy must be invariant as we transform from one inertial frame to another.
Momentum conservation Consider as usual two inertial frames S and S’ with relative velocity v along x axis. • In S , a mass A is moving along + y with speed u 0 . • In S’ , an identical mass B is moving along - y with speed u 0 .

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