In the heliocentric inertial frame

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics

Relativity and Gravitation, Ch Minkowski spacetime, four-vectors and causal structure

Problem

S

, event

A

is a flare on the Sun's surface at

t_A = 0

x_A = 0

, and event

B

is a radio burst from a satellite at

t_B = 2.00\ \mathrm{s}

x_B = 9.00\times10^{8}\ \mathrm{m}

(same

y

and

z

). The frame

S'

moves at

v = 0.800c

along the common

+x

axis of

S

in the standard configuration. Gravity and the motion of the satellite are ignored. A student argues: "In

S

the flare comes first, so the flare triggered the burst. But in

S'

the burst comes first, so in that frame the effect precedes its cause and relativity is inconsistent." ((a)) Compute

\Delta s^2

for the pair

A

B

and classify the separation. ((b)) Compute

\Delta t' = t'_B - t'_A

S'

. ((c)) State in one or two sentences where the student's argument fails. Take

c = 2.998\times10^{8}\ \mathrm{m\,s^{-1}}

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