In the inertial frame of a space station a lamp at the origin fires at : call this event

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

In the inertial frame

S

of a space station a lamp at the origin fires at

t = 0

: call this event

O

. Three further events are recorded in

S

, all on the

x

axis:

A

t = 5.00\ \mu\mathrm{s}

x = 900\ \mathrm{m}

;

B

t = 2.00\ \mu\mathrm{s}

x = 900\ \mathrm{m}

;

C

t = 3.00\ \mu\mathrm{s}

x = 899.4\ \mathrm{m}

. On a spacetime diagram of

S

with

x

horizontal and

ct

vertical to the same scale, the light cone of

O

is the pair of lines

x = \pm ct

. Take

c = 2.998 \times 10^{8}\ \mathrm{m\,s^{-1}}

and give each answer in

\mathrm{m^2}

. ((a)) Compute

\Delta s^2

between

O

and

A

. ((b)) Compute

\Delta s^2

between

O

and

B

. ((c)) Compute

\Delta s^2

between

O

and

C

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