In the inertial laboratory frame a flash of light is emitted at the origin at (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 laboratory frame

S

a flash of light is emitted at the origin at

t = 0

(event

E

) and travels in vacuum along the

+x

axis. It is reflected, with no delay, by a mirror at rest in

S

x = 6.00\ \mathrm{km}

(event

M

) and returns to the origin (event

R

), where a laboratory clock sits at rest at

x = 0

throughout. Draw the spacetime diagram of

S

with

x

horizontal and

ct

vertical, both in kilometres to the same scale, and mark the two light worldlines (slopes

+1

and

-1

) and the vertical worldline of the laboratory clock. Take

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

. ((a)) Read off the value of

ct

M

and at

R

, in kilometres. ((b)) Compute

\Delta s^2

between

E

and

M

. ((c)) Compute

\Delta s^2

between

E

and

R

, and the time between

E

and

R

read by the laboratory clock.

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