In the laboratory frame

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

The Geometry of Gravity, Ch Minkowski spacetime and relativistic dynamics, completed

Problem

In the laboratory frame, a detector fires at event

A

, at

(t,x) = (0, 0)

, and a second detector fires at event

B

, at

(t,x) = (2.0\ \mu\mathrm{s},\ 500\ \mathrm{m})

, both along the

x

-axis. Someone argues: "observers can be boosted arbitrarily close to

c

, so a fast enough observer, say at

v = 0.995c

, will always find some pair of events whose time order is reversed relative to the laboratory, including this one." ((a)) Classify the separation between

A

and

B

from the sign of the invariant interval. ((b)) Compute the time interval

\Delta t'

between the two events as measured by an observer moving at

v = 0.995c

along

x

relative to the laboratory, and use it to show this claim is wrong for this pair. ((c)) State, in one sentence, why no boost below

c

can reverse the order of

A

and

B

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