bei48482_FM

This expression for xwill be the same as that given by Eq. (1.38), namely, xct,

provided that the quantity in the brackets equals 1. Therefore

 1

and

k (1.40)

Finally we put this value of kin Eqs. (1.36) and (1.40). Now we have the complete

transformation of measurements of an event made in Sto the corresponding meas-

urements made in S :

x    (1.41)

xt



 1 ^2 c^2

Lorentz

transformation

1



 1 ^2 c^2

1 



c





1 

k

1

 2  (^1) 
c

40 Appendix to Chapter 1
Each observer detects
light waves spreading
out from own boat
S′
v
S
S′
S
S′
S
Pattern of ripples
from stone dropped
in water
Each observer sees pattern
spreading from boat S
S′
v
S
S′
S
S′
S
(a) Light emitted by flare
(b)
Figure 1.23(a) Inertial frame S is a boat moving at speed in the xdirection relative to another
boat, which is the inertial frame S. When tt 0 0, S is next to S, and xx 0 0. At this moment
a flare is fired from one of the boats. An observer on boat Sdetects light waves spreading out at speed
cfrom his boat. An observer on boat S also detects light waves spreading out at speed cfrom her
boat, even though S is moving to the right relative to S. (b) If instead a stone were dropped in the
water at tt 0 0, the observers would find a pattern of ripples spreading out around Sat different
speeds relative to their boats. The difference between (a) and (b) is that water, in which the ripples
move, is itself a frame of reference whereas space, in which light moves, is not.
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