bei48482_FM

The Lorentz Transformation 45

t   1 

according to Eq. (1.44), while the flare at x 2 and t 0 appears at the time

t   2 

Hence two events that occur simultaneously to one observer are separated by a time

interval of

t   2 t    1 

to an observer moving at the speed relative to the other observer. Who is right? The

question is, of course, meaningless: both observers are “right” since each simply meas-

ures what he or she sees.

Because simultaneity is a relative concept and not an absolute one, physical theo-

ries that require simultaneity in events at different locations cannot be valid. For in-

stance, saying that total energy is conserved in an isolated system does not rule out a

process in which an amount of energy Evanishes at one place while an equal amount

of energy Ecomes into being somewhere else with no actual transport of energy from

one place to the other. Because simultaneity is relative, some observers of the process

will find energy not being conserved. To rescue conservation of energy in the light

of special relativity, then, we have to say that, when energy disappears somewhere

and appears elsewhere, it has actually flowed from the first location to the second.

Thus energy is conserved locallyeverywhere, not merely when an isolated system is

considered—a much stronger statement of this principle.

(x 1 x 2 )c^2



 1 ^2 c^2

t 0 x 2 c^2



 1 ^2 c^2

t 0 x 1 c^2



 1 ^2 c^2

bei48482_ch01.qxd 1/15/02 1:21 AM Page 45