The Special Theory of Relativity 129
different than that of the moving observer. They perceive the same
physical phenomenon differently.
Not only are the spatial perceptions of the stationary and moving
observers different but their temporal perceptions differ also. We saw
evidence of this earlier when we considered the example of the lightning
striking the train. The two observers had a different notion of the
simultaneity of the lightning flashes. Perhaps even more surprising is the
fact that a stationary observer will observe that time in a moving frame
of reference actually slows down. A moving clock runs slower than a
stationary clock.
For example, if a clock is moving at the velocity of 0.866c with
respect to a stationary observer, the time required for the passage of one
hour on the moving clock will take two hours on a clock at rest in the
stationary frame. The moving clock appears to be losing time or slowing
down. In general, a time interval that takes to seconds in the moving
frame of reference will take t = to/ 1 −v^2 /c^2 seconds in the stationary
frame. The time elapsed in the stationary frame for the passage of one
hour of a moving clock is always greater than one hour. Notice that, as
the velocity of the moving clock approaches c, the time for one hour to
elapse in the moving frame, requires an infinite amount of time in the
stationary frame or, in other words, time comes to a standstill in the
moving frame from the point of view of the stationary observer.
Remember that it would be impossible for the moving clock to achieve a
velocity c with respect to a stationary observer because of its finite mass.
The slowing down of time in a moving frame of reference must seem
like science fiction to the average reader who has had no experience with
objects moving at velocities any where near the velocity of light. To an
elementary particle physicist who deals all the time with sub-atomic
particles, which travel at velocities near the velocity of light, the slowing
down of time in a moving frame of reference is a very real thing. It, in
fact, helps him in his study of certain short-lived elementary particles
called mesons. Mesons are created with a high-energy accelerator as
the result of the collision of protons with other protons or nuclei. One
of the mesons created in such a collision is the short-lived π meson,
which lives, on the average, about 10-8 sec before decaying into other
elementary particles. The average lifetime of 10-8 sec quoted for the π
meson is the value of the meson’s lifetime when it is observed at rest. As
the velocity of the meson, with respect to the observer in the laboratory
increases, so does the lifetime of the meson.