bei48482_FM

10 Chapter One

Although time is a relative quantity, not all the notions of time formed by every-

day experience are incorrect. Time does not run backward to anyobserver, for in-

stance. A sequence of events that occur at some particular point at t 1 , t 2 , t 3 ,... will

appear in the same order to all observers everywhere, though not necessarily with the

same time intervals t 2 t 1 , t 3 t 2 ,... between each pair of events. Similarly, no

distant observer, regardless of his or her state of motion, can see an event before it

happens—more precisely, before a nearby observer sees it—since the speed of light

is finite and signals require the minimum period of time Lcto travel a distance L.

There is no way to peer into the future, although past events may appear different to

different observers.

1.3 DOPPLER EFFECT

Why the universe is believed to be expanding

We are all familiar with the increase in pitch of a sound when its source approaches

us (or we approach the source) and the decrease in pitch when the source recedes from

us (or we recede from the source). These changes in frequency constitute the doppler

effect,whose origin is straightforward. For instance, successive waves emitted by a

source moving toward an observer are closer together than normal because of the

advance of the source; because the separation of the waves is the wavelength of the

sound, the corresponding frequency is higher. The relationship between the source

frequency  0 and the observed frequency is

Apollo 11 lifts off its pad to begin the first human

visit to the moon. At its highest speed of 10.8 km/s

relative to the earth, its clocks differed from those on

the earth by less than one part in a billion.

bei48482_ch01.qxd 4/8/03 20:13 Page 10 RKAUL-7 Rkaul-07:Desktop Folder:bei: