University of Virginia Library

TIME AND MEASUREMENT

I

The origins of the concept of time are lost in the mists
of prehistory but from our knowledge of surviving
primitive races it would seem highly probable that the

lives of our remote ancestors were far less consciously
dominated by time than are ours. For example, al-
though the children of Australian aborigines are of
similar mental capacity to white children, they have
great difficulty in telling the time by the clock. They
can read off the position of the hands on the face of
a clock as a memory exercise but they are quite unable
to relate it to the time of the day. There is a cultural
gap between their conception of time and ours which
they find difficult to cross. Nevertheless, all primitive
peoples have some idea of time and some method of
reckoning, usually based on astronomical observations.
The Australian aborigine will fix the time for a pro-
posed action by placing a stone in the fork of a tree,
or some such place, so that the sun will strike it at
the agreed time.

Primitive man's sense of rhythm was a vital factor
in his intuition of time. Before he had any explicit idea
of time, he seems to have been aware of temporal
associations dividing time into intervals like bars in
music. The principal transitions in nature were thought
to occur suddenly, and similarly man's journey through
life was visualized as a sequence of distinct stages—
later epitomized in Shakespeare's “seven ages of man.”
Even in so culturally advanced a civilization as the
ancient Chinese different intervals of time were re-
garded as separate discrete units, so that time was in
effect discontinuous. Just as space was decomposed into
regions, so time was split up into areas, seasons, and
epochs. In other words, time was “boxed.” Even in
late medieval Europe the development of the mechan-
ical clock did not spring from a desire to register the
passage of time but rather from the monastic demand
for accurate determination of the hours when the vari-
ous religious offices and prayers should be said.

It was a long step from the inhomogeneity of magical
time as generally imagined in antiquity and the Middle
Ages with its specific holy days and lucky and unlucky
secular days to the modern scientific conception of
homogeneous linear time. Indeed, man was aware of
different times long before he formulated the idea of
time itself. This distinction is particularly well illus-
trated by the Maya priests of pre-Columbian central
America, who, of all ancient peoples, were probably
the most obsessed with the idea of time. Whereas in
European antiquity the days of the week were regarded
as being under the influence of the principal heavenly
bodies, e.g., Saturn-day, Sun-day, Moon-day, etc., for
the Mayas each day was itself divine. Every monument
and every altar was erected to mark the passage of
time. The Mayas pictured the divisions of time as
burdens carried on the backs of a hierarchy of divine
bearers who personified the respective numbers by
which the different periods—days, months, years, dec
ades, etc.—were distinguished. There were momentary
pauses at the end of each prescribed period, for exam-
ple, at the end of a day, when one god with his burden
(in this case representing the next day) replaced an-
other god with his. A remarkably precise astronomical
calendar was developed embodying correction for-
mulae that were even more accurate than our present
leap year correction which was introduced about a
thousand years later by Pope Gregory XIII in 1582.
Our correction is too long by 0.03 days in a century,
whereas the corresponding Maya correction was 0.02
days too short. Despite this astonishing achievement
the Mayas never seem to have grasped the idea of time
as the journey of one bearer and his load. Instead, each
god's burden came to signify the particular omen of
the division of time in question—one year the burden
might be drought, another a good harvest and so on.

II

Unlike the Mayas, the ancient Greeks were not
obsessed by the temporal aspect of things. At the dawn
of Greek literature two contrasting points of view are
found in Homer and Hesiod. In the Iliad Olympian
theology and morality are dominated by spatial con-
cepts, the cardinal sin being hubris, that is going be-
yond one's assigned province. Homer was not inter-
ested in the origin of things and had no cosmogony.
On the other hand, Hesiod in his Works and Days gave
an account of the origin of the world, and his poem
can be regarded as a moralistic study based on the time
concept.

Two centuries or more later (sixth century B.C.) the
Ionian pioneers of natural philosophy visualized the
world as a geometrical organism or a live space-filling
substance. Heraclitus, on the other hand, believed the
world to be a soul involved in an endless cycle of death
and rebirth, the very essence of the universe being
transmutation. A similar emphasis on time and soul
characterized the Orphic religion which appears to
have provided the mythical background of Pytha-
goreanism. According to Plutarch, when asked what
Time was, Pythagoras replied that it was the soul, or
procreative element, of the universe. Pythagoras is
a shadowy figure but to him was attributed the
celebrated discovery, following experiments with a
monochord, that the concordant intervals of the musi-
cal scale can be expressed by simple ratios of whole
numbers. This was perhaps the most striking illustrative
example of Pythagoras' doctrine that the nature, or
ultimate principle, of things is not some kind of sub-
stance, as the Ionians thought, but is to be found in
number.

For the early Pythagoreans the concept of number
itself had both spatial and temporal significance. Num-

bers were represented by patterns of the type still
found on dominoes and dice. This led to an elementary
theory of numbers based on geometry. Number, how-
ever, was also regarded from a temporal point of view.
This is evident in the Pythagorean use of the gnomon.
Originally, this was a time-measuring instrument—a
simple, upright sundial. The term then came to mean
the figure that remains when a square is cut out of
the corner of a larger square with its sides parallel to
the sides of the latter. Eventually it denoted any num-
ber which when added to a figurate number, for exam-
ple a square number, generates the next number of
the same shape. The early Pythagoreans regarded the
generation of numbers as an actual physical operation
in space and time, beginning with the initial unit or
monad. In general, they failed to make any clear dis-
tinction between the abstract and the concrete and
between logical and chronological priority.

These distinctions were clearly drawn by Parmen-
ides, the founding father of deductive argument and
logical analysis. In his Way of Truth he criticized
current cosmogonies for their common assumption that
the universe began at some moment of time. “And what
need,” he asked, “could have stirred it up, starting from
nothing, to be born later rather than sooner?” This
question was answered by Plato who claimed that time
is coexistent with the universe. But he was deeply
impressed by Parmenides' acute criticism of the ideas
of becoming and perishing and by his conclusion that
time does not pertain to anything that is truly real.

The difficulties involved in producing a logically
satisfactory theory of time and its measurement were
emphasized by Parmenides' pupil Zeno of Elea in his
famous paradoxes. For, although these paradoxes were
primarily concerned with the problem of motion, they
raised difficulties both for the idea of time as continu-
ous or infinitely divisible and for the idea of temporal
atomicity. Unlike the Pythagoreans, who tended to
identify the chronological with the logical, Parmenides
and Zeno argued that they are incompatible.

The influence of Parmenides and Zeno on Plato is
evident in the different treatment of space and time
in Plato's cosmological dialogue the Timaeus. Space
exists in its own right as a given frame for the visible
order of things, whereas time is merely a feature of
that order based on an ideal timeless archetype or realm
of static geometrical shapes (Eternity) of which it is
the “moving image,” being governed by a regular
numerical sequence made manifest by the motions of
the heavenly bodies. Plato's intimate association of
time with the universe led him to regard time as being
actually produced by the revolutions of the celestial
sphere.

This conclusion was not accepted by Aristotle who
rejected the idea that time can be identified with any
form of motion. For, he argued, motion can be uniform
or nonuniform and these terms are themselves defined
by time, whereas time cannot be defined by itself.
Nevertheless, although time is not identical with mo-
tion, it seemed to him to be dependent on motion.
Possibly influenced by the Pythagoreans, he argued that
time is a kind of number, being the numerable aspect
of motion. Time is therefore a numbering process
founded on our perception of “before” and “after” in
motion: “Time is the number of motion with respect
to earlier and later” (Physica, ed. W. D. Ross, Vol II,
Book IV, 219a). Aristotle regarded time and motion
as reciprocal. “Not only do we measure the movement
by the time, but also the time by the movement, be-
cause they define each other. The time marks the
movement, since it is number; and the movement the
time” (ibid.). Aristotle recognized that motion can
cease whereas time cannot, but there is one motion
that continues unceasingly, namely that of the heavens.
Clearly, although he did not agree with Plato, he too
was profoundly influenced by the cosmological view
of time. Moreover, although he began by rejecting any
association between time and a particular motion in
favor of one between time and motion in general, he
came to the conclusion that time is closely associated
with the circular motion of the heavens, which he
regarded as the perfect example of uniform motion.

For Aristotle the primary form of motion was uni-
form motion in a circle because it could continue
indefinitely, whereas uniform rectilinear motion could
not. Any straight line necessarily had finite end points,
since he did not have the modern mathematical con-
cept of the infinitely extended straight line. For Aris-
totle, therefore, time was intimately connected with
uniform circular motion.

Belief in the cyclic nature of time was widespread
in antiquity, since most ancient peoples tended to
regard time as essentially periodic. Long before Aris-
totle, this idea led the Greeks to formulate the concept
of the Great Year, and this is presumably what the
Pythagorean Archytas of Tarentum had in mind when
he said that time is the number of a certain movement
and is the interval appropriate to the nature of the
universe—a definition that may well have influenced
Aristotle. There were, however, two distinct inter-
pretations of the Great Year. On the one hand it was
simply the period required for the Sun, Moon, and
planets to attain the same positions in relation to each
other as they had at a given time. This appears to have
been the sense in which Plato used the idea in the
Timaeus. On the other hand, for Heraclitus it signified
the period of duration of the world from its formation
to its destruction and rebirth. Whereas Plato seems to

have refrained from giving any estimate of the length
of the Great Year, Heraclitus, with no particular astro-
nomical interpretation in mind, gave 10,800 years as
its duration. He may have arrived at this figure by
taking a generation of 30 years as a day and multi-
plying by 360, the (approximate) number of days in
the year.

The two interpretations of the Great Year were
combined by the Stoics who believed that, when the
heavenly bodies return at fixed intervals of time to the
same relative positions as they had at the beginning
of the world, everything would be destroyed by fire.
Then all would be restored anew just as it was before
and the entire cycle would be renewed in every detail.

III

The idea of time in antiquity differed from ours not
only because it was thought to be cyclical but also
because the lack of reliable mechanical clocks pre-
vented its accurate measurement. This impeded the
development of the modern metrical concept of time.
Moreover, the scale of “hours” was not uniform. In-
deed, our present system of dividing day and night
together into twenty-four hours of equal length was
not employed in civil life until the fourteenth century
A.D., although it had already been used by astronomers.
Previously, it was the general custom to divide the
periods of light and darkness into an equal number of
“temporal hours” (horae temporales, as they were
called by the Romans). The number was usually twelve.
Consequently, the length of an hour varied according
to the time of year and also, except at the equinoxes,
a daylight hour was not equal to a nocturnal hour.
Strange as this mode of reckoning time may now seem,
we must remember that most human activities took
place in the hours of daylight and also that early civili-
zations were in latitudes where the period from sunrise
to sunset varies far less than in more northerly parts.
For their standard hours, the astronomers took “equi-
noctial hours” (horae equinoctales). These were the
same as the temporal hours at the date of the spring
equinox.

The only mechanical time-recorders in antiquity
were water clocks, but until the fourteenth century
A.D. the most reliable way to tell the time was by means
of a sundial. Both types of clock were used by the
Egyptians. Later they were introduced into Greece and
eventually became widespread in the Roman Empire.
Vitruvius, writing about 30 B.C., described more than
a dozen different types of sundial. He also described
a number of “clepsydrae” or water clocks. To obtain
a uniform flow of water they were designed so as to
keep the pressure head constant. In order to indicate
“temporal” hours, either the rate of flow or the scale
of hours had to be varied according to the time of year.
The result was that many of the ancient water clocks
were instruments of considerable complexity.

The earliest known attempt to produce mechanically
a periodic standard of time is a device illustrated in
a Chinese text written by Su Sung in A.D. 1092. It was
powered by a waterwheel which advanced in a step-
by-step motion, water being poured into a series of
cups which emptied (or escaped) every quarter of an
hour, when the weight of the water in the cup was
sufficient to tilt a steelyard. The mechanism was then
unlocked until the arrival of the next cup below the
water stream when it was locked again. An astronomi-
cal check on timekeeping was made by a sighting tube
pointed to a selected star. Since the timekeeping was
governed mainly by the flow of water rather than by
the escapement action itself, this device may be re-
garded as a link between the timekeeping properties
of a steady flow of liquid and those of mechanically
produced oscillations.

The fundamental distinction between water clocks
and mechanical clocks, in the strict sense of the term,
is that the former involve a continuous process (the
flow of water through an orifice) whereas the latter
are governed by a mechanical motion which continu-
ally repeats itself. The mechanical clock, in this sense,
appears to have been a European invention of the late
thirteenth or early fourteenth century. The first clocks
of this type were public striking clocks, the earliest,
as far as we know, being set up at Milan in 1309. The
type of motion employed in these clocks, known as
the “verge” escapement—probably from the Latin
virga, a rod or twig—was an ingenious device in which
a heavy bar pivoted near its center was pushed first
one way and then the other by a toothed wheel driven
by a weight suspended from a drum. The wheel ad-
vanced by the space of one tooth for each to and fro
oscillation of the bar. Since the bar had no natural
period of its own, the rate of the clock depended on
the driving weight, but was also affected by variations
of friction in the driving mechanism. Consequently, the
accuracy of these clocks was low and they could not
be relied on to keep time more closely than to about
a quarter of an hour a day at best. An error of an hour
was not unusual. Until the middle of the seventeenth
century mechanical clocks had only one hand and the
dial was divided only into hours and quarters.

The word “clock” is etymologically related to the
French word cloche, meaning a bell. Bells played a
prominent part in medieval life and mechanisms for
ringing them, made of toothed wheels and oscillating
levers, may have helped to prepare for the invention
of mechanical clocks. Indeed, some early clocks were
essentially mechanisms for striking the hours.

Music provides another instance of the growing
importance of temporal concepts in the Middle Ages.
Early medieval music was all plain chant in which
notes had fluid time-values. Mensural music in which
the duration of notes had an exact ratio among them-
selves appears to have been an Islamic invention. It
was introduced into Europe about the twelfth century.
About this time there appeared in Europe the system
of notation in which the exact time-value of a note
is indicated by a lozenge on a pole.

IV

The cardinal factor, however, in causing time to
become a concept of primary importance was the
spread of Christianity. Its central doctrine of the Cruci-
fixion was regarded as a unique event in time not
subject to repetition and so implied that time must be
linear rather than cyclic. Before the rise of Christianity
only the Hebrews and Zoroastrian Iranians appear to
have developed teleological conceptions of the uni-
verse implying that history is progressive. The histori-
cal view of time, with particular emphasis on the
nonrepeatability of events was, however, the very es-
sence of Christianity. The contrast with the Hebrew
view is clearly brought out in the Epistle to the He-
brews (9:25-26): “Nor yet that he should offer himself
often, as the high priest entereth into the holy place
every year with the blood of others; For then must
be often have suffered since the foundation of the
world; but now once in the end of the world hath he
appeared to put away sin by the sacrifice of himself.”

Nevertheless, the idea of denominating the years
serially in a single era count, such as the Olympic
dating from 776 B.C. and the Seleucid from 311 B.C.,
did not originate in the Christian era until it was
introduced by Dionysius Exiguus in A.D. 525, and the
B.C. sequence extending backwards from the birth of
Christ was only introduced in the latter part of the
seventeenth century. In medieval Europe, as in me-
dieval China, ancient Greece, and pre-Columbian
America, time was not conceived as a continuous
mathematical parameter but was split up into separate
seasons, divisions of the Zodiac, and so on, each exert-
ing its specific influence. In other words, magical time
had not yet been superseded by scientific time. More-
over, throughout the whole medieval period, there was
a conflict between the cyclic and linear concepts of
time. The scientists and scholars, influenced by astron-
omy and astrology, tended to emphasize the cyclic
concept. The linear concept was fostered by the mer-
cantile class and the rise of a money economy. For,
as long as power was concentrated in the ownership
of land, time was felt to be plentiful and was associated
with the unchanging cycle of the soil. With the circu
lation of money, however, the emphasis was on mo-
bility. In other words, men were beginning to believe
that “time is money” and that one must try to use it
economically and thus time came to be associated with
the idea of linear progress.

In the course of the fourteenth century many public
mechanical clocks that rang the hours were set up in
European towns. They were very expensive and, de-
spite their lack of accuracy, they were a source of pride
to the citizens. Clocks were made with curious and
complicated movements. It was easier to add wheels
than to regulate the escapement. Moreover, in view
of the general belief that a correct knowledge of the
relative positions of the heavenly bodies was necessary
for the success of most human activities, many early
clocks involved elaborate astronomical representations.
The most celebrated was the Strasbourg clock set up
in 1350, but the most elaborate was the astronomical
domestic clock made at about the same time by Gio-
vanni de' Dondi. From about 1400 there are records
of the purchase of domestic clocks by royalty, but until
the latter part of the sixteenth century these clocks
were very rare.

Although medieval scholars were not concerned with
machines, they became more and more interested in
clocks, particularly because of their connection with
astronomy. Already in the fourteenth century Nicole
Oresme (1323-82), Bishop of Lisieux, likened the uni-
verse to a vast mechanical clock created and set mov-
ing by God so that “all the wheels move as harmoni-
ously as possible.” The great leaders of the scientific
revolution of the seventeenth century were much con-
cerned with horological questions and metaphors.
Early in the century Kepler specifically rejected the
old quasi-animistic magical conception of the universe
and asserted that it was similar to a clock, and later
the same analogy was drawn by Robert Boyle and
others. Thus the invention of the mechanical clock
played a central role in the formulation of the mecha-
nistic conception of nature that dominated natural
philosophy from Descartes to Kelvin. An even more
far-reaching influence has been claimed for the me-
chanical clock by Lewis Mumford who has argued that
it “dissociated time from human events and helped
create the belief in an independent world of mathe-
matically measurable sequences: the special world of
science” (Technics and Civilization, p. 15).

Nevertheless, this development was for a long time
hampered by the lack of any accurate mechanical
means for measuring small intervals of time. Thus, in
his famous experiments on the rate of fall of bodies
rolling down an inclined plane, Galileo measured time
by weighing the quantity of water which emerged as
a thin jet from a vessel with a small hole in it. It is

not surprising that he refrained as far as possible from
giving a concrete value for the acceleration due to
gravity and that when he did state a value it was less
than half the correct amount. The construction of
precision timekeepers was stimulated by the needs of
astronomy and navigators, and they contributed to the
development of science itself.

V

A new era opened in the history of chronometry
when Galileo discovered a natural periodic process that
could be conveniently adapted for the purposes of
accurate timekeeping. As a result of much mathe-
matical thinking on experiments with oscillating pen-
dulums, he came to the conclusion that each simple
pendulum has its own type of vibration depending on
its length. In his old age he contemplated applying
the pendulum to clockwork which could record me-
chanically the number of swings, but this step was first
taken successfully by Huygens in 1656. Strictly speak-
ing, the simple pendulum in which the bob describes
circular arcs is not quite isochronous. Huygens dis-
covered that theoretically perfect isochronism could
be achieved by compelling the bob to describe a cy-
cloidal arc. His first pendulum clock with cycloidal
“cheeks” was constructed in 1656. Great as was
Huygens' achievement, particularly from the point of
view of theory, the ultimate practical solution of the
problem came only after the invention of a new type
of escapement. Huygens' clock incorporated the verge
type, but about 1670 a much improved type, the an-
chor type, was invented that interfered less with the
pendulum's free motion.

The invention of a satisfactory mechanical clock had
a tremendous influence on the general concept of time.
For, unlike the water clocks, etc. that preceded it, the
mechanical clock if properly regulated can tick away
continually for years on end, and so must have greatly
influenced belief in the homogeneity and continuity
of time. This belief was implicit in the idea of time
put forward by Galileo in the dynamical part of Two
New Sciences (1638). For, although he was not the first
to represent time by a geometrical straight line, he
became the most influential pioneer of this idea
through his theory of motion.

Nevertheless, for the first explicit discussion of the
concept of geometrical time it seems that we must go
to the Lectiones geometricae (1669) of Isaac Barrow,
written about thirty years after the publication of
Galileo's book. Barrow, who occupied the chair of
mathematics in Cambridge in which he was succeeded
by Newton in 1669, was greatly impressed by the
kinematic method in geometry that had been devel-
oped with great effect by Galileo's pupil Torricelli.
Barrow realized that to understand this method it was
necessary to study time, and he was particularly con-
cerned with the relation of time and motion. “Time
does not imply motion, as far as its absolute and in-
trinsic nature is concerned; not any more than it im-
plies rest; whether things move or are still, whether
we sleep or wake, Time pursues the even tenour of
its way.” However, he argues, it is only by means of
motion that time is measurable. “Time may be used
as a measure of motion; just as we measure space from
some magnitude, and then use this space to estimate
other magnitudes commensurable with the first; i.e.,
we compare motions with one another by the use of
time as an intermediary.” Barrow regarded time as
essentially a mathematical concept which has many
analogies with a line “for time has length alone, is
similar in all its parts and can be looked upon as
constituted from a simple addition of successive in-
stants or as from a continuous flow of one instant; either
a straight or a circular line” (Geometrical Lectures,
London [1735], Lecture 1, p. 35). The reference here
to “a circular line” shows that Barrow was not com-
pletely emancipated from traditional ideas. Never-
theless, his statement goes further than any of Galileo's,
for Galileo only used straight line segments to denote
particular intervals of time. Barrow was very careful,
however, not to push his analogy between time and
a line too far. Time, in his view, was “the continuance
of anything in its own being.”

Barrow's views greatly influenced his illustrious suc-
cessor in the Lucasian chair, Isaac Newton. In particu-
lar, Barrow's idea that irrespective of whether things
move or are still time passes with a steady flow is
echoed in the famous definition at the beginning of
Newton's Principia (1687). “Absolute, true and mathe-
matical time,” wrote Newton, “of itself and from its
own nature, flows equably without relation to anything
external.” Newton admitted that, in practice, there
may be no such thing as a uniform motion by which
time may be accurately measured, but he thought it
necessary that, in principle, there should exist an ideal
rate-measurer of time. Consequently, he regarded the
moments of absolute time as forming a continuous
sequence like the points on a geometrical line and he
believed that the rate at which these moments succeed
each other is a variable which is independent of all
particular events and processes. His belief in absolute
time was supported by the argument for absolute mo-
tion that he based on his celebrated experiment with
a rotating bucket of water. He thought that it was not
necessary to refer to any other body when attaching
a physical meaning to saying that a particular body
rotates, and from this he concluded that time as well
as space must be absolute.

Newton's views made a great impression on the
philosopher John Locke in whose Essay concerning
Human Understanding (1690) we find the clearest
statement of the “classical” scientific conception of
time that was evolved in the seventeenth century:

(Book II, Ch. 15, Para. 11).

Newton's conception of time has been frequently
criticized. If time can be considered in isolation “with-
out relation to anything external,” what meaning could
be attached to saying that its flow is not uniform and
hence what point is there in saying that it “flows
equably”? This objection does not apply to the idea
of time formulated by Newton's contemporary Leibniz
who rejected the idea that moments of absolute time
exist in their own right. Instead, he thought of them
as classes of events related by the concept of simul-
taneity and he defined time as the order of succession
of phenomena. Today this is generally accepted, and
we regard events as simultaneous not because they
occupy the same moment of time but simply because
they happen together. We derive time from events and
not vice versa. Nevertheless, Leibniz' definition of time
as “the order of succession of phenomena” is in-
complete insofar as it concentrates on the ordinal
aspect of time without explicit reference to its dura-
tional aspect and its continuity.

Newton recognized the practical difficulty of ob-
taining a satisfactory measure of time. He pointed out
that, although commonly considered equal, the natural
days are in fact unequal. We now know that in the
long run we cannot base our definition of time on the
observed motions of any of the heavenly bodies. For
the Moon's revolutions are not strictly uniform but are
subject to a small secular acceleration, minute irregu-
larities have been discovered in the diurnal rotation
of the Earth, and so on. Greater accuracy in the meas-
urement of time can, however, be obtained by means
of atomic and molecular clocks. Indeed, the greatest
accuracy so far achieved is with a frequency standard
in the radio range of the spectrum of the caesium atom
and is of the order of one part in 1011, which corre-
sponds to a clock error of only one second in 3000
years.

Implicit in these developments is the assumption that
all atoms of a given element behave in exactly the same
way, irrespective of place and epoch. The ultimate
scale of time is therefore based on our concept of
universal laws of nature. This was already recognized
last century, long before the advent of modern ultra-
precise time-keeping, in particular by Thomson and
Tait in their treatise Natural Philosophy (1890). In
discussing the law of inertia they argued that it could
be stated in the form: the times during which any
particular body not compelled by force to alter the
speeds of its motions passes through equal spaces are
equal; and in this form, they said, the law expresses
our convention for measuring time. It is easily seen
that this implies a unique time-scale except for the
arbitrary choice of time unit and time zero.

In practical life the precise standardization of time
measurement began with the foundation of the Royal
Observatory in 1675, and was further developed when
Greenwich time could be taken on each ship after John
Harrison had perfected the chronometer, about 1760.
The conventional nature of our choice of time zero
in civil time was clearly revealed when, in 1885, to
cope with the fact that solar time varies by four
minutes in a degree of longitude, it was found necessary
to divide the globe into a series of standard time-belts.

VI

Until the beginning of the present century it was
universally assumed that time is like a moving knife-
edge covering all places in the universe simultaneously
and that the only arbitrary elements in its determi-
nation were our choice of time unit and time zero.
It therefore came as a great shock when, in 1905,
Einstein discovered a previously unsuspected gap in
the theory of time-measurement. For, in his analysis
of the nature of the velocity of light it occurred to
him that time-measurement depends on simultaneity,
and that although this idea is perfectly clear when two
events occur at the same place it was not equally clear
for events in different places. Einstein realized that the
concept of simultaneity for a distant event and one
in close proximity to the observer is an inferred con-
cept depending on the relative position of the distant
event and the mode of connection between it and the
observer's perception of it. If the distance of an exter-
nal event is known and also the velocity of the signal
that connects it and the resulting percept, the observer
can calculate the epoch at which the event occurred
and can correlate this with some previous instant in
his own experience. This calculation will be a distinct
operation for each observer, but until Einstein raised
the question it had been tacitly assumed that, when
we have found the rules according to which the time
of perception is determined by the time of the event,
all perceived events can be brought into a single ob-
jective time-sequence the same for all observers. Ein-

stein not only realized that it was a hypothesis to
assume that, if they calculate correctly, all observers
must assign the same time to a given event, but he
produced cogent reasons why, in general, this hypoth-
esis should be rejected.

Einstein assumed that there are no instantaneous
connections between external events and the observer.
The classical theory of time, with its assumption of
worldwide simultaneity for all observers, in effect
presupposed that there were such connections. Instead,
Einstein postulated that the most rapid form of com-
munication is by means of electromagnetic signals (in
vacuo), including light rays, and that their speed is the
same for all observers at relative rest or in uniform
relative motion. He regarded this assumption as a
consequence of the principle of special relativity (as
it is now called) which asserts that the laws of physics
are the same for all such observers. He found that,
although the invariance of the velocity of light is com-
patible with the idea of worldwide simultaneity for
all observers at relative rest, those in uniform relative
motion would, in general, be led to assign different
times to the same event and that a moving clock would
appear to run slow compared with an identical clock
at rest with respect to the observer.

It is well known that Einstein's theory automatically
explained the failure of the Michelson-Morley experi-
ment for measuring the Earth's velocity through the
luminiferous aether and has been successful in explain-
ing many other results that could not be accounted
for in the classical theory of time. The phenomenon
of the apparent slowing down of a clock in motion
relative to the observer is called “time dilatation.” It
is essentially a phenomenon of measurement applicable
to all forms of matter and is a reciprocal effect: if A
and B are two observers in uniform relative motion,
B's clock seems to A to run slow and equally A's clock
seems to run slow according to B. This reciprocity no
longer holds, however, if forces are applied to change
the motion of one of the observers. In particular, if
A and B are together at some instant and at a later
instant the motion of B is suddenly reversed so that
he eventually comes back to A with the same speed,
the time that elapses between the instant at which B
left A and the instant when he returns to A will be
shorter according to B's clock than according to A's.
Consequently, although we accept Isaac Barrow's view
that “Time is the continuance of anything in its own
being,” the special theory of relativity prevents our
agreeing with him unconditionally when he went on
to say “nor do I believe there is anyone but allows
that those things existed equal times which rose and
perished together.”

Empirical evidence that can only be understood in
terms of time dilatation has come from the study of
cosmic-ray phenomena. Elementary particles known
as mu-mesons, found in cosmic-ray showers, disinte-
grate spontaneously, their average “proper lifetime”
(that is time from production to disintegration accord-
ing to an observer travelling with a meson) being about
two micro-seconds (two millionths of a second). These
particles are mainly produced at heights of about ten
kilometers above the Earth's surface. Consequently,
those observed in the laboratory on photographic
plates must have travelled that distance. But in two
micro-seconds a particle that travelled with the veloc-
ity of light would cover less than a kilometer, and
according to the theory of relativity all material parti-
cles travel with speeds less than that of light. However,
the velocity of these particles has been found to be
so close to that of light that the time-dilatation factor
is about ten, which is the amount required to explain
why it is that to the observer in the laboratory these
particles appear to travel about ten times as far as they
could in the absence of this effect.

Although the theory of relativity has undermined the
classical concept of universal time, the same for all
observers, it has led to time-measurement's becoming
even more significant than before in physics, since time
standards are now tending to be regarded as primary
standards for spatial as well as for temporal measure-
ment. This is because the theory leads us to reject the
classical rigid body concept, since it implies the in-
stantaneous transmission of a disturbance through the
body from one end to the other, and this is incom-
patible with the basic assumption that no signal can
travel faster than light. Instead of spatial measurement
depending on the idea of the rigid body, it can be based
on the radar principle. According to this, distance is
measured in terms of the time taken by light (or other
electromagnetic signals) to traverse it. This technique
is now being used by radio astronomers to redetermine
the scale of the solar system.

Although the laws of nature do not enable us to
define a local standard of rest, in principle this can
be determined by the bulk distribution of matter in
the universe. According to most current cosmological
theories, there is at each place in the universe a prefer-
ential time-scale for the description of the universe,
being that associated with the local standard of rest,
and these local time-scales all fit together to form one
worldwide cosmic time. It is with reference to this that
we can give objective meaning to such concepts as the
age of the Earth, the age of the solar system, the age
of our Galaxy, and the age of the universe. Thus,
despite the theory of relativity, we can still retain the
concept of a unique cosmic time-scale for our descrip-
tion of the physical universe and the dating of events.

BIBLIOGRAPHY

The subject of time and measurement is discussed at
length with many references in G. J. Whitrow, The Natural
Philosophy of Time (London, 1961; New York, 1963). The
history of practical time-measurement is outlined in F. A. B.
Ward, Time Measurement—Part I: Historical Review, 4th
ed. (London, 1958). A more popular account is given in
F. le Lionnais, Time, trans. W. D. O'Gorman, Jr. (London,
1962). A classic work on ancient methods of time-
measurement is M. P. Nilsson, Primitive Time-Reckoning
(Lund, 1920). A good short account will be found in the
chapter by E. R. Leach, “Primitive Time-Reckoning” in A
History of Technology, ed. C. Singer et al., Vol. I (Oxford,
1954). Chinese views are discussed by J. Needham, Time
and Eastern Man (London, 1965). See also J. Needham et
al., Heavenly Clockwork (Cambridge, 1960). Maya achieve-
ments in time-measurement are described by J. E. S.
Thompson, The Rise and Fall of Maya Civilization (Norman,
Okla., 1956). Ancient ideas on time are discussed by S. G. F.
Brandon, History, Time and Deity (New York, 1965); M.
Eliade, Cosmos and History: the Myth of the Eternal Return,
trans. W. R. Trask (New York, 1959); and J. F. Callahan,
Four Views of Time in Ancient Philosophy (Cambridge,
Mass., 1948). Greek ideas are briefly discussed by G. J.
Whitrow, “The Concept of Time from Pythagoras to Aris-
totle,” in Proceedings VIII International Congress of the
History of Science (Ithaca, N.Y., 1962; Paris, 1964). The
invention of the mechanical clock is discussed by C. M.
Cipolla, Clocks and Culture, 1300-1700 (London, 1967).
Ideas on time in different civilizations are described in
various chapters of The Voices of Time, ed. J. T. Fraser (New
York, 1966).

The quotations of Aristotle are from Aristotle, Physica,
trans. R. P. Hardie and R. K. Gaye, in The Works of Aristotle,
ed. W. D. Ross, Vol. II (Oxford, 1930). The cultural influence
of the mechanical clock in modern civilization is discussed
by Lewis Mumford in Technics and Civilization (New York
and London, 1934), Ch. I.

G. J. WHITROW

[See also Astrology; Continuity; Cosmology; Cycles; Music
and Science; Newton on Method; Number; Pythagorean
Doctrines; 2">Relativity; Space; Time.]