RELATIVITY
In the previous lectures of this course we have considered the
antecedent conditions which led up to the scientific movement, and have
traced the progress of thought from the seventeenth to the nineteenth
century. In the nineteenth century this history falls into three parts,
so far as it is to be grouped around science. These divisions are, the
contact between the romantic movement and science, the development of
technology and physics in the earlier part of the century, and lastly
the theory of evolution combined with the general advance of the
biological sciences.
The dominating note of the whole period of three centuries is that the
doctrine of materialism afforded an adequate basis for the concepts of
science. It was practically unquestioned. When undulations were wanted,
an ether was supplied, in order to perform the duties of an undulatory
material. To show the full assumption thus involved, I have sketched in
outline an alternative doctrine of an organic theory of nature. In the
last lecture it was pointed out that the biological developments, the
doctrine of evolution, the doctrine of energy, and the molecular
theories were rapidly undermining the adequacy of the orthodox
materialism. But until the close of the century no one drew that
conclusion. Materialism reigned supreme.
The note of the present epoch is that so many complexities have
developed regarding material, space, time, and energy, that the simple
security of the old orthodox assumptions has vanished. It is obvious
that they will not do as Newton left them, or even as Clerk Maxwell left
them. There must be a reorganization. The new situation in the thought
of to-day arises from the fact that scientific theory is outrunning
common sense. The settlement as inherited by the eighteenth century was
a triumph of organised common sense. It had got rid of medieval
phantasies, and of Cartesian vortices. As a result it gave full reign to
its anti-rationalistic tendencies derived from the historical revolt of
the Reformation period. It grounded itself upon what every plain man
could see with his own eyes, or with a microscope of moderate power. It
measured the obvious things to be measured, and it generalised the
obvious things to be generalised. For example, it generalised the
ordinary notions of weight and massiveness. The eighteenth century
opened with the quiet confidence that at last nonsense had been got rid
of. To-day we are at the opposite pole of thought. Heaven knows what
seeming nonsense may not to-morrow be demonstrated truth. We have
recaptured some of the tone of the early nineteenth century, only on a
higher imaginative level.
The reason why we are on a higher imaginative level is not because we
have finer imagination, but because we have better instruments. In
science, the most important thing that has happened during the last
forty years is the advance in instrumental design. This advance is
partly due to a few men of genius such as Michelson and the German
opticians. It is also due to the progress of technological processes of
manufacture, particularly in the region of metallurgy. The designer has
now at his disposal a variety of material of differing physical
properties. He can thus depend upon obtaining the material he desires;
and it can be ground to the shapes he desires, within very narrow limits
of tolerance. These instruments have put thought onto a new level. A
fresh instrument serves the same purpose as foreign travel; it shows
things in unusual combinations. The gain is more than a mere addition;
it is a transformation. The advance in experimental ingenuity is,
perhaps, also due to the larger proportion of national ability which now
flows into scientific pursuits. Anyhow, whatever be the cause, subtle
and ingenious experiments have abounded within the last generation. The
result is, that a great deal of information has been accumulated in
regions of nature very far removed from the ordinary experience of
mankind.
Two famous experiments, one devised by Galileo at the outset of the
scientific movement, and the other by Michelson with the aid of his
famous interferometer, first carried out in 1881, and repeated in 1887
and 1905, illustrate the assertions I have made. Galileo dropped heavy
bodies from the top of the leaning tower of Pisa, and demonstrated that
bodies of different weights, if released simultaneously, would reach the
earth together. So far as experimental skill, and delicacy of apparatus
were concerned, this experiment could have been made at any time within
the preceding five thousand years. The ideas involved merely concerned
weight and speed of travel, ideas which are familiar in ordinary life.
The whole set of ideas might have been familiar to the family of King
Minos of Crete, as they dropped pebbles into the sea from high
battlements rising from the shore. We cannot too carefully realise that
science started with the organisation of ordinary experiences. It was in
this way that it coalesced so readily with the anti-rationalistic bias
of the historical revolt. It was not asking for ultimate meanings. It
confined itself to investigating the connections regulating the
succession of obvious occurrences.
Michelson’s experiment could not have been made earlier than it was. It
required the general advance in technology, and Michelson’s experimental
genius. It concerns the determination of the earth’s motion through the
ether, and it assumes that light consists of waves of vibration
advancing at a fixed rate through the ether in any direction. Also, of
course, the earth is moving through the ether, and Michelson’s apparatus
is moving with the earth. In the centre of the apparatus a ray of light
is divided so that one half-ray goes in one direction _along_ the
apparatus through a given distance, and is reflected back to the centre
by a mirror in the apparatus. The other half-ray goes the same distance
_across_ the apparatus in a direction at right angles to the former ray,
and it also is reflected back to the centre. These reunited rays are
then reflected onto a screen in the apparatus. If precautions are taken,
you will see interference bands; namely bands of blackness where the
crests of the waves of one ray have filled up the troughs of the other
rays, owing to a minute difference in the lengths of paths of the two
half-rays, up to certain parts of the screens. These differences in
length will be affected by the motion of the earth. For it is the
lengths of the paths in the ether which count. Thus, since the apparatus
is moving with the earth, the path of one half-ray will be disturbed by
the motion in a different manner from the path of the other half-ray.
Think of yourself as moving in a railway carriage, first along the train
and then across the train; and mark out your paths on the railway track
which in this analogy corresponds to the ether. Now the motion of the
earth is very slow compared to that of light. Thus in the analogy you
must think of the train almost at a standstill, and of yourself as
moving very quickly.
In the experiment this effect of the earth’s motion would affect the
positions on the screen of the interference bands. Also if you turn the
apparatus round, through a right-angle, the effect of the earth’s motion
on the two half-rays will be interchanged, and the positions of the
interference bands would be shifted. We can calculate the small shift
which should result owing to the earth’s motion round the sun. Also to
this effect, we have to add that due to the sun’s motion through the
ether. The delicacy of the instrument can be tested, and it can be
proved that these effects of shifting are large enough to be observed by
it. Now the point is, that nothing was observed. There was no shifting
as you turned the instrument round.
The conclusion is either that the earth is always stationary in the
ether, or that there is something wrong with the fundamental principles
on which the interpretation of the experiment relies. It is obvious
that, in this experiment, we are very far away from the thoughts and the
games of the children of King Minos. The ideas of an ether, of waves in
it, of interference, of the motion of the earth through the ether, and
of Michelson’s interferometer, are remote from ordinary experience. But
remote as they are, they are simple and obvious compared to the accepted
explanation of the nugatory result of the experiment.
The ground of the explanation is that the ideas of space and of time
employed in science are too simple-minded, and must be modified. This
conclusion is a direct challenge to common sense, because the earlier
science had only refined upon the ordinary notions of ordinary people.
Such a radical reorganization of ideas would not have been adopted,
unless it had also been supported by many other observations which we
need not enter upon. Some form of the relativity theory seems to be the
simplest way of explaining a large number of facts which otherwise would
each require some _ad hoc_ explanation. The theory, therefore, does not
merely depend upon the experiments which led to its origination.
The central point of the explanation is that every instrument, such as
Michelson’s apparatus as used in the experiment, necessarily records the
velocity of light as having one and the same definite speed relatively
to it. I mean that an interferometer in a comet and an interferometer on
the earth would necessarily bring out the velocity of light, relatively
to themselves, as at the same value. This is an obvious paradox, since
the light moves with a definite velocity through the ether. Accordingly
two bodies, the earth and the comet, moving with unequal velocities
through the ether, might be expected to have different velocities
relatively to rays of light. For example, consider two cars on a road,
moving at ten and twenty miles an hour respectively, and being passed by
another car at fifty miles an hour. The rapid car will pass one of the
two cars at the relative velocity of forty miles per hour, and the other
at the rate of thirty miles per hour. The allegation as to light is
that, if we substituted a ray of light for the rapid car, the velocity
of the light along the roadway would be exactly the same as its velocity
relatively to either of the two cars which it overtakes. The velocity of
light is immensely large, being about three hundred thousand kilometres
per second. We must have notions as to space and time such that just
this velocity has this peculiar character. It follows that all our
notions of relative velocity must be recast. But these notions are the
immediate outcome of our habitual notions as to space and time. So we
come back to the position, that there has been something overlooked in
the current expositions of what we mean by space and of what we mean by
time.
Now our habitual fundamental assumption is that there is a unique
meaning to be given to space and a unique meaning to be given to time,
so that whatever meaning is given to spatial relations in respect to the
instrument on the earth, the same meaning must be given to them in
respect to the instrument on the comet, and the same meaning for an
instrument at rest in the ether. In the theory of relativity, this is
denied. As far as concerns space, there is no difficulty in agreeing, if
you think of the obvious facts of relative motion. But even here the
change in meaning has to go further than would be sanctioned by common
sense. Also the same demand is made for time; so that the relative
dating of events and the lapses of time between them are to be reckoned
as different for the instrument on the earth, for the instrument in the
comet, and for the instrument at rest in the ether. This is a greater
strain on our credulity. We need not probe the question further than the
conclusion that for the earth and for the comet spatiality and
temporality are each to have different meanings amid different
conditions, such as those presented by the earth and the comet.
Accordingly velocity has different meanings for the two bodies. Thus the
modern scientific assumption is that if anything has the speed of light
by reference to any one meaning of space and time, then it has the same
speed according to any other meaning of space and time.
This is a heavy blow at the classical scientific materialism, which
presupposes a definite present instant at which all matter is
simultaneously real. In the modern theory there is no such unique
present instant. You can find a meaning for the notion of the
simultaneous instant throughout all nature, but it will be a different
meaning for different notions of temporality.
There has been a tendency to give an extreme subjectivist interpretation
to this new doctrine. I mean that the relativity of space and time has
been construed as though it were dependent on the choice of the
observer. It is perfectly legitimate to bring in the observer, if he
facilitates explanations. But it is the observer’s body that we want,
and not his mind. Even this body is only useful as an example of a very
familiar form of apparatus. On the whole, it is better to concentrate
attention on Michelson’s interferometer, and to leave Michelson’s body
and Michelson’s mind out of the picture. The question is, why did the
interferometer have black bands on its screen, and why did not these
bands slightly shift as the instrument turned. The new relativity
associates space and time with an intimacy not hitherto contemplated;
and presupposes that their separation in concrete fact can be achieved
by alternative modes of abstraction, yielding alternative meanings. But
each mode of abstraction is directing attention to something which is in
nature; and thereby is isolating it for the purpose of contemplation.
The fact relevant to experiment, is the relevance of the interferometer
to just one among the many alternative systems of these spatio-temporal
relations which hold between natural entities.
What we must now ask of philosophy is to give us an interpretation of
the status in nature of space and time, so that the possibility of
alternative meanings is preserved. These lectures are not suited for the
elaboration of details; but there is no difficulty in pointing out where
to look for the origin of the discrimination between space and time. I
am presupposing the organic theory of nature, which I have outlined as a
basis for a thoroughgoing objectivism.
An event is the grasping into unity of a pattern of aspects. The
effectiveness of an event beyond itself arises from the aspects of
itself which go to form the prehended unities of other events. Except
for the systematic aspects of geometrical shape, this effectiveness is
trivial, if the mirrored pattern attaches merely to the event as one
whole. If the pattern endures throughout the successive parts of the
event, and also exhibits itself in the whole, so that the event is the
life history of the pattern, then in virtue of that enduring pattern the
event gains in external effectiveness. For its own effectiveness is
reënforced by the analogous aspects of all its successive parts. The
event constitutes a patterned value with a permanence inherent
throughout its own parts; and by reason of this inherent endurance the
event is important for the modification of its environment.
It is in this endurance of pattern that time differentiates itself from
space. The pattern is spatially _now_; and this temporal determination
constitutes its relation to each partial event. For it is reproduced in
this temporal succession of these spatial parts of its own life. I mean
that this particular rule of temporal order allows the pattern to be
reproduced in each temporal slice of its history. So to speak, each
enduring object discovers in nature and requires from nature a principle
discriminating space from time. Apart from the fact of an enduring
pattern this principle might be there, but it would be latent and
trivial. Thus the importance of space as against time, and of time as
against space, has developed with the development of enduring organisms.
Enduring objects are significant of a differentiation of space from time
in respect to the patterns ingredient within events; and conversely the
differentiation of space from time in the patterns ingredient within
events expresses the patience of the community of events for enduring
objects. There might be the community without objects, but there could
not be the enduring objects without the community with its peculiar
patience for them.
It is very necessary that this point should not be misunderstood.
Endurance means that a pattern which is exhibited in the prehension of
one event is also exhibited in the prehension of those of its parts
which are discriminated by a certain rule. It is not true that any part
of the whole event will yield the same pattern as does the whole. For
example, consider the total bodily pattern exhibited in the life of a
human body during one minute. One of the thumbs during the same minute
is part of the whole bodily event. But the pattern of this part is the
pattern of the thumb, and is not the pattern of the whole body. Thus
endurance requires a definite rule for obtaining the parts. In the above
example, we know at once what the rule is: You must take the life of the
whole body during any portion of that same minute; for example, during a
second or a tenth of a second. In other words, the meaning of endurance
presupposes a meaning for the lapse of time within the spatio-temporal
continuum.
The question now arises whether all enduring objects discover the same
principle of differentiation of space from time; or even whether at
different stages of its own life-history one object may not vary in its
spatio-temporal discrimination. Up till a few years ago, everyone
unhesitatingly assumed that there was only one such principle to be
discovered. Accordingly, in dealing with one object, time would have
exactly the same meaning in reference to endurance as in dealing with
the endurance of another object. It would also follow then that spatial
relations would have one unique meaning. But now it seems that the
observed effectiveness of objects can only be explained by assuming that
objects in a state of motion relatively to each other are utilising, for
their endurance, meanings of space and of time which are not identical
from one object to another. Every enduring object is to be conceived as
at rest in its own proper space, and in motion throughout any space
defined in a way which is not that inherent in its peculiar endurance.
If two objects are mutually at rest, they are utilising the same
meanings of space and of time for the purposes of expressing their
endurance; if in relative motion, the spaces and times differ. It
follows that, if we can conceive a body at one stage of its life history
as in motion relatively to itself at another stage, then the body at
these two stages is utilising diverse meanings of space, and
correlatively diverse meanings of time.
In an organic philosophy of nature there is nothing to decide between
the old hypothesis of the uniqueness of the time discrimination and the
new hypothesis of its multiplicity. It is purely a matter for evidence
drawn from observations.[5]
Footnote 5:
_Cf._ my _Principles of Natural Knowledge_, Sec. 52:3.
In an earlier lecture, I said that an event had contemporaries. It is an
interesting question whether, on the new hypothesis, such a statement
can be made without the qualification of a reference to a definite
space-time system. It is possible to do so, in the sense that in _some_
time-system or other the two events are simultaneous. In other
time-systems the two contemporary events will not be simultaneous,
though they may overlap. Analogously one event will precede another
without qualification, if in _every_ time-system this precedence occurs.
It is evident that if we start from a given event A, other events in
general are divided into two sets, namely, those which without
qualification are contemporaneous with A and those which either precede
or succeed A. But there will be a set left over, namely, those events
which bound the two sets. There we have a critical case. You will
remember that we have a critical velocity to account for, namely the
theoretical velocity of light _in vacuo_.[6] Also you will remember that
the utilisation of different spatio-temporal systems means the relative
motion of objects. When we analyse this critical relation of a special
set of events to any given event A, we find the explanation of the
critical velocity which we require. I am suppressing all details. It is
evident that exactness of statement must be introduced by the
introduction of points, and lines, and instants. Also that the origin of
geometry requires discussion; for example, the measurement of lengths,
the straightness of lines, and the flatness of planes, and
perpendicularity. I have endeavoured to carry out these investigations
in some earlier books, under the heading of the theory of extensive
abstraction; but they are too technical for the present occasion.
Footnote 6:
This is not the velocity of light in a gravitational field or in a
medium of molecules and electrons.
If there be no one definite meaning to the geometrical relations of
distance, it is evident that the law of gravitation needs restatement.
For the formula expressing that law is that two particles attract each
other in proportion to the product of their masses and the inverse
square of their distances. This enunciation tacitly assumes that there
is one definite meaning to be ascribed to the instant at which the
attraction is considered, and also one definite meaning to be ascribed
to _distance_. But distance is a purely spatial notion, so that in the
new doctrine, there are an indefinite number of such meanings according
to the space-time system which you adopt. If the two particles are
relatively at rest, then we might be content with the space-time systems
which they are both utilising. Unfortunately this suggestion gives no
hint as to procedure when they are not mutually at rest. It is,
therefore, necessary to reformulate the law in a way which does not
presuppose any particular space-time system. Einstein has done this.
Naturally the result is more complicated. He introduced into
mathematical physics certain methods of pure mathematics which render
the formulae independent of the particular systems of measurement
adopted. The new formula introduces various small effects which are
absent in Newton’s law. But for the major effects Newton’s law and
Einstein’s law agree. Now these extra effects of Einstein’s law serve to
explain irregularities of the planet Mercury’s orbit which by Newton’s
law were inexplicable. This is a strong confirmation of the new theory.
Curiously enough, there is more than one alternative formula, based on
the new theory of multiple space-time systems, having the property of
embodying Newton’s law and in addition of explaining the peculiarities
of Mercury’s motion. The only method of selection between them is to
wait for experimental evidence respecting those effects on which the
formulae differ. Nature is probably quite indifferent to the aesthetic
preferences of mathematicians.
It only remains to add that Einstein would probably reject the theory of
multiple space-time systems which I have been expounding to you. He
would interpret his formula in terms of contortions in space-time which
alter the invariance theory for measure properties, and of the proper
times of each historical route. His mode of statement has the greater
mathematical simplicity, and only allows of one law of gravitation,
excluding the alternatives. But, for myself, I cannot reconcile it with
the given facts of our experience as to simultaneity, and spatial
arrangement. There are also other difficulties of a more abstract
character.
The theory of the relationship between events at which we have now
arrived is based first upon the doctrine that the relatednesses of an
event are all internal relations, so far as concerns that event, though
not necessarily so far as concerns the other relata. For example, the
eternal objects, thus involved, are externally related to events. This
internal relatedness is the reason why an event can be found only just
where it is and how it is,—that is to say, in just one definite set of
relationships. For each relationship enters into the essence of the
event; so that, apart from that relationship, the event would not be
itself. This is what is meant by the very notion of internal relations.
It has been usual, indeed universal, to hold that spatio-temporal
relationships are external. This doctrine is what is here denied.
The conception of internal relatedness involves the analysis of the
event into two factors, one the underlying substantial activity of
individualisation, and the other the complex of aspects—that is to say,
the complex of relatednesses as entering into the essence of the given
event—which are unified by this individualised activity. In other words,
the concept of internal relations requires the concept of substance as
the activity synthesising the relationships into its emergent character.
The event is what it is, by reason of the unification in itself of a
multiplicity of relationships. The general scheme of these mutual
relationships is an abstraction which presupposes each event as an
independent entity, which it is not, and asks what remnant of these
formative relationships is then left in the guise of external
relationships. The scheme of relationships as thus impartially expressed
becomes the scheme of a complex of events variously related as wholes to
parts and as joint parts within some one whole. Even here, the internal
relationship forces itself on our attention; for the part evidently is
constitutive of the whole. Also an isolated event which has lost its
status in any complex of events is equally excluded by the very nature
of an event. So the whole is evidently constitutive of the part. Thus
the internal character of the relationship really shows through this
impartial scheme of abstract external relations.
But this exhibition of the actual universe as extensive and divisible
has left out the distinction between space and time. It has in fact left
out the process of realisation, which is the adjustment of the synthetic
activities by virtue of which the various events become their realised
selves. This adjustment is thus the adjustment of the underlying active
substances whereby these substances exhibit themselves as the
individualisations or modes of Spinoza’s one substance. This adjustment
is what introduces temporal process.
Thus, in some sense, time, in its character of the adjustment of the
process of synthetic realisation, extends beyond the spatio-temporal
continuum of nature.[7] There is no necessity that temporal process, in
this sense, should be constituted by one single series of linear
succession. Accordingly, in order to satisfy the present demands of
scientific hypothesis, we introduce the metaphysical hypothesis that
this is not the case. We do assume (basing ourselves upon direct
observation), however, that temporal process of realisation can be
analysed into a group of linear serial processes. Each of these linear
series is a space-time system. In support of this assumption of definite
serial processes, we appeal: (1) to the immediate presentation through
the senses of an extended universe beyond ourselves and _simultaneous_
with ourselves, (2) to the intellectual apprehension of a meaning to the
question which asks what is _now immediately happening_ in regions
beyond the cognisance of our senses, (3) to the analysis of what is
involved in the _endurance_ of emergent objects. This endurance of
objects involves the display of a pattern as now realised. This display
is the display of a pattern as inherent in an event, but also as
exhibiting a temporal slice of nature as lending aspects to eternal
objects (or, equally, of eternal objects as lending aspects to events).
The pattern is spatialised in a whole duration for the benefit of the
event into whose essence the pattern enters. The event is part of the
duration, _i.e._, is part of what is exhibited in the aspects inherent
in itself; and conversely the duration is the whole of nature
simultaneous with the event, in that sense of simultaneity. Thus an
event in realising itself displays a pattern, and this pattern requires
a definite duration determined by a definite meaning of simultaneity.
Each such meaning of simultaneity relates the pattern as thus displayed
to one definite space-time system. The actuality of the space-time
systems is constituted by the realisation of pattern; but it is inherent
in the general scheme of events as constituting its patience for the
temporal process of realisation.
Footnote 7:
_Cf._ my _Concept of Nature_, Ch. III.
Notice that the pattern requires a duration involving a definite lapse
of time, and not merely an instantaneous moment. Such a moment is more
abstract, in that it merely denotes a certain relation of contiguity
between the concrete events. Thus a duration is spatialised; and by
‘spatialised’ is meant that the duration is the field for the realised
pattern constituting the character of the event. A duration, as the
field of the pattern realised in the actualisation of one of its
contained events, is an epoch, _i.e._, an arrest. Endurance is the
repetition of the pattern in successive events. Thus endurance requires
a succession of durations, each exhibiting the pattern. In this account
‘time’ has been separated from ‘extension’ and from the ‘divisibility’
which arises from the character of spatio-temporal extension’.
Accordingly we must not proceed to conceive time as another form of
extensiveness. Time is sheer succession of epochal durations. But the
entities which succeed each other in this account are durations. The
duration is that which is required for the realisation of a pattern in
the given event. Thus the divisibility and extensiveness is within the
given duration. The epochal duration is not realised _via_ its
_successive_ divisible parts, but is given _with_ its parts. In this
way, the objection which Zeno might make to the joint validity of two
passages from Kant’s _Critique of Pure Reason_ is met by abandoning the
earlier of the two passages. I refer to passages from the section ‘Of
the Axioms of Intuition’; the earlier from the subsection on _Extensive
Quantity_, and the latter from the subsection on _Intensive Quantity_
where considerations respecting quantity in general, extensive and
intensive, are summed up. The earlier passage runs thus:[8]
Footnote 8:
Max Müller’s translation.
“I call an extensive quantity that in which the representation of the
whole is rendered possible by the representation of its parts, _and
therefore necessarily preceded by it_.[9] I cannot represent to myself
any line, however small it may be, without drawing it in thought, that
is, without producing all its parts one after the other, starting from a
given point, and thus, first of all, drawing its intuition. The same
applies to every, even the smallest portion of time. I can only think in
it the successive progress from one moment to another, thus producing in
the end, by all the portions of time, and their addition, a definite
quantity of time.”
Footnote 9:
Italics mine, and also in the second passage.
The second passage runs thus:
“This peculiar property of quantities that no part of them is the
smallest possible part (no part indivisible) is called continuity. Time
and space are quanta continua, because there is no part of them that is
not enclosed between limits (points and moments), _no part that is not
itself again a space or a time. Space consists of spaces only, time of
times. Points and moments are only limits_, mere places of limitation,
and as places _presupposing always_ those intuitions which they are
meant to limit or to determine. Mere places or parts that might be given
before space or time, could never be compounded into space or time.”
I am in complete agreement with the second extract if ‘time and space’
is the extensive continuum; but it is inconsistent with its predecessor.
For Zeno would object that a vicious infinite regress is involved. Every
part of time involves some smaller part of itself, and so on. Also this
series regresses backwards ultimately to nothing; since the initial
moment is without duration and merely marks the relation of contiguity
to an earlier time. Thus time is impossible, if the two extracts are
both adhered to. I accept the later, and reject the earlier, passage.
Realisation is the becoming of time in the field of extension. Extension
is the complex of events, _quâ_ their potentialities. In realisation the
potentiality becomes actuality. But the potential pattern requires a
duration; and the duration must be exhibited as an epochal whole, by the
realisation of the pattern. Thus time is the succession of elements in
themselves divisible and contiguous. A duration, in becoming temporal,
thereby incurs realisation in respect to some enduring object.
Temporalisation is realisation. Temporalisation is not another
continuous process. It is an atomic succession. Thus time is atomic
(_i.e._, epochal), though what is temporalised is divisible. This
doctrine follows from the doctrine of events, and of the nature of
enduring objects. In the next chapter we must consider its relevance to
the quantum theory of recent science.
It is to be noted that this doctrine of the epochal character of time
does not depend on the modern doctrine of relativity, and holds
equally—and indeed, more simply—if this doctrine be abandoned. It does
depend on the analysis of the intrinsic character of an event,
considered as the most concrete finite entity.
In reviewing this argument, note first that the second quotation from
Kant, on which it is based, does not depend on any peculiar Kantian
doctrine. The latter of the two is in agreement with Plato as against
Aristotle.[10] In the second place, the argument assumes that Zeno
understated his argument. He should have urged it against the current
notion of time in itself, and not against motion, which involves
relations between time and space. For, what becomes has duration. But no
duration can become until a smaller duration (part of the former) has
antecedently come into being [Kant’s earlier statement]. The same
argument applies to this smaller duration, and so on. Also the infinite
regress of these durations converges to nothing—and even on the
Aristotelian view there is no first moment. Accordingly time would be an
irrational notion. Thirdly, in the epochal theory Zeno’s difficulty is
met by conceiving temporalisation as the realisation of a complete
organism. This organism is an event holding in its essence its
spatio-temporal relationships (both within itself, and beyond itself)
throughout the spatio-temporal continuum.
Footnote 10:
_Cf._ ‘Euclid in Greek,’ by Sir T. L. Heath, Camb. Univ. Press, in a
note on Points.