granted , however , that events at A after E1 and before E2 are in an empirically undetermined order with respect to event eb at B , must we accept Robb &apos;s contention that Einstein was mistaken in allowing A to assign a theoretical epoch to eb ? in other words , if we reject the classical doctrine of time which stipulates that there must be a unique event at A which is absolutely simultaneous with eb , does it follow that Einstein ought not to have ascribed a definite conventional system of time-relations ( earlier than , simultaneous with , and later than ) between eb and all events at A ? the function of convention in the construction of theories is descriptive simplicity , and it must be admitted that Einstein &apos;s special theory of relativity is simpler than Robb &apos;s alternative . but that is not all . as we have seen , Einstein &apos;s conventional rule by which A assigns a theoretical epoch to eb is not a mere convention in the sense of being wholly arbitrary . for , although it is a convention in so far as it is freely chosen and not imposed upon us , it can be isolated uniquely from other admissible rules by means of the axioms stated above . with all due respect to Robb , the essential question is not the conceptual legitimacy of Einstein &apos;s convention but its practical scope , that is , the range of physical contexts to which it can be most usefully applied . 4 . the correlation of time-perspectives . so far we have considered only a single observer A . unlike Frank and Rothe , Whitehead and others who sought to deduce the existence of a finite universal velocity from more primitive postulates , we have not found it necessary to consider the correlation of the space and time coordinates assigned to a distant event by different observers . although this presented no special difficulty for the classical Newtonian physicist who believed in an absolute world-wide simultaneity and an absolute physical space governed by the laws of Euclidean geometry , as soon as these assumptions were abandoned the problem had to be re-examined . it is now generally recognized that the most satisfactory method of solution is to consider first the correlation of two observers &apos; clocks by means of the same experiment in light-signalling as we introduced above ( pp 186-7 ) . there we considered the assignment by A of times to events occurring at B . as we have seen , Einstein &apos;s solution was based on his postulate that the velocity of light according to A is a universal constant , independent of position and direction of propagation . we must now consider the correlation of this theoretical time assigned by A to an event at B with the empirical epoch t&amp;prime; which would actually be recorded on a clock placed at B . to make the problem precise we postulate that B is now an observer similar to A . in particular , this implies that B carries a clock similar to the one carried by A . for example , if A carries a particular type of atomic or molecular clock , we assume that B carries another clock of identical construction . with the aid of this clock , B can partake in A &apos;s light-signalling experiment , the signals being instantaneously reflected back to either observer on arrival at the other , as indicated in figure 7 . in the special theory of relativity it is assumed that A and B are associated with inertial frames of reference . consequently , they are either at relative rest or in uniform relative motion . the principle of relativity on which the theory is based was formulated by Poincar&amp;eacute; in a lecture at Saint Louis , U.S.A in September 1904 . according to his statement , the laws of physical phenomena must be the same for a fixed observer as for an observer who has a uniform motion of translation relative to him : so that we have not , and can not possibly have , any means of discerning whether we are , or are not , carried along in such a motion . shortly afterwards , and independently , the principle was enunciated in a much more explicit form by Einstein : the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good . this principle presupposes that the observers associated with such frames of reference employ similar measuring instruments , for example clocks , and adopt the same metrical rules and definitions . therefore , if A assigns a universal value c to the speed of light , then B must do the same . it is customary when considering the correlation of the clocks and time-perspectives of A and B in Einstein &apos;s special theory to concentrate on the case in which they are in uniform relative motion . instead , in view of its importance for establishing one of the main results in the following chapter , I shall begin by considering the case in which they are at relative rest . if A and B have similarly graduated clocks , then , apart from the possible adjustment of an additive constant depending on the choice of zero-time on each clock , the principle of relativity can be reduced , as far as kinematics is concerned , to the following : axiom 10 . principle of kinematic symmetry : t2 is the same function of t&amp;prime; as t&amp;prime; is of t1 . hence , there must be functional relations of the form &amp;formula; . consequently , the function th , which we will call the signal function correlating A and B , must be such that &amp;formula; . but , since B is at a fixed distance from A and the light-signals travel with constant speed , it follows that ( t2-t1 ) must be a constant . hence , th must be such that &amp;formula; , for all values of t1 and some constant a . if we drop the suffix , an obvious solution of this functional equation is given by &amp;formula; . more generally , by operating on each side of ( 23 ) with th we deduce that &amp;formula; , whence it immediately follows that th(t) must be of the form &amp;formula; , where o(t) is of period 2a . to reduce this to the particular form &amp;formula; , we must consider other similar stationary observers . thus , if A , B , and C are collinear , with B lying between A and C , and f is the signal function correlating B and C , then A and C will be related by the signal function ps given by &amp;formula; . consequently , th and f must be commutative functions . since C is at a fixed distance from B , f must satisfy a functional equation of the form &amp;formula; , where b is some constant . it is then easily proved that &amp;formula; , and so we deduce that A and C are at a fixed distance apart equal to the sum of the respective distances of A and B and of B and C . by operating on both sides of ( 24 ) with the function th and appealing to the commutative property of th and f , we deduce that &amp;formula; , whence it follows that &amp;formula; , where o(t) is of period 2b . hence , o(t) must admit both 2a and 2b as periods . if A , B , and C are any three members of a continuum of relatively stationary observers , then 2a and 2b will , in general , be incommensurable . consequently , by a well-known theorem the only continuous form for the function o(t) is a constant , and so from equation ( 23 ) it follows that &amp;formula; . with this solution for th(t) , equations ( 21 ) give &amp;formula; . by comparison with equation ( 19 ) , we deduce that t&amp;prime; = t , that is , the time recorded on B &apos;s clock when any event occurs at B is the same as the time theoretically assigned to that event by A on the basis of the uniform velocity of light . therefore , all relatively stationary observers assign the same time to any given event , and this time agrees with that actually recorded on the clock kept by the observer at the point where the event occurs . in this conventional sense , there is world-wide simultaneity of events , and therefore universal time , for all relatively stationary observers . the above analysis was based on the kinematic symmetry of relatively stationary observers with similarly graduated clocks who assign the same constant value to the speed of light-signals passing between them in free space . in his special theory of relativity , Einstein showed how the same principle of kinematic symmetry in light-signalling experiments could be extended to observers in uniform relative motion , although the consequences are not entirely the same as for relatively stationary observers . in particular , there is no longer world-wide simultaneity , and hence no universal common time , for the aggregate of uniformly moving observers . consequently , although the theory is based on the hypothesis that the general laws governing physical formulae are of the same form for an observer associated with any inertial frame in uniform relative motion as for an observer associated with any inertial frame at relative rest , there are important differences regarding the epochs assigned to particular events . to see this most simply , we again consider light-signalling from A to B and from B to A , as in figure 7 , but this time we stipulate that the two observers concerned move away from coincidence with each other at a particular epoch with uniform velocity in a radial direction . we also postulate that the two similar clocks were synchronized to read time zero at the original instant of coincidence . as before , we consider a signal emitted by A at time t1 , recorded on A &apos;s clock . we suppose that this signal is instantaneously reflected on arrival at B at time t&amp;prime; , according to B &apos;s clock , returning to A at time t2 , according to A . from the principle of kinematic symmetry it follows that , if &amp;formula; , then &amp;formula; . therefore , &amp;formula; . but &amp;formula; , where r is the distance of B from A , according to A , at the instant of reflection , and t is the epoch theoretically assigned by A to this event . since B is moving away radially from coincidence with A at time zero , it follows that &amp;formula; , where V is the relative speed of B . hence , &amp;formula; , where &amp;formula; . consequently , on comparing ( 25 ) and ( 26 ) we see that the function ps must be such that for all values of the variable t &amp;formula; . by operating on each side of this equation with ps , we deduce that &amp;formula; , whence &amp;formula; , the prime symbol denoting the derivative . the only solution of equation ( 28 ) which is continuous as &amp;formula; ( positively ) is ps&amp;prime;(t)=k , where k is a constant . since t&amp;prime;=0 when t1=0 , it follows that ps(0)=0 , and hence we must have ps(t)=kt . comparison with ( 27 ) yields k2=a2 . in order to obtain the unique solution k=a , and hence &amp;formula; , where a is positive , we must invoke a further axiom : axiom 11 . the order of reception of light-signals by B , according to B , corresponds to the order of emission of these signals by A , according to A . we have seen that , according to A , there is at any point at a given ( theoretically assigned ) epoch a unique value for the speed of light in free space . it follows that the order , according to A , of arrival of light-signals at B must be the same as the order of their emission from A . for , if a signal emitted by A at some epoch were to arrive at B , according to A , before an earlier signal emitted from A , then , assuming continuity , there would be some event occurring in between A and B at which the second signal would overtake the first and pass it . at such an event there would be , according to A , two values for the speed of light in free space . axiom 11 can therefore be regarded as asserting that the theoretically assigned time-order of events at B , according to A , agrees with the time-order of these events as actually experienced by B . in this sense , we can speak of the time-order of these events according to A being in the same sense as the time-order of the same events according to B . by the principle of relativity , A and B are interchangeable in axiom 11 . since t2=at&amp;prime; , t&amp;prime;=at1 , and &amp;formula; , where t is the time theoretically assigned by A to the arrival ( and reflection ) of the signal at B , it follows that &amp;formula; . hence , we deduce that , although A and B agree on the time-order of events at B , they will assign different measures to the time-interval between any two instants at B . 