Chapter 2

The topic of the present chapter is primarily not the concept of simultaneity but rather the word or the verbal expression that denotes this concept. As far as semantic considerations are involved, it suffices at this stage to define the term “simultaneity,” as understood by common sense, as the “temporal coincidence of events.”

The earliest recorded term that has been interpreted as denoting simultaneity is the Egyptian hieroglyph, ^[1] which is a “term, that denotes the simultaneity of events.” As the egyptologist Eberhard Otto showed, however, the original meaning of this term was not a temporal but rather a spatial relation denoting “local proximity or neighbourhood.” It is therefore probably also the earliest known example of the metonymical use (the use of one word for another) of spatial terms to denote temporal relations that is frequently encountered both in ancient and in modern languages.^[2] Today we still speak of a “short” or “long” interval of time; we say “thereafter” instead of “thenafter,” or “always” instead of “at all times.” In fact, we will soon see that the word “simultaneity” itself is such a metonymy.

Let us first point out that in his statement that the hieroglyph denotes “simultaneity of events,” Otto did not use “event” in the sense in which it is used in modern physics. The term “event,” derived from the Latin “e-venire” (to come out), was used at the time of William Shakespeare^[3] to denote an occurrence, process, or phenomenon of indeterminate temporal duration, just like its German equivalent “Ereignis.”^[4] In the terminology of modern physics, however, the word “event,” just like “Ereignis,” became a technical term to denote “an occurrence of negligible spatial extension and temporal duration.”^[5] The use of the term in this sense gained general currency, especially with the advent of Einstein’s 1905 relativity paper, in which the definition of simultaneity is followed by the statement “a system of values x, y, z, t . . . completely defines the place and time of an event.”[^8] In his 1907 review paper[^9] Einstein called such a system a “Punktereignis” (point-event). Hermann Minkowski, in his famous 1905 lecture on space and time, called it a “Weltpunkt” (world-point).[^10] Finally, let us quote from the introduction of a recent treatise on relativity:

“We shall adopt the point of view that the basic problem of science in general is the description of ‘events’ which occur in the physical universe and the analysis of the relationship between these events. We use the term ‘event,’ however, in the idealized sense of a ‘point-event,’ that is, a physical occurrence which has no spatial extension and no duration in time.”^[6]

Using henceforth the term “event” in this sense we can rephrase our preliminary definition of simultaneity as follows: event $e = (x, y, z, t)$ and event $e' = (x', y', z', t')$ are simultaneous if and only if $t = t'$. This thus defined simultaneity will also be called “event simultaneity” to distinguish it from what we call “interval simultaneity,” which refers to continuous sequences of events,called “processes” or “occurrences,” and which we define as follows: process $p$, beginning at time $t_1$ and ending at time $t_2$, and process $p'$, beginning at time $t_1'$ and ending at time $t_2'$, are simultaneous if and only if $t_1 = t_1'$ and $t_2 = t_2'$. If the distance between two simultaneous events is negligibly small we speak of a “local simultaneity,” if not, we speak of a “distant simultaneity.”

Returning now to the hieroglyph mentioned earlier, we see that its interpretation as “simultaneity of events,” as suggested by Otto, does not agree with our definition of “event.” For having always been used in combinations like “at the time of the reign of king...,” where “at the time” was expressed by that hieroglyph, it obviously refers not to events but rather to what we call “processes.” But even its interpretation as “interval simultaneity” would be inaccurate; for the intervals or processes under consideration, say $p$ and $p'$, have temporal durations $\Delta t = t_2 - t_1$ and $\Delta t' = t_2' - t_1'$, which, in general, do not satisfy the condition that $t_1 = t_1'$ and $t_2 = t_2'$, but only the weaker condition that$\Delta{t}$ and $\Delta{t'}$ overlap, that is, are not disjoint (symbolically, $\Delta{t}\subset \Delta{t'} \neg{0}$). Such processes will be called “contemporaneous” in agreement with the etymology of the term “contemporaneity,”^[7] which derives from the Latin “cum” (together, in common) and “tempus” (time). In our terminology the above-quoted hieroglyph denotes therefore not “simultaneity of events” but rather “contemporaneity of processes.”

The interchange of the roles of space and time in the concept of “distant simultaneity” leads to the notion of events that occur at different times at the same location. Note that in contrast to “simultaneity,” which plays an important role in the philosophy of space and time, this space–time-transposed analogue has never been found worthy of any philosophical reflection. In fact, it has never been given even a term of its own unless we accept the term “local recurrence” as a terminus technicus. The term “contemporaneity,” however, has a space–time transposal, namely “collocation,” derived from the Latin “cum” and “locus” (“place”), but it has been used since the seventeenth century primarily with respect to the arrangement of words in the field of literature. From the purely etymological point of view this terminological asymmetry between spatial and temporal terms has no justification, because the etymology of the term “simultaneity” assigns to it no preferential temporal connotation. Its etymological root is the Latin “simul,” which in turn derives from the Sanskrit “sem” (or “sema”), meaning “together,” both in the sense “together in space” and “together in time.” It still survives in the German words “zusam_men,” “_Sam_mlung,” as well as in the Nordic expressions “sam_tidig” (“simultaneous”), “sam_tidighet” (“simultaneity”), and so on. In the Greek language “sema” became "\breve{\alpha}\mu\alpha" (hama),^[8] which was used by Aristotle, for example, in the sense of “together” not only in the temporal sense. Although the German language retained, as we have seen, the Sanskrit root “sem” in several of its words, it never used it to form a term denoting “simultaneity.” Instead, it combined the words “gleich” (equal) and “Zeit” (time) to form “Gleichzeitigkeit” (simultaneity), a term listed previously, and probably for the first time, in Justus Georg Schottel’s dictionary of the German language in 1662.

To avoid equivocations it is imperative to distinguish sharply between certain terms that are often, and in many languages, employed as synonymous with “simultaneity.” Because the terminology involved is almost the same in all languages we confine our discussion to the English language. The most important of such terms are “synchronism” and “isochronism”. The authoritative Oxford English Dictionary defines “simultaneous” as “existing, happening, occurring, operating, etc., at the same time; coincident in time.” It defines “synchronous” as “existing at the same time; coincident in time; belonging to the same period, or occurring at the same moment of time; contemporary, simultaneous.” Finally, it defines “isochronous” as “taking place in or occupying equal times; ...equal in duration, or in intervals of occurrence ...taking place in the same time, or at the same time intervals of time, as something else; equal in duration.”^[9] Webster’s popular New Collegiate Dictionary identifies “synchronous” with “happening at the same time; concurrent in time; simultaneous.”^[10] The Oxford English Reference Dictionary states explicitly that both “simultaneous” and “synchronous” denote “occurring at the same time.”^[11]

This apparently incorrect treatment of different, albeit related, terms as synonyms should not be regarded as an error. When these terms were introduced into the English language or given currency in it, they were usually interpreted in accordance with their etymology. Consider, for example, the term “synchronous”. It derives from the Greek "\sigma\acute{\upsilon}\nu" (together) and "\chi\rho\grave{o}{\nu}o\varsigma" (time). By combining these two words some authors introduced the term in the sense of what we now call “simultaneous,” others in the sense of what we now call “synchronous,” for both interpretations agree with the notion of “together in time.” Similarly, the term “isochronism,” derived from the Greek "\grave{\iota}{\sigma}o\varsigma" (the same) and "\chi\rho\grave{o}{\nu}o\varsigma", was interpreted by some as denoting “simultaneity,” by others as what we now call “isochronism,” when we speak, for example, of the isochronism of vibrations.

In accordance with the modern usage of the terms “simultaneity,” “synchronism,” and isochronism” we distinguish one from the other and explain this difference in terms of their most important application, the use of clocks. As stated in the beginning of this chapter, we define “simultaneity” as the “temporal coincidence of events.” Assuming we have two clocks we regard the coincidence of their hands with certain numbers on their dials as an event. Then we can say that the clocks are “synchronized at a certain moment of time” if and only if at that moment of time the hands of the two clocks are in the same position, that is, they indicate the same time. If this condition is also satisfied at an arbitrary later moment of time we say that the clocks are “synchronized during an interval of time” or simply “synchronized.” If the positions of the hands of the two clocks are the same at a certain moment of time they constitute two, generally separated, simultaneous events. It is therefore clear that the notion of “synchronism” involves or presupposes the concept of “simultaneity.” It is also clear that “synchronism” always refers to two (or more) clocks. In contrast, the term “isochronism” refers to one and only one clock, for we say that a clock is “isochronous,” if and only if it “runs” at a constant (or uniform) rate, that is, if the periods between consecutive “ticks” are equal. Here we face the problem of how to verify that two consecutive time intervals (or, more generally, two temporally separated time intervals) are equal. We cannot shift the later time interval into the position of the preceding (or earlier) time interval. The generally accepted method of calibrating time intervals with the duration of the rotation of the Earth, which defines the length of the mean solar day, is based on the assumption of a uniform rotational velocity of the Earth, but this assumption is not strictly correct because the tidal frictions of the oceans, for example, decelerate the rotation of the Earth. As a closer analysis shows,^[12] even an appeal to the law of inertia, according to which a particle, not subjected to any interaction, moves with constant velocity, that is, moves through equal distances in equal intervals of time, would be of no avail.

Another temporal term, intimately related to “simultaneity” but not identical with “simultaneously,” is the adverb “now.” The English term “now,” like the Latin “nunc” and the Greek "\nu\tilde{\upsilon}\nu" derives from the Sanskrit “nu.”^[13] It deserves our attention not only because it is an “indexical”^[14] term, related to simultaneity, but also because, as we will see in due course, it probably expressed the earliest human awareness of the conception of simultaneity and it played an important role in Aristotelian and medieval philosophy. In modern times Hans Reichenbach classified it as a “token-reflexive word, comparable in this respect with ‘I’, for it means the same as ‘the time at which this token is uttered.’”^[15] Ludwig Wittgenstein, in his discussion of time-language,^[16] declared that “the function of the word ‘now’ is entirely different from that of a specification of time” and has a logic of its own. Einstein, “said that the problem of the Now worried him seriously. He explained that the experience of the Now meant something special for man, essentially different from the past and the future, but that this important difference does not and cannot occur in physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation.”^[17]

The relation between “now” and “simultaneity” has scarcely ever been discussed. A noteworthy exception is Eugen Fink’s statement: “The fundamental meaning of the Now is that of a universal simultaneity ... it contains the whole world-wide extent of the simultaneous,” a statement that perhaps explains Einstein’s worry, because his theory of relativity denies the existence of a universal simultaneity. A comprehensive discussion of “simultaneity” cannot ignore the relation between this concept and the “now,” even if it is true that such a relation holds only, as some philosophers of language contend, in what they call a “tenseless language.”^[18]

In classical physics, based on the Newtonian conception of absolute time, which “flows equably without relation to anything external,”^[19] and on the assumption of the existence of instantaneous actions at a distance, none of the terms “simultaneity,” “synchronism,” “isochronism,” or “now” raised any conceptual difficulties.

Even a notion like “spatial recurrence” in the meaning of repeated presence at the same local position, whether of an object, event, or process, had a clear-cut meaning in Newtonian physics, according to which “absolute space, in its own nature, without relation to anything external, remains always similar and immovable.”^[20] In modern physics, however, which denies the existence of absolute time, absolute space, and instantaneous actions, all these terms or notions involve serious problems as we will see in due course. Finally, note that, in conformance with our terminology, spatially separated events can be defined as simultaneous if synchronized clocks, located in their immediate vicinities, indicate the same readings at the occurrences of these events. Clock synchronization and simultaneity are therefore intimately related concepts, at least insofar as the operational establishment of one of them assures the existence of the other.

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Footnotes

1. See, for example, A. H. Gardiner, Egyptian Grammar (London: Oxford University Press, 1957), p. 579. For later or less frequently used hieroglyphic expressions of a similar meaning see E. A. Wallis Budge, First Steps in Egyptian(London: Kegan Paul, Trench, Trubner & Co., 1923), pp. 43, 81, 116, 250. ↩︎

2. For examples of such space–time metonymies in Sumerian and ancient Hebrew, see M. Jammer, Concepts of Space (Cambridge, Massachusetts: Harvard University Press, 1954; enlarged edition, New York: Dover Publications, 1993), pp. 3–4. ↩︎

3. Cf. J. Bartlett, A Complete Concordence of Shakespeare (London: Macmillan, 1966), p. 455. ↩︎

4. The word “Ereignis” derives from “ir-ougen” (to appear to the eye), related to the German word “Auge” (eye). From the etymological point of view the German word “Ereignis” resembles the word “phenomenon,” which derives from the Greek “
    ” (to make visible). ↩︎

5. Ibid., p. 548. ↩︎

6. G. L. Naber, The Geometry of Minkowski Spacetime—An Introduction to the Mathematics of the Special Theory of Relativity (New York: Springer-Verlag, 1992), p. 1. For other modern usages of the term “event” see Q. Smith, Language and Time (Oxford: Oxford University Press, 1993), p. 24. ↩︎

7. For variations of this term, like “contemporariness” etc. and historical details see The Oxford English Dictionary (Oxford: Clarendon Press, 1933, 1961), vol. 2, pp. 894–895. ↩︎

8. Recall that in Greek the letter s is often replaced by the aspirate h as, e.g., in "\alpha\lambda\varsigma" (hals), which is the Latin “sal” and the English “salt” (cf., halogen = salt-forming). ↩︎

9. _The Oxford English Dictionary _(Oxford: Clarendon Press, 1931, 1961), s.v. ↩︎

10. New Collegiate Dictionary (Springfield, Massachusetts: Merriam, 1960). ↩︎

11. J. Pearsell and B. Trumble (eds.), The Oxford English Reference Dictionary (New York: Oxford University Press, 1996), p. 1352. “Synchronous” and “isochronous” are also treated as synonyms in F. C. Graham’s The Basic Dictionary of Science (New York: Macmillan, 1966), pp. 467 and 209. ↩︎

12. See, for example, H. Reichenbach, The Philosophy of Space and Time (New York: Dover Publications, 1958), chapter 2, § 17. ↩︎

13. According to the Oxford English Dictionary (Oxford: Clarendon Press, 1970), vol. 7, p. 245, “now” denotes “at this time; at the time spoken of or referred to.” The German “nun” (now), also derived from the Sanscrit “nu,” has a more frequently used synonym “jetzt,” corresponding to the adjective “jetzig,” which is a derivation of the medieval “iezuo.” ↩︎

14. So called by Rudolf Carnap, because it “points” to the person who utters the word (“index” in Latin means “forefinger,” “indicate” means “to point at”). For indexical terms see Y. Bar-Hillel, “Indexical expressions,” Mind 63, 359–379 (1954). ↩︎

15. H. Reichenbach, The Elements of Symbolic Logic (New York: The Free Press, 1947), p. 284. ↩︎

16. L. Wittgenstein, The Blue and the Brown Books (Oxford: Blackwell, 1958), pp. 107–108. ↩︎

17. R. Carnap, “Intellectual autobiography” in P. A. Schilpp, The Philosophy of Rudolf Carnap (La Salle, IL: Open Court [The Library of Living Philosophers, vol. XI], 1963), p. 37. ↩︎

18. See, for example, Q. Smith, Language and Time (New York: Oxford University Press, 1993), chapter 1. ↩︎

19. ”Tempus absolutum, verum et mathematicum, in se et natura sua absque relatione ad externum quodvis, aequabiliter fluit.” I. Newton, Philosophiae Naturalis Principia Mathematica (London: Streater, 1687), p. 5. ↩︎

20. ”Spatium absolutum natura sua absque relatione ad externum quodvis semper manet similare et immobile.” Ibid., p. 5. ↩︎