*Duration and Simultaneity*. Paragraph headings are my own. My personal commentary is in brackets.]

*Duration and Simultaneity*

*simultaneous events.*If, for instance, I say, "That train arrives here at 7 o'clock," I mean something like this: "The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events" (Einstein

*The Principle of Relativity*39, qtd. in Mook & Vargish 56bc).]

*m*and C

*n*. An observer stands between these two clocks, and can "embrace from there, in a single act of instantaneous vision, any two events occurring at points C

*m*and C

*n*respectively when these two clocks show the same time" (61a). In particular, he will "embrace in this instantaneous perception the two concordant readings on the two clocks" (61ab). In this way, all simultaneities indicated by the clocks will then "be converted into intuitive simultaneity inside the system" (61).

**this is merely a convention used to "preserve the integrity of physical laws"**(64d). And in fact, these laws were devised by first assuming that simultaneity and succession are relative, given one's point of view. (underlining and boldface mine)

the passing from stability to mobility having doubled the meaning of the work, you slip all the materiality and solidity of the first meaning into the second. I would say that instead of forewarning the philosopher against this error, you want to draw him into it, did I not realize the advantage you derive, as a physicist, from using the word simultaneity in both senses: you remind yourself in this way that learned simultaneity began as innate simultaneity and can always turn into it again should thought immobilize the system anew. [66b]

**Einstein's theory is bilateral, so all motion is reciprocal, and there are no privileged systems. Hence "the observer in S is as much in the right in seeing succession in S' as is the observer in S' in seeing simultaneity there"**(66d boldface mine). Thus regarding journeys P and Q "The observer in S' is not mistaken, since, for him, P is equal to Q: the observer in S is no more mistaken, since, for him, the P and Q of system S' are unequal" (66d). Now, in this double (bilateral) relativity, we have regarded some system as privileged. Then, the mathematics works-out the same as if it were single (unilateral) relativity. So in our minds, we think of double relativity as if it were single relativity.

We then act as if - the two passages P and Q appearing unequal when the observer is outside S' - the observer inside S' were mistaken in designating these passages as equal, as if events in the physical system S' had been broken up in actuality at the dissociation of the two systems, when it is merely the observer outside S' who rules them broken up in following his own definition of simultaneity. We forget that simultaneity and succession have then become conventional, that they retain of the original simultaneity and succession merely the property of corresponding to the equality or inequality of the two journeys P and Q. It was then still a question of an equality and inequality found by an observer inside the system and therefore final and unchanging. [67ab]

the philosopher, who wants to know what to believe regarding the nature of time, who wonders whether or not the track and the train have the same real time - that is, the same lived or livable time the philosopher must always remember that he does not have to choose between the two systems; he will place a conscious observer in both and will seek out the lived time of each. [69a].

But, in marking the double set of arrows, we have given up adopting a system of reference; we have mentally placed ourselves on the track and in the trainat one and the same time; we have refused to turn physicist. We were not, in fact, looking for a mathematical representation of the universe; the latter must naturally be conceived from one point of view and conform to the laws of mathematical perspective. We were asking ourselves what is real, that is, observed and actually recorded. (69d, boldface and underline mine)

**They will be mere abstractions; "his notation of it will then no longer correspond to anything perceived or perceptible; it will therefore no longer be a notation of the real but of the symbolic"**(70, boldface mine). But the same will hold for the observer in the train, who transposes all other systems to his own. There will be a discrepancy between a) the observer's recordings for the observers he sees and b) the recordings that those observers themselves obtain. However, the same laws of nature will hold for each. And this is the ground for us saying there is a universe independent of our observations. "The magnitudes appearing in these two visions will be generally different, but, in both, certain relations among magnitudes, which we call the laws of nature, will remain the same, and this identity will precisely express the fact that the two representations are of one and the same thing, of a universe independent of our representation" (70b).

A philosophy which assumes the viewpoints of both track and train, which then notes as simultaneity in the train what it notes as simultaneity on the track, no longer stands halfway between perceived reality and scientific construction; it is completely in the real, and is moreover, only completely appropriating Einstein's conception which is that of the reciprocity of motion.But that idea, as complete, is philosophical and no longer physical. To convey it in physicist's language we must take the position of what we called the hypothesis of unilateral relativity. And as this language asserts itself we do not perceive that we have for a moment adopted this hypothesis. We then speak of a multiplicity of times that are all on the same plane, all real, therefore, if one of them is real. But the truth is that the latter differs fundamentally from the others. It is real, because it is really lived by the physicist. The others, merely thought of, are auxiliary, mathematical, symbolic. [70-71, boldface mine]

*l*, from N'. Suppose they all share the same event. We know that the event cannot happen simultaneously, for an observer that is not moving the speed of this system. Also consider a determinate event happening for N' at a certain moment. Depending on the relative speed between this system and the observing system, the event will happen at some other time for the other points. So the event is not determinate at the other points [it could happen at any time, depending on the relative speed of the observer].

*v*. Recall in chapter 1 our discussion of the breakup of simultaneities. We described how each clock separated by

*l*lagged by

*v*stands for the velocity of the system, and the

*c*stands for the speed of light. So let's substitute the speed of light for the speed of the system, and see what the limit is for the length of lines M'E' and P'F'.

The two systems S and S' are in a state of complete reciprocity; it is for the convenience of study, to erect a physics, that we have immobilized one or the other into a system of reference. All that a real, flesh-and-blood observer observes at N, all that he would instantaneously, telepathically observe at no matter how remote a point in his system would be identically perceived by a real flesh-and-blood observer located at N' in S'. Hence, that portion of history of places M' and P' which really enters the present of the observer at N'for him, what he would perceive at M' and P' if he had the gift of instantaneous vision at a distance, is determinate and unchanging, whatever the speed of S' in the eyes of the observer inside system S. It is the same portion that the observer at N would perceive at M and P. [74-75]

*in his eyes*, underline contemporaneous events" (75d). The events that seem contemporaneous for those in S' appear successive to the observer in S; "or rather,

*they appear as having to be noted down as successive*, by reason of his definition of simultaneity" (75d).

For this last observer, it must be added, there is no further question of a flesh-and-blood existence; he has been surreptitiously drained of his content, in any case, of his consciousness; from observer he has become simply observed, since it is the observer in N who has been given the status of physicist-builder of all science. (76a)

asvincreases, our physicistnotesas pushed back ever farther into the past of place M', advanced ever more into the future of place P', the always identical event which, whether it be at M' or P', is part of the really conscious present of an observer at N', and consequently part of his own. There are not, therefore, different events at place P' which enter by turns, for increasing speeds of the system, into the real present of the observer at N'. But the same event of place P', which is part of the present of the observer at N', under the assumption of the system's immobility, is noted by the observer at N as belonging to a future ever more remote for the observer at N', as the speed of the mobilized system S' increases. If the observer at N did not so note, it must be added, his physical conception of the universe would become incoherent, for his written measurements of phenomena occurring in a system would express laws that he would have to vary with the system's speed; thus, a system identical with his, whose every point would have identically the same history as the corresponding point in his, would not be governed by the same physics (at least in what concerns electromagnetism). [76b.c]

For the observer at N', therefore, there is not, at M' and P', next to events that we consent to leave in the "absolute past" or in the "absolute future," a whole mass of events which, past and future at those two points, enter his present whenever we attribute the appropriate speed to system S'.There is, at each of these points, only one event making up a part of therealpresent of the observer at N', whatever the speed of the system; it is the very one that, at M and P, is part of the present of the observer at N.But this event will be noted down by the physicist as located more or less back in the pastof M', more or less forward in the future of P', according to the speed attributed to the system. It is always, at M' and P', the same couple of events that form together with a certain event at N' the present of Paul located at this latter point. Butthis simultaneity of three events appears incurvated into past-present-futurewhen beheld in the mirror of motion by Peter picturing Paul. [77c.d, boldface and underline mine]

**only an effect of mental torsion**" (78d); "the line of simultaneity between the three points M', N', P'

**appears**turned about N' by a certain angle, so that one of its extremities lags behind in the past while the other encroaches upon the future" (79a, boldface mine).

*really*have the same length or if in reality they do not. Bergson calls real whatever is perceived or perceptible. But the measurements and calculations that S and S' reckon for each other's systems are merely mathematical abstractions. We can only go by what is really perceived or perceivable. That means we must turn to Peter and Paul and ask them what their perceptions are of the lengths in their own system. Both of them consider their length to be at rest, so they both obtain the same measure. When we consider their systems in motion, that means we may interchange their perspectives. And that means both their measurements will be the same.

Hence, in the thesis of special relativity, the extended can no more really contract than time slow down or simultaneity actually break up. But, when a system of references has been adopted and thereby immobilized, everything happening in other systems must be expressed perspectively, according to the greater or lesser difference that exists, on a size-scale, between the speed of the system referred to and the speed, zero by hypothesis, of the referrer system. [80bc]

*Inside Relativity*. Princeton: Princeton University Press, 1987.

*Duration and Simultaneity*. Ed. Robin Durie. Transl. Mark Lewis and Robin Durie. Manchester: Clinamen Press, 1999.

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