## 22 Dec 2009

### Simultaneous Relativities. E: Les deux simultanéitiés. Ch. 4. Concerning the Plurality of Times. Duration and Simultaneity. Henri Bergson

by Corry Shores
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[The following summarizes part of chapter 4 in Bergson's Duration and Simultaneity. Paragraph headings are my own. My personal commentary is in brackets.]

Simultaneous Relativities

Henri Bergson

Duration and Simultaneity

Ch. 4. Concerning the Plurality of Times

Les deux simultanéitiés

Previously Bergson explained that the theory of relativity leads us to conclude that there is just one universal real time.

§83 Distance & Simultaneity

Bergson will now deal with the issue of the breakup of simultaneities.

First he will review what he has said about intuitive simultaneity [see §42]. Bergson will also give simultaneity this formal definition: "it is an identity between the readings of clocks synchronized through an exchange of; optical signals, and concluding that simultaneity is relative to the synchronizing" ["c'est une identité entre les indications d'horloges réglées les unes sur les autres par un échange de signaux optiques, conclure de là que la simultanéité est relative au procédé de réglage."] (60a/116b).

Bergson acknowledges that we compare clocks to determine an event's time. However, "the simultaneity of an event with the clock reading that gives us its time does not follow from any synchronizing of events with clocks, it is absolute" (60b).

[Note Einstein's definition of simultaneity: We have to take into account that all our judgments in which time plays a part are always judgments of 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).]

[Recall the issue of synchronizing clocks that are at a distance (look about midway into this entry from chapter 1. Or perhaps better, look at section 3.4 of this entry, which shows more clearly how distant clocks would be synchronized by a third person midway between them).] Image two people each have a clock, but they stand at a distance to each other. A third person stands equidistant between them. The clock-operators send signals to the center person. The signals take the same amount of time, because they are equally distant from the center person, and light always travels the same speed. This third person regards both clocks as being in his own system of reference. So even distant simultaneities suppose there being the immediate sort of simultaneity that we see between a clock and a nearby event. (60c.d)

§84 Distant Clocks in One Mind

Bergson returns to the examples of systems S and S', which are in motion with respect to each other. We begin by taking system S as our system of reference. By doing so, we immobilize it. In this system, the clocks have been synchronized by using an exchange of optical signals. Because the system is motionless, the signals make the same trip out and back.

We will now designate points where distant clocks are located: points Cm and Cn. 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 Cm and Cn 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).

§85 Distant Clocks Worlds Away

Now we will turn to system S'. An observer in this system regards it as his reference system. So he too immobilizes it. He likewise synchronizes his clocks. "Hence, when two of his clocks show the same time, the simultaneity they indicate could be lived and become intuitive" (61).

§86 The Nature of Simultaneity

Simultaneity in these cases is intuitive. "Thus, there is nothing artificial or conventional in simultaneity whether we apprehend it in one or the other of the two systems" (61bc).

§87 Conventions of Succession

We will now see how an observer in S judges events in S'. For S, the S' system is in motion. Consider the example of a person walking on a boat. She seems to herself to be walking at a certain speed. But from the perspective of someone on the dock, she moves both her speed plus the boat's speed. The person in S is like someone on the dock, watching moving system S'. The optical signals between clocks move distances that include the motion of the system itself. So the signals do not make the same trip one way as the do on their return. The exception of course is if the clocks are positioned perpendicular to the system's motion. Here we see they make diagonal lines, which are equal.

Now recall what we said about the moving system and the disruption of simultaneity, from our simplification.

We see that the moving system sees each beam at a different time, but the stationary person sees them at the same time. The situation with S and S' is different. Here we are dealing with the optical signals going from one clock to the other and back. Unless the light's path is perpendicular to the system's relative motion, the path will be different there and back. But light will be the same speed. That means time and space in the moving system distorted from the perspective of the motionless observer. So the clocks that have been synchronized from the point of view of system S', are instead successive from the viewpoint of system S.

Note what it is that the observer in S considers to be a succession. The clocks on moving system S' were synchronized. But they did so under the assumption that light had the same distance to travel from one clock to the next. But from the viewpoint of S, they had a different distance. So the clocks in system S' read the same time only one-after-the-other. But if the person on S took the perspective of S', he could have considered the concordant readings of the clocks as simultaneous. So we see that the definition of 'succession' is merely a convention. Yet as we noted, the simultaneity of events in one person's consciousness, however, is not relative and hence not conventional.
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§87 Ultimate Simultaneity

Bergson will now verify that in fact simultaneity is not conventional.
We assume that S' is a duplicate of S. The same history unfolds in each. And they are moving relative to each other. So it is arbitrary which one we consider motionless. We choose S, then, as our reference system.

The faster S' moves away, the more time and space will seem to distort, and the more simultaneities will become successively separated.

We will say that events A, B, C, D of system S are simultaneous for the observer in S. There are thus identical events in S', events A', B', C', D'. These are simultaneous for the observer in S'.

We will now imagine a supreme consciousness that is "capable of instantly sympathizing or telepathically communicating with the two consciousnesses in S and S' " (62b). Because he experiences what both observers experience, and because both observers experience simultaneity, the supreme consciousness as well perceives A, B, C, D and A', B', C', D' each as simultaneities.

Now, we can also imagine that S' returns to S. [We saw in section C of this chapter already that the time spans for each person would be the same. See this entry for more compelling reason to reject the solutions to the twin paradox which say the times are different]. So both observers in the different systems lived the same total duration. Now, let's imagine that we divide this extent of time into equal slices. There would be the same number of slices for both observers. Let's say that events A, B, C, D happen at moment M, which lies at the extremity of a slice. Then the moment M', when A', B', C', D' are simultaneous, also occurs at the extremity of the corresponding slice. Because the slices are equal, that means if we juxtapose both durations, M and M' will be aligned with each other. Hence M and M' are simultaneous. Thus A, B, C, D and A', B', C', D' as well are simultaneous altogether. "We can therefore continue to imagine, as in the past, instantaneous slices of a single time and absolute simultaneities of events" (62d).

§88 Physicists are Not In-Synch with Philosophers

But physicists would not come to the same conclusion. They see things this way: S is at rest, and S' is in motion. Experiments in S give the same results as those in S'. But how do we get the same results when light in the one system travels different distances? We see things this way only when we first take the point of view of the observer in S. By doing so, the observer in S' becomes merely something imagined in the S observer's mind. We cannot say that both observers are conscious at the same time, because doing so means that we make both of them the system of reference. But that means their systems would be motionless, yet we already stated that they are in reciprocal motion. "To be sure, we shall leave men in the moving one; but they will have momentarily abdicated their consciousness or, at least, their faculties of observation; they will retain, in the eyes of the single physicist, only the physical side of their person as long as it is a question of physics" (63b).

But Bergson's argument involved us taking both observers' consciousnesses together equally. So Bergson's rendition will not hold under the physicist's conception, which necessitates that one observer's consciousness be provisionally eliminated. We then take the perspective of the motionless observer. He sees light moving the same speed in system S' as it does in his own system. However, he also sees light maintaining this speed even though it covers different distances and even though the observer in S' clocks the light as taking the same amount of time. The observer in S then regards the simultaneities in S' to really be successions. So, because S' synchronized its clocks, and because those synchronies were really successions, that allows for light to be considered as always traveling the same speed. Thus the observer in S chooses to define simultaneity in terms of the synchronization of clocks. However, Bergson showed before that even these synchronizations involved the simultaneities of distant events perceived or conceived in the mind of one person's consciousness. Hence this physics definition of simultaneity does not also prevent us from defining simultaneity as the "real, lived simultaneities, not governed by clock synchronizations" (63d).

§89 Curves of Time

Because physicists have their own way to conceive simultaneity and succession, we must distinguish between the two different varieties. One type involves the lived experience of duration, while the other is a product of mathematical abstractions. "The first is inside events, a part of their materiality, proceeding from them. The other is merely laid down over them by an observer outside the system. The first says something about the system itself; it is absolute. The second is changeable, relative, imaginary; it turns upon the difference, changing with speed, between this system's immobility for itself and its mobility with respect to another; there is an apparent incurvation from simultaneity into succession. The first simultaneity and the first succession belong to an aggregate of things; the second, to the observer's image of them, obtained in mirrors that distort the more, the greater the speed attributed to system" (64-65). The laws of physics requiring that simultaneity incurvate into succession are the same for both the moving and immobilized observer.

§90 You Cannot Steal Someone's Simultaneity

Bergson now supposes that he is in system S'. So he considers it immobilized. Bergson stands equidistantly between the locations of two distant events O' and A'. Bergson synchronizes the clocks at the two events by taking into account that the light signal makes the same trip from O' to A' as it does on the way back. We call P the trip from O' to A', and we call Q the trip back.

Bergson now has two ways to recognize simultaneity in this situation.

1) The Intuitive Way: He could view what happens at both A' and O' in one act of consciousness.

2) The Derivative Way: He could consult the clocks and see that both events concurred with the same time on each clock.

For the person inside system S', trips P and Q are equal. But from outside system S' who regards S' as in motion, these distances seem unequal. So we first take the perspective of S' and say that the trips are equal, then we leave that perspective and take up other ones, and see them as unequal. And the faster that system S' seems to be going from our different perspective, the more unequal P and Q become. "I then declare that the events that were simultaneous before are becoming successive, and that their temporal separation is increasing" (64d). Yet, Bergson says, 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)

So, Bergson wonders, when considering simultaneity and succession in this manner, are we dealing with real simultaneity or succession? Recall first how we defined real time: "there is no time without a before and an after verified or verifiable by a consciousness that compares one with the other, were this consciousness only an infinitesimal consciousness coextensive with the interval between two; infinitely adjacent instants" (65b). The person in S' perceives a simultaneity or a succession, and both are thus real. It is true that we might take-up a point-of-view outside this system, and see as successions what are simultaneities for the consciousness of a person on S'. But that then is using a mathematical convention, which yields a conventional reality. It does not change the fact that the person on S' experiences real simultaneity and real succession.

§91 The Physicist's Sleight of Hand Simultaneity

Now consider before we stepped outside system S'. At that previous time, we considered distant events simultaneous because our mind grasped them together. The simultaneity in our consciousness is intuitive or innate simultaneity. And then we come to consider the distant events as simultaneous, so this is a learned simultaneity. However, in this case, the two types of simultaneity coincide. But when we regard S' as being in motion, then the two simultaneities no longer coincide. The faster we consider S' to be going, the less simultaneous the events seem to be. So we would no longer call the learned simultaneity a simultaneity. We might have to invent some other word for it. But we still need to speak of the clocks being read, which means that an event is simultaneous with the clock's position. Now, consider how a perspective deemed motionless with respect to S'. From this perspective we could use math to determine that events which seem successive on S' are in fact simultaneous. So we keep this intuitive meaning for simultaneity, but transpose its reality from one perspective to another. Bergson says to the physicist

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]

§92 A Unilateral Shift in Argumentation

Bergson will return to the view of unilateral relativity where there is an absolute time and an absolute clock-time. This is the time of the observer located in privileged system S. We again assume that S' first coincides with S, then moves-off.

§93 Physicists Confuse Reality with Science

We will also say that the clocks in S' are synchronized using optical signals, in the ways we mentioned before. So distant clocks will show the same time when, from the perspective of absolute time, they should be different. The simultaneities in S break-up and become successions in S' on account of its motion. The observer in S' sees them still as simultaneities, even though they are really successions.

But 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]

§94 Lightning & Relativity

Bergson will now explain why it is natural to confuse these two viewpoints when we read certain pages in Einstein's writing. The physicist might not be interested in drawing these distinctions, because they are mathematically indiscriminable. However, philosophers will view time differently depending on whether they take-up the single or double relativity theory.

Bergson now discusses the train example, which matches our demonstration from before. In this case, lightning strikes two parts of a train track. Someone stands in the middle, equally distant from both flashes. This person sees the flashes as simultaneous. However, the people in the train are moving toward one of the flashes in the process.

To understand how, we imagine that the middle of the train and the center point of the track are aligned when the lightning strikes on both ends of the track. The train moves forward and sees the one flash in front of it before later seeing the one behind it. The stationary person midway between both flashes, however, sees both flashes at the same time.
This is Bergson's diagram:

Hence "Events simultaneous with respect to the track are no longer so with respect to the train, and vice versa (relativity of simultaneity). Each system of reference has its own time; a time reading has meaning only if we indicate the system of comparison used for the measurement of time" (68cd).

§95 Bergson is More Egalitarian Than Einstein

We see that in our example, Einstein chooses the person along the track to be the frame of reference. This is why the train is moving in the direction of the arrow. But Bergson draws the situation with arrows along the track moving the other way, to indicate the reciprocal motion between the train and the track.

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].

So Bergson draws additional arrows. He also adds letters A' and B' to mark the extremities of the train.

§96 Train's and Thunderbolts

We will now say that lighting strikes. But we will not say that the place the bolts strike is on the ground or on the train. "The points from which they set out no more belong to the ground than to the train; the waves advance independently of the motion" (69bc).

§97 The World is Upside Down

So we are regarding the train and the track as mutually and reciprocally moving past each other. We see then that we cannot say that either system has some priority. We could take the perspective of the train, or of the track. Hence, the two systems are interchangeable. [Whatever would make events not-simultaneous for the train would also make them not simultaneous for the track. Now let's consider if we made the train the immobilized systems, and the ground moves in relation. Then point M' would perceive the flashes simultaneously, and point M on the track would not, because the track is moving-off toward one of the bolts all while fleeing the other. Hence Bergson writes,] "It then becomes evident at once that the two systems are interchangeable, and that exactly the same thing will occur at M' as at the corresponding point M. If M is the middle of AB, and if it is at M that we perceive a simultaneity on the track, it is at M', the middle of B'A', that we shall perceive this same simultaneity in the train" (69c).

§98 Different Times are the Same

[So we see that for either perspective, train or track, simultaneity is the same thing. When we talk to either the train or the track observer, we find that they both experienced a simultaneity; they both experienced the same temporality. Bergson writes:] "Accordingly, if we cling to the perceived, to the lived, if we question a real observer on the train and on the track, we shall find that we are dealing with one and the same time - what is simultaneity with respect to the track is simultaneity with respect to the train" (69cd).

§99 Philosophers See Things Their Own Way

[But if we think about things like physicists, we would say that both the train observer and the track observer could not have been both at the midpoint and also observed a simultaneity. This is because we would take one perspective over the other, in Einstein's example, we take the track's perspective. This allows us to formulate our mathematics and make our physical determinations. But when we ask ourselves about the reality of the lived experience of time, we will not prefer one observer's experience over the other, so we have to assume that the train-observer sees the ground-observer fly-off into the distance. Hence from the train-observer's perspective, it is the ground-observer who reaches one flash before the other. So because we take both perspectives, we are concerned with the real nature of time as it was experienced by each observer. Bergson writes:]

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 train at 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)

§100 The Reality Behind Relativity

The physicist makes a distinction, however, between the chosen system of reference versus all the other systems. So the physicist regards his own recordings as what are so, and he transposes into his own system the possible recordings of the other moving observes. Yet his calculations then will no longer be what those other observers actually experienced. 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).

§101 Philosophers Do Not Like the Physicist's Privileges

Bergson returns to the train example. The physicist at point M sees the simultaneity of the two flashes of lightning. But he cannot also be at point M' as well. So he can only "say that he ideally sees the recording at M' of a nonsimultaneity between the two flashes" (70b). All his mathematical representations of the world depend on him considering the earth his system of reference. So from his perspective, the train moves, and thus the train does not see a simultaneity at M'. But for the ground observer, M' is just a mathematical representation. It is not a fully conscious being who takes his own system as the system of reference. He just imagines an observer. So for the ground observer, 'what is simultaneity with respect to the track is not so with respect to the train. But there is an observer on the train as well, and for him, the track is the one that is speeding towards one flash and away from the other. So for the train observer, the ground point M' does not perceive the simultaneity. Hence as well, 'what is simultaneity with respect to the track is not so with respect to the train' (70d). So we see that if we take both the track and the train viewpoints, we are no longer dealing with scientific constructions. We are dealing with reality. This is the consequence of taking up Einstein's theory in its fullest. But physicists cannot do so. They must assume provisionally unilateral relativity. So for them, there is a multiplicity of times, because they take one perspective to be real, the immobilized system, and all the rest to be abstractions. But when we do not choose a privileged system, there is only just one time experienced by every observer.

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]

§101 Diverging Lines of Time

Bergson will explain this point another way. We are to imagine a system S'. On it are three points, M', N', and P'.

The system moves in the direction of this line. M' and P' are at an equal distance, 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].

We will call this system's speed v. Recall in chapter 1 our discussion of the breakup of simultaneities. We described how each clock separated by l lagged by

seconds. So now suppose that there is an event at N' that seems for the observer there to also be simultaneous at M' and P'. From the perspective of an observer moving at a different speed, "it is the past at M' and the future at P' that enter within the present context of the observer at N'. What, at M' and P', is a part of the present of the observer at N' appears to this outside observer as being the farther back in the past history of place N', the farther forward in the future history of place P, the greater the system's speed" (72b).

Bergson will now drop, in opposite directions, two lines M'H' and P'K', which are perpendicular to M'P'.

We will assume that the events in the past history of M' are spaced along M'H'. And those events of the future history of place P' are spaced along P'K'. [What is really simultaneous with N' is something in the past at M' and something in the future at P'.] So we will draw a line from past event E' at place M', through N', to F'. All these events will be simultaneous for an outside observer moving at a certain relative speed. We may call this line the "line of simultaneity" (72b). Event E' is at a interval

in the past, and F' is at the same interval into the future. [As the speed increases, time distorts event more; hence] the line M'N'P' continues to diverge as the system's speed increases (72c).

§102 Mirages of Time

Bergson notes that we might be misled into certain paradoxical conclusions. For example, imagine that we are at point N' in the center. And suppose it were possible for us to instantaneously leap to point P'. We might think that we would then be able to see a part of the future, as if we would jump to point F'.

Bergson says this is a mirage. In fact, the Minkowski scheme serves to intensify this illusion. Bergson will not yet go into detail regarding Minkowski's diagrams. He will now merely convey some of Minkowski's ideas, using the above figure.

§103 The Presence of the Past and Future

So recall that the line of simultaneity E'N'F' diverges from line M'N'P' the faster the relative speed.

But nothing goes faster than light. So there is a limit to how much the line may diverge. Recall as well that the diagonal line raises or lowers according to how many

seconds the time dilates. This tells us the length of lines M'E' and P'F', whose lengths represent the extent of the temporal distortion. The 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'.

So the distance cannot exceed.

Consider also how we think that time goes on and on into the past and future, and the extent of this time is beyond what anyone could foresee in system S'. This is because there is a certain limit to how far the diagonal line can reach up or down the lines representing the past and future at the ends of the line. So "nothing of this past or future can be a part of the present of the observer at N' (73bc).

However, note also that the future and past at the lines' extremities are supposedly contemporaneous with the event at N', from the perspective of the exterior observer. So we cannot also say that these events are absolutely future and past. In a sense, they are present as well. So if the observer at N' could have an instantaneous vision of the extremities, then the past and future would be contemporaneous with his present. But exactly how far into the past and future that he sees will be a matter of how fast the system is moving, relatively. (73c)

§104 Relativity Theorists Claim that Prophesy is Theoretically Possible

Relativity theoreticians make this claim that an observer at N' could presently perceive the future at P', if he were to have "the gift of instantaneous vision at a distance" (73d). However, such theoreticians say, light cannot travel fast enough to the observer at N', so he cannot have such instantaneous vision. And hence he cannot see into the future at P'; "that future can with impunity be included in the present of the person at N'; practically, it remains nonexistent for him" (74a).

§105 Unfolding the Mirage of Time

Bergson will now evaluate whether or not this distortion of time is a mirage.

Recall that for relativity theory, "the temporal relations among events unfolding in a system depend solely upon the speed of that system, not upon the nature of those events" (74b).

Now let's assume that S' is a double of S. That means the events will unfold in the same way in both systems.

§106 Doubled Observation

So we will also assume that in system S there is a line MNP. It begins by coinciding with line M'N'P. Then the two diverge after system S' moves-off from system S. Hence "an observer located at M' and one at M, being at two corresponding places in two identical systems, each witnesses the same history of the place, the same march of events" (74b). The same goes for the observers at N and N', and also for the observers at P and P'.

We will focus on the observers at the midpoints, N and N'.

§107 Determining What is Indeterminate

Consider the situation for the observer at N. Because he is motionless, the events at M and P are simultaneous. They are not indeterminate as with the events at M' and P'. The time that these events lag from the event at N' depends on the relative speed of S'. But S is considered immobile, so its events at M and P are determinate.

§108 Relatively, It's All the Same

We will now imagine that system S' somehow instantaneously (without acceleration) moves away at a certain speed. All the while, the system S' remains for the person at N' a motionless system. So for the observer at N', the events at M' and P' are simultaneous and not in the past or future, just as for the observer at N the events and M and P are simultaneous with the present.

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]

§109 Time & Reciprocity

Systems S and S' are in reciprocal motion. So it does not matter which perspective we take; the systems are interchangeable. This means that "the clocks of S' run for the observer at N' absolutely like those of S for the observer at N" (75a). And also on account of this reciprocity, "When the clocks located at M, N, P, and which are optically synchronized, show the same time and when there is then by relativist definition, simultaneity among the events occurring at these points, the same is true for the corresponding clocks in S'; and there is then, still by definition, simultaneity among the events occurring at M', N', P' - events respectively identical with the former ones" (75b).

§110 Simultaneity & Immobility

Yet to make our calculations, we immobilize one system, even though they are in reciprocal motion. When we do so, the simultaneities of the clocks in S are absolutely simultaneous.

§111 Time Has Come Unhinged

But then, the observer in S notices that the distances and times distort in system S'. The clocks that are simultaneous for the people in S' are not simultaneous in the eyes of the observer; "the clocks that show the same time in system S' do not, 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).

§112 Relativity is not Reality;
It's Just a Mathematical Shorthand

Consider if the speed of S' increases. For the observer at S, "the observer at N drives farther into the past of point M' and projects farther into the future of point P' - by the numbers he assigns them - events, occurring at these points, which are contemporaneous both for him in his own system and also for an observer located in system S' " (75-76).

By doing so, the observer at S no longer considers the consciousness of the observer in the other system.

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)

The physicist in S calculates that time is distorted in the other system. But this is just a calculation that he needs to perform so that his measurements for moving systems may come into accord.

as v increases, our physicist notes as 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]

§113 Physics Makes Philosophers Delusional

Recall from §104 the position of relativity theorists. They say that the person at N' could theoretically see into the future, if he had instantaneous vision across great distances. But light takes time to travel, so no such vision is possible. Hence also no such ability to see the future is possible either. Yet we have seen that if we do take-on this observer's perspective, moving in system S, then we would no longer consider that system to be in motion, and hence there would just be simultaneities present to him, both theoretically and practically. Yet the relativity theorist does think that the future is present yet unavailable to the person at N'. Bergson notes: "Certainly no physical or mathematical error will result from this statement; but great would be the delusion of the philosopher who would take the physicist at his word" (77bc).

§114 The Appearance of Relativity

So we see that there is not the perpendicular lines extending from M' and P'.

These are merely mathematical abstractions that are created when we fix one outside observer. So it might seem from the diagram that there is a continuum of past and future moments that could become simultaneous with N', depending on the speed of the observer.

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 the real present 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 past of 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. But this simultaneity of three events appears incurvated into past-present-future when beheld in the mirror of motion by Peter picturing Paul. [77c.d, boldface and underline mine]

§115 Illusions of Relativity

Bergson will now attack this problem from another direction. So let's assume again that S is identical to S', and the two systems are superposed upon each other. Then, S' breaks off and "instantly attained its speed" (77d).

Let's take-on the relativist hypothesis that time really does change. And let's also assume that the observer at N has instantaneous vision at a distance. This means he would see the future at P'. Now let's also assume that he has instantaneous communication. And recall that the systems are identical. So the observer at N could then forewarn the person at P what is to come.

[However, as we saw, the same would hold for the person in S', that he would be able to look into the future in the S system.] Really what happens is that on account of certain principles of optics, time just appears distorted in the other system. But this is an optical illusion. If the person at N had instantaneous vision at a distance, he would see the same things happening at P' which are also happening at P. "This 'skewed vision' makes the line of simultaneity passing through points M, N, P in system S appear the more oblique in system S', duplicate of S, the greater the speed of system S', the duplicate of what is occurring at M thus finds itself pushed back into the past, the duplicate of what is occurring at P, pulled forward into the future; but the long and short of it is that we have here 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).

§116 The Long and the Short of Longitudinal Contraction

Recall also that according to relativity theory, distances contract in the moving system, from the perspective of the immobilized one. Bergson will now show that the longitudinal contraction is also an optical illusion like the breakup of simultaneities. Bergson has us consider points A' and B' in moving system S'.

System S' is moving along, until at one moment coinciding parallel to its stationary double, system S. When it does so, points A' and B' settle over points A and B. Now, there are clocks at A' and B'. They were synchronized together, so they show the same time.

But let's now take the perspective of the person at S. For him, system S' is moving relative to his own system. So he thinks that the clock at B' lags behind the one at A'. So that means A and A' coincide first, but then B' will coincide with B slightly after. For this to be possible, figures the person at S, that means the length of A'B' is shorter than AB.

But, for the observer in S', his own system is the motionless one. So for S', the clock at A appears to be lagging behind B. Hence A coincides with A' only after B coincides with B'. So he will figure that the length of AB has contracted.

Bergson now wonders if AB and A'B' 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]

Mook, Delo E. & Thomas Vargish. Inside Relativity. Princeton: Princeton University Press, 1987.

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

The original French version is available online at: