## 11 Dec 2009

### Projections of Relativity. C: Le voyage en boulet. Ch. 4. Concerning the Plurality of Times. Duration and Simultaneity. Henri Bergson

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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.]

Projections of Relativity

Henri Bergson

Duration and Simultaneity

Ch. 4. Concerning the Plurality of Times

Le voyage en boulet

Previously we discussed the relativity of times between moving systems. This seemed to suggest that there are multiple different times. Bergson showed that in reality there is just one time shared by all systems.

§72 Around the Cosmos in Two Hundred Years

There is another way that the plurality of times has been conceived, and it has led to a paradoxical interpretation.

"Imagine," we are told, "a passenger in a projectile launched from the earth at about one twenty thousandth less than the speed of light, which meets a star and returns to the earth at the same speed. Having aged, say two years up to the time he gets out of his vehicle, he discovers that our globe has aged two hundred years" (53d). But this is not so.

§73 Peter & Paul's Projectile

We consider the earth motionless. The projectile is fired from a cannon on the earth. Peter stands next to the cannon. So we consider the earth as our system S. Paul sits in the projectile. So his system is S'. Peter lives two hundred more years. At the end of that time, Paul returns. "Peter has therefore been considered living and conscious; two hundred years of his inner flow have really elapsed for Peter between the departure and return of Paul" (54).

§74 Peter and Paul Are Sharing Time Together While Separated by Light-Years

But what about Paul? How much time has he lived? We are concerned not with the way Paul appeared to Peter. Rather, we are considering "the living, conscious Paul."

Paul regards his projectile as his own reference system, and thereby he immobilizes it. We now are adopting his own point of view. But then, it is no longer the projectile that is moving: "the projectile has stopped; it is the cannon, with the earth attached, which flies through space" (54b). Their systems' motion is reciprocal, so both people are interchangeable. So now we repeat for Paul everything we said of Peter. One thing we observed was a particular flow in Peter's consciousness. We now find the exact same flow in Paul's consciousness. "If we said that the first flow lasted two hundred years, the other flow will also last two hundred years. Peter and Paul, earth and projectile, will have gone through the same duration and aged equally" (54b).

§75 The Physicist Must Prefer Either Peter or Paul

Hence, "Our two people have actually seemed to be living two hundred years at one and the same time because we place ourselves at both their viewpoints. This was necessary in order to interpret philosophically Einstein's thesis, which is that of the radical relativity and, therefore, the perfect reciprocity of rectilinear, uniform motion" (54d). As philosophers, we can consider both Peter's and Paul's viewpoints equally. But for the physicist to perform her calculations, she must choose one as a reference. So when she places herself mentally in Peter's position, she records "for Peter the time that Peter records for himself, namely, the time really lived by Peter, and for Paul the time that Peter attributes to him" (55a). Likewise if she takes Paul's position. She then would render Peter's times in relation to Paul's. By necessity she must choose one or the other. So if she does in fact take Peter's perspective, then she would record Peter having lived 200 years, while Paul only lived 2.

§76 No Math Can Separate Peter from Paul

Yet, "The fact is that Peter and Paul are involved with the same physics. They observe the same relations among phenomena, discover the same laws in nature. But Peter's system is motionless and Paul's is in motion" (55c). The laws of phenomena are the same in both Peter's and Paul's systems. The way objects move in Peter's system is the same for Paul's. However, electromagnetic phenomena, for example light, may originate in the system we deem moving, but they do not share the system's motion. [Light moves the same speed no matter the speed of the system it is in]. Nonetheless, "the interrelations of these phenomena, their relations with the phenomena carried along in the system's motion are still for Paul what they are for Peter" (55c). So let's assume that for Peter, Paul's projectile goes nearly the speed of light. But phenomena for Paul still occur the same way as they would have for Peter. [The problem is this. Recall the two diverging systems and the light running perpendicular to the system's motion. Paul is in motion. But light stays the same speed. Because Paul is in motion, that means from Peter's perspective, the light beam, which is perpendicular to the direction of motion, needs to go a greater distance.
But Paul's clock reads the same amount of time for the light's passage as Peter's does. Peter's solution is to say that from his own perspective, Paul's time went slower, and his distances contracted. So if Peter had Paul's measurements, Peter would apply Lorentz' formulas to transform them so that they comply with the movements that Peter sees. But we see that this supposes Paul himself records the same readings as Peter, because Peter performed the same experiment. In other words, Peter assumes that Paul experienced the same phenomena in the same way.]

Peter can only express this persistence of relations by crediting Paul with a hundredfold slower time than his own, as we see in the Lorentz equations. Were he to reckon otherwise, he would not put down in his mathematical representation of the world that Paul in motion discovers among all phenomena - including the electromagnetic - the same relations as Peter does at rest. He is thus really implicitly granting that Paul, the referent, could become Paul, the referrer, for why are the relations maintained for Paul, why must they be recorded by Peter for Paul as they appear to Peter, if not because Paul could rule himself motionless by the same right as Peter? [55d]

Peter says that Paul's time is a hundred times slower than his own. However, this slower time is not lived-time; it is "attributed time." "The time lived by Paul would be the time of Paul referring and no longer referent - it would be exactly the time that Peter just found" (56a).

§77 The Livability of Time

Hence we have returned to this point: "there is a single real time, and the others are imaginary" (56a, emphasis mine). Such a real time could not be anything but a lived or livable time. And such other imaginary, unreal, auxiliary times would be unlivable.

§78 Philosophers Are Always Right

Bergson will now formulate the source of the confusions he has addressed.
a) Relativity theory supposes that there is no privileged frame of reference. So motion is reciprocal. We cannot say that body A moves away from B, unless we pick a point of reference that sees the motion in this way. We could also have taken B's viewpoint, and regarded A as moving away.
b) Now, we want a mathematical formula that expresses this reciprocity. It would tell us how to convert the measurements of one so that they accord with what the other one measures. Doing this requires first that we pick the one system that will be translated, and the other system which will do the translating, so that its figures accord with the other. Hence such formulae that express reciprocity in the first place express the non-reciprocity involved in the translation.
c) The system that we select as the motionless one has nothing inherent to it which makes it the preferred choice. It is an arbitrary selection. Before we considered two hypotheses: The first was that there is a motionless ether to which all other moving systems can be related. The second was that there is no privileged motionless system, and hence all are relative. One must be arbitrarily selected and hypothetically immobilized, so that the calculations for all systems can be brought into accord.

So there are two hypothetical situations. 1) Unilateral relativity, where there is an absolutely motionless system; and 2) Bilateral relativity, where no system is inherently motionless, so one is arbitrarily taken to be immobilized in relation to the rest. We will use the same formulas regardless of which hypothesis we assume.

But are both hypotheses the same for the philosopher?

Let's assume first that there is a truly motionless observer, Peter; and, Paul really is moving away from him. That means Paul cannot say that Peter moves away from him. It would be clear that Paul is the one in motion. Hence Paul cannot translate Peter's readings to his own, as if Paul were the reference frame. This is Peter's privilege. So in fact, Paul would experience a different temporality.

But if instead their motion were reciprocal, then either one can be the reference frame. The time they experience would be the same. But to explain their own observations of the other system, they need to apply formulae so that they are in accord.

Hence, the hypothesis of reciprocity gives us at least as much reason for believing in a single time as does common sense; the paradoxical idea of multiple times asserts itself only in the theory of the privileged system, even when we have begun by granting reciprocity; and the physicist, feeling free of the theory of reciprocity once he has done it homage by freely choosing his system of reference, surrenders it to the philosopher and henceforward expresses himself in the language of the privileged system. Paul will enter the projectile, believing in this physics. He will come to realize on the way that philosophy was right. [56d]

§79 Philosophers Know the Difference between Real Physicists and Imaginary Ones

Special theory of relativity assumes that any system can be the reference system. The formulae were designed so that the physicist can choose any system whatsoever as the reference frame, and from that perspective bring the measurements of all other systems into accord with that one. So the physicist can take any point of view and in each case produce calculations and measurements that are reciprocally relative to the others. Hence it is on this basis that it is absolutely arbitrary for the physicist to choose one reference frame over another. Given that any point-of-view is equitable with the others, he has every right to choose his own as the reference frame. The philosopher can also use this fact to determine real time from imaginary time. "The real is that which is measured by a real physicist, and the imaginary, that which is represented in the mind of the real physicist as measured by imaginary physicists" (57c).

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: