## 10 Dec 2009

### Systems of Relation. A. Réciprocité des apparences. 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.]

Systems of Relation

Henri Bergson

Duration and Simultaneity

Ch. 4. Concerning the Plurality of Times

Réciprocité des apparences

Previously Bergson discussed the nature of time. It is not an empty mathematical abstraction. Rather, concrete duration is filled with real change that cannot be abstracted away from its flow. And for there to be a passage of time, there needs to be the combination of the past and the present. For otherwise it is just the instantaneous present, which has no temporal character. And for the past to be retained, there must be something like memory. Hence duration requires consciousness. There are different durational flows around us, like the river and the flying bird. These are two simultaneous flows, that are united in a third flow, which is the flow of consciousness that is conscious of the flowing-together of these two flows.

§55 Why Won't Light Just Slow Down?

Bergson returns now to topics from the first chapter: Einstein's time, the ether, and the Michelson-Morley experiment. The experiment showed that no matter the speed of the earth, light still travels the same speed. Bergson wonders now how to explain this.

§56 Firm of the Earth

[So suppose our friend walks across a boat. We see her from the dock. For her, she is going her walking speed. But for us, she travels her walking speed plus the boat's speed.] The Michelson-Morley experiment was conducted at different times of the year, when the earth goes different speeds. But this is relative to the sun. Could it not have been relative to just about anything? Do we add to the earth's speed around the sun, and also the sun's speed in the galaxy? But then to what point do we orient the galaxy? It is all relative. We arbitrarily choose our reference frame. In the case of light moving on earth, our reference frame is the earth. [See chapter 2]. So the earth is motionless under this view. This is one reason Bergson gives for why light does not change speed.

§57 The Sun and Earth Spin Right-Round Each Other

But still systems in motion are relative. Physicists who take the earth as the reference frame will calculate things differently than solar physicists who regard the sun as the reference frame.

§58 Peter Measures Paul

Recall the situation of Peter and Paul, from chapter 1. They both were in different systems. Peter's system S remained motionless in the ether. Paul's system S' was moving-off at a constant velocity. Nonetheless, they both found that light traveled the same speed in the other's system. But they expect to find different speeds for light in the other's system, because the other's system is moving away. We explained this phenomenon by saying that it results from "the slowing of time, the contractions in length and the breakup of simultaneity that motion brought about in system S' " (49b). But then after more consideration in chapter 2, we came to regard there to be no privileged motionless ether to serve as an absolute frame of reference. Rather, any system can be considered motionless or in motion, depending on whether or not it is considered the frame of reference. Nonetheless, before while supposing the ether, we did learn some things that apply to stationary systems. And we may apply that knowledge to the system that we now arbitrarily designate as motionless.

So Bergson will make some assumptions to illustrate his ideas.
1) We give the names S and S' to two systems in mutual displacement.
2) We assume that somehow the whole universe reduces to these two systems.

Now let's say that system S is the system of reference. He finds that light moves at the same speed in both his system as it does in system S'. A physicist in S would think these things:
a) The other system S' travels at speed v with respect to me, and I am motionless.
b) Yet, the Michelson-Morley experiment gives the same results on the moving system as it does here.
c) Hence what must be happening is that distance in system S' contracts in the direction of its motion. A length l becomes l multiplied by

d) Also, relative to the motionless system, time in the moving system contracts. So when a clock in system S' ticks-off a t' number of seconds, there has really elapsed

of them.
e) There are clocks distant from each other in S'. When the physicist in S' thinks they are simultaneous, they really are not. Their moments succeed each other by

of his seconds, and thus by

of my seconds. These would be the conclusions of the physicist in system S. And he would only use the space and time measurements of his colleague in system S' if they first underwent Lorentz transformation.

§59 Paul Measures Peter

But, the physicist in system S' would do everything the same way as the physicist in system S. He would consider his own system motionless. Then he would repeat all of measurements and calculations that the physicist in S performed. And likewise, he would use the Lorentz formulae to correct the figures of his colleague in system S.

§60 Pictures at a Cosmic Exhibition

So we find that the mathematical representations that each physicist finds for the universe are completely different from the other, if we are only considering their numerical figures. But consider how from each one's own perspective, the laws of nature hold the same in both systems. This is because the relations among phenomena are the same for each one, from their own perspective. So their perspectives are different, but what they perceive is the same. This is the grounds for us identifying them in the first place. "When we take different photographs of an object while walking around it, the variability of the details only expresses the invariability of their interrelations, in other words, the permanence of the object" (50c).

§61 Welcome to the Meanings of Relativity

So we now are dealing with these things:
1) multiple times
2) simultaneities that are successions
3) successions that are simultaneities
4) lengths that must be measured differently according to whether they are ruled stationary or moving.
But now we face 'the definitive form of the theory of relativity' (50d). We need now examine the meanings of these expressions we are using.

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: