Part 1

Two Difficulties Regarding Time

As long as we do not go outside the domain of consciousness, the notion of time is relatively clear.

We easily distinguish our present sensation from the remembrance of past sensations or the anticipation of future sensations.

When we say that two conscious facts are simultaneous, we mean that they profoundly interpenetrate, so that analysis can not separate them without mutilating them.

For an aggregate of sensations to have become a remembrance capable of classification in time, it must have ceased to be actual. We must have lost the sense of its infinite complexity. Otherwise, it would have remained present.

It must have crystallized around a center of associations of ideas which will be a sort of label. It is only when they thus have lost all life that we can classify our memories in time as a botanist arranges dried flowers in his herbarium.

But these labels can only be finite in number.

Thus, psychologic time should be discontinuous.

Whence comes the feeling that between any two instants there are others?

We arrange our recollections in time, but we know that there remain empty compartments. How could that be, if time were not a form pre-existent in our minds? How could we know there were empty compartments, if these compartments were revealed to us only by their content?

Into this form, we wish to put not only the phenomena of our own consciousness, but those of which other consciousnesses are the theater.

But more, we wish to put there physical facts, these I know not what with which we people space and which no consciousness sees directly. This is necessary because without it science could not exist.

Thus, psychologic time is given to us and creates scientific and physical time. There the two difficulties begin.

Think of two consciousnesses, which are like two worlds impenetrable one to the other.

By what right do we strive to put them into the same mold, to measure them by the same standard?

Is it not as if one strove to measure length with a gram or weight with a meter? Why do we speak of measuring?

We know perhaps that some fact is anterior to some other, but not by how much it is anterior.

Therefore, two difficulties:

1. Can we transform psychologic time, which is qualitative, into a quantitative time?
• This difficulty have long been noticed and has been settled
1. Can we reduce to one and the same measure facts which transpire in different worlds?

We have not a direct intuition of the equality of two intervals of time. The persons who believe they possess this intuition are dupes of an illusion. What do I mean when I say, from 12 noon to 1 pm, the same time passes as from 2 pm to 3 pm?

The least reflection shows that by itself it has no meaning at all. It will only have the meaning that I give to it, making it arbitrary.

Psychologists could have done without this definition. But physicists and astronomers could not.

To measure time, physicists use the pendulum. They suppose by definition that all the beats of this pendulum are of equal duration.

But this is only a first approximation. The following make the pace of the pendulum vary:

• temperature
• the resistance of the air
• the barometric pressure
• make the pace

If we could escape these sources of error, we should obtain a much closer approximation. But it would still be only an approximation.

New causes, hitherto neglected, electric, magnetic or others, would introduce minute perturbations.

In fact, the best chronometers must be corrected from time to time. The corrections are made by the aid of astronomic observations. Arrangements are made so that the sidereal clock marks the same hour when the same star passes the meridian.

In other words, it is the sidereal day (the duration of the rotation of the earth) which is the constant unit of time.

It is supposed, by a new definition substituted for that based on the beats of the pendulum, that two complete rotations of the earth about its axis have the same duration.

However, the astronomers are still not content with this definition. Many of them think:

• that the tides act as a check on our globe
• that the rotation of the earth is becoming slower and slower.

Thus would be explained the apparent acceleration of the motion of the moon, which would seem to be going more rapidly than theory permits because our watch, which is the earth, is going slow.

One will say that all this is unimportant. Our instruments of measurement are imperfect. But it suffices that we can conceive a perfect instrument.

This ideal can not be reached. But it is enough to have conceived it and so to have put rigor into the definition of the unit of time.

The problem is that there is no rigor in the definition.

We use the pendulum to measure time. But what postulate do we implicitly admit?

It is that the duration of two identical phenomena is the same; or, if you prefer, that the same causes take the same time to produce the same effects.

At first sight, this is a good definition of the equality of two durations. But is it impossible that experiment may some day contradict our postulate?

Suppose that at a certain place in the world the phenomenon α happens. It causes at the end of a certain time the effect α'. At another place in the world very far away from the first, happens the phenomenon β. It which causes the effect β'.

The phenomena α and β are simultaneous, as are also the effects α' and β'.

Later, the phenomenon α is reproduced under approximately the same conditions as before. Simultaneously, the phenomenon β is also reproduced at a very distant place in the world and almost under the same circumstances.

The effects α' and β' also take place. Let us suppose that the effect α ′ {\displaystyle \alpha ‘} {\displaystyle \alpha ‘} happens perceptibly before the effect β ′ {\displaystyle \beta ‘} {\displaystyle \beta ‘}.

If experience made us witness such a sight, our postulate would be contradicted. For experience would tell us that the first duration α α ′ {\displaystyle \alpha \alpha ‘} {\displaystyle \alpha \alpha ‘} is equal to the first duration β β ′ {\displaystyle \beta \beta ‘} {\displaystyle \beta \beta ‘} and that the second duration α α ′ {\displaystyle \alpha \alpha ‘} {\displaystyle \alpha \alpha ‘} is less than the second duration β β ′ {\displaystyle \beta \beta ‘} {\displaystyle \beta \beta ‘}. On the other hand, our postulate would require that the two durations α α ′ {\displaystyle \alpha \alpha ‘} {\displaystyle \alpha \alpha ‘} should be equal to each other, as likewise the two durations β β ′ {\displaystyle \beta \beta ‘} {\displaystyle \beta \beta ‘}. The equality and the inequality deduced from experience would be incompatible with the two equalities deduced from the postulate.

Now can we affirm that the hypotheses I have just made are absurd? They are in no wise contrary to the principle of contradiction. Doubtless they could not happen without the principle of sufficient reason seeming violated. But to justify a definition so fundamental I should prefer some other guarantee.

In physical reality, one cause does not produce a given effect, but a multitude of distinct causes contribute to produce it, without our having any means of discriminating the part of each of them.

Physicists seek to make this distinction. But they make it only approximately, and, however they progress, they never will make it except approximately.

It is approximately true that the motion of the pendulum is due solely to the earth’s attraction; but in all rigor every attraction, even of Sirius, acts on the pendulum.

The causes which have produced a certain effect will only be reproduced approximately.

• It follows that we should modify our postulate and our definition.

Instead of saying: ‘The same causes take the same time to produce the same effects,’ we should say: ‘Causes almost identical take almost the same time to produce almost the same effects.’

Our definition therefore is no longer anything but approximate.

Besides, as M. Calinon very justly remarks in a recent memoir:[1]

One of the circumstances of any phenomenon is the velocity of the earth's rotation; if this velocity of rotation varies, it constitutes in the reproduction of this phenomenon a circumstance which no longer remains the same. But to suppose this velocity of rotation constant is to suppose that we know how to measure time.

Our definition is therefore not yet satisfactory. It is certainly not that which the astronomers of whom I spoke above implicitly adopt, when they affirm that the terrestrial rotation is slowing down.

What meaning according to them has this affirmation? We can only understand it by analyzing the proofs they give of their proposition. They say first that the friction of the tides producing heat must destroy vis viva. They invoke therefore the principle of vis viva, or of the conservation of energy.

They say next that the secular acceleration of the moon, calculated according to Newton’s law, would be less than that deduced from observations unless the correction relative to the slowing down of the terrestrial rotation were made. They invoke therefore Newton’s law.

In other words, they say that time should be defined in a way that Newton’s law and that of vis viva may be verified.

Newton’s law is an experimental truth; as such it is only approximate, which shows that we still have only a definition by approximation.

If another way of measuring time is adopted, the experiments on which Newton’s law is founded would nonetheless have the same meaning.

• Only the enunciation of the law would be different, because it would be translated into another language.
• It would be much less simple.

So that the definition implicitly adopted by the astronomers may be summed up thus: “Time should be so defined that the equations of mechanics may be as simple as possible.”

In other words, there is not one way of measuring time more true than another; that which is generally adopted is only more convenient.

Of 2 watches, we have no right to say that the one goes true, the other wrong; we can only say that it is advantageous to conform to the indications of the first.

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