Part 6 of The Measure of Time

No Intuition of Simultaneity

September 28, 2021

Two psychological phenomena happen simultaneously in two different consciousnesses. What does simultaneous mean?

What do I mean by “a physical phenomenon which is before or after a psychological phenomenon”?

In 1572, Tycho Brahe noticed a new star. It took 200 years for the light from that star to reach our earth. That star therefore began before the discovery of America. But this statement has no meaning and is just an outcome of a convention.

VII

We should first ask ourselves how one could have had the idea of putting into the same frame so many worlds impenetrable to one another.

We should like to represent to ourselves the external universe, and only by so doing could we feel that we understood it. We know we never can attain this representation= our weakness is too great. But at least we desire the ability to conceive an infinite intelligence for which this representation could be possible, a sort of great consciousness which should see all, and which should classify all in its time, as we classify, in our time, the little we see.

This hypothesis is crude and incomplete because this supreme intelligence would be only a demigod ; infinite in one sense, it would be limited in another, since it would have only an imperfect recollection of the past;

and it could have no other, since otherwise all recollections would be equally present to it and for it there would be no time. And yet when we speak of time, for all which happens outside of us, do we not unconsciously adopt this hypothesis; do we not put ourselves in the place of this imperfect god; and do not even the atheists put themselves in the place where god would be if he existed?

Why we have tried to put all physical phenomena into the same frame?

But that can not pass for a definition of simultaneity, since this hypothetical intelligence, even if it existed, would be for us impenetrable. It is therefore necessary to seek something else.

VIII

The ordinary definitions which are proper for psychologic time would suffice us no more. Two simultaneous psychologic facts are so closely bound together that analysis can not separate without mutilating them. Is it the same with two physical facts? Is not my present nearer my past of yesterday than the present of Sirius?

It has also been said that two facts should be regarded as simultaneous when the order of their succession may be inverted at will. It is evident that this definition would not suit two physical facts which happen far from one another, and that, in what concerns them, we no longer even understand what this reversibility would be; besides, succession itself must first be defined.

IX

Let us then seek to give an account of what is understood by simultaneity or antecedence, and for this let us analyze some examples.

I write a letter; it is afterward read by the friend to whom I have addressed it. There are two facts which have had for their theater two different consciousnesses. In writing this letter I have had the visual image of it, and my friend has had in his turn this same visual image in reading the letter. Though these two facts happen in impenetrable worlds, I do not hesitate to regard the first as anterior to the second, because I believe it is its cause.

I hear thunder, and I conclude there has been an electric discharge; I do not hesitate to consider the physical phenomenon as anterior to the auditory image perceived in my consciousness, because I believe it is its cause.

Behold then the rule we follow, and the only one we can follow= when a phenomenon appears to us as the cause of another, we regard it as anterior. It is therefore by cause that we define time; but most often, when two facts appear to us bound by a constant relation, how do we recognize which is the cause and which the effect? We assume that the anterior fact, the antecedent, is the cause of the other, of the consequent. It is then by time that we define cause. How save ourselves from this petitio principii?

We say now post hoc, ergo propter hoc; now propter hoc, ergo post hoc; shall we escape from this vicious circle?

X

Let us see, not how we succeed in escaping, for we do not completely succeed, but how we try to escape.

I execute a voluntary act A {\displaystyle A} A and I feel afterward a sensation D {\displaystyle D} D, which I regard as a consequence of the act A {\displaystyle A} A; on the other hand, for whatever reason, I infer that this consequence is not immediate, but that outside my consciousness two facts B {\displaystyle B} B and C {\displaystyle C} C, which I have not witnessed, have happened, and in such a way that B {\displaystyle B} B is the effect of A {\displaystyle A} A, that C {\displaystyle C} C is the effect of B {\displaystyle B} B, and D {\displaystyle D} D of C {\displaystyle C} C.

But why? If I think I have reason to regard the four facts A , B , C , D , {\displaystyle A,B,C,D,} {\displaystyle A,B,C,D,} as bound to one another by a causal connection, why range them in the causal order A B C D {\displaystyle ABCD} {\displaystyle ABCD}, and at the same time in the chronologic order A B C D {\displaystyle ABCD} {\displaystyle ABCD}, rather than in any other order?

I clearly see that in the act A {\displaystyle A} A I have the feeling of having been active, while in undergoing the sensation D {\displaystyle D} D I have that of having been passive. This is why I regard A {\displaystyle A} A as the initial cause and D {\displaystyle D} D as the ultimate effect; this is why I put A {\displaystyle A} A at the beginning of the chain and D {\displaystyle D} D at the end; but why put B {\displaystyle B} B before C {\displaystyle C} C rather than C {\displaystyle C} C before B {\displaystyle B} B?

If this question is put, the reply ordinarily is= we know that it is B {\displaystyle B} B which is the cause of C {\displaystyle C} C because we always see B {\displaystyle B} B happen before C {\displaystyle C} C. These two phenomena, when witnessed, happen in a certain order; when analogous phenomena happen without witness, there is no reason to invert this order.

Doubtless, but take care; we never know directly the physical phenomena B {\displaystyle B} B and C {\displaystyle C} C. What we know are sensations B ′ {\displaystyle B’} {\displaystyle B’} and C ′ {\displaystyle C’} {\displaystyle C’} produced respectively by B {\displaystyle B} B and C {\displaystyle C} C. Our consciousness tells us immediately that B ′ {\displaystyle B’} {\displaystyle B’} precedes C ′ {\displaystyle C’} {\displaystyle C’} and we suppose that B {\displaystyle B} B and C {\displaystyle C} C succeed one another in the same order.

This rule appears in fact very natural, and yet we are often led to depart from it. We hear the sound of the thunder only some seconds after the electric discharge of the cloud. Of two flashes of lightning, the one distant, the other near, can not the first be anterior to the second, even though the sound of the second comes to us before that of the first?

XI

Another difficulty; have we really the right to speak of the cause of a phenomenon? If all the parts of the universe are interchained in a certain measure, any one phenomenon will not be the effect of a single cause, but the resultant of causes infinitely numerous; it is, one often says, the consequence of the state of the universe a moment before. How enunciate rules applicable to circumstances so complex? And yet it is only thus that these rules can be general and rigorous.

Not to lose ourselves in this infinite complexity, let us make a simpler hypothesis. Consider three stars, for example, the sun, Jupiter and Saturn; but, for greater simplicity, regard them as reduced to material points and isolated from the rest of the world. The positions and the velocities of three bodies at a given instant suffice to determine their positions and velocities at the following instant, and consequently at any instant. Their positions at the instant t {\displaystyle t} t determine their positions at the instant t + h {\displaystyle t+h} {\displaystyle t+h} as well as their positions at the instant t − h {\displaystyle t-h} {\displaystyle t-h}.

Even more; the position of Jupiter at the instant t {\displaystyle t} t, together with that of Saturn at the instant t + a {\displaystyle t+a} {\displaystyle t+a}, determines the position of Jupiter at any instant and that of Saturn at any instant

The aggregate of positions occupied by Jupiter at the instant t + e {\displaystyle t+e} {\displaystyle t+e} and Saturn at the instant t + a + e {\displaystyle t+a+e} {\displaystyle t+a+e} is bound to the aggregate of positions occupied by Jupiter at the instant t {\displaystyle t} t and Saturn at the instant t + a {\displaystyle t+a} {\displaystyle t+a}, by laws as precise as that of Newton, though more complicated. Then why not regard one of these aggregates as the cause of the other, which would lead to considering as simultaneous the instant t {\displaystyle t} t of Jupiter and the instant t + a {\displaystyle t+a} {\displaystyle t+a} of Saturn?

In answer there can only be reasons, very strong, it is true, of convenience and simplicity.

XII

But let us pass to examples less artificial; to understand the definition implicitly supposed by the savants, let us watch them at work and look for the rules by which they investigate simultaneity.

I will take two simple examples, the measurement of the velocity of light and the determination of longitude.

When an astronomer tells me that some stellar phenomenon, which his telescope reveals to him at this moment, happened, nevertheless, fifty years ago, I seek his meaning, and to that end I shall ask him first how he knows it, that is, how he has measured the velocity of light.

He has begun by supposing that light has a constant velocity, and in particular that its velocity is the same in all directions. That is a postulate without which no measurement of this velocity could be attempted. This postulate could never be verified directly by experiment; it might be contradicted by it if the results of different measurements were not concordant. We should think ourselves fortunate that this contradiction has not happened and that the slight discordances which may happen can be readily explained.

The postulate, at all events, resembling the principle of sufficient reason, has been accepted by everybody; what I wish to emphasize is that it furnishes us with a new rule for the investigation of simultaneity, entirely different from that which we have enunciated above.

This postulate assumed, let us see how the velocity of light has been measured. You know that Roemer used eclipses of the satellites of Jupiter, and sought how much the event fell behind its prediction. But how is this prediction made? It is by the aid of astronomic laws; for instance Newton’s law.

Could not the observed facts be just as well explained if we attributed to the velocity of light a little different value from that adopted, and supposed Newton’s law only approximate? Only this would lead to replacing Newton’s law by another more complicated. So for the velocity of light a value is adopted, such that the astronomic laws compatible with this value may be as simple as possible. When navigators or geographers determine a longitude, they have to solve just the problem we are discussing; they must, without being at Paris, calculate Paris time. How do they accomplish it? They carry a chronometer set for Paris. The qualitative problem of simultaneity is made to depend upon the quantitative problem of the measurement of time. I need not take up the difficulties relative to this latter problem, since above I have emphasized them at length.

Or else they observe an astronomic phenomenon, such as an eclipse of the moon, and they suppose that this phenomenon is perceived simultaneously from all points of the earth. That is not altogether true, since the propagation of light is not instantaneous; if absolute exactitude were desired, there would be a correction to make according to a complicated rule.

Or else finally they use the telegraph. It is clear first that the reception of the signal at Berlin, for instance, is after the sending of this same signal from Paris. This is the rule of cause and effect analyzed above. But how much after? In general, the duration of the transmission is neglected and the two events are regarded as simultaneous. But, to be rigorous, a little correction would still have to be made by a complicated calculation; in practise it is not made, because it would be well within the errors of observation; its theoretic necessity is none the less from our point of view, which is that of a rigorous definition. From this discussion, I wish to emphasize two things= (1) The rules applied are exceedingly various. (2) It is difficult to separate the qualitative problem of simultaneity from the quantitative problem of the measurement of time; no matter whether a chronometer is used, or whether account must be taken of a velocity of transmission, as that of light, because such a velocity could not be measured without measuring a time.

13= Conclusion

We have not a direct intuition of simultaneity, nor of the equality of two durations.

If we think we have this intuition, this is an illusion.

We replace it through little rules applicable to each particular case.

We choose these rules, not because they are true, but because they are the most convenient= “The simultaneity of two events, or the order of their succession, the equality of two durations, are to be so defined that the enunciation of the natural laws may be as simple as possible. In other words, all these rules, all these definitions are only the fruit of an unconscious opportunism.”