The Cause Of A Phenomenonby H. Poincare
Do we have 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 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 determine their positions at the instant
t + h as well as their positions at the instant
t − h.
Even more; the position of Jupiter at the instant
t, together with that of Saturn at the instant
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 and Saturn at the instant
t + a + e is bound to the aggregate of positions occupied by Jupiter at the instant
t and Saturn at the instant
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 of Jupiter and the instant
t + a of Saturn?
In answer there can only be reasons, very strong, it is true, of convenience and simplicity.
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.
- 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, 50 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.
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: