IV
Project Gutenberg EPUB3 edition
Poincaré, Henri and Halsted, George Bruce
All this is unimportant, one will say; doubtless 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 trouble is that there is no rigor in the definition. When we use the pendulum to measure time, 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.
And at first blush, this is a good definition of the equality of two durations. But take care. Is it impossible that experiment may some day contradict our postulate?
Let me explain myself. I suppose that at a certain place in the world the phenomenon α happens, causing as consequence 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, which causes as consequence 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, and 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´ happens perceptibly before the effect β´.
If experience made us witness such a sight, our postulate would be contradicted. For experience would tell us that the first duration αα´ is equal to the first duration ββ´ and that the second duration αα´ is less than the second duration ββ´. On the other hand, our postulate would require that the two durations αα´ should be equal to each other, as likewise the two durations ββ´. 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.