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We spoke of the "Properties of Things," and of the degree to which these properties could be investigated. As an extreme thought, the following question was proposed:
Supposing it were possible to discover all the properties of a grain of sand, would we then have gained a complete knowledge of the whole universe? Would there then remain no unsolved component of our comprehension of the universe?
Einstein declared that this question was to be answered with an unconditional affirmative. "For if we had completely and in a scientific sense learned the processes in the grain of sand, this would have been possible only on the basis of an exact knowledge of the laws of mechanical events in time and space. These laws, differential equations, would be the most general laws of the universe, from which the quintessence of all other events would have to be deducible."
[This thought may be spun out in yet another direction. Every piece of research, however specialized it may appear and of whatever minor importance it may be, retains a relationship with researches into the universe, and may prove to be valuable for this latter task. If we accept the view that science is capable of realizing perfection, then every contribution to knowledge, even the most insignificant, is essentially indispensable for attaining this goal.]
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Can a physical law alter with time? In more precise language, can time, as such, enter explicitly into laws, so that, for example, an experiment that is carried out at different times leads to different results? This question has been treated several times, among others, by Poincaré, who answered it with an emphatic "No!" but also by others to whom the invariability of physical laws did not seem to hold for all eternity. If my memory does not play me false, Helmholtz once expressed faint doubts about the constancy of laws.
Einstein answered this question with a decided negative. "For a law of physical nature is, by definition, a rule to which events conform wherever and whenever they take place. Thus, if we were to be compelled as a result of experience to make a law dependent on time, it would be a necessary step to seek a law independent of time, which would include in itself the law dependent on the time as a special case. The latter would be excluded from the category of physical laws, and would henceforward play the part only of a result deduced from the law which is independent of the time."
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What attitude should we adopt if, in studying a scientific doctrine, we encounter paradoxical results even though the inferences have been drawn correctly—that is, if we meet with a deduction to which our reasoning powers object, although no fallacy is discoverable in the argument?