Reading Notes: August 11th, 2022

“The law of any phenomenon, when expressed in mathematical form, is a differential equation connecting some measured quantity which is observed in a certain place at a certain time with some other measured quantity which is observed in some other (or it may be the same) place at some other (or it may be the same) time. The law will also involve the distance between the two places and the time-lapse between the two dates….Now it is clear that such laws are, in the end, only in so far as they express relations between actually measured magnitudes, such as clock-readings, deflexions of galvanometers or magnetometers, number of weights put into a balance, number of times that a certain rod has to be laid down to get from one place to another, and so on. We may take these measures to represent so much time-lapse, so great a current or magnetic force, such and such a gravitational attraction, so much length, etc.; and we may if we like (and if we can make clear what we mean), raise the question whether these actual measures which we read off our instruments “truly” represent the “real” physical magnitudes in question. But, so far as our laws and their verification are concerned, the measured magnitudes are the important things, and the question of what they stand for in the physical world is a secondary matter of theoretical interpretation. E.g., Maxwell’s equations, so far as they can be verified, state relations between the readings of electrometers, magnetometers and galvanometers in various places; the readings of clocks in these places; and the number of times rods have to be laid down to get from one place to another.” (Broad, Scientific Thought, 149-150)