All we know about the world teaches us that the effects of A and B are always different-in some decimal place-for any A and B. Thus asking "are the effects different?" is foolish.
In a few years, all great physical constants will have been approximately estimated, and that the only occupation which will be left to men of science will be to carry these measurements to another place of decimals.
For so it is, O Lord my God, I measure it! But what it is I measure, I do not know.
Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next. Between two and three there is a jump. In the case of quantity, there is no such jump; and because jump is missing in the world of quantity, it is impossible for any quantity to be exact. You can have exactly three tomatoes. You can never have exactly three gallons of water. Always quantity is approximate.
Unless a thing can be defined by measurement, it has no place in a theory. And since an accurate value of the momentum of a localized particle cannot be defined by measurement it therefore has no place in the theory.
Can quantum mechanics represent the fact that an electron finds itself approximately in a given place and that it moves approximately with a given velocity, and can we make these approximations so close that they do not cause experimental difficulties?
Every glass thermometer has subtle variations in the size and shape of the bulb at the bottom and the capillary tube inside, as well as variations in the width of gradations on the side. The compounded effect of these uncertainties is that each thermometer reads temperature slightly differently.
Had we really succeeded therefore in altering the period of vibration, which Maxwell, as I have just noted, held to be impossible? Or was there some disturbing circumstances from one or more factors which distorted the result?
For as long as one has no further point of reference, apart from the position of the maximum, the wavelength thus remains uncertain by an integral factor.
