To observe any object in the sense world we need an appropriate medium of observation. For ordinary things, light provides this. In the sense in which light is understood to-day, this is possible because the spatial extension of the single light impulses, their so-called wavelength, is immeasurably smaller than the average magnitude of all microscopically visible objects. This ensures that they can be observed clearly by the human eye. Much smaller objects, however, will require a correspondingly shorter wave-length in the medium of observation. Now shorter wave-lengths than those of visible light have been found in ultra-violet light and in X-rays; and these, accordingly, are now often used for minute physical research.
In this way, however, we are led by nature to a definite boundary; for we now find ourselves in a realm where the dimensions of the observation medium and the observed object are more or less the same. The result, unfortunately, is that when the 'light' meets the object, it changes the latter's condition of movement. On the other hand, if a 'light' is used whose wave-length is too big to have any influence on the object's condition of movement, it precludes any exact determination of the object's location.
Thus, having arrived at the very ground of the world - that is, where the cosmic laws might be expected to reveal themselves directly - the scientist finds himself in the remarkable situation of only being able to determine accurately either the position of an observed object and not its state of motion, or its state of motion and not its position. The law he seeks, however, requires that both should be known at the same time. Nor is this situation due to the imperfection of the scientific apparatus employed, but to its very perfection, so that it appears to arise from the nature of the foundation of the world - in so far, at least, as modern science is bound to conceive it.
If it is true that a valid scientific knowledge of nature is possible only in the sphere open to a single-eyed, colour-blind observation, and if it is true - as a science of this kind, at any rate, is obliged to believe - that all processes within the material foundation of the world depend on nothing but the movements of certain elementary particles of extremely small size, then the fact must be faced that the very nature of these processes rules out the discovery of any stable ordering of things in the sense of mathematically formulable laws. The discovery of such laws will then always be the last step but one in scientific investigation; the last will inevitably be the dissolution of such laws into chaos. For a consistent scientific thinking that goes this way, therefore, nothing is left but to recognize chaos as the only real basis of an apparently ordered world, a chaos on whose surface the laws that seem to hold sway are only the illusory picturings of the human mind. This, then, is the principle of Indeterminacy as it has been encountered in the course of practical investigation into the electrical processes within physical matter.
In the following way Professor Schrödinger, another leading thinker among modern theoretical physicists, explains the philosophical basis for the principle of Indeterminacy, which scientists have established in the meantime:1
'Every quantitative observation, every observation making use of measurement, is by nature discontinuous. ... However far we go in the pursuit of accuracy we shall never get anything other than a finite series of discrete results. ... The raw material of our quantitative cognition of nature will always have this primitive and discontinuous character. ... It is possible that a physical system might be so simple that this meagre information would suffice to settle its fate; in that case nature would not be more complicated than a game of chess. To determine a position of a game of chess thirty-three facts suffice. ... If nature is more complicated than a game of chess, a belief to which one tends to incline, then a physical system cannot be determined by a finite number of observations. But in practice a finite number of observations is all that we could make.'
Classical physics, the author goes on to show, held that it was possible to gain a real insight into the laws of the universe, because in principle an infinite number of such discrete observations would enable us to fill in the gaps sufficiently to allow us to determine the system of the physical world. Against this assumption modern physics must hold the view that an infinite number of observations cannot in any case be carried out in practice, and that nothing compels us to assume that even this would suffice to furnish us with the means for a complete determination, which alone would allow us to speak of 'law' in nature. 'This is the direction in which modern physics has led us without really intending it.'
What we have previously said will make it clear enough that in these words of a modern physicist we meet once more the two fundamentals of Hume's philosophy. It is just as obvious, however, that the very principle thus re-affirmed at the latest stage of modern physical science was already firmly established by Hooke, when he sought to prove to his contemporaries the unreality of human ideas.
Let us recall Hooke's motives and results. The human reason discovers that certain law-abiding forms of thought dwell within itself; these are the rules of mathematical thinking. The eye informs the reason that the same kind of law and order is present also in the outer world. The mind can think point and line; the eye reports that the same forms exist in nature outside. (Hooke could just as well have taken as his examples the apex and edge of a crystal.) The reason mistrusts the eye, however, and with the help of the microscope 'improves' on it. What hitherto had been taken for a compact, regulated whole now collapses into a heap of unordered parts; behind the illusion of law a finer observation detects the reality of chaos!
Had science in its vehement career from discovery to discovery not forgotten its own beginnings so completely, it would not have needed its latest researches to bring out a principle which it had in fact been following from the outset - a principle which philosophy had already recognized, if not in quite the same formulation, in the eighteenth century. Indeterminacy, as we have just seen it explained by Schrödinger, is nothing but the exact continuation of Humean scepticism.