"In every previous application of the quantum law, Planck's law, that the energy is h times the frequency, had been used to deduce the energy of a quantum when the frequency of the radiation was already known. In the present case the formula was used the other way; the energy of the emitted photon was known to begin with, and the formula was utilized to deduce its frequency. The frequencies calculated in this way are found to agree completely and exactly with those of the spectrum of hydrogen."

“For, for aught we know, or for aught that the new science can say to the contrary, the gods which play the part of fate to the atoms of our brains may be our own minds. Through these atoms our minds may perchance affect the motions of our bodies and so the state of the world around us. To-day science can no longer shut the door on this possibility; she has no longer any unanswerable arguments to bring against our innate conviction of free-will. On the other hand, she gives no hint as to what absence of determinism or causation may mean. If we, and nature in general, do not respond in a unique way to external stimuli, what determines the course of events? If anything at all, we are thrown back on determinism and causation; if nothing at all, how can anything ever occur? As I see it, we are unlikely to reach any definite conclusions on these questions until we have a better understanding of the true nature of time.”

“Heisenberg now approached the problem from a new philosophical angle. He discarded all models, pictures and parables, and made a clear distinction between sure knowledge we gain from observation of nature and the conjectural knowledge we introduce when we use models, pictures and parables. Sure knowledge... can only be numerical, so that Heisenberg's results were inevitably mathematical in form, and could not disclose anything about the true nature of physical properties or entities.”

“...when the experiment was attempted by Michelson and Morley it failed, thus showing that space and time assumed in the picture were not true to the facts of nature. ...the pattern of events was the same whether the world stood at rest in the supposed ether, or had an ether wind blowing through it at a million miles an hour. It began to look as though the supposed ether was not very important in the scheme of things... and so might as well be abandoned. But if the bell-rope is to be discarded, what is to ring the bell?”

“First we notice an investigation which Prof. Planck of Berlin published in 1899. His aim was that it should fit the observed facts of radiation, and show why the energy of bodies was not wholly transformed into radiation. ...his investigation seemed to show that continuity had to be given up, suggesting that in the last resort changes in the universe do not consist of continuous motions in space and time, but in some way are discontinuous.”

“The final truth about a phenomenon resides in the mathematical description of it; so long as there is no imperfection in this, our knowledge of the phenomenon is complete. We go beyond the mathematical formula at our own risk; we may find a model or a picture which helps us understand it, but we have no right to expect this, and our failure to find such a model or picture need not indicate that either our reasoning or our knowledge is at fault. The making of models or pictures to explain mathematical formulas and the phenomena they describe is not a step towards, but a step away from reality; it is like making a graven image of a spirit.”

“Then the theory of relativity came and explained the cause of the failure. Electric action requires time to travel from one point of space to another, the simplest instance of this being the finite speed of travel of light... Thus electromagnetic action may be said to travel through space and time jointly. But by filling space and space alone with an ether, the pictorial representations had all supposed a clear-cut distinction between space and time.”