[S]ets of concepts... defined in physics. ...[F]our systems... have ...attained ...final form. The first… — Werner Heisenberg
[S]ets of concepts... defined in physics. ...[F]our systems... have ...attained ...final form.
The first ...Newtonian mechanics ...for the description of all mechanical systems, ...motion of fluids and ...elastic ..; it comprises , , aerodynamics.
The second closed system of concepts... the theory of heat. Though... connected with mechanics through... statistical mechanics, it... [is] not... a part of mechanics. ...[T]he phenomenological theory of heat uses ...[some] concepts that have no [physics] counterpart ...like: , specific heat, entropy, free energy, etc. ...[F]rom ...phenomenological ...to a statistical interpretation ...considering heat as energy, distributed statistically among ...many degrees of freedom due to ...atomic structure... heat is no more connected with mechanics than with electrodynamics or other ...physics. The central concept ...is ...probability, closely connected with ...entropy ...Besides this ...the statistical theory of heat requires the concept of energy. But any coherent set ...in physics will ...contain ...concepts of energy, and and the law that these ...be conserved. This follows if the ...set is ...to describe ...features ...correct at all times and everywhere; ...[i.e.,] features that do not depend on space and time ...[i.e.,] are invariant under arbitrary translations in space and time, rotations in space and the Galileo— or Lorentz—transformation. Therefore, the theory of heat can be combined with any of the other closed systems of concepts.
The third... electricity and magnetism... reached... final form... through... Lorentz, Einstein and Minkowski. It comprises electrodynamics, special relativity, optics, magnetism, and one may include the de Broglie theory of s of all different sorts of elementary particles, but not the wave theory of Schrodinger.
[F]ourth... the quantum theory... Its central concept is the probability function, or... "statistical matrix"... It comprises quantum and wave mechanics, the theory of atomic spectra, chemistry, and the theory of other properties... like electric conductivity, , etc.
...The first set is contained in the third as the limiting case where the velocity of light can be considered as infinitely big, and is contained in the fourth as the limiting case where of action can be considered as infinitely small. The first and partly the third set belong to the fourth as a priori for the description of the experiments. The second set can be connected with any of the other three sets without difficulty and is especially important in its connection with the fourth. The independent existence of the third and fourth sets suggests the existence of a fifth set, of which one, three, and four are limiting cases. This fifth set will probably be found someday in connection with the theory of the elementary particles.
Source: Wikiquote · CC BY-SA 4.0
More from this book
But the resemblance of the modern views to those of Plato and the Pythagoreans can be carried somewhat further. The elementary particles in Plato's Timaeus are finally not substance but mathematical forms. "All things are numbers" is a sentence attributed to Pythagoras. The only mathematical forms available at that time were such geometric forms as the regular solids or the triangles which form their surface. In modern quantum theory there can be no doubt that the elementary particles will finally also be mathematical forms but of a much more complicated nature.
The law of causality is no longer applied in quantum theory and the law of conservation of matter is no longer true for the elementary particles. Obviously Kant could not have foreseen the new discoveries, but since he was convinced that his concepts would be "the basis of any future metaphysics that can be called science" it is interesting to see where his arguments have been wrong.
The equation of motion holds at all times, it is in this sense eternal, whereas the geometrical forms, like the orbits, are changing. Therefore, the mathematical forms that represent the elementary particles will be solutions of some eternal law of motion for matter. Actually this is a problem which has not yet been solved.
