[Posted to commemorate the 40th anniversary of Heisenberg’s death.]
The Mathematical Nature of the Universe
In the philosophy of Democritus the atoms are eternal and indestructible units of matter, they can never be transformed into each other. With regard to this question modern physics takes a definite stand against the materialism of Democritus and for Plato and the Pythagoreans. The elementary particles are certainly not eternal and indestructible units of matter, they can actually be transformed into each other. All particles are made of the same substance: energy.
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. 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.
Potentiality in Nature
The matter of Aristotle is not a specific matter like water or air, nor is it simply empty space; it is a kind of indefinite corporeal substratum, embodying the possibility of passing over into actuality by means of the form. The matter of Aristotle, which is mere ‘potentia’, should be compared to our concept of energy, which gets into ‘actuality’ by means of the form, when the elementary particle is created.
Modern physics is not satisfied with only qualitative description; it must try on the basis of careful experimental investigations to get a mathematical formulation of those natural laws that determine the ‘forms’ of matter, the elementary particles and their forces. Each elementary particle not only is producing some forces and is acted upon by forces, but it is at the same time representing a certain field of force.
The Strange Duality of Nature
Of the inexplicable wave-particle duality of elementary particles, Heisenberg writes:
The two pictures are of course mutually exclusive, because a certain thing cannot at the same time be a particle (i.e., substance confined to a very small volume) and a wave (i.e., a field spread out over a large space), but the two complement each other. By playing with both pictures, by going from the one picture to the other and back again, we finally get the right impression of the strange kind of reality behind our atomic experiments.
Strangely enough, I’m reminded of John Calvin’s argument against Transubstantiation in “Institutes of the Christian Religion“, viz. that Christ cannot be both in Heaven and in the Bread and Wine, because His resurrected body must occupy a definite space, if it be a true body and not a spirit.
It may be silly of me to draw a parallel between the wave-particle duality of light and the God-man duality of Jesus, the Light of the world, for I don’t have the least understanding of either. But if the invisible attributes of God are clearly seen in His creation, as St. Paul writes, it is possible that the mystery of the dual nature of Christ is also made visible, to some extent, in the nature of light, just as the mystery of His resurrection is seen in a grain of wheat.
As Heisenberg, a devout Christian himself, is quoted to have said,
The first gulp from the glass of natural sciences will turn you into an atheist, but at the bottom of the glass God is waiting for you.
- Heisenberg, Werner. Physics and Philosophy: The Revolution in Modern Science. London: George Allen & Unwin. 1958. Internet Archive. https://archive.org/details/PhysicsPhilosophy