Multiple Quantization and the Concept of Information

The understanding of the meaning of quantization seems to be the main problem in understanding quantum structures. In this paper first the difference between quantized particle vs. radiation fields in the formalism of canonical quantization is discussed. Next von Weizsäcker’s concept of ”multiple quantization” which leads to an understanding of quantization as an iteration of probability theory is explained. Finally a connection between quantization and the idea of a ”general theory of information” is considered. This brings together semantic information with the different levels of quantization and expresses the philosophical attitude of this paper concerning the interpretation of quantum theory. 1 Quantum Field Theory When quantizing a field one has to differentiate between the quantization of a classical radiation field such as the electromagnetic field and a quantum field such as the Schrödinger, Klein-Gordon, or Dirac field. Only in the latter cases is the field quantization indeed a ”second quantization”. From a fundamental point of view the electromagnetic field is one of the gauge fields in physics which describes one of the fundamental forces, whereas the Dirac field describes the fundamental fermions such as quarks and leptons. For the sake of simplicity I will only consider the electron and the photon as examples of the fundamental particle and gauge fields. Physically there is a clear difference between them: the electron is a fermionic field of matter which describes particles and the photon is a bosonic gauge field which describes interaction. Published: International Journal of Theoretical Physics, Vol. 35, No. 11, p. 2219 2225, 1996 2 Institute of Philosophy, Ruhr-University Bochum, D-44780 Bochum, FRG, email: [email protected] Multiple Quantization and the Concept of Information 2 On the other hand the canonical formalism for the field quantization seems to make no difference between this physical meaning of the fields: they are both quantized fields and therefore several authors maintain that there is no more wave-particle-dualism on the level of quantum field theory. According to the usual interpretation a quantized field is understood as a totality of field quanta which can be created and annihilated. Quantum field theory therefore is essentially a many-particle theory. 1.1 The Dirac Field The quantization of the Dirac spinors ψ, ψ̄ leads to the operators ψ̂(x) = ∑