Prog. Theor. Phys. Supplement No.76 (1983) pp. 186-223

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The Theory of Finite Degree of Freedom

— Its Philosophical Background and Physical Consequences —

Takao Tati

Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima 725

(Received August 26, 1982)

Abstract:

The theory of finite degree of freedom is the investigation of the possibility of describing elementary particles in terms of a finite number of variables. Its philosophical background and physical consequences are mentioned. The infinite degree of freedom of field theory which describes elementary particles is closely connected with the concept of space-time, and the theory of finite degree of freedom can be consistent only in the non-spatio-temporal description in which the concept of space-time is decomposed and the condition of unification of its constituent concept of space-time is decomposed and the condition of unification of its constituent concepts (`space-time condition') can be loosened. The non-spatio-temporal description is considered to point the notion of `objective time'. The theory of finite degree of freedom introduces a universal timelike vector, N_µ, into the Minkowski space and specifies a degree of freedom consisting of a finite number of points on a hyper-plane, σ_N, perpendicular to the vector N_µ. In this case, a high momentum part is cut off referring to the vector N_µ.
Possible consequences of the cutoff are discussed, in terms of a model of hadronic matter of which hadrons are made, for matter in ultrahigh energy phenomena relating to the various fire-balls found by Chacaltaya emulsion chamber cosmic ray experiments and for matter at ultrahigh densities relating to Wheeler's issue of the final state. In particular, exotic fire-balls observed in cosmic ray experiments are interpreted as phenomena peculiar to fire-balls with very large Lorentz factors. In this case, nonappearance of exotic fire-balls in collider experiments is attributed to the existence of universal time realized by the cutoff of the momentum degree of freedom of basic particles. In the theory of finite degree of freedom, the hyper-surface on which the quantum mechanical measurement prepares the state is fixed to the above-mentioned hyper-plane σ_N. A possible experimental means to find the hyperplane σ_N is discussed in connection with the reduction of wave packet in quantum mechanics. Finally, the effect of gravitation on the vector N_µ is considered, and it is argued that the vector N_µ depends on the position in macroscopic space-time and can be considered to coincide on an average with Weyl's cosmic time in a cosmological model.

URL : http://ptp.ipap.jp/link?PTPS/76/186/
DOI : 10.1143/PTPS.76.186

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Citing Article(s) :

Progress of Theoretical Physics Vol. 78 No. 5 (1987) pp. 996-1008 :
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Progress of Theoretical Physics Vol. 83 No. 3 (1990) pp. 638-648 :
Local Quantum Mechanics and Lorentz Transformation

Alberto S. de Arruda, Benedito L. da Silva and Takao Tati