The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines

In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each numberN and Turing machineQ there exists a HamiltonianHNQ and a class of appropriate initial states such that if c is such an initial state, thenψQN(t)=exp(−1HNQt)ψQN(0) correctly describes at timest3,t6,⋯,t3N model states that correspond to the completion of the first, second, ⋯, Nth computation step ofQ. The model parameters can be adjusted so that for an arbitrary time intervalΔ aroundt3,t6,⋯,t3N, the “machine” part ofψQN(t) is stationary.

[1]  F. Dyson.  The Radiation Theories of Tomonaga, Schwinger, and Feynman , 1949 .

[2]  J. Neumann.  Mathematical Foundations of Quantum Mechanics , 1955 .

[3]  Martin D. Davis,et al.  Computability and Unsolvability , 1959, McGraw-Hill Series in Information Processing and Computers.

[4]  Michael Danos,et al.  The Mathematical Foundations of Quantum Mechanics , 1964 .

[5]  A. Shimony.  Role of the Observer in Quantum Theory , 1963 .

[6]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[7]  J Schwinger,et al.  Relativistic quantum field theory. , 1966, Science.

[8]  Jr. Hartley Rogers.  Theory of Recursive Functions and Effective Computability , 1969 .

[9]  R. Landauer,et al.  Minimal energy dissipation in logic , 1970 .

[10]  Rolf Landauer,et al.  Minimal Energy Dissipation and Maximal Error for the Computational Process , 1971 .

[11]  K. Hepp,et al.  QUANTUM THEORY OF MEASUREMENT AND MACROSCOPIC OBSERVABLES. , 1972 .

[12]  Philip J. Davis,et al.  Fidelity in mathematical discourse: is one and one really two? , 1972 .

[13]  F. Feiock,et al.  Models in nonequilibrium quantum statistical mechanics , 1972 .

[14]  Charles H. Bennett,et al.  Logical reversibility of computation , 1973 .

[15]  J. Bell.  On Wave Packet Reduction in the Coleman-HEPP Model , 1974 .

[16]  Rolf Landauer,et al.  Fundamental Limitations in the Computational Process , 1976 .

[17]  John Archibald Wheeler,et al.  Include the Observer in the Wave Function , 1977 .

[18]  Illustrative calculations using projection techniques , 1977 .

[19]  I. Prigogine.  Time, Structure, and Fluctuations , 1978, Science.