Computer Science – Sound
Scientific paper
Mar 1973
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973phrvd...7.1609v&link_type=abstract
Physical Review D, vol. 7, Issue 6, pp. 1609-1619
Computer Science
Sound
Scientific paper
The theory is based on a new hypothesis on the nature of matter. This hypothesis is that the elementary particles, atoms, and molecules we have found in nature are not part of the real world, but constitute information about the real world. They are the wave components of a generalized Fourier analysis of our observations (which in the final analysis are always space-time distributions of photon- or particle-counter clicks). This Fourier analysis should be so general that every observation can be expressed in its terms; it thereby becomes axiomatic. Physicists of past generations, with their sound instincts, were intuitively approaching this most general and most powerful possible analysis of our observations. With the discovery of quantum mechanics, this development had advanced so far that the precise formulation of this ultimate analysis could be guessed. The model which can guide us to this mathematical formulation is that of an ideal optical observation on a physical object. This observation is made by illuminating the object with a finite number of laser beams of known amplitude and phase, and observing the amplitude and phase of the finite number of light beams emerging from the object space. The assumption that this is all the information we can ever obtain about the object leads to a wave function of the object which consists of light waves, extrapolated from the photon detectors back to the object space. It is suggested that these light waves should be presented as a product of amplitudes in a 4n-dimensional space, where n is the number of light quanta in the signal. Most important, force, or interaction, can then be described as a linear transformation in this space. The actual mathematical formalism proposed on the basis of that model is Xf=it d fdt. X is the Hamiltonian of the whole universe with n0≅1080 particles. It is a 4n0×4n0 linear matrix operator. f is a 4n0-component vector wave function representing waves traveling at the speed of light. The coordinates are the homogeneous coordinates (xj, yj, zj, uj) of the n0 particles in the closed universe. The eigenvalue ω, in Xf=ωf, is a 4n0×4n0 Hermitian matrix. It can be divided into n0×n0, 4 × 4 submatrices, each representing a complete set of dynamic and inertial quantities of elementary particles, or interaction quanta between particles. it d fdt=ωf is therefore a complete expression of the dynamic conservation laws. A special orthogonal transformation α0 transforms the solution into a standard solution with eigenvalue ω0, representing n0 identical elementary particles. The assumption that the universe is of maximum probability then leads to simple explicit expressions for all matrix elements of ω0. This means that the energy levels of all n-particle systems (atoms or molecules) of the theory can be directly calculated. The equations demand relations between cosmological constants and atomic constants. In a universe of the size and mass of our observed universe, the elementary particle would have to be the size of the proton.
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