Introduction: The basic notion of time moving as a point moving from past to future dominates Western thinking. In a recent paper in Quantum Reports, I showed that wavefunction propagation in spacetime (through the Feynman path integral or the Schrodinger equation) can be rewritten as a recursive Fourier transformation.
This approach distinguishes between measurable coordinates, which correspond to physical interactions or endpoints, and unmeasurable parameters, which are non-physical. This distinction is illustrated by a hologram, in which the holographic image you see (coordinate) is distinct from the film in the background (parameters). The result is a holistic view of time, in which the basic element of time is not a point but a line between interactions. Treating time as fundamentally holistic allows one to construct theories which connect present with future, i.e., post-select a given end state to experience a meaningful coincidence or synchronicity in the present time.
Methods: Drawing off two related formalisms—Fourier optics and the Feynman path integral—an equation for wavefunction propagation is presented which reflects the mathematics of holograms. The ontology of this formalism is simple, consisting of spacetime and its Fourier dual. The traditional approach of a spatial wavefunction which is dependent upon the time variable is discarded in favor of a 4-dimensional spacetime distribution (block multiverse) which does not evolve. In spite of the static nature of the block multiverse, equations of motion of a system are encoded as-a-whole into its phase profile. Dynamical change is thus possible even though the wave distribution does not evolve.
Discussion: Bohm sought to develop quantum mechanics into the implicate and explicate order. Bohm’s structure emerges naturally in this formalism. This is unsurprising because Bohm’s favorite metaphor was the hologram and the Fourier transform, which serve as the basis for the formalism presented here. Just as digital images and audio data can be converted into spaceless and timeless representations, respectively, the implicate order described here is without space or time parameter. The timelessness and spacelessness applies universally and generates fruitful lines of inquiry, such as the retroactive flexibility of histories, as well as the requirement that all physical properties are defined subjectively.
References
Bohm, D. (1980). Wholeness and the implicate order. Routledge.
Feynman, R. P. (1948). Space-time approach to non-relativistic quantum mechanics. Reviews of Modern Physics, 20, 367–387.
Goodman, J. W. (1996). Introduction to Fourier optics (2nd ed.). McGraw-Hill Book Co.
Nelson-Isaacs, S. (2021). Spacetime paths as a whole. Quantum Reports, 3(1), 13-41. https://doi.org/10.3390/quantum3010002
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Published on June 13, 2023
