preprints.org > physical sciences > applied physics > doi: 10.20944/preprints202301.0179.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 7 January 2023 / Approved: 10 January 2023 / Online: 10 January 2023 (07:42:05 CET)

This paper shows that by applying the Nyquist-Shannon sampling theorem, the spatial and temporal resolution of a simulation can be no more than half the resolution of the simulating reality. This has significant implications for not only the values of the observables in the simulation but also its physical laws. This progressive halving of nested simulations coupled with the minimum resolution compatible with the production of a simulation also sets a limit to the nestedness of a lineage of simulations (it is by no means infinite). The limit of nestedness is then used to calculate the probability that we are living in a simulation assuming a single base reality. This will be shown to be significantly lower than popular expectation. A Kardashev-like scale, with three variants, is also developed to gauge the technological advancement of a civilization in relation to the extent to which it can extract information from space and time.

simulation hypothesis; simulating reality; resolution of a simulation; nested simulations; Nyquist-Shannon sampling theorem; probability

Physical Sciences, Applied Physics

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