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Programming Planck units from a virtual electron: a simulation hypothesis

Abstract.

The simulation hypothesis proposes that all of reality is an artificial simulation. In this article I describe a simulation model that derives Planck level units as geometrical forms from a virtual (dimensionless) electron formula \(f_{e}\) that is constructed from 2 unit-less mathematical constants; the fine structure constant \(\alpha\) and \(\Omega = 2.00713494 \ldots\) (\( f_{e} = 4\pi^{2}r^{3}\), \( r = 2^{6} 3 \pi^{2} \alpha \Omega^{5}\)). The mass, space, time, charge units are embedded in \( f_{e}\) according to these ratios; \( M^{9}T^{11}/L^{15} = (AL)^{3}/T\) (\( {\rm units} = 1\)), giving mass \( M=1\), time \(T=2\pi\), length \( L=2\pi^{2}\Omega^{2}\), ampere \( A = (4\pi \Omega)^{3}/\alpha\). We can thus, for example, create as much mass M as we wish but with the proviso that we create an equivalent space L and time T to balance the above. The 5 SI units kg, m, s, A, K are derived from a single unit \( u = \sqrt{({\rm velocity/mass})}\) that also defines the relationships between the SI units: \( {\rm kg}= u^{15}\), \( {\rm m}= u^{-13}\), \( {\rm s}= u^{-30}\), \( {\rm A}= u^{3}\), \( k_{B} = u^{29}\). To convert MLTA from the above \( \alpha\), \( \Omega\) geometries to their respective SI Planck unit numerical values (and thus solve the dimensioned physical constants G, h, e, c, me, kB) requires an additional 2-unit-dependent scalars. Results are consistent with CODATA 2014. The rationale for the virtual electron was derived using the sqrt of momentum P and a black-hole electron model as a function of magnetic-monopoles AL (ampere-meters) and time T.

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References

  1. 1

    Nick Bostrom, Philos. Quart. 53, 243 (2003)

    Article  Google Scholar 

  2. 2

    Øystein Linnebo, Platonism in the Philosophy of Mathematics, in The Stanford Encyclopedia of Philosophy edited by Edward N. Zalta, (2017) https://plato.stanford.edu/entries/platonism-mathematics/

  3. 3

    https://en.wikipedia.org/wiki/Philosophy-of-mathematics (22, Oct 2017)

  4. 4

    Max Tegmark, Found. Phys. 38, 101 (2008)

    ADS  MathSciNet  Article  Google Scholar 

  5. 5

    M. Planck, Ann. Phys. 4, 69 (1900)

    Article  Google Scholar 

  6. 6

    Michael J. Duff et al., JHEP 03, 023 (2002) (Trialogue on the number of fundamental constants)

    ADS  Article  Google Scholar 

  7. 7

    Paul Dirac, The Evolution of the Physicist’s Picture of Nature, (2010) https://blogs.scientificamerican.com/guest-blog/the-evolution-of-the-physicists-picture-of-nature/

  8. 8

    Fine structure constant, en.wikipedia.org/wiki/Fine-structure-constant/ (2015)

  9. 9

    Fine structure constant, http://physics.nist.gov/cgi-bin/cuu/Value?alphinv

  10. 10

    planckmomentum.com/SUH-formulas.zip (a list of the formulas in maple format)

  11. 11

    Rydberg constant, http://physics.nist.gov/cgi-bin/cuu/Value?ryd

  12. 12

    Planck constant, http://physics.nist.gov/cgi-bin/cuu/Value?ha

  13. 13

    Elementary charge, http://physics.nist.gov/cgi-bin/cuu/Value?e

  14. 14

    Electron mass, http://physics.nist.gov/cgi-bin/cuu/Value?me

  15. 15

    Boltzmann constant, http://physics.nist.gov/cgi-bin/cuu/Value?k

  16. 16

    Gravitation constant, http://physics.nist.gov/cgi-bin/cuu/Value?bg

  17. 17

    Vacuum of permeability, http://physics.nist.gov/cgi-bin/cuu/Value?mu0

  18. 18

    Magnetic monopole, en.wikipedia.org/wiki/Magnetic-monopole/ (2015)

  19. 19

    Macleod, Malcolm, God the Programmer, the philosophy behind a Virtual Universe (2017) http://platoscode.com/

  20. 20

    Ariel Amir, Mikhail Lemeshko, Tadashi Tokieda, Surprises in numerical expressions of physical constants, arXiv:1603.00299 [physics.pop-ph]

  21. 21

    J. Barrow, J. Webb, Sci. Am. 292, 56 (2005)

    Article  Google Scholar 

  22. 22

    https://en.wikipedia.org/wiki/Theory-of-everything (2016)

  23. 23

    Leonardo Hsu, Jong-Ping Hsu, Eur. Phys. J. Plus 127, 11 (2012)

    Article  Google Scholar 

  24. 24

    A. Burinskii, arXiv:hep-th/0507109 (2005)

  25. 25

    A. Burinskii, Gravit. Cosmol. 14, 109 (2008)

    ADS  MathSciNet  Article  Google Scholar 

  26. 26

    Malcolm Macleod, A virtual black-hole electron and the sqrt of Planck momentum, http://vixra.org/pdf/1102.0032v9.pdf

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Correspondence to Malcolm J. Macleod.

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Macleod, M.J. Programming Planck units from a virtual electron: a simulation hypothesis. Eur. Phys. J. Plus 133, 278 (2018). https://doi.org/10.1140/epjp/i2018-12094-x

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