# 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.

This is a preview of subscription content, access via your institution.

## References

1. 1

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

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)

5. 5

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

6. 6

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

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)

22. 22
23. 23

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

24. 24

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

25. 25

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

26. 26

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

## Author information

Authors

### Corresponding author

Correspondence to Malcolm J. Macleod.

## Rights and permissions

Reprints and Permissions