Open Journal of Mathematics and Physics | Volume 2, Article 84, 2020 | ISSN: 2674-5747 https://doi.org/10.31219/osf.io/cevm3 | published: 18 Feb 2020 | https://ojmp.wordpress.com DG [microresearch] Diamond Open Access Electromagnetic mass as a superposition of Planck masses Open Quantum Collaboration∗† February 24, 2020 Abstract At the Planck scale, the electromagnetic mass is composed by infinite negative Planck masses. keywords: Planck scale, quantum gravity, quantum electromagnetism Introduction 1. This work was inspired by [1–4]. 2. We use the following renormalization procedure [5,6], ∞ 1 S = Q n = 1 + 2 + 3 + 4 + 5 + 6 + ::: = − : n=1 12 ∗All authors with their affiliations appear at the end of this paper. †Corresponding author: [email protected] | Join the Open Quantum Collaboration 1 When gravity is equal to the electric force 3. GM 2 ke2 = r2 r2 4. k M 2 = e2 G 5. The fine structure constant of the relativistic quantum electromagnetism is given by ke2 1 α = ∼ : hc̵ 137 6. The Planck mass is ¾ hc̵ M = : P G 7. From (5) and (6), k e2 M 2 = P G α 8. From (4) and (7), M 2 M 2 = : P α 9. √ M = αMP 10. M M ∼ P 12 2 Renormalization scheme 1 1 11. From (2), S = −12, then −S = 12. 12. Using (11) in (10), M ∼ −SMP : 13. Using (2) in (12), ∞ M ∼ − Q nMP n=1 14. M ∼ −MP − 2MP − 3MP − 4MP − 5MP − 6MP − ::: Quantization 15. Quantizing (14), SM⟩ = − SMP ⟩ − 2 SMP ⟩ − 3 SMP ⟩ − 4 SMP ⟩ − 5 SMP ⟩ − 6 SMP ⟩ − ::: Final Remarks 16. From (3), the√ electric charge near the Planck scale is related to the mass by e = GM. 17. M = √e can be seen as an electromagnetic mass. G 18. The quantum electromagnetic mass state, SM⟩, is the superpo- sition of negative Planck masses. 19. It is believed that all the fundamental forces of nature are comparable near the Planck scale [1]. 3 Open Invitation Review, add content, and co-author this article [7, 8]. Join the Open Quantum Collaboration. Send your contribution to [email protected]. Ethical conduct of research This original work was pre-registered under the OSF Preprints [9], please cite it accordingly [10]. This will ensure that researches are con- ducted with integrity and intellectual honesty at all times and by all means. References [1] Adler, Ronald J. “Six easy roads to the Planck scale.” American Journal of Physics 78.9 (2010): 925-932. https://arxiv.org/pdf/1001.1205.pdf [2] Faraoni, Valerio. “Three new roads to the Planck scale.” American Journal of Physics 85.11 (2017): 865-869. https://aapt.scitation.org/doi/pdf/10.1119/1.4994804 [3] Adler, Ronald J., and David I. Santiago. “On gravity and the uncer- tainty principle.” Modern Physics Letters A 14.20 (1999): 1371-1381. https://arxiv.org/pdf/gr-qc/9904026.pdf [4] Lobo, Matheus P. “The Curvature of Space Due to One Photon Is Inaccessible.” OSF Preprints, 4 Sept. 2019. https://doi.org/10.31219/osf.io/wru6z [5] Lobo, Matheus P. “Sum of All Natural Numbers.” OSF Preprints, 17 Feb. 2020. https://doi.org/10.31219/osf.io/yx28b [6] Lobo, Matheus P. “The Infinity Theorem.” OSF Preprints, 4 Feb. 2020. https://doi.org/10.31219/osf.io/9zm6b 4 [7] Lobo, Matheus P. “Microarticles.” OSF Preprints, 28 Oct. 2019. https://doi.org/10.31219/osf.io/ejrct [8] Lobo, Matheus P. “Simple Guidelines for Authors: Open Jour- nal of Mathematics and Physics.” OSF Preprints, 15 Nov. 2019. https://doi.org/10.31219/osf.io/fk836 [9] COS. Open Science Framework. https://osf.io [10] Lobo, Matheus P. “Electromagnetic Mass as a Superpo- sition of Planck Masses.” OSF Preprints, 18 Feb. 2020. https://doi.org/10.31219/osf.io/cevm3 The Open Quantum Collaboration Matheus Pereira Lobo (lead author, [email protected])1,2 1Federal University of Tocantins (Brazil); 2Universidade Aberta (UAb, Portugal) 5.