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Gravity beyond Einstein? Part III: numbers and coupling constants, contradictory experiments, hypercomplex gravity like-fields, propellantless space propulsion

Jochem Hauser EMAIL logo and Walter Dröscher


This article, the last in a series of three articles, attempts to unravel the underlying physics of recent experiments regarding the contradictory properties of the neutron lifetime that has been a complete riddle for quite some time. So far, none of the advanced theories beyond the  Standard Models (SMs) of particle physics and cosmology have shown sufficient potential to resolve this mystery. We also try to explain the blatant contradiction between the predictions of particle physics and experiments concerning the nature and properties of the (so far undetected) dark matter and dark energy particles. To this end the novel concepts of both negative and hypercomplex matter (giving rise to the concept of matter flavor) are introduced, replacing the field of real numbers by hypercomplex numbers. This extension of the number system in physics leads to both novel internal symmetries requiring new elementary particles – as outlined in Part I and II, and to novel types of matter. Hypercomplex numbers are employed in place of the widely accepted (but never observed) concept of extra space dimensions – and, hence, also to question the corresponding concept of supersymmetry. To corroborate this claim, we report on the latest experimental searches for novel and supersymmetric elementary particles by direct searches at the Large Hadron Collider (LHC) and other colliders as well as numerous other dedicated experiments that all have come up empty handed. The same holds true for the dark matter search at European Council for Nuclear Research (CERN) [CERN Courier Team, “Funky physics at KIT,” in CERN Courier, 2020, p. 11]. In addition, new experiments looking for dark or hidden photons (e.g., FUNK at Karlsruhe Institute of Technology, CAST at CERN, and ALPS at Desy, Hamburg) are discussed that all produced negative results for the existence of the hitherto unseen but nevertheless gravitationally noticeably dark matter. In view of this contradicting outcome, we suggest a four-dimensional Minkowski spacetime, assumed to be a quasi de Sitter space, dS 1,3, complemented by a dual spacetime, denoted by DdS 1,3, in which the dark matter particles that are supposed to be of negative mass reside. This space is endowed with an imaginary time coordinate, −it and an imaginary speed of light, ic. This means that time is considered a complex quantity, but energy m(ic)2 > 0. With this construction visible and dark matter both represent positive energies, and hence gravitation makes no distinction between these two types of matter. As dark matter is supposed to reside in dual space DdS 1,3, it is principally undetectable in our spacetime. That this is evident has been confirmed by numerous astrophysical observations. As the concept of matter flavor may possibly resolve the contradictory experimental results concerning the lifetime of the neutron [J. T. Wilson, “Space based measurement of the neutron lifetime using data from the neutron spectrometer on NASA’s messenger mission,” Phys. Rev. Res., vol. 2, p. 023216, 2020] this fact could be considered as a first experimental hint for the actual existence of hypercomplex matter. In canonical gravity the conversion of electromagnetic into gravity-like fields (as surmised by Faraday and Einstein) should be possible, but not in cosmological gravity (hence these attempts did not succeed), and thus these conversion fields are outside general relativity. In addition, the concept of hypercomplex mass in conjunction with magnetic monopoles emerging from spin ice materials is discussed that may provide the enabling technology for long sought propellantless space propulsion.

Corresponding author: Jochem Hauser, HPCC-Space, Bendestorf and Ostfalia Univ. of Applied Sciences, Suderburg 21227, Germany; and Institut für Grenzgebiete der Wissenschaft, Innsbruck 6010, Austria, E-mail:


This article is dedicated to the eminent Andreas Resch, P Dr. Dr., C.Ss.R. Professor and Director at the Institut für Grenzgebiete der Wissenschaft, Innsbruck, Austria to acknowledge his lifelong scientific work, Imago Mundi, whose prime subject was and is the creation of a consistent Weltbild, to unify both science and humanities, bridging the gap that still seems to divide these two disciplines and to Hozumi Gensho Roshi , Professor of applied sciences at Hanazono University, Kyoto, Japan, for his teachings (teisho) of more than thirty years (e.g. youtube videos) in Europe explaining the nature of reality. These two eminent scholars, though coming from a very different background, have dedicated their works to the quest for ultimate reality, thus elucidating the underlying reality of the Cosmos.

The first author would like to express his deep gratitude and hence dedicate this article to his friend, colleague, and (former) boss at the European Space Agency (ESA), the eminent Dr. Williamson (William, Bill) Berry on the occasion of his 85th birthday in 2020. Unfortunately, this article could not be finished in 2020 as the subject matter turned out to be more challenging than anticipated. As head of the Propulsion and Aerothermodynamics Division at the European Space research and Technology Center (ESTEC) at Noordwijk, The Netherlands, for more than twenty-six years, Bill, as one of the leading propulsion experts in Europe, not only exerted a major influence on the scientific thinking of JH but also on the European aerospace industry to further his goal in making European rocketry competitive with U.S. and Russian industry and relentlessly was looking for novel advanced propulsion concepts to advance the state of the art.

In particular, we are most grateful to Greg Daigle, former professor, and adjunct at the University of Minnesota, for constructive proofreading as well as for his numerous comments to improve the contents and the readability of this paper. Greg read the original manuscript, pointed out weaknesses and suggested many improvements in the presentation and also provided many helpful hints to the newest references with regard to magnetic monopoles and dark matter. We are also indebted to Prof. Dr. Thomas Waldeer, Ostfalia Univ., for numerous discussions and for providing relevant literature.

In particular, the TIKZ programming efforts of Dr. rer. nat H.-G. Paap, HPCC Regensburg, friend, colleague and former student (first author), in preparing the figures and his GNU Octave simulation results on the neutron lifetime are greatly appreciated as well as his proofreading of part of the formulas.

We are extremely grateful to the reviewer(s) who do their work in anonymity for their time and effort to peer review this lengthy manuscript. Their remarks on coupling constants are greatly appreciated and resulted, among other corrections, in a reformulation of Section 2.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.


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Received: 2021-05-29
Accepted: 2021-10-03
Published Online: 2021-11-04
Published in Print: 2022-01-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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