GRAVITY BEYOND EINSTEIN?
PART II: FUN DAM EN TAL PHYSICAL PRINCIPLES,
NUMBER SYSTEMS, NOV EL GRO UP S, DAR K ENE RG Y AN D DARK MATTE R, MOND
Jochem Hauser 1, Walter Dröscher 2
1HPCC-Space, Hamburg and
Ostfalia Univ. of Applied Sciences, Suderburg, Germany
2Institut für Grenzgebiete der Wissenschaft, 6010 Innsbruck, Austria
This article attempts to explain the underlying physics of several recent experiments and astrophysical observations
that have been mystifying the physics community for quite some time. So far, none of the advanced theories beyond
the SMs of particle physics and cosmology have shown sufﬁcient potential to resolve these mysteries. The reason for
this failure may lie in the fact that these theories are based on the concept of extra space dimensions that appears
to be in conﬂict with numerous experiments, in particular with recent LHC data. Therefore, the novel idea of extra
number systems is introduced, replacing the idea of extra space dimensions. This approach is complemented by a
set of fundamental physical principles that provide the constraints and guidelines for a modiﬁed physical formu-
lation in agreement with known experimental reality. However, such a theory requires novel physical concepts in
conjunction with novel symmetry groups. These groups give rise to additional types of matter, termed hypercomplex
masses (which are responsible for the extreme hypercomplex gravitational ﬁelds, see below) and are also denoted as
matter ﬂavor), including, for instance, particles of negative mass, identiﬁed with dark matter. Furthermore, four-
dimensional Minkowski spacetime, assumed to be a quasi de Sitter space dS1,3, is complemented by a dual spacetime,
DdS1,3,with imaginary time coordinate, that is, time is a complex quantity. The three spatial coordinates are shared
by the two spacetimes. Dark matter is assumed to reside in DdS1,3,and therefore is principally invisible. On the
other hand, its gravitational interaction with ordinary matter (m≥0) in spacetime dS1,3is directly perceptible. The
novel group structure predicts the existence of a forth particle family of negative masses, that is, besides the dark
matter particle χof mass mχ≈ −80.77 GeV/c2there is the dark neutrino νχof mass mνχ≈ −3.23 eV. Moreover,
the hypercomplex group structure of gravity (SU(2)×SU(2)) postulates three gravitational bosons for cosmolog-
ical ﬁelds (resulting from Einstein’s GR), the graviton νGNwith spin 2, the novel gravitophoton νgp with spin 1
(existence of weak gravitomagnetic ﬁelds of GR), and the quintessence particle νqwith spin 0, that, when present,
mediates an interaction between ordinary matter (m≥0) and the ubiquitous scalar ﬁeld of dark energy. In addi-
tion, the existence of extreme gravity ﬁelds (hypercomplex-gravity) is postulated, based on the second group SU (2),
and an interaction between electromagnetism and hypercomplex-gravity is predicted, mediated by three additional
hypercomplex-gravity bosons. Some long-standing problems of cosmology will be addressed, namely the big bang
scenario and the origin of dark energy and the nature of dark matter and their relation to the MOND hypothesis
will be discussed.
*This article will be published in Zeitschrift für Naturforschung (ZNA) Physical Sciences A, de Gruyter in 2019. The full paper will be available
upon publication on Researchgate. Requests for personal preprint, comments or criticism should be sent to the corresponding author: Jochem
Hauser, E-mail: firstname.lastname@example.org.
Table of Contents
2Mysteries in Physics and the Universe 3
3Verdict of the LHC Data 8
3.1 LHC Data and New Particles ...................................... 9
4Cosmic Principles 10
4.1 Formulation of Cosmic Physical Principles ............................... 12
4.2 Cosmic Principles and No-Go Theorems ................................ 16
4.3 Cosmic Principles and Gravitation ................................... 18
5Cosmic Symmetry Group 19
5.1 Hermetry Forms ............................................. 20
5.2 Extra Number Systems versus Extra Space Dimensions ......................... 21
5.3 Lagrangians, Symmetries, and Groups .................................. 21
5.4 Cosmic Symmetry Group from Hypercomplex Numbers ......................... 24
6Cosmological Riddles 33
6.1 Novel Physical Concepts for Cosmology ................................ 34
6.2 Speeds of Light and Gravitation ..................................... 35
6.3 Big Bang Scenario Questioned ...................................... 36
6.4 Origin of Dark Energy, Dark Matter, and Baryonic Matter ....................... 38
6.4.1 Dark Energy, Inﬂation, and EHT ................................ 38
6.4.2 Existence of Dark Matter? .................................... 41
6.5 Masses of Dark Matter Particles ..................................... 45
6.6 Dark Matter Space ............................................ 46
6.7 Spacetime Lattice and Propagation Speeds ............................... 48
7Principles of Propellantless Space Propulsion 50
7.1 Physically Impossible Propulsion Concepts ............................... 52
8Summary of Physical Concepts of EHT 53
9Physics, Cosmology, and Technology
Method of Theoretical Physics:
Albert Einstein, 1933
The Herbert Spencer Lecture1
Pure logical thought cannot
yield us any knowledge of the
empirical world, all knowledge
of reality starts from experience
and ends in it. Propositions ar-
rived at by purely logical means
are completely empty as regards
It is now a 100 years since Sir Arthur Stanley Edding-
ton, the ﬁrst relativistic astrophysicist, led the 1919 expe-
dition to photograph the sun during a total solar eclipse in
order to ﬁnd out whether photons from distant stars were
deﬂected (bent) passing the sun as predicted by Einstein’s
theory of General Relativity (GR). The theory was con-
ﬁrmed, (within the accepted experimental accuracy of the
time) and as a result, Einstein became an instant celebrity
in the popular press. Since then, GR has passed all tests
with ﬂying colors, ruling out alternative theories, demon-
strating perfect agreement with all experimental evidence
(cf. string theory) up to today.
We deliberately start this paper with the above citation
from Einstein, which is used as a roadmap for the novel
physical concepts presented in this paper. Einstein’s re-
marks also purport a stern warning. Expressed in simpler
terms, A. Einstein reminds us that the description of phys-
ical reality is the ultimate goal of physics, which in the
end is a purely empirical science. Theoretical constructs
are certainly necessary but are subordinate to experiment
and have no life of their own unless conﬁrmed by proper
data. Approval by experimental data is the yardstick for
any theoretical model. If this cannot be achieved then it
is not a physical theory, and those ideas should be trans-
ferred to the mathematics or philosophy department. Re-
garding the present situation in theoretical physics, as dis-
cussed in Part I,3the scientiﬁc community seems to have
forgotten – at least to some extent – this admonition of
Einstein 1. A recent, highly informative and expertly writ-
ten account (from a physics point of view) on LHC data
and the state of Grand Uniﬁcation Theories is presented
by S. Hossenfelder in her excellent book: Lost in Math
whose conclusion can be summarized by one word: fail-
ure.42 In Chap. 8 of her book a brief account of string the-
ory along with a long list of its problems and attempts to
escape from experimental evidence is given. Eventually,
the author concludes It (string theory), does not, however,
describe our universe. Hardly a success story after more
than four decades.
In Sec. 2 the importance and challenge of numer-
ous experiments from particle physics and astrophysical
observations are presented, as well as measurements of
gravitational phenomena. The LHC data are also pre-
sented in Section 3 because of their importance. Based
on these empirical ﬁndings alternative physical concepts
termed matter ﬂavor and hypercomplex-gravity are intro-
duced in non-mathematical form to emphasize their phys-
In Sec. 3 the latest LHC data with emphasis on the
CERN exotic search program, both from Run-1 √s=
7−8 TeV and Run-2 √s=13 TeV, will be employed to
evaluate their impact on the validity of physical theories
based on the existence of extra space dimensions. The
key ﬁnding is that these data impose extremely tight con-
straints, which may be employed to question the whole
theoretical approach, in particular when combined with
other experimental results discussed in Sec. 2. It seems,
therefore, justiﬁed to search for alternative explanations.
In the remaining part of this article the novel concept
of extra number systems (subsumed under the name EHT,
2see Part I) is introduced, and its consequences regarding
the group structure of particle physics will be considered.
Of prime importance is the prediction of additional gravi-
tational bosons that would allow the generation of extreme
gravity ﬁelds outside GR, as will be outlined further in de-
tail in Sec. 5. With regard to cosmology, a tentative ex-
planation of the origin of dark energy is given, where the
picture of a hot Big Bang is questioned by the idea of a
Quantized Bang (Sec. 6).
In Sec. 4, we start with Einstein’s advice by present-
ing in detail an assembly of fundamental physical prin-
ciples, termed cosmic physical principles, meant to gov-
ern all physical processes. This set of twelve principles,
of which the duality principle is the most important, will
be presented one by one and their impact on the vari-
1The meaning of Einstein’s words is that mathematics cannot be used as a replacement for physics as he said: "Ideas are more important than
knowledge". Physics must not be separated from experiment. We quote N. N. Taleb in Skin in the Game, Random House, 2018, p. 27: "Intellec-
tualism has a sibling: scientism, a naive interpretation of science as complication rather than science as a process and a skeptical enterprise. Using
mathematics when it’s not needed is not science but scientism". Naive in this context should be understood as without any empirical evidence.
2Note: No, EHT (Extended Heim THeory) is not Heim theory,43 despite the similarity of the names. The name EHT was selected to honor B.
Heim’s ideas of internal gauge space and elemental surface in order to construct a polymetric tensor of all physical interactions and a spacetime
lattice. The concept of eight-dimensional internal space employed in EHT is reminiscent of B. Heim’s initial (but insufﬁcient) six-dimensional
approach, but otherwise the two approaches are employing different physical concepts and there are no further relationships, except for the name,
of course. As it turned out, Heim’s ideas about the internal structure of elementary particles and his calculation of the spectrum of elementary
masses turned out to be incorrect as well as his ideas about cosmology, in particular the range of attractive gravitation.
ous physical phenomena will be discussed as the basis
for a different (but not too different) model of particle
physics and cosmology. It turns out that the effects stem-
ming from these simple sounding principles are amazing,
leading to the formulation of nine so-called no-go theo-
rems. Moreover, these principles require the introduction
of novel physical concepts. The most far-reaching conse-
quence is the replacement of extra spatial dimensions by
extra number systems. The physical reality of the postu-
lated extra spatial dimensions appears no longer tenable,
because the range of Newton’s law of gravitation was re-
cently experimentally found to extend down to the range
of the atomic size (10−10 m, details in the next section). A
recent discussion of the modiﬁcation of Newton’s law in
accordance with GR for cosmological distances, but not
for small distances, is given by Eingorn, Kiefer, and Zhuk
in,2demonstrating a Yukawa-type exponential screening
of the gravitational potential at distances >λ(λbeing due
to the existence of cold DM) termed the cosmic screening
by the authors who found the cosmic background to be re-
sponsible for this type of screening. Their results are con-
sistent with the largest known structure in the Universe,
the Great GRB Wall (or Hercules Corona Borealis Great
Wall), with the size of the order of 3,000 Mpc. It should
be mentioned that these results have no impact on MOND
In Sec. 5 the most striking consequences from the
novel concept of an extra system of numbers with regard
to allowable physical symmetries are presented – displac-
ing the most likely experimentally disproved concept of
extra dimensions. A novel group, termed Cosmic Group,
is introduced to cover all physical phenomena as well as
its effects on both particle physics and spacetime. The
most signiﬁcant outcome is the prediction of two different
types of gravity, represented by groups SU (2)×SU(2),
resulting in the postulation of a total of six gravitational
bosons. The ﬁrst SU(2)group gives a description of Ein-
stein’s GR enhanced by the additional interaction of mat-
ter with the dark energy ﬁeld. The associated gravitational
ﬁelds are termed cosmological gravitational ﬁelds and are
of purely geometrical origin.The effect, inﬂuenced by the
presence of dark energy, is very weak and is a result of the
distribution of matter on spacetime curvature. GR also de-
scribes the feedback of spacetime curvature on the distri-
bution of matter. The observed weakness of cosmological
gravitational ﬁelds demonstrates the rigidity of the space
lattice, allowing the Universe to assume an enormous spa-
The gravitational bosons of the second SU(2)group
mediate much stronger gravitational ﬁelds that are pro-
posed to result from the interaction with electromag-
netism. According to the duality principle, the three cos-
mological and the three hypercomplex-gravity ﬁelds are
caused by two different sources, namely pure geometry
(spacetime curvature) and charge (in the form of elec-
tric charge and mass, represented by particles of hyper-
complex mass), and thus should not be uniﬁable. A to-
tal of four groups derived from hypercomplex numbers
(quaternions) q∈H) can be found that describe the phys-
ical properties of matter in general, i.e., both bosons and
fermions, as well as the external spacetime. The exter-
nal spacetime is complemented by an an (internal) gauge
space, termed Heim space, or, H8. An important out-
come is that there should exist four families of leptons
and quarks (Fig. 5.4), where the fourth family of particles
possesses negative masses and is assumed to represent
dark matter, living in dual spacetime (see below), and thus
cannot be observed directly in our Minkowski spacetime.
A new concept arises, denoted matter ﬂavor (analogous
to quark ﬂavor), which is derived from the hypercomplex
group structure that incorporates both dark and ordinary
matter as well as the hypercomplex masses of the three
bosons representing the postulated hypercomplex-gravity
In Sec. 6 several of the so-called cosmological riddles
are addressed (to be revisited in Part III), reconsidering
the role of the Einstein ﬁeld equations in the formation
and evolution of the Universe and critically dealing with
the presently favored idea of a Big Bang as well as dis-
cussing the origin of dark energy and dark matter, as they
result from the concept of extra number systems.
In Sec. 7 we present a preliminary discussion of pro-
pellantless propulsion (propulsion without fuel) where the
proposed gravitational spin 1 bosons are introduced. It
will be argued that the associated hypercomplex-gravity
ﬁelds can be generated in order to provide the en-
abling acceleration mechanism for propellantless propul-
sion – provided that a suitable material composition is se-
lected. A brief description of other currently considered
propellantless propulsion concepts is given, namely the
EM drive, the Woodward effect, Mach’s principle, and
Becker’s electrodynamics, demonstrating that these sys-
tems/concepts cannot function in practice.
In Sec. 8 the novel physical concepts of EHT are sum-
marized and discussed.
The ﬁnal section provides an outlook on the repercus-
sions of the novel physical concepts with regard to particle
physics, cosmology, and novel gravitational technology as
well as novel schemes for energy generation based on the
existence of hypercomplex-gravity ﬁelds.
The above discussion should have made clear that cur-
rent physics is far from complete, instead there are se-
vere challenges that are still to be resolved. The so-called
advanced physical theories, developed over the last ﬁve
decades, have not provided the tools to successfully tackle
these puzzles. Therefore, in Part I and also in this article,
alternative ideas are presented in an attempt to contribute
to an explanation, at least to some extent, of the basic con-
tradictions posed by recent experiments and astrophysical
... behind all the discernible
laws and connections,
there remains something subtle,
intangible and inexplicable.
2. Mysteries in Physics and the Universe
In the following, we present an attempt to construct an
alternative physical picture to resolve the riddles posed by
recent experiments that are either contradictory or remain
still unexplained. In particular, this concerns the null re-
sults of the LHC in seeing any supersymmetric particles,
the different lifetimes of the neutron, the varying size of
the proton, the discrepancies in the measured magnitude
of the gravitational constant, the enigma of missing dark
matter particles, the non-explainable existence of dark en-
ergy, and a possible spatial variation of the ﬁne structure
constant α. In cosmology there are fundamental ques-
tions concerning the Big Bang describing the origin of the
Universe, the long standing problem of the deviation from
Newton’s gravitational law for the rotational velocities of
stars in orbit about their galactic center, the measured de-
viations of Newton’s gravitational constant GN, and, most
recently, observed small differences by LIGO in the prop-
agation speeds of gravitational waves and photons. These
problems are severe, demonstrating a lack of understand-
ing at the most fundamental level of physics.
The predictions of presently favored advanced phys-
ical concepts, i.e., supersymmetry and superstring the-
ories, when compared to most recent experimental re-
sults, are even more in conﬂict (no superpartners, no uni-
ﬁcation, no naturalness3, no dark matter particles) with
observation than they were in early 2017, when Part I
of this article3was published (Fig. 6). Supersymme-
try predictions are not only in contradiction to experi-
ments from atomic and particle physics, but also from as-
trophysics as well as gravitational measurements. Most
recent results (Winter 2018) from the LHC collider AT-
LAS cooperation5have not found any excess above the
expected SM background, running for about three years
at √s=13 TeV 4. That is, none of the ﬂurries of pre-
dicted elementary particles (neither from the ATLAS nor
from CMS experiment) have been revealed up to parti-
cle masses of 1.6 TeV/c2and 2.4 TeV/c2for spin-0 res-
onances 5. These ﬁndings are conﬁrmed by most recent
ACME data (22 October 2018)6(the table-top experi-
ment is operational since 2014) and more recent results
can be found at: https://www.nature.com/articles/s41586-
018-0599-8 that constrain the value of the electron dipole
moment, EDM, to be smaller than |de|<1.1×10−31 e
m, where edenotes the electron charge. As stated in12
pp. 33-46 the electron seems to be perfectly round which
means that the new types of particles, assumed to cause a
deviation from the spherical electron orbits about atomic
nuclei, as postulated by numerous theories, do not seem to
exist. A direct consequence of these measurements is the
quasi conﬁrmation of the SM of particle physics that pre-
dicts an EDM of |de| ≈ 1.0×10−46 e m at the four loop
level and the ruling out of the predictions of supersym-
metric theories, for instance, see Fig. 4 p. 39 in,12 mean-
ing the mass of the undiscovered heavy particles to have
shifted above the 10 TeV/c2level, and thus SUSY can no
longer contribute to the solution of the hierarchy problem
and, again had to be moved out of the experimental reach,
a process going on for more than four decades, resulting
in a substantial loss of scientiﬁc credibility. Nevertheless,
theoreticians have been quick to construct a substantial
number of models consistent with these data,6predicting
particle masses in the range between 3 TeV/c2and 109
TeV/c2, hardly an informative result. However, the SM
of particle physics cannot be the ﬁnal answer and there
is a need to go beyond the SM, in order to discuss three
mysteries, namely the extreme ﬁne tuning of the Higgs
boson mass and to ﬁnd a solution of the long standing
problem of the matter-antimatter asymmetry. The third
problem, the existence of dark matter, is addressed in this
article. A perfectly round electron does not exhibit any
asymmetry, and thus its electric dipole moment must be
zero, i.e., the center of mass and the center of charge of
3A theory is called natural if it does not contain numbers that are extremely small or extremely large. The opposite is ﬁne-tuning. In that sense,
Nature is not natural, just look at the cosmological constant or compare 1 AU (astronomical unit) to the distance to the closest star, i.e., the stars
appear ﬁxed. Large numbers need explanation.
4The square root of the Lorentz invariant Mandelstam variable sprovides the sum of the particle energies in a scattering experiment, that is, for the
LHC collider with its two oppositely moving proton beams the laboratory observer is at the center-of-mass, and the total momentum of the two beams
p1+p2=0.Thus, the total beam energy calculated using the four-momenta p1,p2is s= ( p1+p2)2c2= (E1+E2,(p1+p2)c)2= (E1+E2)2=4E2.
With E2= (pµpµ−m2
0c2)c2≈p2c2in the relativistic limit, one obtains √s≈2cpp2=mpc2(1−v2/c2)−1=2×6.5=13 TeV (6.5 TeV for
each beam pipe), where mpis the proton rest mass and vdenotes the proton speed. This energy is available since the 2015 LHC upgrade.
5To be more exact, the experimenters are searching for both spin-0 resonances produced from gluon-gluon fusion and spin-2 resonances pro-
duced from gluon-gluon or quark-antiquark initial states. The 95% conﬁdence level is utilized as usual.
the electron (almost) coincide. The standard model pre-
dicts an electron EDM of |de| ≤ 1.0×10−46 e m. This
means that the center of mass and charge must be sepa-
rated by a distance of about 1.0×10−46 m, far below the
Planck length, and thus their distance is practically zero.
This distance is non-physical if there exists a spacetime
lattice with a grid spacing of the Planck length `Pl ≈10−35
m. The result of the standard model is not surprising, as it
is based on a continuous and ﬂat spacetime. The ACME
measurements already are at 10−31 m and dipole moments
less than 10−35 m cannot be distinguished anymore if the
Planck length is the limit, and not the ESA Integral satel-
lite value. The recent constraints on the EDM also have an
important consequence for the high energy scale, termed
grand uniﬁcation, that assumes the equality of the cou-
plings of the three subgroups SU(3)c⊗SU(2)w⊗U(1)
(uniﬁcation of couplings does not occur in the SM). To go
beyond the SM the hypothesis was made that there exists
a simple group Gat this energy scale that does embed the
three subgroups of the SM. This GUT group is assumed
to represent the complete particle content of the SM. The
smallest group possible is the group SU(5), without con-
sidering right handed neutrinos, or SO(10)if right handed
neutrinos are accounted for. At the MGUT mass scale
this group spontaneously breaks down into the three sub-
groups of the SM. However, based on the recent measure-
ments of the EDM, this is no longer possible, for a group
SO(10)at the GUT high scale is ruled out, see Fig. 4 on
p. 39 of.12 This fact also is in support of our statement
(Sec. 4) that a uniﬁcation of the four fundamental interac-
tions should not be possible because it would contradict
the principle of duality. Also the concept of technicolor
appears to be invalid. In particular, the CMS collabora-
tion started an extensive search for the neutralino and top
squark in 2016 based on proton-proton collisions at the
center-of-mass energy of 13 TeV, but so far no signiﬁcant
excess of events could be observed above the expectation
values of the SM and most likely will not be found.
Moreover, no dark matter (DM) particles have been
found by the LHC, conﬁrming the futile search of the
three dozen experiments performed over the last 35 years
(with zero results, according to S. Hossenfelder42 Chap.
9, dressed up as interesting bounds). The LUX exper-
iment (ongoing since 2013) has provided zero evidence
for DM particles, thus independently supporting both the
LHC and ACME measurements. In particular, the ﬁnd-
ings of the DAMA collaboration of a statistically signif-
icant annual modulation in the rate of nuclear interaction
events was ruled out by the Cosine -100 collaboration in
their recent publication in Nature on 5 December 2018.7
No evidence for an excess of events above the expected
background was found, and hence, there are no WIMPS.
The upper bound for the WIMP-sodium cross section is
1.14 ×10−40 cm2for WIMPS of mass 10 GeV/c2at the
90% conﬁdence level. Annual modulation is expected for
the velocity of the Earth varies relative to the Galaxy?s
dark-matter halo owing to the orbital motion of the Earth
around the Sun. According to the so-called standard dark-
matter halo model, this result rules out WIMP?nucleon in-
teractions and thus cannot be the cause of the annual mod-
ulation that was possibly observed by the DAMA collabo-
ration. As a direct consequence, supersymmetric particles
have become increasingly unlikely to exist in Nature.
Confusion reigns, as demonstrated by controversial
experimental ﬁndings and about twenty articles written
by well known physicists, published in the recent book by
the late J. Brockman (ed.)8entitled This Idea Must Die,
6portraying a highly controversial picture (of the physics
of string theory and supersymmetry). Therefore, present
experimental ﬁndings may suggest that it is these two the-
oretical concepts that may have to be retired despite inter-
esting mathematical features. Similar confusion is visible
with respect to key concepts of cosmology, i.e., the Big
Bang, DM, inﬂation, the multiverse idea as well as pre-
dictions concerning the ultimate fate of the Universe.
Furthermore, in Part I it was shown that Newton’s law
has been proven to uphold down to the length scale of
about 1µm(upper Figure 6). As recently as December
2017, the validity of Newton’s law has been extended by
four orders of magnitude down to 10−10 m or 0.1 nm by
Haddock et al.10 It appears that Newton’s law holds in
the atomic range as indicated by the scattering of neu-
trons. As the electron mass is about two-thousand times
smaller than the nucleon mass, gravity must result from
the nucleons (protons and neutrons) whose size is about
10−15 m, hence, gravity must be governed by the sub-
atomic length scale (lower Figure 6). Newton’s law must,
therefore, be working on the subatomic scale as well, thus
no energy could have escaped into the postulated higher
dimensions at this length scale. So far, higher space di-
mensions seem to be in basic conﬂict with all direct mea-
surements (in particular no evidence for extra spatial di-
mensions in the universe based on gravitational wave data
was found). It is now clear from the recent LIGO data that
large-wavelength gravitational waves and short-frequency
photons experience the same number of spacetime dimen-
sions18 and non-compact space dimensions do not exist, a
result that is more or less obvious, because these dimen-
sions should have been detected a long time ago. No de-
viation of the gravitational amplitude from the inverse lu-
minosity distance relationship in accordance with GR has
been observed. In other words, there is no leakage of en-
ergy into (non-compact) extra space dimensions, and that
concept, according to Fig. 6, appears to be no longer ten-
able as it seems to have been excluded by Nature. This has
far reaching consequences, not only for particle physics,
6An idea that may have to die is the idea of the existence of extra (real) space dimensions that has blocked progress in physics since its inception
in 1919 by Kaluza, because alternatives were not pursued.
but also for cosmology (e.g., the existence of multiverses).
The experimental results cited in Part I already ruled out
to a large extent any modiﬁcation of the classical gravita-
tional law proportional to r−2. This includes any modiﬁed
Newtonian law operating in D=d+3 dimensions (d de-
notes the number of extra space dimensions), that is,
instead of the classical gravitational law being propor-
tional to r−2. With the new data from Haddock’s experi-
ment (Fig. 6, lower picture) the idea of a Cosmos in the
form of a brane world where gravitons freely roam the
bulk space (i.e., the higher dimensional embedding space
for the spatial 3d-brane world) has become untenable.
Advocates of a brane world hoped that if an extra spatial
dimension of extension 10−4m existed, the strength of
the gravitational interaction would resemble the strength
of the electroweak interaction. In this case, the so-called
hierarchy problem (see Part I) where the relationship of
the Planck mass, mPl , GUT mass, mGUT , and the mass of
the vector boson, W±,
mPl mGUT mW,
requiring a large ratio of mGUT /mW>1013 could have
been interpreted as a so-called holographic effect. It was
proposed that a Planck length in our 3d-brane would now
be much smaller than the (large) compactiﬁed dimension,
i.e., `Pl 10−4m, leading to the holographic effect. This
scenario is deﬁnitely ruled out by experiment.
Most recent results from experimental particle physics
seem to tell us that dark matter particles do not ex-
ist, whereas astrophysical observations (starting about
85 years ago with Zwicky in 1933)19 have provided ir-
refutable experimental evidence for their existence, e.g.,
based on gravitational lensing. However, the original as-
sumption of DM was that it occurred inside galaxies, but
the recent astronomical observations by Bidin, ESA 2010,
2012 and conﬁrmed in December 2014 seem to prove
the absence of dark matter (DM) inside galaxies, con-
ﬁning DM to the galactic halo. Despite the criticism by
Tremaine and Jovy 2012 (see Part I) this leads to a sce-
nario requiring an entirely new physical mechanism for
the explanation of the deviating galactic orbital velocities.
Dark matter has been elusive for more than eight decades
and the recent community report4with more than 100
authors (suggesting numerous novel small experiments,
as the large experiments have turned up empty handed)
sounds like a desperate attempt to ﬁnally detect the miss-
Also unexplained is that, based on observations of
hundreds of galaxies, it is evident that the velocities of
stars orbiting the galactic center deviate from Newton’s
gravitational law at small accelerations, assuming the to-
tal gravitational galactic mass is based on the amount of
luminous matter. The MOND (Sec. 5.4) hypothesis gives
the correct numerical values but lacks any physical expla-
An important idea coming from the novel concept of
hypercomplex groups, as will be discussed in Sec.5, is the
closely associated idea of matter ﬂavor – as an analogy
to quark ﬂavor or color ﬂavor. Different types of mat-
ter, positive, negative, and hypercomplex matter (includ-
ing imaginary matter) result from the introduction of extra
number systems that make the idea of extra space dimen-
Another mystery is that cosmology has no explanation
for about 68% of the energy in the Universe 7that comes
in the form of dark energy (DE) as conﬁrmed by Planck
satellite data in 2013. In Sec. 6 a novel idea is presented,
attributing the existence of DE to the evolving structure of
spacetime and therefore according to EHT DE cannot be
produced in accelerators. Such a form of energy neither
exists in the SM of particle physics, nor in the proposed
supertheories. That is, DE would be the direct result of
7The term Universe is used to mean the observable universe which is the spherical region of the universe comprising all matter that can be
observed from Earth at the present time by light or neutrino signals or gravitational waves – all with ﬁnite propagation speed – that have had
time to reach our planet since the beginning of the cosmological expansion. There is currently no accepted experimental proof for the existence
of superluminal signals. The distance a photon traversed, emitted by a galaxy tph =100 million years ago, also termed the lookback time, is
dph =ct ph as the speed of light in vacuum is independent of time. However, the distance to the other galaxy dgx >dph at the arrival of these
photons. This distance is difﬁcult to determine because it is changing while the photons are traveling owing to cosmic expansion (governed by the
Friedmann equation), characterized by Hubble’s parameter H=H(t). Its present value is called the Hubble constant H0≈22 km/s per Mly.
Hence, the spatial dimension of the Universe dU>ctU, where tU≈13.8 billion years (Planck satellite data) denotes the age of the Universe, that is,
the maximal lookback time. Notice, that cosmic expansion has no impact on physically bound systems like atoms, solar systems, or even galaxies,
because it is not strong enough to modify the effective gravitational potential into a potential that has no reversal points as shown in detail in Sec.
9.8 in the book by the authors.12 Of course, everything depends on the temporal evolution of H=H(t).
8It may be argued that superluminal speed is present in the path integral formulation of Feynman. Any arbitrary path from an initial location
xito the ﬁnal location xfis represented by a polygon in the x−tplane with the corresponding time interval [ti,tf]subdivided into ndiscrete time
intervals ∆t. For each of these (supposedly small) time intervals, however, the integration over space (x-coordinate) goes from −∞to +∞, i.e., the
length of a path is not restricted. Clearly this would mean superluminal speed for any material particle going along this path, but the path integral
formulation associates a probability amplitude hxiti|xftfiP, that is, a complex number to each path P. Hence, the resulting probability amplitude
for a particle to arrive at location xfand time tfis given by the sum over all possible paths hxiti|xftfi=∑Phxiti|xftfiP. Often the amplitude over
path Pis written in the form φ[x(t)]P:=hxiti|xftfiPto denote that φ[x(t)]Pis a functional, that is, it depends on the entire path x(t)and not on a
single number. In order to calculate such a probability amplitude the genius of Feynman, remembering remarks by Dirac concerning the role of
classical action Sin QM, postulated the relation φ[x(t)]P:=Cexp(i/¯
hS[x(t)]), where the constant Cis chosen to normalize φand S=Rtf
is the classical action and Ldenotes the Lagrange function, e.g. kinetic minus potential energy, Ekin −V. Apart from the fact that it is not clear
how to do the integration over all paths, it seems strange that the length of path x(t)does not play any role. All possible probability amplitudes
the formation of the smallest units of space. 8
Regarding novel aspects of gravity outside Einstein’s
general relativity, three different types of experiments
(2006-2011) are mentioned that may have generated ex-
treme gravity-like ﬁelds at cryogenic temperatures. In
Sec. 5 additional gravitational bosons and different types
of matter are introduced that may resolve the apparently
conﬂicting data obtained from recent experiments and as-
trophysical observations as well as elucidating the nature
of dark matter and dark energy. In particular, it will be
argued that the interaction between electromagnetism and
gravity, as already surmised by Einstein in 1916, may ex-
ist owing to the phenomenon of symmetry breaking in
combination with the generation of virtual particles of
hypercomplex mass. However, this requires a differ-
ent type of gravity, dubbed hypercomplex-gravity, outside
Einstein’s GR but not inconsistent with GR.
As reported in Part I of this article3recent data from
atomic physics and particle physics as well as astrophys-
ical observations appear to have invalidated so called
supertheories developed over the last four decades and
meant to replace the standard model (SM) of particle
physics developed in the early 70s of the last century. In
Sec. 3 a review of the current search for novel particles
based on the latest LHC data will be presented along with
the repercussions on the so-called supertheories. Accord-
ing to particle physics experiments a dark matter parti-
cle does not exist, i.e., nothing was ever observed. On
the other hand, for astrophysicists the existence of dark
matter is beyond scientiﬁc doubt – it is an empirical fact.
Without dark matter there would be no galaxies. Even
worse, astrophysical measurements (according to recent
Planck satellite data) have determined 68% of the total
energy in the Universe as dark energy. Such a form of
energy does neither exist in the SM of particle physics,
nor in the proposed supertheories. As a consequence, it
may be concluded that the Universe should not exist. It
is obvious that the present extension of the symmetry of
the SM (SUc(3)×SUw(2)×Uem(1)) has led to a major
confrontation with physical reality. Already, in 1967, B.
Pontecorvo postulated a new particle, termed the sterile
neutrino, with a mass of about +1 eV/c2and generally in-
terpreted as some kind of fourth neutrino. Such a particle
may indeed exist, as indicated by the most recent experi-
mental data from the MiniBooNE experiment. However,
according to EHT, its physical properties need to be com-
pletely different from the three known lepton families yet
this is not matched by the postulated sterile neutrino, as
will be discussed in further detail in Sec. 6.4.2.
A new era of astronomical observation began with the
advent of the Hubble space telescope in the 1990s. Over
the last few years numerous additional satellites and tele-
scopes were sent into space and, in combination with so-
phisticated highly powerful ground based telescopes, e.g.
the VLT (Very Large Telescope) of the European South-
ern Observatory (ESO) in Chile, the new research ﬁeld of
astroparticle physics was initiated. It is possible that as-
troparticle research may not just supplement earthbound
accelerator research, but actually compete with it. As dis-
cussed in Part I, the future of the next generation acceler-
ator with a circumference of about 100 km is uncertain,
and Fermi’s 1954 proposition for Globatron, an acceler-
ator that spans the Earth, is no longer a realistic alterna-
tive (because of space debris apart from technical issues).
Instead, a high luminosity upgrade of the LHC, termed
HL-LHC, to 60 fb−1is planned for 2026 (ﬁve times the
number of the present number of collisions per unit time
and area at the collision point of the two colliding beams),
with a further increase to 3,000 fb−1in 2035. In any
case, the particle energy provided by the cosmic accel-
erator cannot be matched, but perhaps improved record-
ing equipment may enable us to make use of it. Already,
when CERN was established in 1953, the study of cosmic
rays was formulated as one of the major scientiﬁc goals of
The recent results of the H.E.S.S. collaboration (ﬁn-
ished 2015) starkly question another cornerstone of to-
day’s astrophysics, namely the occurrence of the Big
Bang. From the proposed hot Big Bang nucleosynthesis
comes the main evidence for dark matter as a type of ex-
otic, non-baryonic matter. Supersymmetry (SUSY), based
on extra dimensions, provides the framework for a parti-
cle species that ﬁts the observed properties of dark mat-
ter. The lightest supersymmetric particle (LSP), which
is stable, comes in the form of four neutralinos, consid-
ered to be the perfect WIMP. WIMPS (Weakly Interacting
Massive Particles) can only weakly interact with ordinary
matter, e.g. nucleons. Nevertheless, several experiments
(XENON1T, DAMA, CMDS, Edelweiss, PandaX, see be-
low), have been operating for decades, to directly detect
collisions of WIMPs and ordinary matter, but to no avail.
For instance, in 2012 the XENON100 experiment at the
Gran Sasso Laboratories produced a WIMP cross section
limit of 2.0×10−49 m2for a WIMP mass of 55 GeV/c2
appear to arrive at the same time tfinterfering simultaneously at xf, resulting in a single amplitude, which, when squared, gives the probability
to ﬁnd the particle at location (xf,tf). A single probability amplitude cannot be measured and thus has no physical reality, i.e., it is not a signal,
that is, it cannot be used to transport information. The information is contained in the square of the probability amplitude (upon interference of
amplitudes took place) which gives the probability to ﬁnd the particle at xfin an interval dx and at time tfin an interval dt. In other words, as
probability amplitudes are not physical entities, they cannot be used to send physical signals. The measured probability does not provide any hint on
the structure of the interference pattern. Different sets of probability amplitudes represent different interference pictures, but if the same probability
distribution results, they describe the same physical reality. Hence, there is no possibility to distinguish between these different sets of probability
amplitudes. In other words, a changing interference pattern cannot be detected so long the resulting probability distribution remains invariant. In a
similar way, the exchange of two identical particles in a physical system cannot be observed, which may be realized with superluminal speed, but
this process is not accompanied by any information transport.
at 90% conﬁdence level. On 18 May 2017 XENON1T,
the successor experiment, reduced this limit (for a spin-
independent WIMP-nucleon elastic scattering cross sec-
tion) to 7.7×10−51 m2for a 35 GeV/c2WIMP mass at
90% conﬁdence level.20 Hence, together with recent AT-
LAS and CMS data (Sec. 3), evidence is mounting that
WIMPs do not exist.
This futile search also questions the hypothesis of a
hot Big Bang (Sec. 6). If the Universe was ﬁlled with a
hot plasma immediately after the Big Bang the relativistic
WIMPs would have collided with each other and ordinary
particles would have been produced by WIMP annihila-
tion. This process would have slowed with the cooling of
the expanding universe. Given the strength of the weak
force, it can be calculated that today there must be ﬁve
times more cold relic WIMPs (DM) than ordinary parti-
cles. Not a single WIMP was ever detected. Hence, the
hot Big Bang picture may not be correct.
In addition, many supersymmetry theories predict
their lightest superpartner to be stable in form of a neutral,
weakly interacting particle – WIMP. This ghostly particle
is searched for by the LHC – as will be discussed in Sec.
3 – so far in vain.
According to the ideas of EHT, to be discussed below,
the concept of a Big Bang may have to be replaced by a
Quantized Bang (Sec. 6.3). In addition, these nil ex-
perimental results also speak against two key concepts in
physics, namely supersymmetry and extra spatial dimen-
sions, the cornerstones in all advanced particle theories.
Gravity and electromagnetism are the two-long range
interactions known in current physics. In 1911 Heike
Kamerlingh Onnes in Leiden reported on the phenomenon
of superconductivity in mercury below a critical tem-
Cshowing that the electrical resistance of a
conducting material effectively could be zero. In anal-
ogy, the EHT model predicts the existence of a similar
effect for gravity, for which the name hypercomplex-
gravity was coined. That, however, has to be outside GR
which is based on the curvature of spacetime. By con-
trast, hypercomplex-gravity ﬁelds arise from the interac-
tion with electromagnetic ﬁelds in spacetime through (ad-
ditional) gravity mediator bosons of spin 1, and not by
acting on spacetime. These ﬁelds represent a new, second
type of gravitational interaction that is of the same type
as the electromagnetic, weak nuclear force, and the strong
nuclear force. In that sense it would be correct to state the
existence of four fundamental interactions, whereas GR is
to be considered as the interaction of the spacetime lat-
tice with any kind of matter, i.e., affecting the motion of
all physical entities that carry energy. Einsteinian grav-
itation does not exhibit the classical property of being a
force mediated by bosons. Of course, a spin 2 boson,
termed the graviton, can be postulated in order to comply
with the general picture of physical force, but it is more
a mathematical convenience, and not a physical necessity.
Moreover, such a boson was never observed. Einstein’s
equivalence principle predicts the equality of inertial mass
and gravitational mass, but it is not clear that this idea
holds at the quantum level and the latest experiment, July
2018, did not ﬁnd any hint for the existence of a graviton
particle. It also seems that a gravitational Casimir effect
does not exist. Quantum theory allows the superposition
of states, which means that a massive particle may be in
two different states at the same time and because different
states do have different energy levels they necessarily (re-
member Einstein’s E=mc2) represent different masses.
Then the total mass gets also fuzzy and thus may be in
conﬂict with Einstein’s equivalence principle (so far no
deviation has been found). It seems that if a particle obeys
Heisenberg’s uncertainty principle (meaning that the sys-
tem has two non-commuting observables) it necessarily
may be in conﬂict with Einstein’s equivalence principle
(see the recent paper by Zych and Brukner14). How-
ever, a lively discussion on the quantum nature of grav-
ity already took place in 1957 (see the ﬁnal chapter in16),
pp. 260, including the eminent physicists R. P. Feynman,
Bondi, Rosenfeld, Bargmann, de Witt, Belinfante, and J.
Wheeler. This question has not been decided upon, as
the recent paper by Marletto and Vedral15 shows. They
suggest the gravitational ﬁeld be probed by two masses,
extending a proposal by R.P. Feynman of 1957 discussed
in.16 The ﬁrst mass, being in a superposition of two loca-
tions, becomes entangled with the ﬁeld (similar to dipho-
ton entanglement), while the second mass, also in a super-
position, is used to report the entanglement. First, if two
quantum systems (i.e., two masses) can be spatially super-
posed and become entangled through the interaction of a
gravitational ﬁeld, then that gravitational ﬁeld itself must
be quantum capable of possessing two non-commuting
This prediction allowed the pair to propose tests that
would tease out the quantum behavior of gravitational ac-
celeration. So far, the major difference between the two
classical long range forces is that electromagnetic ﬁelds
can be generated in the laboratory, while gravitational
ﬁelds (so long as gravity is considered to be of geometric
nature) cannot be engineered. By contrast, hypercomplex-
gravity ﬁelds should be similar in strength to electromag-
netic ﬁelds for they do not originate from geometry.
According to GR gravitational ﬁelds can only be pro-
duced by large static or moving masses, e.g., planets or
stars. In Einstein’s time (1915) EM was the only other
known interaction and Einstein devoted the rest of his ca-
reer trying to unify these two forces, but also searched for
a direct interaction between electromagnetism and gravity
as Faraday had already surmised. The gravitomagnetic
ﬁelds predicted by GR are far too small to be of techni-
cal interest. This situation will not change because recent
observations and simulations by Parsa et al.17 are con-
ﬁrming GR also in the nonlinear range. In other words,
ten biography on the life and scientiﬁc work of Burkhard
Heim was published by von Ludwiger (in German).107 A
few years later, the need for advanced space propulsion
methods based on ﬁeld propulsion was discussed again in
the books by Seifert, 1959108 and Corliss, 1960111 as well
as by Samaras.112 In the ﬁfties and sixties of the last cen-
tury, ﬁeld propulsion, i.e., space propulsion without pro-
pellant, was a domain of intense research, but, as is well
known, this once active ﬁeld did not produce any space
propulsion technology, and in the following decades re-
search in this area completely subsided. At that time there
existed an active scientiﬁc program aimed beyond the ever
attractive force of Newtonian gravity.
The ﬁeld saw a revival with the NASA break-
through physics propulsion program (1996-2001)113 ,
which ended without having generated usable practical or
theoretical consequences concerning novel space propul-
sion methods. It became clear from this project that en-
gineering reﬁnement of existing technology as well as
known physical laws were not suitable in providing break-
through propulsion. A review of the state of the art as of
2003 was then given by J. E. Allen.114 In his ﬁnal critique,
Sec. 5, Allen concludes that the necessary breakthrough
has not been achieved.
The quest for propellantless propulsion has a long
history, meaning propulsion systems that rely upon the
exchange of momentum and energy with their reference
frame through the use of physically generated forces. In
particular, in the 1950’s in the United States, a compre-
hensive research program on gravity control propulsion
was set up in aerospace industry as well as 14 universities.
First, three concepts are discussed that recently have been
investigated as a physical basis for breakthrough propul-
sion. It will be shown that the EM drive, the Woodward
propulsion idea, based on Mach’s principle, which states
that the acceleration of massive particles can only be mea-
sured relative to other matter in the UnIverse, i.e., its in-
ertia must depend on the distribution of the other matter
in the Universe as well as any concept based on Kaluza-
Klein theory are physically unfeasible. Any breakthrough
in propulsion or energy generation, in order to become a
real game changer, needs to be functioning without fuel.
This insight is not new, and was already discussed in the
book on space propulsion by Corliss, 1960,111 termed
ﬁeld propulsion, and was actively researched in indus-
try and academia at that time. Rocket propulsion cannot
be abandoned at present, because it is currently the only
technology available that is providing sufﬁcient thrust to
deliver material to low earth orbit (LEO) or communi-
cation satellites to geostationary orbit. Second, if we
are serious about spaceﬂight, a crash propulsion research
program based on fundamental physics should be started
forming a task force dedicated to the aim of studying
whether there exists novel gravitational physics that could
lead to the development of propellantless propulsion.
This physical principle was already envisioned by W.
Corliss and other physicists half a century ago. A novel
physical principle for spaceﬂight as well as energy gen-
eration is needed ﬁrst, then everything else will fall into
place, i.e., the proper technology will follow from this
principle. The technology must be feasible, whereas
wormholes and spacetime warping may be unrealistic or
impossible and antimatter for spaceﬂight is technologi-
cally unobtainable in the foreseeable future, but it should
be accepted that, at least in the beginning, the science of
any novel propulsion system, necessarily, will have to be
speculative, for it cannot be based on current physics.
What could this new physical principle be? Obvi-
ously, it has to do with both gravitation and spacetime.
Planetary gravitation needs to be overcome during launch,
and once in space, a vehicle is moving through a medium
called spacetime. Spacetime is considered a dynamical
physical ﬁeld, because it is inseparably associated with
the all pervading ﬁeld of dark energy, and thus assumed
to carry both energy (in form of information) and momen-
tum. Momentum exchange between the space vehicle and
spacetime needs to take place, which is assumed to re-
sult in additional spacetime dynamics, that is, contraction
or expansion. Instead of interacting with its fuel, the
spacecraft is interacting with the surrounding spacetime.
How? Through the generation of gravity-like (acceler-
ation) ﬁelds outside GR by the mechanism of (delayed)
The only approach that may have the potential as
breakthrough may be the generation of gravity-like ﬁelds
that are outside GR. In order to overcome the enormous
technical challenges posed on conventional propulsion
systems by the drag of gravity, it becomes obvious that
only propulsion without propellant can solve this prob-
lem. Field propulsion, aptly named by W. R. Corliss in
his book Propulsion Systems for Space Flight Space, Aca-
demic Press, 1960, was then an active topic of research,
however, without delivering any practical results. Space
propulsion is still dealing with the technologies (and haz-
ards) developed in the 50s and 60s of the last century,
and the vision portrayed by Wernher von Braun in his fa-
mous article in Collier’s magazine in 1952, entitled Man
on the Moon, did not become a reality. A manned Mars
mission, despite all the claims made by the various Mars
projects — as the ﬁrst author, while working at the Euro-
pean Space Agency, knows from ﬁrst hand experience —
will not take place any time soon, unless a breakthrough
in propulsion physics can be achieved.
Recently several authors published propulsion con-
cepts on Weber’s electrodynamics but Weber’s electrody-
namics was developed before Maxwell and does not seem
to provide any additional physics.
There are recent articles citing Weber’s EM formula-
tion as if something new could be obtained from it. First,
Weber was before Einstein, and it is not clear whether or
not his formulation is even Lorentz invariant.
Maxwell’s description of EM has accounted for all ob-
served EM phenomena since its inception in 1864. More-
over, and this is most important, Maxwell’s theory is the
foundation for QED (quantum electrodynamics) that has
been conﬁrmed to extreme experimental accuracy.
Even the slightest misconception in Maxwell’s EM
would have been detected and corrected. Nothing like that
was ever observed. Even in the latest LHC data taken at
13 TeV the tiniest deviation would have been seen. So,
even if Weber were also correct (which is doubtful, but
unknown) nothing can be gained from Weber’s theory that
cannot be explained with Maxwell’s theory that is much
easier to handle, and, as we know, is Lorentz invariant, it
remains correct at relativistic speed. Any research in this
direction will not lead to any new results.
Extreme gravitomagnetic ﬁelds, termed hypercomplex-
gravity (see below) may be generated by the interaction
between gravity and electrodynamics (in the so-called
Heim experiment), seem to be the only physically realis-
tic chance for propellantless propulsion. Extreme grav-
itomagnetic (or hxpercomplex) ﬁelds might have been
measured by M. Tajmar as was analyzed in12 as well as in
several other papers. However, there is no smoking gun
proving their existence.
There is no way for hypercomplex gravitational ﬁelds
to exist within Einstein’s GR, which means that com-
pletely novel physics concepts have to be introduced as
discussed in this article.
7.1. Physically Impossible Propulsion Concepts
Unphysical EM Drive
Recently the EmDrive, see, http://www.newscientist.com
/data/images/archive/2568/25681402.jpg, that has been
around since 1999, was hailed as the Engine That Might
Break Physical Laws by generating an asymmetric force
owing to different EM radiation pressures on the side
walls of a closed cylindrical resonator. But this is wish-
ful thinking.109 By squeezing a closed Coke can on one
side and trapping electromagnetic radiation inside, the can
is supposed to move in the direction of the smaller cross
section. This will never happen. This is a pure electro-
magnetic phenomenon and all descriptions citing an in-
teraction with the vacuum are equally false. As recent ex-
periments have shown (see the above reference) the vac-
uum is extremely stable and extracting energy from the
vacuum, i.e., bringing the vacuum to a lower energy state
requires extreme amounts of energy. No simple EM phe-
nomenon can cause such an interaction with the vacuum.
Therefore, regardless who has measured what, these are
artifacts. According to W. Pauli: This is not right. It is
not even wrong.
Microwave ovens don’t ﬂy. There is absolutely no ex-
perimental evidence for a varying speed of light, c, within
the truncated cone cavity, nor does cchange outside the
cavity. It is mentioned in the New Scientist article that
1 kW of power is needed to generate 1.2 mN of thrust.
Compare this to the Saturn V that generated 33,000 kN of
thrust (5 F-1 engines each at 6.7 MN thrust). Using an EM
drive would amount to generating a power of 2.75 ×1010
kW, that is, one would need about 30,000 large nuclear
power plants to produce this amount of thrust. Apart from
the fact that this kind of energy source would destroy any
material device, it would be the most inefﬁcient way to
ﬂy. It also might be a little heavy, because nuclear power
plants are not lightweight. There is no reasonable phys-
ical principle backing the EM drive, not even an uncon-
ventional theoretical idea.
Using de Broglie’s (1928 and later D. Bohm’s 1952 )
interpretation of QM, does not result in any new physics.
We are talking about a novel (at that time) interpretation
of QM different from (now outdated) Bohr’s idea. Never
did Bohm postulate that the virtual particles of the vac-
uum can affect his necessary non-local (i.e., faster than
light) pilot wave!
An interaction with dark matter particles, as men-
tioned in the article, with the microwaves inside is not
possible either. Dark matter, as its name is telling us, is
not charged and electromagnetically inactive, otherwise it
would have been detected. DM is not subject to electro-
magnetic interaction. There is no physical basis for the
EM drive, which is based on a solely conventional EM
phenomenon. Otherwise, just squeeze a coke can on one
side and get some microwave radiation inside, and the can
should start moving in the direction of the smaller surface.
Regardless of what has been measured, this cannot be real
Mach’s Principle Retired
The Woodward drive is also discussed in,109, 110 being
developed since the 1990s, and it is equally physically un-
feasible. It is based on Mach’s principle which, as is now
known, is physically incorrect.
First, Mach’s principle is not part of General Relativ-
ity. With the existence of the Higgs boson conﬁrmed by
the LHC (postulated 1964, measured July 2012 at CERN)
particle mass comes from the interaction with the scalar
Higgs ﬁeld and not from the interaction with the other
masses in the Universe as postulated by E. Mach in the
19th century. Mach’s principle is also in conﬂict with Ein-
stein’s GR as the rest mass of a particle is a relativistic
invariant that is an intrinsic property and does not depend
on the distribution of the surrounding masses in the Cos-
mos as claimed by E. Mach. His idea is not based on
physical facts but more on philosophy.
Moreover, if the inertial mass of a proton were af-
fected by mass distributions on the cosmological scale,
then there must be an anisotropy in the inertia of every
proton on Earth! Because of the mass distribution in our
own galaxy any proton would be accelerated towards the
galactic center and would have a mass different from a
proton subject to an acceleration in the opposite direction,
simply because the mass of the galaxy is concentrated in
the galactic center.
This could be measured very accurately by the Moess-
bauer effect and NMR technique (frequency) but such an
effect was never observed.
For any experiment performed on the rotating Earth,
the proton mass should depend on direction – according
to Mach. This is clearly not the case! With the existence
of the Higgs boson, Mach’s principle became an outdated
idea and is a relic of the 19th century mechanistic world-
view. Hence, there is no physical principle for the Wood-
ward drive. Inertia is an intrinsic property of matter and is
not related to other masses. The Higgs boson was found,
and it is the source giving matter to otherwise massless
particles. As we know, Einstein’s Weak Equivalence Prin-
ciple (WEP) has proved to be correct to a very high de-
gree, and thus it is correct to state that mI=mGE.
Kaluza-Klein theory of ﬁve dimensions is incorrect.
This theory is physically wrong, because it requires
Fµν Fµν =0,and thus leads to the wrong Lagrangian for
EM. That is, any ﬁve-dimensional theory (four spatial di-
mensions) is necessarily incompatible with EM.
Prediction is very difﬁcult,
especially if it is about the fu-
8. Summary of Physical Concepts of EHT
Finally, it seems appropriate to summarize the novel
physical ideas, collected under the name EHT and pre-
sented in the previous sections to demonstrate their drastic
physical implications in extending both the SM of particle
physics and cosmology. The inﬂux of recent experiments
(Sec. 5.2) played a major role in the formulation of these
principles. In particular, EHT requires giving up the cher-
ished concept of extra space dimensions replacing it by
introducing extra systems of numbers. As a direct result,
see Eq. 5.2, two novel types of matter were introduced,
which are termed negative matter (dark matter) and hyper-
complex matter (virtual particles) that are not described
in both SR and GR. Hence, physical phenomena that are
based on the presence of this type of matter, that is, ﬁelds,
may not be subject to the constraints imposed by these
At the core root of these extensions is the set of foun-
dational physical principles (Sec. 4) that have dramatic
consequences for both cosmology and particle physics 32.
The concept of duality proved to be of overriding im-
portance. It is at the foundation for the existence of the
Cosmos, because the two fundamental energy concepts of
EHT, namely the energy of information due to Szilàrd, as
expressed by Eq. 4.2, and the energy of mass, that is,
Einstein’s famous equation E=mc2, are considered as a
physical realization of this principle. These two energy
forms can be converted into each other. Information en-
ergy of the expanding spacetime lattice is transformed into
matter energy. That is, the potential energy of the evolv-
ing spacetime lattice transforms into dark energy (DE),
the precursor of matter.
Hence, string theory and supersymmetry as postulated
under EHT are rendered untenable and also Grand Uniﬁ-
cation Theories (GUT) will not be feasible in their cur-
rently foreseen form. Nevertheless, in cosmology, the
concept of the Big Bang seems to have to be replaced by
aQuantized Bang (see below). Also, the GUT era in the
course of cosmic evolution appears to be infeasible.EHT
also makes novel predictions. Extreme gravitational ﬁelds
outside GR should exist, dubbed hypercomplex gravita-
tional ﬁelds, a fourth family of leptons and quarks is pre-
dicted, and the existence of dark energy and dark matter
are explained in the context of EHT. Furthermore, both
time, t, as well as the speed of light in vacuum, c, get pro-
moted from real to complex that requires an extension of
the concept of Einstein’s spacetime. Finally, the concept
of matter is promoted from real to hypercomplex matter.
1. The formulation of EHT is based on the set of fun-
damental physical principles that cannot be proved,
but are formulated according to generally accepted
physical principles in accordance with the known
experimental results (Sec. 4). These principles have
far reaching consequences for both the SM of parti-
cle physics and cosmology.
2. The complete uniﬁcation of physical interactions is
not possible according to the principle of duality.
3. The concept of extra number systems replaces the
idea of extra space dimensions. Since the 1970s,
32Further physical justiﬁcation of these principles is not possible and necessarily leads into the realm of metaphysics. This does not mean that
arguments from metaphysics are to be rejected, but simply states that these rules are outside of physics. Another major example that leads also
outside of physics are the numerical values of the physical coupling constants that, at least in EHT, are based on number theory. It should be clearly
stated that the roots of the Cosmos are to be sought outside of physics and thus cannot be explained. Hence, the question which process may be
responsible for setting up the proper blueprints governing the evolution of the Cosmos cannot be decided by physics. Science in general and physics
in particular can only take the observed facts as a given and try to construct adequate models, but are incapable of providing explanations for any
underlying objective. These restrictions and the ensuing contradictions were clearly described in B. Heim’s paper entitled Welt der Weltbilder.118
Figure 10. The group structure obtained from extra number systems in the form of hypercomplex numbers leads to additional groups that results in a total of
15 gluons and 6 gravitational bosons as well as three photons.
string theory and supersymmetry have been con-
tradicting all experiments of particle and atomic
physics that were speciﬁcally conceived to prove
their existence. In particular, the continuously
improved measurements of the range of validity
of Newton’s gravitational law down to the atomic
scale has rendered the concept of extra space di-
mensions untenable (Fig. 6). The paradigm shift
of EHT therefore replaces extra dimensions by ex-
tra number systems that give rise to the concept
of hypercomplex masses. A direct physical con-
sequence is the existence of extreme gravitomag-
netic ﬁelds, that are outside GR. These novel types
of mass are also considered to be responsible for
the existence of a fourth family family of leptons
and quarks which are instrumental in the explana-
tion for dark matter.
4. The fundamental mathematical group is O(32,H)
that is broken down into four symmetry groups
5. The unphysical concept of the Big Bang is replaced
by the Quantized Bang. The evolution of the uni-
verse originates from generation of the ﬁrst discrete
elemental surface by quantum ﬂuctuations, mark-
ing the transition from nonexistence to existence.
The next quantum ﬂuctuation can cause the ele-
mental surface to disappear or it may create a sec-
ond elemental surface that interacts with the ﬁrst
one due to the spin of these two metrons. This re-
leases a quantum of information energy that is con-
verted into a quantum of dark energy that immedi-
ately will act to expand the spacetime comprising
two metrons. Therefore, the probability for a third
metron to be generated is higher than the probabil-
ity for the second metron to disappear. Thus the
increase in the number of space atoms will be ex-
ponential, driven by the generated dark energy. A
highly simpliﬁed model of this inﬂation model is
given in Chap. 9 in .12 The spacetime lattice goes
quickly from discrete to continuous, allowing the
use of the Einstein ﬁeld equations in conjunction
with dark energy (responsible for inﬂation). Even-
tually, photons are generated from dark energy –
ending inﬂation – and mediate the force that de-
ﬁnes electric charge which are also the source for
ordinary and dark matter.
6. Another basic modiﬁcation concerns the notion of
spacetime as formulated by Einstein. There is a
dual spacetime, dS(3,1)that contains dark matter
making dark matter principally unobservable in our
spacetime. However, the gravitational impact of
DM can be observed.
7. As a result of the four O(8,H)groups there ex-
ist six gravitational bosons. Three of these bosons
νGE,νgp ,νqare for the cosmological gravitational
ﬁelds that are of purely geometric nature, and can-
not be uniﬁed with the three other forces.
8. The three particles representing the extreme gravit-
omagnetic ﬁeld are believed to result from an inter-
action with electromagnetism, and are spin 1 ﬁelds.
This type of gravitation, termed , is thought to be
uniﬁable with the strong interaction.
9. DM seems to be absent within galaxies but is con-
centrated in halos. Thus, the result of the MOND
formula (which does give the correct acceleration)
cannot be explained by DM as DM does not exist
within galaxies. A discussion was presented to ob-
tain the MOND formula based on the presence of
two types of DE particles, attractive and repulsive,
i.e., by polarization through the higher mass density
inside galaxies that is 107times higher compared to
10. The extreme gravitomagnetic ﬁelds may be utilized
as a means for space propulsion without propellant.
The key seems to be a speciﬁc material composition
(two or more metallic components) that might work
at ambient temperature.
The basis for the novel physics presented is a collec-
tion of foundational physical principles which individu-
ally are generally accepted and proved by experience and
experiment. The application of these principles results
in major implications for cosmology, including a closed
topology of the universe, modifying the cosmic genesis by
replacing the hot big bang with a quantized bang and ex-
plaining the nature of dark energy and its role in inﬂation.
Furthermore, these principles predict the non-existence of
singularities (i.e., wormholes are not considered feasible
physical objects). In addition, the fundamental principles
are employed to discuss the MOND hypothesis and to give
a derivation of the MOND formula but without giving up
on Newton’s gravitational law.
An extended group structure for the description of el-
ementary particles is produced by introducing extra sys-
tems of numbers – quaternions (hypercomplex numbers,
non- commutative) Hand octonions (non- associative)
O. The extra number systems also account for addi-
tional types of matter (negative, −mand hypercomplex
im,j m ,κm), replacing the extra space dimensions of
These novel types of matter are instrumental because
the existence of a fourth family of particles of negative
mass is predicted representing dark matter.
It is postulated that dark matter particles are located
in dual de Sitter spacetime DdS1,3but their gravitational
interaction is observed in normal spacetime. Dd S1,3
is marked by an imaginary time component, i t , but
shares the spatial components of our spacetime manifold
dS1,3. Hence, dark matter particles cannot be detected
in our spacetime. The existence of (virtual) hypercom-
plex masses may explain the measured discrepancies of
the proton diameter and the contradiction in the measured
lifetimes of the neutron.
The group structure using the ﬁeld of hypercom-
plex numbers gives rise to twelve elementary charges
and six gravitational bosons with three gravitational con-
stants Gp,Ggp ,Gq(see text). The six gravitational bosons
comprise two groups, the ﬁrst three are the cosmologi-
cal bosons νGE(the graviton, spin 2 particle from Ein-
stein’s theory of gravity), νgp (spin 1 ), νq(spin 0) that
might mediate the forces for the cosmological ﬁelds, un-
less they are of pure geometric origin. In addition, ac-
cording to EHT, an interaction between gravity and elec-
tromagnetism should occur, mediated by three additional
gravitational bosons ˜
νgp (spin 1 ), ˜
νq(spin 0), that
are produced either at low temperatures in the laboratory
(symmetry breaking) or at high temperatures in the vicin-
ity of quasars. In both cases extreme gravitomagnetic (or
hypercomplex) ﬁelds Bgp should have been generated that
may be up to 18-20 orders of magnitude larger than the
gravitomagnetic ﬁelds of GR. If their existence can be
conﬁrmed they are clearly outside general relativity. The
reported change in the ﬁne structure constant αfseen in
the vicinity of quasars may be another hint of the pres-
ence of these extreme gravitomagnetic ﬁelds which are
believed to modify the permeability of free space, µ0. The
extreme gravitomagnetic ﬁelds may be produced by those
rotating black holes in the form of quasars. New propul-
sion and energy generation technology might follow from
extreme gravitomagnetic ﬁelds that are owing their exis-
tence to the conversion of photons γinto gravitophotons
νgp reﬂecting the particle nature of the resulting extreme
Any sufﬁciently advanced tech-
nology is indistinguishable from
Arthur C. Clarke
9. Physics, Cosmology, and Technology
One of the key features of EHT lies in the formula-
tion of the underlying physical principles employed by
Nature, because everything follows once these principles
have been set up. Einstein himself considered this the very
ﬁrst step before any mathematical formulation of a theory
should take place.
If we are wrong at this step then there is no hope in
setting up a comprehensive theory of both space and mat-
ter. An incorrect theory means that the theory has to be
adjusted – creating more epicycles.
As of winter 2018, the LHC data have provided zero
evidence for any of the concepts employed in advanced
physical theories that have ruled particle physics for more
than four decades, namely, supersymmetry, extra space di-
mensions, and GUT (Grand Uniﬁcation Theory). This is
a strong sign that Nature is using a different set of rules.
Hence, in this article novel ideas were presented in order
to resolve the long standing deadlock.
The new concepts of hypercomplex numbers, dual
spacetime, and elemental surfaces for spacetime neces-
sarily lead to different physics in the form of negative
and hypercomplex mass as well as different groups
in physics based on the ﬁeld of hypercomplex numbers.
For instance, there should be a fourth family of particles,
however accounting for DM. In addition, the existence of
hypercomplex masses is postulated (virtual particles that
are supposed to be generated in the interaction between
electromagnetism and gravitation) that give rise to grav-
ity bosons of spin 1, thus producing the much stronger
ﬁelds, as discussed above. In other words, there should
exist a second type of gravity outside GR. By contrast,
the cosmological gravity ﬁelds are aptly described by Ein-
stein’s GR. Moreover, the Big Bang hypothesis should be
replaced by the Quantized Bang idea, based on the exis-
tence of the metron (elemental surface). DM is composed
of negative mass and residing in dual spacetime while
only its gravitational interaction can be observed in our
spacetime. That is, DM particles cannot be detected in
our spacetime, nor can they be produced by accelerators.
As there are no singularities in the Cosmos, the geometry
of the Universe must be closed, and eventually expansion
(symmetry breaking) is converted into contraction. The
baryonic asymmetry is attributed to cosmic motion.
The overriding principle in physics as discussed here
is the principle of duality. This may sound vague but,
as was shown, duality imposes severe constraints both on
any physical theory of matter and cosmology. The long
sought grand uniﬁcation of all physical laws, even at ex-
treme energies, does not seem to be possible.
For instance, duality requires that from the very ﬁrst
instant of the Cosmos both spacetime (ﬁrst as a lattice,
later on in the evolution as a manifold) and dark energy
are formed at the same time. Together with the quantiza-
tion principle for elemental surfaces, it leads to a Quan-
tized Bang strictly obeying energy conservation (apart
from quantum ﬂuctuations). In other words, there was
no Big Bang violating the principle of energy conserva-
tion. Based on the existence of the metron the Big Bang
hypothesis should be replaced by the Quantized Bang.
The Cosmos seems to be governed by two energy prin-
ciples that are dual to each other: Szilard’s energy prin-
ciple that measures the energy resulting from informa-
tion (or organization), and Einstein’s energy principle of
matter (or radiation). In the evolution (including inﬂa-
tion) of the Universe the information energy (potential en-
ergy, negative) of the spacetime lattice (sugar cube crystal
model) is converted into the precursor of matter energy,
i.e., dark energy (positive energy density). This quantized
bang cosmology accounts for the existence of dark energy
as well as the subsequent inﬂation period.
There must be a symmetry breaking mechanism that
converts DE into DM and OM (or NOM), reducing the
amount of DE and putting an end to inﬂation. As there
are no singularities in the Cosmos, the geometry of the
Universe must be closed, and eventually expansion (by
symmetry breaking) is converted into contraction. The
baryonic asymmetry is attributed to cosmic motion.
The other key idea is the extension of the isospin space
concept to an 8-dimensional gauge space H8, Heim space,
with subspace structure 1-3-2-2, from which the overall
group structure for matter and spacetime is derived. There
are no extra space dimensions (no strings). Instead extra
number systems, i.e., Nature utilizes the ﬁeld of hyper-
complex numbers, which extends the idea of matter and
antimatter. This in turn leads to the idea of extreme grav-
itomagnetic ﬁelds mediated by virtual particles of hyper-
complex mass that act like a catalyzer, i.e., they trigger the
reaction but are not visible in the initial and ﬁnal states of
The duality principle further impacts matter and
spacetime. These are two different quantities that cannot
be uniﬁed, instead they represent two sides of the same
In this regard, there is no way to unify all physical
interactions. Einstein’s cosmological ﬁelds may be rep-
resented by three mediator gravity bosons, but are the re-
sult of spacetime geometry (time dependent curvature is
equivalent to the propagation of gravity waves). It is not
at all clear that gravitational spin 2 bosons really exist that
can be measured like photons. They may, however, exist
as auxiliary physical entities.
In accordance with the duality principle, matter is dif-
ferent from geometry and cannot be expressed by geome-
try. This means the geometrization of physics as foreseen
by Wheeler et al. may not be feasible. Furthermore, the
Einstein ﬁeld equations cannot describe an equality be-
tween matter and geometry, but express an equivalence
only. Rather, matter and spacetime inﬂuence each other
and therefore can be expressed only as an equivalence. As
a result, the Planck length may not represent a meaningful
length scale for pure geometry phenomena. The results
of the ESA Integral satellite indicate a length scale much
smaller than the Planck length for the grid spacing of the
spacetime lattice. Hence, Planck’s constant ¯
occur in an expression for this grid spacing. Instead, the
Schwarzschild radius of the proton (18 orders of magni-
tude smaller than the Planck length) may be the correct
measure. It should be noted that presently we presume
there is no gravitational interaction (Einstein) among lep-
tons, only hadron-hadron and hadron-lepton, in addition
to the novel gravitational interaction, with the dark en-
ergy ﬁeld itself, manifested by the expansion of space-
time (which is too small to be measured in propellantless
The other idea is that a dual spacetime exists. In our
spacetime matter is positive, while in dual spacetime mat-
ter is negative. Both spacetimes share the same three spa-
tial coordinates, but time is real in our spacetime while it
is imaginary in dual spacetime. The same holds for the
speed of light.
However, the extreme gravitomagnetic or ﬁelds, group
SU(2), are mediated by three gravity bosons that are like
other mediator bosons from particle physics, and thus are
completely different from the Einstein cosmological grav-
Moreover, because of duality the weak and EM forces
can be uniﬁed and the strong and the force may be uniﬁed.
The uniﬁcation of the two remaining interactions should
not be possible. This said, there could not have been a
GUT era in the early cosmic evolution when gravity be-
came distinct from the other three forces, that still were
united at the GUT energy.
Coupling constants are outside physics and are (in
EHT) based on number theory, meaning there could be a
relationship between prime numbers and the structure of
irreducible groups in physics. However, we do not have
a really convincing derivation of these numbers, a lot of
guesswork and speculation is involved.
The above ideas have major ramiﬁcations for the two
standard models of particle physics and cosmology, and
require major extensions of both models. In particular,
there are no strings, and in the SM of cosmology there is
no Big Bang. Dark matter cannot be found in our space-
time, instead it resides in dual space, because its mass is
negative. This straightforwardly leads to a forth family of
particles and also requires 15 gluons. The largest modiﬁ-
cation concerning gravity are ﬁelds that are both attractive
and repulsive and interact with the other three interactions
as well as with the dark energy ﬁeld. Moreover, the uni-
verse is closed and at some time in the future expansion
should change into contraction. In addition, the MOND
formula is correct, but Newton’s law is valid down to the
atomic scale. The origin of DE and DM are explainable
from the novel ideas of EHT. The predictions concern-
ing the generation of extreme gravitomagnetic or ﬁelds
should be fairly easy to test by setting up proper experi-
This, in a nutshell is, how we see the framework of
EHT, but there remain a lot of details to be ﬁlled in.
Needless to say, there are still a lot of riddles and many
other topics exist to be explored, such as the principle of
structure formation and organization. The Universe is def-
initely not the result of so called-self organization or acci-
dental processes, but there seems to be a governing mech-
anism that is directing all physical processes. Hence, the
entelechial and aeonic dimensions in internal Heim space
This article is dedicated to the eminent Andreas Resch,
P Dr. Dr., C.Ss.R. Professor and Director at the Insti-
tut für Grenzgebiete der Wissenschaft, Innsbruck, Austria
to acknowledge his scientiﬁc work, Imago Mundi, whose
prime subject was and is the creation of a consistent Welt-
bild, 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 em-
inent scholars, though from very different backgrounds,
have dedicated their works to the quest for ultimate real-
ity, thus elucidating the underlying reality of the Cosmos.
The authors are most grateful to Prof. Greg Daigle,
former adjunct professor at the Univ. of Minnesota,
U.S.A., for numerous e-mail discussions and literature
hints as well as his relentless efforts to improve the style,
clarity, and contents of this paper.
The TIKZ programming efforts of Dr. H.-G. Paap,
HPCC Regensburg in preparing the ﬁgures are greatly ap-
preciated as well as the discussions with my colleague
(ﬁrst author), Prof. Dr. T. Waldeer, Ostfalia University.
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