### APPENDIX 1. CONSEQUENCES OF *h*‑SPACE THEORY BEYOND MODERN PHYSICS

**TETRANEUTRON, DIPROTON, DINEUTRON, MULTI-MUONS**

In the suggested theory, protons and neutrons are seen to be complexes of electrons and positrons. Unstable complexes having even more electrons and positrons are also possible, such as the tetraneutron (*Sherrill, B.M. and Bertulani, C.A. 2004 Proton-tetraneutron elastic scattering Phys. Rev. C 69, 027601*), the diproton (*Raciti, G. et al., 2008 Experimental Evidence of 2He Decay from 18Ne Excited States Phys. Rev. Lett. 100, 195203–06*) and the dineutron (*Spyrou, A. et al., 2012 First Observation of Ground State Dineutron Decay: 16Be Phys. Rev. Lett. 108: 102501. doi:10.1103/PhysRevLett.108.102501*) (see Fig. 14a). According to modern theoretical concepts, these complexes do not exist. Muons, in the suggested theory, have the same composition as protons, but in contrast to the proton, an unstable spatial configuration. Because of this, we can also consider as real the multi-muons, as unstable complexes, clusters of electrons and positrons. Multi-muons have been detected in collisions of protons and antiprotons (*CDF Collaboration 2008 Study of multi-muon events produced in p-pbar collisions at sqrt(s)=1.96 TeV arXiv:0810.5357*). Another unstable cluster can be a complex of three protons shown in figure 13a.

**VARIABILITY OF CONSTANTS**

In the proposed theory, the speed of light and the “Planck constant” are both constants. The charge of the electron corresponds to the density of n=0-objects(I) *ρ _{0}*and, accordingly, decreases with time. This reduction in charge can explain the results obtained by astronomer John K. Webb, who in 1999, discovered that light from a distant quasar 12billion light years, is absorbed by metal ions in interstellar clouds, but the absorbed photons do not correspond to the spectra of the metals. Since the interaction of light with matter is determined by the fine-structure constant,

*α*, then it has been suggested that

*α*had a different value. This assumption is not consistent with modern physical concepts. All three constants, which determine the alpha (

*α*=

*e*/

^{2}*hc*) – the electron charge (

*e*), the speed of light (

*c*) and the Planck constant (

*h*), cannot be changed. In the proposed theory, however, the electron charge is not constant. Accordingly, the alpha should decrease with time, offering an explanation for the observed change in the absorption/emission spectrum of metals.

**BOUNDARY OF GRAVITY AND KUIPER BELT**

In the proposed theory, the effect of gravity has a boundary that is determined by the density and size of a body. In the suggested theory, it is assumed that the Sun has a maximum density *ρ _{M}* , similar to the density of atomic nuclei. Under these conditions, the density of n=0‑objects(I)

*ρ*is maximal and equal to

_{M }*ρ*,

_{0}*ρ*=

_{M}*ρ*= 10

_{0}^{10}. The boundary of the Sun’s gravity can be calculated, taking into account the linear dimension of the Sun, and is ≈ 10

^{13}m (see “Gravitational attraction”). This is comparable to the distance from the Sun to the Kuiper Belt, ≈ 10

^{13}m.

To assess the limits of gravity of the planets (see “Gravitational attraction”), their density *ρ _{M}* is assumed to be less than that of the Sun. Then, the density of n=0-objects(I)

*ρ*is ≈ 10

_{M }^{6}–10

^{7}. The calculation for the Earth shows that the boundary of its gravitational action is around 10million kilometers.

**ANTI-GRAVITY**

The cause of gravity in the proposed theory is due to the reduction in density of n=0-objects(I) *ρ _{0}*, or, more precisely, the change in the density of the vacuum

*ρ*, around the body, as a result of the displacement of n=0‑objects(I) by the body. In addition to gravity, a change in the density of n=0-objects(I)

_{M}*ρ*takes place during the generation of magnetic field. It is characterized by the density

_{0}**appearing as the result of electrons/positrons motion. Changes in the magnetic field, i.e. the changes in the density of n=0-objects(I)**

*ρ*_{Δ }**, is associated with changes in the density of n=0‑objects(I)**

*ρ*_{Δ}*ρ*, and therefore should lead to a change in the gravitational attraction, which is associated with the decrease in the density

_{0}*ρ*.

_{0}**COLD FUSION – LOW ENERGY NUCLEAR REACTION (LENR)**

After the report in 1989 by Martin Fleischmann and Stanley Pons, the majority of cold fusion (LENR) experiments were performed by electrolysis of heavy water with a palladium cathode. The results (excess heat, helium generation,nuclear transmutations, neutron and tritium radiation) were inconsistent and contrary to the official current view on the synthesis of helium nuclei from deuteron. In another type of LENR experiment, nickel rods saturated with hydrogen were heated, and an excess heat was reported (*Anomalous Heat Production in Ni-H Systems. 1994 S. Focardi, R. Habel and F. Piantelli, IL NUOVOCIMENTO VOL. 107A, N. 1; Large excess heat production in Ni-H systems. 1998 S. Focardi, V. Gabbani, V. Montalbano, F. Piantelli and S. Veronesi, IL NUOVO CIMENTO VOL. 111A, N. 11*). In 2011, interest in LENR research was bolstered by the public demonstration of the E-cat device, performed by Andrea Rossi. In the E-cat, nickel powder is saturated with hydrogen and heated under high pressure, resulting in a significant excess of heat. The fuel in the E-cat contained additional elements besides the nickel, and according to the patent application, analysis of the fuel after its use in the E-cat showed that it contained a number of different elements, indicating that both nuclear fusion and fission had occurred during operation of the device (*http://www.journal-of-nuclear-physics.com/files/Patent_WO-2009-125444.pdf*). In 2013, a test of an improved design (E-cat HT) confirmed the previously observed thermal effects (*Levi, G., et al., 2013 Indication of anomalous heat energy production in a reactor device arXiv:1305.3913*), and in 2014 another independent test of Rossi’s device was performed (http://www.sifferkoll.se/sifferkoll/wp-content/uploads/2014/10/LuganoReportSubmit.pdf). The investigators detected lithium, aluminum and iron in the initial fuel. The heat excess was again confirmed and it was found out that nickel and lithium in the ash had different isotopic ratios in comparison with the initial fuel. Of particular significance was a decrease in the amount of ^{7}Li, indicating the possibility of its fission.

In the proposed theory, LENR can be explained by the positron-electron composition of nuclei and the Coulomb law at atomic scales. According to the proposed theory:

- in atom, at distances between 10
^{−}^{15}to 10^{−}^{10 }meters, there is no attraction/repulsion of electrons and positrons; - in atom, attraction/repulsion increases from zero at 10
^{−}^{10 }meters to a maximum at 10^{−}^{5 }meters from the nucleus; - in the nucleus there is no strong interaction. Electrons and positrons are held by their attraction and repulsion to each other with a velocity of 10
^{−}^{2 }meters per second.

Thus, in the proposed theory the problem of overcoming the Coulomb repulsion between the nuclei and protons is not relevant for a range of distances from 10^{−}^{15 }to 10^{−}^{10}meters. In the range of distances 10^{−}^{5}–10^{−}^{10 }meters the repulsion exists and decreases from 10^{−}^{5 }meters to 10^{−}^{10 }meters. The same decrease is true for the distance bigger than 10^{−}^{5}meters. In condense matter, in the range of 10^{−}^{5}–10^{−}^{10 }meters, the repulsion between the nuclei and protons can be compensated by an attraction to the electrons placed at the same distance from the nucleus.

The heating of a proton-saturated nickel powder would increase the mobility of electrons and protons. Additionally, the pulsed magnetic field can also accelerate protons and electrons. The protons released from nickel powder can collide with themselves and lithium nuclei (as well as with nickel, aluminum and other elements nuclei). The protons in nickel lattice can collide with themselves, electrons and nickel nuclei. All these can lead to:

- the fission of proton and lithium nuclei (as well as nickel, aluminum and other elements nuclei);
- the fusion reactions generating neutrons and the nuclei not present initially, as the complexes of positrons and electrons.
- fission of nickel nuclei and nuclei of other elements.

The LEN fission reactions should be more effective at the distance range of micrometers since at the distances from 10^{−}^{5}to 10^{−}^{10 }meters the Coulomb repulsion between the nuclei and protons decreases. This implies that nickel powder in size of microns can be favorable for effective LEN reactions. For this distance in space between the nickel particles, the colliding protons and lithium nuclei will have the decreasing Coulomb repulsion from maximum to zero. If the distance between the protons and lithium nuclei is bigger than 10^{−}^{5 }meters, their collisions will face the opposite effect, the increase of the Coulomb repulsion having maximum at 10^{−}^{5 }meters. This makes less probable the collision of the protons and lithium nuclei, followed by their fission, from the distance bigger than 10^{−}^{5 }meters.

All fission reactions will generate heat and nuclear transmutations. The high level of heat production seen in the E-cat is due to the fission of lithium due to the interaction of lithium nuclei with protons, resulting in synthesis of beryllium, ^{8}_{4}Be, followed by the ^{8}_{4}Be fission to two alpha particles. The energy of generated alpha particles can be consumed further by protons, and this will keep the LEN reactions in self sustain mode, without external heating. The low efficiency of the earlier experiments with nickel rods can be explained by a lower rate of protons and nickel nuclei fission in comparison with E-cat having lithium as fuel.

In the proposed theory, nuclear fusion is possible as secondary reactions, but they will not produce the heat excess in LENR devices. The claimed thermonuclear effect of deuterium fusion in the thermonuclear explosion can be interpreted as the lithium fission since lithium (6Li) deuteride fuel was used in this process.

**FORMATION OF FOUR-DIMENSIONAL SPACE**

In the proposed theory, after a while three-dimensional space is predicted to be replaced by four-dimensional space. The important question then is when this can happen. To answer this it is necessary to compare the length of objects of four-dimensional space with the current linear dimension of the universe. Today, the linear size of the universe is estimated at ≈ 10^{26} m. With the creation of four-dimensional space, the length of objects of four-dimensional space, and the total length of the universe in absolute length units is 10^{30}. Since the absolute unit of length is equal to ≈ 10^{−}^{5} m, it follows that the current size of the universe is close to the total length of the beginning of four-dimensional space. Thus, the change from three-dimensional space to four-dimensional space could be very soon. Another estimate of the time of transition can be obtained by assuming the identity of the constant *c *= 1/√*ε _{0}μ_{0 }*and the velocity

*v*. The transition to four-dimensional space, as has been stated above, can happen at a linear size of the universe equal to the length of n=4-object. In this case, the velocity

_{0}ρ_{0}*v*will be reduced to the value equal to the velocity of one-dimensional objects, i.e. to the speed of light. A comparison of the values of the constant

_{0}ρ_{0 }*c*(velocity

*v*) and the speed of light can provide a rough estimation of the transition time. The constant

_{0}ρ_{0}*c*is the inverse square root of the product of the vacuum permeability,

*μ*, and the vacuum permittivity,

_{0}*ε*. In this product, the value of

_{0}*μ*is accurate and does not require the definition from the experiment. On the contrary

_{0 }*ε*is determined from experiment.

_{0 }Changes that will accompany the emergence of four-dimensional space, as noted in the section “Electrostatics”, are the change of electrostatic interaction from an inverse dependence on the square of the distance to the third degree of distance. This will lead to the destruction of atoms, which can be later regenerated. Electrons will be located at closer positions in the new atoms. Accordingly, the gravitational attraction will also change its dependence on distance, from the inverse square of distance to the inverse third degree of distance.

**CHARGE CLUSTERS**

The phenomenon of charge clusters was studied by Ken Shoulders (*http://www.rexresearch.com/ev/ev.htm**;**http://www.svn.net/krscfs/Charge%20Clusters%20In%20Action.pdf*). These clusters have sizes in the micrometer range, and have an excess of electrons in the ratio of the order of one positive ion for 100,000 electrons. The number of electrons in the cluster is 10^{8}–10^{11}. Stability of the clusters, and the absence of repulsion between the electrons in them, has no explanation in modern physics. In the proposed theory, the size and stability of the clusters can be explained by electrostatic interaction at a distance of less than 10^{−}^{5} m (see “Electrostatics” and “Atoms and Spectra”). The number of electrons also fits with the size of clusters. The linear arrangement of electrons (having a linear size 10^{−}^{15} m), when numbering 10^{8}–10^{11}, correlates with the cluster size, of around 10^{−}^{6} m. If the cluster size becomes larger, i.e. the distance between the electrons increases, this will change the nature of the electrostatic interaction between electrons, and the cluster will not be sustainable.