### THE PHYSICAL CONTENT OF h‑SPACE THEORY

**CLASSICAL MECHANICS**

Classical mechanics is based on Newton’s laws and the principle of Galilean relativity. Let us consider each of Newton’s laws in terms of the proposed theory.

Newton’s first law says. “*Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed(from the original Latin of Newton’s Principia translated to English; http://en.wikipedia.org/wiki/Newton’s_laws_of_motion*).”Given that atoms are made up of n=0-objects(II)”−”,”+”, the laws of classical mechanics describe the relative motions of the n=0‑objects(II)”−”,”+”. The velocity of n=0-objects(II)”−”,”+” is constant in the absence of their attraction or repulsion and the generation of n=1-, n=2- and n=3-objects. Consequently, the Newton’s first law express nothing but the constancy of the velocity of n=0‑objects(II)”−”,”+”.

The second law of Newton states the following. “*The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed (from the original Latin of Newton’s Principia translated to English; http://en.wikipedia.org/wiki/Newton’s_laws_of_motion*).”In modern physics, a force is defined as the product of the acceleration and the inertial mass. In the proposed theory, the concept of inertial mass is defined as the amount of n=0-objects(II)”−”,”+”. Gravitational mass has the same definition. The direct proportionality of gravitational and inertial mass is due to the definition of mass as the amount of n=0-objects(II)”−”,”+”. Acceleration is a change in velocity per unit of time. The time unit, as discussed in the first pages of the theory, is a unit of velocity. Accordingly, the concept of force is a secondary concept, which is more convenient for determination of motion with variable speed, but it can be reduced to a derivative of the velocity. More simply stated, the concept of force is nothing more than another designation of a change in velocity. In the proposed theory, the central force acting on an object (as in the case of gravitational and electrostatic interactions) is defined in terms of the change of velocity due to the density gradient of n=0-objects(I) around n=0‑objects(II)”−”,”+” (electrons, positrons). The gradient is determined in inverse proportion to the square of the distance, which is due to the three-dimensionality of space. In other words, accelerated motion, i.e. movement with increasing velocity, is not a result of a force acting on a body but rather a consequence of its location in a region of space with a characteristic density gradient of n=0‑objects(I). Since distance is expressed in absolute units, i.e. in lengths of n=0‑objects(I), then velocity varies discretely. This differs from classical mechanics, in which there is no discreteness and velocity changes continuously.

The concept of inertial forces is consistent with the suggested theory, since it describes nothing more than motion with variable velocity by changing the direction of motion. There is then no need for a source of inertial forces, as the concept of force is an auxiliary concept, in contrast to the fundamental concept of velocity.

Newton’s third law states. “*To every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions (from the original Latin of Newton’s Principia translated to English; http://en.wikipedia.org/wiki/Newton’s_laws_of_motion*).”In the proposed theory, this law is due to the symmetry of repulsion of n=0‑objects(II)”−”,”+”.

In classical mechanics, momentum is defined as a product of velocity and inertial mass, and the momentum conservation law establishes the equality of a product of velocity and inertial mass for the closed system in two different states. Inertial mass determines the number of n=0‑objects(II)”−”,”+”. Thus, the law of conservation of momentum reflects the fact that the change in velocities of n=0-objects(II)”−”,”+” in a closed system is a result of a redistribution of the velocities of n=0‑objects(II)”−”,”+”. In the suggested theory, the momentum conservation law is valid for a system consisting of only n=0‑objects(II)”−”,”+”, i.e. electrons and positrons. In contrast to the modern physics, the interaction of the photon and electron causes no redistribution of momentum. The photon is absorbed by an electron, leading to an increase in electron velocity in the direction of the photon. If the photon is reflected from the positron, the positron will not change its velocity. Thus, the law of conservation of momentum cannot be applied to electromagnetic quanta. This statement is supported by the results of experiments with EmDrive (*Harold White, Paul March, James Lawrence, Jerry Vera, Andre Sylvester, David Brady, and Paul Bailey 2016, Measurement of Impulsive Thrust from a Closed Radio-Frequency Cavity in Vacuum, Journal of propulsion and power, pages: 1-12, DOI: 10.2514/1.B36120*).

In contrast to momentum, energy is proportional to the square of velocity, and is not a vector, but a scalar. This concept of energy is different from that used in the proposed theory, in which energy is the opposite of length. Why is the classical concept of energy defined by the square of velocity? We consider this is due to the orthogonality of Euclidean space. In such space the square of velocity is a scalar form of velocity, which allows the algebraic operations of addition and subtraction in the three-dimensional space, i.e. along three orthogonal axes. Accordingly, describing the energy of n=0-object(II)”−”,”+”, i.e. square of the velocity of n=0‑object(II)”−”,”+”, enables one to express the conservation of n=0‑objects(II)”−”,”+” velocities in the form of a scalar sum of squares of velocities of n=0-objects(II)”−”,”+”.

**COMMENTS**

The proposed theory is entirely consistent with the laws of classical mechanics. It holds the principle of relativity of Galileo and Newton’s laws. In contrast to classical mechanics, the proposed theory provides an unambiguous definition of mass as the number of n=0-objects(II)”−”,”+” (electrons/positron). The concept of force is defined as an auxiliary, secondary notion. The motion of n=0-objects(II)”−”,”+” is primary, and change of their velocity defines the concept of force (for the given amount of moved n=0‑objects(II)”−”,”+”). The laws of conservation of momentum and energy are consequences of the primacy and constancy of motion of n=0-objects(II)”−”,”+”. In contrast to classical mechanics, in the proposed theory velocity changes discretely in potential fields: gravitational and electrostatic. I.e. in these fields there is a minimal change of velocity.

**SPECIAL THEORY OF RELATIVITY**

Special Theory of Relativity (STR)was built as an electrodynamics of moving bodies based on two postulates. One of them is the constancy of the speed of light in all inertial frames of reference, or, in other words, the independence of the speed of light from the motion of the light source. The second is the principle of relativity. It is assumed that all inertial frames of reference are equivalent and there is no special frame of reference for the laws of electrodynamics – Maxwell’s equations, or for the laws of mechanics. Why did these postulates and STR based on them appear in physics? At the time when STR was created, the existence of an ether, an all pervading, fundamental reference frame, was being actively discussed. The Michelson-Morley experiment gave negative results in the detection of an ether wind (light was considered as a wave in the ether, and the ether wind would change the speed of light). If an ether had been detected, then it would have represented a special frame of reference for the phenomena of electrodynamics, and the STR would not have been necessary. However, in the absence of an ether, all inertial frames of reference were considered to be equivalent and therefore the Maxwell’s equations had to maintain their form in different frames of reference, similar to classical mechanics. Experimentally, this was not found to be the case. There was asymmetry between frames of reference due to the fact that, for example, the speed of charge current and, consequently, the existence of a magnetic field depended on the choice of the frame. Also, the speed of light was supposed to be constant on the basis of experimental data, but the use of Galilean transformation required changes of it. Instead of Galilean transformation, Einstein proposed to use the Lorentz transformation and by this means eliminated the asymmetry between different inertial reference frames. In this way, he implemented the principle of relativity and the postulate of the constancy of the speed of light.

The proposed theory is consistent with the postulate of STR regarding the constancy of the speed of light, but in contrast to STR the constancy of the speed of light has a cause – the spatial dimension. Since light quanta are n=1-objects, i.e. objects of one-dimensional space, they are always moving at the same velocity relative to n=0‑objects(II)”−”,”+” of zero-dimensional space, regardless of the speed of n=0-objects(II)”−”,”+”. If the reference system is changed, the constancy of the speed is provided by the inverse relation of the length of photons, as expressed by the Doppler effect (see section on “Optics”). Further, if in Maxwell electrodynamics and so also in the STR, the electromagnetic field and electromagnetic quanta have the same nature and are defined by Maxwell’s equations, then in the proposed theory the electromagnetic quanta and the electromagnetic field are different entities of nature. The field consists of objects of zero-dimensional space, n=0-objects(I), while photons are the objects of one-dimensional space, n=1-objects. (As noted above, there is a connection between them. Electromagnetic field change can lead to the generation of n=1-objects.) Therefore, the speed of light in the Michelson-Morley experiment would not change relative to an ether wind because light is not a wave in the ether. In the proposed theory, the ether exists as moving n=0‑objects(I) creating three-dimensional Euclidean space. Because of this, an attraction/repulsion of charges (electrons/positrons) is defined in the Maxwell’s equations by the maximum density of n=0-objects(I) ρ_{0}(for an electrostatic field) or its change **ρ _{Δ }**(for a magnetic field), generated by the motion of electrons/positrons.

In contrast to the STR, the proposed theory posits that different frames of reference are not equal. I.e. the second postulate, the relativity principle, is not valid for phenomena of electrodynamics. There is a unique absolute frame of reference – an ether, the frame associated with the space of n=0-objects(I) moving relative to each other. Since the electrostatic field of the charge is defined by the density of n=0-objects(I),ρ_{0}, it cannot be changed (without gravity) when the frame of reference is changed. In the absence of gravity, magnetic induction also does not depend on the choice of the reference frame, since it determines the change in density of directed n=0-objects(I), **ρ _{Δ}**, relative to undirected n=0-objects(I) of density ρ

_{0}. As suggested above, in Maxwell’s equations the constant ccorresponds to a product of velocity v

_{0}and maximum density of n=0-objects(I) ρ

_{0}, v

_{0}ρ

_{0}, and it is not the speed of light. Therefore, it should not obey Galilean transformation for velocity. The maximal velocity v

_{0}ρ

_{0}decreases with time, since density ρ

_{0}was greater in the past than at present. To date, it is comparable with the speed of light and corresponds to the constant c.

According to the proposed theory, it is also wrong to use STR to describe the motion of a body consisting of atoms. If, in the case of photons, STR is consistent with the proposed theory, it is because of the photons length, as the objects of one-dimensional space, is changing in Doppler effects and keeping constancy of the speed of light. The same changes in length are not applicable to the objects of zero-dimensional space, n=0-objects(II)”−”,”+” (electrons and positrons) composing atoms. In other words, there is no Lorentz contraction of lengths of physical objects in the suggested theory. Also, STR is not suitable for explaining the dynamics of bodies composed of atoms. The increase in mass of a body with increasing velocity is not possible. The inertial mass is determined by the number of electrons/positrons, and this number cannot depend on the velocity of electrons/positrons. Therefore, there is no infinitely large mass at the speed of light. The velocity of electrons/positrons are not limited by the speed of light. In the early universe, the velocity of electrons/positrons was greater than the speed of light because the density of n=0-objects(I) ρ_{0}was higher than today, giving them a higher velocity of electrostatic interaction.

Another difference between the proposed theory and STR is the conception of time. In the proposed theory, as in classical mechanics, time is just a matter of agreement. Time is an artificial concept, introduced for convenience to describe the motion of objects, and must be defined as the same in all inertial frames of reference. In special relativity, because of the heterogeneity of time in different frames of reference, there are temporal paradoxes, such as the twin paradox, due to time dilation in the moving frame of reference. In the proposed theory, this is not possible.

**GENERAL THEORY OF RELATIVITY**

The concept of space-time is used in General Theory of Relativity (GTR) as it is in the special theory of relativity. In general relativity, the gravitational potential is identified with the space-time metric. Space-time is curved by a body having mass, and this causes a gravitational attraction. In the proposed theory, all phenomena take place in Euclidean space. Since both general and special relativity use the concept of space-time rather than Euclidean space, we consider these theories to be incorrect models to describe phenomena.

Phenomena, which in modern physics are explained only by general relativity, have their own interpretations in the proposed theory. For example, the gravitational redshift in general relativity is explained by gravitational time dilation. In the proposed theory, it is explained by a decrease in the density of n=0-objects(I) ρ_{0}around the gravitating body (see “Gravitational attraction”). The existence of black holes can also be explained by changes in density of n=0-objects(I) ρ_{0}. Due to the high density of electrons and positrons, a density gradient of n=0-objects(I) will be formed where the speed of gravitational attraction is greater than the speed of light, causing photons to be unable to overcome this attraction. The same reason will also cause the gravitational delay of electromagnetic quanta – the effect of Shapiro. Another phenomenon predicted by general relativity is the gravitational deflection of light. In the proposed theory, this results from the same attraction as for the Shapiro effect. Because of the high speed of light, gravitational attraction of photons is not as noticeable as for slow-moving electrons and positrons (n=0-objects(II)”−”,”+”). The precession of the orbit of Mercury in the suggested theory has no obvious explanation. However, this value can be the result of the influence of other planets in the solar system, since in the proposed theory gravitational attraction has a maximal boundary.

**COMMENTS**

In the proposed theory, in contrast to the STR, the speed of a body is not limited by the speed of light. The velocity of electromagnetic interactions is limited by a maximum density of the vacuum particles, n=0‑objects(I),ρ_{0}. The velocity determined by this density ρ_{0}, v_{0}ρ_{0}, is comparable to the speed of light, the velocity of object of one-dimensional space. The objects of two- and three-dimensional space move at velocities greater than this, 10 and 20 orders of magnitude above the speed of light, respectively.

What is considered in GRT as the curvature of spacetime, caused by a gravitating body, is the curvilinear motion in three-dimensional Euclidean space. For example, the deviation of light by the gravitational field is the result of the attraction of light quanta, as well as any physical body moving near another gravitating body.

In the proposed theory, phenomena explained by relativistic and gravitational time dilation are interpreted differently. For example, atomic clocks were employed in the Hafele–Keating experiment to accurately measure time, but these devices are based on the emission/absorption of electromagnetic quanta, and such processes depend on the elementary charge. Accordingly, a change of elementary charge caused by a change in gravitational potential will affect electromagnetic emission/absorption in the atomic clock and so “change” the time. Because of this, the atomic clocks of GPS satellites must be calibrated. Similarly, the change of the elementary charge is responsible for the observed effect in an experiment with masers – in the Gravity Probe A experiment.

**QUANTUM MECHANICS**

Quantum mechanics was created to explain the atom, since a classical planetary model was not satisfactory and was valid only as the Bohr model. Without the Bohr postulates, the atom would have to die as a result of energy loss by electrons (in the form of electromagnetic radiation) and their collapse into the nucleus. This paradox was formally resolved by quantum mechanics, where electrons were not allowed to have trajectories. Quantum mechanics has parameters related only to the initial and final stationary states of the electrons in atom, but not to any trajectories. Instead of the coordinates and velocities of the electron, probability values were used to describe these stationary states.

The proposed theory of the atom returns to the classical description of electron motion as having a trajectory. Electrons can move closer to the nucleus from more remote positions. At the closer distance, a photon can be generated if it complies with the integer value of the energy of the emitted photon. In this case, emission of a photon reduces the velocity of the electron. Ultimately, the electron can occupy the minimum distance at which its velocity becomes equal to zero relative to the nucleus. This distance is ≈ 10^{−}^{10} m. If there is no such compliance, then the electron will not radiate, and will continue to move to the other side of the nucleus, and away from it until its attraction to the nucleus leads to a complete stop and subsequent reversal back to the nucleus at a speed corresponding to a given distance from the nucleus. In contrast to the planetary model, the proposed theory predicts that electrons do not have strictly defined orbits, but rather changing trajectories. This distinguishes also the proposed theory from quantum mechanics, where there is no concept of electron trajectories in the atom. One can say that the electron oscillates around the nucleus, with a maximum distance from the nucleus of ≈10^{−}^{5} m. At the distance ≈10^{−}^{10} m, the electron is at rest relative to the nucleus. The absorption of a photon by an electron will increase electron velocity and distance from the nucleus.

Another problem that was solved by quantum mechanics is the wave-particle duality. When particles pass through a thin metal film, diffraction rings are formed on a screen behind the film. A similar pattern is observed in the case of X-rays. Since X-radiation is believed to be a wave, it was suggested that particles can act in a similar manner, like waves. This phenomenon was termed the wave-particle duality. To explain this in quantum mechanics, it was decided to replace the notion of a trajectory with the concept of a superposition of states, more precisely, the superposition of probability of alternative states, i.e. probability for a particle to be at the same time in alternative states. In this context, the particle in each experiment can be detected with a certain probability, in one of these states. In the suggested theory, there is no wave-particle duality. Wave feature of particles in such phenomena as diffraction and interference are not due to the wave nature of the particles, but because of the generation of waves in the vacuum, which consists of n=0-objects(I) (see “Optics”). The cause of waves of the n=0‑objects(I) is the motion of photons or other particles, since they displace the n=0-objects(I). The displaced n=0-objects(I) move like a wave and the velocity of these waves is close to the speed of light (slightly higher). Waves of n=0‑objects(I) create waves of particles, moving relative to the n=0‑objects(I). This mechanism can explain the interference in the double-slit experiment, where the intensity of particles was set so low that only one particle could pass through the slits at any time. The same interference pattern is observed at both high and low particle fluxes. Quantum mechanics argues that this result is the inherent property of the particles, their nondeterministic, probabilistic behavior, according to the uncertainty principle. In the proposed theory, this interference pattern arises from the interference of waves of n=0-objects(I), displaced by moving particles. In this way, the interpretation of the two-slit experiment is returned to the deterministic view.

The proposed theory also explains the discreteness of atomic spectra. Space, in the proposed theory, is composed a finite number of n=0-objects(I), so space is not infinitely divisible, i.e. matter is discrete. Since the number of n=0-objects(I), defining their density in the certain area of the space, is finite, then the difference of densities for different electron positions are also integers that determines the length of the generated n=1-object, as a multiple of an integer unit (see “Atoms and spectra”).

**QUANTUM TUNNELING**

In the proposed theory, explanation of the phenomenon of quantum tunneling does not require the uncertainty principle. As presented above (see “Superconductivity”), the tunneling of the electron has the same nature as superconductivity. It is due to the lack of interaction of the tunneling electron with the nucleus and electrons between 10^{−}^{15} m and 10^{−}^{10} m from the nucleus of atom.

**THE CASIMIR EFFECT**

The Casimir effect is the attraction of electrically neutral conductors and insulators. The distance, from which the effect becomes detectable, is a few micrometers. With decreasing distance the attractive force increases in inverse proportion to the distance in power of four. In modern physics, the effect is explained by quantum fluctuations of virtual particles of the electromagnetic field. In the proposed theory, the effect can be due to density fluctuations of n=0-objects(I). The fact that the length of a n=0‑object(I), ≈ 10^{−}^{5} m, is comparable with the distance at which the Casimir effect begins to appear (several micrometers) fits with the proposed interpretation.

**COMMENTS**

The main difference between the proposed theory and the quantum theory is the deterministic character of physical phenomena and the rejection of their probabilistic nature. The uncertainty principle is not a principle of nature; at best it is a statistical description, at worst – it is a delusion. Quantization of physical quantities is a manifestation of the discreteness and finiteness of matter of our universe.