Chapter 6. Epola Waves and Electromagnetic Radiation

6.1 Half-wave clusters of bulk deformation waves in elastic media

In uniform elastic media, such as gases or bulks of liquids far (deep) from their surfaces, the only propagating waves are the bulk deformation waves. They consist of half-wave clusters of increased density, thus increased pressure, which are followed by half-wave clusters of reduced density, thus reduced pressure. In other words, in some half-wave clusters, there is an excess number $\Delta N$ of molecules, $\Delta N > 0$, while in the neighboring half-wave clusters, the number of molecules is less than the normal number $N$, and $\Delta N$ is negative. With the tremendous number of molecules in any half-wave cluster, usually $N >> \Delta N$, and $\Delta N >> 1 \$ (except in shock-waves: see also Section 7.7).

In each half-wave cluster, the molecules of the substance vibrate (in addition to the random thermal vibrations) with the frequency of the wave in all possible directions. Relative to any chosen direction of wave propagation, there are molecules vibrating along this direction, as well as molecules vibrating in directions perpendicular to the direction of wave propagation. Therefore, bulk deformation waves may show effects of longitudinal and transversal waves, depending on the means of detection.

A polarizer screen, with a slit in the way of the waves, lets out, in addition to longitudinal waves, the transverse waves in which molecules vibrate parallel to the slit. However, the polarizer screen also changes conditions in the wave. First, due to the increased pressure at the screen. part of the molecules are forced to change the direction of their vibrations, so that more wave energy is "squeezed" through the slit. The slit also induces diffraction and interference, affecting not only the space-distribution of wave-energy, but also the energy distribution between the different transverse modes and the longitudinal mode of vibration. These effects will be further enhanced by the analyzer screen, placed in the way of waves, which passed the polarizer. Hence, the energy distribution among the various modes of vibration in the waves which passed the slits does not depict this distribution in the natural bulk deformation wave.

Bulk deformation waves are usually traveling waves, in which during each half period, the phase of vibrations, e.g., the phase of maximum positive deflection, and the vibrational energy of each molecule, are transferred a distance of half a wavelength in any chosen direction of propagation, with a singular velocity $v_d$ of the bulk deformation waves.

6.2 Half-wave clusters in standing waves

Bulk deformation waves can also be standing waves. These result from the superposition of two waves of identical frequencies and amplitudes traveling in opposite directions, as, e.g., a direct wave and the reflected wave. In a standing bulk deformation wave, every molecule vibrates with a constant amplitude, thus keeping its vibrational energy constant (in addition to the energy of random vibrations). In the standing half-wave deformation cluster, the molecules on the boundary of the cluster have zero amplitude and zero vibrational energy. These values increase towards the center of the cluster, where they reach a maximum. Hence, while energy is flowing in a standing wave in both directions, there is no net energy transfer in it.

The pressure in each half-wave cluster of a standing wave is changing in each half period from maximum to minimum, in phases opposite to those in the neighboring half-wave standing cluster. Thus, there is a flow of pressure, i.e., of excess molecules between neighboring clusters. While one cluster has a more than normal number of molecules, $\Delta N > 0$, the other has slightly less than normal, $\Delta N < 0$, and on the boundaries of the clusters, the pressure is normal, $\Delta N = 0$. Because of this flow of pressure or of molecules between the half-wave clusters, energy can be drawn from a standing wave, though there is no net energy flow in the wave. This can be achieved, e.g., by inserting a tube or pipe into the center of a half-wave cluster. Then, energy will flow from the wave through the "contact" $-$ the mouth of the pipe $-$ right into the pipe.

6.3 Velocity calculation or bulk deformation waves in unbounded NaCl crystals

The propagation velocity $v_d$ of bulk deformation waves in a uniform elastic medium of density $d$ can be expressed through the bulk elastic modulus of the medium as

The bulk elastic modulus $B$ is defined as

where $V$ is the volume and $p$ is the hydrostatic pressure. Thus, the bulk elastic modulus is the rate of change of pressure with the change of volume; it also represents the elastic energy-density in the medium.

Let us now consider an unbounded $\mathrm{NaCl}$ crystal so large, that as large as its single-crystal grains may be, the crystal as a whole is polycrystalline, identical in all directions, thus representing a uniform elastic medium. In such $\mathrm{NaCl}$ lattice, the bulk elastic modulus was found to be

where ${}_b E$ and ${l_0}^3$ are the mean binding energy and volume per ion in the lattice. The velocity $v_d$ is, by substituting the above expression for $B$ into formula 1, therefore,

With $m_i$ as the mean ion mass, the density $d$ is $d = m_i / {l_0}^3$, thus

Substituting the $\mathrm{NaCl}$ data: ${}_b E = 4 \ \mathrm{eV}$ and $m_i = 29 \ \mathrm{AMU}$, we find the velocity $v_d$ of bulk deformation waves in the huge $\mathrm{NaCl}$ crystal, ${v_d = 3600 \ \mathrm{m/s}}$.

6.4 Velocity of sound in NaCl crystals

The velocity of sound $v_s$ in gases and in the bulk of liquids (far from their surface) is the velocity $v_d$ of bulk deformation waves. In large $\mathrm{NaCl}$ crystals, in which the effects of the surfaces in all directions can be disregarded (i.e., in crystals not shaped as rods or plates), there are still six different values for the sound velocity, depending on the direction of propagation in relation to the directions in the unit cube of the $\mathrm{NaCl}$ lattice and on the mode of vibration of the sound. These values are presented in the table.

In the unthinkably large $\mathrm{NaCl}$ crystal, which can be considered as a uniform elastic medium, the ions in every half-wave cluster are vibrating in all possible directions, as described in Section 6.1. Because of the unavoidable polycrystallinity of the huge crystal, all directional differences are averaged out and the velocity of sound should be the average of all six values listed in the table. This average value really is 3.6 km/s, exactly equal to the velocity of bulk deformation waves, calculated in Section 6.3. Thus, the velocity of sound in an unbounded very large $\mathrm{NaCl}$ crystal has a unique value equal to the velocity of bulk deformation waves in this crystal, $v_s = v_d = \left( {}_b E / m_i \right)^{1/2} = 3600 \ \mathrm{m/s}$. Therefore, sound waves in such $\mathrm{NaCl}$ crystals are due to bulk deformation waves in it.

6.5 Velocity calculation of epola deformation waves and of light

The directional differences in the epola may possibly be detected on distances of up to a billion lattice units, which is a few micrometers. On larger distances, the directional differences average out, and the epola is a perfectly uniform elastic medium. Hence, the velocity of bulk deformation waves in the epola can be calculated in the same way as it was done in the huge $\mathrm{NaCl}$ lattice. The derived formula for $v_s, v_d = \left( {}_b E / m_i \right)^{1/2}$, can therefore be used in the epola. Here, the per-particle binding energy ${}_b E$ is $m_e c^2 = 511 \ \mathrm{keV}$, and the average ion mass $m_i$ is the mass of the electron $m_e$. Substituting these values, we obtain

or

Thus, the velocity of bulk deformation waves in the epola is equal to the unique vacuum light velocity $c$. In other words, electromagnetic radiation propagates with the same unique velocity $c$, as do bulk deformation waves in the epola. Thus, electromagnetic waves and radiation are just as closely connected with bulk deformation waves in the electron-positron lattice, as sound waves are connected with bulk deformation waves in the unbounded $\mathrm{NaCl}$ crystal.

6.6 Epola bulk waves and the transverseness of electromagnetic waves

Electromagnetic waves and bulk deformation waves in the epola propagate with the same velocity $c$, but are not identical. In the epola waves, real particles are vibrating around their lattice sites with the frequency $f$ of the wave motion. The waves are multi-faceted, and one of the ways to detect them is through their electric and magnetic fields, which are caused by the vibrations of the electrons and positrons in the waves.

The vibrations of the electric and magnetic fields spread throughout with the velocity and frequency of the bulk deformation waves, causing corresponding vibrations of electrically charged particles in all reached materials, susceptible to such vibrations. The vibrations of the electric and magnetic fields are described by the vibrations of the coupled electric and magnetic vectors $\vec{\varepsilon}$ and $\vec{H}$. These vectors are always found to be perpendicular to each other and to the direction of their propagation-velocity or the vector $\vec{c}$. This transverseness of the electromagnetic waves is seemingly opposed to the epola bulk deformation waves, in which electrons and positrons vibrate in all directions.

Clearly, the electrical charges of all electrons and positrons in equilibrium, positioned along any chosen direction in the epola, are equal and neutralize each other perfectly. When these electrons and positrons come into vibrations along this chosen direction, there is no violation of charge neutrality along this direction, because in longitudinal vibrations electrons or positrons do not cross the line of the chosen direction. Their numbers remain equal to each other and their charges neutralize each other as perfectly as in equilibrium. Therefore, the longitudinal component $\varepsilon_l$ of the electric vector along any chosen direction of wave propagation in the epola, caused by the vibrations of epola particles along this direction, is always zero, $\varepsilon_l = 0$.

Electrons and positrons of the epola, vibrating in directions perpendicular to the chosen direction of propagation, cross the lines of this direction in equal numbers, i.e., the negative charge above the lines is always equal to the positive charge below them. Therefore, these vibrations, too, do not cause any deviations from charge neutrality along the chosen direction. Hence, they do not contribute to the longitudinal component $\varepsilon_l$ of the electric vector, which remains zero. However, these vibrations change the amounts of electrical charge in directions perpendicular to the direction of wave propagation. This results in a vibrating transverse component $\varepsilon_t$, of the electric vector. In points where the positive charge of the perpendicularly deflected epola particles to one side of the chosen direction is maximal, the transverse component $\varepsilon_t$ of the electric vector has maximum, $\varepsilon_t = \mathrm{max}$. In points where the negative charge of the perpendicularly deflected epola particles has a maximum, the transverse component of the electric vector has a maximum in the opposite direction, $\varepsilon_t = - \mathrm{max}$.

Epola electrons and positrons vibrating in directions other than along the chosen direction or perpendicular to it, contribute to the transverse component of the electric vector only with their deflection-component which is perpendicular to the chosen direction. The component of their deflection along the chosen direction does not contribute to the longitudinal component of the electric vector, which is always zero.

The zero value of the longitudinal electric vector also yields a zero value of its coupled magnetic vector. The non-zero value of the transverse electric vector produces a non-zero coupled magnetic vector. To summarize,

the transverseness of the electromagnetic waves is due to the fact that, for any deflection of an electron or positron of the epola, the deviation from charge neutrality is largest perpendicular to the deflection, while along the deflection charge neutrality is not violated.

Therefore,

the oscillations of the epola particles along any direction of propagation of the electromagnetic wave (or the maternal bulk deformation wave) do not contribute to $\vec{\varepsilon}$ and $\vec{H}$; hence, the longitudinal components of $\vec{\varepsilon}$ and $\vec{H}$ are always zero.

We may conclude that electromagnetic radiation is an observable result of epola bulk deformation waves. It is also right to say that electromagnetic radiation causes bulk deformation waves in the epola, or that

electromagnetic radiation is both the observed result and the observed cause of bulk deformation waves in the epola.

6.7 The epola as carrier of electromagnetic radiation

The fact that electromagnetic radiation is caused by and also causes bulk deformation waves in the epola, suggests that the epola is the carrier of electromagnetic radiation. As such, the epola is not an ether. The density of the epola, calculated as

is $10^5$ times smaller than that of 'dense' particles, electrons, atomic nuclei and nuclear matter. However, the epola is almost a billion times denser than the densest solids on Earth and has a binding energy $10^5$ times larger than these solids.

From the epola viewpoint, atoms and atomic bodies (including ourselves) are conglomerates of loosely connected particles, separated from each other by $10^4$ epola lattice constants. The bodies may move undisturbedly through the epola, sweeping their atomic electrons and nuclei in channels between the epola particles. This, provided that the epola particles move apart when their lattice unit is entered by an electron or nucleus of the atomic body. Such 'opening of the gates' in the epola units in front of the moving particles and closing of the gates behind them is a wave motion in the epola. It will be shown later that this wave motion has the de Broglie wavelength of the moving particle and is responsible for making the epola vacuum-transparent for the motion of the particle and of the whole atomic body, to which the particle belongs (Section 8.1).

Our conclusion is that in the motion of Earth around the Sun, the production of epola waves with the corresponding de Broglie wavelengths is the only effect on the epola. Obviously, the motion cannot drag the epola, nor can it cause in it the wind, expected of an ether in Michelson-Morley's experiment. Only bodies of nuclear matter can cause such effects. Compared with the density of the epola, it is the Earth and earthy bodies which are the etherous ones. This contradicts our natural perception of the emptiness or etherosity of space, which we proved false, based on Anderson's experiments (Chapter 4). It also contradicts the natural perception of earthy objects and ourselves as bodies of continuous dense matter, proven false by Rutherford.

Except for contradicting our mentioned natural perceptions, the epola as carrier of electromagnetic radiation is in full agreement with all observed phenomena and experimental results. With the epola as such carrier, all these phenomena and experiments are given a full physical explanation without hiding behind complicated mathematical derivations and ad hoc invented postulates and principles.

6.8 Derivation of the mass-energy equivalence

With the energy $m_e c^2 = 0.51 \ \mathrm{MeV}$ proven to be the binding energy ${}_b E$ of the epola particle (Section 4.5) we have calculated the velocity $v_d$ of epola bulk deformation waves, $v_d = \left( {}_b E / m_e \right)^{1/2}$ and shown that it is equal to the vacuum light velocity $c$ (Section 6.5). Let us rewrite the formulas for the velocity $v_d$ of bulk deformation waves (Sections 6.3, 6.5), to read

for the $\mathrm{NaCl}$ lattice, and

for the epola.

The binding energy ${}_b E$ is the mean energy of freeing an ion or particle of its bonds in these lattices. Therefore, the formulas say that

to free ions or particles of their bonds in a (fcc) lattice, one must supply to them energy, equal to their mass, multiplied by the velocity-squared of bulk deformation waves in the lattice. This energy is released in the lattice when an ion or particle is caught or entrapped into the lattice.

Multiplying the formula ${}_b E = m_e c^2$ by an arbitrary integer $n$, so that $n \cdot {}_b E = E$, and $n \cdot m_e = m$, we obtain

This is Einstein's equation for the equivalence of mass and energy. The equivalence is therefore a direct consequence of the epola structure of space. In the epola here and in it only, $0.51 \ \mathrm{MeV}$ is equivalent to the electron mass $m_e$ because $0.51 \ \mathrm{MeV}$ is half the energy of freeing an electron-positron pair from its bonds. However, as is known, $0.51 \ \mathrm{MeV}$ is much less than the not-yet-known energy, which might really create or destroy an electron.

We must point out that in the $E = m c^2$ formula, $E$ is a radiative energy, i.e., energy of epola waves, emitted or absorbed in the epola when the mass $m$ of electrons and positrons or of similar dense particles is caught into the epola or freed from it. Thus, $E$ and $m$ are not just any energy and any mass. So it also was in Einstein's derivation; his extrapolation onto any energy and any ponderable mass was unjustifiable (see Sections 2.3, 2.6).

6.9 The Mass-energy equivalence in the NaCl crystal

In the $\mathrm{NaCl}$ lattice, with $v_d = v_s$, the velocity of sound, we have

Multiplying by the arbitrary integer $n$, so that $n \cdot {}_b E = E$, and $n \cdot m_i = m$, we have

This is the mass-energy equivalence formula for the unbound huge $\mathrm{NaCl}$ crystal. In it and in it only, $8 \ \mathrm{eV}$ is equivalent to $58 \ \mathrm{AMU}$ (or to $110,000 \ m_e$), because $8 \ \mathrm{eV}$ is sufficient to free an $\mathrm{Na^+}$ $\mathrm{Cl^-}$ ion pair of its bonds, making the $58 \ \mathrm{AMU}$ mass appear in the lattice. Obviously, $8 \ \mathrm{eV}$ cannot create $58 \ \mathrm{AMU}$.

By virtue of the above, we may conclude that in both the epola and the $\mathrm{NaCl}$ lattice,

the mass-energy 'equivalence' formulas result from the lattice structure of the media and express energy relations for the freeing of masses or for their entrapment, not for their real creation or destruction.

6.10 The rocksalters' mass-energy saga

Let us conceive a tremendously huge rocksalt crystal with imaginary intelligent creatures floating in it. Being unable to detect the $\mathrm{Na^+}$ and $\mathrm{Cl^-}$ ions bound to the lattice sites in the crystal, the rocksalters have no indication on the existence of the crystal. Therefore, they consider themselves living in an emptiness, a rocksalters' vacuum. As their scientific knowledge developed, they observed some strange limitations, enforced on positions and motions in this vacuum. However, by introducing no less strange postulates, principles and exclusions, they somehow found ways to account for the observed limitations. Thereafter, each time when calculations did not fit new facts, they would make them fit by adding new postulates, space-dimensions or exotic particles. In such a manner, through a complete denial of physical causality, they could keep the idea of the emptiness of their space. This success made the rocksalters believe that the ability to calculate is the only thing which matters and the only proof of truth, that physical understanding is not only impossible but also meaningless, and that the natural desire for such understanding is a sign of ignorance, if not a sin.

Having developed 'high-energy' techniques, the rocksalt creatures observed, that when $8 \ \mathrm{eV}$ of energy are absorbed in their vacuum, out of it a sodium and a chlorine ion may appear, and that when such a pair of ions disappears, $8 \ \mathrm{eV}$ of energy emerges. The appearance of the ion pair is then interpreted as its creation out of nothing by the $8 \ \mathrm{eV}$ of energy; the reverse disappearance of the ion pair is its 'obvious' annihilation into nothing, by emitting $8 \ \mathrm{eV}$ of energy. This interpretation necessarily leads to a conclusion that $8 \ \mathrm{eV}$ must be equivalent to the mass of the ion pair, i.e., to $58 \ \mathrm{AMU}$, otherwise it would not be able to create the pair. With the use of very complicated mathematics, the rocksalters had previously derived their formula for the equivalence of mass and energy,

wbere $v_s$ is the rocksalt-vacuum sound velocity, proclaimed as a universal constant. Substituting the value of $m_i$,

and the value of $v_s$,

they obtained

This result represented a triumph for the rocksalters' interpretations of their vacuum space, of ion creation out of it and of ion annihilation into it, as well as for the genius of their mathematicians. A rocksalter was trying to spoil the jubilation by reiterating that the $8 \ \mathrm{eV}$ is just the binding energy of the ion-pair to an undetected $\mathrm{NaCl}$ lattice, and that the celebrated mass-energy formula is just a formula for the velocity of sound in this lattice. However, his harm was minimal, because he was not allowed to publish his crazy ideas and nobody had the time and willingness to listen to him.