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@@ -17,5 +17,6 @@
   "chapter9-atomic-bodies-motion": "Chapter 9: Motion of Orbital Electrons, Atoms and Bodies of Atoms in the Epola",
   "chapter10-wave-propagation": "Chapter 10: Epola Wave Propagation and Interaction with Matter",
   "chapter11-cosmological-aspects": "Chapter 11: Cosmological Aspects of the Epola Structure of Space",
-  "chapter12-epola-interactions": "Chapter 12: Interactions Carried by the Epola"
+  "chapter12-epola-interactions": "Chapter 12: Interactions Carried by the Epola",
+  "chapter13-summary": "Chapter 13: Summary"
 }
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diff --git a/pages/chapter13-summary.mdx b/pages/chapter13-summary.mdx
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+
+
+<div style={{textAlign: 'center'}}>
+
+# Chapter 13. Summary
+
+</div>
+
+
+### 13.1 Experimental founding of the epola
+
+The epola model of space is established on the basis of three crucial
+experiments: Michelson-Morley's (1887), Rutherford's (1911) and Anderson's
+(1932). Numerous other experiments prove and substantiate this model.
+Actually, there is not a single relevant experimental fact which would deny the
+epola model or which could not be explained on the basis of this model.
+
+The Michelson-Morley experiment (Section 1.3) is an unbeatable proof that
+the ether does not exist. Unfortunately, it is often presented as denying the
+existence of *any* material carrier of electromagnetic radiation. However, what
+was actually proven by this experiment is that
+
+> light emitted and received by earthy atomic bodies propagates with a
+velocity independent of Earth's motion around the Sun.
+
+This excludes the existence of an etherous carrier, in which the motion would
+cause measurable winds. However, it does not deny the existence of a carrier of
+light, in which Earth's motion is *unable* to cause winds. Such is the epola, whose
+electrons and positrons are thousand times closer to one another than the
+electrons and nuclei of atoms of Earth and earthy bodies. Expecting that the
+motion of such bodies would cause winds in the epola is like expecting to catch
+sardines with a net, the threads of which are a hundred meters apart.
+
+The velocity of light in the epola does not depend on the motions of its
+atomic sources and receivers (Sections 10.9&ndash;10.12), even if their velocities were
+to approach the limits allowed for atomic bodies (2.4 Mm/s, Section 9.6), which
+exceed the velocity of Earth by eighty times. Hence, the epola carrier of light is
+in full agreement with the results of Michelson-Morley's experiment. Moreover,
+the existence of the epola is the only physical explanation of these results.
+
+Proof of the very low particle-density in atomic bodies was given by
+Rutherford. His experiments on the scattering of alpha-particles in atomic
+bodies proved that only a millionth of a billionth part of the volumes of atomic
+bodies is occupied by electrons and atomic nuclei. The rest of the volume, thus,
+practically all the volume, is 'empty'; as empty as space itself and penetrable
+to 'dense' particles.
+
+The much higher particle-density of the 'empty' space follows from
+Anderson's experiments, in which electron-positron pairs are obtained from
+*any* point in space,and the number of obtained pairs directly depends on the
+density of the gamma-ray energy flux (Chapter 4). Then comes the fact that
+electrons alone or positrons alone cannot be created or annihilated by
+submission or removal of energies, even in the thousand MeV range.
+This proves that electrons and positrons do exist in space but in a bound form.
+They are, therefore, indetectible by usual means, and 1.02 MeV is just the
+binding energy of an electron-positron pair to its counterparts in space.
+
+Quantum effects in electromagnetic radiation can be physically explained
+only by a lattice form of its carrier. It follows from Anderson's experiment
+that electrons and positrons are the building particles of the carrier. Hence, the
+closest solid-state analog of this lattice is shown to be the ionic sodium-chloride
+(rocksalt) crystal lattice (Section 5.1). Using this structural analogy, with the
+known electron and positron mass and the known binding energy, we calculated
+the lattice constant of the epola (4.4 femtometer, ± 0.5 fm; Section 5.6). This is
+a hundred thousand times shorter than the distances between atoms in solids.
+
+
+### 13.2 Calculations and derivations with tbe epola model of space
+
+Based on the analogy between the epola and the rocksalt lattice, we use the
+formula for the velocity of bulk deformation waves in an unbounded crystal to
+calculate the velocity of such waves in the epola (Section 6.5). It turns out that
+
+> the velocity of bulk deformation waves in the epola is the vacuum light
+velocity $c$.
+
+This fact strengthens our arguments in favor of the epola as carrier of
+electromagnetic radiation. A slight transform of the velocity formula for bulk
+deformation waves in the epola yields Einstein's mass-energy relation $E = m c^2$
+(Section 6.8). Einstein's formula is therefore a result of the lattice structure of
+the carrier of electromagnetic radiation; it expresses energy relations for the
+freeing of masses from the epola and for their entrapment, not for their real
+creation out of energy or true conversion into energy.
+
+The energy and momentum transfer process in an epola wave (electromagnetic wave)
+is described either as their transfer among the half-wave
+deformation clusters (Section 7.2) or by the motion of photons (Section 7.3).
+
+This enabled the derivation of Planck's law (Section 7.4), which was postulated
+in 1900 and always remained a postulate.
+
+Our presentation of epola waves and derivation of Planck's law allowed to
+introduce and calculate numbers, characterizing the half-wave deformation
+clusters. For the Compton wave (of 0.51 MeV photon energy, equal to the
+binding energy of an epola particle) we found that in the cluster there is at any
+instant one photon, and the cluster contains 11 million epola particles. The
+clusters of longer wavelength radiation or of epola *compressibility* waves
+(Section 7.6) are spherical, the numbers of epola particles and photons in them
+are proportional to the cube of the wavelength, and at any instant, they contain
+one photon per every 11 million particles. The clusters of the shorter-wavelength
+epola *impact* waves (Section 7.7) are ellipsoids and the number of
+epola particles in them decreases very rapidly with wavelength, however they
+always contain one photon. In the half-wave cluster of the shortest epola wave
+(Section 7.10), there is one only epola particle, carrying the single photon of the
+calculated 140 MeV "cutoff" energy.
+
+The de Broglie wavelength of the electron is derived as the wavelength of a
+real epola wave, caused in the epola by the motion of the electron (Section 8.1).
+Such waves, accompanying the motions of dense particles, propagate with the
+velocity of light and pre-form the epola for the motion. Hence, the epola
+becomes vacuum-transparent for particles moving much slower than the
+accompanying wave.
+
+The accompanying waves of sublumic particles (i.e., having velocities close
+to the light velocity) do not have sufficient time to pre-form the epola ahead.
+The particle has to push apart the epola particles on its way, losing the more
+energy the faster it moves. This resistance of the epola to sublumic motion is
+accounted by assuming an increase in the 'effective' mass of the particle
+(Sections 8.11, 8.12), which includes also the photon mass of the accompanying
+wave. This allows a very simple derivation of Einstein's equation for the
+dependence of mass on velocity (Section 8.13). Hence, this experimentally
+proven relation, laboriously derived by Einstein with four-vectors, Lorentz
+transforms and other heavy cannons of relativity is actually a simple result of the
+epola structure of space.
+
+Our derivation of the expressions for the masses and momenta of photons
+and half-wave deformation clusters (Sections 8.8. 8.9) also serves as a physical
+basis in the derivation of the uncertainty principle (Section 8.7), which was
+postulated by Heisenberg 60 years ago and has remained an unexplained pos-tulate
+all these years.
+
+The epola model enables the derivation of Bohr's postulated conditions and
+formulas for the allowed orbits of the hydrogen atom (Section 9.1). The
+interaction of radiation with moving atomic bodies, discussed in Section 10.9,
+leads to the derivation of formulas for the Doppler effect (Sections 10.10, 10.11)
+and the independence of the velocity of electromagnetic radiation of the
+motions of its atomic sources and receivers (Section 10.12). This was proven by
+Michelson-Morley's experiment and stated in Einstein's second postulate
+(though with illegal generalizations onto any emitting body and requests of a
+universal unconditional constancy of the vacuum light velocity; Section 2.1).
+
+The epola is shown to be the carrier of not only the electric and magnetic
+interactions but also of the gravitational interaction. The gravitational interaction
+is derived from the differences in the short-range repulsive interaction
+between epola particles, which itself is a derivative of the electromagnetic
+interaction. This explains the 37 orders of magnitude lower strength of the
+gravitational interaction (Sections 12.1-12.3).
+
+
+### 13.3 Epola explanations of the otherwise inexplicable
+
+The proportionality of the photon (or quantum) energy to the radiation
+frequency, postulated by Planck in 1900 (Section 3.1), contradicts the fact that
+vibrational and wave energy is proportional to the amplitude-square and
+independent of frequency; hence, it was not and cannot be understood in
+quantum physics. In the epola model, the photon is a quasi-particle representing
+the per-particle energy and momentum transferred in the epola wave from one
+epola particle to the next in line (Section 7.3). While the vibrational energy of
+each epola particle in the wave is proportional to the amplitude-square, the
+per-particle energy of the half-wave deformation cluster is shown to be inversely
+proportional to the wavelength; and so is the energy, transferred in the wave by
+the photon-holding epola particles. Hence, this energy, i.e., the energy of the
+photon is proportional to the radiation frequency (Section 7.4).
+
+The corpuscular properties of electromagnetic waves, unexplainable in
+quantum physics, are due to the fact that the waves result from coherent
+vibrations of epola electrons and positrons. The energy and momentum
+transferred by a photon to a dense free particle is actually the energy and
+momentum transferred to the free particle by the last epola electron or positron
+on the path of the photon. The wave properties of particles are due to the epola
+deformation-clusters around them, when at rest, and to the epola accompanying
+waves, when they are moving. The clusters or accompanying waves are the
+physical basis for the quantum-mechanical 'waves of matter'. They cause the
+diffraction and interference phenomena and define the probability of finding the
+particle (because the cluster or wave really is around the particle; Section 8.5).
+Hence, we obtain a full physical explanation of the particle-wave duality
+principle (Section 8.6) postulated and never explained in quantum physics.
+
+Einstein's postulated principle of frequency invariance is shown to be a
+simple result of the epola structure of space. The frequency is kept stable by the
+huge masses of quadrillions of epola particles which participate in the wave and
+vibrate with this frequency (Section 8.9). A full physical explanation is given to
+the stability conditions of allowed elliptic orbits, the meaning of the four
+quantum numbers (Sections 9.1, 9.2) and to the exclusion principle (Section
+9.4), postulated by Pauli in 1925 and unexplained until now.
+
+The observed zero-point energy of helium atoms, along with other
+unexplained zero-point effects, is presented (Section 5.13) as due to random
+vibrations of epola particles. These vibrations establish an epola temperature,
+which in 'our' surrounding epola region is about 3 degrees centigrade above the
+absolute zero temperature. Hence, the mysterious 3 K background radiation
+observed everywhere on our skies is presented as the thermal radiation of the
+surrounding epola (Sections 5.14, 11.2).
+
+Absorption, also non-linear, of electromagnetic radiation, is revealed as
+partially due to epola random vibrations (Sections 10.1, 10.2). Physical
+explanations are then given to the interaction of radiation with the electron gas
+in metals and semiconductors (Section 10.5) and to transparency and reflectivity
+of solids in different regions of the radiation spectrum (section 10.6). The
+reduction of the velocity of visible light in atomic matter, as compared with the
+velocity of X-rays and gamma-rays, is explained by the strong coupling between
+visible light and orbital electrons, leading to the absorption of the visible light
+and its re-emission (Section 10.7).
+
+
+### 13.4 Epola dismissals, replacements and restorations
+
+To establish the epola model, we had to disprove and turn over two of our
+natural perceptions: of a dense continuous atomic matter, which we replaced by
+its experimentally proven emptiness and discreteness, and of the emptiness of
+space, which we replaced by a dense population of bound electrons and
+positrons, forming a discrete lattice. The penetrability of space to atomic matter
+is due to the fact that neither is continuous and that both are built of
+femtometer-size particles positioned at distances, which exceed their diameters.
+
+Thanks to this, we could explain the results of Michelson-Morley's
+experiment without the unproven and antinatural requests of relativity. First,
+we rehabilitate our natural perception of the three-dimensional space, raising it
+up again to the rank of proven physical reality. Hence, we dismiss the
+never-proven existence of a four, five, eleven, 506 or any $\mathrm{N}$-dimensional space.
+Naturally, we do not question the legality of using such imaginary spaces in
+calculations and do gratefully acknowledge the working results of such use.
+However, working results do not make the spaces real, just as real results
+obtained with complex numbers do not turn these numbers real. We may go
+farther and say that the real results obtained in education with "Alice in
+Wonderland" do not turn the wonderland real, not even with Disney's 'working
+models'.
+
+Second, we dismiss the postulated universal constancy of the vacuum
+light-velocity; replaced by the velocity of bulk deformation waves in the epola, it
+depends on "local" conditions in the epola. We also dismiss the postulated
+universal validity of laws and magnitudes established in our backyard, even if
+obtained with astrophysical data; we limit their validity to 'our' uniform epola
+region. Physical laws and magnitudes, established and measured on Earth, may
+possibly be useful and applicable to other regions, but the *a priori* tyrranic
+demand of their universal validity and unchangeability is rejected. Hence, the
+epola model restores the natural rights of all autonomous regions of the universe
+to manage their affairs according to local conditions and legislature.
+
+We dismiss the interpretation of Einstein's $E = m e^2$ formula as expressing
+the equivalence of mass and energy and restore the mass-conservation law to its
+full pre-relativistic glory. We reject the Big Bang interpretations of the 3 K
+radiation of our skies and of the Hubble redshift as due to the runaway of
+nebulae. The 3 K radiation is the radiation of the surrounding epola, due to the
+random thermal vibrations of its particles, and the Hubble redshift is due to
+three more physical phenomena, in addition to the Doppler effect. The Doppler
+effect is suspected to shorten the wavelength in radiation spectra of some
+nebulae, because then the up to 50 percent diversities in the Hubble constant are
+physically explained. Hence, not everything is running away from us, the
+universe is not necessarily expanding or exploding and the Big Bang theory is
+dismissed as a groundless fantasy.
+
+
+### 13.5 Epola suggestions and propositions
+
+We mention first the suggestion to measure the epola temperature from
+zero-point and other low-temperature effects (Section 5.14). This is connected
+with establishing a rating-factor for efforts needed to reach and maintain each
+particular temperature below 4.2 K. The plot of this factor against the
+temperaure should have a special point at the epola temperature.
+
+Our half-wave deformation-cluster presentation of epola waves (Chapters 6
+and 7), which enables the derivation of Planck's law and the calculation of
+numbers characterizing the waves in all spectral regions, can be successfully
+applied to waves in any elastic media.
+
+Of interest might be the suggested possibility of superlumic motion (Sections
+8.14 - 8.16) and the spectral characteristics of small and large avotons in such
+motion. This includes the unified approach to the Cherenkov radiation here and
+to the accompanying wave in sublumic motion, which both are the response of
+the epola to the motion of avotons.
+
+The derived velocity-limits of atomic bodies (Section 9.16) cannot be proven
+experimentally, because we are very far from the ability to reach such velocities.
+So low are also the known velocities of planets and comets. It might however
+become possible to accelerate ions to velocities, sufficient to turn them into
+higher order ions and so to check our approximate formula. The "runaway"
+velocities of celestial bodies, calculated from their redshifts, have little to do
+with the real velocities of these objects relative to Earth (Sections 11.6&ndash;11.10)
+and cannot be considered.
+
+It might be possible to prove experimentally the proposed orbit-adjustment
+redshift (or blueshift) in the emission spectra of atomic radiation sources moving
+parallel to Earth (Section 9.7) but with a different velocity.
+
+The non-linear absorption of radiation on epola random vibrations could be
+verified by the proposed measurement of the fading of 60 Hz radiation (Section
+10.2). The effect of epola distortion on the propagation of light can be tested by
+the proposed measurement in a micrometer-wide channel between massive
+bodies (Section 1O.8). This would also allow us to check our proposed treatment of
+the bending of light in a way similar to the treatment of the mirage.
+
+Our explanation of the limited lifetime of free positrons by the abundance of
+free electrons in our region of the epola suggests that there might be regions with
+an abundance of free positrons and atomic anti-matter. The possibilities are also
+suggested of the creation of atomic bodies, as well as bodies of nuclear matter
+and black holes by local collapses in the epola. Hence, atomic bodies could be
+created in the epola "on premises", without collecting atoms from vast volumes
+of the universe, as is assumed in the "gravitational collapse" hypotheses
+(Sections 11.5, 11.11).
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