ENTROPY ANNIHILATION IN VORTICES

ENTROPY ANNIHILATION IN VORTICES1 Preface The impressive turntable experiment is well known, in which a slow turning movement can be transformed into a very rapid one by pulling-in the outstretched arms. In the same way, a skater generates kinetic energy during a pirouette. With the equations (1) and (2) this fact is shown based on the conservation of angular momentum. The kinetic energy of a vortex also increases when mass particles are brought closer to the vortex axis. For reasons of energy conservation, the (needed) work to be done against the centrifugal forces therewith must (be in) agree(ment) with the increase in kinetic energy. If the vortex is compressed/compact(ifi)ed by external pressure forces, the shearing stresses, (i.e.?) the viscous forces, have a retarding/delaying and dissipative effect. Surprisingly, the shear stresses behave/act in the opposite way when the force is reversed, i.e. when the external over-pressure is replaced by the internal under-pressure. The then spontaneously accelerating and spontaneously contracting vortices receive the energy required for this from the store of internal energy, because with increasing speeds is associated (an) increasing cooling. The process is inverse to the generation of frictional heat, it is anti-dissipative and, contrary to the usual/common interpretation of the 2nd law of Thermodynamics, entropy-destroying. Spontaneous vortex acceleration sets in when a certain threshold condition is exceeded or an external force field acts, which can be entirely/fully static and conservative. Applied vortex physics leads to a new concept for nuclear fusion. C O N T E N T S: T h e s t a n d p o I n t ………………………………………………………………………………………………………….. 2 T h e v o I c e o f a r e a d e r …………………………………………………………………………………………… 5 T h e m o s t I m p o r t a n t v o r t e x l a w s / s t a t e m e n t s …………………………………….. 6 F u s I o n ………………………………………….…………………………………………………………………………………. 23 L I t e r a t u r e …………………………………………………………………………………………………………………… 25 1 Translation (with remarks provided in the footnotes) by S. Nedić (finished on August 26, 2022) of the first Section of the book of articles/materials “Die Welt der Wirbel und Atome - Der wissenshftliche Nachlass von Dipl.Phys. Wilhelm M. Bauer,” Band 1, DELTA PRO DESIGN UND VERLAG GmbH, Wilhelmsaue 31, 10713 Berlin, as the reprint from the previous Edition published by the WERKSTADT FUER DEZENTRALE ENERGYEFORCHUNG e.V. Berlin in 1996; for convenience of the reader, the scanned copies of both Band 1 and Band 2 are made available at https://www.dropbox.com/sh/29kl9391bzdfpas/AACgqEZMtDmK9w2oItTXA55Fa?dl=0 The Standpoint Many have recognized what the importance explicatory power has the immaculate conception of God's omnipotence with the emperor's new clothes, the arsenal of weapons, voluntary community service, the social market economy, civil liberties, Western culture, exorcism. Findings of this kind are better be kept to oneself because of legal or practiced professional bans and other harassments. Great thinkers fought against unreasonableness, superstition and popular deception without being able to, for example, even merely stop the religiously motivated genocides. The situation is similar with modern physics, which nowadays resembles a creed. Many have recognized that it rests on pillars erected on swamp, but most remain silent. An exception are celebrities like Mohorovičić, the Nobel Prize winners Soddy and Lenard, of whom there is so few (so) that they can be ignored by the scientific hierarchy, and a handful of rebels who recognize the basic errors/flaws/mistakes of modern physics, but mostly do not have the necessary tools for the way out of the impasse. In order to intimidate them, to silence them and to deprive them of their financial existence, a certain ritual is practiced, as the author can testify from his own long-term, painful experience. Human is not free, he/she is subject to social and material constraints/enforcements from the cleaning lady to the president, from the rebel to the Holy Father. Even against his better judgment, Carter cannot admit that the Israelis are militant racists, guilty of atrocities and whose right to their fathers' land goes back much further into the past and is far more questionable than that of Cubans on African soil, which they don't even claim for themselves. Can the Pope affirm communism while condemning capitalism? Can Brezhnev become a Catholic if he wanted to? Physicists are also people who are subject to constraints. Anyone who works in the nuclear industry cannot publicly speak out against nuclear power, and a physics professor who spreads his tales of lies clinging to his teaching post has to avoid factual criticism. When reason becomes inaccessible to a whole caste, they dig their own grave. The priests have been driven out, the pastors are beginning to die out, the idiotic feudal nobility have been forced to abdicate, and the students will shut up no less idiotic professorial despots. This publication is primarily aimed at physics students, but also at graduates, autodidacts and anyone who wants to form their own opinion about the development status of classical basic/fundamental physics. Secondary school level knowledge of mathematics is required. Modern physics rests on three pillars: the theory of relativity, quantum mechanics and quantum statistics. People stick to the theory of relativity because experts like Prof. Sexl, lacking sufficient knowledge of classical physics, can only derive certain empirical facts relativistically, but not classically. The theory of relativity is based on the assertion that the vacuum speed of light cannot be exceeded. This claim is false, even when using appropriately manipulated units of measurement and measurement procedures. The theory of relativity only achieves useful results in a few special cases. The speed of propagation of an electrical signal when using silver or gold wires is greater than the speed of light in a vacuum. In all media with an optical refractive index less than one, such as fuchsin(e), the speed of light is greater than in a vacuum. Quantum mechanics, the practical importance of which is vastly overestimated, has as its object a way of representing that expresses probabilities. It can be applied to anything and everything and is therefore seen as a kind of basic principle, with classical mechanics then being only the borderline case of certainty. Quantum mechanics does not shed any light on the processes in the atomic nucleus; these processes can only be understood and quantitatively clarified on the basis of classical vortex concepts. The same applies to processes in the gravitational field, in electric and magnetic fields, for chemical bonds and the structural analysis of crystals, even if the opposite is often claimed or only insufficient computer performance is blamed for the failure of quantum mechanics. The quantum-mechanical method stands and falls with the uncertainty relation, whose range of validity is not unlimited. For determining the position of an atom emitting Mossbauer radiation, the uncertainty principle delivers completely unrealistic results. Quantum statistics adopts the 2nd law of thermodynamics from classical statistics and therewith an incorrect entropy law. It stands in contradiction to the chemical reaction kinetics, in particular of cyclic compounds, to botanical processes and elementary life processes, to rubber elasticity and to the mechanical behavior of other polymers. Last but not least, the adherence of modern physics to the universal validity of the 2nd law (of thermodynamics) leads to a cosmic world view that lacks any scientific approach. With the 2nd law of thermodynamics the modern physics claims that the entropy of a closed system can only increase, so that the destruction of entropy is fundamentally impossible. In contrast, the present work shows that entropy annihilation always occurs when vortices spontaneously accelerate under suitable conditions. Vortex processes form the basis not only of flow theory, the theory of flow resistance, turbulence and cavitation, meteorology and other parts of astrophysics, but also of classical electrodynamics and the classical theory of atoms, particles and atomic nuclei. The present work is an abridged version of earlier works by the author, in particular: "Mechanik elektromagnetischer Vorgänge" (Mechanics of Electromagnetic Processes), Zürich (1965), "Wirbelphysik" (Vortex Physics) Salzburg (1975), and "Quantum Physik" (Quantum Physics), Salzburg (1978). Salzburg, August 1978 The voice of a reader Professor Mohorovičić, discoverer of the - after him named - layer inside the Earth and among other things author of the section “Optik bewegter Körper” in the Handbook of the Physical Optics (physikalischen Optik), by E. Gehrke, Leipzig (1928) writes: “Highly esteemed dear college, A short time ago I received your instructive book "Mechanik elektromagnetischer Vorgänge" (Mechanics of Electromagnetic Processes), which I studied with great interest. I would now like to congratulate you on this very successful work, in which you rightly have revived the Vortex Physics. Therefore please have my best thanks for your mailing it to me. I will quote your investigations more often when I have the opportunity, since your work deserves to become known. With best greetings, I remain with highest esteem, sincerely yours, Stjepan Mohorovičić The most important vortex laws/statements 1) The contemporary teaching on the structure of Universe is based on false foundations. The red shift of the spectral lines of distant objects is caused by a decrease in the energy E of the light quanta, which is proportional to the light frequency, on their long journey through the by no means empty space ( E=hν ). An interpretation of the red shift by the Doppler effect lacks any justification. Cosmic cyclical processes are determining/determinative for all world events, without beginning and end. Fantasies of a primeval explosion, an expansion of universe, and the (universe) heat death are on a par with religious delusions. 2) Cosmic cycle processes are made up of the well-known dissipative sub-processes and a hitherto incomprehensible anti-dissipative sub-process, which appears (comes to be) as (in form of) the spontaneous vortex acceleration. 3) Spontaneous vortex acceleration is the reverse process of generating frictional heat. The occurrence of spontaneous vortex accelerations is not compatible with the usual/common orthodox interpretation of the 2nd law of thermodynamics. Meteorology professor Starr (MIT) believes that he can eliminate this contradiction by introducing a negative viscosity. Despite his high reputation, his book “Physics of Negative Viscosity Phenomena” (1968) was however met with only flat/outright rejection. 4) When compressing a vortex - e.g. during fuel vortexing in a diesel engine - kinetic energy E is generated because when the center distance r is reduced, the velocities w of the mass particles m increase due to the conservation of the angular momentum J: J = m r w , w = const / r (1) m w2 E= = const / r 2 (2) 2 5) Contrary to other experience, in the process of vortices compression produced is not heat but cold. The heat released is transformed into kinetic energy. In the case of spontaneous vortex acceleration, the released heat is the only source of the generated kinetic energy. The facts are impressively demonstrated by Kapiza's turbo detander for air liquefaction, with which not only liquid air is produced on a large scale, but also electricity is generated at the same time by driving a generator. While the air flows radially outwards in turbo compressors, a pressure difference in the ‘detander’ forces the reverse flow direction. (Overall efficiency 80 percent.) 6) Indicative of the general ignorance of vortex issues is the ignorance of a part of the energy that is characteristic of vortex processes, the vortex energy E γ . This is a result of the erroneous view that Euler's acceleration equation for turbulent, stationary flows cannot be integrated. The Bernoulli equation resulting from the integration of Euler's equation contains when applied to vortex-afflicted, stationary flows, an (closer) undefined constant B, of which one only knows that it changes its value from streamline to streamline. Since the path integral of an acceleration represents energy referred to mass, (that) B and the other terms of Bernoulli's equation are/represent the (to mass referred) energies. As the author was able to explain to his supervisor in painstaking detailed work – w x Curl w for turbulent, stationary flows allows to be derived from a potential which, as a path integral of an acceleration, represents an energy referred to the mass, the vortex energy E γ , and which is identical to the Bernoulli's constant. 7) The calculation of vortex processes is based on the following partial energies referred to the mass: ∫ Kinetic energy: w2 / 2 = a ds Potential energy (pressure work): Internal energy: Enthalpy (heat content): Energy transferred by shear stress pv Vortex energy: u = p v /( κ − 1 ) i = u + pv q Eγ = − ∫ (w x Curl w ) d r , whereby a is acceleration and κ denotes the ratio between the specific heats (the heat capacity ratio at constant pressure and at constant volume). Additional partial energies have to be taken into account when mixing occurs or when phase transitions occur. Heat conduction and heat radiation are usually negligible in vortex processes. It applies on the one hand the energy law/statement (principle of energy conservation): w2 d + d i + d Eγ = d q , 2 and on the other – the Vazsonyi equation: d q = T d s = d i0 + d E γ . (3) (4) Here, T is the absolute temperature, s – the entropy referred to mass, and i0 is the enthalpy of the stagnation(zero in-/outflow velocity?)/stationary (pressure, volume, temperature?) point (boiler state/condition?). In (3) and (4) d q represents (stands for) the total(/absolute?) differentials. Considered over the whole space/volume, the incoming and outgoing works are balanced : ∫ q dm = 0. (5) Unbalanced however in general are the produced and annihilated entropies: ∫ ds = ∫ dq > or < 0 T (6) In the case of spontaneous vortex acceleration, entropy annihilation predominates. 8) For reasons of conservation, angular momenta can only arise and disappear pairwise, whereby the angular momenta belonging to a pair must be of opposite(ly) equal magnitude(s). If in a gaseous medium a mass has angular momentum, this angular momentum can be distributed under (due to) the effect (influence) of viscosity. The mass can come to still-stand. With constantly retained angular momentum, however, the velocities can also be increased through the compressing effect of external pressure forces, so that a stable vortex is formed as a result. The process, which has not been understood so far, is basically simple if broken down into a series of sub-processes that go (over) from one into another: I. Start(ing) phase/stage: Shear stresses act in the sense of the displacing/pushing/ousting(?) of the vortex lines ( Curlw - lines) and their collection into the vortex core. A potential vortex gets formed. In the case of compression/densification by external pressure the mechanical compression work is no longer converted only into heat, but also into kinetic energy. In spite of the accelerations, the angular momentum remains substantially preserved. The potential vortex remains a potential vortex. Compression/dansifying/compactifying proceeds/occurs adiabatically. The entropy is constant, the temperatures rise. The energy law applies: w2 d + d i = d i0 = p d v 2 (7) w2 + i = i0 ( t ) 2 (8) The dependence of the kinetic energy and the enthalpy on the reciprocal square of the distance from center for the consecutive points in time is shown in Fig. 1: II. Fig. 1. Threshold(ing) phase: There is a certain state that must be passed over in order for the velocities of a vortex to spontaneously increase, with concomitant cooling, until the steady state is reached. After this threshold has been overcome, the initial compression triggered/caused by external pressure forces turns into an independent (working on its own) compression/’compacting’. A corresponding automatic contraction experiences an electric current in a conducting plasma (pinch-effect), whereby the analogy is not an accidental one, as can be shown on the basis of classical conceptions/notions. The threshold is not a steep wall, but rather comparable with (resembling) a flat hill. During the unstable start-up phase, the vortex returns back to the quiescent state, when the external forces cease to act. In the stabilizing end-phase, the vortex continues to develop independently of external influences until the stationary end state is reached. In between lies a broad indifferent region, in which vortices left to their own (device) behave largely stationary, without being subject to the viscosity of the medium. For example, vortices can be observed as produced by smokers - moving unchanged and at a constant speed over tens of meters. III. Final phase: The Vazsonyi equation (4) applies to the spontaneously accelerated final phase. Its representation in the p v -diagram lies flatter than the isotherms. Densification/compactification along the Vazsonyi-line is consequently associated with cooling, whereby the released heat contrary to the usual interpretation of the 2nd law (of thermodynamic) - is immediately transformed, under/with/along annihilation of entropy, into kinetic energy. In a Laval-nozzle, the speed in the narrowest cross-section is critical and thus in amount equal to the local wave speed (speed of sound propagation) referred to the co-moving coordinates. If one transfers this fact to the conditions in a vortex, one recognizes that when a vortex is densened/compact(ifi)ed by internal or external forces the critical speed cannot be exceeded, since otherwise, as in the Laval-nozzle behind the narrowest cross-section expansion would occur, which/what in a vortex - for reason of the angular momentum conservation - would be associated with reductions in velocities. At supersonic speeds, behind the narrowest cross-section of the Laval nozzle, can occur compression shocks and thus vortex formation. The same applies when the velocities at the core boundary of a vortex become critical. The oblique compression shock that forms has however/though properties that differ in part from known compression shocks. a) The mass passing through the compression shock, at the core boundary, increases the mass of the core, so that the pressure and density of the core increase, the shock is thus not stationary. b) b) As the vortex approaches its stable, stationary state, the compression shock transforms into a vortex layer, the Vazsonyi layer. c) Stagnation/stationary point enthalpy and stagnation/stationary point temperature are not preserved in the densification/compacting shock at the core boundary, in contrast to other shocks. This follows from the Vazsonyi equation (4) because of the generation of vortex energy and the annihilation/’destruction’ of entropy. d) Since the rotation/curling of the velocity disappears in the potential vortex and since vortex lines ( Curl w - lines) in the core of the Beltrami flow and streamlines run parallel, the Lamb vector disappears both in the potential vortex and in the core. The occurrence/appearance of the Lamb vector − w x Curl w is thus concentrated on the extremely thin shock front i. e. the Vazsonyi layer between the potential vortex and the core. In contrast to other compression shocks, comparatively strong, radially aligned forces emanate from the shock front and Vazsonyi layer, which cause the pressure and density ratio in the stable end state to be several orders of magnitude greater than would correspond to the Hugoniot curve. 9) Vortex rings migrate/move, with the ring plane generally being perpendicular to the direction of translation. The speed of translation w t can be changed by external influences. Stationary(ly) , (to) each translation speed is assigned a specific ring diameter. An infinitely large ring diameter would correspond to the state of rest. When a vortex ring encounters a flat obstacle, it expands until it is destroyed. In general, the stationary ring diameter is inversely proportional to the translation speed. The same applies to the mostly axis-parallel flow component of a vortex ring, which is predominantly concentrated in the core. It alone determines the resulting intrinsic angular momentum or spin of the vortex ring. If the diameter of the ring-shaped core changes, then its axial flow velocity also changes in the inverse ratio due to conservation of angular momentum. Translational speed and axial speed therefore change proportionally and both speeds are of the same order of magnitude. Irrespective of the particular translation speed, in the stable, stationary state the core volume must have a minimum value. The speed in the core must therefore be critical. With comparatively small translation velocities and thus also small axial velocities, this is only possible if the stagnation point enthalpy of the core i0 is greatly reduced compared to the stagnation point enthalpy i00 of the environment, i.e. (that is) corresponding changes in the vortex energy and entropy occur in the Vazsonyi equation (4). With normal compression shocks, the increase in density outweighs the increase in pressure, i.e. the pressure decreases faster than the specific volume increases. The result is that with normal compression surges/shocks, the product pv decreases, so the temperatures drop. In the case of compression shocks at the core boundary, the situation is reversed as soon as, in contrast to ordinary compression shocks, the enthalpy of the stagnation point decreases significantly, due to (conditioned by) the generation of vortex energy and the annihilation of entropy. A lowering of the stagnation point enthalpy occurs when - at/with the vortex compression/densification/ompating due to external causes - the velocity at the core boundary becomes critical. If the translational speed of the vortex is overcritical, then a normal compression surge/shock connected with a Mach cone is created. Behind this surge/shock, the speed in relation to co-moving coordinates is again sub-critical, until it may again become critical at the core border/limit. In pv -diagram the starting phase shows up as thermodynamic adiabate, while the final phase is represented by the much flatter Vazsonyi line. Their intersection is the critical point of the adiabate. It represents the state in the threshold phase. 10) The three phases according to point 8) can also be understood from the effect of the shear stresses: In the initial phase I, the shear stresses act as expected for a medium with nonvanishing viscosity as is to expect upon (as per) the Navier-Stokes equation, i.e. the vortex accelerations and an associated generation of kinetic energy require external pressure forces. In the starting phase II, however, vortices behave unexpectedly as if the medium had no viscosity. A mass with the density of a smoking ring can be moved in air for tens of meters without a drive/impetus and with constant speed only when it forms a vortex ring which is in the threshold phase, that is after passing through the final phase, (it) has reached the stable final state. The Navier-Stokes equation is a vector(ial) acceleration equation. The vector component given by the so-called dissipative term becomes ineffective when it is perpendicular to the direction of velocity and is balanced by an opposing pressure gradient. In the starting phase I, the vector given by the dissipative term rotates starting from a position in the opposite direction to the speed, up to its perpendicular position as it reaches the threshold phase II. In the starting phase the shear stresses therefore have a retarding effect. In the end phase III, the vector continues to rotate so that it gains/gets a component that falls in the direction of the speed and thus has an accelerating effect. With approaching the final stable state, it turns back again, to eventually be standing vertically to (the) speed (vector) again. In the final phase, shear stresses thus do not have a decelerating effect, but rather the accelerating one. Therewith the known friction/viscosity effect transforms into its opposite. Starr rightly speaks in this context of negative viscosity and he would have been guaranteed (himself) immortal fame if he had grasped its true nature and had not attempted to make the phenomenon compatible with the customary, incorrect interpretation of the 2nd law. As it is, however, Starr only uses the negative viscosity as a lurid/’sensational’/garish lead-in/prelude/stage for a/the vortex strengthening postulated by him through the merging of many small sub-vortices. 11) The common/usual interpretation of the 2nd law excludes spontaneous vortex acceleration. With Boltzmann, one is of the opinion that the completely disordered state of gas, absolute chaos, has the greatest probability and that the viscosity of flowing media necessarily increases the disordered, thermal movements, and accordingly reduces the ordered movements associated with the kinetic energy of the flow. In the most probable state, state of rest understood as heat death, all the kinetic flow energy would thus disappear. On the other hand, it principally holds that the potential energy tends towards a minimum during stabilization processes. In a flowing medium, the potential energy is proportional to the work pv of the pressure forces. Their minimum corresponds to a maximum of kinetic flow energy. With/at the shown/proven presence of stabilizing forces, it thus is not the state of rest, but the state of movement which/that autonomously (on its own) occurs/establishes (takes place) independently of external influences. Entropy annihilation, anti-dissipation, negative viscosity, self-acceleration are just different names for the same thing. Their reality is not decided by an unfounded postulate of probability. Much more decidable/decisive is the fact that under suitable conditions the acceleration a d given by the so-called dissipative term of the Navier-Stokes equation can generate kinetic energy. This is not possible with an expanding vortex, because then decrease in kinetic energy associated with the conservation of angular momentum predominates. If, on the other hand, the velocities in a vortex compression have a component directed towards inside, the vector a d , insofar as it has a component falling in the direction of the velocity, results in an additional acceleration, associated with the kinetic energy increase. The direction of the vector a d results from the directions of the vector parts Grad Div w and − Curl Curl w . For reasons of symmetry, the vector part Grad Div w for/at positive divergence, i.e. with expanding vortices, is directed outwards, and for/at/with negative divergence – inwards, that is it always has a component falling in the direction of velocity. The vector − CurlCurl w can also have an accelerating effect and increase the kinetic energy. In the vortex core, the streamlines ( w -) and the vorticity lines ( Curl w - lines) are coiled/wounded around the vortex axis. In a right-handed vortex, the stream and vorticity lines are in the same direction, in a left-handed vortex they are in opposite directions. With right-handed helicity (right-hand wound helix) of the vorticity lines and left-handed(ly) wound vortices, the vectorpart − CurlCurl w has a component falling in the direction of velocity, as long as the conditions are not stationary and the vector part (then) is perpendicular to the direction of velocity. The same applies to right-handed wound vortices with the left-handed helicity of the vorticity lines. In the surrounding potential vortex, Curl w disappears and with it the vector part − CurlCurl w . The effect of the vector-part − CurlCurl w in the vortex core boundary layer results from its structure: On the inside of the boundary layer created by a compression shock, the tangential velocity is smaller than on the outside for reasons of (angular) momentum conservation. Viewed at in the cross-section, the speed difference is perceived (taken up) like/as (in the way/art of) a ball bearing – through thin vortex threads that are coiled(-up)/wound around the core and, for example in atomic vortex rings, appear as neutrinos. Within these threads − CurlCurl w 'acts'/works/performs in the same way as in the core. In the steady state is Grad Div w = 0 , and the partial vector Grad Div w vanishes. In the non-stationary case, during the formation or annihilation of a vortex, with cylinder/cylindrical symmetry and the radial velocity component wr applies: Div w = wr dwr + . r dt (9) To determine the wr as a function of r, the flow for the instant under consideration can be considered as a stationary vortex source or sink, that is to say (the) superimposition of a stationary vortex and a stationary source or sink flow. From the equation of continuity then follows2 with the radial velocity wr = component wr : q , 2 r πρ (10) where the (shear-!?) yielding q per unit length is positive for expansion and negative for contraction. The radial distribution of the density ρ depends on the type of instantaneous state change. It is initially adiabatic, then approaches the isotherm and finally, in the end phase, goes over (in)to the Vazsoniy change/alternation. Bearing this in mind, one can set/formulate ρ with the variable χ : ρ= C . rχ (11) It follows with the constants contained/encompassed in/by k : 2 In derivation from the presumed use of (26), with time-independent density, an integration constant might be missing, namely after integration of dwr dr dρ =0. + + we r r wr = k r χ−1 (12) Div w = k r χ− 2 + k (χ − 1) r χ− 2 = k χ r χ− 2 = k χ r χ− 2 ( ) Grad Div w = k χ 2 − 2 χ r χ−3 r0 . (13) (14) In the case of vortex compression/compactification, k is with (negative) q also negative, and the same applies to the expression in brackets between χ = 0 and χ = 2 . In order for the vector part Grad Div w of the viscosity term of the NaiveStokes equation to be directed inwards, χ must therewith be greater than two. The process of vortex formation is a comparatively slow process. Therefore, to answer many questions, the instantaneous state can be regarded as stationary and the viscosity (can) be neglected. Instead of the Navier-Stokes equation, Euler's equation then applies: a = − v Grad p . (15) In the stationary state, the acceleration a is directed radially inwards and in the potential vortex with the velocity3 C / r the following applies4: C 02 a=− 3 . r (16) C02 dp = −v . 3 dr r (17) With (15) it follows: In order to be able to integrate (17), p must be known as a function of v . With the polytrophic exponent n , the polytrophic equation applies: p v n = p0 v0 = const . (18) p v = C1 v − n (19) n 3 This shouldn’t be the same constant as in (11); likewise C 0 , as in the sequel … !? 4 It is not clear as to why is that so – shouldn’t there figure r 2 instead of r 3 !? dp = − C1 n v − n−1 dv , (20) and in connection with (17)5: C02 − dr = −C1 n v − n dv r3 (21) n 1 v − n+1 = −C 2 2 − n +1 r v = C3 (22) 1 r (23) 2 /( − n+1 ) ρ = C3 r 2 /( − n+1 ) . (24) Between the variable χ and the polytrophic exponent n thus exists dependence: χ= 2 . − n +1 (25) At χ = 2 , as has been shown, the vector-part Grad Div w changes its sense of direction. If it falls below this value, it has a compressing/’companding’ effect and thus the self-accelerating one. According to (25), the value χ = 2 corresponds to the polytrophic exponent n = 0 . If, in the case of initially adiabatic vortex compression – with n equal to the ratio κ of the specific heats – the pressure in the interior of the vortex is/gets increased so far that it remains constant, the further state changes at the core boundary thus taking place isobarically, the retarding effect of the vector-part then changes into an anti-dissipative, entropydestroying/annihilating self-acceleration. The self-accelerating effect of the partial vector Grad Div w = 0 results also from the density distribution. With the continuity equation: Div (ρ w ) = ρ Div( w ) + w Grad(ρ ) = − for the vector-part follows: 5 Missing integration constant in (22). ∂ρ ∂t (26)   1 ∂ρ w Grad Div w = − Grad  + Grad(ρ ) .   ρ ∂t ρ (27) This vector is directed inwards and is therefore self-accelerating if the expression in brackets is positive. With each vortex compression/compactifiation, the local density change ∂ρ ∂t is positive, (being) most pronounced in a compression shock at the core boundary. Since the density itself cannot become negative, the first term of the expression in the brackets is necessarily positive. The second term becomes positive when Grad (ρ ) is directed inwards, (i.e./thus/so) the density increases as the distance between the axes decreases. A/the/one condition that though is not fulfilled in the isoenergetic potential vortex, but by far is fulfilled in a compression shock at the core boundary. Since the velocity in vortex compression has an inward directed component, the scalar product of w Grad(ρ ) also becomes positive for/at/with the inward directed (density) gradient. In summary, one can say that spontaneous vortex acceleration is fundamentally possible and always occurs in gas vortices when the speed of compression through external forces reaches the critical value and a compression shock forms at the core boundary. In the/that process, unordered heat movements are transformed into ordered flow movements, entropy is destroyed, the total entropy of the system is thus reduced and the validity range of the 2nd law of thermodynamics is to be (can be) restricted accordingly - even if the faculty members do not like it. 12) As the stable final state is approached, Div w disappears and with it also the partial vector Grad Div w . The pressure gradient built up by it and the centrifugal force are then balanced by the Lamb vector − CurlCurl w , i.e. (by) the gradient of the built-up vortex energy E γ . The seat of the Lamb vectors is the Vazsonyi layer, since in the core the stream and vorticity lines run parallel and in the outer potential vortex Curl w disappears. In the final state the highly compressed core is held together by the Vazsonyi layer, which creates a kind of surface tension. 13) The described spontaneous self-acceleration and stabilization of vortices is not tied to any external conditions, apart from the initial conditions. There is also a second type of spontaneous vortex acceleration, which requires the presence of an external force field. Clear statements can be made about self-acceleration in centrifugal fields, gravitational fields and combined centrifugal-gravitational fields such as on the Earth's surface, in full agreement with the available observation material. Nothing is currently known about self-acceleration of vortices in electric and magnetic fields. 14) A centrifugal force field can easily be generated, e.g. in flat tubes on turntables or in cylindrical vessels rotating around their axes. Due to the viscosity of a gas, which in any case does not disappear, one is mistakenly of the opinion that in a vessel rotating at a constant winding speed, an enclosed gas, but also a liquid, finally comes to rest with respect to the walls, i.e. carries out a rigid rotation. Experience, in particular the experiments of G.I. Taylor (1923), show that this is not the case, i.e. that gas forms stable stationary vortices in rotating vessels with respect (referred) to co-rotating coordinates. If the vessel walls are made nonpermeable to heat and if the steady-state shear stresses (being) 'absorbed' by the walls are neglected, the contents of the vessel can be regarded as a closed system whose stable state is characterized by a minimum of potential and a maximum of kinetic energy. Therefore, under certain restrictive conditions related to the magnitude of the viscosity and the geometrical dimensions, the stable state is not the resting state. The fact that vortices can persist despite their non-vanishing viscosity according to 9) and 10) also applies in/to the rotating system. 15) If the stable, rigid rotation of a gas were possible, the centrifugal force would have to be balanced at every point by a corresponding pressure gradient. So it should apply a=− w2 r0 = − v Grad p r (28) or, since with rigid rotation the velocity w is proportional to distance from center: C r dr = v dp , (29) where the mutual dependence of v and p corresponding to the equation of state is given by a polytropic equation p v n = const . (30) For n = χ the state points lie on a thermodynamic adiabate. The entropy in the entire system then has the same constant value, which is often mistakenly regarded as a criterion for the state towards which the system, left to itself, is striving. In the rotating system, the adiabatic stratification leads to temperature differences and is therefore not stable, if only (or, already) because of the gradual temperature equalization that then occurs. Since for the same reason the state is unstable for all n ≠ 1 , only the behavior remains to be investigated when the state points lie on an isotherm, i.e. n is equal to one. If in the rotating system a mass particle is displaced in the radial direction by a temporary small disturbance, under stable conditions the original state is automatically restored. Heat conduction can be neglected during a short-term disturbance. The shifted/displaced mass particle therefore expands adiabatically if/when it is displaced inwards, while it is compressed adiabatically if/when it is displaced outwards. The pressure of the displaced mass particle adapts immediately to its new environment. Density and temperature, on the other hand, are reduced with inward displacement and increased with outward displacement. The centrifugal force of the shifted/displaced particles is no longer balanced because of the changed density caused by the pressure gradient. The resulting movements are reversible6, but only very slowly, so that heat conduction must not be neglected. Due to the heat absorbed, the density and temperature of the environment are adjusted long before the particle (had) reached its original position. Isothermal stratification is also unstable, which shows that for gases and liquids of sufficiently low viscosity there is no stable state of relative rest under the action of centrifugal forces, in the full agreement with the experience as for example Taylor's experiments with rotating liquid 6 In the original stands ‘rückführend’ (‘leading-back’, ’returning’), and not ‘reversibel’, likely due to the possible not yet adopted English word(s) by the time of writing; still, the possible more appropriate would have been the German word ‘rückkehrend’ (‘returning back’). columns show. If a conservative gravitational field takes the place of a conservative field of centrifugal forces, a stable, stationary state of motion is formed in a similar way to the rotating closed system, which is comparable to thermal or thermo-syphon cooling, and (which) is referred to as the Sama-state7. Fusion Without an understanding of atomic nuclei, modern physics uses the trial and error method in the alchemist's way. Senseless and aimless large-scale experiments grow into gigantic ones. Tax payers' billions are squandered on abominable /disgraceful deeds that make the pyramids of the pharaohs look like children's toys. Ever new sensational brought up reports in the mass media have been unable to cover up the decades-long total lack of real success. In terms of classical physics, according to W. Thomson, later Lord Kelvin, atoms are small vortex rings. The ring-shaped cores of these vortices are the atomic nuclei. Their ring diameter is comparable to the atomic dimensions and is therefore larger by a power of ten8 than previously assumed. The Coulomb barrier, which stands in the way of a unison of positively charged nuclei, becomes less important, since its effect increases with decreasing core dimensions. In the case of quantum-mechanical point-shaped nuclei, the Coulomb barrier would represent an insurmountable obstacle. Classically, the fusion of two nuclei involves the merging of their Vazsonyi layers. The energies required for this are low and not very different from the energies occurring during neutron capture. The real obstacle to nuclear fusion under normal conditions is the ubiquity of electrons. They coil around the nuclei or slip between them before fusion of the Vazsonyi layers can occur9. 7 nd This is related to [2,3], where the 2 law of thermodynamics is disproved based on the cooling of the higher layer of the atmosphere due influence of gravity; the term “sama” is the Sanskrit’s word with meaning - “the same”… 8 In original German text is stands ‘um Zehnerpotenz’, number 10 with an exponent; or, ‘several orders of magnitude’!? 9 According to the “General Aetherodynamics” (Общая Ефиродинамика, РадиоСофт 2016), of V.A. Atsukovsky, it rather are the electron layers/clouds, of the kind similar to the core’s ones, enveloping the atomic and molecular structures, as well as proton vortices to form the neutrons … for readers’ convenience, electronic versions of some previous editions, along the rough English translations of certain chapters are made available at http://www.atsuk.dart.ru/ https://www.dropbox.com/sh/b320a0is6fdc2e2/AADfjs_LnbRBSaNXfxjPkTaqa?dl=0 . The task is therefore not to generate extremely high temperatures, but to remove as many electrons as possible from a moderately heated plasma. The electrical equilibrium in a plasma is always disturbed when magnetic field lines are cut as the plasma moves. MHD generators or the earth's charge belts, named after van Allen, are examples of this. Naturally, the electrical neutrality of a plasma can also be cancelled by an electrostatic field. The classically predictable effect of a fusion reaction uninhibited by the elimination of interfering electrons could long since have been experimentally tested. The author submitted a corresponding proposal to the responsible authorities as early as 1976. A cross-beam experiment similar to the MIGMA-experiment was proposed, with two ion beams meeting at an acute angle and having different speeds, with electrostatic extraction of interfering electrons. The heavy water reaction appears possible: 2 H + + 2 H + = 4 H + + + 32 MeV . The sun's radiant energy is the converted rotational energy. At the time of star formation, the rotational energy was very large due to vortex-physical reasons. The measured rotation speed of young stars is close to the limit given by the centrifugal force. Today the rotational energy of the sun has dropped to a small fraction of its original value. The process of converting rotational energy into radiant energy is a magnetohydrodynamic process associated with the periodic fluctuations in the activity of the sun and its differential rotation. Due to the conservation of angular momentum, the process is also associated with changes in the movement of the planets, such as the tide-related decrease in angular momentum of the earth is connected with an increase in angular momentum, primarily (of) the moon. The long outdated, but recurring in popular scientific publications, assertion that the sun produces its energy by thermonuclear means only serves to justify the absurd fusion experiments. It is not different with the hydrogen bomb. Here, fusion reactions are not caused by extreme temperatures, but by disturbances in the electrical balance caused by highenergy β -radiation. In interstellar gas clouds, in which are originating young stars, the abundance of the elements, particularly hydrogen and helium, is not very different from that in the sun and the major planets. On the other hand, elements with a higher atomic number predominate in smaller planets that cool down more quickly. Consequently, fusion reactions are favored at comparatively low temperatures of perhaps a few thousand degrees. In the rotating, thermally highly ionized interior of the earth, analogous to the van Allen belts in the outer space of the earth, form two inner charge belts. Rotating with the earth, they represent convection currents, the resulting magnetic field of which forms the earth's magnetic field. Magnetic field and charge belt form a on times selfconsistent, but generally oscillating capable system. The location of the fusion reactions in the earth's interior is the outer - largely freed of electrons - of the two inner charge belts. L i t e r a t u r e10 10 For the references [3] and [4] parts of the title of the article “Die atmosphaerische Temperaturabnahme nach oben und aehnliche Erscheinungen als Wirkung der Schwereraft, der Sama-Zustand der Materie”; similarly, the title of reference [6] (Isentrope Wirbelbildung Konservtiver Kraefte) is a kind of ‘extraction of essence’ from the same dated article with the title “«Ueber einem Fall der adiabatischen Bewegung”, which is available in the book with Kochin’s works (СОБРАНИЕ СОЧИНЕНИЙ, TOM I, USSR Academy of Sciences, 1947) in Russian translation: “OБ ОДНОМ СЛУЧАЕ АДИАБАТИЧЕСКОГО ДВИЖЕНИЯ,” from page 27…