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Origin of Symmetries and Symmetry-breaking in Physics Sylwester Kornowski
Abstract: The fundamental spacetime is perfectly symmetrical. In the era of inflation there appeared the four-neutrino symmetry. The CPT symmetry is incomplete so wrongly understood. Symmetry-breaking is characteristic for the phase transitions of the fundamental spacetime based on the half-integral spin constancy. The matter-antimatter asymmetry is due to the fourth phase transition of the fundamental spacetime, not due to a CPT-symmetry violation.
1. Introduction In paper  I described the cause of the big bang. The ultimate theory should start from infinite nothingness and pieces of space. Sizes of pieces of space depend on their velocities , . The fundamental spacetime arose as the liquid-like spacetime due to collision of big pieces of space. In the era of inflations, the liquid-like spacetime transformed into perfect gas composed of superluminal pieces of space – they are the gravitationally massless tachyons carrying the inertial mass only that depends on their volumes. The fundamental spacetime is surrounded by timeless wall . The collisions of the tachyons with the timeless wall are perfectly elastic. This means that the initial conditions concerning the fundamental spacetime are invariant. The fundamental spacetime arose from some timeless region of very big piece of space due to the energy-inflow caused by the squeezing of this piece during the collision. We can see that the inflation started from timeless state but it is not true that we cannot say about time before the beginning of the inflation. Just there was the external time associated with motions of the colliding big pieces of space. In physics, geometry is associated with spacetime, more precisely, with the perfect gas composed of the moving pieces of space. I assume that the Occam’s razor says the true i.e. that ultimate theory should start from simplest ideas and should contain least number of assumptions. In saturated geometry  a reference frame should consist of only three perpendicular/orthogonal directions. This means that there can be maximum 6 semi-axes tagged in couples. This means that phase space of the moving pieces of space should contain maximum 6 elements that describe position, shape and motions of the pieces of space. Our knowledge of Nature leads to conclusion that the 6 elements should be the 3 spatial coordinates (x, y, z), mean radius (r) of the pieces of space that defines their mean inertial mass, their mean linear velocity (v) that is directly associated with time, and their mean angular velocity (ω) that on higher levels, due to the phase transitions of the fundamental spacetime, leads to the internal helicities of the Principle-of-Equivalence particles. It is the
2 saturated geometry. From such spacetime, from such conditions should start the ultimate theory and it is in the Everlasting Theory . The first phase transition of the fundamental spacetime leads to closed strings. Their phase space contains 10 elements. The second phase transition leads to the Einstein-spacetime components. Their phase space contains 26 elements. It is not true that the 10 - 4 = 6 are the higher spatial dimensions . I will prove that the observed symmetries follow from the invariance of the initial conditions whereas the symmetry-breaking is associated with the phase transitions of the fundamental spacetime. 2. The fundamental symmetries 1. Invariance-symmetry: translation in time; conserved quantity: energy It follows from the fact that both the mean kinetic energy of all tachyons, i.e. of the free and bound tachyons, and the mean rotational energy cannot change in time. The invariance of the initial conditions leads to the law of conservation of energy. We can define the universal unit of time as the mean time between the collisions of the all free tachyons. Such global unit of time is invariant. Local units of time, due to the gravitational fields, can vary. In stronger gravitational field fundamental spacetime is more stretched so time is going slower. But due to the tremendous pressure in the fundamental spacetime (in approximation 10180 Pa ) and constancy of the volume of this space as a whole, the state of the fundamental spacetime does not change under the translation in time. 2. Invariance-symmetry: translation in space; conserved quantity: linear momentum Due to the elastic collisions of the tachyons with the timeless wall, the mean linear speed of all tachyons is invariant in time. The same concerns the mean volume of all tachyons that is directly proportional to their mean inertial mass. From it follows the invariance of the product of the mean inertial mass and mean speed i.e. the invariance of linear momentum. 3. Invariance-symmetry: rotation in space; conserved quantity: angular momentum The mean size of the tachyons and their mean angular velocity are invariant so the product of the mean inertial-mass of tachyons, their mean spin speed and mean radius, i.e. their mean angular momentum, is invariant. 4. Invariance-symmetry: coordinate inversion (P); conserved quantity: spatial parity This symmetry is wrongly understood. Due to the first phase transition of the fundamental spacetime (it was at the beginning of the inflation), the mean linear speed of the bound tachyons “split” into the invariant spin speed of the closed strings  and the mean linear speed of the closed strings. The spin speed of the closed string and the mean angular speed of the bound tachyons lead to the internal helicity of the closed strings. Since the perfect symmetry of the fundamental spacetime must be invariant so the closed strings appeared as multiple-twin quadruples. Spin of each closed string is half-integral . In a pair of the closed strings the spins of the components are parallel (their directions overlap) whereas the internal helicities are opposite. It is obvious that such configuration of the components cause that the pairs are most stable. This means that spin of a pair is equal to 1. Since total spin must be equal to zero then there were produced the pairs of pairs with opposite spins of the components of a quadruple. The quadruple symmetry is very important in Nature . Denote the helicity inversion by H whereas the spin inversion by S. Then the coordinate inversion P of a closed string is P = HS. Assume that direction of spin of a closed string does not cross plane of a mirror. Then under the mirror-reflection inversion, there change the signs of both
3 the H and S, i.e. the coordinate inversion P of closed string is invariant. It is characteristic for the all fermions that appear due to the succeeding phase transitions of the fundamental spacetime. They are the neutrinos, electrons, baryons and the protoworlds that appeared after the era of inflation . This means that there is valid the four-neutrino symmetry . 5. Invariance-symmetry: charge conjugation (C); conserved quantity: charge parity This symmetry is wrongly understood. Due to the second phase transition there appear the weak charges of neutrinos whereas due to the third phase transition there appear the negative and positive electric charges . To change a negative charge into its positive charge we must change only sign of the global internal helicity H  i.e. C = H. We must as well change the senses of the local spins of the components of the charge  but it does not change the charge parity. 6. Invariance-symmetry: time reversal (T); conserved quantity: time parity This symmetry is wrongly understood. Due to the first phase transition there appeared the spin speed and the internal time of a closed string is defined by the sense of spin. It is because the time is defined by some unit of time associated with linear motions. In the fundamental spacetime it is the mean time between the collisions of the tachyons whereas for the closed strings it can be the period of spinning. This means that the “time reversal” means “spin reversal” i.e. T = S. This concerns the all fermions that appeared due to the phase transitions of the fundamental spacetime. 7. Invariance-symmetry: CPT; conserved quantity: product of parities This symmetry is wrongly understood. On base of the points 4-6, there is satisfied following formula for a fermion and its antifermion: CPT = HHSS = H2 S2 = 12 12 = (-1)2 (-1)2 = 1 (always). (1) This means that symmetry-breaking of a system composed of fermion-antifermion pairs is impossible. The observed in our Universe the baryon-antibaryon asymmetry does not follow from a CPT-symmetry violation. This leads to conclusion that the observed baryon-antibaryon asymmetry did not appeared in the era of inflation. The observed baryon-antibaryon asymmetry follows from the fact that due to the second phase transition there appeared the Einstein spacetime composed of the neutrino-antineutrino pairs. Due to the fluctuations in the Einstein spacetime and due to the fourth phase transition of the fundamental spacetime, there appeared the four protoworlds that total spin and total internal helicity was equal to zero. Our Universe arose due to the evolution of one of the four protoworlds. Our Protoworld had left internal helicity and such internal helicity have neutrons so their production was preferred. Today we do not see any internal helicity of the Universe. It is due to the inverse phase transitions that caused the exit of our Universe from the black-hole state. All these phenomena in detail are described here . 3. Summary The fundamental spacetime is perfectly symmetrical. In the era of inflation there appeared the four-neutrino symmetry. The CPT symmetry is incomplete so wrongly understood. Symmetry-breaking is characteristic for the phase transitions of the fundamental spacetime. The matter-antimatter asymmetry is due to the fourth phase transition of the fundamental spacetime, not due to a CPT-symmetry violation.
4 References  S. Kornowski (17 March 2013). “Infinity, Spacetimes and the Origin of Nature”. http://www.rxiv.org/abs/1303.0124.  S. Kornowski (3 December 2012). “The Everlasting Theory and Special Number Theory”. http://www.rxiv.org/abs/1203.0021 [v2].