E_min < E(x) < E_crit

dR_A(t)/dt = v_f > 0

We are developing a new unification theory. Remember that any theory is only a possible solution, not a certainty, and moreover works only in narrow areas! The achievements of existing theories serve to test our theory, which must explain phenomena equally well, or even better. SPACE B (Base Crystal) B is a 4-dimensional geometric crystal structure. Dimensions of B: - 3 rectilinear dimensions (X, Y, Z) - invariant spatial coordinates of lattice points. - 1 looped dimension (W) - shaped like a circle with a huge radius, oscillates over a very long period. Lattice points in B have fixed positions in space B (do not move), but can vibrate. In B, there is no time as understood in A. Only geometry and vibrations exist. SPACE A (Our reality) A is a 2-dimensional sphere that is a projection of processes occurring in B. Observer in A sees only the "now sphere" - a cross-section of B at a constant value of the looped dimension W. Time in A is radial (propagates from the center/seed) and rectilinear for the observer. The time value (sphere radius) determines which cross-section of B we view as "now". LOOPED DIMENSION W It is looped (steady state), not "looping" during the process. The direction of value increase on circle W (clockwise/counterclockwise) defines the chirality (handedness) of the entire crystal B. This chirality is the source of right-handed preference on a cosmic scale (e.g., rotation of galaxies). We suspect that the looping was created by external forces, as happens in the cores of iron planets, where pressure and temperature force a change in the configuration of the metal's crystal lattice. For current considerations, this is not important, however it is a probable cause of the dimension looping in space B, which after analysis of physical constants in A suggests a constant structure (this directed us to the initial assumption of a phase transition in the liquid and that the crystallization wave causes emission of energy flashes, which in A we see as photons, and vibrations of crystal lattice defects, whose image are quarks and other particles - excitations of the energy field in A). Currently, we are leaning towards the process of crystal lattice melting, which we discuss here. PARABOLIC ROTATION AND TRANSFORMATION Cause of transformation A process of dimension looping occurred in B (historically). To avoid overlapping of physical points, a lattice reconstruction was necessary - parabolic rotation. Exceeding the strength limit of lattice B caused a physical shift of points in B to new coordinates, creating a structure with a looped dimension. Effects of parabolic rotation The looped dimension W becomes radial time in A. The 3 geometric dimensions of B are projected onto the 2D plane of A as follows: - Two dimensions (X, Y) form the plane tangent to the "now" sphere. - The third dimension (Z) retains its direction but has the opposite orientation (negative values). It becomes the carrier of holographic information - encodes depth. Dimensions after transformation are perpendicular to the direction of time (this explains why the universe is flat in observations). Holographic information For a point in B with coordinates (X, Y, Z, W), in A we see: - Point on the plane: (X', Y') - Holographic value: H = -Z (depth) Angles between vectors in B are projected onto A as angles between their projections, but distorted by differences in depth. This gives the impression of 3D perspective on a flat screen A. Do points in B physically change coordinates, or do only stresses appear? I will describe it step by step, including the process of looping formation: Initial state: We have B with 4 rectilinear dimensions. For some reason, stresses build up. Cause: There is an attempt to loop one of the dimensions (W). In crystal B, points cannot occupy the same place. If the dimension were to "collapse" into a circle with too small a radius, different points would start to overlap. Effect (Stresses): To prevent this, gigantic stresses arise in the crystal lattice B. This is not just an abstraction. In a crystal, stress is a physical deformation of the lattice – atoms are "pressed" into new positions, distances between them change, bond angles too. Parabolic rotation as a reaction to stresses: Exceeding the strength limit of the lattice (like in iron) causes a restructuring. Parabolic rotation is the mathematical description of this restructuring. It is a transformation of the coordinates of points in B to a new, stable system. Answer to the question: Therefore, at the moment of this phase transition (looping), the points in B PHYSICALLY CHANGE THEIR POSITION (COORDINATES) within 4D B. They transition from a rectilinear system to a system where one dimension is looped. This is a process analogous to the transformation of graphite into diamond – carbon atoms physically jump to new positions in the lattice. Final state: After this restructuring, for an observer in A, the looping is already "constant and imposed from the beginning", because A only sees the effect (projection) of this new, stable structure of B. But in the history of B, it was a dynamic process. Do the same phenomena occur in iron/carbon? Yes. A phase transition (e.g., iron alpha to iron gamma, or graphite to diamond) is precisely the change in the position of atoms in the lattice under the influence of temperature/pressure (external factors, which in B are analogous to geometric stresses). Change in packing: It changes volume. In diamond, atoms are more densely packed than in graphite. This packing absorbs energy (supplied from outside, e.g., in the form of pressure and temperature), and during the reverse transformation (diamond to graphite) it releases energy. Where does the energy go: In the case of diamond formation, energy is stored in the form of potential energy of bonds in the new, denser lattice. During diamond combustion, this energy is released. In the B model, the energy needed for looping (restructuring) comes from the oscillator system (vibrations of the crystal itself) and is "stored" in the topology of the new, looped lattice. Diamond from iron? Iron can also have allotropic varieties (different crystal structures). We don't call them diamonds, but they are different "crystals" of iron (Fe-α, Fe-γ). In extreme conditions, iron atoms can also form very dense, hard structures. Defect in diamond B as projection A: It is possible that what we perceive as fundamental laws of physics or constants in A is precisely the reflection of the ideal, flawless structure of B, which was rebuilt by the looping of one dimension in space B. HOLOGRAPHIC INFORMATION CARRIER Question: What information is carried in the dimension that retains its direction but has the opposite orientation? It's only one value for each point on the plane. Answer: It is one scalar value per point on the plane (A). But this one value encodes depth in a 3D simulation. It is analogous to a height map in computer graphics. Mathematical relationship of angles: In parabolic rotation, after transformation, in A we have: - Two dimensions from B (let's call them X and Y) form the plane tangent to the "now" sphere. Points of A lie on it. - The third dimension from B (let's call it Z) becomes "exposed" perpendicular to this plane, but has the opposite orientation (negative values compared to the original in B). Now the angles: If a point in B had coordinates (X, Y, Z, W), then in A we see: - Point on the plane: (X', Y') - Holographic value: H = -Z (this is the one value per point) The angles in question are the angles of inclination of the vector connecting two points in B to the XY plane. If we have two points in B: P1 = (X1, Y1, Z1) and P2 = (X2, Y2, Z2), then in A we see: - Their projections: (X1', Y1') and (X2', Y2') - Their depths: H1 = -Z1, H2 = -Z2 The actual distance between them in B is: dB = √[(X1−X2)² + (Y1−Y2)² + (Z1−Z2)²] In A we see this as the distance on the plane plus the depth difference: dA = √[(X1′−X2′)² + (Y1′−Y2′)² + (H1−H2)²] Angles: If H1 ≠ H2, then the vector between points is inclined to plane A. The angle of inclination θ satisfies: tan(θ) = |H1−H2| / √[(X1′−X2′)² + (Y1′−Y2′)²] And if we have a third point, the angles between vectors in B are projected onto A as angles between their projections, but distorted by depth differences. This distortion gives the impression of 3D perspective on a flat screen A. In summary: H (holographic value) carries information about "how far behind the plane" or "how far in front of the plane" point B is located at the moment of its projection. Space B is a 4D geometric crystal, considered for simplicity of the model, in which one dimension has been looped. Thus, each point in space B has specific 3 invariant spatial coordinates and a fourth oscillating over a very long time, because this circle is huge - if such a phenomenon of local looping of a geometric dimension were to occur in A, the circle of this dimension would be the size of the equator of a black hole's event horizon, but this is an illusion in A, because the entire process occurs in B. When a geometric dimension loops, due to the impossibility of physical points overlapping in the crystal, a parabolic rotation occurs (in the process of logical deduction, hyperbolic rotation was rejected), so that points do not physically overlap. Thus, in the crystal, one coordinate oscillates, which leads to the creation of an oscillator system effect. This effect is responsible for phase transitions in the crystal. The crystal heats up and energy is transported to the center. This phenomenon causes the achievement of critical energy and overheating of the liquid phase. The seed of crystallization in the phase transition becomes the central point, where interaction forces cancel out. B becomes a crystal. As a crystal, it heats up again through energy generated by the oscillator system. We have a closed cycle, thanks to the four geometric dimensions in B. Mathematics shows that at the moment of inducing parabolic rotation in 4D, it is the moment of looping the fourth dimension in B, this causes large stresses in the 3D points of space B, the transformation is forced. The transformation is physical in B and permanent. This is the beginning of space A. It can be treated as a crack in crystal B, or a change in its structure (ordering) throughout its volume. Why then does the parabolic rotation transformation occur, in which the looped dimension becomes time in A? Time is radial, because it spreads from the center (seed in B). Therefore, the remaining geometric dimensions align perpendicular to the time dimension. This causes the formation of a sphere in A with radius time, for each point of space B, but because time becomes rectilinear, in A we can only consider the 'now' sphere. The rest of the image of crystal B is in the past or future for an observer in A. The 3 geometric dimensions form the plane of this sphere, with the caveat that in parabolic rotation one dimension retains its direction consistent with the direction in B, but has the opposite orientation (values have a minus sign). We suspect that this dimension becomes the carrier of holographic information, and the remaining two dimensions from B form the planes of spheres with radii corresponding to values on the time line in A. The crystallization process in B we have developed, but we cannot verify if it is correct because we have no observations on this topic. We assume that in A, on the sphere of radius 'now', we observe the melting front of the crystal in B, which is confirmed by observations made by people. Vacuum is not empty, which would be the case if B were completely crystalline, because there would be no stimulation of the crystal lattice in B. Because in A we observe the concentration of matter into hot stars, we assume that a melting process occurs in B. We assume that melting introduces defects in the crystal lattice into growing vibrations, which are transmitted to the rest of the crystal lattice. They are not visible in A because it is the future for the observer, however in B, where there is no time, such vibrations occur, probably throughout the entire volume of the crystal - which could explain the fifth state of matter in A. The past for an observer in A is therefore the liquid phase of crystal B. Released defects of the crystal lattice B give the effect of photons in A - therefore photons have different frequencies, because defects in B are released at different rates - we are talking here about observations in A, where time flows! Dark matter in A is probably vibrations caused by released defects that do not have enough energy to produce a flash in A. We ask, whether in a sphere of metal heated from the center, do such effects occur as we observe in the sky - do concentrations of hot points form on the propagating melting front, which then merge into one liquid area (black hole in A), or do vortices form, like galaxies that we observe? Does the phenomenon of crystal lattice collapse occur, that is, does gravity appear, i.e., does the ordered crystal lattice collapse from the point of view of an external observer, because the liquid phase of the metal occupies less space? Star in A: It is an image of the region of B that is currently melting. That's why we see continuous flashes (released energy of defects and growing vibrations that stimulate the crystal lattice to create resonances) – it's the melting process. The more intense the melting, the brighter the star. Black hole in A: It is an image of a region of B that earlier, below this layer, was completely melted (liquid) and due to the decrease in volume of the crystal, the plastic crystal lattice was sucked into that place. So there is no release of defects (flashes), so we see a dark area. Instead, we see a difference in the vibrations of the crystal lattice, which in this area are more damped, because the lattice is plastic. Free space (vacuum) in A: It is an image of the not-yet-melting crystal lattice B. Because the lattice vibrates (has energy), it is stimulated by stresses from defects released in the melting process, vacuum in A also has energy (which is consistent with QED – vacuum fluctuations), because in A the image of these vibrations on the 'now' sphere are field excitations in the form of quarks. Further findings: since we are on a 2D 'now' sphere, which shows like a screen, what is happening currently, at any point on the sphere, what is happening in the mother space, with the same time value, i.e., the looped dimension - here we remember that it's a large circle, therefore changes occur slowly, this parameter changes with each moment, but the change in its value is minimal! Atoms in A do not overlap, because in B points cannot physically overlap! Collisions in A are an image (illusion) of 2D processes in 3D B! Photons, nor any other particles, do not move in A! They are successively lighting diodes in the scheme of releasing defects in the crystal lattice in B, which gives in A the effect of trembling in place and the effect of motion, but it's an illusion! Particles (quarks) in A are an image of defect vibrations in B - therefore they do not occur singly, because only a trio of defects can create a stable self-sustaining vibration system! Here we are dealing with a spatial system of defects in B! including for the observer in A from the future! This gives different vibration strengths! Those on the melting front have greater vibrations, those deep in the crystal lattice have smaller ones, but that's the future for the observer on the 'now' sphere! Proton, electron, or other particles in the understanding of other theories, in our understanding are stable resonances of defect vibrations in B! All things, matter, in A are an image of vibrations of defect systems in B and patterns forming on the melting front in B! This explains all interactions! However, a mathematical apparatus is lacking, but first we must establish a logically concise and economically justified probable version of the occurring phenomena, which we see in experiments, in observations in A. Gravitational lensing therefore is different paths of propagation of disturbances (vortices) forming on the melting front, which must go around bumps or valleys on the 'now' sphere. It's a plane, so as observers we only see segments, but with additional, holographic information, therefore it seems to us that it's 3D space. It's an illusion! Time dilation is a phenomenon related to the disturbance 'climbing' a bump - if there are valleys, we should see time accelerating in A. Can valleys be created in the melting process? Here we consider another phenomenon. We are on a 2D sphere. All visible objects are cross-sections of vortices and other patterns on the melting front in B of radius 'now'. Therefore, where we see stars, they are tongues of heat that melt the crystal, defects are released from freezing, which causes flashes and vibrations of the remaining crystal lattice, which lies in the future for the observer in A. Since these are warmer places, suction of the plastic crystal lattice occurs, which stretches, giving fewer and fewer, and for the observer means slower and slower, flashes of released energy. If the area is completely filled with crystal lattice, we no longer see any new flashes (photons). When a star swells, it means in B the melting area is expanding. Special explanation is required for supernovae and their remnants. When an area in B melts, the liquid phase is denser than the solid and occupies a smaller volume. A volume difference arises, which causes the plastic crystal lattice to collapse. This phenomenon we call gravity and a black hole. Therefore, we do not observe white black holes. Then tongues of liquid would enter the crystal lattice and although dark inside, they would release large amounts of defect energy at their edges. For now, we do not observe such phenomena. The heated crystal lattice becomes plastic. This area may overheat without signs of violent melting, after which a very large emission of energy from released defects of the crystal lattice appears. This wave affects the vibrations of the entire crystal lattice, which is visible in changes in the image of dark matter in these areas. In A we see clear disturbances radiating in the excitations of the energy field in A. The remnant is the sucked-in crystal lattice, which creates patterns of releasing new defects, creating subsequent frames of the film. Dripping from the crystal lattice may occur, whose drops are melted and flashes occur, jets of energy. When area B collapses, resonances (images of particles) are "shifted" in A towards the center of collapse. This gives the impression of falling. The sucked-in crystal lattice will melt later, therefore there is not much photon emission there. However, the crystal lattice vibrates, which should appear in the image of dark matter. In the future, these delayed areas may catch up with the 'now' sphere and flare up anew. Do the sizes of black holes change over time? They should, because it's a plastic area in B, which can expand if a tongue of heat starts melting it, can shrink if further down, deeper, crystal lattice is being sucked in, can flare up if melting of this area occurs. A neutron star after an explosion is an image of a new, more stable melting pattern in a constantly sucked-in crystal lattice. Rotation of galaxies, stars, planets is an image of the rotation of the melting front in B. The source of rotation is the chirality of crystal B (direction on the looped dimension W). Vortices arise naturally during the collapse of melting areas (conservation of angular momentum). Empty places in the background radiation are areas further from the heat (melting) in B at the time radius 'now' in A, which do not release defects. Unfortunately, as observers (points) on the plane of the sphere, we only see a fragment, which runs in arcs from the observed point to the observer. These are arcs on the sphere, but the sphere is huge - radius over 13 billion years - which is visible in the differences in observations of stellar parallax in the sky. The measurement triangle corresponds to a triangle on the sphere. They don't differ much with such a huge sphere. Our observation area is almost flat. Red shift is the effect of the expansion of the 'now' sphere and the shrinking of the observation radius of the observer in A, who stands on the peak of the curvature of the 'now' sphere, which constantly grows. PARABOLIC ROTATION, NOT HYPERBOLIC Hyperbolic rotation (from GR) is mixing dimensions within one structure (spacetime). Parabolic rotation in the PMES model (photon membrane equilibrium singularity) is a phase transition: one dimension (geometric in B) is liquidated as geometric, and its degrees of freedom are recoded into a new quality – rectilinear time in A. Why did we experience parabolic rotation, and not hyperbolic? If the transformation were hyperbolic (as in GR), we would observe: - Continuity of dimensions (4D spacetime) - Possibility of transforming time into space (time dilation) - Lack of fundamental quantization Meanwhile, we observe: - Discrete particle spectrum (quarks, leptons) – image of discrete vibration modes in B - Holographic nature of information (Bekenstein-Hawking entropy proportional to surface area, not volume) - Flatness of the Universe (Ω ≈ 0) – natural for a 2D sphere, which locally we do not distinguish from a plane Conclusion: We experience parabolic rotation because we live on a 2D sphere that is an image of 3D processes in B, with time emerged as a separate category from the looped geometric dimension. THE ESSENCE OF THE LAW OF INFORMATION CONSERVATION IN THE PROCESS OF DIMENSIONALITY CHANGE "A shrinking multidimensional area must still contain all physical points" – This is the core of the problem. When in Mother space B one of the dimensions collapses (loops), the number of geometric dimensions decreases. "Physical points" (information carriers) cannot simply disappear. "Minimal area (volume) that can physically contain all these points" – It means that information about these points must be stored somewhere in the new, created space A. It cannot be stored in the volume that no longer exists (in the collapsed dimension). "It saves itself by changing their coordinates through transformation" – This is precisely the "parabolic rotation". Points are no longer distributed in 3 out of 4 geometric dimensions, but their information is stored in a new way: as a configuration on a 2-dimensional sphere, with time flowing radially. "Transformation plus position of points equals position of points in higher-dimensional (mother) space" – This is the key equation of the model. It states that the state in space A (transformation + position) is equivalent to (contains the same information as) the state in space B. Information is not lost, it is merely recoded. Law of information conservation in the process of dimensionality change: The amount of information (number of physical points) that can be stored in a collapsing multidimensional area is limited by the surface area of the horizon (equator) of the new space. Moreover, the recording of this information on this surface is complete. Difference: Cause vs. Effect There is however a subtle but important difference in interpretation between the PMES model and the standard formulation of the holographic principle: In standard physics: The holographic principle says that if we have an area of a given volume, information about it can be encoded on its surface. This is a property of the mathematical description, often resulting from the properties of gravity and the quantum nature of reality. In the PMES model: This same statement takes on a dynamic and causal character. It is the collapse of the dimension (shrinking) that is the process that forces such encoding of information. This "minimal area" (horizon surface) is a necessary condition for points to exist at all in the new reality. This is a very original and profound approach, which gives the holographic principle the status of a law resulting from deeper geometric dynamics. Angle between geometric dimensions in A We ask whether the geometric dimensions in A (those tangent to the "now" sphere) are arranged at arbitrary angles, or are they somehow ordered. Arbitrariness of angles: In the PMES model, the dimensions in A are remnants of dimensions from B that have undergone holographic projection onto the sphere. On the surface of the sphere, at a given point, we can define two local, perpendicular directions (like longitude and latitude). However, at what global angle these local directions are oriented relative to some external system is completely arbitrary and physically insignificant. What matters is the local geometry (metric) on the sphere, which is isotropic – it does not distinguish any direction. This explains why in our Universe (A) we do not observe a distinguished direction on a cosmic scale. Dimension with a minus – holographic information: The meaning of the dimension that has the opposite orientation ("minus sign") in the transformation is extremely profound. In standard mathematics, when transitioning from a higher to a lower dimension, information about the "negative" direction (inward/radial coordinate) is lost as a free degree of freedom, but becomes encoded as a scalar value on the new surface. In the PMES model: - The radial dimension in B (the one that looped) becomes time in A (flows radially). - The transverse dimension in B (the one that "disappeared" in a geometric sense) becomes the carrier of holographic information in A. Its "orientation" manifests not in space, but in the value of charges, spins, and other quantum properties of particles, which are manifestations of defects in B. This is precisely the "common part of both spaces" – a mathematical object (e.g., a scalar or spinor field) on sphere A that carries information about the geometry of B. Mathematical description of the transformation B → A This is the most difficult, but also the most important question. There is no single, ready-made formula, but one can indicate the direction in which to look for mathematics for the PMES model. It will not be a single equation, but rather a structure: Step 1: Description of Mother space B. We assume that B is a 4-dimensional manifold (crystal) with metric g_ij (i,j = 1..4). The state of the crystal (stresses, defects) is described by some field Φ. Step 2: Condition of looping (collapse). In a certain region, stresses reach a critical value. Topologically, a transition occurs: R⁴ → S¹ × R³ (one dimension closes into a circle). Step 3: Parabolic rotation and holographic projection. This is the core of the transformation. The boundary surface (horizon) of the collapsed region in B is a 3-dimensional hypersurface (light-like). The holographic principle states that all information about the interior (4D) can be encoded on this boundary (3D). In the PMES model, this boundary becomes the new space A. Mathematically, we can write this as: Metric in B (non-collapsed region): ds_B² = g_ij dxⁱ dxʲ = h_μν dx^μ dx^ν + g₄₄ (dx⁴)² where μ, ν = 1, 2, 3 are the three spatial dimensions, and x⁴ is the dimension that will undergo looping. The collapse process: Dimension x⁴ undergoes compactification onto a circle of radius R(τ), which decreases to zero (or to the Planck length). At this moment, it ceases to exist as a spatial dimension. Formation of A (holographic space + time): The new reality is described by: - Time t – arises from the dynamics of the collapse of dimension x⁴. It is radial, which can be described as a radial coordinate on the sphere. - Space A – is a 2-dimensional sphere S² at each moment t. Its metric is the standard metric on a sphere of radius R_A(t): ds_A² = -dt² + R_A(t)² dΩ₂², where dΩ₂² is the metric on the unit sphere. The minus sign by dt² means that time is perpendicular to space. This is precisely the "perpendicularity" forced by the transformation. Information field Ψ on A: On this sphere "live" fields Ψ(θ,φ,t), which are the image (holographic projection) of the state of field Φ from the collapsed dimension B. The equation linking Ψ and Φ is precisely the holographic transformation: Ψ(x^μ,t) = H[Φ(x^μ,x⁴)] where H is a projection operator, which "integrates" over the collapsed dimension x⁴, but in a non-local way, preserving all quantum information. Key conclusion: The equation for R_A(t) (i.e., the scale of the Universe) and the dynamics of fields Ψ (which we perceive as particles, galaxies, etc.) follow directly from the geometry and stress state in B that led to the looping. The "radius of time" R_A(t) grows because the crystallization wave front in B propagates outward. This is the cause of the Universe's expansion, not dark energy. How to verify the orientation of "holographic information"? We cannot do this directly, because we have no access to B. But we can infer it from the properties of A. This orientation manifests in the form of constants and laws of physics that we observe: Coupling constants: The values of constants (e.g., the fine-structure constant α ≈ 1/137) may be the "shadow" of the angles at which dimensions in B were set relative to each other. They are "frozen" at the moment of crystallization (transition B → A). The invariance of these constants in time and space in A suggests that the direction of holographic information (the "dimension with a minus") is globally constant in B - this follows from the large circle of the looped dimension. Symmetry breaking: The hierarchy of particle masses (why is the electron lighter than the muon?) may result from the fact that different types of defects in B (different "angles" in the lattice) resonate with this oriented informational dimension in different ways. Possible observable anisotropies: If the radius of the crystallization wave were comparable to the size of the observable Universe, we could observe subtle but systematic differences in particle properties or constants depending on the direction in the sky (direction relative to the "blowing wind" of crystallization). The fact that we do not see them means that the scale of crystallization in B is huge compared to our horizon, which is consistent with our thesis. Why do particles tremble? (Dynamics and causality) This explains why particles in A have a quantum nature and are subject to fluctuations. Cause of vibrations: Defects D₁, D₂, D₃,... arise in B in slightly different places in the crystal lattice. Their position in B is determined by the local stress structure. When they are projected onto sphere A, these small differences in position in B translate into slightly different positions of their images on sphere A. From our perspective (in A), this looks as if the particle "trembles" around a certain average position. It is not a particle that "moves", it is an image of a sequence of different, but causally related defects. Stability and decays of particles One scheme of released defect stresses – many particles: A defect in B has its internal structure (topology, stresses in different directions). When it is projected onto sphere A, this complex structure can be interpreted by our holographic "interface" as several separate, but quantum-entangled objects – for example, three quarks forming a proton. This is why quarks are confined – they are different aspects of the same defect in B or system of defects. It is an image of crystal lattice vibrations. Defect decay – particle decay: If a defect in B decays (changes its topology, e.g., due to interaction with other defects), its image on sphere A also changes. What was perceived in A as a stable particle (e.g., proton) suddenly disappears, and an image of the new state of the defect appears – so in A we see this as the decay of a particle into others (e.g., proton decays, although in the Standard Model it is stable, but in Grand Unification theories it may decay – this is precisely this type of mechanism). Inheritance of stresses: A new defect that arises in B does not arise in a vacuum. Its stress (energy) is the sum of stresses inherited from the crystal lattice and from previous defects that have decayed. In A, this manifests as conservation laws (energy, momentum, charge) – what "was" in particles before decay "transfers" to new particles, because it is encoded in the structure of defects in B, i.e., in the future for the observer in A. Does the mechanism of releasing new defects in the melting of the crystal lattice, exciting the entire crystal lattice, stabilize patterns on the wave front? Cause of similarity: The fact that images of defects (particles of the same type, e.g., electrons) are "almost identical" results from the regularity of the crystal lattice B. Defects arising under similar stress conditions (e.g., in "valleys" of the lattice potential) will have a very similar structure. Their images in A will therefore also be very similar. This is not stabilization, it is quantization: This similarity is not the result of any stabilizing mechanism in A, but results from the discrete nature of the lattice itself in B. This is why the electron charge is always the same – it is a "quantum" of lattice stress that can be carried by a defect. This is a deeper explanation of charge quantization than anything offered by the Standard Model. Adopting the melting model, rather than crystallization, solves several problems at once: Nature of vacuum: Vacuum in A is an image of a stable but thermally vibrating crystal B – this explains zero-point energy. Flatness: Still holds. Many Universes?: Many regions of melting in B would explain the existence of "voids" and potentially observable, though extremely distorted, images of other domains in our sky. Horizon: Explains why we see it as smooth, but with subtle fluctuations – it is the sum of lattice vibrations and overlapping images. The PMES model becomes not only coherent, but also verifiable. Each of these concepts (origin of vacuum fluctuations, nature of voids, possible anisotropies on the horizon) can be compared with observational data (from Planck, WMAP probes, telescopes like JWST). ENERGY LEVELS OF LATTICE MELTING – QUANTIZATION Can melting of a crystal lattice have energy levels? Yes! This is the key to quantization. In B: The crystal lattice has discrete energy levels for defects. A defect cannot have arbitrary energy. It can exist only in specific excited states (like an electron in an atom). This follows from the very nature of the lattice – it is a quantum system. In A: The image of these allowed energy levels of defects in B are the discrete values of particle masses/energies. This is why quarks have strictly defined masses (although we do not measure them directly), and particles occur in families (generations). Each higher generation is an image of a defect at a higher excitation level in B. Analogy to metal: In metal, heating (supplying energy) causes atoms in the lattice to vibrate with greater amplitude. Eventually, vibrations are so strong that the lattice melts – it loses long-range order. In the PMES model, our reality (A) is precisely the image of this "melting zone" in B. What we see as particles are images of local, violent processes of releasing stresses (defects) in this zone. The melting process has its own dynamics, and its different phases can give different images in A. Photon as an image of an event, not an object. In B (process): The crystal lattice heats up (melts). Defects in the lattice vibrate with increasing amplitude (higher energy). At the moment when the vibration energy exceeds the lattice's strength threshold, the defect is released – the bonds that held it in the crystal structure break. This is a violent release of accumulated vibration energy. In A (image): We do not see this moment of release as a "particle approaching". We see it as a flash – the appearance of an image of this released energy. This is a photon. Its energy (color) is an image of how violent the release was (how much defect vibration energy was released). The more vibration energy the defect had before release, the more energetic (shorter wavelength) photon we see in A. It is possible that there is no photon membrane mechanism. The appearance of a photon may mean the final vibration level of a defect in B. WHAT ARE QUARKS? In B (process): The lattice vibrates. In a certain area, a group of defects is not released individually (like in the case of a photon), but enters a state of continuous, coordinated resonant vibrations. This is not one defect, it is a system of several defects that mutually sustain their vibrations. They vibrate, but are not released – they are in a state of "excited metastability" at the melting boundary. In A (image): This continuous, sustained process in B has its image in A. This image is a quark. A quark is not an image of a single defect, but an image of the entire resonating system. Because the system vibrates (changes its internal state), its image in A also changes over time (pulsates, has a phase). The fact that in the next moment a "new" image appears, and the old one disappears, is precisely the image of this dynamics in B. A quark is an image of a stable (for a moment), resonating system of defects in B that has not yet been released. It can be influenced by the entire crystal lattice, which lies in the future for the 'now' sphere. WHAT IS A PROTON? A proton is an image of a stable pattern over time. In B: We have a melting process. In a certain spatial region, in successive moments (in the understanding of B), a sequence of resonating defect systems appears. Let's say, at time t1 (of the process in B) we have system U1, at t2 – system U2, at t3 – U3. These systems (U1, U2, U3) are different (because they are new defects), but their computable property (e.g., the way they combine with other images) is identical. They are "copies" of each other in successive moments. In A: We see a sequence of images of these systems: image U1, then image U2, then image U3. Because the property of these images is identical, we, in A, interpret this as one, lasting object – a proton. The proton "exists" because in B, in this place, new defect systems with the same image properties constantly appear. It is an animation. A proton is not a thing, it is a pattern in the stream of images. WHAT IS DARK MATTER? In B: Most defects in the lattice vibrate, but not all enter resonance (forming systems) and not all are released (forming photons). A huge number of defects simply vibrate, transferring energy through the lattice, but without spectacular effects. In A: These "quiet", non-resonant and non-released defects do not have a distinct image. We do not see them as quarks (because they are not systems) nor as photons (because they are not released). However, their collective vibration energy has its image. This image is precisely dark matter – we feel its presence, but we do not see it. FREQUENCIES OF VIBRATIONS AND QUANTIZATION In a crystal (real, physical), atoms cannot vibrate with arbitrary amplitude and frequency. They are limited by the lattice structure. Only discrete vibration modes are allowed – these are phonons. This is the basis of solid-state physics. Transferring this to B: B is a 4D crystal. Its defects (being lattice disturbances) can also vibrate only at discrete, allowed energy levels. This is natural, resulting from the very definition of a crystal lattice. In A: The image of these discrete vibration levels of defects in B are the discrete masses of quarks and other particles. Therefore, quarks cannot have arbitrary mass. Therefore, there are generations (families) of particles – these are images of defects at different, allowed excitation levels. This explanation is coherent and does not require contriving quantum field theory in A. THE PROBLEM OF TIME AND FUTURE In B, there is no time. There is only the state of the lattice. What we in A call the "past" is an image of areas of B that have already melted (liquid). There is no lattice there, no defects, no vibrations. What we in A call the "future" is an image of areas of B that are still a solid crystal, but already strongly heated. These areas "will" vibrate and release defects. We do not see this yet, because our 'now' sphere has not yet reached them. What we in A call "now" is an image of the transitional zone – the melting front – where the crystal is maximally heated, defects vibrate, are released, and enter resonances. The future in A is an image of areas of B that are still a solid crystal, but already heated. They are already there, already vibrating, already forming resonances and defect systems. Their images exist potentially. When our "now" (the sphere imaging the melting front) moves along the time axis of A (which is an image of the progress of melting in B), it reaches these areas. Then their images become visible to us. Background radiation (CMB) Observation: The microwave background radiation is extremely homogeneous (fluctuations ~10⁻⁵), but has characteristic fluctuations. Interpretation: - Homogeneity: Image of the homogeneity of the crystal lattice B on a large scale. - Fluctuations: Image of thermal vibrations of the lattice in the pre-melting front zone. The magnitude of fluctuations (~10⁻⁵) corresponds to the ratio of thermal energy to lattice bond energy. The model does not require inflation to explain homogeneity. Expansion of the Universe and redshift Observation: Distant galaxies are receding from us at a speed proportional to distance (Hubble's Law). Interpretation: In the model, there is no "expansion of space". The 'now' sphere in A has an increasing radius R_A(T), because: R_A(T) = R_B ⋅ f(T) where R_B is the radius of the looped dimension in B (constant), and f(T) is a function of the progress of melting. The observer on the sphere sees: - Growing sphere radius – the further we look, the more we "move away" geometrically. - Shrinking observation circle – the larger the sphere, the smaller its fragment we see locally. Redshift (z) is given by the formula: 1 + z = R_A(observation time) / R_A(emission time) This is the same formula as in standard cosmology, but with a different physical interpretation. Black holes Hawking radiation is an image of the last defects released at the melting boundary (horizon), before the area is completely filled with the solid phase on the sphere of radius 'now'. 4D ENGINE: The Cyclic Nature of B and the Source of Structure 1. Liquid state. In the liquid state, points still oscillate in the looped dimension, but are not bound in a lattice. 2. Superheating phase. All physical points have fixed positions (x¹, x², x³). The looped dimension oscillates for each point: x⁴(τ) = R sin(ωτ + φ₀). Oscillations generate stresses σ(τ). Oscillator systems generate energy in the system, which is transported to the center. 3. Critical energy. Phase transition. As a result of energy accumulation, a phase transition occurs, whose seed is the central point, where all interaction forces cancel out. 4. Crystallization. The liquid changes phase to solid. 5. Heating. Oscillator systems continue to release energy in the system. 6. Melting. It occurs from the central point, where energy is accumulated. After reaching critical energy E_crit, local areas undergo melting. The lattice disappears, but points retain their positions (x¹, x², x³). Only the phase changes. 7. Liquid state. In the liquid state, points still oscillate in the looped dimension, but are not bound in a lattice. Remnants after cycles as a source of structure Each melting/crystallization cycle leaves traces in B: - Areas of increased defect density – seeds of future galaxies. - Areas of decreased density – future voids. - Systems of ordered stresses – equivalents of crystal "memory". These inhomogeneities are inherited by subsequent cycles. This explains why the large-scale structure of the Universe is not random, but has specific correlations. Consistency with observations: The observed large-scale structure of the Universe (galaxy network, filaments, voids) is consistent with the image of a cyclic process leaving "scars". In the B cycle, we have a liquid phase (after complete melting of the crystal). In this phase, physical points still have fixed positions (x¹, x², x³), but are not connected by a lattice – they are free, like "atoms" in a 4D plasma. Each point continues to oscillate in dimension x⁴ (according to the equation x⁴(τ) = R sin(ωτ + φ₀)), generating stresses. Problem: How does a new crystal arise from this plasma? Solution (model logic): Transport of energy to the center: Oscillations of each point generate local stresses. These stresses propagate through the medium. Due to the geometry (looped dimension and fixed positions of points), this energy is transported to specific areas – centers of crystallization. These are places where seeds remained from previous cycles in the form of defect clusters or areas with a slightly different structure. Equation of energy transport in B (postulated): ∂E/∂τ + ∇ ⋅ j_E = S(x,τ), where j_E is the stress energy flux, and S are sources (point oscillations). Reaching critical energy: In centers, energy accumulates. When it reaches a critical value E_crit, the properties of the medium change locally. We define E_crit as the energy at which free points begin to feel mutual interactions strongly enough that they can form crystal lattice bonds. Superheating of the liquid: Just before the phase transition itself, in the center area, the liquid is superheated – it has energy higher than the melting temperature, but still remains in the liquid phase (metastable state). This is crucial, because without superheating there would be no controlled nucleation. Crystallization seed – point of force cancellation: In GR, a singularity is a point where energy density tends to infinity. In our model, a singularity is a point where all forces (interactions between points) cancel to zero. It is not infinity, it is a point of perfect equilibrium. What forces in a 4D liquid? - Oscillatory forces – resulting from vibrations in dimension x⁴ (each point "pushes" with its field). - Topological forces – resulting from the looped dimension (points are bound by cyclicity). - Residual forces – remnants from the previous lattice (defect traces). At the singular point (seed), all these forces balance. The net force acting on a point at this location is zero. This is the state in which a new ordering can arise. Mathematically: Σ_i F_i(x₀) = 0, where F_i are forces from neighboring points, oscillations, and topology. Initiation of crystallization: When such an equilibrium point (seed) appears in a superheated liquid, it becomes the center of crystallization. Points around it begin to arrange into a lattice, because it is a lower energy state. The process propagates in waves (crystallization front) outward, until the entire area of B becomes a crystal again. Consistency with materials physics: In real crystals, crystallization from a superheated liquid requires the presence of seeds – points where local density fluctuations reach a critical value. Our model transfers this mechanism to the fundamental level.