{"id":15674,"date":"2026-01-18T10:04:59","date_gmt":"2026-01-18T09:04:59","guid":{"rendered":"https:\/\/instytut-iskra.pl\/?page_id=15674"},"modified":"2026-01-18T10:24:33","modified_gmt":"2026-01-18T09:24:33","slug":"niezmienniczosc-lorentza","status":"publish","type":"page","link":"https:\/\/instytut-iskra.pl\/en\/niezmienniczosc-lorentza\/","title":{"rendered":"Lorentz invariance"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"15674\" class=\"elementor elementor-15674\">\n\t\t\t\t<div class=\"elementor-element elementor-element-f881072 e-flex e-con-boxed e-con e-parent\" data-id=\"f881072\" data-element_type=\"container\">\t\t\t<div class=\"e-con-inner\">\r\n\t\t<div class=\"elementor-element elementor-element-8a55e8c e-con-full e-flex e-con e-child\" data-id=\"8a55e8c\" data-element_type=\"container\">\t\t<div class=\"elementor-element elementor-element-639d762 elementor-widget elementor-widget-pxl_menu\" data-id=\"639d762\" 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class=\"pxl-menu-item-text\">Paradoxes of Physics<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14870\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14870\"><a href=\"https:\/\/instytut-iskra.pl\/en\/alpha\/\"><span class=\"pxl-menu-item-text\">ALPHA decoded<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-14981\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-14981\"><a href=\"https:\/\/instytut-iskra.pl\/en\/czastki-w-maya\/\"><span class=\"pxl-menu-item-text\">Particles in MAYA<i class=\"pxl-arrow-none pxl-hide pxl-ml-4\"><\/i><\/span><\/a><\/li>\n<li id=\"menu-item-15368\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-15368\"><a href=\"https:\/\/instytut-iskra.pl\/en\/mechanika-kwantowa\/\"><span class=\"pxl-menu-item-text\">Quantum mechanics<i class=\"pxl-arrow-none pxl-hide 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elementor-widget elementor-widget-pxl_heading\" data-id=\"a2c2509\" data-element_type=\"widget\" data-widget_type=\"pxl_heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\r\n<div id=\"pxl-pxl_heading-a2c2509-4582\" class=\"pxl-heading px-sub-title-default-style\">\r\n\t<div class=\"pxl-heading--inner\">\r\n\t\t\r\n\t\t<h2 class=\"pxl-item--title style-default highlight-default\" data-wow-delay=\"ms\">\r\n\r\n\t\t\t<span class=\"pxl-heading--text\">\r\n\r\n\t\t\t\t\t\t\t\t\tThe theory of coded reality and the problem of Lorentz invariance\t\r\n\t\t\t\t\t\r\n\r\n\t\t\t<\/span>\r\n\t\t<\/h2>\r\n\t\t\r\n\t<\/div>\r\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bd3ebe9 elementor-widget elementor-widget-pxl_text_editor\" data-id=\"bd3ebe9\" data-element_type=\"widget\" data-widget_type=\"pxl_text_editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pxl-text-editor highlight-gradient\">\r\n\t<div class=\"pxl-item--inner\" >\r\n\t\t<h4 class=\"break-words last:mb-0\" dir=\"auto\">What is Lorentz invariance<\/h4><p class=\"break-words last:mb-0\" dir=\"auto\">Lorentz invariance is often presented simplistically as the statement that \"the laws of physics are the same for all observers in uniform motion.\" This formulation is correct, but superficial. In fact, it concerns a much deeper, more restrictive condition, far beyond the simple symmetry of the equations.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">Lorentz invariance means that there is no physically unique frame of reference. No state of uniform motion is more \"true,\" more fundamental, or closer to the structure of the world than any other. There is no local experiment that can distinguish rest from uniform motion with respect to space itself.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">In other words, spacetime is locally isotropic: no spatial or spatiotemporal direction is physically privileged. Any observable anisotropy \u2014 even a trace \u2014 would imply the existence of a hidden background, a distinctive structure, or an absolute reference. This is also true for time: the existence of global simultaneity or a shared \"now\" would already violate this principle.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">The consequence of this fact is a radical shift in the concept of time and space. They are no longer separate, absolute entities, but quantities that blend with each other when the frame of reference changes. Different observers may disagree about the length, duration, or simultaneity of events, but they always agree on the causal structure: which events can interact and which are causally isolated. The lack of absolute simultaneity here is not an interpretation, but a structural feature of the theory.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">The formal expression of this property is the invariance of the space-time interval described by the Minkowski metric:<\/p><p style=\"text-align: center\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>d<\/mi><msup><mi>s<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mo>\u2212<\/mo><msup><mi>c<\/mi><mn>2<\/mn><\/msup><mi>d<\/mi><msup><mi>t<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>d<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>d<\/mi><msup><mi>y<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>d<\/mi><msup><mi>z<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\"> ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2 <\/annotation><\/semantics><\/math><\/p><p class=\"break-words last:mb-0\" dir=\"auto\">or in covariant notation:<\/p><p style=\"text-align: center\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>d<\/mi><msup><mi>s<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><msub><mi>\u03b7<\/mi><mrow><mi>\u03bc<\/mi><mi>\u03bd<\/mi><\/mrow><\/msub><mtext>\u2009<\/mtext><mi>d<\/mi><msup><mi>x<\/mi><mi>\u03bc<\/mi><\/msup><mi>d<\/mi><msup><mi>x<\/mi><mi>\u03bd<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\"> ds^2 = \\eta_{\\mu\\nu}\\, dx^\\mu dx^\\nu <\/annotation><\/semantics><\/math><\/p><p class=\"break-words last:mb-0 translation-block\" dir=\"auto\">wheren <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03b7<\/mi><mrow><mi>\u03bc<\/mi><mi>\u03bd<\/mi><\/mrow><\/msub><mo>=<\/mo><mrow><mi mathvariant=\"normal\">d<\/mi><mi mathvariant=\"normal\">i<\/mi><mi mathvariant=\"normal\">a<\/mi><mi mathvariant=\"normal\">g<\/mi><\/mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mo>+<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mo>+<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\"> \\eta_{\\mu\\nu} = \\mathrm{diag}(-1, +1, +1, +1) <\/annotation><\/semantics><\/math>\u00a0is a constant metric of flat spacetime.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">It is this invariance\u2014not any additional assumptions\u2014that underlies the entire theory of special relativity and determines its mathematical structure. The following follow directly from it:<\/p><p class=\"break-words last:mb-0\" dir=\"auto\"><strong>Lorentz transformations (for the boost in the direction of the axis <\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> x <\/annotation><\/semantics><\/math><strong>):<\/strong><\/p><p style=\"text-align: center\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>t<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msup><mo>=<\/mo><mi>\u03b3<\/mi><mrow><mo fence=\"true\">(<\/mo><mi>t<\/mi><mo>\u2212<\/mo><mfrac><mrow><mi>v<\/mi><mi>x<\/mi><\/mrow><msup><mi>c<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><msup><mi>x<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msup><mo>=<\/mo><mi>\u03b3<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>\u2212<\/mo><mi>v<\/mi><mi>t<\/mi><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mi>\u03b3<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><msqrt><mrow><mn>1<\/mn><mo>\u2212<\/mo><msup><mi>v<\/mi><mn>2<\/mn><\/msup><mi mathvariant=\"normal\">\/<\/mi><msup><mi>c<\/mi><mn>2<\/mn><\/msup><\/mrow><\/msqrt><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\"> t&#8217; = \\gamma \\left( t &#8211; \\frac{v x}{c^2} \\right), \\quad x&#8217; = \\gamma (x &#8211; v t), \\quad \\gamma = \\frac{1}{\\sqrt{1 &#8211; v^2\/c^2}} <\/annotation><\/semantics><\/math><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p><p class=\"break-words last:mb-0\" dir=\"auto\">energy-momentum relationship:<\/p><p style=\"text-align: center\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>E<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>p<\/mi><mn>2<\/mn><\/msup><msup><mi>c<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>m<\/mi><mn>2<\/mn><\/msup><msup><mi>c<\/mi><mn>4<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\"> E^2 = p^2 c^2 + m^2 c^4 <\/annotation><\/semantics><\/math><\/p><p class=\"break-words last:mb-0\" dir=\"auto\">relativistic increase in effective mass:<\/p><p style=\"text-align: center\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>m<\/mi><mo>=<\/mo><mfrac><msub><mi>m<\/mi><mn>0<\/mn><\/msub><msqrt><mrow><mn>1<\/mn><mo>\u2212<\/mo><msup><mi>v<\/mi><mn>2<\/mn><\/msup><mi mathvariant=\"normal\">\/<\/mi><msup><mi>c<\/mi><mn>2<\/mn><\/msup><\/mrow><\/msqrt><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\"> m = \\frac{m_0}{\\sqrt{1 &#8211; v^2\/c^2}} <\/annotation><\/semantics><\/math><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"msupsub\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p><p class=\"break-words last:mb-0\" dir=\"auto\">and the fact that the speed of light is the same structural limit for all observers:<\/p><p style=\"text-align: center\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>v<\/mi><mo>=<\/mo><mi>c<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> v = c <\/annotation><\/semantics><\/math><\/p><p class=\"break-words last:mb-0\" dir=\"auto\"><strong>Physically this means that:<\/strong><\/p><p class=\"break-words last:mb-0\" dir=\"auto\">\u2013 it is impossible to detect \u201cmotion relative to space itself\u201d (no aether), \u2013 there is no absolute clock or global grid of simultaneity, \u2013 the speed of light is not a property of a specific object, but a boundary of the causal structure, \u2013 the light cone remains invariant \u2014 what lies inside the causal cone remains inside for every observer.<\/p><p class=\"break-words last:mb-0 translation-block\" dir=\"auto\">It is this property that makes special relativity so ruthlessly restrictive. It does not tolerate even the slightest trace of effects that would betray the existence of a privileged background, a distinguished direction, a global time synchronization mechanism, or anisotropy of dynamics. Modern tests for violation of Lorentz invariance (LIV) reach a sensitivity of the order of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><msup><mn>0<\/mn><mrow><mo>\u2212<\/mo><mn>20<\/mn><\/mrow><\/msup><mtext>\u2013<\/mtext><mn>1<\/mn><msup><mn>0<\/mn><mrow><mo>\u2212<\/mo><mn>23<\/mn><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\"> 10^{-20} \u2013 10^{-23} <\/annotation><\/semantics><\/math>, which makes this symmetry one of the best confirmed properties of reality.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">Therefore, any discrete fundamental model that aspires to describe the physical world must not only reproduce the formal equations of special relativity, but also explain why its own ontology and dynamics introduce neither detectable anisotropy nor absolute simultaneity.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">This condition is not an aesthetic addition. It is a test of ontological coherence.<\/p><h4 class=\"break-words last:mb-0\" dir=\"auto\">Why lattice theories have a problem with this<\/h4><p class=\"break-words last:mb-0\" dir=\"auto\">Here a classic tension arises, one that for decades was considered nearly insurmountable. Lattice theories \u2014 and more broadly, all approaches that assume a discrete substrate for reality \u2014 seemed, by definition, to be inconsistent with Lorentz invariance.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">The reason is seemingly obvious. Regular grid:<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">\u2013 it has distinguished directions (axes, planes, diagonals), and is therefore anisotropic, \u2013 it has a distinguished scale (minimum step, e.g. Planck length), \u2013 it has a natural \u201crest state\u201d with respect to which motion can be defined, \u2013 and \u2013 even if implicitly \u2013 a common updating scheme that acts as a global clock.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">This last point is crucial. Every regular step-by-step evolution, every global update of the mesh state, every configuration definition \"in the moment\" <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> t <\/annotation><\/semantics><\/math>\u201d introduces absolute simultaneity. And absolute simultaneity denotes a distinguished frame of reference.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">If reality were to be composed of such a structure, intuition and calculation suggest that an observer moving relative to the grid should be able to detect it. Propagation speeds should depend on direction. Wave dispersion should reveal granularity. Clocks based on local processes should \"feel\" the global updating rhythm.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">For precisely this reason, for decades, the discrete structure of spacetime and strict Lorentz invariance were thought to be mutually exclusive. At best, it was hoped that Lorentz symmetry would only emerge as an approximation\u2014in the low-energy limit\u2014with minor corrections at the Planck scale.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">This position quickly proved problematic.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">First, even extremely small violations of isotropy and Lorentz invariance lead to observable effects that we simply don't see. Second, \"approximate\" symmetry ceases to be symmetry in the fundamental sense \u2014 it becomes an artifact of a specific energy regime. Third, and finally, there was no mechanism explaining why this particular symmetry should reproduce itself with such absurd precision.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">Formally, the problem is very clear.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">In continuous, isotropic space-time the dispersion relation has the form:<\/p><p style=\"text-align: center\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>E<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>p<\/mi><mn>2<\/mn><\/msup><msup><mi>c<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>m<\/mi><mn>2<\/mn><\/msup><msup><mi>c<\/mi><mn>4<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\"> E^2 = p^2 c^2 + m^2 c^4 <\/annotation><\/semantics><\/math><\/p><p class=\"break-words last:mb-0\" dir=\"auto\">In a regular mesh, rotational symmetry is broken and directionally dependent dispersion corrections almost inevitably appear, which are a direct trace of the substrate anisotropy:<\/p><p style=\"text-align: center\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>E<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>p<\/mi><mn>2<\/mn><\/msup><msup><mi>c<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>m<\/mi><mn>2<\/mn><\/msup><msup><mi>c<\/mi><mn>4<\/mn><\/msup><mo>+<\/mo><msub><mi>\u03be<\/mi><mn>1<\/mn><\/msub><mfrac><mrow><mo stretchy=\"false\">(<\/mo><mi>p<\/mi><mo>\u22c5<\/mo><mi>n<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>4<\/mn><\/msup><\/mrow><msubsup><mi>M<\/mi><mi>P<\/mi><mn>2<\/mn><\/msubsup><\/mfrac><mo>+<\/mo><msub><mi>\u03be<\/mi><mn>2<\/mn><\/msub><mfrac><mrow><mo stretchy=\"false\">(<\/mo><msup><mi>p<\/mi><mn>2<\/mn><\/msup><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><msubsup><mi>M<\/mi><mi>P<\/mi><mn>2<\/mn><\/msubsup><\/mfrac><mo>+<\/mo><mo>\u2026<\/mo><\/mrow><annotation encoding=\"application\/x-tex\"> E^2 = p^2 c^2 + m^2 c^4 + \\xi_1 \\frac{(p \\cdot n)^4}{M_P^2} + \\xi_2 \\frac{(p^2)^2}{M_P^2} + \\dots <\/annotation><\/semantics><\/math><\/p><p class=\"break-words last:mb-0\" dir=\"auto\">where <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>n<\/mi><\/mrow><annotation encoding=\"application\/x-tex\"> n <\/annotation><\/semantics><\/math>\u00a0is the vector of the distinguished direction of the grid, and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03be<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>\u03be<\/mi><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\"> \\xi_1, \\xi_2 <\/annotation><\/semantics><\/math><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> are coefficients of order of unity, depending on the geometry of the truss and the propagation rules.<\/p><p class=\"break-words last:mb-0 translation-block\" dir=\"auto\">The key is that these corrections grow as <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>p<\/mi><mn>4<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\"> p^4 <\/annotation><\/semantics><\/math>. This means that their influence becomes dramatically visible precisely where tests are most sensitive today: in observations of gamma-ray bursts, cosmic rays with energies above <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><msup><mn>0<\/mn><mn>19<\/mn><\/msup><mtext>\u2009<\/mtext><mrow><mi mathvariant=\"normal\">e<\/mi><mi mathvariant=\"normal\">V<\/mi><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\"> 10^{19}\\, \\mathrm{eV} <\/annotation><\/semantics><\/math>, cosmic neutrinos, and the stability of pulsar signals. These experiments proved merciless for classical grid models.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">In practice, this meant one thing: the mesh revealed its anisotropic nature.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">Therefore, most approaches to date have not attempted to explain the origin of Lorentz invariance, but merely imitate or mask it. Typical strategies have included:<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">\u2013 random distribution of points \u2014 statistical isotropy at the expense of local stability and particle dynamics, \u2013 hiding anisotropy in entangled structures \u2014 with residual directional effects at high energies, \u2013 tuning of propagation rules or boundary conditions \u2014 technically effective but ontologically inelegant, \u2013 very long graph evolutions \u2014 with apparent emergence of symmetries but a visible trace of the mesh on small scales.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">None of these approaches solved the problem at its source. They merely shifted it. Either at the expense of locality, or of stable particles, or of minimalism, or of full agreement with observational data.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">This wasn't a failure of the specific implementation. It was a failure of the assumption that Lorentz invariance and isotropy are properties that should be imposed on the mesh, rather than properties that should follow from the mechanism of its operation.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">This description level error is exactly where M\u0101y\u0101 changes the rules of the game.<\/p><h4 class=\"break-words last:mb-0\" dir=\"auto\">Isotropy as a property of the execution process, not of space<\/h4><p class=\"break-words last:mb-0\" dir=\"auto\">The most profound difference is that in M\u0101y\u0101 isotropy is not a property of space, but a property of the rendered process, which occurs in local time and not in a global temporal background.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">What we observe as isotropic spacetime is not a direct reflection of the planxel structure, but rather the result of a rendering occurring on scales much smaller than any physical experiment. The anisotropy is not hidden or masked\u2014it vanishes ontologically before a level of description at which it could be measured arises.<\/p><p class=\"break-words last:mb-0 translation-block\" dir=\"auto\">Each planxel has its own local computational clock <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>t<\/mi><mi>p<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\"> t_p <\/annotation><\/semantics><\/math>, the length of which depends on the local information density and synchronization cost. There is no common clock or global unit of time. Time is the number of completed local execution cycles.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">This means that the rendering of reality always occurs locally \u2013 each fragment of the world is generated at its own pace, not \u201cat the same time\u201d as the rest of the network.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">At the same time, each act of rendering is performed on the same execution principle:<\/p><p class=\"break-words last:mb-0 translation-block\" dir=\"auto\">\u2013 information can only be passed to the immediate neighborhood, \u2013 propagation takes place in the full 26-neighborhood, \u2013 each synchronization step takes exactly one local cycle <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>t<\/mi><mi>p<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\"> t_p <\/annotation><\/semantics><\/math><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">As a result, the limiting speed is not defined relative to external time, but as the local ratio of the synchronization step to the local execution time:<\/p><p style=\"text-align: center\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>c<\/mi><mo>\u2261<\/mo><mfrac><msub><mi mathvariant=\"normal\">\u2113<\/mi><mi>p<\/mi><\/msub><msub><mi>t<\/mi><mi>p<\/mi><\/msub><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\"> c \\equiv \\frac{\\ell_p}{t_p} <\/annotation><\/semantics><\/math><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"msupsub\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p><p class=\"break-words last:mb-0 translation-block\" dir=\"auto\">Since both <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi mathvariant=\"normal\">\u2113<\/mi><mi>p<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\"> \\ell_p <\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>t<\/mi><mi>p<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\"> t_p <\/annotation><\/semantics><\/math> are defined by the same runtime act, their ratio is locally invariant, no matter how much the rendering rate differs in different regions of the network.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">Therefore, despite the lack of global time, all observers reconstruct the same terminal velocity. Not because time is absolute, but because every velocity measurement is local.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">At this level, the anisotropy suppression mechanism begins to operate.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">The full 26-neighborhood ensures that information propagation is nearly spherical in nature, even in a single local cycle. The correlation front does not develop along the grid axis, but spreads evenly in all available execution directions.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">Additionally, each local cycle contains a phase rotation by the golden angle \u2248137.036\u00b0, which causes the propagation sequences to never close periodically with respect to any distinguished direction. The phase propagation directions are continuously decoupled.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">As a result, after a very small number of local measures:<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">\u2013 directional correlations undergo destructive interference, \u2013 axial preferences disappear, \u2013 the trace of the cubic lattice structure is no longer physically available.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">This extinction occurs on scales far smaller than any experimental scale. By the time an object, wave, or particle that could be used as a probe is created, the anisotropy has already been ontologically destroyed by the rendering process itself.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">Therefore, what we record is not an \u201caveraged grid\u201d but a continuous image generated by local acts of performance in which:<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">\u2013 there is no common moment, \u2013 there is no global direction, \u2013 there is no possibility of comparing propagation \u201cat the same time\u201d.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">Isotropy is not a symmetry of space. It is a stable point of execution dynamics in local time.<\/p><h4 class=\"break-words last:mb-0\" dir=\"auto\">Why this really closes the Lorentz problem<\/h4><p class=\"break-words last:mb-0\" dir=\"auto\">Thanks to this connection:<\/p><ul><li class=\"break-words last:mb-0 translation-block\" dir=\"auto\">local time <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>t<\/mi><mi>p<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\"> t_p <\/annotation><\/semantics><\/math><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li><li class=\"break-words last:mb-0 translation-block\" dir=\"auto\">local velocity definition <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>c<\/mi><mo>=<\/mo><msub><mi mathvariant=\"normal\">\u2113<\/mi><mi>p<\/mi><\/msub><mi mathvariant=\"normal\">\/<\/mi><msub><mi>t<\/mi><mi>p<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\"> c = \\ell_p \/ t_p <\/annotation><\/semantics><\/math><\/li><li>26-neighborhood rendering, \u2013 golden angle phase rotation<\/li><\/ul><p>Not only do LIV amendments not appear, but there is no ontological level at which they could appear.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">Anisotropy disappears before observable dynamics arise. There is no global clock, so absolute rest does not exist. Lorentz transformations describe the relationships between different rendering rhythms, not motion relative to the ground.<\/p><p class=\"break-words last:mb-0\" dir=\"auto\">This is not isotropy. It is the absence of a condition under which anisotropy could ever become established.<\/p>\t\t\r\n\t<\/div>\r\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-97c4e3c elementor-widget elementor-widget-pxl_button\" data-id=\"97c4e3c\" data-element_type=\"widget\" data-widget_type=\"pxl_button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"pxl-pxl_button-97c4e3c-6476\" class=\"pxl-button pxl-atc-link\" data-wow-delay=\"ms\">\r\n    <a href=\"https:\/\/instytut-iskra.pl\/en\/o-emergencji-matematyki\/\" class=\"btn pxl-icon-active btn-block-inline  btn-text-underline pxl-icon--right\">\r\n                    <span class=\"pxl--btn-icon\">\r\n                <i aria-hidden=\"true\" class=\"flaticon flaticon-right-arrow-long\"><\/i>                            <\/span>\r\n                <span class=\"pxl--btn-text\" data-text=\"Odkrywaj wi\u0119cej\">\r\n            Discover more        <\/span>\r\n    <\/a>\r\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\r\n\t\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Przedmowa Geneza teorii MAYA Problemy wsp\u00f3\u0142czesnej fizyki Dlaczego informacja? Jednostki Plancka Planxel Implikacje mechanizmu planxeli dla fizyki Reinterpretacja Wzor\u00f3w Czas w modelu M\u0101y\u0101 Przestrze\u0144 w modelu Maya Grawitacja Paradoksy Fizyki ALPHA odkodowana Cz\u0105stki w MAYA Mechanika kwantowa O emergencji matematyki Emergentna niezmienniczo\u015b\u0107 Lorentza Teoria kodowej rzeczywisto\u015bci a problem niezmienniczo\u015bci Lorentza Czym jest niezmienniczo\u015b\u0107 Lorentza Niezmienniczo\u015b\u0107 [&hellip;]<\/p>","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-15674","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/pages\/15674","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/comments?post=15674"}],"version-history":[{"count":10,"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/pages\/15674\/revisions"}],"predecessor-version":[{"id":15692,"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/pages\/15674\/revisions\/15692"}],"wp:attachment":[{"href":"https:\/\/instytut-iskra.pl\/en\/wp-json\/wp\/v2\/media?parent=15674"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}