Ether Theory of Everything
Ether Theory of Everything is a Theory of Everything based on corrected and refined concepts of the luminiferous ether, gravitating ether, atom, light, electric current, physical fields, and other physical concepts, as well as the origin of life, consciousness, and society.
Ether is a synonym for the physical theory of the philosophical concept of “matter”. Sometimes in the English version, “ether” is “aether” or “æther”.
The capital letter Æ is used for the initial letter of abbreviations of names related to modern ether science.
In the English version, the abbreviation for “Ether Theory of Everything” is “ÆToE”.
Ether Theory of Everything includes “Ether Theory of Matter”, “Ether Theory of Life”, “Ether Theory of Consciousness,” and “Ether Theory of Society”. In the English version, the abbreviation for “Ether Theory of Matter” is “ÆToM”. In English, the abbreviation for “Ether Theory of Life” is “ÆToL”. In the English version, the abbreviation for “Ether Theory of Consciousness” is “ÆToC”. In the English version, the abbreviation for “Ether Theory of Society” is “ÆToS”.
Ether Theory of Everything is based on the philosophy of “Evolutionary Ether Materialism”. In the English version, the abbreviation for “Evolutionary Ether Materialism” is “EÆM”.
The philosophy of “evolutionary ether materialism” is based on the “principle of infinite evolution”. “The principle of infinite evolution” is a shorthand term for the “principle of sufficient provision for the boundless, fully hierarchical evolution of matter in finite fundamental dimensions”. According to the “principle of infinite evolution”, the full evolution of matter is only possible in three-dimensional space, since two-dimensional space is too little for the evolution of matter, and four-dimensional space is too much. The absence of obstacles to the evolution of matter upon reaching the ultimate coordinates of fundamental space and time is ensured by their cyclical closure.
Next is a brief summary of the Ether Theory of Matter.
Ether Theory of Matter is built on the concept of transparent inertial ether.
The concept of transparent inertial ether is based on the idea that discrete absolute matter exists in discrete Euclidean three-dimensional absolute space and in discrete absolute time.
All ether in all space and time can be conventionally called “space-time-ether”. In English, the abbreviation for “space-time-ether” is “STÆ”.
Ether Theory of Matter uses the “Ether System of Units”. In the English version, the abbreviation for “Ether System of Units” is “ÆSoU”.
The unit of measurement of discrete quantity in the ether system of units is “æn”. The reference discrete quantity is expressed by an even natural number and is denoted by $N_Æ$. When modeling for a 64-bit signed integer data type, the maximum $N_Æ$ is two to the sixty-third power: $N_Æ=2^{63}$. For a 32-bit signed integer data type, the maximum $N_Æ$ is two to the thirty-first power: $N_Æ=2^{31}$. For a 16-bit signed integer data type, the maximum $N_Æ$ is two to the fifteenth power: $N_Æ=2^{15}$:
\[N_{Æ} \in 2\mathbb{Z}^{+}\] \[N_{Æ} = 2^{n}\]The space $S_Æ$ consists of identical “cells”.
The unit of measurement for the number of space cells in the ether system of units is “æс”.
The number of cells in the space can be finite. In the case of a finite space, the overflow of the absolute space coordinate does not affect physical laws. In the simplest model, the “number of cells in the space on each coordinate axis” $L_Æ$ is equal to the “standard discrete quantity” $N_Æ$. The space $S_Æ$ is a three-dimensional integer lattice with a toroidal topology:
\[L_{Æ} = N_{Æ}\] \[S_{Æ} = \left\lbrace (x, y, z) \in \mathbb{Z}^3 \mid -\frac{L_{Æ}}{2} \le x, y, z \le \frac{L_{Æ}}{2}-1 \right\rbrace\]“Space wrapping function” $WS_Æ(n)$, which maps any integer $n$ into the interval $[ -L_Æ/2, L_Æ/2 - 1 ]$ taking into account the cyclic nature of the space:
\[W_{\text{S.Æ}}(n) = \left( n + \frac{L_{Æ}}{2} \right)\pmod{L_{Æ}} - \frac{L_{Æ}}{2}\]The unit of measurement of the extent of space in the ether system of units is “æl”. The size of a space cell is 1 æl:
\[l_æ = 1 æl\]The unit of measurement of the volume of space in the ether system of units is “æs”.
The reference distance is denoted by $D_Æ$. In the simplest model, the reference distance is one less than the reference quantity:
\[D_Æ = N_Æ -1\]The coordinate of absolute position ($p_{abs}$) in absolute space has a range from $-L_Æ/2$ to $L_Æ/2-1$. The coordinate of relative position ($p_{rel}$) in absolute space has a range from $-D_Æ$ to $D_Æ$:
\[p_{abs} = (x, y, z) \in \mathbb{Z}^3 \mid -\frac{L_Æ}{2} \le x, y, z \le \frac{L_Æ}{2}-1\] \[p_{rel} = (x, y, z) \in \mathbb{Z}^3 \mid -D_Æ \le x, y, z \le D_Æ\]$V_Æ$ is the discrete volume of the entire space. Formula for the discrete volume of the entire space:
\[V_Æ = L_Æ \cdot L_Æ \cdot L_Æ\]Neighboring cells are considered to be the nearest orthogonal cells. In the simplest model, the nearest diagonal cells are not considered neighboring cells. This definition of neighboring cells can be argued by the absence of diagonal cells in one-dimensional space.
Time is divided into equal ticks.
The number of time ticks can be finite. In the case of finite time, the overflow of the absolute time counter does not affect physical laws.
The unit of measurement for time in the ether system of units is “æt”.
$T_Æ$ is the discrete size of all time. In the simplest model, the discrete size of all time is equal to the “standard discrete quantity” $N_Æ$. Therefore, in the simplest model, the discrete size of all time is equal to the discrete size of all space:
\[T_Æ=N_Æ\] \[T_Æ=L_Æ\]$T_Æ=L_Æ$ is a conditional formula for the principle of numerical equivalence of all time and the size of all space. Space and time have the same fundamental numerical periodicity.
The current time tick is denoted by $t_Æ$ and is a discrete cyclic time coordinate. Time ticks are numbered from $-T_Æ/2$ to $T_Æ/2-1$. For a separate designation for the discrete cyclic structure of time, the concept of “history” $H_Æ$ is used. The word “history” emphasizes that we are not talking about just a numerical parameter $t_Æ$, but about a set of admissible states of the time coordinate with a cyclic structure and sequence. The space $S_Æ$ and the history $H_Æ$ are two types of fundamental discrete regions in which the spatial and temporal coordinates live, respectively. The history of $H_Æ$ is actually the space of the time coordinate, and not the history of any object in the usual sense. The name “history” for $H_Æ$ allows us not to confuse time as a cyclic structure with the size of this structure $T_Æ$ and with the current time coordinate $t_Æ$. The history $H_Æ$ is a cyclic sequential one-dimensional integer sequence:
\[H_{Æ} = \left\lbrace (t_Æ) \in \mathbb{Z} \mid -\frac{T_{Æ}}{2} \le t_Æ \le \frac{T_{Æ}}{2}-1 \right\rbrace\]A “history wrapper function” $W_{\text{H.Æ}}(n)$ that maps any integer $n$ to the interval $[ -T_Æ/2, T_Æ/2 - 1 ]$, taking into account the cyclic nature of history:
\[W_{\text{H.Æ}}(n) = \left( n + \frac{T_{Æ}}{2} \right)\pmod{T_{Æ}} - \frac{T_{Æ}}{2}\]The tick number $0$ is called the “zero tick”. In the simplest model and in the simplest computer simulations, the “start of time” occurs at “zero tick”. The zero tick at the “start of time” is called the “start tick.” After the tick number $T_Æ/2-1$, there is another tick number $-T_Æ/2$:
\[t_Æ = W_{\text{H.Æ}}(t_Æ+1)\]In the simplest model, the “history wrapper function” $W_{\text{H.Æ}}(n)$ is equivalent to the “space wrapper function” $W_{\text{S.Æ}}(n)$. For simplicity, in the simplest model, we can use the “dimension wrapper function” $W_{\text{D.Æ}}(n)$ as a general synonym for the “space wrapper function” $W_{\text{S.Æ}}(n)$ and the “history wrapper function” $W_{\text{H.Æ}}(n)$:
\[W_{\text{D.Æ}}(n) = W_{\text{S.Æ}}(n) = W_{\text{H.Æ}}(n)\]Each ether object is conventionally assigned to one of eight levels of matter. In physics and chemistry, the term “level” is used to denote a wide variety of relationships, which can lead to confusion in terminology in this context. Therefore, a “level of matter” can also be referred to as a “stair of matter”, “rung of matter”, “stage of matter”, or “step of matter”. Collectively, these “stages of matter” form a “ladder of matter”, or “stairs of matter”. For brevity, the level of matter can be denoted by the capital letter $Æ$ with a number corresponding to the level of matter. Æ1 is the designation for the first level of matter, Æ2 for the second, Æ3 for the third, Æ4 for the fourth, Æ5 for the fifth, Æ6 for the sixth, Æ7 for the seventh, Æ8 for the eighth. A stair of matter is a qualitative type of collective organization of ether objects.
Etheron is the name of a discrete particle of matter at the first level of matter. Etheron is considered an ether object of the first level of matter. Etheron is denoted by the sign $æ$. In formulas, a separate sign $æ$ denotes one etheron from the set of all etherons.
Ether is etherons. Ether is denoted by the symbol $Æ$. In the formulas, the separate sign $Æ$ denotes the set of all etherons.
The principle of the etheronic basis of measurement states that while a physical unit may apply to quantities associated with objects at various levels of matter, its fundamental definition must be reducible to the characteristics of a single etheron via basic etheronic units. This principle serves as a metrological tenet of ÆToE; it is a criterion that all ÆToE physical units — including derived ones — must satisfy. Every physical unit must possess an etheronic basis. This principle ensures end-to-end quantitative compatibility: if units are defined on an etheronic basis yet remain applicable to objects at all levels, the theory can quantitatively describe etherons, atoms, macroscopic bodies, and astronomical objects within a single system of units. For STÆ computer simulations, it is crucial that the base units be discrete and grounded in etherons, as this enables a unified computational model.
The principles governing etheronic units of measurement comprise the applied rules of the ÆSoU system — derived from the principle of the etheronic basis of measurement — covering the notation and interpretation of these units. Although etheronic units apply to physical quantities associated with objects and processes at all levels of matter, their physical definitions trace back to the fundamental characteristics of a single etheron. Consequently, the notation for these units employs the prefix æ to indicate their etheronic basis. Thus, the presence of the æ prefix in a unit’s notation does not imply that the measured quantity or object itself is an etheron; rather, the prefix signifies the fundamental level against which the unit is defined. For instance, æt, æl, and æv are units of time, length, and velocity, respectively, defined on an etheronic basis, yet they can be used to quantitatively describe objects and processes at any level of matter. In other words, the æ in æt should not be interpreted as meaning “an etheron is time”. The symbol æ in a unit of measurement indicates that the unit has an etheronic basis. There is no contradiction between a unit’s “etheronic origin” and its “etheric application”. A unit’s prefix is determined not by its field of application, but by the level at which its physical basis is established.
Ether objects of the second and subsequent levels of matter are called “ether hyperobjects”.
In ether theory, the prefix “hyper” for any physical object or any informational object means “non-elementarity” of this object. Non-elementarity of an object of any type means that the object consists of subobjects of the same type.
In ether theory, the prefix “sub” for any physical object or any informational object means “nestedness” of this object in an object of a higher level. Nestedness of an object of any type means that the object is a component part of an object of the same type but of a higher level. The stair of matter does not increase with each act of nesting. An increase in the stair of matter occurs only when a new qualitative type of organization of the interaction between ether objects emerges.
Subobjects of ether hyperobjects are called “ether subobjects”. In the English version, “ether subobject” is “ether subobject”.
The criterion for classifying an ether hyperobject as belonging to a certain level of matter is not the quantitative parameters of the ether hyperobject, but the characteristic qualitative aspect of the interaction of ether subobjects of ether hyperobjects of this level of matter.
The hierarchical level of an ether subobject within a certain ether hyperobject at a specific stair of matter is called the rank of that ether object at that stair of matter. The greater the depth of nesting of an etheric subobject within a certain ether hyperobject at a given stair of matter, the lower the rank of that ether object at that stair of matter.
The hierarchical configuration notation for an ether object follows a format that, in its full version, includes: the designation of the matter stair; the designation of the ether object’s class within that matter stair; the designation of the ether object part; information about the specific instance of the ether object; and information about the ether object’s structure. The dot symbol is used in hierarchical identifiers as a hierarchical separator for stairs of matter, classes of ether objects, parts of ether objects, and sub-parts of ether objects. The colon symbol is used as a “role-qualification operator” (medium, substantial, or field) for a single etheron ($æ$) or the ether as a whole ($Æ$). The dot describes the structure of an object; the colon qualifies an object or a set of objects based on a relational property. Information about an instance of an ether object is specified after a hyphen within curly braces, in a certain format. Information about the structure of the ether object is indicated in parentheses, separated by a hyphen. Information regarding the structure of an ether object includes the notations of that object’s ether subobjects, separated by an apostrophe or other characters serving as connectors between the ether subobjects. The aspect of an ether quantity within an ether assertion can be used to define various facets of that quantity (for example, the “kinematic” aspect and the “inertnic” aspect). The kinematic aspect is the default aspect of an ether quantity unless another aspect is explicitly specified. A subaspect of an ether quantity within an ether statement can be used to define part-relation quantities (e.g., the “substance-field” subaspect). Object parts (such as substance and field) are designated in the object notation, while the relations between object parts are designated in the quantity’s subaspect. This rule separates object ontology from the semantics of the measured quantity. The symbolic philosophy of the grammar of an ether assertion: a rich physico-mathematical alphabet for quantities, but a strict machine alphabet for classes, objects, and context. An ether file is a sequence of ether statements and comments. The comments and the list of ether statements in the ether statement file refer not to the canonical notation of a single ether statement, but to the syntax of the ÆToE file’s source text. Comments must not be included in the abstract syntax tree of an ether statement. A comment must either be discarded entirely by the lexical analyzer or, in a special mode, preserved as metadata of the source file. The list of ether statements can be used in abstract syntax trees and their corresponding application programming interfaces, while the ether file serves as a physical text format. “.etoe” is an extension for an ether file. This notation can serve both as a compact human-readable representation and as a state serialization for a simulator:
ether-file
= { source-item } ;
source-item
= comment
| ether-statement, statement-terminator ;
ether-statement-list
= ether-statement
, { statement-terminator, ether-statement }
, [ statement-terminator ] ;
statement-terminator
= ";" ;
comment
= line-comment
| block-comment ;
line-comment
= hash-comment
| slash-comment ;
hash-comment
= "#", { comment-char } ;
slash-comment
= "//", { comment-char } ;
block-comment
= "/*", ? block-comment body ?, "*/" ;
comment-char
= ? any character except the end of the line ? ;
ether-statement = notation ;
notation
= e-notation
| chemical-notation
| quantity-expression
| constant-expression
| measurement-expression ;
e-notation = e-object | e-level | e-unit ;
object
= e-object
| chemical-notation ;
chemical-object
= object
| chemical-mass-only
| chemical-group
| protium-core
| proton
| neutron ;
e-object
= e-full-object
| e-compact-object
| e-ether
| e-etheron ;
e-full-object
= "Æ", level, ".", class, [".", object-context]
, [ instance ], [ structure ] ;
e-level = "Æ", level ;
e-compact-object
= "Æ", class, [".", object-context]
, [ instance ], [ structure ] ;
e-ether
= "Æ"
, [ etheron-qualifier ]
, [ instance ], [ structure ] ;
e-unit = "æ", unit-suffix ;
e-etheron
= "æ"
, [ etheron-qualifier ]
, [ instance ], [ structure ] ;
etheron-qualifier
= ":", etheron-role
| ":", etheron-role, ".", etheron-subrole ;
etheron-role = "m" | "s" | "f" | "sf" | "h" | "mf" ;
etheron-subrole = "br" | "dr" | "di" | "do" ;
level = "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" ;
unit-suffix = "n" | "c" | "l" | "s" | "t" | "m" | "v" | "i" ;
class
= "c"
| "b" | "hb"
| "sp" | "hsp"
| "mj" | "hmj"
| "el" | "ps"
| "p" | "n" | "a" | "pna"
| "ha"
| "ml" | "hml"
| "bd" | "hbd"
| "as" | "has";
object-context = part, [".", subpart, [".", subsubpart]] ;
part = "s" | "f" | "m" | "mf" ;
subpart = "tr" | "br" | "dr" | "di" | "do" | "core" | "atm" ;
subsubpart = ident;
chemical-notation
= chemical-full ;
chemical-full
= element, [ ":", element-subsort ],
[ "-", atomic_mass ],
[ "-", atomic_mass ],
[ chemical-structure ]
| molecule, [ ":", molecule-subsort ],
[ "-", atomic_mass ],
[ "-", atomic_mass ],
[ chemical-structure ] ;
chemical-mass-only
= atomic_mass, [ chemical-structure ] ;
proteon
= proton
| neutron
| protium-element ;
proton = "p" ;
neutron = "n" ;
protium-element = "H" ;
protium-mass = "1" ;
protium-structure = "(0)" ;
protium-atm = "()" ;
protium-core = "0" ;
chemical-structure
= "-" , protium-mass
| "-" , "(", [ chemical-object-list ], ")" ;
element
= "H" | "D" | "T" | "Ht" | "He"
| "Li" | "Be" | "B" | "C" | "N"
| "O" | "F" | "Ne" | "Na" | "Mg"
| "Al" | "Si" | "P" | "S" | "Cl"
| "Ar" | "K" | "Ca" | "Sc" | "Ti"
| "V" | "Cr" | "Mn" | "Fe" | "Co"
| "Ni" | "Cu" | "Zn" | "Ga" | "Ge"
| "As" | "Se" | "Br" | "Kr" | "Rb"
| "Sr" | "Y" | "Zr" | "Nb" | "Mo"
| "Tc" | "Ru" | "Rh" | "Pd" | "Ag"
| "Cd" | "In" | "Sn" | "Sb" | "Te"
| "I" | "Xe" | "Cs" | "Ba" | "La"
| "Ce" | "Pr" | "Nd" | "Pm" | "Sm"
| "Eu" | "Gd" | "Tb" | "Dy" | "Ho"
| "Er" | "Tm" | "Yb" | "Lu" | "Hf"
| "Ta" | "W" | "Re" | "Os" | "Ir"
| "Pt" | "Au" | "Hg" | "Tl" | "Pb"
| "Bi" | "Po" | "At" | "Rn" | "Fr"
| "Ra" | "Ac" | "Th" | "Pa" | "U"
| "Np" | "Pu" | "Am" | "Cm" | "Bk"
| "Cf" | "Es" | "Fm" | "Md" | "No"
| "Lr" | "Rf" | "Db" | "Sg" | "Bh"
| "Hs" | "Mt" | "Ds" | "Rg" | "Cn"
| "Nh" | "Fl" | "Mc" | "Lv" | "Ts"
| "Og" | "Nm" | "X" ;
element-subsort = subelement ;
subelement = ident | number ;
molecule-ident
= molecule-letter
, { molecule-letter | digit | "_" } ;
identifier-not-element = molecule-ident - element - proteon;
molecule = identifier-not-element ;
molecule-subsort = ident | number ;
quantity-expression
= quantity, [".", science-context]
, aspect-expression
, [".", character]
, ".", object-notation ;
const-identifier = "const" ;
quantity = quantity-ident - const-identifier;
quantity-ident
= quantity-letter
, { quantity-letter | digit | "_" } ;
science-context
= science-domain
, [".", science-subdomain
, [".", science-subdomain]] ;
science-domain
= core-science-domain
| "sc_", extension-science-domain ;
science-subdomain
= core-science-subdomain
| "scsd_", extension-science-subdomain ;
extension-science-domain = ident ;
extension-science-subdomain = ident ;
core-science-domain
= "physics"
| "mathematics"
| "chemistry"
| "biology"
| "neuroscience"
| "cognitive_science"
| "social_science" ;
core-science-subdomain
= "mechanics"
| "kinematics"
| "dynamics"
| "statistical"
| "thermodynamics"
| "electromagnetism"
| "optics"
| "gravitation"
| "fluid"
| "plasma"
| "atomic"
| "molecular"
| "nuclear"
| "particle"
| "condensed_matter"
| "astrophysics"
| "cosmology"
| "information"
| "algebra"
| "geometry"
| "number_theory"
| "probability"
| "statistics"
| "optimization"
| "discrete"
| "evolution"
| "abiogenesis"
| "neural_networks"
| "consciousness"
| "society" ;
aspect-expression
= [ ".", dimension-aspect ]
, [ ".", dynamic-aspect ]
, [ ".", relation-aspect ]
, [ ".", e-state-aspect ]
, [ ".", e-delay-aspect ] ;
dimension-aspect
= "dimension" | "D"
| "space" | "S"
| "time" | "T"
| "history" | "H" ;
dynamic-aspect
= "kinematic" | "ka"
| "inertnic" | "ia"
| "collisional" | "ca" ;
relation-aspect
= "substance_field" | "sf"
| "hyperobject_medium" | "hm" ;
e-state-aspect
= "state1" | "s1" | "rest"
| "state2" | "s2" | "interaction"
| "state3" | "s3" | "departure"
| "state4" | "s4" | "arrival"
| "jump" | "jmp" | "s3s4"
| "free_cycle" | "freec" | "s1s3s4"
| "collision_cycle" | "collc" | "s1s2s3s4" ;
e-delay-aspect
= "base"
| "spontaneous" | "spont" | "random" | "rnd"
| "compensatory" | "comp"
| "additional" | "add"
| "step"
| "move" ;
character
= "avg" | "max" | "min" | "inst" | "rms"
| "tot" | "net" | "abs" | "rel"
| "peak" | "mean" | "std"
| "norm" | "syn"
| "parallel" | "par"
| "perpendicular" | "perp"
| "old" | "new"
| "crit" ;
object-notation = e-notation | chemical-notation ;
constant-expression
= const-full
| const-compact-letter
| const-compact-at ;
const-full
= const-identifier,
".", quantity,
".", character,
".", const-object ;
const-compact-letter = "Ꞓ", const-name ;
const-compact-at = "@", const-name ;
const-object
= e-notation
| chemical-notation ;
const-name = ident | number ;
measurement-expression = number, e-unit ;
instance = "-", "{", [ pair-list ], "}" ;
pair-list = pair, { ",", pair } ;
pair = key, "=", value ;
key = ident ;
value
= ident
| measurement-expression
| number
| string ;
structure = "-", "(", [ object-list ], ")" ;
object-list = object, { separator, object } ;
chemical-group
= "(", [ chemical-object-list ], ")" ;
chemical-object-list
= chemical-object, { separator, chemical-object } ;
notation-list = notation, { separator, notation } ;
separator = separator-char, [ separator-instance ] ;
separator-char
= etheron-separator-char
| batch-separator-char
| spiral-separator-char
| major-separator-char
| atom-separator-char
| mol-separator-char
| body-separator-char
| astr-separator-char ;
etheron-separator-char = "|" ;
batch-separator-char = "!" ;
spiral-separator-char = "$" ;
major-separator-char = "*" ;
atom-separator-char = "'" ;
mol-separator-char = "^" ;
body-separator-char = "&" ;
astr-separator-char = "~" ;
separator-instance = instance ;
ident = letter, { letter | digit | "_" } ;
letter
= "a"|"b"|"c"|"d"|"e"|"f"|"g"|"h"|"i"|"j"|"k"|"l"|"m"
| "n"|"o"|"p"|"q"|"r"|"s"|"t"|"u"|"v"|"w"|"x"|"y"|"z"
| "A"|"B"|"C"|"D"|"E"|"F"|"G"|"H"|"I"|"J"|"K"|"L"|"M"
| "N"|"O"|"P"|"Q"|"R"|"S"|"T"|"U"|"V"|"W"|"X"|"Y"|"Z";
quantity-letter
= letter
| greek-letter
| greek-variant-letter
| letterlike-symbol ;
molecule-letter = letter;
atomic_mass = non_zero, { digit } ;
number = [ "-" ], digits, [ ".", digits ] ;
digits = digit, { digit } ;
zero = "0" ;
non_zero
= "1" | "2" | "3" | "4"
| "5" | "6" | "7" | "8" | "9" ;
digit = zero | non_zero ;
hex-digit
= digit
| "A" | "B" | "C" | "D" | "E" | "F"
| "a" | "b" | "c" | "d" | "e" | "f" ;
string = '"', { string-char }, '"' ;
string-char
= unescaped-char
| escape-sequence ;
escape-sequence = "\", escape-code ;
escape-code
= '"' | "\" | "b" | "f" | "n" | "r" | "t"
| "u", hex-digit, hex-digit
, hex-digit, hex-digit ;
greek-letter
= "Α" | "α" | "Β" | "β" | "Γ" | "γ" | "Δ" | "δ"
| "Ε" | "ε" | "Ζ" | "ζ" | "Η" | "η" | "Θ" | "θ"
| "Ι" | "ι" | "Κ" | "κ" | "Λ" | "λ" | "Μ" | "μ"
| "Ν" | "ν" | "Ξ" | "ξ" | "Ο" | "ο" | "Π" | "π"
| "Ρ" | "ρ" | "Σ" | "σ" | "Τ" | "τ" | "Υ" | "υ"
| "Φ" | "φ" | "Χ" | "χ" | "Ψ" | "ψ" | "Ω" | "ω" ;
greek-variant-letter
= "ϵ" | "ϑ" | "ϖ"
| "ϱ" | "ϰ" | "ϕ" ;
letterlike-symbol
= "ℏ" | "ℎ" | "ℓ"
| "ℐ" | "ℑ" | "ℒ"
| "ℱ" | "ℜ" | "ℵ"
| "℘" ;
unescaped-char
= ? Unicode scalar value,
except U+0000–U+001F, U+0022, U+005C ? ;
The EBNF grammar of the dialect “ISO/IEC 14977:1996” for the ÆToE ether statement defines the statement as a linear sequence of symbols in which structural relationships between segments are expressed by explicit delimiters: the dot (.), colon (:), hyphen (-), curly braces ({}), parentheses (()), apostrophe ('), and comma (,). The ÆToE EBNF grammar does not recognize LaTeX markup and contains no rules for LaTeX commands, LaTeX groups, or LaTeX subscripts. LaTeX markup introduces an additional layer of representation to the ether statement that is not part of the ÆToE grammar; for instance, Greek letters and letter-like symbols may be encoded using LaTeX commands (such as tau, rho, chi, Pi, hbar, etc.). The relationship between the EBNF form of an ether statement and its LaTeX form is one of representation rather than identity: the LaTeX form is one possible external representation of the ether statement, whereas the EBNF form constitutes its canonical form within the ÆToE grammar. In a LaTeX document where an ether statement is written in LaTeX form, subscripts and superscripts implicitly serve as structural delimiters — roles that are expressed by the dot in the EBNF form. In other words, the LaTeX form of an ether statement implicitly includes an “invisible dot” before every subscript and superscript; this structural delimiter is written explicitly in the EBNF form but omitted in the LaTeX form as visually redundant. An ether statement in LaTeX form cannot be fed directly into the parser for the ÆToE EBNF grammar. Before parsing, an ether assertion in LaTeX form must undergo de-LaTeX-ization — the conversion of the LaTeX form of the ether assertion into its EBNF form. De-LaTeX-ization of an ether assertion is a deterministic transformation that maps each LaTeX construct within the assertion to its EBNF equivalent. De-LaTeX-ization is neither part of the ÆToE EBNF grammar nor part of the ÆToE semantic validator; rather, it is a preparatory step performed before the ÆToE EBNF grammar is applied. For example, LaTeX commands for Greek letters and letter-like symbols are replaced by the corresponding Unicode characters from the greek_letter, greek_variant_letter, and letterlike_symbol sets. LaTeX constructs lacking an EBNF equivalent in the ÆToE grammar are either mapped to the nearest valid EBNF segment or flagged as a grammar extension requiring a separate solution. De-LaTeX-ization is a preliminary stage in processing an ether assertion found within a LaTeX document; it does not replace semantic validation. Following de-LaTeX-ization, the ether assertion in EBNF form is fed into the ÆToE EBNF grammar and subsequently into the ÆToE semantic validator. In ÆToE formulations where ether assertions are written in LaTeX form, subscripts and superscripts should be interpreted as LaTeX representations of EBNF segments rather than as independent EBNF segments. This rule separates the representation of an ether statement from its canonical form and prevents the mixing of LaTeX markup with the ÆToE EBNF grammar. Reliable de-LaTeXing requires a deterministic pipeline: LaTeX tokenization; parsing into an AST; converting the AST into an EBNF-AST based on explicit rules; serialization into an EBNF string; and validation against the ÆToE grammar.
The semantic validator for the ether assertion notation verifies the physical and mathematical correctness of both the ether assertion itself and the structure of the ether objects within that assertion. For example, the ether object of a certain stair of matter cannot contain, as sub-objects, the ether objects of subsequent stairs of matter.
Serializing the ether assertion notation into a programming language identifier must ensure that the identifier is valid in major programming languages, maintain a one-to-one mapping between the notation and the identifier, and allow for lossless reversibility. The serialization process may employ either a fixed-length escape-encoding scheme or a base64url encoding scheme. The escape-encoding scheme preserves the recognizability of the notation, whereas the base64url encoding scheme ensures a compact identifier. Both schemes may incorporate a prefix (e.g., “etoe_”). Serialization layers for a programming language, database, or file system may provide canonical ASCII aliases for each ether quantity (e.g., “tau” for “τ”).
A unified evolutionary emergent etheronic simulation, visualization, and formalization of all levels of matter must be based on a code and data architecture that enables the use of multi-level, hierarchical etheronic hyperpatterns to identify and formalize the physical laws governing every level of matter. This approach implies that the simulation, visualization, and formalization process begins at the level of etherons — the fundamental constituents — to derive, in sequence, the governing principles of all subsequent levels of matter. An evolutionary emergent etheronic simulation does not require the creation of separate simulators for each successive level of matter; rather, a universal simulator should feature a single microscopic core — modeling space, time, and etherons — upon which the detection, tracking, and formalization of stable, collective structures at higher levels of matter are built. The goal of the simulator is to initiate a unified, discrete dynamic of a multitude of etherons, demonstrating that the stable structures of subsequent levels — along with their properties and observable patterns — emerge as organizational layers of this same micro-dynamic. The simulation architecture must consist of three strictly delineated layers: 1. the micro-dynamic layer, comprising the sole fundamental simulation of etherons; 2. the emergent-analytical layer, dedicated to the detection and measurement of collective structures; and 3. the formalization layer, which translates these stable structures into mathematical models, ÆToE assertions, conservation laws, effective equations, and visual representations. Furthermore, any macro-level formula must have a traceable derivation: etherons → local interactions → statistical patterns → objects at the next level → macro-laws. Any macroscopic value must be computable via inverse aggregation from a microstate. The simulation must support a unified system of emergent detectors. The visualization component must function as a multi-level window into the same simulation state. Any macro-level visualization must include a “drill-down” mode, allowing one to descend all the way to the corresponding etherons. The formalization framework must be capable of transitioning from raw trajectories to effective laws of motion by deriving the equations for these laws — using regression techniques applied to the microdynamics. The architecture must feature a precise micro-kernel, adaptive coarse-graining, and multi-scale refinement. The simulation must yield an executable and verifiable hierarchy tracing the origins of physical laws. No post-etheron level should possess its own fundamental physics that does not derive from the level of etherons; rather, each successive level must be a detectable, stable pattern of dynamics from the preceding level, and every effective rule at that level must be a derivable statistical consequence of the level below it. In such an architecture, visualization, simulation, and formalization should be three representations of the same object state, rather than three independent subsystems.
Ether subobjects of ether objects of the second level of matter are etherons. An etheron has two distinct, conceptual “identity axes”: “etheron role” and “etheron affiliation”. The etheron role answers the question: “What does the etheron do within a given ether hyperobject?” Etheron affiliation answers the question: “Of which ether hyperobject is the etheron currently a part?” The affiliation of the etheron is discrete yet hierarchical. The role of the etheron is discrete yet relational. When affiliation changes, the role does not necessarily change as part of the same event. When the role changes, affiliation does not necessarily change as part of the same event. An ether hyperobject can preserve the pattern of role distribution among etherons. The physical individuality of an ether hyperobject is determined not by the specific etherons that comprise it, but by the configuration of relationships maintained between them. The bearer of the ether hyperobject’s stability is not the etheron, but the organization of a multitude of etherons. The role of an etheron is the relational classification of its motion. The affiliation of an etheron is the hierarchical relationship of its inclusion. An ether hyperobject is a stable collective pattern of etheron roles and motions.
An ether subobject containing ether subobjects of a lower level is called “ether subhyperobject”.
An etheron that is not a subobject of any ether hyperobject is called “medium etheron”. “Medium etheron” can be denoted by $æ:m$.
“Ether medium” is medium etherons. “Medium ether” can be denoted by $Æ:m$:
\[Æ:m=\{æ\in Æ\mid role(æ)=m\}.\]The spatial, temporal, and velocity parameters of the ether medium constitute the configuration of the ether medium.
The configuration of the ether medium depends on ether hyperobjects.
An etheron that is not a subobject of a given ether hyperobject is called “external etheron” for this ether hyperobject.
“External ether” for an ether hyperobject is external etherons.
The external ether for an ether hyperobject includes all etherons of the ether medium and all etherons of all other ether hyperobjects, except for the etherons of this ether object.
The concept of “ether medium” and the concept of “external ether” are not synonyms. The concept of “external ether” is specific to each ether hyperobject.
The spatial, temporal, and velocity parameters of the external ether constitute the configuration of the external ether for the ether hyperobject.
The process by which an etheron becomes part of an ether hyperobject is conventionally called synthesization. The process by which an etheron becomes part of an ether medium is conventionally called chaotization. The process by which an etheron leaves a trail in an ether medium or an ether hyperobject is conventionally called trailization. The basis of synthesization, trailization and chaotization is the process of interaction of etherons.
The total number of etherons in space does not change.
Mass is the number of etherons.
The unit of measurement for mass in the ether system of units is “æm”.
$m_Æ$ is the discrete mass of the entire ether, measured in æm.
$ρ_Æ$ is the discrete density of ether, measured in æm/æs and equal to the ratio of the discrete mass of ether $m_Æ$ to the discrete volume of space $V_Æ$:
\[ρ_Æ=m_Æ/V_Æ\]The mass of an etheron is 1 æm.
In the simplest version, the total number of etherons in the Universe is equal to the number of cells of absolute space in the Universe. In the case of equality of the amounts of matter and space, the discrete density of the Universe’s ether is equal to unity: $ρ_Æ=m_Æ/V_Æ=1$. Therefore, with equality of the amounts of matter and space in the Universe, the discrete mass of ether in the Universe is equal to the discrete volume of the Universe: $m_Æ=V_Æ$. The equality of the quantities of matter and space in the Universe is called the “principle of numerical equivalence of matter and space”.
Hypothetically, the “initial” Universe could have space with one etheron in each cell.
It is likely that if, with the existing amount of motion of matter, the amount of matter were “significantly less” or “significantly more” than the amount of space, then full evolution of matter in the Universe would be impossible.
Several etherons can be in one space cell at the same time. A space cell in which there is one etheron or several etherons at a given time tick is called an “occupied cell”.
Several etherons can interact simultaneously in one cell of space. The interaction of etherons can be conventionally called “collision of etherons”. A “group of collisional etherons in a space cell” is designated as $Æ1.c$ (or $Æc$ for short) and is considered a composite ether object of the first stair - a “collisional group of etherons” or a “collisional ether object of the first stair”. A “collisional group of etherons” is not a second-stage ether hyperobject of matter, but it can become one upon the completion of the etheron collision. A group of interacting etherons is treated as a single composite object within the framework of a specific collision event. A collision composition does not imply an increase in the level of matter. A collision group can be interpreted as a pre-emergent configuration. Collision group Æ1.c is a temporary composite ether object of the first stair, comprising a multitude of etherons that mutually participate in a single local act of interaction within a single spatial cell during a single tick or a specific collision cycle. “Etheron collision” is an event, and Æ1.c is the object/configuration of that event.
In one space cell, interacting etherons and etherons that do not interact with the interacting etherons can be present simultaneously.
A space cell may have no etherons for some time. A space cell in which there are no etherons at a given time tick is called an “empty cell”.
Ether is called transparent due to the possibility of several etherons being in one space cell at the same time.
If an etheron is depicted as occupying the entire cell of absolute space, then in the image, oncoming etherons will pass through each other.
Each etheron stores information about its state and about the parameters determining the position and motion of the etheron in space. In computer simulation programs of transparent inertial ether, information related to the etheron may include additional data that speeds up the simulation process and simplifies the simulation logic. In optimized computer simulations of space-time-ether models, a “structure of arrays” (SoA) scheme can sometimes be used to store information about etherons. However, in standard object-oriented code for space-time-ether models, an “array of structures” (AoS) scheme should be used, as it is natural and familiar in most programming languages.
The parameters of an etheron can change upon interaction with other etherons that are in the same space cell as the etheron itself.
The “state” of an etheron is denoted by $s_æ$. Each etheron can be in one of four states:
\[s_æ \in \{1, 2, 3, 4\}\]Ether is called multistate because etherons are in different states.
In the simplest STÆ model, each state of an etheron lasts for at least one time tick and is processed only once during the current time tick. Therefore, in general, in a computer simulation, each etheron may need a “counter of ticks of the time an etheron is in its state” - $t_æ$, as well as a “flag for processing the current state in the current time tick” - $f_æ$. At the beginning of each time tick, the flags of all etherons are reset to zero, and after processing ($F_æ$) in the current time tick ($t_Æ$) by an etheron of its state, the etheron’s flag is set to one, and the etheron can no longer process its state in the current time tick again:
\[\forall æ \quad f_{æ}^{(t_Æ+1)} = 0\] \[f_{æ}^{(t_Æ)} = \Phi(\, f_{æ}^{(t_Æ)} \lor F_{æ}^{(t_Æ)} \,)\]The first state of the etheron is the “rest of the etheron” in the cell of space. The first state of the etheron is designated $s1$æ. The duration of the first state of the etheron is denoted by $τ_{\text{s1.æ}}$. The duration of the first state of the etheron is at least one tick of time:
\[τ_{\text{s1.æ}} \ge 1\]The first tick in the “rest” state is conventionally called the “tick of the basic delay”. The duration of the “basic delay” of the etheron is denoted by $τ_{\text{s1.base.æ}}$:
\[τ_{\text{s1.base.æ}} \ge 1\]If the etheron spontaneously remains in the first state for one more tick when it should have passed to the third state, then such a tick is conventionally called the “tick of the spontaneous delay”. The duration of the “spontaneous delay” of the etheron is denoted by $τ_{\text{s1.rnd.æ}}$:
\[τ_{\text{s1.rnd.æ}} \ge 0\]If the etheron remains in the first state for one more tick to compensate for the deficit of jumps in the direction of its continuous movement, then such a tick is conventionally called the “tick of the compensatory delay”. The duration of the “compensatory delay” of the etheron is denoted by $τ_{\text{s1.comp.æ}}$:
\[τ_{\text{s1.comp.æ}} \ge 0\]If the etheron remains in the first state for one more tick to implement a decrease in the continuous speed in the direction of its continuous movement in accordance with the fifth parameter of the etheron, then such a tick is called the “tick of the additional delay”. The duration of the “additional delay” of the etheron is denoted by $τ_{\text{s1.add.æ}}$:
\[τ_{\text{s1.add.æ}} \ge 0\]The duration of the first state of the etheron consists of the duration of the “basic delay”, the duration of the “compensatory delay”, the duration of the “additional delay” and the duration of the “spontaneous delay”:
\[τ_{\text{s1.æ}} = τ_{\text{s1.base.æ}} + τ_{\text{s1.comp.æ}} + τ_{\text{s1.add.æ}} + τ_{\text{s1.rnd.æ}}\]The second state of the etheron is the “interaction of the etheron” in a cell of space with other etherons located in the same cell. The second state of the etheron is denoted $s2$æ.The etheron always passes into the second state from the first state if there are other etherons in the first state in the cell of space. The duration of the second state of the etheron is denoted by $τ_{\text{s2.æ}}$. The duration of the second state of the etheron is at least one tick of time:
\[τ_{\text{s2.æ}} \ge 1\]The third state of an etheron is “movement from the cell” in which the etheron is located. The third state of an etheron can be called “the departure of an etheron”. The third state of the etheron is denoted $s3$æ. An etheron usually moves to the third state from the first state if there are no other etherons in the first state in the space cell, and if a time tick has arrived in which, in accordance with the parameters of the etheron’s movement, it is necessary to move from the space cell. But sometimes an etheron can spontaneously remain in the first state for another time tick, even if it should have moved to the third state. If an etheron spontaneously remains in the first state, then when other etherons appear in the cell, the etheron will move to the second state, not to the third state. An etheron also moves to the third state from the second state. The duration of the third state of the etheron is denoted by $τ_{\text{s3.æ}}$. The duration of the third state of an etheron is at least one tick of time:
\[τ_{\text{s3.æ}} \ge 1\]The fourth state of the etheron is “movement to the neighboring cell” that corresponds to the parameters of the etheron’s movement, and in which the etheron will be. The fourth state of the etheron is called “arrival of the etheron”. The fourth state of the etheron is denoted $s4$æ. The etheron moves to the fourth state from the third state. The etheron moves to the first state from the fourth state. The duration of the fourth state of the etheron is denoted by $τ_{\text{s4.æ}}$. The duration of the fourth state of the etheron is at least one tick of time:
\[τ_{\text{s4.æ}} \ge 1\]The third state of the etheron and the fourth state of the etheron together constitute the “etheron jump” from the cell in which the etheron is located to the neighboring cell in which the etheron will be located, in accordance with the parameters of the etheron’s movement. The duration of the etheron jump is denoted by $τ_{\text{jump.æ}}$. The duration of the etheron jump is at least two time ticks:
\[τ_{\text{jump.æ}} = τ_{\text{s3.æ}} + τ_{\text{s4.æ}}\] \[τ_{\text{jump.æ}} \ge 2\]The duration of the basic delay of the etheron in the resting state $τ_{\text{s1.base.æ}}$ together with the duration of the etheron jump $τ_{\text{jump.æ}}$ make up the basic duration of the etheron movement $τ_{\text{move.æ}}$. The basic duration of the etheron movement is at least three ticks of time:
\[τ_{\text{move.æ}} = τ_{\text{s1.base.æ}} + τ_{\text{s3.æ}} + τ_{\text{s4.æ}} = τ_{\text{s1.base.æ}} + τ_{\text{jump.æ}}\] \[τ_{\text{move.æ}} \ge 3\]The relative number of time ticks after which an etheron, which is in a state of rest at a given time tick, will be in the next cell of space in a state of rest is called the duration of the etheron step $τ_{\text{step.æ}}$:
\[τ_{\text{step.æ}} = 1 + τ_{\text{s3.æ}} + τ_{\text{s4.æ}} = 1 + τ_{\text{jump.æ}}\]The cycle of an etheron is a sequence of states starting with the first state and ending with the fourth state. The duration of the etheron cycle is denoted by $τ_æ$.
An etheron cycle without the second state of the etheron is called a “free cycle”. The duration of the free cycle of etheron is denoted by $τ_{\text{freec.æ}}$. The duration of the free cycle of etheron is made up of the duration of the first state, the duration of the third state, and the duration of the fourth state:
\[τ_{\text{freec.æ}} = τ_{\text{s1.æ}} + τ_{\text{s3.æ}} + τ_{\text{s4.æ}}\] \[τ_{\text{freec.æ}} \ge 3\]An etheron cycle with the second state of the etheron is called a “collisional cycle”. The duration of the collision cycle of the etheron is denoted by $τ_{\text{collc.æ}}$. The duration of the collision cycle of the etheron is made up of the duration of the first state, the duration of the second state, the duration of the third state, and the duration of the fourth state:
\[τ_{\text{collc.æ}} = τ_{\text{s1.æ}} + τ_{\text{s2.æ}} + τ_{\text{s3.æ}} + τ_{\text{s4.æ}}\] \[τ_{\text{collc.æ}} \ge 4\]Velocity relative to absolute space is called “absolute velocity”.
The unit of measurement for velocity in the ether system of units is “æv”.
The kinematic displacement of an etheron from a cell to an adjacent cell is called “jump displacement”. The speed of the jump displacement is called “jump velocity”.
Free motion of an etheron is a sequence of states starting after the state of interaction with other etherons and ending before the state of interaction with other etherons.
The cell of space in which the etheron was located when interacting with other etherons is called the “initial cell” of free motion. The etheron collision actually creates a new starting point of free movement for the etherons participating in the etheron collision.
The jump of the etheron after interacting with other etherons is called the “initial jump” of free motion.
The jump of the etheron before interacting with other etherons is called the “final jump” of free motion.
The cell of space in which the etheron was located before interacting with other etherons is called the “final cell” of free motion.
The final cell of the previous free motion is the initial cell of the next free motion.
The trajectory of the jumps of the etheron through the cells of space from the initial jump of free motion to the final jump of free motion is called a “free discrete path”. The free discrete path begins in the initial cell of free motion and ends in the final cell of free motion. The free discrete path is a discrete approximation of a straight line. The average speed of an etheron along a free discrete path is called the “discrete speed”.
The kinematic displacement of the etheron from the initial cell of free motion to the final cell of free motion is called “continuous displacement”. The speed of continuous displacement is called “continuous velocity”.
The continuous velocity of an etheron is a discrete approximation of constant velocity.
An etheron is called inertial due to the conditionally rectilinear and conditionally uniform free motion of the etheron.
Ether is called inertial due to the conditionally rectilinear and conditionally uniform free motion of etherons.
The average absolute continuous speed of an etheron is denoted by the capital Latin letter $C$.
Absolute continuous speeds of an etheron can only be in a narrow range around $C$. An etheron with an absolute continuous speed below $C$ is considered “low-speed”. An etheron with an absolute continuous speed above $C$ is considered “high-speed”.
A freely moving etheron is considered an inertial reference frame.
Continuous velocity relative to an inertial reference frame is called “relative velocity”.
Transformations of coordinates and continuous velocity of an etheron or group of etherons when transitioning in the description of their motion from one inertial reference frame to another correspond to Galilean transformations.
The first parameter of an etheron is the absolute position of the cell in which the etheron is located at the current time tick. The first parameter of an etheron is called “position”. The first parameter of the etheron is briefly denoted as $\vec{r}{\text{æ}}$. The first parameter of the etheron has a kinematic aspect and may be denoted as $\vec{r}{\text{ka.æ}}$. At the starting tick of time in the simplest model, in each cell of space there is one etheron with the first parameter equal to the position of the cell in which this etheron is located.
The second parameter of an etheron is the absolute position of the cell in which the etheron interacted with other etherons once again. The second parameter of the etheron is called the “collision position” and has a collisional aspect. The second parameter of the etheron is denoted by $\vec{r}_{\text{ca.æ}}$. The second parameter of the etheron actually determines where the current free section of its movement begins. At the starting tick of the simplest model, the value from the first parameter of the etheron is entered into the second parameter of the etheron. At each zero tick of the simplest model’s computer simulation, to protect against incorrect calculations of the etheron’s future position, the value from the first parameter of the etheron can be entered into the second parameter of the etheron.
The third parameter of an etheron is the absolute time tick in which the etheron interacted with other etherons once again. The third parameter of the etheron is called the “collision tick” and has a collisional aspect. The third parameter of the etheron is denoted by $t_{\text{ca.æ}}$. The third parameter of the etheron actually determines when the current free section of the etheron’s movement begins. If an etheron spontaneously lingers in the first state for an additional time tick, then the third parameter of an etheron is increased by one. At the starting tick of the simplest model, the third parameter of the etheron is reset to zero. At every zero tick of the simplest model’s computer simulation, to protect against incorrect calculations of the etheron’s future position, the third parameter of the etheron can be reset to zero.
The fourth parameter of an etheron is the relative position of the distant cell to which the etheron moves after interacting with other etherons. The fourth parameter of the etheron is called “direction” and has a kinematic aspect. The fourth parameter of the etheron is denoted briefly as $\vec{d}{\text{æ}}$ and fully as $\vec{d}{\text{ka.æ}}$. The fourth parameter of an etheron is the reference direction vector, the coordinates of which have a range from $-D_Æ$ to $D_Æ$, where $D_Æ$ is the reference distance. The length of the reference direction vector is approximately equal to $D_Æ$. The reference direction vector is the vector of displacement by the reference distance $D_Æ$. In the simplest simulator, the random “direction” vector $\vec{d}_æ$ for the etheron can be obtained through angles in a spherical coordinate system:
\[\vec{d}_æ = \Bigl( \mathop{\text{round}}\bigl(D_Æ \cdot \sin\theta \cdot \cos\varphi\bigr), \mathop{\text{round}}\bigl(D_Æ \cdot \sin\theta \cdot \sin\varphi\bigr), \mathop{\text{round}}\bigl(D_Æ \cdot \cos\theta\bigr) \Bigr)\]where:
The fifth parameter of the etheron is the “total additional delay” of the etheron in ticks of time in the “rest” state, with which the etheron, when moving freely, will reach the cell whose position is the sum of the absolute position of the cell specified in the second parameter and the relative position of the cell specified in the fourth parameter. The fifth parameter of the etheron is called “delay” and has an inertnic aspect. The fifth etheron parameter is denoted briefly as $a_{\text{æ}}$ and fully as $a_{\text{ia.æ}}$. The letter ‘a’ in the designation of the fifth parameter of the etheron comes from the English word “addition”, since the meaning of “delay” is an addition to some time or an addition to some duration. The fifth parameter of the etheron can be expressed as an unsigned integer from a certain range. In the simplest case, the range of values of the fifth parameter lies from $0$ to $D_Æ$, where $D_Æ$ is the reference distance. In the simplest model, the fifth parameter is the “total additional delay” in the Euclidean free continuous displacement of the etheron over the Euclidean reference distance $D_Æ$. The value of the fifth parameter of the etheron cannot overflow. The zero value of the fifth parameter of the etheron corresponds to the maximum value of the range of absolute continuous velocities of the etheron. And the maximum value of the fifth parameter of the etheron corresponds to the minimum value of the range of absolute continuous velocities of the etheron. The average value of the fifth parameter of the etheron in the simplest model is equal to half of $D_Æ$:
\[a_{avg.æ}= \frac{D_Æ}{2}\]The fifth parameter of the etheron is the “total additional delay” of the etheron in time ticks in the “rest” state, with which the etheron, in free movement, will reach the cell whose position is the sum of the absolute position of the cell specified in the second parameter and the relative position of the cell specified in the fourth parameter. The fifth parameter of the etheron is called the “delay”. The fifth parameter of the etheron is denoted by $a_æ$. The fifth parameter of the etheron can be expressed as an unsigned integer from a certain range. In the simplest case, the range of values of the fifth parameter lies from $0$ to $D_Æ$, where $D_Æ$ is the reference distance. In the simplest model, the fifth parameter is the “total additional delay” during the Euclidean free continuous movement of the etheron by the Euclidean reference distance $D_Æ$. The value of the fifth parameter of the etheron cannot overflow. The zero value of the fifth parameter of the etheron corresponds to the maximum value of the range of absolute continuous speeds of the etheron. And the maximum value of the fifth parameter of the etheron corresponds to the minimum value of the range of absolute continuous speeds of the etheron.
In the simplest model, copying the “position” parameter ( $\vec{r}$æ ) of each etheron into the “collision position” parameter ( $\vec{r}$ca.æ ) of that etheron and zeroing the “collision tick” parameter ( $t_{\text{ca.æ}}$ ) of each etheron at zero tick of time ( $t_Æ=0$ ) prevents uncertainty in the time elapsed since collisions:
\[\forall æ \quad \vec{r}_{\text{ca.æ}}^{(t_Æ=0)} = \vec{r}_{æ}\] \[\forall æ \quad t_{\text{ca.æ}}^{(t_Æ=0)} = 0\]At the start of the Universe and at the start of the computer simulation, there are essentially no previous etheron collisions. Therefore, before the first etheron interaction, it is conventionally assumed that the initial etheron collision occurred at the moment of the launch of space-time-ether, right here and right now. On the starting tick, “where the etheron is actually located” coincides with “where it should be according to its free movement”.
In the fourth state of the etheron, the absolute position of the space cell to which the etheron has arrived is entered into the first parameter of this etheron.
The free motion of an etheron is always calculated based on the current time tick and all the parameters of the etheron. Knowing the space cell of the last collision and the time tick of the last collision in which the etheron participated, as well as knowing the relative direction and the total additional delay, it is always possible to determine where the etheron should be at a certain time tick so that the trajectory and velocity of the etheron in free motion are a discrete approximation of uniform and rectilinear motion. The calculation of uniform free motion can be made based on the number of jumps from the space cell of the last collision to the conditional target cell, to which the direction of the etheron points. The number of jumps to the target cell, given the orthogonality of the etheron’s jumps, is equal to the “Manhattan distance” to this cell. In the simplest model, for an etheron that is alone in the “rest” state in a certain cell at a given time tick, the position in space is calculated, to which this etheron should reach in accordance with the etheron’s motion parameters in the time required for the etheron to jump. If the calculated position in space does not coincide with the current cell of the etheron, then this means that the time tick for this etheron to enter the state of “moving from the cell” has come. If the cell of space into which the etheron must enter is not an adjacent cell, then a three-dimensional version of the Bresenham algorithm can be used to calculate the next cell so that the trajectory of orthogonal jumps best approximates a straight line to this cell.
The trajectory of the etheron jumps always approximates a straight line, and the Euclidean speed of movement along this straight line is approximately constant. Etherons with different directions of movement, but with the same “delay” parameters, move with the same Euclidean speed due to a different number of their “compensatory delay ticks” at rest. The number of jumps to the target cell depending on the direction of movement is determined by the “Manhattan distance” to the target cell in this direction. The greater the number of jumps in the direction of movement, the fewer “compensatory delay ticks” at rest. The smaller the number of jumps in the direction of movement, the more “compensatory delay ticks” at rest. Etherons with the same directions of movement, but with different “delay” parameters, with the same number of “compensatory delay ticks” move with different Euclidean speeds due to a different number of “additional delay ticks”.
Compensatory delay ticks are necessary to ensure that the total time of movement over the reference Euclidean distance ($D_Æ$) remains constant, regardless of direction. This time is calibrated by the “slowest” direction — the diagonal in space where the number of jumps is maximum. The number of compensatory delay ticks ($T_{\text{comp.æ}}$) depends on the Manhattan distance for the direction vector $\vec{d_æ} = (d_{æ,x}, d_{æ,y}, d_{æ,z})$ and is calculated by the formula:
\[T_{\text{comp.æ}} = τ_{\text{move.æ}} \cdot (D_Æ\cdot\sqrt{3} - (|d_{æ,x}| + |d_{æ,y}| + |d_{æ,z}|))\]where:
“Reference ether delay” is the number of time ticks required to perform the maximum number of jumps over the reference Euclidean distance $D_Æ$:
\[τ_Æ = τ_{\text{move.æ}} \cdot D_Æ \cdot \sqrt{3}\]The total time ($T_æ$) spent by the etheron on Euclidean motion over a distance of $D_Æ$ is made up of the base time ($T_{\text{move.æ}}$), the time for compensatory delays ($T_{\text{comp.æ}}$), and the time for additional delays ($T_{\text{add.æ}}$):
\[T_{\text{move.æ}} = (|d_{æ,x}| + |d_{æ,y}| + |d_{æ,z}|) \cdot τ_{\text{move.æ}}\] \[T_{\text{comp.æ}} = τ_{\text{move.æ}} \cdot (D_Æ\cdot\sqrt{3} - (|d_{æ,x}| + |d_{æ,y}| + |d_{æ,z}|))\] \[T_{\text{add.æ}} = a_æ\]If we add these components, the terms containing the direction vector $(\lvert d_{\text{æ,x}}\rvert + \lvert d_{\text{æ,y}}\rvert + \lvert d_{\text{æ,z}}\rvert)$ cancel each other out. As a result, the total time is independent of direction:
\[T_æ = T_{\text{move.æ}} + T_{\text{comp.æ}} + T_{\text{add.æ}} = τ_{\text{move.æ}} \cdot D_Æ \cdot \sqrt{3} + a_æ = τ_Æ + a_æ\]The independence of the total time spent by the etheron on Euclidean motion from the Euclidean direction ensures the same Euclidean speed for etherons with the same “delay” parameter, regardless of the trajectory of their jumps.
The absolute position of the etheron in space $\vec{p}_æ$, where at some point in time $t$ the etheron should be located under the condition of its free movement, is calculated on the basis of the total time spent by the etheron on the Euclidean movement over the distance $D_Æ$:
\[\vec{p}_æ(t) = W_{\text{S.Æ}}(\vec{r}_{\text{ca.æ}} + \frac {W_{\text{H.Æ}}(t - t_{\text{ca.æ}})\cdot \vec{d_æ}} {τ_Æ + a_æ})\]Due to frequent etheron collisions in real space-time-ether, when calculating the “absolute position of an etheron in space” $\vec{p}$æ(t), the moment of time $t$ is always close to the “moment of time of the last etheron collision of the etheron” $t_{\text{ca.æ}}$:
\[W_{\text{H.Æ}}(t-t_{\text{ca.æ}}) \ll T_Æ\]Therefore, in real space-time-ether, no “special protection” is required against incorrectly calculating the future position of an etheron that has been moving freely without collisions with other etherons for a very long time. Therefore, most likely, in real space-time-ether there is neither such “special protection” nor “artifacts” from such “special protection”. “Special protection” in a computer simulation is needed not because cyclic time is physically “broken”, but because the computer in the general case needs to limit the interpretation of the old initial parameters of the free movement of etherons. Nature does not need to install “special protection” because the collision dynamics itself regularly updates the reference points of the free movement of etherons.
The number of etherons in the “rest” state ( $s1$æ ) in a cell of space with position $\vec{p}$ is denoted by $N_{\text{s1.Æ}}(\vec{p})$ and is expressed through summation over all etherons from the set $Æ$ using the Kronecker delta symbol $\delta$:
\[N_{\text{s1.Æ}}(\vec{p}) = \sum_{æ \in Æ} \delta(\vec{r}_{\text{æ}}, \vec{p}) \cdot \delta(s_{\text{æ}}, 1)\]The transition of an etheron from the “rest” state ( $s1$æ ) to the “moving from the cell” state ( $s3$æ ), provided that there are no other etherons in the “rest” state in the cell, occurs if its position in space ( $\vec{r}$æ ) at the current time tick ( $t$Æ ) does not coincide with the position $\vec{p}$æ$(t$Æ$)$, where the etheron should be:
\[s_{\text{æ}}^{(1)} \longrightarrow s_{\text{æ}}^{(3)}, \quad \text{for} \quad ( N_{\text{s1.Æ}}(\vec{r}_{\text{æ}}) = 1 ) \land (\vec{r}_{\text{æ}} \neq p_{\text{æ}}(t_{\text{Æ}}))\]In the “moving out of cell” state ($s3$æ), the etheron determines which neighboring cell $\vec{p}$n it must go to in order to get to the cell $\vec{p}$t where it should be. In a computer simulation, an algorithm similar to a digital differential analyzer (DDA) adapted to toroidal space can be used to find the next neighboring cell $\vec{p}$n on the way from the current cell $\vec{r}$æ to the cell $\vec{p}$t where the etheron should be:
\[\vec{r}_æ = (x_æ, y_æ, z_æ) \in S\] \[\vec{\delta} = \vec{p}_t - \vec{r}_æ = (\delta_x, \delta_y, \delta_z)\] \[\vec{\delta'} = (W_{\text{Æ}}(\delta_x), W_{\text{Æ}}(\delta_y), W_{\text{Æ}}(\delta_z)) = (\delta'_x, \delta'_y, \delta'_z)\] \[i_{dom} = \mathop{\text{argmax}}\limits_{i \in \{x, y, z\}} |\delta'_i|\] \[\vec{e}_x = (1, 0, 0) ; \vec{e}_y = (0, 1, 0) ; \vec{e}_z = (0, 0, 1)\] \[\Delta\vec{p} = \mathop {\text{sgn}(\delta'_{i_{dom}})} \cdot \vec{e}_{i_{dom}}\] \[\vec{p}_{n} = (W_{\text{Æ}}(x_æ + \Delta p_x), W_{\text{Æ}}(y_æ + \Delta p_y), W_{\text{Æ}}(z_æ + \Delta p_z))\]In the state of “moving to a cell” ($s4$æ), the etheron’s “position” parameter $\vec{r}_æ$ becomes equal to the position of the cell $\vec{p}$n it arrived at:
\[s_{\text{æ}} = s^{(4)} \implies \vec{r}_{\text{æ}} = \vec{p}_{n}\]The modulus of the Euclidean continuous velocity of an etheron $v_{\text{æ}} = \lvert \vec{v}_{\text{æ}} \rvert$ is the ratio of the Euclidean distance traveled to the time spent on its passage. The modulus of the maximum continuous velocity of an etheron does not depend on the direction of movement, since the difference in time arising from a different number of jumps is completely compensated by a different number of ticks of the compensatory delay. The modulus of the continuous velocity of an etheron $v_æ$ is determined only by its “delay” parameter $a_æ$.
Formula for the module of continuous velocity of etheron $v_æ$:
\[v_æ = \frac{D_Æ }{ τ_{\text{move.æ}} \cdot D_Æ\cdot\sqrt{3} + a_æ }=\frac{D_Æ }{ τ_Æ + a_æ }\] \[a_æ = \frac{D_Æ}{v_æ} - { τ_{\text{move.æ}} \cdot D_Æ\cdot\sqrt{3}}= \frac{D_Æ}{v_æ} - τ_Æ\]where:
The unit vector of continuous velocity of the etheron $\hat{v_æ}$, indicating the direction of the vector of continuous velocity of the etheron $\vec{v_æ}$, is equal to the ratio of the reference direction vector $\vec{d_æ}$ to the reference distance $D_Æ$. The formula for the unit vector of continuous velocity of the etheron $\hat{v_æ}$:
\[\hat{v_æ} = \frac{\vec{d_æ}}{D_Æ}\]The continuous velocity vector of the etheron $\vec{v_æ}$ is equal to the product of the unit continuous velocity vector of the etheron $\hat{v_æ}$ and the modulus of the velocity of the etheron $v_æ$. Formula for the continuous velocity vector of the etheron $\vec{v_æ}$:
\[\vec{v_æ} = \frac{\vec{d_æ}}{D_Æ} \cdot v_æ = \frac{\vec{d_æ}}{D_Æ} \cdot \frac{D_Æ }{ τ_Æ + a_æ } = \frac{\vec{d_æ}} { τ_Æ + a_æ }= \frac{\vec{d_æ}} { τ_{\text{move.æ}} \cdot D_Æ\cdot\sqrt{3} + a_æ }\] \[\vec{d_æ} = \frac{\vec{v_æ}\cdot D_Æ}{|\vec{v_æ}|}\]The modulus of the continuous velocity of the etheron $v_æ$ is maximum at the minimum value of the “delay” parameter ($a_æ=0$):
\[v_{max.æ} = \frac{D_Æ }{ τ_{\text{move.æ}} \cdot D_Æ\cdot\sqrt{3}} = \frac{1}{ τ_{\text{move.æ}}\cdot\sqrt{3}}\]The modulus of the continuous velocity of the etheron $v_æ$ is minimal at the maximum value of the “delay” parameter ($a_æ=D_Æ$):
\[v_{min.æ} = \frac{D_Æ }{ τ_{\text{move.æ}} \cdot D_Æ\cdot\sqrt{3} + D_Æ}= \frac{1}{ τ_{\text{move.æ}}\cdot\sqrt{3}+1}\]The average value of the modulus of the continuous velocity of the etheron occurs at the average value of the “delay” parameter ($a_æ=\frac{D_Æ}{2}$):
\[{v_{avg.æ}} = \frac{D_Æ }{ τ_{\text{move.æ}} \cdot D_Æ\cdot\sqrt{3} + \frac{D_Æ}{2}}= \frac{1}{ τ_{\text{move.æ}}\cdot\sqrt{3}+\frac{1}{2}}\]The ratio of the modulus of the maximum continuous velocity of the etheron to the modulus of the minimum continuous velocity of the etheron:
\[\frac{v_{max.æ}}{v_{min.æ}} = \frac{ τ_{\text{move.æ}}\cdot\sqrt{3}+1 }{τ_{\text{move.æ}}\cdot\sqrt{3}} = 1 + \frac{1}{ τ_{\text{move.æ}}\cdot\sqrt{3}} = 1+ v_{max.æ}\]The ratio of the modulus of the maximum continuous velocity of the etheron to the modulus of the average continuous velocity of the etheron:
\[\frac{v_{max.æ}}{v_{avg.æ}} = \frac{ τ_{\text{move.æ}}\cdot\sqrt{3}+\frac{1}{2} }{τ_{\text{move.æ}}\cdot\sqrt{3} + 1}\]The difference between the module of the maximum continuous speed of etheron and the module of the minimum continuous speed of etheron:
\[\begin{aligned} {v_{max.æ}}-{v_{min.æ}} = \frac{1}{ τ_{\text{move.æ}}\cdot\sqrt{3}} - \frac{1}{ τ_{\text{move.æ}}\cdot\sqrt{3}+1} = \frac{ τ_{\text{move.æ}}\cdot\sqrt{3}+1 - τ_{\text{move.æ}}\cdot\sqrt{3}}{(τ_{\text{move.æ}}\cdot\sqrt{3})\cdot (τ_{\text{move.æ}}\cdot\sqrt{3}+1)} = \\\\ = \frac{ 1}{(τ_{\text{move.æ}}\cdot\sqrt{3})^2+ (τ_{\text{move.æ}}\cdot\sqrt{3})} \end{aligned}\]At the minimum value of the basic duration of the movement of etheron from cell to cell ($τ_{\text{move.æ}}=3$), the modules of continuous etheron velocities have a maximum range, approximately equal to the range from $0.9 \cdot v_{avg.æ}$ to $1.1 \cdot v_{avg.æ}$.
The inertness vector of the etheron $\vec{i}_{\text{æ}}$ is a vector directed opposite to the unit vector of the continuous velocity of the etheron $\hat{v}_{\text{æ}}$ and having a modulus equal to the ratio of the “total additional delay” of the etheron $a_{\text{æ}}$ to the reference distance $D_{\text{Æ}}$. In its meaning, the modulus of the inertness vector of the etheron is a “normalized delay”.
\[i_æ=|\vec{i}_æ|=\frac{a_æ}{D_Æ}\] \[i_{avg.æ}=\frac{a_{avg.æ}}{D_Æ}=\frac{1}{2}\] \[a_æ=i_æ \cdot D_Æ\] \[v_æ=\frac{D_Æ }{ τ_Æ + i_æ \cdot D_Æ }= \frac{1}{ τ_{\text{move.æ}}\cdot\sqrt{3} + i_æ }\] \[i_æ=\frac{1}{v_æ}-τ_{\text{move.æ}}\cdot\sqrt{3}\] \[\hat{i}_æ=-\hat{v}_æ = -\frac{\vec{d_æ}}{D_Æ}\] \[\vec{i}_æ = \hat{i}_æ \cdot |\vec{i}_æ| = -\hat{v}_æ \cdot \frac{a_æ}{D_Æ}=-\frac{\vec{d_æ}}{D_Æ} \cdot \frac{a_æ}{D_Æ} = -\frac{\vec{d_æ}\cdot{a_æ}}{D_Æ^2}\] \[\vec{d}_æ = -\frac{\vec{i}_æ \cdot D_Æ }{ |\vec{i}_æ|}\] \[\vec{v_æ} = -\frac{\vec{i}_æ \cdot D_Æ }{ |\vec{i}_æ| \cdot (τ_Æ + |\vec{i}_æ| \cdot D_Æ)}= -\frac{\vec{i}_æ}{ |\vec{i}_æ| \cdot (τ_{\text{move.æ}}\cdot\sqrt{3} + |\vec{i}_æ|)}\]The modulus of the inertness vector of the etheron $\lvert \vec{i}_{\text{æ}} \rvert$ is equal to zero at the maximum continuous velocity of the etheron $v_{max.æ}$ and is maximum at the minimum continuous velocity of the etheron $v_{min.æ}$.
The unit of measurement for inertness in the ether system of units is “æi”.
The interaction of several etherons in a cell of space occurs according to the local principle of minimal changes in the inertness configuration and is reduced to a change in the second and third parameters of these etherons, as well as to a possible change in the fourth and fifth parameters of these etherons.
During the interaction of several etherons in a space cell, the absolute position of this space cell is entered into the second parameter of each etheron.
During the interaction of several etherons in a space cell, the current time tick is entered into the third parameter of each etheron.
During the interaction of only two etherons in a space cell, the fourth parameter and fifth parameter of each of these etherons do not change.
Transit interaction of etherons is considered to be interaction of etherons, in which the speeds and directions of etherons do not change.
Interaction of only two etherons in a cell of space is always a “transit interaction” of etherons. Transit interactions can be not only two-etheron interactions.
The velocity of an etheron over the aggregate of free motions of the etheron alternating with only transit interactions of etherons is called “transit velocity”.
The transit velocity of an etheron is always less than the continuous velocity of the etheron and depends on the probability of transit interaction with other etherons.
During the interaction of three or more etherons in a space cell, the fourth and fifth parameters of each of these etherons change in accordance with the “substance-field pattern” of the distribution of relative continuous velocities of etherons in the group of etherons, as well as in accordance with the law of conservation of momentum, in accordance with the law of conservation of energy, and in accordance with the range of absolute continuous velocities of etherons.
When three or more etherons interact in a cell of space, the fourth and fifth parameters of each of these etherons can change in accordance with the “substance-field pattern” of the distribution of continuous velocities of etherons in a group of etherons, as well as in accordance with the “law of conservation of inertness” and in accordance with the range of absolute continuous velocities of etherons. If there is no satisfactory solution to the problem of distributing continuous velocities for the parameters of the interacting etherons, then after the interaction, the velocities and directions of the interacting etherons remain unchanged, and the interaction itself is considered transit.
The “law of conservation of inertness” during the interaction of three or more etherons in a cell of space consists in the fact that for collision etherons ($Æ1.c$) in a cell of space, the “sum of their inertness vectors” ($\vec{I}$Æ1.c) before the collision is equal to the “sum of their inertness vectors” after the collision, and also the “sum of their inertness vector moduli” (${ℐ}$Æ1.c) before the collision is equal to the “sum of their inertness vector moduli” after the collision:
\[\vec{I}_\text{Æ1.c} = \sum_{\text{æ} \in Æ1.c} \vec{i}_\text{æ} = const\] \[{ℐ}_\text{Æ1.c} = \sum_{\text{æ} \in Æ1.c}{i}_\text{æi} = const\]The “law of conservation of inertness” states that during any interaction of etherons, the following are simultaneously conserved: the total vector of etheron inertness; and the total scalar inertness of etherons. The “law of conservation of inertness” includes the “first law of conservation of inertness” and the “second law of conservation of inertness.”
The first law of conservation of inertness is equivalent to the conservation of the weighted sum of etheron directions:
\[\sum_{\text{æ} \in Æ1.c} a_\text{æ} \vec {d}_\text{æ} = \mathrm{const}\]The second law of conservation of inertness is equivalent to the conservation of the total delay:
\[\sum_{\text{æ} \in Æ1.c} a_\text{æ} = \mathrm{const}\]The “law of conservation of inertness” can be written in its most compact form as the conservation of a pair of invariants under any collisions of etherons:
\[\left( \sum_{\text{æ} \in Æ1.c}\vec {i}_\text{æ}, \sum_{\text{æ} \in Æ1.c}|\vec {i}_\text{æ}| \right) = \mathrm{const}\]The “law of conservation of inertness” can be written in its equivalent, most compact form as the conservation of a pair of invariants under any collisions of etherons:
\[\left( \sum_{\text{æ} \in Æ1.c} a_\text{æ} \vec {d}_\text{æ}, \sum_{\text{æ} \in Æ1.c} a_\text{æ} \right) = \mathrm{const}\]In the simplest model, the “amount of inertness” in the Universe is constant. “Σiæ=const” is a conventional notation for the constancy of the Universe’s inertness. $\vec{I}{_Æ}$ is the “sum of the inertness vectors” of all etherons. ${ℐ_Æ}$ is the “sum of the inertness vector modules” of all etherons. Formulas for the constancy of the Universe’s inertness:
\[Σiæ=const\] \[\vec{I}_\text{Æ} = \sum_{\text{æ} \in Æ} \vec{i}_\text{æ} = \vec{0}\] \[{ℐ}_\text{Æ} = \sum_{\text{æ} \in Æ}{i}_\text{æ} = \frac{m_\text{Æ}}{2}\]The introduction of the term “inertness” as a vector into the theory allows for the operation of a conserved pair of invariants as a single object, simplifying the formulation of conservation laws and making them more compact. The term “inertness” does not replace the multi-valued, macro-level classical concept of “inertia”, but rather provides a convenient semantic and mathematical construct for the laws of the primary discrete motion of etherons. The theory deliberately distinguishes between the concept of “inertia” and the new term “inertness,” thereby establishing a terminological barrier to prevent the new fundamental invariants from being conflated with conventional Newtonian physics. For the first level of matter, due to the specific nature of its laws, the term “inertness” takes precedence over the term “velocity”.
Due to the nonlinear relationship between the etheron’s inertness vector and the etheron’s continuous velocity vector, strict adherence to the law of conservation of inertia does not guarantee strict conservation of classical Newtonian momentum and classical Newtonian energy for a small number of etherons. The higher the level of matter, the less deviation from the classical Newtonian laws of conservation of momentum and energy during the interaction of ether objects at that level. The substantial-field pattern of inertness distribution also determines the distribution of the “burden” of observing classical Newtonian conservation laws between the ether substance and the ether field.
The interaction of three or more etherons in a cell of space with a change in the speeds and directions of the interacting etherons is called “synthesizing interaction” of etherons.
In the general case, the substance-field pattern of distribution of continuous velocities of etherons in a group of etherons means that some etherons in a group move relative to the trajectory of other etherons in the same group with approximately the same moduli of continuous velocities, but in different directions.
Etherons in a group of etherons, moving relative to the trajectory of other etherons in the same group with approximately the same modules of continuous velocities, but in different directions, are called “field etherons”.
Etherons in a group of etherons, relative to the trajectory of which other etherons in the same group move with approximately the same modules of continuous velocities, but in different directions, are called “substantial etherons”.
In the simplest version of the substance-field pattern, for any “group of collision etherons” ($Æ1.c$), their “delays” and “directions” after a collision are calculated in such a way that the one etheron that most closely resembles the substantial etheron in the pattern of inertness distribution between the collision etherons becomes the substantial etheron ($æ:s$), and all other etherons in the collision become field etherons ($æ:f$). After which, the same “inertness vector modulus” ($\lvert \vec{i}_{\text{æ:f}} \rvert$) is first calculated for all field etherons, provided that the directions of the field etherons do not change after the collision, that the “inertness vector modulus” does not go beyond the range of the “inertness vector modulus”, and that the law of conservation of inertness is satisfied. The “inertness vector” of the substantial etheron ($\vec{i}$æ:s) is then calculated, from which the “delay” ($a_{æ:s}$) and “direction” ($\vec{d}$æ:s) of the substantial etheron are derived. Changing the distribution of inertness between field etherons does not always require changing the “inertness vector” of the selected substantial etheron. In general, a change in the inertness of the selected substantial etheron is not a necessary condition for a synthesizing collision. The inertness modules of all or part of the field etherons may change, but the “inertia vector” of the selected substantial etheron may remain the same. If the “inertness vector” of the selected substantial etheron has changed, then the new “delay” and new “direction” for the substantial etheron will compensate for the changes in the “inertness vector magnitudes” of the field etherons.
If the inertness vectors of the etherons of a multi-etheron collision have not changed before ($\vec i_j$) and after $(\vec i_j’)$ the multi-etheron collision, then: such a collision is considered transit; the inertial roles of the etherons and the affiliations of the etherons do not change:
\[\forall j: \quad \vec i_j'=\vec i_j\] \[\forall j: \quad (\vec d_j',a_j')=(\vec d_j,a_j)\]If the inertness vectors of several etherons of a multi-etheron collision have changed before ($\vec i_j$) and after $(\vec i_j’)$ the multi-etheron collision, then: such a collision is considered synthesizing; the affiliations of the etherons change; the inertial roles of etherons can change:
\[\exists j: \quad \vec i_j' \ne \vec i_j\] \[\exists j: \quad (\vec d_j',a_j')\ne(\vec d_j,a_j)\]Ontological scheme of the etheron collision:
\[\text{Æ1.c} \quad\longrightarrow\quad \begin{cases} \text{transit}\\ \text{synthesis of Æ2.b} \end{cases}\]The constancy of the directions of continuous movement of field etherons before and after synthesizing collisions is a structural condition for the existence of stable, scattered ether fields of ether hyperobjects and ensures the preservation of sufficiently long correlations of the directions of field etherons. If each new contact with the external ether also arbitrarily rotated the direction of the already scattered field etheron of an ether hyperobject, the ether field of the ether hyperobject would quickly lose its connection with its original geometry, and instead of a spatially organized field, a nearly isotropic kinetic background would result. An ether field requires not simply the inertness of its etherons, but the coherence of their directions of movement. An etheron collision can redistribute the sum of the inertness moduli of the colliding etherons, but does not destroy the spatial geometry of the directed flow of etherons. The direction of a field etheron is the carrier of the geometric information of the ether field, and the modulus of inertness of a field etheron is the carrier of the amplitude information of the ether field. The preservation of the directions of field etherons can be interpreted as a minimally reorganizing branch of the solution to the collision problem in accordance with the principle of minimizing the restructuring of inertness. The ether field of an ether hyperobject is constructed precisely as a spatiotemporal accumulation of scattered field etherons carrying directional information. Directional stability at the microscopic level is one of the mechanisms from which a macroscopic multicomponent field structure emerges at subsequent levels.
The selection of a substantial etheron in a “group of collision etherons in a spatial cell” ($Æ1.c$) occurs according to the “principle of least action of etheron collision”. The “principle of least action of etheron collision” is a local rule for selecting the closest permissible redistribution of inertness and consists of redistributing the inertness of collision etherons in accordance with the substance-field pattern through minimal changes in the inertness of collision etherons. The “least action” of an etheron collision means that from several admissible options for local redistribution, the option that requires the least change in the inertness configuration is chosen. The principle of least action of etheron collision is equivalent to minimizing the total value of inertтness rearrangement.
The exact algorithm for selecting a substantial etheron in a “group of collision etherons in a cell of space” ($Æ1.c$) amounts to finding the “etheron index” ($æ_s$) with the minimum future value of inertness changes for the entire collision group by comparing candidates ($k$) via the quadratic functional of the minimal rearrangement of the inertness configuration of the collision group. For each candidate $(æ_k)$, a fully defined admissible post-collision state $(\vec i’_j{}^{(k)})$ is constructed for the entire collision group. The quadratic measure means that a large local change is penalized superlinearly compared to many small changes. This is a natural mathematical realization of the idea that “the system prefers to distribute rearrangements rather than concentrate them in one place.” The formula for the exact algorithm for selecting a substantial etheron via the quadratic collision action functional is:
\[æ_s = \arg\min_{k\in{1,\ldots,N}} (\frac12 \sum_{j=1}^{N} \left| \vec i'_j{}^{(k)}-\vec i_j \right|^2)\]A fast heuristic approximate algorithm for selecting a substantial etheron in a “group of collision etherons in a cell of space” ($Æ1.c$) takes into account the vectors of the etheron directions and comes down to finding the “etheron index” ($æ_s$) with the minimum value of the modulus of the difference between the “inertness vector of a collision etheron” ($\vec{i}$æ) and the “sum of the inertness vectors of all other collision etherons in the cell”:
\[æ_s = \arg\min_{æ \in Æ1.c} (| \vec{i}_\text{æ} - \frac{1}{2} \sum_{\text{æ}' \in Æ1.c} \vec{i}_{\text{æ}'} |)\]A fast heuristic approximate algorithm for selecting a substantial etheron can be written in an equivalent, most compact form as finding the “etheron index” ($æ_s$) whose weighted direction is minimally different from the sum of the weighted directions of all other etherons in the group:
\[\text{æ}_s = \arg\min_{\text{æ} \in Æ1.c} (| a_\text{æ}\,\vec{d}_\text{æ} - \frac{1}{2} \sum_{\text{æ}' \in Æ1.c} a_{\text{æ}'}\,\vec{d}_{\text{æ}'} |)\]The “principle of least action” of macrophysics is an emergent principle arising from the statistics of a large number of etheron collisions.
The algorithm for calculating the simplest version of the substance-field pattern for a group of collision etherons in the amount equal to $N$, in the analytical version is reduced to solving the quadratic equation $ax²+bx+c=0$, where $x=i_{æ:f}$ is the modulus of the inertness vector of each field etheron after the collision. The formulas of the algorithm contain the following notations. Vectors are denoted by symbols with an arrow on top. Unit vectors are denoted by symbols with a cap on top. Vector moduli are denoted either by simple symbols or by symbols with an arrow on top in two vertical lines around the symbols. The number of a substantial etheron is equal to $N$. Field etheron numbers start with $1$ and end with $N-1$. $\vec{i}$æ:s is the inertness vector of a substantial etheron after the collision. $\vec{i}$æ,j is the inertness vector of an etheron with the number $j$ before the collision. $\vec{I}$old is the sum of the inertness vectors of all etherons before the collision. $\vec{I}$new is the sum of the inertness vectors of all etherons after the collision. $ℐ_{\text{old}}$ is the sum of the moduli of the inertness vectors of all etherons before the collision. $ℐ_{\text{new}}$ is the sum of the moduli of the inertness vectors of all etherons after the collision. Formulas for the calculation algorithm of the simplest version of the substance-field pattern:
\[\vec{I}_{\text{old}} = \sum_{j=1}^N \vec{i}_{æ,j}\] \[\vec{I}_{\text{new}} = \sum_{j=1}^{N-1} i_{æ:f} \cdot \hat{i}_{æ,j} + \vec{i}_{æ:s}\] \[\vec{I}_{\text{new}} = \vec{I}_{\text{old}}\] \[ℐ_{\text{old}} = \sum_{j=1}^N {i}_{æ,j}\] \[ℐ_{\text{new}} = (N-1)\cdot i_{æ:f} + i_{æ:s}\] \[ℐ_{\text{new}} = ℐ_{\text{old}}\] \[\vec{i}_{æ:s} = \sum_{j=1}^N \vec{i}_{æ,j} - i_{æ:f}\cdot \sum_{j=1}^{N-1} \hat{i}_{æ,j}\] \[(N-1) \cdot i_{æ:f} + |\sum_{j=1}^N \vec{i}_{æ,j} - i_{æ:f} \sum_{j=1}^{N-1} \hat{i}_{æ,j}| = \sum_{j=1}^N {i}_{æ,j}\] \[|\sum_{j=1}^N \vec{i}_{æ,j} - i_{æ:f} \cdot\sum_{j=1}^{N-1} \hat{i}_{æ,j}|^2 = (\sum_{j=1}^N {i}_{æ,j} - (N-1) \cdot i_{æ:f})^2\] \[\begin{aligned} |\sum_{j=1}^N \vec{i}_{æ,j}|^2 + i_{æ:f} ^2 \cdot| \sum_{j=1}^{N-1} \hat{i}_{æ,j}|^2 - 2\cdot i_{æ:f} \cdot(\sum_{j=1}^N \vec{i}_{æ,j})\cdot (\sum_{j=1}^{N-1} \hat{i}_{æ,j}) = \\\\ = (\sum_{j=1}^N {i}_{æ,j})^2 + ((N-1) \cdot i_{æ:f})^2 - 2\cdot (\sum_{j=1}^N {i}_{æ,j}) \cdot ((N-1) \cdot i_{æ:f}) \end{aligned}\] \[\begin{aligned} i_{æ:f} ^2 \cdot (| \sum_{j=1}^{N-1} \hat{i}_{æ,j}|^2-(N-1)^2) + \\\\ + i_{æ:f} \cdot (-2\cdot(\sum_{j=1}^N \vec{i}_{æ,j})\cdot (\sum_{j=1}^{N-1} \hat{i}_{æ,j}) + 2\cdot (\sum_{j=1}^N {i}_{æ,j}) \cdot (N-1 )) + \\\\ + (|\sum_{j=1}^N \vec{i}_{æ,j}|^2-(\sum_{j=1}^N {i}_{æ,j})^2)=0 \end{aligned}\] \[a \cdot i_{æ:f}^2 + b \cdot i_{æ:f} + c = 0\] \[i_{æ:f} = \frac{-b \pm \sqrt{b^2 - 4\cdot a \cdot c}}{2\cdot a}\] \[a_{æ:f} = i_{æ:f} \cdot D_Æ\] \[a_{æ:s} = |\vec{i}_{æ:s}| \cdot D_Æ\] \[\vec{d}_{æ:s} = -\frac{\vec{i}_{æ:s} \cdot D_Æ }{ |\vec{i}_{æ:s}|}\]In the iterative version, the algorithm for calculating the simplest version of the substance-field pattern for a group of collision etherons in a quantity equal to $N$ can be based on the Newton-Raphson method for solving the conservation equation. Maximum number of iterations: $K_{\max}$. Accuracy: $\varepsilon = 10^{-8}$. If $\lvert \vec{V}^{(k)} \rvert = 0$, then use the bisection method. If $i_{æ:f}^{(k)} \notin [0, 1]$, then project onto the permissible range.
\[i_{æ:f}^{(0)} = \frac{ℐ_{\text{old}}}{N}, \quad k = 0\] \[\vec{U} = \sum_{j=1}^{N-1} \hat{\vec{i}}_\text{æ,j}\] \[NEXT: \vec{V}^{(k)} = \vec{I}_\text{old} - i_{æ:f}^{(k)} \cdot \vec{U}\] \[F(i_{æ:f}^{(k)}) = (N-1) \cdot i_{æ:f}^{(k)} + |\vec{V}^{(k)}| - ℐ_{\text{old}}\] \[F'(i_{æ:f}^{(k)}) = (N-1) - \frac{\vec{V}^{(k)} \cdot \vec{U}}{|\vec{V}^{(k)}|}\] \[i_{æ:f}^{(k+1)} = i_{æ:f}^{(k)} - \frac{F(i_{æ:f}^{(k)})}{F'(i_{æ:f}^{(k)})}\] \[\text{IF } (|i_{æ:f}^{(k+1)} - i_{æ:f}^{(k)}| < \varepsilon) \text{ THEN } i_{æ:f} = i_{æ:f}^{(k+1)}\] \[\text{ELSE } \{ k = k + 1; \text{GOTO NEXT} \}\]The interaction of etherons in a cell of space, as a result of which the modules of continuous velocities and reference directions of etherons have changed, is called synthesizing due to the synthesis from this group of etherons of an etheric object of the second level of matter, consisting of substantial and field etherons.
An ether object of the second level of matter is conventionally termed an “ether batch” and designated as Æ2.b (or Æb for short). The transition $Æ1.c \rightarrow Æ2.b$ (from a collision group of etherons ($Æ1.c$) to an elementary ether batch ($Æ2.b$)) represents a shift from a collision process to an ether hyperobject, whereas the transition $Æ2.b \rightarrow Æ2.hb$ (from an elementary ether batch ($Æ2.b$) to an ether hyperbatch ($Æ2.hb$)) constitutes a transition to a collective pattern.
An etheron that has become a field etheron during synthesizing interaction is called “scattered field etheron”. In the simplest model of the ether field, only “scattered field etherons” are defined, and therefore in the simplest model, “field etheron” and “scattered field etheron” are one and the same.
An etheron that has become a substantial etheron during synthesizing interaction with a scattered field etheron and another etheron is called “dragged substantial etheron”. If a “dragged substantial etheron” experiences attraction to the ether hyperobject of a scattered field etheron, then such an etheron is considered an “dragged-in substantial etheron.” If an “dragged substantial etheron” experiences repulsion to the ether hyperobject of a scattered field etheron, then such an etheron is considered an “dragged-out substantial etheron.”
An etheron that has become a substantial etheron during synthesizing interaction with a dragged substantial etheron and another etheron is also called “dragged substantial etheron”.
Substantial etherons of an ether hyperobject form the “ether substance” of the ether hyperobject. The “ether substance” of an ether hyperobject can be conditionally divided into the “bearing part” of the “ether substance” and the “dragged part” of the “ether substance.” The “dragged part” of the “ether substance” of an ether hyperobject can be conditionally divided into the “dragged-in part” of the “ether substance” and the “dragged-out part” of the “ether substance.”
Ether is called multirole due to the fact that etherons perform different inertial roles. “Substantial/field” is the role of the etheron, whereas “bearing/dragged/dragged-in/dragged-out” is a sub-role within the substantial component.
The spatial, temporal, and velocity parameters of the ether substance of an ether hyperobject constitute the configuration of the ether substance of the ether hyperobject.
Field etherons of an ether hyperobject form the “ether field” of the ether hyperobject.
Medium etherons and field etherons together constitute the “medium-field ether”. For an ether hyperobject, the “external medium-field ether” is considered to be “the medium-field ether excluding the field etherons of that ether hyperobject”.
Usually, an ether hyperobject has ether substance and ether field. Typically, the higher the level of an ether hyperobject, the smaller the ratio of the mass of its ether substance to the mass of its ether field. Therefore, the ratio $R_{\text{sf.Æ(n)}}$ of the “mass of the ether substance of all ether hyperobjects of a certain level” $m_{\text{Æ(n):s}}$ to the “mass of the ether field of all ether hyperobjects of this level” $m_{\text{Æ(n):f}}$ decreases with the growth of the level $Æ(n)$. Obviously, the ratio $R_{\text{sf.Æ}}$ of the “mass of all substantial etherons” $m_{\text{Æ:s}}$ to the “mass of all field etherons” $m_{\text{Æ:f}}$ is between $R_{\text{sf.Æ8}}$ and $R_{\text{sf.Æ2}}$. “The mass of all etherons of all ether hyperobjects” $m_{\text{Æ:h}}$ includes “the mass of all substantial etherons” $m_{\text{Æ:s}}$ and “the mass of all field etherons” ${\text{Æ:f}}$. “The mass of all etherons” $m_{\text{Æ}}$ includes “the mass of all etherons of all ether hyperobjects” $m_{\text{Æ:h}}$ and “the mass of all medium etherons” $m_{\text{Æ:m}}$. Obviously, the ratio $R_{\text{hm.Æ}}$ of “the mass of all etherons of all ether hyperobjects” $m_{\text{Æ:h}}$ to “the mass of all medium etherons” $m_{\text{Æ:m}}$ is much less than $1$.
\[m_{\text{Æ:h}}= m_{\text{Æ:s}} + m_{\text{Æ:f}}\] \[m_{\text{Æ}}= m_{\text{Æ:m}} + m_{\text{Æ:h}}\] \[m_{\text{Æ:h}} = m_{\text{Æ}} - m_{\text{Æ:m}}\] \[m_{\text{Æ:h}} \ll m_{\text{Æ:m}}\] \[R_{\text{hm.Æ}}=\frac{m_{\text{Æ:h}}}{m_{\text{Æ:m}}} \ll 1\] \[R_{\text{sf.Æ}}=\frac{m_{\text{Æ:s}}}{m_{\text{Æ:f}}}\] \[R_{\text{sf.Æ(n)}}=\frac{m_{\text{Æ(n):s}}}{m_{\text{Æ(n):f}}}\] \[R_{\text{sf.Æ2}} > R_{\text{sf.Æ3}} > R_{\text{sf.Æ4}} > R_{\text{sf.Æ5}} > R_{\text{sf.Æ6}} > R_{\text{sf.Æ7}} > R_{\text{sf.Æ8}}\] \[R_{\text{sf.Æ(n)}} > R_{\text{sf.Æ(n+1)}}\] \[R_{\text{sf.Æ2}} > R_{\text{sf.Æ}} > R_{\text{sf.Æ8}}\]Field etherons of an ether hyperobject can be low-speed and high-speed.
The spatial, temporal, and velocity parameters of the ether field of an ether hyperobject constitute the configuration of the ether field of the ether hyperobject.
The configuration of the ether field of an ether hyperobject depends on the configuration of the ether substance of the ether hyperobject and on the configuration of the external ether.
The configuration of the ether substance of an ether hyperobject and the configuration of the ether field of an ether hyperobject constitute the configuration of the ether hyperobject.
Ether fields of ether hyperobjects obey the “principle of ether superposition”.
The principle of ether superposition means that the ether fields of ether subhyperobjects of an ether hyperobject overlap each other and form the ether field of the ether hyperobject.
The interaction trail of an ether object is a discrete spatio-temporal configuration of cumulative changes in the external medium-field ether, which arose as a result of a sequence of transit and synthesizing interactions of the etherons of the ether object with the medium etherons and with the field etherons of other ether objects. The interaction trail of an ether object is not the ether field of that ether object, but is the changes in the ether fields of other ether objects and the changes in the ether medium that arise in them from interaction with the etherons of that ether object. The interaction trail of an ether object is not “ether waves” in the strict sense of the term. Trailization is conditionally includes “transit trailization” and “synthesizing trailization”. Transit trailization only causes a decrease in the effective velocity of etherons. Synthesizing trailization causes a decrease in the effective velocity of etherons, as well as a change in the ownership of some or all etherons involved in the trailization.
The etherons of the bearing part of the ether substance of the ether batch are located in spatial cells located close to one another. The directions of absolute continuous motion and absolute continuous velocities of the etherons of the bearing part of the ether substance of the ether batch are approximately equal.
The ether field of an ether batch is called “batch ether field”. The batch ether field almost always lags behind the ether substance of the ether batch.
The kinematic classification of the ether fields of ether batches determines the longitudinal or transverse nature of the ether field relative to the axis of motion of the batch’s ether substance — that is, relative to its own kinematic direction. For the ether batch $Æ2.b$ comprising a set of substantial etherons $Æ2.b.s$, the formula for its kinematic axis of motion $\hat{e}_\text{ka.Æ2.b}$ is:
\[\hat{e}_\text{ka.Æ2.b}= \frac{\sum\limits_{\text{æ} \in \text{Æ2.b.s}} \vec{v}_\text{æ}} {| \sum\limits_{\text{æ} \in \text{Æ2.b.s}} \vec{v}_\text{æ} |}\]For an ether batch $Æ2.b$ comprising a set of substantial etherons $Æ2.b.s$, the formula for its inertnic axis of motion $\hat{e}_\text{ia.Æ2.b}$ is:
\[\hat{e}_\text{ia.Æ2.b}=-\frac{\sum\limits_{\text{æ} \in \text{Æ2.b.s}} \vec{i}_\text{æ}} {| \sum\limits_{\text{æ} \in \text{Æ2.b.s}} \vec{i}_\text{æ} |}\]For substantial etherons of a coherent ether batch, the directions $\vec{v}$æ and $-\vec{i}$æ almost coincide; therefore, the formulas $\hat{e}$ka.Æ2.b and $\hat{e}$ia.Æ2.b will yield practically identical results. However, if the inertness magnitudes of the etherons differ significantly, the directions of the sums $\vec{v}$æ and $-\vec{i}$æ may diverge slightly. Both sums are weighted sums of the same unit directions $-\hat{i}$æ, but with different weights: in the velocity sum, the weight of an etheron is $\dfrac{1}{\tau {\text{move.æ}}\sqrt{3} + i{\text{æ}}}$ — that is, it decreases as $i_{\text{æ}}$ increases — whereas in the inertness sum, the weight is $i_{\text{æ}}$ — that is, it increases as $i_{\text{æ}}$ increases. Therefore, fast etherons (low $i_{\text{æ}}$) dominate the velocity sum, while slow etherons (high $i_{\text{æ}}$) dominate the inertness sum. For determining the axis of the batch’s motion, the formula based on $\vec{v}$æ is intuitively clearer and closer to kinematics. The “axis of motion” intuitively signifies “where the object is moving”. The kinematic axis of motion is the direction of the total momentum of the substance. The inertnic axis is the direction aligned with the conserved sum of inertnesses. The kinematic axis indicates the direction in which the group is actually moving. The inertnic axis indicates the direction of the group’s conserved inertnic “charge” — the attribute that determines its response to interactions and is conserved during collisions. This is neither the “direction of motion” nor the “direction of momentum.” Rather, it is the direction of the group’s inertnic core — the part that is “heaviest” in terms of lag and most resistant to reconfiguration. An inertnic axis is a direction that: does not change during internal collisions within the group; determines how the group redistributes inertness upon colliding with external etherons; and serves as a “hidden” parameter — invisible in the motion itself, yet governing the interaction. The divergence between the kinematic and inertnic axes is a measure of the group’s internal kinematic inhomogeneity. It indicates the extent to which the group’s fast and slow etherons “disagree” on the direction of motion.
The axial misalignment angle $\chi_\text{Æ2.b}$ of the ether batch $Æ2.b$:
\[\chi_\text{Æ2.b} = \arccos\!\left(\hat{e}_\text{ka.Æ2.b} \cdot \hat{e}_\text{ia.Æ2.b}\right), \qquad 0 \le \chi_\text{Æ2.b} \le \pi\]Synonyms for “axial misalignment angle” include “kinematic-inertnic divergence”, “inertnic incoherence angle”, and “axis dissonance”. When a batch collides with an external etheron, it is the inertnic axis that determines the direction in which the batch “reacts”. However, the actual motion following the collision is determined by the new kinematic axis. The greater the value of $\chi_\text{Æ2.b}$, the more significantly the batch alters its direction of motion in response to the same external influence. If $\chi_\text{Æ2.b}$ increases over time, it indicates the accumulation of internal heterogeneity and potential disintegration or restructuring. If $\chi_\text{Æ2.b}$ decreases, the batch is “maturing” into a more coherent structure.
For each field etheron $\text{æ:f}$ of the ether field $Æ2.b.f$ belonging to the ether batch $Æ2.b$, its velocity $\vec{u}$æ:f relative to the substance $Æ2.b.s$ (which has an average velocity $\vec{v}$Æ2.b.s) is:
\[\vec{u}_\text{æ:f} = \vec{v}_\text{æ:f}-\vec{v}_\text{Æ2.b.s}\] \[u_\text{æ:f} = |\vec{u}_\text{æ:f}|\] \[\vec{u}_\text{æ:f}= \vec{u}_{\parallel_\text{æ:f}}+ \vec{u}_{\perp_\text{æ:f}}\] \[\vec{u}_{\parallel_\text{æ:f}}= (\vec{u}_\text{æ:f}\cdot\hat{\mathbf e}_\text{ka.Æ2.b})\hat{\mathbf e}_\text{ka.Æ2.b}\] \[\vec{u}_{\perp_\text{æ:f}}= \vec{u}_\text{æ:f}-\vec{u}_{\parallel_\text{æ:f}}\] \[\cos\theta_\text{æ:f}= \frac{\vec{u}_\text{æ:f}\cdot\hat{\mathbf e}_\text{ka.Æ2.b}} {|\vec{u}_\text{æ:f}|}\]For the ether batch $Æ2.b$ with a set of field etherons $Æ2.b.f$, the formula for its kinematic field axis $\hat{e}_\text{ka.Æ2.b.f}$ is:
\[\hat{e}_\text{ka.Æ2.b.f}= \frac{\sum\limits_{\text{æ} \in \text{Æ2.b.f}} \vec{v}_\text{æ}} {| \sum\limits_{\text{æ} \in \text{Æ2.b.f}} \vec{v}_\text{æ} |}\]The angle of kinematic substantial-field axial misalignment $\chi_\text{a.sf.Æ2.b}$ for the ether batch $Æ2.b$ is:
\[\chi_\text{a.sf.Æ2.b} = \arccos\!\left(\hat{e}_\text{ka.Æ2.b.s} \cdot \hat{e}_\text{ka.Æ2.b.f}\right), \qquad 0 \le \chi_\text{a.sf.Æ2.b} \le \pi\]Synonyms for “kinematic substance-field axial misalignment” include “kinematic substance-field divergence”, “angle of kinematic substance-field incoherence”, and “kinematic substance-field dissonance”. For example, if the batch’s substance moves to the right and the field is directed primarily to the right, then $\chi_\text{ka.sf.Æ2.b}\approx0$, and this is a matched - or conditionally co-phased - batch. If the substance moves to the right while the field is directed primarily to the left, then $\chi_\text{ka.sf.Æ2.b}\approx\pi$, and this is an oppositely directed - or anti-dissonant - batch. If the substance moves to the right and the field is distributed almost uniformly in all directions, then $\sum\limits_{\text{æ} \in \text{Æ2.b.f}} \vec{v}_\text{æ}\approx0$, and the direction of the field becomes ill-defined. A zero resultant field vector does not imply the absence of a field.
The average longitudinality $L_\text{Æ2.b.f}$ and average transversality $T_\text{Æ2.b.f}$ of the batch field $Æ2.b.f$:
\[L_\text{Æ2.b.f}= \frac{\sum\limits_{\text{æ} \in \text{Æ2.b.f}} |\vec{u}_\text{æ}|\cos^2\theta_\text{æ}} {\sum\limits_{\text{æ} \in \text{Æ2.b.f}} |\vec{u}_\text{æ}|}\] \[T_\text{Æ2.b.f}= \frac{\sum\limits_{\text{æ} \in \text{Æ2.b.f}} |\vec{u}_\text{æ}|\sin^2\theta_\text{æ}} {\sum\limits_{\text{æ} \in \text{Æ2.b.f}} |\vec{u}_\text{æ}|}\] \[L_\text{Æ2.b.f}+T_\text{Æ2.b.f}=1\]Then $L_\text{Æ2.b.f} \approx 1$ signifies a longitudinal-field batch, $T_\text{Æ2.b.f} \approx 1$ a transverse-field batch, and $L_\text{Æ2.b.f} \approx T_\text{Æ2.b.f}$ a mixed one.
Field longitudinality $\Pi_{\text{Æ2.b.f}}$ of the batch field $\text{Æ2.b.f}$:
\[\Pi_\text{Æ2.b.f}=L_\text{Æ2.b.f}-T_\text{Æ2.b.f}\] \[-1\leq\Pi_\text{Æ2.b.f}\leq1\] \[\Pi_\text{Æ2.b.f}\rightarrow+1 \quad\Rightarrow\quad \text{strongly longitudinal field}\] \[\Pi_\text{Æ2.b.f}\rightarrow-1 \quad\Rightarrow\quad \text{strongly transverse field}\] \[\Pi_\text{Æ2.b.f}\approx0 \quad\Rightarrow\quad \text{isotropic/mixed field}\]The average relative velocity $\bar u_\text{æ:f}$ and the average normalized relative velocity $s_\text{norm.æ:f}$ of the field etheron $\text{æ:f}$ of the ether field $Æ2.b.f$ of the ether batch $Æ2.b$:
\[\bar u_\text{æ:f}= \frac{\sum\limits_{æ \in Æ2.b.f} u_\text{æ}}{m_\text{Æ2.b.f}}\] \[s_\text{norm.æ:f}=\frac{\bar u_\text{æ:f}}{C}\] \[s_\text{norm.æ:f}< s_\text{norm.avg} \quad\Rightarrow\quad \text{медленно-полевой}\] \[s_\text{norm.æ:f}> s_\text{norm.avg} \quad\Rightarrow\quad \text{быстро-полевой}\]Based on the criteria of ether field longitudinality and the average relative velocity of field etherons, ether batches can be tentatively classified into longitudinal-slow-field, longitudinal-fast-field, transverse-slow-field, and mixed-field types.
The kinematic coherence coefficient $K_\text{Æ2.b.f}$ of the ether field $Æ2.b.f$ belonging to the ether hyperbatch $Æ2.b$. When $K_\text{Æ2.b.f}\approx1$, the field is highly directional. When $K_\text{Æ2.b.f}\approx0$, the field is nearly isotropic:
\[K_\text{Æ2.b.f}= \frac{ \left|\sum\limits_{æ \in Æ2.b.f}\hat{u}_\text{æ}\right| }{ m_\text{Æ2.b.f} }\] \[0\leq K_\text{Æ2.b.f}\leq1\]The kinematic coherence coefficient $K_\text{Æ2.b.f}$ of the ether field $Æ2.b.f$ (of the ether hyperbatch $Æ2.b$) and the field longitudinality $\Pi_\text{Æ2.b.f}$ measure different things. It is possible to have $K_\text{Æ2.b.f}\approx1$ and $\Pi_\text{Æ2.b.f}\approx0$ — that is, a highly coherent but transversely oriented field. Conversely, one can have $\Pi_\text{Æ2.b.f}\approx1$ and $K_\text{Æ2.b.f}\ll1$ if the field is longitudinal on average but exhibits significant directional dispersion.
The frequency parameters of the batch ether field of an ether batch are determined by the substance-field pattern of the distribution of relative continuous velocities of etherons in the group of etherons after each synthesizing interaction of any etheron of the ether batch with external etherons. Each synthesizing interaction of any etheron of the ether batch with external etherons leads to the scattering of field etherons with approximately the same moduli of relative continuous velocities, but in different directions. The moduli of relative continuous velocities of scattered field etherons from different synthesizing interactions of etherons of the ether batch with external etherons usually differ.
Ether batches can pass through each other.
The average absolute continuous velocity of an ether batch is approximately equal to $C$.
During the synthesizing interaction of etherons, the ether substance of the synthesized ether batch accelerates in the direction of the difference between the vector sum of the continuous velocity vectors of the substantial etherons after the interaction and the vector sum of the continuous velocity vectors of these etherons before the interaction.
Acceleration of an etheron of the first ether hyperobject in the direction toward the etherons of the ether substance of the second ether hyperobject during synthesizing interaction of this etheron with an etheron of the ether field of the second ether hyperobject and with an external etheron is called attraction of the etheron of the first ether hyperobject to the second ether hyperobject.
Most often, attraction of an etheron of the first ether hyperobject to the second ether hyperobject occurs during synthesizing interaction of this etheron with a low-speed etheron of the ether field of the second ether hyperobject and with a high-speed medium etheron. In this case, it is considered that attraction by the ether field of the second ether hyperobject of the etheron of the first ether hyperobject to the second ether hyperobject occurs, and that repulsion by the ether medium of the etheron of the first ether hyperobject in the direction toward the second ether hyperobject occurs. At the same time, the modulus of the absolute continuous velocity of the high-speed etheron of the ether medium decreases. As a result of such decreases in the moduli of absolute continuous velocities of high-speed etherons of the ether medium, the repulsive ability of the ether medium decreases with decreasing distance to the ether substance of the second ether hyperobject, and the attractive ability of the ether medium increases with decreasing distance to the ether substance of the second ether hyperobject.
Attraction of the first ether hyperobject in the direction toward the second ether hyperobject consists of attractions of etherons of the first ether hyperobject to the second ether hyperobject.
Acceleration of an etheron of the first ether hyperobject in the direction away from the etherons of the ether substance of the second ether hyperobject during synthesizing interaction of this etheron with an etheron of the ether field of the second ether hyperobject and with an external etheron is called repulsion of the etheron of the first ether hyperobject from the second ether hyperobject.
Most often, repulsion of an etheron of the first ether hyperobject from the second ether hyperobject occurs during synthesizing interaction of this etheron with a high-speed etheron of the ether field of the second ether hyperobject and with a low-speed medium etheron. In this case, it is considered that repulsion by the ether field of the second ether hyperobject of the etheron of the first ether hyperobject from the second ether hyperobject occurs, and that attraction by the ether medium of the etheron of the first ether hyperobject in the direction away from the second ether hyperobject occurs. At the same time, the modulus of the absolute continuous velocity of the high-speed etheron of the ether field of the second ether hyperobject decreases. As a result of such decreases in the moduli of absolute continuous velocities of high-speed etherons of the ether field of the second ether hyperobject, the repulsive ability of the ether field of the second ether hyperobject decreases with increasing distance to the ether substance of the second ether hyperobject, and the attractive ability of the ether field of the second ether hyperobject increases with increasing distance to the ether substance of the second ether hyperobject.
Repulsion of the first ether hyperobject in the direction away from the second ether hyperobject consists of repulsions of etherons of the first ether hyperobject from the second ether hyperobject.
Together, attraction and repulsion constitute “ether field interaction” of ether hyperobjects.
The result of ether field interaction of two ether hyperobjects can be either acceleration toward each other or acceleration away from each other.
Synchronization of the motion of one ether hyperobject with changes in the ether fields of other ether hyperobjects can lead to predominance of attraction to other ether hyperobjects or predominance of repulsion from other ether hyperobjects. Predominance of attraction to other ether hyperobjects or predominance of repulsion from other ether hyperobjects as a result of synchronization of the motion of one ether hyperobject with changes in the ether fields of other ether hyperobjects is called “ether field synchronization”.
Due to synthesizing interactions of etherons of an ether batch with external etherons, the mass of the ether batch can grow to a certain value, and the ether batch can increase its degree of stability. The increase in the mass of the ether batch is a field-induced increase. An ether batch formed as a result of multiple interconnected synthesizing interactions of etherons is called an ether hyperbatch. An elementary ether batch is ephemeral. Only an ether hyperbatch can be stable. An ether hyperbatch can be conditionally considered a self-sustaining kinetic cluster of etherons that captures and drags external etherons by means of its own ether field. The bearing component of the ether substance of an ether hyperbatch can be considered, provisionally and approximately, as a coherent, moving cluster of etherons. The ether hyperbatch forms a kinematic corridor around its trajectory. The ether hyperbatch takes the form of a narrow, angular cone.
The fundamental criterion for the self-sustainment of an ether hyperbatch, $R_{\rm syn.Æ2.b}$, can be defined as the average number of new, stably linked synthesizing interactions generated by a single preceding interaction:
\[R_{\rm syn.Æ2.b}\approx 1\]If $R_{\rm syn.Æ2.b}<1$, the ether hyperbatch decays. If $R_{\rm syn.Æ2.b}=1$, a critically stable ether hyperbatch structure is formed. An ether hyperbatch can continuously lose some etherons and acquire others while maintaining a virtually unchanged structure. If $R_{\rm syn.Æ2.b}>1$, a cascading growth of the ether hyperbatch occurs. As the mass of the ether hyperbatch increases, maintaining its unified kinematic organization becomes increasingly difficult.
Kinematic coherence coefficient $K_\text{Æ2.b.s.br}$ of the bearing substance $Æ2.b.s.br$ of the ether hyperbatch $Æ2.b$:
\[K_\text{Æ2.b.s.br}= \frac{ \left|\sum\limits_{æ \in Æ2.b.s.br}\vec{v}_\text{æ}\right| }{ \sum\limits_{æ \in Æ2.b.s.br}|\vec{v}_\text{æ}| }\]In this case, the range of the kinematic coherence coefficient for the bearing substance of the ether hyperbatch is $0 < K_\text{Æ2.b.s.br} \le 1$. For perfectly unidirectional motion of the etherons of the bearing substance of the ether hyperbatch, $K_\text{Æ2.b.s.br} = 1$. For a nearly isotropic set of velocities of the etherons of the bearing substance of the ether hyperbatch, $K_\text{Æ2.b.s.br} \to 0$. In that case, the hyperbatch can be considered stable if $K_\text{Æ2.b.s.br} > K_{\rm crit}$ and the mass of the ether hyperbatch is sufficiently large. A cascade of synthesizing collisions is the natural mechanism behind the emergence of an ether hyperbatch. The synthesis of an ether hyperbatch generates a spatially directed ether field characterized by an increased probability of subsequent syntheses involving the bearing substance; the longitudinal/quasi-collinear component of the hyperbatch’s ether field ensures the kinematic coherence of the cascade. The ether hyperbatch is a dissipative/dynamic object: it constantly interacts with the environment, continuously reconfigures its field, and simultaneously preserves its own structure and motion. A cascade of synthesizing etheron collisions reproduces the kinematic configuration of the ether hyperbatch itself faster than it disintegrates. The ether hyperbatch possesses a stable mode of reproducing the same kinematic pattern through coupled syntheses. It is possible that three-dimensional space possesses the maximum dimensionality in which a hyperbatch is capable of self-sustenance.
The inclusion of an elementary ether batch in an ether hyperbatch signifies not a transition to a different type of ether object, but a compositional complexification of an object of the same type. An elementary batch is the result of a single synthesizing interaction of etherons. An elementary batch possesses its own substance and field but lacks a sufficiently long history of linked syntheses to stably reproduce its configuration. A hyperbatch differs from an elementary batch primarily in the topology and dynamics of the interaction network. The transformation of an elementary batch into a hyperbatch does not represent the emergence of a new type of ether object, but rather signifies a transition from a singular pattern to a self-sustaining pattern. It can be tentatively assumed that the transition from an elementary batch to a hyperbatch does not give rise to a qualitatively different type of interaction between ether objects that would lead to the emergence of ether objects belonging to the next stair of matter. Therefore, the elementary ether batch and the ether hyperbatch belong to the same class of ether objects at the same stair of matter.
The speed of an etheron over the aggregate of free motions of the etheron alternating with transit interactions of etherons and synthesizing interactions of etherons is called “effective speed”.
The speed of light in vacuum is close to the average absolute effective speed of an etheron.
An ether object of the third level of matter is called “ether spiral”.
An ether spiral is a spiral cluster of ether batches united by ether fields of ether batches. In an ether spiral, there is a “leading ether batch” and one or more “follower ether batches,” which are held by the ether field of the leading ether batch. The follower ether batches of the ether spiral orbitally rotate around the trajectory of motion of the leading ether batch of the ether spiral.
An ether spiral typically arises from the “ether budding” of a single “large” ether hyperbatch into several “small” ether hyperbatches. Within a “large” ether hyperbatch, “lagging” “small” ether subhyperbatches gradually form; after their mass increases sufficiently, they “bud off” from the leading parent ether hyperbatch and begin to orbit the trajectory of that parent hyperbatch. Physically, hyperbatch ether budding constitutes the fragmentation of a hyperbatch followed by the orbital stabilization of its daughter fragments. The parent hyperbatch possesses a longitudinal field associated with the longitudinal cascade of hyperbatch formation and maintenance, as well as a transverse field component that can become significant at the hyperbatch’s periphery. Following the budding process, the relative motion of the daughter hyperbatch must transition from mere recession from the parent into a bound orbital trajectory. The parent hyperbatch becomes the “leading” one because it retains the majority of the original substance after fragmentation. Thus, the concept of hyperbatch ether budding posits that an ether spiral generally emerges through the fragmentation-driven orbital budding of a large ether hyperbatch, wherein subhyperbatches form within its ether substance due to a spatially inhomogeneous cascade of synthesizing interactions. Upon reaching a specific range of mass and relative kinetic energy, these subhyperbatches detach from the parent substance — while maintaining a dynamic connection to its ether field — and enter bound orbital trajectories around the path of the leading hyperbatch.
The transition from an ether batch to an ether hyperbatch represents a quantitative and configurational complication, whereas the transition from a hyperbatch to a spiral creates a new qualitative type of organization for the ether object. An increase in the complexity of an ether object does not imply an increase in the stair of matter. When the ether spiral emerges, a new organization of interaction arises: intrabatch synthesizing coherence within ether hyperbatches gives rise to the interbatch orbital organization of the ether spiral. It is likely that only three-dimensional space allows for the type of field and kinematic stability of the ether hyperbatch from which the ether spiral subsequently emerges naturally.
The ether field of an ether spiral is called “spiral ether field”.
The frequency parameters of the spiral ether field of an ether spiral are determined by the periodicity of motion of the follower ether batches in the ether spiral. The greater the mass of a follower ether batch in the ether spiral, the lower the speed of orbital rotation of this ether batch around the trajectory of motion of the leading ether batch of the ether spiral. The frequency parameters of ether spirals have natural limitations, as the mass of an ether spiral has natural limitations.
Ether spirals can pass through each other.
The average absolute continuous velocity of an ether spiral is approximately equal to C.
The configuration of an ether spiral determines its ether field interaction with other ether spirals.
If the frequency of the first ether spiral is higher than the frequency of the second ether spiral, then the first ether spiral is “negative” relative to the second ether spiral, and the second ether spiral is accordingly “positive” relative to the first ether spiral, and these ether spirals attract.
If the frequency of the first ether spiral is approximately equal to the frequency of the second ether spiral, then the first ether spiral is “neutral” relative to the second ether spiral, and these ether spirals repel.
One and the same ether spiral of a certain frequency can simultaneously be “positive” relative to an ether spiral with a higher frequency, “neutral” relative to an ether spiral with a similar frequency, “negative” relative to an ether spiral with a lower frequency.
The laws of ether spirals determine multi-level layered clustering of ether spirals in elementary atoms.
The laws of ether spirals also determine multi-level hierarchical clustering of elementary atoms in nonelementary atoms.
Light is radiation consisting of sparse packets of ether spirals. The ether spirals of a light packet are practically not connected to each other. The packet of ether spirals of light is formatted by the periodic motion of the radiation source. The packet of ether spirals in some non-ether physical interpretations is called a “photon”. The wavelength of the light packet of ether spirals is determined by the frequency parameters of the motion of the radiation source.
An ether object of the fourth level of matter is called “ether major”.
An ether major is a chaotic cluster of ether spirals united by ether fields of ether spirals. Ether majors include protium atoms, protons, neutrons, extra-atomic electrons, positrons, as well as some other particles.
An ether major can emerge as a result of the “ether budding” of a single “large” ether hyperspiral into several “small” ether hyperspirals, followed by the “ether wrapping” of these hyperspirals into a closed system of hyperbatch-hyperspiral organization — an ether toroid. Linear ether budding of an ether hyperbatch is followed by orbital ether budding of the ether hyperspiral; this, in turn, is followed by the ether wrapping of the hyperspirals into an ether toroid, after which closed orbital ether budding of the ether torus itself becomes possible. Thus, the concept of hyperspiral ether budding posits that, during repeated hyperbatch budding, daughter hyperbatches can organize not only into separate orbital structures but also into a closed spatial system, provided the field of the parent hyperstructure supports stable circulation and flow closure. A sufficiently large hyperspiral system — through repeated budding and the subsequent self-consistent closure of trajectories — can acquire a toroidal topology, forming an independent object at a higher level of organization: an ether major. Each successive level of matter emerges not simply because objects at the previous level have grown larger, but because a new organization of motion arises: first local coupling, then cascading coupling, then orbitality, and finally closed circulation. Budding leads to self-coiling, which in turn leads to self-closure.
The ether field of an ether major is called “major ether field”.
An ether major has spin.
The average absolute effective velocity of an ether major can be zero.
The major ether field can be omnidirectional.
The frequency parameters of the major ether field are determined by the periodicity of motion of ether spirals in the ether major, as well as the mass of the ether major and the configuration of the ether major.
The major ether field can be conditionally divided into two components - into “electric field” and “magnetic field”. The electric field is the superimposed spiral ether fields of ether spirals moving in different directions. The magnetic field is the superimposed spiral ether fields of ether spirals moving in the same direction.
The electric charge of an ether hyperobject is determined by the predominance in the ether hyperobject of ether spirals with frequency parameters in a certain range.
Electric charge in ether theory is not two-signed, but multi-signed. The sign of electric charge depends on the configuration of the ether spirals predominant in the ether hyperobject. The lower the range of frequency parameters of the ether spirals predominant in the ether hyperobject, the higher the sign of the electric charge of the ether hyperobject. The number of signs of electric charge is limited, as the frequency parameters of ether spirals have natural limitations.
The first electric charge is “negative” electric charge. The sign of the first electric charge is the sign “-“. Instead of the sign “-“ for the first electric charge, the sign “1” can be used. The second electric charge is “positive” electric charge. The sign of the second electric charge is the sign “+”. Instead of the sign “+” for the second electric charge, the sign “2” can be used. The sign of the third electric charge is “3”, fourth - “4”, fifth - “5”, sixth - “6”, seventh - “7”, eighth - “8”, ninth - “9”, tenth - “A”, eleventh - “B”, twelfth - “C”, thirteenth - “D”, fourteenth - “E”, fifteenth - “F”, and so on up to some limiting sign.
Ether hyperobjects with electric charge of the same sign electrically repel. Ether hyperobjects with electric charges of different signs electrically attract. The closer the signs of electric charges are to each other, the greater the force of electric attraction of ether hyperobjects with electric charges of these signs. The higher the signs of electric charges, the greater the force of electric attraction and electric repulsion of ether hyperobjects with electric charges of these signs.
The flow of ether spirals in a cluster of ether spirals is “electric current”. Packets of ether spirals of light are not electric current.
Oppositely directed flows of ether spirals with approximately the same parameters of ether spirals repel. Unidirectional flows of ether spirals with approximately the same parameters of ether spirals attract.
Proteon is the general name for the protium atom, proton, and neutron. The term “proteon” in hyperatomic physics is an alternative to the term “nucleon” in nuclear physics.
The simplest notation for the Protium atom is H. The symbol for the Protium atom, with its atomic mass, is H-1. The symbol for the Protium atom without the H sign and with the atomic mass indicated is 1.
A proteon is considered an “elementary atom”. The non-hierarchical core composed of ether spirals within a proteon can be conditionally termed the “proteon nucleus” or the “nucleus of the elementary atom”.
The protium atom has several layers with increased probability of finding ether spirals with mass in a certain range in them. The deeper, the more often heavier ether spirals can be found in the proteon. The closer to the surface, the more often lighter ether spirals can be found in the proteon. In the outer layer of the protium atom, the probability of finding ether spirals of the smallest mass is maximum. The upper layers of the protium atom are called the “atmosphere of the atom” of protium. The lower layers of the protium atom are called the “clot of the atom” of protium. In nuclear-electronic atomic models, the outer layer of the protium atom is considered the “atomic electron”.
Usually, an “extra-atomic electron” arises as a result of clustering of light ether spirals ejected from the outer layer of the atmosphere of the protium atom.
A proton is a protium atom that has lost its outer layer.
Proteons are usually synthesized in the inner cores of planets and in the inner cores of stars from ether spirals captured by the gravity of these cosmic bodies. Superheavy proteons in the inner cores of planets and in the inner cores of stars can divide into proteons of smaller masses.
The “Ether Proteon Model” is the first part of the “Ether Atomic Model”. In the English version, the abbreviation for “Ether Atomic Model” is “ÆAM”. In the English version, the abbreviation for “Ether Proteon Model” is “ÆPM”.
An ether object of the fifth level of matter is called “hyperatom”.
A hyperatom is a hierarchical cluster of proteons united by proteon ether fields and strong common multilayered atmospheres consisting of ether spirals.
A hyperatom is considered a “non-elementary atom”. The hierarchical core composed of ether subatoms within a hyperatom can be conditionally termed the “hyperatom nucleus” or the “nucleus of a non-elementary atom”.
Introducing the “atomic nucleus” into ÆToE is permissible and can significantly improve ÆToE’s compatibility with the standard language of atomic and nuclear physics. However, the “atomic nucleus” is defined here as a structural concept within ÆToE, rather than being imported into the framework along with the nuclear-electronic model. The introduction of the “atomic nucleus” into ÆToE does not require the introduction of the atomic electron as a distinct shell particle of the atom. In ÆToE, the “atomic nucleus” is the internal structural component of the atom that forms its atomic core and stands in contrast to its atmosphere. ÆToE retains the concept of the “atomic nucleus” but redefines its physical realization. An elementary atomic nucleus is a non-hierarchical core within an elementary atom, composed of ether spirals. A non-elementary atomic nucleus is a hierarchical core within a non-elementary atom, composed of subatoms. Since the “proteon” is specifically introduced in ÆToE as an alternative to the “nucleon”, the system gains the ability to retain a significant portion of familiar terminology without automatically adopting the standard nuclear-electronic picture. In ÆToE, the “atomic nucleus” is a structurally bound inner part of the atom, not a geometric center. In ÆToE, the atomic nucleus can be central, displaced, deformed, multilayered, or hierarchical. The “nucleus of the ether hyperobject” in ÆToE is the “internal organized part of an object of a given class”, rather than a single specific physical object. In ÆToE, the same linguistic unit can be applied at different levels, provided its fundamental meaning remains defined. ÆToE does not reject the term “atomic nucleus”, but accepts it as a traditional structural term and alters its physical interpretation. “The principle of continuity of traditional physical terminology”: ÆToE retains a traditional term where its structural function is preserved, but allows for the redefinition of its microphysical realization.
The hierarchy of a cluster of ether objects of any type means that a complex cluster of ether objects of this type consists of less complex clusters of ether objects of this type, and that less complex clusters of ether objects of this type in turn consist of even less complex clusters of ether objects of this type, and so on up to the ether objects of this type themselves.
The hierarchy of a hyperatom means that a complex hyperatom consists of less complex hyperatoms, and that less complex hyperatoms in turn consist of even less complex hyperatoms, and so on up to the proteons themselves. Proteons and hyperatoms belong to different stairs of matter, yet both are considered atoms. Therefore, the atomic level is reckoned starting from proteons. The atomic level of a hyperatom is always one unit higher than the level of the hyperatom itself. The atomic level is the position of an atom within the hierarchy of atomic organization, determined by the number of successively nested levels of atomic structure.
The Protium atoms in a hyperatom are called Protium subatoms. A Protium subatom is an elementary subatom.
Hyperatoms can be sub-objects of higher-level hyperatoms. Hyperatoms in higher-level hyperatoms are called subhyperatoms. A subhyperatom is a non-elementary subatom. Subhyperatoms in a hyperatom also have a strong common multi-layered atmosphere consisting of ether spirals.
If the statement refers to an “atom” and not to a “Protium atom”, then it refers to an atom as such, which could be a Protium atom or any hyperatom. If the statement refers to “atoms”, then it refers to atoms as such, which could be Protium atoms or any hyperatoms.
If the statement refers to a “subatom” and not to a “Protium subatom”, then it refers to a subatom as such, which could be a Protium subatom or any subhyperatom. If the statement speaks of “subatoms”, then it is about subatoms as such, which can be both Protium subatoms and any subhyperatoms.
In stable hyperatoms there are no protons and neutrons, but only elementary subatoms and non-elementary subatoms.
The hyperatom’s atmosphere of ether spirals of certain masses unites the hyperatom’s subatoms and separates this hyperatom from other atoms.
Usually, the deeper the protium subatom in the hyperatom, the heavier and denser the ether spirals of this protium subatom.
Usually, a positron arises as a result of clustering of relatively heavy ether spirals ejected from the inner layer of the atmosphere of the protium atom.
Usually, a neutrino arises as a result of clustering of a small number of relatively light ether spirals that for one reason or another detached from the atmosphere of a hyperatom subatom.
The following paragraph provides several examples of the structure of simple hyperatoms. The combined cluster of two Protium subatoms with a strong common atmosphere forms the Deuterium hyperatom. The combined cluster of three Protium subatoms with a strong common atmosphere forms the Helithreeum hyperatom. Helithreeum is the name of the He-3 hyperatom in the ether hyperatomic model. Ht is the symbol for the chemical element Helithreeum and the symbol for the Helithreeum hyperatom. The combined cluster of the Deuterium subhyperatom and the Protium subatom with a strong common atmosphere forms the Tritium hyperatom. The combined cluster of two Deuterium subhyperatoms with a strong common atmosphere forms the Helium hyperatom. The combined cluster of the Helium subhyperatom and the Protium subatom with a strong common atmosphere forms the Helium-5 hyperatom.
Two Protium subatoms in a Deuterium hyperatom or two subatoms in a Deuterium subhyperatom are called “paired” Protium subatoms. If a Protium subatom in a hyperatom is not a subatom of a Deuterium hyperatom or a subatom of a Deuterium subhyperatom, then such a Protium subatom is called an “unpaired” Protium subatom.
Usually, a hyperatom consists of two subatoms. In three subatoms of a hyperatom, a skew in the distribution of the binding spiral mass of the hyperatom usually arises toward one of the pairs of subatoms of the hyperatom, as a result of which this pair of subatoms of the hyperatom either forms a subhyperatom in this hyperatom or pushes out the third subatom from the hyperatom, transforming the original hyperatom with three subatoms into a molecule consisting of a hyperatom now with two subatoms and the former third subatom that has become a separate atom.
A hyperatom configuration is a description of the hyperatom structure. A chemical element is a set of hyperatom configurations. A chemical subelement is a subset of a chemical element. If hyperatoms associated with a given chemical element differ with respect to the chemical elements to which their immediate subatoms belong, then such hyperatoms are conventionally considered to belong to different chemical sub-elements of that chemical element. A chemical number is the standard number of a chemical element. The designation of a chemical subelement consists of the designation of the chemical element, the ‘:’ sign, and the conventional ordinal number of the subelement. If an ether statement specifies the standard designation of a chemical element along with its structural formula but omits atomic masses, the statement typically refers to the chemical elements and chemical sub-elements themselves, rather than to specific hyperatoms. For example, Se:1 designates the first chemical sub-element Se:1-(Zn'N) of the chemical element Selenium (Se); Se:2 designates the second chemical sub-element Se:2-(Zn'O) of the chemical element Selenium (Se); Se:1-78-(Zn-64'N-14) designates the hyperatom Se-78 with the chemical sub-element number explicitly specified; and Se:2-80-(Zn-64'O-16) designates the hyperatom Se-80 with the chemical sub-element number explicitly specified.
Atomahedron is a general name for geometric shapes of hyperatoms and molecules. The basic atomahedrons are diatomahedron, triatomahedron, tetraatomahedron, pentaatomahedron. A diatomahedron is an atomahedron consisting of two atoms. A triatomahedron is a triangular atomahedron consisting of three atoms. A tetraatomahedron is an atomahedron-tetrahedron consisting of four atoms. A pentaatomahedron is an atomahedron in the form of a trigonal bipyramid consisting of five atoms. Hyperatomahedron is a general name for atomahedrons of the second and subsequent levels. Subatomahedron is a general name for atomahedrons in a hyperatomahedron. Subhyperatomahedron is a hyperatomahedron of the previous level in a hyperatomahedron of the next level. For example, the Deuterium hyperatom has the shape of a diatomahedron; The Helium hyperatom He-4 has the shape of a tetraatomahedron; the Zinc hyperatom Zn-64 has the shape of a third-level tetraatomahedron.
The tetrahedron is considered a periodic geometric shape of hyperatoms. The tetraatomahedron is considered a completed atomahedron. The pentaatomahedron is considered an overfilled atomahedron. Subhyperatoms of a hyperatomahedron may have an unfinished atomahedron of the previous level. A filled hyperatomic configuration is the hyperatomic configuration of a hyperatom with a filled hyperatomic periodic form. An unfilled hyperatomic configuration is the hyperatomic configuration of a hyperatom with a partially filled hyperatomic periodic form. A hyperatomic sequence is a sequence of hyperatomic configurations becoming more complex. The arity of a hyperatomic sequence is the maximum number of subatoms of the preceding level contained within the hyperatoms of the hyperatomic sequence. If the arity of a hyperatomic sequence is not explicitly specified, a binary hyperatomic sequence is implied. The sequence of configurations of hyperatoms in the sequential hierarchical filling of a periodic hyperatomic geometric shape with Protium subatoms is considered “primary” and forms a “primary binary sequence of hyperatoms”. The hierarchical filling of a periodic hyperatomic geometric shape means that a Protium subatom, when added to an unpaired Protium subatom, forms a Deuterium hyperatom or a Deuterium subhyperatom with it, and also means that subhyperatoms also form pairs. Hyperatoms of the primary sequence of hyperatoms are called primary. The atomic mass of a primary hyperatom can be used as a full designation for this hyperatom. For example, “1” is the designation for a Protium atom; “2” is the symbol for the hyperatom of Deuterium; “3” is the symbol for the hyperatom of Tritium; “4” is the symbol for the hyperatom of Helium; “5” is the symbol for the hyperatom of Helium-5.
A hyperatom is usually notated so that the structure of the hyperatom can be uniquely identified. A hyperatom notation may include the notation of the chemical element of the hyperatom, the atomic mass of the hyperatom, and the formula of the hyperatom. The parts of a hyperatom notation are separated from each other by the minus sign ‘-‘. For example, “D” is the simplest symbol for the hyperatom of Deuterium. “D-2” is the symbol for the hyperatom of Deuterium with its atomic mass indicated. “2” is the symbol for the hyperatom of Deuterium with only its atomic mass indicated, which is the primary atomic mass. A hyperatom can be designated by indicating only its atomic mass only if the hyperatom is part of the primary sequence of hyperatoms.
The formula of a hyperatom is an expression consisting of the designations of the subatoms of that hyperatom, separated by an apostrophe “’” and joined by parentheses. For example, “(H’H)” is the formula of the hyperatom of Deuterium D-2. The formula of a hyperatom can be specified in the designation of the hyperatom. The formula of a hyperatom in the designation of a hyperatom is separated by the minus sign ‘-‘. For example, “D-2-(H’H)” is the designation of the hyperatom of Deuterium D-2, which contains the formula of the hyperatom of Deuterium D-2.
For any permutation of immediate subatoms, hyperatom structures that differ only in the order of the subatoms are usually considered semantically equivalent:
\[(sa_1'\cdots'sa_k) \equiv (sa_{\sigma(1)}'\cdots'sa_{\sigma(k)}).\]The following paragraph provides several examples of notations for simple hyperatoms. H-1-1. D-2-(1’1). T-3-(2’1). Ht-3-(1’1’1). He-4-(2’2). He-5-(4’1). Li-6-(4’2). Li-7-(4’3). Be-8-(4’4). Be-9-(8’1). Be-10-(5’5). B-10-(8’2). B-11-(8’3). C-12-(8’4). C-13-(8’5). C-13-(12’1). N-14-(8’6). N-15-(8’7). O-16-(8’8). O-17-(16’1). O-18-(16’2). F-19-(16’3). Ne-20-(16’4). Ne-21-(16’5).
Hyperatomic transformation is the transition of a hyperatom from one hyperatomic configuration to another. For example, the hyperatomic transformation of Beryllium-10 ($Be-10-(5’5)$) into Boron-10 ($B-10-(8’2)$).
A hyperatom configuration is a structural description of a hyperatom in terms of its immediate subatoms. The arity ($arity(ha)$) of a hyperatom ($ha$) is equal to the number of immediate subatoms of the hyperatom. The arity of a proteon is zero:
\[\text{arity}(ha)=|\text{subatoms}(ha)|\] \[\text{arity}(proteon)=0.\]The immediate subatoms (${sa_1,\ldots,sa_k}$) of a hyperatom ($ha$) form a finite multiset. The arity of the Deuterium-2 ($D-2-(1’1)$) hyperatom is two. The arity of the Helithreeum-3 ($Ht-3-(1’1’1)$) hyperatom is three:
\[\text{subatoms}(ha) = \{\!\{sa_1,\ldots,sa_k\}\!\}, \qquad k=\text{arity}(ha)\] \[\text{arity}(D-2-(1'1))=2\] \[\text{arity}(Ht-3-(1'1'1))=3.\]The use of a multiset implies that the order of subatoms within a standard stable hyperatom has no fundamental physical or mathematical significance, whereas the multiplicity of identical subatoms does matter. Therefore:
\[(2'1)\equiv(1'2),\]but:
\[(1'1'1)\not\equiv(1'1).\]A canonical textual representation is selected for each hyperatom. In the canonical notation, immediate subatoms are arranged in non-decreasing or non-increasing order based on a specific canonical key; in the simplest and most common case, the subatom with the higher atomic mass is written first. Thus, of the two semantically equivalent notations
\[(2'1)\]and
\[(1'2)\]the first is the canonical notation, while the second is non-canonical. The canonical notation of a hyperatom configuration serves as the unique chosen representative of its equivalence class and is used for the serialization, comparison, indexing, and machine processing of hyperatom configurations. The canonical representation must satisfy the condition:
\[m_{atomic}(sa_1)\ge m_{atomic}(sa_2)\ge\cdots\ge m_{atomic}(sa_k).\]For a hyperatomic configuration ($ha$), an atomic mass $m_{atomic}(ha)$ can be defined. For hierarchical compositions in the simplest additive model:
\[m_{atomic}\!\left(\text{composition}(sa_1,\ldots,sa_k)\right) = \sum_{j=1}^{k}m_{atomic}(sa_j).\]In particular:
\[m_{atomic}(1'1)=2,\] \[m_{atomic}(1'1'1)=3,\] \[m_{atomic}(2'1)=3.\]In the general case, atomic mass is not a sufficient identifier for a hyperatomic configuration. Specifically, different hyperatoms may have the same atomic mass:
\[m_{atomic}(Be\!-\!10-(5'5)) = m_{atomic}(B\!-\!10-(8'2)) = 10,\]while
\[(5'5)\ne(8'2).\]Therefore, in the general case, the complete identity of a hyperatom must be defined by its canonical structural configuration, whereas atomic mass is a separate numerical attribute.
A hyperatomic sequence is defined as an ordered sequence of hyperatomic configurations. Typically, for the sake of algorithmic simplicity, the protium atom ($H-1$) is considered the first element of any atomic sequence, even though it is not a hyperatom:
\[P_{atomic}=(a_1,ha_2,\ldots,ha_N,\ldots),\] \[a_1≡H-1.\]Equivalently, a hyperatomic sequence can be defined as a mapping:
\[P_{atomic}:\mathbb N^+\rightarrow\mathcal H,\]where $P_{atomic}(n)=ha_n$, and $n$ is called the hyperatomic number of the sequence element.
The hyperatomic number is the index of an element in a numbered hyperatomic sequence and should not be automatically equated with the atomic mass for all hyperatoms. For primary hyperatoms in the simplest primary sequence, the hyperatomic number coincides with the atomic mass; however, for all other hyperatoms, the same atomic mass can correspond to several different configurations.
Hierarchical compositions of hyperatoms can be broadly categorized into three types: “primary”, “secondary”, and “tertiary”. The type of hierarchical composition of a hyperatom does not indicate the depth of the hyperatom’s nesting; rather, it constitutes a classification based on the numbering properties of both the hyperatom itself and its immediate subatoms. The terms “primary”, “secondary”, and “tertiary” denote types of hyperatom composition, not the depth of hyperatom nesting. “Primary” compositions are “numbered” hierarchical compositions of hyperatoms. All primary hyperatoms are binary — that is, they have an arity of two. “Secondary” compositions are “unnumbered compositions with numbered subatoms”. Secondary hyperatoms can have an arity greater than two. For example, the secondary hyperatom Helithreeum Ht-3-(1’1’1) has an arity of three; that is, it is a secondary ternary hyperatom. “Tertiary” hyperatoms are “unnumbered and have at least one unnumbered subatom”. Tertiary hyperatoms can have an arity greater than two. “Primary” hyperatoms constitute a “primary” binary hyperatomic sequence. “Primary” and “secondary” hyperatoms together constitute a “double” hyperatomic sequence. “Primary”, “secondary”, and “tertiary” hyperatoms together constitute a “triple” hyperatomic sequence. In calculations and simulations, it usually makes sense to use “double” and “triple” sequences only with binary hyperatoms. If the arity of a “double” or “triple” hyperatomic sequence is not explicitly specified, the term refers to a binary hyperatomic sequence:
\[C_1=\text{Primary Hyperatom Compositions}\] \[C_2=\text{Secondary Hyperatom Compositions}\] \[C_3=\text{Tertiary Hyperatom Compositions}\] \[C=C_1\sqcup C_2\sqcup C_3 = \text{Hyperatom Compositions}\] \[S_1=C_1=\text{Primary Hyperatomic Sequence}\] \[S_2=C_1\cup C_2=\text{Double Hyperatomic Sequence}\] \[S_3=C_1\cup C_2\cup C_3=\text{Triple Hyperatomic Sequence}\] \[\text{Primary}\subset\text{Double}\subset\text{Triple}.\]The primary hyperatom sequence is a sequence of configurations obtained through the successive hierarchical filling of a periodic hyperatomic geometric shape with Protium subatoms.
For the first primary atom:
\[a_1=1.\]For each $n\ge2$, the following are defined:
\[p(n)=2^{\lfloor\log_2(n-1)\rfloor},\] \[q(n)=n-p(n),\]after which the primary configuration is defined recursively:
\[ha_n= \text{canon}\!\left(ha_{p(n)},ha_{q(n)}\right).\]Consequently:
\[ha_2=(1'1),\] \[ha_3=(2'1),\] \[ha_4=(2'2),\] \[ha_5=(4'1),\] \[ha_6=(4'2),\] \[ha_7=(4'3),\] \[ha_8=(4'4),\] \[ha_9=(8'1),\]and so on.
A hyperatom is primary if and only if its canonical structure coincides with the structure of an element of a primary hyperatomic sequence having the same atomic mass. The primality of the hyperatom is not determined by mass being some special number; on the contrary, mass becomes a sufficient notation precisely because it uniquely reconstructs the primary configuration:
\[P_{atomic.primary,1}=1\] \[P_{atomic.primary,n}= \text{canon} \left( P_{atomic.primary,2^{\lfloor\log_2(n-1)\rfloor}}, P_{atomic.primary,n-2^{\lfloor\log_2(n-1)\rfloor}} \right), \qquad n\ge2\] \[\text{primary}(ha) \iff \text{canon}(ha)=P_{atomic.primary,m_{atomic}(ha)}\] \[\text{ShortNotation}(ha)=m_{atomic}(ha) \iff \text{primary}(ha).\]The atomic level of the primary hyperatom sequence containing the hyperatom with number $n$ is defined as:
\[L_{atomic.primary}(n)=\lfloor\log_2 n\rfloor+1.\]For $L_{atomic.primary}\ge2$, the number of primary hyperatoms with atomic level $L_{atomic.primary}$ is:
\[|P_{atomic.primary,L_{atomic.primary}}|=2^{L_{atomic.primary}-2}.\]The number of primary hyperatoms from the first atomic level up to and including atomic level $L$ is:
\[\sum_{\ell=1}^{L}|P_{atomic.primary,\ell}| = 2^{L-1}.\]Hierarchical programmatic generation of hyperatomic sequences is performed according to the atomic levels of the hyperatoms:
\[m_{atomic}(\text{composition}(sa_1,sa_2))=m_{atomic}(sa_1)+m_{atomic}(sa_2),\] \[L_{atomic}(\text{composition}(sa_1,sa_2)) =1+\max(L_{atomic}(sa_1),L_{atomic}(sa_2)).\]The generator is not required to output elements in order of atomic mass. The primary generation order is hierarchical: at each structural level ($L$), all valid unordered pairs of previously formed subatoms are considered for which
\[\max(L_{atomic}(sa_1),L_{atomic}(sa_2))=L-1.\]During generation, new structures are canonicalized and added only if no structural duplicate exists. The primary sequence is constructed according to a recursive rule:
\[P_1=1,\] \[P_n=\text{composition}(P_{p(n)}, P_{q(n)}),\]где
\[p(n)=2^{\lfloor\log_2(n-1)\rfloor}, \qquad q(n)=n-p(n), \qquad n\ge2.\]The generation of a double hyperatomic sequence involves binary pairs of references to primary hyperatoms. If the result is novel and distinct from the corresponding primary configuration, it is classified as secondary. The generation of a triple sequence involves pairs containing previously formed configurations. If the result is neither primary nor secondary, it is classified as tertiary. The physical rule governing the admissibility of secondary and tertiary hyperatoms may be defined by specific predicates. The generation algorithm itself must not substitute an arbitrary heuristic filter for an unknown physical rule.
The algorithm for constructing the “complete hyperatom map” involves several passes. The first pass is data collection. The module traverses the *.etoe files across all chemical element directories within the data/atom/element directory, separates active statements from comments, and extracts two primary types of records: chemical element definitions (e.g., Se-(Zn'N)) and hyperatom definitions (e.g., Se-78-(64'14)). The second pass is linking. After all files have been read, global indices for elements and hyperatoms are generated. Subsequently, element references are matched against available elements, and sub-atom references within hyperatom structures are matched against available sub-atom configurations. The third pass is numbering and diagnostics. Unique active rules are assigned stable sub-element identifiers based on the order of their appearance during the sorted file traversal. Rules lacking corresponding hyperatoms are retained as unfilled, and ambiguous links are not resolved arbitrarily.
A neutron is a protium subatom that for one reason or another left its hyperatom and lost part of its outer layer. The parameters of a neutron mainly depend on where in the hyperatom the protium subatom that became this neutron was located.
A neutron upon entering a hyperatom can capture part of the hyperatom’s atmosphere with its ether field. The loss by the hyperatom of part of its atmosphere upon entry of a neutron reduces the stability of the hyperatom.
A proton upon entering a hyperatom can capture part of the hyperatom’s atmosphere with its ether field. The loss by the hyperatom of part of its atmosphere upon entry of a proton reduces the stability of the hyperatom.
A light hyperatom upon entering a heavy hyperatom can capture part of the heavy hyperatom’s atmosphere with its ether field. The loss by the heavy hyperatom of part of its atmosphere upon entry of a light hyperatom reduces the stability of the heavy hyperatom.
Hyperatoms are synthesized in the inner cores of planets and in the inner cores of stars. The synthesis of hyperatoms occurs with accumulation of energy, not with release of energy. Outside the cores of planets and outside the cores of stars, heavy hyperatoms begin to decay with release of energy.
A hyperatom can lose part of its ether spirals as a result of external influence. The loss of ether spirals by a hyperatom reduces the stability of the hyperatom. A decrease in the stability of a hyperatom can lead to the decay of the hyperatom into subatoms.
The decay of hyperatoms into subatoms is accompanied by expansion of these subatoms. The expanding subatoms of the decaying hyperatom collide. The collision of expanding subatoms of the decaying hyperatom leads to the scattering of subatoms with certain velocities. Usually, in the decay of a hyperatom into subatoms, most of the energy is provided by the scattering subatoms released from the hyperatom, not by the ether spirals released from the hyperatom.
The “Ether Hyperatomic Model” is the second part of the “Ether Atomic Model”. In the English version, the abbreviation for “Ether Hyperatomic Model” is “ÆHAM”.
The Ether Atomic Model is a model of elementary atoms and a model of nonelementary atoms.
The stability of a hyperatom upon entry of a neutron depends on the place in the hyperatom where this neutron entered. The entry of a neutron into a hyperatom can lead to the decay of the hyperatom.
A reactor designed for controlled decay of hyperatoms by protons and neutrons is called a “hyperatomic reactor”. For simplicity, a hyperatomic reactor can be conventionally called an “ether reactor”.
In a hyperatomic reactor, hyperatoms and proteons in targets and beams must be oriented so that upon collision of hyperatoms with proteons and hyperatoms with hyperatoms, the highest probability of the necessary hyperatomic reactions is ensured. In a hyperatomic reactor, hyperatoms and proteons are specially oriented by an external magnetic field.
So-called “thermonuclear reactors” are considered in the ether atomic model as “hyperatom decay reactors,” not “hyperatom synthesis reactors”.
An ether object of the sixth level of matter is called a “molecule”.
A molecule is a cluster of atoms united by their ether fields and having a weak common atmosphere of ether spirals. Molecules include the hydrogen molecule, oxygen molecule, water molecule, and all other molecules.
The “Ether Molecular Model” is a physical model of molecules based on the ether atomic model. In the English version, the abbreviation for “Ether Molecular Model” is “ÆMM”.
Molecules can be conditionally divided into hierarchical levels. A simple molecule can be a subobject of a complex molecule. A subobject of a complex molecule is called a “submolecule”. A complex molecule is called a “hypermolecule”. A complex submolecule is called a “subhypermolecule”.
The formula of a molecule is an expression consisting of the designations of the atoms of that molecule, separated by the caret sign ^ and united by parentheses. For example, (H^H) is the formula of the Hydrogen molecule H₂. The formula of a molecule can be indicated in the designation of the molecule. The formula of a molecule in the designation of a molecule is separated by the - sign. For example, H₂-(H^H) is the designation of the Hydrogen molecule H₂, which contains the formula of the Hydrogen molecule H₂.
The disintegration of heavy hyperatoms outside the planet’s core in the early stages of the planet’s existence after the planet’s surface has cooled results in the energy-provided diversity of organic molecular forms, objects and processes necessary for the emergence of primary living ether objects. The disintegration into identical subatoms of identical heavy hyperatoms in a single chain of submolecules in a hypermolecule can lead to the transformation of this hypermolecule into a double-chain one. The copper hyperatom Cu-62-(31’31) consists of two phosphorus subhyperatoms P-31-(16’15). The copper hyperatom Cu-62-(31’31) is an unstable hyperatom. The copper hyperatom Cu-62-(31’31) usually disintegrates into two phosphorus hyperatoms P-31-(16’15). ProtoDNA is a hypermolecule that is a single chain of subhypermolecules of double protonucleotides. The subhypermolecule of the double protonucleotide is a subhypermolecule consisting of a copper hyperatom Cu-62-(31’31) linked by submolecular bonds to the base of the double protonucleotide. The base of the double protonucleotide is that part of the subhypermolecule of the double protonucleotide that does not include the copper hyperatom Cu-62-(31’31) itself. The base of the double protonucleotide corresponds to two complementary nucleotides without phosphorus hyperatoms P-31-(16’15). When one copper hyperatom Cu-62-(31’31) in the protoDNA hypermolecule disintegrates into two phosphorus hyperatoms P-31-(16’15), the subhypermolecule of the double protonucleotide is transformed into an ordinary double complementary nucleotide, which is an element of the double chain in an ordinary DNA hypermolecule. When all copper hyperatoms Cu-62-(31’31) in a protoDNA hypermolecule disintegrate, the protoDNA hypermolecule becomes a regular DNA hypermolecule. Sometimes, when the last copper hyperatom Cu-62-(31’31) in a protoDNA hypermolecule disintegrates, the two nucleotide chains of the resulting regular DNA hypermolecule separate and become two complementary regular RNA hypermolecules. The transformation of a protoDNA hypermolecule into a DNA hypermolecule and the separation of a DNA hypermolecule into complementary RNA hypermolecules may, in some cases and under certain conditions, serve as the starting point of organic evolution. The explanation of the origin of life based on the transformation of protoDNA into DNA underlies the concept of “Ether Transformational Abiogenesis”. The concept of “Etheric Transformational Abiogenesis” is a component of the “Ether Theory of Life”.
An ether object of the seventh level of matter is called a “body”.
A body is a cluster of atoms and molecules united by their ether fields. Bodies and parts of bodies can be in solid, liquid, and gaseous states. Bodies include primary galactic stars, stars, planets, asteroids, as well as all other clusters of atoms and molecules.
Bodies can be conditionally divided into hierarchical levels. A simple body can be a subobject of a complex body. A subobject of a complex body is called a “subbody”. A complex body is called a “hyperbody”. A complex subbody is called a “subhyperbody”.
The “Ether Body Model” is a physical model of bodies based on the ether atomic model and ether molecular model. In the English version, the abbreviation for “Ether Body Model” is “ÆBM”.
The “Ether Cosmic Body Model” is a physical model of cosmic bodies based on the ether body model. In the English version, the abbreviation for “Ether Cosmic Body Model” is “ÆCBM”.
The “Ether Solar Model” is a physical model of the Sun based on the ether cosmic body model. In the English version, the abbreviation for “Ether Solar Model” is “ÆSM”.
The cores of long-formed planets and the cores of long-formed stars are in a solid and cold state.
Planets and stars accumulate fissionable material in the form of accumulations of heavy hyperatoms. Accumulation of fissionable material above the critical mass in a cosmic body of near-stellar mass leads to a chain hyperatomic reaction of decay of heavy hyperatoms of the fissionable material. If the rate of accumulation of fissionable material in a cosmic body is higher than the rate of consumption of fissionable material in hyperatomic explosions of the fissionable material, then the cosmic body becomes an active star. The stability of heavy hyperatoms in an active star that has accumulated a certain mass can increase. An active star can go out due to an increase in the stability of heavy hyperatoms due to the growth of the star’s mass. An extinct star, having accumulated fissionable material from heavier and unstable hyperatoms, can ignite again. Hyperatomic explosions of fissionable material in cosmic bodies of stellar mass can lead to the ejection of a large amount of the star’s material into space. From the material ejected by cosmic bodies of stellar mass, cosmic bodies of planetary mass can form.
A “galactic prime” is the primary supermassive star of a galaxy.
A galactic prime, transitioning to an active state, can, as a result of hyperatomic explosions of its fissionable material, eject an amount of material sufficient for the formation of a star.
An ether object of the eighth level of matter is called an “astr”.
An astr is a hierarchical cluster of cosmic bodies united by their etheric fields and moving along gravitational orbital trajectories. Astrs include planetary systems, star systems, galaxies, galaxy clusters, and larger-scale clusters.
Astrs can be conditionally divided into hierarchical levels. A simple astr can be a subobject of a complex astr. A subobject of a complex astr is called a “subastr”. A complex astr is called a “hyperastr”. A complex subastr is called a “subhyperastr”.
The formula of an astr is an expression consisting of the designations of the elements of this aster, separated by a comma and united by parentheses. For example, (Earth, Moon) is the formula of an astr consisting of the Earth and the Moon.
Tired light is the phenomenon of cosmological attenuation of light and the phenomenon of cosmological expansion of light. The phenomenon of cosmological expansion of light manifests as cosmological redshift. Cosmological redshift is caused by an increase in the distance between ether spirals of light packets due to a decrease in the frequency of transit and synthesizing interactions of light etherons with external etherons in interstellar space and intergalactic space. Cosmological attenuation of light is caused by the decay of ether spirals of light packets due to a decrease in the frequency of transit and synthesizing interactions of light etherons with external etherons in interstellar space and intergalactic space.
Cosmic microwave background radiation is caused by the decay of protons in interstellar space and intergalactic space.
The rotation curve of a disk galaxy is determined by the fact that the repulsive ability of the ether field of an ether hyperobject decreases with increasing distance to the ether substance of this ether hyperobject, and the attractive ability of the ether field of an ether hyperobject increases with increasing distance to the ether substance of this ether hyperobject, as well as by the fact that the repulsive ability of the ether medium decreases with decreasing distance to the ether substance of an ether hyperobject, and the attractive ability of the ether medium increases with decreasing distance to the ether substance of an ether hyperobject.
The model of levels of matter in the Ether Theory of Matter is called the “Ether Standard Model of Matter”. In the English version, the abbreviation for “Ether Standard Model of Matter” is “ÆSMoM”.
This concludes the brief summary of the Ether Theory of Matter.
Next is a brief summary of the Ether Theory of Consciousness.
The Ether Theory of Consciousness is built on the concept of “Ether Neural Network”.
In the English version, the abbreviation for “Ether Neural Network” is “ÆNN”.
Ether neural networks are considered by the “Ether Neural Network Theory”. In the English version, the abbreviation for “Ether Neural Network Theory” is “ÆNNT”.
The information-technological name for “Ether Neural Network” is “Associative Broadcast Neural Network”. In the English version, the abbreviation for “Associative Broadcast Neural Network” is “ABNN”.
Information is patterns and associations between patterns.
Intelligence is the ability of neural networks to carry out the evolution of information for the purpose of evolution of matter.
The concept of ether neural network stems from the idea that each neuron of a natural neural network has an output broadcast electric pattern in the electrically conductive network between neurons, which can be selectively recognized by some other neurons of the neural network with which this neuron may not have direct synaptic contact.
A neuron during its axonal spike can transmit its output broadcast electric pattern into the electrically conductive network around neurons through the dendrites of other neurons that synaptically contact the axon of this neuron. Although the main mechanism in axodendritic synapses is chemical transmission through neurotransmitters, the fact of the spike in the axon is accompanied by transmembrane currents that create local changes in electric potential in the extracellular environment.
Dendrites not only receive signals through receptors but are themselves conductive cables with membrane potential that can be modulated by external electric currents. External electric currents propagate not only in the intercellular fluid but also along the dendrite membrane. The spatial configuration of a neuron’s dendrites allows the neuron to confidently recognize a certain set of broadcast output electric patterns from other neurons.
This concludes the brief summary of the Ether Theory of Consciousness.
Next is a brief summary of the Ether Theory of Society.
The Ether Theory of Society is built on the concept of ether society.
Ether society is a materialistic society based on the philosophy of evolutionary ether materialism.
The concept of ether society stems from the idea that the inexhaustibility of hyperatomic energy obtained in hyperatomic reactors and the superiority of the global universal artificial intelligence of the socialized global artificial neural network will accelerate evolutionary social processes and ensure the overcoming of all fundamental social contradictions.
At its core, man is a group predatory animal with natural limitations of time, energy, memory, knowledge, intelligence and spirituality.
The natural limitations of man in the conditions of private ownership of matter, energy, knowledge, intelligence and management give rise to fundamental social contradictions.
Overcoming fundamental social contradictions is possible only if knowledge, matter, energy, intelligence, and management are socialized.
Socialized knowledge includes the theory of matter, theory of life, theory of consciousness, theory of society, as well as all other socially significant knowledge.
Socialized matter includes land, subsoil, infrastructure, people’s enterprises, as well as all other socially significant material objects.
Socialized energy includes all energy obtained for social purposes at hyperatomic power plants and at power plants with other types of energy installations.
Socialized intelligence includes the entire intellectual process in the socialized global ether neural hypernetwork intended for purposes of social development.
Socialized management includes people’s democracy, people’s organizations, people’s control, as well as all other socially significant elements of society management.
Ether science within the framework of artificial evolution of living beings will provide the possibility of creating genetically compiled humans with protection against genetic errors in cell division and functioning of the body. Artificial evolution of humans will eliminate the limitations of natural evolution.
The social system in which fundamental social contradictions are overcome by the intellectual evolutionary materialistic path is called evolutionary ether communism.
This concludes the brief summary of the Ether Theory of Society.
The above is a brief summary of the Ether Theory of Everything for dialogues with AI systems.