The New Integrated Physical and Mathematical Axiomatics of the Universal Law

by Georgi Stankov, Copyright 1999, 52 pages

Abstract

In 1995, I discovered the Universal Law (the Law) of Nature: I proved that all known physical laws and their appli­cations can be derived from this one law within mathe­matical forma­lism and can be explained for the first time from an epis­te­mo­­logical and cog­nitive point of view. The discovery of the Law is the logical result of the consistent implementation of the principles of mathe­ma­tical for­ma­­lism to the structu­re of present-day physics. This endea­vour has led to the develop­ment of a unified theo­ry of physics and cos­mology, which is a full axioma­tisa­tion (axio­ma­tics) of phy­sics. It could be shown that physics is applied mathe­matics to the physical world. The major results of the new theo­ry are: All terms, quan­ti­ties, constants, and other physical magnitudes can be axio­ma­ti­cal­ly deri­­ved from the pri­mary term, energy = space-time, which is the primary term of human conscious­ness. The pri­mary axiom of the new axiomatics estab­lishes the semantic and ma­the­­matical equi­va­­lence between all words or abstract symbols that can be arbitra­rily used for the prima­ry term. This is called the „principle of last equivalence“; it is the first and only a priori axiom of the new integ­rated physical and mathe­ma­tical axio­ma­tics. According to it, energy (spa­ce-time) is closed, infinite, con­ti­­nuous, inho­mo­ge­neous (dis­crete), and con­stant; it is in a state of permanent ener­gy ex­chan­ge. It can be proven that the conti­nuum (the set of all num­­­bers) is equivalent to the pri­­ma­ry term. There­fore, it is the common basis of both physics and mathe­matics. The new axiomatics is veri­fied by all mathe­matical (nume­ri­cal) results that have been theo­retically or ex­pe­­rimentally obtained in physics so far. However, it eli­mi­nates so­me fun­da­men­tal forma­lis­tic blun­ders that have been intro­du­ced in this natural science through­­out its history by implementing the prin­cip­les of mathe­matical forma­­lism in a inconsistent, and hence, wrong manner. In this way, the va­li­dity of mathe­ma­tics as chal­lenged by Gö­del’s theo­rem can be proven in the real world (proof of exis­ten­ce). This eli­mi­nates the con­ti­nu­um hypo­thesis and the on­go­ing foun­dation crisis of ma­­thematics as artefacts that are based on wrong assump­tions.

The Uni­ver­sal Law descri­bes spa­ce-ti­me in ma­the­­ma­tical terms. The uni­ver­­­­sal equa­­tion is E = EAf, whe­re E is energy ex­chan­ge, EA is a speci­fic constant amount (quan­tum) of ex­chan­ged energy, cal­led “action po­tential“, and f = E/EA is cal­led „ab­­so­lute time“. The latter is a dimen­sion­less quotient. The Uni­versal Law is a law of ener­gy. Energy (space-time) is the only real thing. All physi­cal quan­tities such as mass, char­ge, force, and momentum are abstract sub­sets of space-time that are first de­fined within ma­the­ma­tics (objects of thought) and are then mea­su­red in the real world. They are dimen­sion­less numbers that be­long to the conti­nuum. Since they contain space-ti­me as an ele­ment (U-sub­sets), they can be axioma­ti­cally derived from the pri­mary term. For instan­ce, it can be proven in an irrevocable man­ner that mass, as it is currently defi­ned in physics, is actually a sy­nonym for energy (space-time) rela­tion­ship, and charge is a synonym for area (two-dimensional space), that is, the SI unit 1 coulomb is equi­va­lent to 1m2. There­fore, photons are not mass­-less par­tic­les, as is believed in physics today, but exhibit energy relation­ships (masses), just as all other material systems such as gravitational objects. By eliminating such fundamental for­ma­listic blunders in physics, gravi­tation can be integ­­­rated for the first time with the other three fundamental forces. At the same time, it can be cogently proven that the big-bang-hypothesis, and hence all the basic con­cepts of modern cos­mo­logy, are entirely wrong. The new theory is outlined in two com­prehensive volu­mes of more than 1000 pa­ges and encom­pas­ses the full axiomatic pre­sen­­tation of the fundamental phy­­­sical disciplines. The present pub­lication sum­ma­rizes the basic axioms and con­clusions of the new integrated physical and mathematical theory of the Law.

 Key words: Universal Law, universal equation, pri­mary term, space-ti­me, energy, integrated physical and ma­­the­­­ma­tical axioma­tics, mathema­tical formalism, space, absolute time f, primary axiom, continuum, pro­ba­bility set, epistemology of mathematical equations.

 Introduction

Since Einstein, it has been the dream of many physicists to dis­cover the „universal field equation“ and derive all known laws from same. Contrary to this endeavour, mo­dern physics teaches that nature is re­gu­lated by many distinct physical laws. They are products of various dis­ciplines, such as clas­sical mechanics, ther­mo­­­dy­na­mics, wave theo­ry, electromagnetism, quan­tum mecha­nics, theory of rela­tivity, QED, QCD, etc. We encounter various laws, the most prominent of which are: Newton’s axioms of clas­sical me­chanics, his law on gravity, Kep­ler’s laws, the first and second law of thermodynamics, Boltzmann’s law, laws of radia­tion (Wien’s displacement law, Stefan-Boltz­mann’s law), clas­sical wave equation, va­rious laws of electricity and magne­tism, which can be regarded as precursors of Maxwell’s four equa­tions of electro­magnetism, Schrödinger wave equation of quantum mecha­nics, etc. Unfortu­na­tely, physicists have failed to explain why Natu­re needs so many laws, and how it co-ordi­nates them in a simulta­neous manner, so that it functions as an ordered whole. The new axiomatic ap­proach in phy­sics proves that these diffe­rent laws are, from ontolo­gical point of view, equivalent ma­the­­matical presen­tations of one single law of nature – they are derivations of the Uni­versal Law for specific energy inter­actions. This exten­sive proof forms the basis of the new unified theory of physics and cosmology, which adheres to the prin­ciples of mathematical formalism (see Tables 1 & 2).

Although the necessity of axiomatizing physics on the basis of ma­­the­matical forma­lism was postulated some time ago (1), this tar­get has not yet been achieved. The dis­covery of the Universal Law of Na­tu­­re has led to the estab­lishment of a general theory of physics and cos­­­mology, which is an axiomati­zation of physics on the basis of mathe­matical formalism (2-5). It confirms without any excep­tion all the mathe­ma­tical (theoretical) and experimental results ob­tai­ned in phy­sics so far. At the same time, it reveals that some basic verbal inter­pre­tations of the­­se results are essen­tially wrong from an epis­temological point of view. Such mistaken con­clusions have pre­cluded the unifi­ca­tion of phy­sics. The major re­sults of the new integ­rated physical and mathematical axiomatics can be sum­ma­rized as follows:

 1.  Energy (space-time) has only two dimensions (con­­sti­tuents), spa­­ce and abso­lute time. They are canonically conjugated recipro­cal mag­ni­­tudes that can be expressed as nume­rical, dimensionless relationships. All phy­si­cal quan­tities as mea­sured by the SI sys­tem can be derived from these two quantities (see Table 2). This pro­ves that the SI system is an anthropocentric surrogate and should be abolished from theoretical physics.

 2.  There is no va­cuum. There are instead photons (pho­ton level) percei­­ved as space (ex­tent). The photon le­vel has the same pro­per­ties as mat­ter, for instance, it can be asses­sed in terms of mass (space-time relationship) and char­ge (area). Two new fundamental constants have been deri­ved: mass m= 0.737´10-50 kg and char­ge qp=1.29669´10-39m2 of the basic pho­ton h, also known as Planck’s constant.

 3.  All known physical con­stants can be derived from these two constants by ap­ply­ing the uni­ver­sal equation (see Table 1). Thus the energy (space-time) of the basic photon h is the hidden real reference system of SI system, from which all other SI units and quantities are obtained in a secondary manner according to the prin­ciple of circular argument. This is a basic proof that the phy­sical world is a uni­ty.

 4.  A no­vel method has been developed, which enables the deri­vation of many new phy­sical constants within mathematical for­ma­lism and their empirical verification by various well known experiments. All na­tural constants are dimensionless num­bers - their magnitudes are in­­­de­pen­dent of the choice of the surrogate reference system such as SI system – therefore, the SI system should be eliminated from theoretical physics.

 5Charge is a sy­no­­nym for geometric area: 1 coulomb = 1 squa­re meter.

 6.  The basic terms – time, temperature, and relativistic mass - are di­mensionless num­­bers (quotients), the definition of which is ma­the­matics. They are physical sets of the probability set (0£P(A)£1) as intro­du­ced by Kolmo­go­­­roff in his theo­ry of pro­ba­­bilities. The probability set is equivalent to the primary term P(A) == space-time = energy.

 7.  The standard model of cos­mo­lo­gy (the hot big bang hypo­thesis) must be refuted – the uni­verse does not expand. Instead, there is an in­ces­sant exchange of energy (and mass) between pho­­tons and mat­ter. This ex­change is responsible for gra­vitation, as has been con­fir­med by the dis­co­very of many new cos­­­mo­logical cons­tants. With the help of these new constants gravitation can be integ­rated for the first time with elec­tro­­magnetism and the other two funda­mental forces. These con­­stants build a nu­merical input-out­­put mo­del of the universe. This model is equi­valent to the con­­ti­nuum.

 8.  The standard mo­del of phy­sics must be refu­ted in its reduc­tional attempt to ex­plain na­ture on the basis of a few ele­­­men­ta­ry particles. At the same time, the new theory confirms all the ma­­the­matical re­sults ob­tained in QED and QCD.

 9.  Although the various ma­the­matical expressions of the se­cond law of ther­­­­mo­­dyna­mics are deri­va­tions of the universal equa­tion, the notion of growing en­tropy in the universe as stated by this law must be rejected.

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The extensive mathematical proofs of these results are given in volumes I and II (2-4), which take due account of the basis of mo­dern phy­sics and cosmology. The new inte­grated phy­sical and mathe­ma­tical axiomatics fol­lows the prin­ciple of inner con­sis­tency and lack of contra­dictions. There­fore, it would be suf­ficient to reject only one of the afo­re­mentioned re­sults to renounce the existence of the Law.  However, this is not possible.

 

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