ARTICLE | doi:10.20944/preprints202107.0632.v1
Subject: Physical Sciences, Acoustics Keywords: Principle of equivalence; Landauer principle; Entropic forces; Information; Einstein free falling elevator
Online: 28 July 2021 (12:25:35 CEST)
Gedanken experiments illustrating exemplifications of the Landauer principle in the free falling Einstein elevator are treated. Double-well simplest information system embedded into the free falling elevator is addressed. Infinitesimal horizontal force applied to the particle m transfers it from position “0” to position “1”, emerging from the free falling double-well system confining mass m. When thermal noise is considered, the potential barrier of kBT should be surmounted for the erasing of one bit of information. Entropic forces arising in the free falling elevator are considered. The maximal change in the entropy of free-joint polymer chain attached to the free falling elevator is estimated as ΔSmax≅kB, and it is remarkably independent of the mass attached to the chain and the parameters of the chain itself. Free falling minimal Szilard engine is treated. The informational re-interpretation of the minimal Szilard process is shaped as follows: the energy kBTln2 necessary for erasing of 1 bit of information is spent for lifting up mass, whatever, is the value of this mass. Appropriate choice of frames enables elimination of gravity in the considered system; however elimination of the thermal noise (dissipation processes) by the same procedure is impossible.
ARTICLE | doi:10.20944/preprints202202.0331.v1
Subject: Physical Sciences, Acoustics Keywords: equivalence-principle; Einstein-Lift; EP; formal binary logic; inhomogenious gravity- field; acceleration- field; radial-field; tidal-forces
Online: 25 February 2022 (09:46:25 CET)
Mass plays a strange multiple role in classical physics. This results in a difference between gravity and all other forces - a difference that stood at the beginning of Einstein's development of his general theory of relativity. The equivalence principle (EP) deals with homogenious gravitational fields, which, in fact, don‘t exist in nature. There is only an approximation for this field in Einstein-Lift possible for local situations. Nevertheless this EP can be true, because in classical formal binary logic there can be formulated a true conclusion from a wrong premise or assumption.
Subject: Physical Sciences, General & Theoretical Physics Keywords: supersymmetry; elementary particles; equivalence of formalisms; quantum mechanics
Online: 31 July 2020 (05:50:57 CEST)
In this article we first write a brief review of supersymmetric quantum mechanics and then we discuss the equivalence of two co-existing formalisms viz. tensor product formalism and partner hamiltonian formalism for 1-D SUSY Harmonic oscillator. Finally, we present a Mathematica code with which one can calculate the eigenstates of any 1-D SUSY partner Hamiltonian along with two illustrated examples of 1-D SUSY HO and 1-D SUSY infinite potential box.
Subject: Life Sciences, Other Keywords: consciousness; cognition; life; equivalence relation; synchrony; compartmentalization; closure; connectivity
Online: 16 February 2020 (15:01:47 CET)
In an analogous manner as occurred during the development of a connected metabolism that at some point reached characteristics associated with what is called ‘life’ ―due mainly to a catalytic closure phenomenon when chemicals started to autocatalyze themselves forming a closed web of chemical reactions― it is here proposed that cognition and consciousness (or features associated with them) arose as a consequence of another type of closure within the nervous system, the brain especially. Proper brain function requires an efficient web of connections and once certain complexity is attained due to the number and coordinated activities of the brain cell networks, the emergent properties of cognition and consciousness take place. Seeking to identify main features of the nervous system organization for optimal function, it is here proposed that while catalytic closure yielded life, neuroglial closure produced cognition/consciousness.
ARTICLE | doi:10.20944/preprints202112.0358.v1
Subject: Engineering, General Engineering Keywords: ecigarette; regulatory science; substantial equivalence; public health; tobacco product comparison.
Online: 22 December 2021 (12:04:52 CET)
This study introduces and demonstrates a comprehensive, accurate, unbiased approach to robust quantitative comparison of Electronic Nicotine Delivery Systems (ENDS) appropriate for establishing substantial equivalence (or lack thereof) between tobacco products. The approach is demonstrated across a family of thirteen pen- and pod-style ENDS products. Methods employed consist of formulating a robust emissions surface regression model, quantifying the empirical accuracy of the model as applied to each product, evaluating relationships between product design characteristics and maximum emissions characteristics, and presenting results in formats useful to researchers, regulators, and consumers. Results provide a response surface to characterize emissions (total particulate matter and constituents thereof) from each ENDS appropriate for use in a computer model and for conducting quantitative exposure comparisons between products. Results demonstrate that emissions vary as a function of puff duration, flow rate, E-Liquid composition, and device operating power. Further, results indicate that regulating design characteristics of ENDS devices and consumables may not achieve desired public health outcomes; it is more effective to regulate maximum permissible emissions directly. Three emissions outcome measures (yield per puff, mass concentration and constituent mass ratio) are recommended for adoption as standard quantities for reporting by manufacturers and research laboratories. The approach provides a means of (a) quantifying and comparing maximal emissions from ENDS products spanning their entire operating envelope, (b) comparative evaluation of ENDS devices and consumable design characteristics, and (c) establishing comparative equivalence of maximal emissions from ENDS. A consumer-oriented product emissions dashboard is proposed for comparative evaluation of ENDS exposure potential. Maximum achievable power dissipated in the coil of ENDS is identified as a potentially effective regulatory parameter.
Subject: Engineering, Energy & Fuel Technology Keywords: Transport Corrected SP3; Nodal Expansion Method; Generalized Equivalence Theory; Discontinuity Factors
Online: 3 September 2021 (08:12:14 CEST)
The Simplified Spherical Harmonic (SPN) approximation was first introduced as a three-dimensional (3-D) extension of the plane-geometry Spherical Harmonic (PN) equations. A third order SPN (SP3) solver, recently implemented in the Nodal Expansion Method (NEM), has shown promising performance in the reactor core neutronics simulations. This work is focused on the development and implementation of the transport corrected interface and boundary conditions in NEM SP3 solver, following recent published work on the rigorous SPN theory for piecewise homogeneous regions. A streamlined procedure has been developed to generate the flux zero and second order/moment discontinuity factors (DFs) of the generalized equivalence theory to eliminate the error introduced by pin-wise homogenization. Moreover, several color set models with varying size and configuration are later explored for their capability of generating DFs that can produce results equivalent to that using the whole-core homogenization model for more practical implementations. The new developments are tested and demonstrated on the C5G7 benchmark. The results show that the transport corrected SP3 solver shows general improvements to power distribution prediction compared to the basic SP3 solver with no DFs or only zero order/moment DFs. The complete equivalent calculations using the DFs can almost reproduce transport solutions with high accuracy. The use of equivalent parameters from larger size color set models show better prediction in the whole-core calculations. By coupling different color set models DFs can offer the best accuracy at both eigenvalues and power distributions.
ARTICLE | doi:10.20944/preprints202105.0681.v1
Subject: Materials Science, Biomaterials Keywords: numerical homogenization; prefabricated floor slab; concrete; composite structure; strain energy equivalence
Online: 27 May 2021 (14:34:45 CEST)
The need for quick and easy deflection calculations of various prefabricated slabs causes that simplified procedures and numerical tools are used more and more often. Modelling of full 3D finite element (FE) geometry of such plates is not only uneconomical but often requires the use of complex software and advanced numerical knowledge. Therefore, numerical homogenization is an excellent tool, which can be easily employed to simplify a model, especially when accurate modelling is not necessary. Homogenization allows for simplifying a computational model and replacing a complicated composite structure with a homogeneous plate. Here, a numerical homogenization method based on strain energy equivalence is derived. Using the method proposed, the structure of the prefabricated concrete slabs reinforced with steel spatial trusses is homogenized to a single plate element with an effective stiffness. There is a complete equivalence between the full 3D FE model built with solid elements combined with truss structural elements and the simplified homogenized plate FE model. The method allows for the correct homogenization of any complex composite structures made of both solid and structural elements, without the need to perform advanced numerical analyses. The only requirement is a correctly formulated stiffness matrix of a representative volume element (RVE) and appropriate formulation of the transformation between kinematic constrains on RVE boundary and generalized strains.
Subject: Engineering, General Engineering Keywords: mass timber; life cycle assessment; embodied carbon; sustainable design; functional equivalence
Online: 20 August 2020 (03:59:10 CEST)
Efforts to quantify and reduce greenhouse gas (GHG) emissions of the built environment often neglect embodied emissions, instead focusing on reducing emissions from building operations. Utilizing sustainably sourced mass timber offers low embodied carbon alternatives to traditional concrete and steel structural systems, however the variability in embodied carbon for different mass timber approaches remains understudied. In this study, we used life cycle assessment (LCA) to compare the whole building embodied carbon of nine mass timber design options and two typical concrete and steel reference cases for an eight-story mixed-use building, ensuring structural, acoustic, thermal, programmatic, and fire-rating equivalence between the designs. The study found that the mass timber designs vary significantly, ranging between a 14-52% reduction in whole building embodied carbon from the most impactful reference case, and a 31-73% reduction when considering the structural systems alone. This study demonstrates the value that whole building LCA (WBLCA) provides as a primary driver for low-carbon structural system design and architectural development of mass timber buildings, beyond that of single material comparisons using environmental product declarations (EPDs).
ARTICLE | doi:10.20944/preprints201709.0091.v1
Subject: Physical Sciences, Condensed Matter Physics Keywords: Hamiltonian systems; classical statistical mechanics; ensemble equivalence; long-range interacting systems
Online: 20 September 2017 (04:08:44 CEST)
We investigate the stationary and dynamic properties of the celebrated Nosé-Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé-Hoover dynamics aims to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé-Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a size-independent timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that diverges with the system size. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé-Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé-Hoover and canonical equilibrium.
ARTICLE | doi:10.20944/preprints202102.0157.v1
Subject: Physical Sciences, Acoustics Keywords: Einstein's equations; gravitation; general relativity; principle of equivalence; gravitational aether; vacuum mechanics.
Online: 5 February 2021 (11:11:36 CET)
When solving the Einstein's equations for an isolated system of masses, V. Fock introduces harmonic reference frame and obtains an unambiguous solution. Further, he concludes that there exists a harmonic reference frame which is determined uniquely apart from a Lorentz transformation if suitable supplementary conditions are imposed. It is known that wave equations keep the same form under Lorentz transformations. Thus, we speculate that Fock's special harmonic reference frames may have provided us a clue to derive the Einstein's equations in some special class of non-inertial reference frames. Following this clue, generalized Einstein's equations in some special non-inertial reference frames are derived based on the theory of vacuum mechanics. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explain all the experiments which support the theory of general relativity. There exist some differences between this theory and the theory of general relativity.
Subject: Physical Sciences, General & Theoretical Physics Keywords: mass; energy; gravity; inertial force; principle of equivalence; strongly correlated electron; hole;
Online: 15 October 2020 (15:59:19 CEST)
The energy E takes the place of the gravitational mass mG to produce gravity . We wonder whether the inertial mass mi in the inertial force is also replaced by E. The experiments to measure the inertial force and weight of a carrier are presented. Now we can test the principle of equivalence and study foundations of physics in condensed matter.
ARTICLE | doi:10.20944/preprints201811.0193.v2
Subject: Arts & Humanities, Linguistics Keywords: translation equivalence (TE); translation equivalents (TEs); vocabulary knowledge; receptive vocabulary; word learnability
Online: 12 November 2018 (05:29:18 CET)
One of the most pivotal challenges that learners may face, during foreign language learning, is building a reliable lexicon. Insufficient vocabulary knowledge may put serious obstacles in the foreign language learning process. Thus, students need to equip themselves with different strategies to cope with these difficulties. Translation equivalence (TE) is one of these strategies. Since the success or failure of any vocabulary learning strategy depends on two main factors: developing the learners’ vocabulary knowledge and the extent of difficulty or ease with which the learner acquires new words, this research aims at investigating the impact of this strategy on EFL learners’ vocabulary knowledge and word learnability. 258 Tunisian 9th graders participated in this project. Two vocabulary recognition tests, one using translation equivalence and the other using only-English strategies, were used to test the hypotheses. Different statistical tests and techniques were employed to analyze data. Findings showed that TE has a positive impact on learners’ vocabulary knowledge and revealed that students, at this level of proficiency, learn vocabulary through translation better than any other strategy using only English.
ARTICLE | doi:10.20944/preprints202209.0029.v1
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Convolution; Boehmian; fractional Hilbert transform; Hilbert transform; equivalence class; delta sequences; compact support
Online: 2 September 2022 (02:54:50 CEST)
The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.
ARTICLE | doi:10.20944/preprints202106.0009.v1
Subject: Engineering, Mechanical Engineering Keywords: corrugated cardboard; numerical homogenization; strain energy equivalence; perforation; creasing; flexural stiffness; torsional stiffness
Online: 1 June 2021 (09:40:56 CEST)
The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. That is why numerical analyzes are becoming a common standard in this branch of manufacturing. Such trend causes either the use of advanced computational models that take into account the full 3D geometry of the flat and wavy layers of corrugated board, or the use of homogenization techniques to simplify the numerical model. The article presents theoretical considerations that extend the numerical homogenization technique already presented in our previous work. The proposed here homogenization procedure also takes into account the creasing and / or perforation of corrugated board, i.e. processes that undoubtedly weaken the stiffness and strength of the corrugated board locally. However, it is not always easy to estimate how exactly these processes affect the bending or torsional stiffness. What is known for sure is that the degradation of stiffness depends, among other things, on the type of cut, its shape, the depth of creasing, as well as their position or direction in relation to the corrugation direction. The method proposed here can be successfully applied to model smeared degradation in a finite element or to define degraded interface stiffnesses on a crease line or a perforation line.
ARTICLE | doi:10.20944/preprints202008.0331.v1
Subject: Engineering, Construction Keywords: small particle size; porous ultra-thin overlay; scattering resistance; construction scheme; energy equivalence principle
Online: 15 August 2020 (05:48:32 CEST)
To address the severe distresses of asphalt pavement, a new type of pavement maintenance treatment, porous ultra-thin overlay (PUTO) with small particle size was proposed. The PUTO has a thickness of 1.5~2.5 cm and a large void ratio of 18~25%. As a newly asphalt mixture, the structure characteristics differ from traditional pavement. Therefore, it is necessary to investigated the fabrication schemes in laboratory and on-site, respectively. In this study, the optimal fabrication schemes, including compaction temperature and number of blows of PUTO were determined based on Cantabro test and volumetric parameters. Then, the corresponding relationship between laboratory and on-site compaction work was then established based on the energy equivalent principle. On this basis, the numbers of on-site rolling passes and the combination method were calculated. The results show that increased compaction temperature and number of blows reduce the height and enhance the compactness of the Marshall sample. With the same temperature and number of blows, the scattering resistance of coarse gradation (PAC-1) is better than that of fine gradation (PAC-2), and the increased asphalt viscosity significantly improves the scattering resistance of the asphalt mixture. To ensure the scattering resistance and volumetric characteristic, the initial compaction temperature of the PAC-1 and PAC-2 should not be lower than 150 °C and 165 °C, respectively. Then, the laboratory compaction work and on-site compaction work were calculated and converted based on the principle of energy equivalence. Consequently, the on-site compaction combination of rolling machines for four asphalt mixtures was determined. According to the volumetric parameters, the paving test section proved that the construction temperature and the on-site rolling combination determined by laboratory tests are reasonable, and ultra-thin overlay has good structural stability, drainage and skid resistance.
ARTICLE | doi:10.20944/preprints202105.0403.v1
Subject: Engineering, Mechanical Engineering Keywords: corrugated cardboard; converting; numerical homogenization; strain energy equivalence; finite element method; shell structures; transverse shear
Online: 18 May 2021 (10:01:06 CEST)
Corrugated cardboard is an ecological material, mainly because, in addition to virgin cellulose fibers also the fibers recovered during recycling process are used in its production. However, the use of recycled fibers causes slight deterioration of the mechanical properties of the corrugated board. In addition, converting processes such as printing, die-cutting, lamination, etc. cause micro-damage in the corrugated cardboard layers. In this work, the focus is precisely on the crushing of corrugated cardboard. A series of laboratory experiments were conducted, in which the different types of single-walled corrugated cardboards were pressed in a fully controlled manner to check the impact of the crush on the basic material parameters. The amount of crushing (with a precision of 10 micrometers) was controlled by a precise FEMat device, for crushing the corrugated board in the range from 10 to 70 % of its original thickness. In this study, the influence of crushing on bending, twisting and shear stiffness as well as a residual thickness and edge crush resistance of corrugated board was investigated. Then, a procedure based on a numerical homogenization, taking into account a partial delamination in the corrugated layers to determine the degraded material stiffness was proposed. Finally, using the empirical-numerical method, a simplified calculation model of corrugated cardboard was derived, which satisfactorily reflects the experimental results.
ARTICLE | doi:10.20944/preprints202105.0667.v1
Subject: Materials Science, Biomaterials Keywords: corrugated cardboard; converting; crushing; numerical homogenization; strain energy equivalence; finite element method; shell structures; transverse shear
Online: 27 May 2021 (13:13:08 CEST)
As long as the non-contact digital printing is not a common standard in the corrugated packaging industry, corrugated board crushing is a real issue that affects the load capacity of the boxes. Crushing mainly occurs during the converting of corrugated board (e.g. analog flexographic printing or laminating) and is a process that cannot be avoided. However, as show in this study, it can be controlled. In this work, extended laboratory tests were carried out on the crushing of double-walled corrugated board. The influence of fully controlled crushing (with a precision: ±10 μm) in the range from 10 to 70 % on different laboratory measurements was checked. Most of the typical mechanical tests were performed e.g. edge crush test, four-point bending test, shear stiffness test, torsional stiffness test, etc. on reference and crushed specimens. The residual thickness reduction of the crushed samples was also controlled. All empirical observations and performed measurements were the basis for building an analytical model of crushed corrugated board. The proven and verified model was then used to study the crushing effect of the selected corrugated board on the efficiency of simple packages with various dimensions.
ARTICLE | doi:10.20944/preprints202002.0067.v1
Subject: Physical Sciences, General & Theoretical Physics Keywords: Landauer principle; inertial frame of references; non-inertial frame of references; minimal thermal engine; equivalence principle
Online: 5 February 2020 (13:41:19 CET)
The informational re-interpretation of the basic laws of the mechanics exploiting the Landauer principle is suggested. When a physical body is in rest or it moves rectilinearly with the constant speed, zero information is transferred; thus, the informational affinity of the rest state and the rectilinear motion with a constant speed is established. The analysis of the minimal Szilard thermal engine as seen from the non-inertial frame of references is carried out. The Szilard single-particle minimal thermal engine undergoes the isobaric expansion relatively to the accelerated frame of references, enabling the erasure of 1 bit of information. The energy ΔQ spent by the inertial force for the erasure of 1 bit of information is estimated as: ΔQ≅5/3 k_B T ̅, which is larger than the Landauer bound but qualitatively close to it. The informational interpretation of the equivalence principle is proposed: the informational content of the inertial and gravitational masses is the same.
ARTICLE | doi:10.20944/preprints202204.0001.v1
Subject: Biology, Other Keywords: tick-borne encephalitis virus; cryo-electron microscopy; TBEV; envelope protein; membrane protein; lipid factor; glycoprotein; quasi-equivalence
Online: 1 April 2022 (03:24:38 CEST)
Tick-borne encephalitis virus (TBEV) is a pathogenic, enveloped, positive-stranded RNA virus in the family Flaviviridae. Structural studies of flavivirus virions have primarily focused on mosquito-borne species with only one cryo-electron microscopy (cryo-EM) structure of a tick-borne species published. Here, we present a 3.3 Å cryo-EM structure of the TBEV virion of the Kuutsalo-14 isolate, confirming the overall organisation of the virus. We observe conformational switching of the peripheral and transmembrane helices of M protein, which can explain the quasi-equivalent packing of the viral proteins and highlights their importance in stabilizing the membrane protein arrangement in the virion. The residues responsible for the M protein inter-actions are highly conserved in TBEV but not in the structurally studied Hypr strain, nor in mosquito-borne flaviviruses. These interactions may compensate for the lower number of hydrogen bonds between E proteins in TBEV compared to the mosquito-borne flaviviruses. The structure reveals two lipids bound in the E protein, which are important for virus assembly. The lipid pockets are comparable to those recently described in mosquito-borne Zika, Spondweni, Dengue, and Usutu viruses. Our results thus advance the understanding of tick-borne flavivirus architecture and virion-stabilising interactions.
ARTICLE | doi:10.20944/preprints202009.0215.v3
Subject: Physical Sciences, General & Theoretical Physics Keywords: time; gravitomagnetics; mass-energy equivalence; quantum mechanics; relativity theory; symmetry; inertial and non-inertial coordinates; space-time linearity
Online: 6 June 2022 (09:27:33 CEST)
Differences between the quantum mechanical and relativistic concepts of time are explained by using the equivalence principle. The resulting clock model calls for microscopic equations of motion to be formulated in Minkowski space, and for photons to be described as four-dimensional localizations of field. Because the properties of energy are universal the equations have been extended to include galaxies in spite of vast differences in lifetime. The comparison is possible due to a fundamental symmetry based on the conjugate variables energy and time.
ARTICLE | doi:10.20944/preprints202002.0077.v1
Subject: Life Sciences, Biophysics Keywords: special relativity; efficient coding hypothesis; temporal order judgement; circular vection; vestibulo-ocular reflex; time perception; Lorentz transformation; accelerated reference frame; equivalence principle; optimization of perception
Online: 6 February 2020 (03:08:56 CET)
An event occurring within a stationary environment, in the direction toward which an observer self-rotates, is perceived to precede a simultaneous event, in the direction away from which she moves. When self-rotation results from angular acceleration in the dark, perception of space is also distorted, such that the subjective straight-ahead shifts in the opposite direction to motion and temporal event promotion. A reference frameshift theory, based on the special theory of relativity, is proposed to explain these findings. Here, a hyperbolic tangent transformation of objective angular velocity constrains subjective self-rotation velocity within finite bounds, consistent with it being a limited perceptual resource. Identifying this subjective variable with vestibular nystagmus slow-phase angular velocity, the asymptotic perceived self-rotation velocity is estimated at ~200 °⁄s. When included in the Lorentz transformations of the new formalism, this value predicts experimental simultaneity distortion. Hypothetically, the hyperbolic tangent objective-to-subjective transfer function would maximize the differential entropy of the percept, and thereby also the stimulus/percept mutual information, if angular velocities of body rotation encountered in naturalistic environmental interaction have a logistic probability density distribution of scale 100 °⁄s, a proposed experimental test of the scheme.
ARTICLE | doi:10.20944/preprints201907.0314.v1
Subject: Physical Sciences, Mathematical Physics Keywords: entropy; Boltzmann statistics; Lorentz-factor; mereology; analytical philosophy; conservation laws; vacuum energy; cosmologic constant problem; invariance; hypercomplex numbers; Octonions; energy-mass equivalence; Ur-Alternatives; mereotopology; mereophysics
Online: 28 July 2019 (14:39:59 CEST)
Mereology stands for the philosophical concept of parthood and is based on a sound set of fundamental axioms and relations. One of these axioms relates to the existence of a universe as a thing having part all other things. The present article formulates this logical expression first as an algebraic inequality and eventually as an algebraic equation reading in words: The universe equals the sum of all things. “All things” here are quantified by a “number of things”. Eventually this algebraic equation is normalized leading to an expression The whole equals the sum of all fractions. This introduces “1” or “100%” as a quantitative – numerical - value describing the “whole”. The resulting “basic equation” can then be subjected to a number of algebraic operations. Especially squaring this equation leads to correlation terms between the things implying that the whole is more than just the sum of its parts. Multiplying the basic equation (or its square) by a scalar allows for the derivation of physics equations like the entropy equation, the ideal gas equation, an equation for the Lorentz-Factor, conservation laws for mass and energy, the energy-mass equivalence, the Boltzmann statistics, and the energy levels in a Hydrogen atom. It further allows deriving a “contrast equation” which may form the basis for the definition of a length and a time scale. Multiplying the basic equation with vectors, pseudovectors, pseudoscalars and eventually hypercomplex numbers opens up the realm of possibilities to generate many further equations.