scholarly journals Indeterminism in quantum mechanics: beyond and/or within causation

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Energy Conservation ◽  
Mathematical Problem ◽  
Classical Mechanics ◽  
Axiom Of Choice ◽  
Classical Physics ◽  
Least Action ◽  
Matrix Mechanics ◽  
Principle Of Least Action ◽  
The Axiom Of Choice

The problem of indeterminism in quantum mechanics usually being considered as a generalization determinism of classical mechanics and physics for the case of discrete (quantum) changes is interpreted as an only mathematical problem referring to the relation of a set of independent choices to a well-ordered series therefore regulated by the equivalence of the axiom of choice and the well-ordering “theorem”. The former corresponds to quantum indeterminism, and the latter, to classical determinism. No other premises (besides the above only mathematical equivalence) are necessary to explain how the probabilistic causation of quantum mechanics refers to the unambiguous determinism of classical physics. The same equivalence underlies the mathematical formalism of quantum mechanics. It merged the well-ordered components of the vectors of Heisenberg’s matrix mechanics and the non-ordered members of the wave functions of Schrödinger’s undulatory mechanics. The mathematical condition of that merging is just the equivalence of the axiom of choice and the well-ordering theorem implying in turn Max Born’s probabilistic interpretation of quantum mechanics. Particularly, energy conservation is justified differently than classical physics. It is due to the equivalence at issue rather than to the principle of least action. One may involve two forms of energy conservation corresponding whether to the smooth changes of classical physics or to the discrete changes of quantum mechanics. Further both kinds of changes can be equated to each other under the unified energy conservation as well as the conditions for the violation of energy conservation to be investigated therefore directing to a certain generalization of energy conservation.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

scholarly journals Action in Economics: Mathematical Derivation of Laws of Economics from the Principle of Least Action in Physics

2021 ◽  
Author(s):  
Sayan Kombarov
Keyword(s):  
Mathematical Formulation ◽  
Classical Mechanics ◽  
Human Action ◽  
Fundamental Principle ◽  
Austrian School ◽  
Rate Theory ◽  
Main Stream ◽  
Marginal Value ◽  
Least Action ◽  
Principle Of Least Action

The thesis of this paper is mathematical formulation of the laws of Economics with application of the principle of Least Action of classical mechanics. This paper is proposed as the rigorous mathematical approach to Economics provided by the fundamental principle of the physical science – the Principle of Least Action. This approach introduces the principle of Action into main-stream economics and allows reconcile main principles Austrian School of Economics and the laws of market, such Say’s law and marginal value and interest rate theory, with the modern results of mathematical economics, such as Capital Asset Pricing Model (CAPM), game theory and behavioral economics. This principle is well known in classical mechanics as the law of conservation of action that governs any system as a whole and all its components. It led to the revolution in physics, as it allows to derive the laws of Newtonian and quantum mechanics and probability. Ludwig von Mises defined Economics is the science of Human Action. Action is introduced into Economics by the founder of Austrian School of Economic, Carl Menger. Production or acquisition of any goods, services and assets are results of purposeful acts in the form of expenditure of work and energy in the form of flow of money and material resources. Humans take them to achieve certain desired goals with given resources and time. Any economic good and service, financial, productive, or real estate asset is the result of such action.

scholarly journals Extended harmonic mapping connects the equations in classical, statistical, fluid, quantum physics and general relativity

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Xiaobo Zhai ◽  
Changyu Huang ◽  
Gang Ren
Keyword(s):  
General Relativity ◽  
Quantum Physics ◽  
Harmonic Maps ◽  
Classical Mechanics ◽  
Harmonic Mapping ◽  
Geodesic Equation ◽  
Lagrange Equations ◽  
Least Action ◽  
Principle Of Least Action ◽  
Fundamental Equations

Abstract One potential pathway to find an ultimate rule governing our universe is to hunt for a connection among the fundamental equations in physics. Recently, Ren et al. reported that the harmonic maps with potential introduced by Duan, named extended harmonic mapping (EHM), connect the equations of general relativity, chaos and quantum mechanics via a universal geodesic equation. The equation, expressed as Euler–Lagrange equations on the Riemannian manifold, was obtained from the principle of least action. Here, we further demonstrate that more than ten fundamental equations, including that  of classical mechanics, fluid physics, statistical physics, astrophysics, quantum physics and general relativity, can be connected by the same universal geodesic equation. The connection sketches a family tree of the physics equations, and their intrinsic connections reflect an alternative ultimate rule of our universe, i.e., the principle of least action on a Finsler manifold.

scholarly journals Time: From the Totality to Quantum Information

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Physical World ◽  
Axiom Of Choice ◽  
Quantum Bits ◽  
The World ◽  
Time Order ◽  
The Axiom Of Choice

The paper justifies the following theses: The totality can found time if the latter isaxiomatically represented by its “arrow” as a well-ordering. Time can found choice and thusinformation in turn. Quantum information and its units, the quantum bits, can be interpreted astheir generalization as to infinity and underlying the physical world as well as theultimate substance of the world both subjective and objective. Thus a pathway ofinterpretation between the totality via time, order, choice, and information to the substance ofthe world is constructed. The article is based only on the well-known facts and definitions andis with no premises in this sense. Nevertheless it is naturally situated among works and ideasof Husserl and Heidegger, linked to the foundation of mathematics by the axiom of choice, tothe philosophy of quantum mechanics and information.

scholarly journals Time and information in the foundations of physics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Physical World ◽  
Axiom Of Choice ◽  
Quantum Bits ◽  
Foundations Of Physics ◽  
The World ◽  
Time Order ◽  
The Axiom Of Choice

The paper justifies the following theses: The totality can found time if the latteris axiomatically represented by its “arrow” as a well-ordering. Time can found choice andthus information in turn. Quantum information and its units, the quantum bits, can beinterpreted as their generalization as to infinity and underlying the physical world as wellas the ultimate substance of the world both subjective and objective. Thus a pathway ofinterpretation between the totality via time, order, choice, and information to the substance ofthe world is constructed. The article is based only on the well-known facts and definitions andis with no premises in this sense. Nevertheless it is naturally situated among works and ideasof Husserl and Heidegger, linked to the foundation of mathematics by the axiom of choice, tothe philosophy of quantum mechanics and information.

scholarly journals The Principle of Least Action for Reversible Thermodynamic Processes and Cycles

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 542 ◽  
Author(s):  
Tian Zhao ◽  
Yu-Chao Hua ◽  
Zeng-Yuan Guo
Keyword(s):  
Heat Release ◽  
Optimization Problems ◽  
Optimal Path ◽  
Classical Mechanics ◽  
Carnot Cycle ◽  
Heat Absorption ◽  
Least Action ◽  
Principle Of Least Action ◽  
Thermodynamic Processes ◽  
Release Processes

The principle of least action, which is usually applied to natural phenomena, can also be used in optimization problems with manual intervention. Following a brief introduction to the brachistochrone problem in classical mechanics, the principle of least action was applied to the optimization of reversible thermodynamic processes and cycles in this study. Analyses indicated that the entropy variation per unit of heat exchanged is the mode of action for reversible heat absorption or heat release processes. Minimizing this action led to the optimization of heat absorption or heat release processes, and the corresponding optimal path was the first or second half of a Carnot cycle. Finally, the action of an entire reversible thermodynamic cycle was determined as the sum of the actions of the heat absorption and release processes. Minimizing this action led to a Carnot cycle. This implies that the Carnot cycle can also be derived using the principle of least action derived from the entropy concept.

The principle of greatest freedom

2013 ◽  
Vol 26 (3) ◽  
pp. 430-437
Author(s):  
Sylvain Battisti
Keyword(s):  
Quantum Mechanics ◽  
Elementary Particles ◽  
Transfer Energy ◽  
Least Action ◽  
Principle Of Least Action ◽  
Wave Particle Duality ◽  
The Common ◽  
The Universe ◽  
Coherent Relationship

Elementary particles are the common capital of any being in the universe. However, a being is characterized by its behavior as well as its capital and the principle of least action shows the common behavior of partners that transfer energy. However, the concept of action does not apply to all transfers; what is the action when two men transfer words? Here we show that the “principle of greatest freedom” reveals the common behavior of any partner during nondestructive relationship that is to maximize the number of its accessible states, i.e., its freedom. It gives a common interpretation to quantum mechanics, to wave-particle duality and to relativity. It defines the coherent relationship, which explains why objects behave consistently according to laws and why they construct compound beings that evolve.

The whole of physics

2017 ◽  
Author(s):  
Jennifer Coopersmith
Keyword(s):  
Physical Chemistry ◽  
General Relativity ◽  
Electromagnetic Waves ◽  
Materials Science ◽  
Classical Mechanics ◽  
Least Action ◽  
Principle Of Least Action ◽  
Theory Of Gravitation ◽  
Mathematical Equations ◽  
Deep Significance

How the Principle of Least Action underlies all physics (all physics that can be reduced to mathematical equations) is explained at a qualitative, semi-popular level. It even applies to smartphones. The domains of classical mechanics, continuum mechanics, materials science, light and electromagnetic waves, special and general relativity (Einstein’s Theory of Gravitation), electrodynamics, quantumelectrodynamics (QED), hydrodynamics, physical chemistry, statistical mechanics, and the quantum world, are examined. It is shown that the Principles of Least Time, Least Resistance, and Maximal Ageing, and Lenz’s Law are, in fact, examples of the Principle of Least Action. It is also shown how Planck’s constant is a measure of “absolute smallness,” and its units are the units of action. Never again, post quantum mechanics, can there be any doubt about the deep significance of action in physics.

scholarly journals The indeterminist objectivity of quantum mechanics versus the determinist subjectivity of classical physics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Free Will ◽  
Hidden Variables ◽  
Classical Mechanics ◽  
Niels Bohr ◽  
Necessary Condition ◽  
Human Beings ◽  
Classical Physics ◽  
Physical Universe ◽  
Max Born

Indeterminism of quantum mechanics is considered as an immediate corollary from the theorems about absence of hidden variables in it, and first of all, the Kochen – Specker theorem. The base postulate of quantum mechanics formulated by Niels Bohr that it studies the system of an investigated microscopic quantum entity and the macroscopic apparatus described by the smooth equations of classical mechanics by the readings of the latter implies as a necessary condition of quantum mechanics the absence of hidden variables, and thus, quantum indeterminism. Consequently, the objectivity of quantum mechanics and even its possibility and ability to study its objects as they are by themselves imply quantum indeterminism. The so-called free-will theorems in quantum mechanics elucidate that the “valuable commodity” of free will is not a privilege of the experimenters and human beings, but it is shared by anything in the physical universe once the experimenter is granted to possess free will. The analogical idea, that e.g. an electron might possess free will to “decide” what to do, scandalized Einstein forced him to exclaim (in a letter to Max Born in 2016) that he would be а shoemaker or croupier rather than a physicist if this was true. Anyway, many experiments confirmed the absence of hidden variables and thus quantum indeterminism in virtue of the objectivity and completeness of quantum mechanics. Once quantum mechanics is complete and thus an objective science, one can ask what this would mean in relation to classical physics and its objectivity. In fact, it divides disjunctively what possesses free will from what does not. Properly, all physical objects belong to the latter area according to it, and their “behavior” is necessary and deterministic. All possible decisions, on the contrary, are concentrated in the experimenters (or human beings at all), i.e. in the former domain not intersecting the latter. One may say that the cost of the determinism and unambiguous laws of classical physics, is the indeterminism and free will of the experimenters and researchers (human beings) therefore necessarily being out of the scope and objectivity of classical physics. This is meant as the “deterministic subjectivity of classical physics” opposed to the “indeterminist objectivity of quantum mechanics”.

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