12 research outputs found
Probabilistic and Geometric Languages in the Context of the Principle of Least Action
This paper explores the issue of the unification of three languages of
physics, the geometric language of forces, geometric language of fields or
4-dimensional space-time, and probabilistic language of quantum mechanics. On
the one hand, equations in each language may be derived from the Principle of
Least Action (PLA). On the other hand, Feynman's path integral method could
explain the physical meaning of PLA. The axioms of classical and relativistic
mechanics can be considered as consequences of Feynman's formulation of quantum
mechanics.Comment: 13 pages, 1 figures; translation from Russian correcte
Philosophical and Methodological Problems of the Principle of Least Action.
Twenty extremal principles of the natural sciences are reformulated to the general ontological scheme. The hypothesis is substantiated that the unique role of the principle of least action is based on its probabilistic interpretation. It is shown how most of the variational principles can be reduced to the principle of maximal probability, which is based on a realistic interpretation of Feynman’s path integral method
Possible Worlds and Possibilities of Substances
Despite the notions of possible worlds and substances are very important subjects of contemporary metaphysics, there are relatively few attempts to combine these in a united framework. This paper considers the metaphysical model of the origins and the evolution of possible worlds that occurs from an interaction between substances. I involve Leibniz’s doctrine of the striving possibles that every possibility of substance has its own essence and tendency towards existence. It is supposed that the activities of substances are constantly aimed at using this tendency in all possible ways. Only the consistent and stable interactions between the substances give birth to stable objects in one of many worlds. Thus activity of substances changes from the possible modality of being to the actual modality of being in form of existence of the worlds. I divide substance’s possibility into two aspects—dynamic (possible or virtual history) and static (possible or potential mutual state). Thanks to the summation of virtual histories, in the possible modality of being, the maximal number of virtual histories is combined into the actual history in the actual modality
Metaphysics of the principle of least action
Despite the importance of the variational principles of physics, there have
been relatively few attempts to consider them for a realistic framework. In
addition to the old teleological question, this paper continues the recent
discussion regarding the modal involvement of the principle of least action and
its relations with the Humean view of the laws of nature. The reality of
possible paths in the principle of least action is examined from the
perspectives of the contemporary metaphysics of modality and Leibniz's concept
of essences or possibles striving for existence. I elaborate a modal
interpretation of the principle of least action that replaces a classical
representation of a system's motion along a single history in the actual
modality by simultaneous motions along an infinite set of all possible
histories in the possible modality. This model is based on an intuition that
deep ontological connections exist between the possible paths in the principle
of least action and possible quantum histories in the Feynman path integral. I
interpret the action as a physical measure of the essence of every possible
history. Therefore only one actual history has the highest degree of the
essence and minimal action. To address the issue of necessity, I assume that
the principle of least action has a general physical necessity and lies between
the laws of motion with a limited physical necessity and certain laws with a
metaphysical necessity.Comment: 35 page
Three Approaches to the Issue of Quantum Reality and the Second Quantum Revolution
The framework of a simple opposition realism – anti-realism is not enough to analyze the views on the reality of unobservable objects of quantum theory. First, it is necessary to distinguish between realism in relation to the theory and realism in relation to the theory’s objects. Secondly, realism in relation to classical objects can be combined, both with realism and with anti-realism in relation to quantum objects. Third, the concept of “existence” and “to exist objectively” can have different meanings. To take into account these factors, the article describes three approaches: classical realism, quantum anti-realism, and quantum realism. I show that the debate around quantum reality has intensified in recent decades due to a series of new quantum experiments. The current stage of the debate is caused by the second quantum revolution relating to the transfer and processing of quantum information. Classical realism and old versions of quantum anti-realism have become insufficiently effective to explain the results of a series of experiments. Proponents of quantum realism, in turn, refer to the possibility of using the wave function to manipulate quantum objects before their measurement. In conclusion, I assume that not only theoretical discussions but also experiments and new technologies can have a major impact on the seemingly purely philosophical debate about reality
Probabilistic and Geometric Languages in the Context of the Principle of Least Action
This paper explores the question of the unification of the three basic languages of physics, the geometric language of forces, the geometric language of fields or 4-dimensional space-time, and the probabilistic language of quantum mechanics. I will show that on the one hand, equations in each of these languages may be derived from any form of the Principle of Least Action (PLA). On the other hand, Feynman's `path integral' method could explain the physical sense of these particular forms of PLA. In conclusion, I will show that the axioms of classical and relativistic mechanics become consequences of Feynman's formulation of quantum mechanics