New Concept of Conservation Laws

The laws of conservation describe the fundamental characteristics of nature. In this paper we show some unifying results that we have not seen before in standard textbooks or in professional publications. We show that most of the laws of nature can be derived from or are equivalent to the laws of conservation. In particular, we show that Newton’s second law, the third law, and the second law of thermodynamics belong to the class of laws of conservation. Also we show that the derivative in calculus is a law of conservation. Since the differential equation is based on the derivatives, then it must also be a law of conservation. We conclude that every system follows the laws of conservation, because they can be described by a set of simultaneous differential equations. Thus in nature, we have only one kind of laws – the laws of conservation. We also show that the laws of conservation are memory laws and that the nature is completely deterministic. In this paper we do not consider relativistic effects.

It is shown that field theories possessing a. certain type of nonlinearit,y, termed intrinsic, also possess a new t?-pe of collsrrvation Inw in \vhicxh the row s e r v e d quIltit? is an integer even in the 11nquantized theor?-. Vor the example o f general relntivity t h e consewed quarrtit!-is sho\m to assllme t h e values JI = 0, ~1, f2, . . . This conscrwtion 1:rw ("conservation of metricit!") is valid regardless of any interaction of the metric field with other field:: and regardless even of the equntjion of motion assllmed for the metric field itself. The basis of the work is the principle that :L quantity which is t;nch:lnged in value 1)~ an arhit,rnry continrlons deformation is a ,fortiori unchanged in valnc l))-the p:wagc of time. Some properties of metricit>-and of its carrirr are given.

We focus on classical mechanical systems with a finite number of degrees of freedom and make no apriori assumption about the existence of Lagrangian, Hamiltonian or canonical momenta. Our work sheds new light on inverse problem of physics, Noether theorem inversion and symplectic canonical nature of classical phase space. The main results of this work are derived by the use of the Poisson Bracket, whose expression in local variables is given. Following our new approach, conserved quantities are related to Noether symmetries and Lie symmetries.

In recent times, authoritative statements have emerged suggesting that the law of energy conservation is being violated in cosmology. However, an analysis of the motion of cosmic photons in bidirectional (i.e., symmetric) time confirms that the energy conservation law is, in fact, being maintained in cosmology. This paper is a Russian-to-English translation of the abstract of my talk at the 8th Conference "Foundations of Fundamental Physics and Mathematics" (OFFM-2024) .

Looking at moving objects, this paper tries to make it clear that space, time, mass and energy are conserved and act as if it is all the same. That space and time are also a form of energy. On speeding p or under gravitational situations, space and time " lose " some contribution. The overall factor is the gamma factor; while mass and energy gain, this happens at the cost of space and time, so it seems. This implies the idea that space time, matter and energy are in a linked bond with each other, in such a way that they are mutually conserved. The same is also observed in gravity. Also the Casimir effect directly shows this space, time, energy, mass conservation principle. This calls for a conservation law.

Journal of Mathematical Physics, 2017

A new approach, combining the Ibragimov method and the one by Anco and Bluman, with the aim of algorithmically computing local conservation laws of partial differential equations, is discussed. Some examples of the application of the procedure are given. The method, of course, is able to recover all the conservation laws found by using the direct method; at the same time we can characterize which symmetry, if any, is responsible for the existence of a given conservation law. Some new local conservation laws for the short pulse equation and for the Fornberg–Whitham equation are also determined.

Philosophy of Science, 2011

A conservation law in physics can be either a constraint on the kinds of interaction there could be or a coincidence of the kinds of interactions there actually are. This is an important, unjustly neglected distinction. Only if a conservation law constrains the possible kinds of interaction can a derivation from it constitute a scientific explanation despite failing to describe the causal/mechanical details behind the result derived. This conception of the relation between “bottom-up” scientific explanations and one kind of “top-down” scientific explanation is motivated by several examples from classical and modern physics.

How can Noether’s theorem expand to accommodate quantum mechanics? What is the relationship between conservation laws, explicit time-dependence, the Hamiltonian, and Noether’s theorem? How do these apply to the conservation properties of symmetries and unitary operators? To what extent can these apply to the unitary evolution matrices that help define QFT locality? I hope to create a fundamental outline that proposes what it means to be conservative, or why something is conserved in physics by using the following properties: The speed of light, Noether’s theorem, symmetries, and unitarity. I hope to generalize conservation properties and help determine if something will be conserved (developing fundamental conservation rules) through these properties, and maybe others.

Physics Letters A, 2003

We propose a new approach in which several paradoxes and shortcomings of modern physics can be solved because conservation laws are always conserved. Directly due to the fact that conservation laws can never be violated, the symmetry of the theory leads to the very general consequence that backward and forward time evolution are both allowed. The generalization of the approach to five dimensions, each one with real physical meaning, leads to the derivation of particle masses as a result of a process of embedding.

The Universal Law of Conservation of Energy says that "Energy is neither created nor destroyed). But the Modified Law of conservation says that "Energy is created at a certain point and is destroyed up to the certain limit. In between creation and destruction, there is 'conservation' which means, one energy gets converted into other energy" "At present it is assumed that energy is neither created nor lost. It is converted from one form to other". But scientists are experimenting with results that contradict the present assumption. Recently, USA and China have created energy by way of fusion reaction which means energy is created at a certain point during the process of fusion reaction.