Mathematical hypothesis in physics is a form of a scientific hypothesis , one of the methods of cognition widely used in theoretical physics , which consists in spreading to a new, unexplored field of well-known mathematically expressed laws from any of the adjacent fields in a modified form.
In contrast to the classical natural-science hypothesis, which, as a rule, is aimed at directly identifying the characteristic features of the object or phenomenon being studied, the mathematical hypothesis proceeds from the assumption of similarity between the studied and unexplored objects or phenomena [1] . Thus, the mathematical hypothesis formulates the law for a fairly wide class of objects or phenomena, for particular cases of which physical interpretations are sought, consequences are derived, which may be verified by experiment . A mathematical hypothesis with confirmed predictive power grows into a systematic theory .
Although only elements of the method of the mathematical hypothesis are noted in the development of classical sections , in modern areas it is the main one corresponding to the idea of the subject of theoretical physics as an interpretation of the mathematical apparatus [2] . The method gains particular relevance in the conditions of the microworld and megaworld , when the sensory experience of the macrocosm loses its effectiveness [3] .
Typology
There are several types of mathematical hypotheses in physics [4] :
- modifying, generalizing well-known equations - introducing new components, components,
- introducing into the equations quantities of a different nature or of a different nature,
- considering new boundary, boundary, limit conditions,
as well as their combinations.
For example, Maxwell's equations , which are formulated by introducing into a previously known relationship describing electromagnetic phenomena, a new component - bias current - generalized previously known laws, while no new classes of quantities or other boundary conditions were introduced [1] . The electronic version of Maxwell's equations constructed by Lorentz is an example of introducing a quantity of a different nature without modifying the law. The consideration of quantities of a different nature in the equations of quantum mechanics is also characteristic, for example, the Schrödinger equation actually preserves the form of the classical wave equation , but gives its components a new physical meaning. Extension of boundary or limiting conditions is widely used in the general theory of relativity , cosmology [1] .
Principles
In the development of new mathematical hypotheses, the main role is played by the intuition of the researcher [3] , while a number of general principles are noted, according to which mathematical hypotheses are developed in theoretical physics [1] .
According to the correspondence principle, a well-known regularity should be deduced from a mathematical hypothesis in a particular or limiting case. The invariance principle imposes a requirement of generality, invariance of the law with respect to coordinate substitutions and geometric transformations accepted as standard in a particular area (for example, Lorentz transformations in systems using pseudo-Euclidean spaces as a space-time model). The principle of observing a certain system of conservation laws imposes a restriction on the preservation of a number of fundamental laws. According to the principle of causality, a phenomenon can depend only on phenomena preceding it in time. The principle of simplicity and harmony requires preferring rather simple, concise, logically strict, symmetrical laws that do not contain complex components (such as derivatives of large orders, high degrees) [1] .
Notes
- ↑ 1 2 3 4 5 Konstantinov, Philosophical Encyclopedia .
- ↑ Styopin, Elsukov, 1974 , p. 137-138.
- ↑ 1 2 Styopin, Elsukov, 1974 , p. 141.
- ↑ Konstantinov, Philosophical Encyclopedia , the source proposes 4 types, the third type being a combination of types 1 and 2, then there is a judgment on the combinability of types 2 and 4, as well as 1 and 4.
Literature
- Konstantinov F.V. Mathematical hypothesis . Philosophical Encyclopedia (1960-1970). Date of treatment February 21, 2014.
- V.S. Styopin, A.N. Yelsukov. Methods of scientific knowledge. - Minsk: Higher School, 1974. - 152 p.