The precise formulation of what is now recognized as modern and valid statements of the laws of nature dates back to the 17th century in Europe, with the beginning of precise experimentation and the development of advanced forms of mathematics. During this period, natural philosophers such as Isaac Newton (1642-1727) were influenced by a religious view derived from medieval concepts of divine law that assumed that God had established absolute, universal, and immutable physical laws. [21] [22] In chapter 7 of Le Monde, René Descartes (1596-1650) describes “nature” as matter itself, immutable as created by God, so that the changes in part “are attributable to nature. The rules by which these changes take place are what I call the “laws of nature.” [23] The modern scientific method that was taking shape at the time (with Francis Bacon (1561-1626) and Galileo (1564-1642)) contributed to a tendency to separate science from theology, with minimal speculation about metaphysics and ethics. (Natural law in the political sense, conceived as universal (i.e. separate from sectarian religion and coincidences of place), was also elaborated during this period by scholars such as Grotius (1583-1645), Spinoza (1632-1677) and Hobbes (1588-1679). The most fundamental concept in chemistry is the law of conservation of mass, which states that there is no detectable change in the amount of matter during an ordinary chemical reaction. Modern physics shows that it is energy that is conserved, and that energy and mass are linked; A concept that is becoming important in nuclear chemistry. The conservation of energy leads to the important concepts of equilibrium, thermodynamics and kinetics.

The action is a functional rather than a function because it depends on the Lagrangian path, and the Lagrangian effect depends on the path q(t), so the action depends on the entire “form” of the path for all times (in the time interval from t1 to t2). There are an infinite number of paths between two moments of time, but the one for which the action is stationary (up to the first order) is the true path. The stationary value for the entire continuum of Lagrangian values corresponding to a path, not just a value of the Lagrangian value, is required (in other words, it is not as simple as “differentiating a function and setting it to zero, then solving the equations to find the points of the maxima and minima, etc. but this idea is applied to the entire “form” of the function, For more information about this procedure, see Calculating variations). [12] Laws differ from scientific theories in that they do not postulate a mechanism or explanation of phenomena: they are merely distillations of the results of repeated observations. As such, the applicability of a law is limited to circumstances similar to those already observed, and the law may prove erroneous when extrapolated. Ohm`s law only applies to linear lattices; Newton`s law of universal gravity applies only in weak gravitational fields; early laws of aerodynamics, such as Bernoulli`s principle, do not apply in the case of compressible flow, as occurs in transonic and supersonic flight; Hooke`s law applies only to strains below the yield strength; Boyle`s law applies with perfect precision only to ideal gas, etc. These laws remain useful, but only under the specified conditions under which they apply. It is postulated that a particle (or a system of many particles) is described by a wave function, and this satisfies a quantum wave equation: namely the Schrödinger equation (which can be written as a non-relativistic wave equation or a relativistic wave equation). The solution of this wave equation predicts the temporal evolution of the system`s behavior, analogous to Newton`s solution of Newton`s laws in classical mechanics. The term “scientific law” has traditionally been associated with the natural sciences, although the social sciences also contain laws. [11] For example, Zipf`s law is a law in the social sciences based on mathematical statistics.

In these cases, laws may describe general trends or expected behaviours rather than being absolute. A law can usually be formulated in the form of one or more statements or equations in order to be able to predict the outcome of an experiment. The laws differ from the assumptions and assumptions proposed during the scientific process before and during validation by experiment and observation. Assumptions and assumptions are not laws because they have not been verified to the same extent, although they may lead to the formulation of laws. Laws are narrower than scientific theories, which may include one or more laws. [3] Science distinguishes a law or theory from facts. [4] To characterize a law as factual is ambiguous, exaggerated or ambiguous. [5] The nature of scientific laws has been much debated in philosophy, but essentially scientific laws are simply empirical conclusions obtained by scientific methods; They should not be burdened with ontological obligations or statements of logical absolutes. In Europe, the systematic theory of nature (physis) began with the first Greek philosophers and scientists and continued to the Hellenistic and Roman empires, when the intellectual influence of Roman law was increasingly paramount. The formula “natural law” first appears as “a living metaphor” favored by the Latin poets Lucretius, Virgil, Ovid and Manilius, and over time has acquired a strong theoretical presence in the prose treatises of Seneca and Pliny. Why this Roman origin? According to [classical historian and scholar Daryn] Lehoux [19], the idea was made possible by the central role of codified law and forensic reasoning in Roman life and culture.

For the Romans. The place par excellence where ethics, law, nature, religion and politics intersect is the court. When we read Seneca`s Natural Questions and observe again and again how he applies standards of proof, witness evaluation, reasoning and evidence, we can see that we are reading one of the great Roman rhetoricians of his time, completely immersed in forensic methods. And not just Seneca. Legal models of scientific judgment appear everywhere and prove, for example, to be an integral part of Ptolemy`s approach to verification, where the mind is assigned the role of magistrate, the meaning of disclosure of evidence, and dialectical reason that of law itself. [20] is the eccentricity of the elliptical orbit, the semi-major axis A and the semi-minor axis B, and L is the half-latus rectum. This equation in itself is not physically fundamental; Simply the polar equation of an ellipse in which the pole (origin of the polar coordinate system) is positioned at the focus of the ellipse, where the orbited star is located. Some laws are only approximations of other more general laws and are good approximations with limited scope. For example, Newtonian dynamics (based on Galilean transformations) is the low-velocity limit of special relativity (since the Galilean transformation is the slow approximation of the Lorentz transformation). Similarly, Newton`s law of gravity is a low-mass approximation of general relativity, and Coulomb`s law is an approximation of long-range quantum electrodynamics (relative to the range of weak interactions). In such cases, it is customary to use simpler and approximate versions of the laws instead of the more specific general laws.

Classical mechanics, including Newton`s laws, Lagrangian equations, Hamiltonian equations, etc., can be derived from the following principle: Some examples of widely accepted impossibilities in physics are perpetual motions, which violate the law of conservation of energy and exceed the speed of light, which violates the implications of special relativity, the uncertainty principle of quantum mechanics, which claims the impossibility of simultaneously the position and momentum of a particle and Bell`s theorem: No physical theory of local hidden variables can ever reproduce all the predictions of quantum mechanics. The more general equations are the convection-diffusion equation and the Boltzmann transport equation, which have their roots in the continuity equation. The distinction between natural law in the political-legal sense and natural law or physical law in the scientific sense is modern, both terms also derive from physis, the Greek word (translated into Latin as natura) for nature. [24] The following general approaches[13][14] to classical mechanics are summarized below in the order of their foundation. These are equivalent formulations. Newton`s equations are often used for simplification, but Hamilton`s and Lagrange`s equations are more general and their scope can extend to other branches of physics with appropriate modifications.