Physical law

Laws of science or scientific laws are statements that describe or predict a range of natural phenomena. A scientific law is a statement based on repeated experiments or observations that describe some aspect of the natural world. The term law has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, biology, geology, astronomy, etc.). Laws are developed from data and can be further developed through mathematics; in all cases they are directly or indirectly based on empirical evidence. It is generally understood that they implicitly reflect, though they do not explicitly assert, causal relationships fundamental to reality, and are discovered rather than invented.u = velocity field of fluid (m s−1)Ψ = wavefunction of quantum system S = ∫ t 1 t 2 L d t {displaystyle {mathcal {S}}=int _{t_{1}}^{t_{2}}L,mathrm {d} t,!} Using the definition of generalized momentum, there is the symmetry:The Hamiltonian as a function of generalized coordinates and momenta has the general form: Newton's laws of motionwhere Λ = cosmological constant, Rμν = Ricci curvature tensor, Tμν = Stress–energy tensor, gμν = metric tensorwhere Γ is a Christoffel symbol of the second kind, containing the metric.If g the gravitational field and H the gravitomagnetic field, the solutions in these limits are:where m is the rest mass of the particlce and γ is the Lorentz factor.For two point masses:An equivalent statement to Newton's law is:where where L is the orbital angular momentum of the particle (i.e. planet) of mass m about the focus of orbit, where M is the mass of the central body (i.e. star).Second law of thermodynamics: There are many statements of this law, perhaps the simplest is 'the entropy of isolated systems never decreases',Third law of thermodynamics:Gauss's law for electricitySchrödinger equation (general form): Describes the time dependence of a quantum mechanical system.Planck–Einstein law: the energy of photons is proportional to the frequency of the light (the constant is Planck's constant, h). Schrödinger equation (original form): ψ ( ⋯ r i ⋯ r j ⋯ ) = ( − 1 ) 2 s ψ ( ⋯ r j ⋯ r i ⋯ ) {displaystyle psi (cdots mathbf {r} _{i}cdots mathbf {r} _{j}cdots )=(-1)^{2s}psi (cdots mathbf {r} _{j}cdots mathbf {r} _{i}cdots )} The formula 'law of nature' first appears as 'a live metaphor' favored by Latin poets Lucretius, Virgil, Ovid, Manilius, in time gaining a firm theoretical presence in the prose treatises of Seneca and Pliny. Why this Roman origin? According to Lehoux's persuasive narrative, the idea was made possible by the pivotal role of codified law and forensic argument in Roman life and culture.For the Romans . . . the place par excellence where ethics, law, nature, religion and politics overlap is the law court. When we read Seneca's Natural Questions, and watch again and again just how he applies standards of evidence, witness evaluation, argument and proof, we can recognize that we are reading one of the great Roman rhetoricians of the age, thoroughly immersed in forensic method. And not Seneca alone. Legal models of scientific judgment turn up all over the place, and for example prove equally integral to Ptolemy's approach to verification, where the mind is assigned the role of magistrate, the senses that of disclosure of evidence, and dialectical reason that of the law itself. Laws of science or scientific laws are statements that describe or predict a range of natural phenomena. A scientific law is a statement based on repeated experiments or observations that describe some aspect of the natural world. The term law has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, biology, geology, astronomy, etc.). Laws are developed from data and can be further developed through mathematics; in all cases they are directly or indirectly based on empirical evidence. It is generally understood that they implicitly reflect, though they do not explicitly assert, causal relationships fundamental to reality, and are discovered rather than invented. Scientific laws summarize the results of experiments or observations, usually within a certain range of application. In general, the accuracy of a law does not change when a new theory of the relevant phenomenon is worked out, but rather the scope of the law's application, since the mathematics or statement representing the law does not change. As with other kinds of scientific knowledge, laws do not have absolute certainty (as mathematical theorems or identities do), and it is always possible for a law to be contradicted, restricted, or extended by future observations. A law can usually be formulated as one or several statements or equations, so that it can be used to predict the outcome of an experiment, given the circumstances of the processes taking place. Laws differ from hypotheses and postulates, which are proposed during the scientific process before and during validation by experiment and observation. Hypotheses and postulates are not laws since they have not been verified to the same degree, although they may lead to the formulation of laws. Laws are narrower in scope than scientific theories, which may entail one or several laws. Science distinguishes a law or theory from facts. Calling a law a fact is ambiguous, an overstatement, or an equivocation. The nature of scientific laws has been much discussed in philosophy, but in essence scientific laws are simply empirical conclusions reached by scientific method; they are intended to be neither laden with ontological commitments nor statements of logical absolutes. A scientific law always applies under the same conditions, and implies that there is a causal relationship involving its elements. Factual and well-confirmed statements like 'Mercury is liquid at standard temperature and pressure' are considered too specific to qualify as scientific laws. A central problem in the philosophy of science, going back to David Hume, is that of distinguishing causal relationships (such as those implied by laws) from principles that arise due to constant conjunction. Laws differ from scientific theories in that they do not posit a mechanism or explanation of phenomena: they are merely distillations of the results of repeated observation. As such, a law is limited in applicability to circumstances resembling those already observed, and may be found false when extrapolated. Ohm's law only applies to linear networks, Newton's law of universal gravitation only applies in weak gravitational fields, the early laws of aerodynamics such as Bernoulli's principle do not apply in case of compressible flow such as occurs in transonic and supersonic flight, Hooke's law only applies to strain below the elastic limit, Boyle's law applies with perfect accuracy only to the ideal gas, etc. These laws remain useful, but only under the conditions where they apply. Many laws take mathematical forms, and thus can be stated as an equation; for example, the law of conservation of energy can be written as Δ E = 0 {displaystyle Delta E=0} , where E is the total amount of energy in the universe. Similarly, the first law of thermodynamics can be written as d U = δ Q − δ W {displaystyle mathrm {d} U=delta Q-delta W,} , and Newton's Second law can be written as F = ​dp⁄dt. While these scientific laws explain what our senses perceive, they are still empirical, and so are not like mathematical theorems (which can be proved purely by mathematics and not by scientific experiment). Like theories and hypotheses, laws make predictions (specifically, they predict that new observations will conform to the law), and can be falsified if they are found in contradiction with new data. Some laws are only approximations of other more general laws, and are good approximations with a restricted domain of applicability. For example, Newtonian dynamics (which is based on Galilean transformations) is the low-speed limit of special relativity (since the Galilean transformation is the low-speed approximation to the Lorentz transformation). Similarly, the Newtonian gravitation law is a low-mass approximation of general relativity, and Coulomb's law is an approximation to Quantum Electrodynamics at large distances (compared to the range of weak interactions). In such cases it is common to use the simpler, approximate versions of the laws, instead of the more accurate general laws.