# Physical law

A physical law describes in a general form how the physical quantities that characterize the states of a physical system are related to one another and, if necessary, change. Generally this is expressed in mathematical form. In the physical context, these laws are also referred to as or identified with natural laws .

A physical law is very likely to apply within its area of ​​validity. This area of ​​validity is checked through targeted physical experiments and observations . If their results are in line with expectations, the law is deemed to have been confirmed .

Every physical law is part of a physical theory that should be uniform and free of contradictions. A theory whose predictions have not yet been confirmed is called a hypothesis (such as string theory ). A closed theory is the set of laws that fully describe an area. To describe z. B. Maxwell's equations - in their range of validity - the entire classical electrodynamics .

The scientifically accepted physical laws determined the material view of the world from around the middle of the 19th to the beginning of the 20th century. They were in contrast to the view that natural processes can be influenced by influences that originate from outside the system understood as nature (e.g. by higher beings). Since then, the prevailing view has been that physical laws have statistical validity, that is, they are more or less likely to apply depending on the phenomena observed and the way they are observed . Physical laws are therefore considered a paradigm for natural laws . However, whether all scientific rules can be traced back to physical laws and what ontological status they have is the subject of epistemological debates (see also Scientific Realism ).

## Physical laws and natural laws

Physics describes the behavioral regularities of its objects of observation without giving any information about how they could fit into a comprehensive worldview as natural laws. This task is taken over by metaphysics or natural philosophy . The term “law” may suggest that nature behaves similarly to a person under the compulsion of laws passed by an intelligent being. Such a notion is known as occassionalism . In doing so, the laws were viewed as God's rules of action, which God makes come true on certain (albeit predictable) occasions out of his free will. Such a way of thinking was discussed in the 17th century, but is practically meaningless today due to the methodical atheism within the philosophy of science.

## Physical laws as a mirror of scientific progress

Scientific advancement in physics often consists in tracing seemingly independent laws back to a common foundation in a larger context. An example of this are the numerous forces of mechanics and the laws of their action, all of which can ultimately be traced back to electromagnetic interactions at the atomic level and to gravity between and in the bodies involved.

Another type of scientific progress can be seen in the transition from classical mechanics to the theory of relativity . Here, terms and laws that had been accepted as irrefutable and universally valid were recognized as only approximately valid models for a limited area, in this case for low speeds and masses.

In this sense, we are looking for “last” fundamental and generally applicable laws. Examples of these efforts are string theory , quantum gravity, and large unified theory ; they are all still hypothetical . A world law with which “everything” can be explained and built up would be comparable to the axioms of mathematics.

## Example: formulation of a law

In order to describe the processes exactly, natural laws are mostly formulated mathematically . An example of this is the law of gravity by Isaac Newton . It reads: The force of attraction F between two masses and is proportional to the size of the masses and inversely proportional to the square of the distance . ${\ displaystyle m_ {1}}$${\ displaystyle m_ {2}}$${\ displaystyle r ^ {2}}$

${\ displaystyle F = G {\ frac {m_ {1} m_ {2}} {r ^ {2}}}.}$

G is a proportionality factor of the masses and and the inverse of the distance square sets each other in relation. As experience shows that this factor, known as the gravitational constant , has the same value in all investigated physical systems and describes a fundamental physical interaction (the attraction of masses to one another), it is called a natural constant . ${\ displaystyle m_ {1}}$${\ displaystyle m_ {2}}$${\ displaystyle 1 / {r ^ {2}}}$