Conservation of mass

The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov-Lavoisier law), states that the mass of a closed system will remain constant, regardless of the processes acting inside the system. An equivalent statement is that matter cannot be created/destroyed, although it may be rearranged. This implies that for any chemical process in a closed system, the mass of the reactants must equal the mass of the products.

The law of "matter" conservation (in the sense of conservation of particles) may be considered as an approximate physical law that holds only in the classical sense before the advent of special relativity and quantum mechanics. Mass is also not generally conserved in open systems, when various forms of energy are allowed into, or out of, the system. However, the law of mass conservation for closed systems, as viewed from their center of momentum inertial frames, continues to hold in modern physics.

This historical concept is widely used in many fields such as chemistry, mechanics, and fluid dynamics.

Historical development and importance
An early yet incomplete theory of the conservation of mass was stated by Nasīr al-Dīn al-Tūsī (1201-1274) in the 13th century. He wrote that a body of matter is able to change, but is not able to disappear.

The law of conservation of mass was first clearly formulated by Lavoisier (1743-1794) in 1789, who is often for this reason (see below) referred to as a father of modern chemistry. However, Mikhail Lomonosov (1711-1765) had previously expressed similar ideas in 1748 and proved them in experiments. Others who anticipated the work of Lavoisier include Joseph Black (1728-1799), Henry Cavendish (1731-1810), and Jean Rey (1583-1645). Historically, the conservation of mass and weight was kept obscure for millennia by the buoyant effect of the Earth's atmosphere on the weight of gases, an effect not understood until the vacuum pump first allowed the effective weighing of gases using scales. Once understood, conservation of mass was of key importance in changing alchemy to modern chemistry. When scientists realized that substances never disappeared from measurement with the scales (once buoyancy had been accounted for), they could for the first time embark on quantitative studies of the transformations of substances. This in turn led to ideas of chemical elements, as well as the idea that all chemical processes and transformations (including both fire and metabolism) are simple reactions between invariant amounts/weights of these elements.This law is used by scientists all over the world.

Generalization
In special relativity, the conservation of mass does not apply.

The principle that the mass of a system of particles is equal to the sum of their masses, even though true in classical physics, is false in special relativity. The mass-energy equivalence formula implies that bound systems have a mass less than the sum of their parts. The difference, called a mass defect, is a measure of the binding energy — the strength of the bond holding together the parts (in other words, the energy needed to break them apart). The greater the mass defect, the larger the binding energy. The binding energy is released when the parts combine to form the bound system, and the mass decreases when the energy leaves the system.

The conservation of mass may be cast in terms of the conservation of a system combination of energy and momentum, which is conserved, and which gives the same invariant mass of any system (such as the two-photon system) for any observer.

The conservation of mass applies to particles created by pair production. The invariant mass of closed systems does not change when new particles are created.