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The law of conservation of mass can only be formulated in classical mechanics, in which the energy scales associated with an isolated system are much smaller than , where is the mass of a typical object in the system, measured in the frame of reference where the object is at rest, and is the speed of light.
All of the conservation laws listed above are local conservation laws. A local conservation law is expressed mathematically by a continuity equation, which states that the change in the quantity in a volume is equal to the total net "flux" of the quantity through the surface of the volume. The following sections discuss continuity equations in ...
Sharper upper limits on the mass of light have been obtained in experiments designed to detect effects caused by the galactic vector potential. Although the galactic vector potential is large because the galactic magnetic field exists on great length scales, only the magnetic field would be observable if the photon is massless.
The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes. In general, the conservation law states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed.
Because of momentum conservation laws, the creation of a pair of fermions (matter particles) out of a single photon cannot occur. However, matter creation is allowed by these laws when in the presence of another particle (another boson, or even a fermion) which can share the primary photon's momentum. Thus, matter can be created out of two photons.
Noether's theorem: Any quantity with a continuously differentiable symmetry in the action has an associated conservation law. Conservation of mass was the first law to be understood since most macroscopic physical processes involving masses, for example, collisions of massive particles or fluid flow, provide the apparent belief that mass is ...
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Lagrangian mechanics provides a convenient framework in which to prove Noether's theorem, which relates symmetries and conservation laws. [67] The conservation of momentum can be derived by applying Noether's theorem to a Lagrangian for a multi-particle system, and so, Newton's third law is a theorem rather than an assumption. [19]: 124