Conservation law

As a conservation law is called in physics the formulation of the observed fact that a quantity called conserved quantity, in certain physical processes does not change.

The best-known conservation law is that of energy. Colloquially it is, what you put into it ahead of energy also comes back out again; no energy is lost and there is no out of nowhere. The most common conservation laws apply to the sizes of energy, momentum, angular momentum, electric charge, baryon number and lepton number. For certain classes of physical processes (see fundamental forces of physics ) other conservation laws are added.

According to the Noether theorem has any physical symmetry, which is continuous, a conservation law result.

States of a system

Conserved quantities can be calculated from the variables that describe the state of a system, such as locations and velocities of particles. While changing the state variables in movement with time, calculated from the conserved quantities remain constant over time. Thus the energy of a particle of mass depends on potential

Of from its speed and its location. Even if both the speed change and the location of the passage of time, as is the energy

Unchanged over time.

Conservation laws limit the conceivable motion of the physical system. For example, it follows from the energy and momentum conservation in the Compton scattering as the energy of the scattered photon is related to its scattering angle and with what energy and the direction in which the initially resting electron after (depending on the scattering angle of the photon, which is not set) the scattering moves.

Many conserved quantities, such as the total momentum, are additive. In two- and Mehrteilchensystemen the value of the additive conserved quantity is the sum of the individual values ​​. The total momentum, for example, is the sum of the individual pulses. This apparent self-evidence is valid only for particles that do not (more) interact. During the interaction fields can absorb energy and momentum and transferred to other particles.

Examples

• Conservation of energy: The total energy remains constant ( corresponding symmetry: the physical processes do not depend on the choice of time zero, homogeneity of time ).
• Conservation of momentum: The vector sum of all pulses remains constant ( corresponding symmetry: The physical processes do not depend on the choice of origin, homogeneity of space ).
• Conservation of angular momentum: the sum of all angular momentum remains constant ( corresponding symmetry: The physical processes do not depend on the choice of reference directions isotropy of space ).
• Charge conservation: The (electrical, color ) charge remains constant ( corresponding symmetry: the phase of the charged particle can be chosen arbitrarily ). Is a charge in an area given as the integral of a charge density over this area, it is a conserved quantity, when used together with a current density continuity equation

• Baryonenzahlerhaltung and lepton number conservation: Both the number of baryons ( composed of quarks fermions ) and the number of leptons (eg electrons, neutrinos ) in a system is maintained. Here, particles and antiparticles have positive negative baryon and lepton number.

Conservation laws and integrability

Does the physical system under consideration as many conserved quantities as degrees of freedom, so can specify the time evolution by integrals. One speaks of a integrable system if the are in involution, ie, the Poisson bracket

For all, zero.

This corresponds to the commutativity of belonging to the conserved quantities symmetry transformations for sequential execution.

In the simplest case, energy conservation movement a degree of freedom, one solves the energy equation

According to the speed of

The derivative of the reverse function, that indicates the time at which the particle passes through the place is the reciprocal,

Integrating this equation over from a lower limit to an arbitrary upper limit, we obtain

It is therefore the inverse function determined as a function of the upper limit of an integral of the given function. The start time and the initial energy is selectable.

Conservation laws in the 19th century

The conservation laws are part of the modern physics of the 20th century. End of the 19th century, listed the major German encyclopedia under "maintenance " three thematic areas: the case of " conservation of energy " they refer directly to the force at " conservation of land " on the central movement, same with the " the beacon in equal times surface spaces describes " ( now called: conservation of angular momentum ). The only conservation law, which occupied as such broader space, was a declared by the authors as difficult, the " preservation of the world ":

" Preservation of the world, both by its matter continues in the church doctrine of the act of the divine will by which the universe as created by finished its shape. Condition of E [ rhaltung the world ] is the creation, while at first the doctrine of E [ rhaltung the world ] the calls that the world government on mankind followed. The difficulty of the concept lies in the ratio of those effects which. Absorbed by the second causes, the natural and human forces that go out to the omnipotence of the first and final cause, God. "