If physical-system coordinates transform, some physical properties remain unchanged {conservation laws}|.
fermions
all same-type fermions are identical. For example, all electrons are identical. Physical laws are symmetric for fermion replacement with same-type fermion.
mass
For non-relativistic conditions, mass stays constant. For example, mass does not change in chemical reactions. However, physical laws are not symmetric with respect to matter-antimatter for weak force.
baryon number
Baryon number stays constant
lepton number
Lepton number stays constant.
parity
Parity conserves, except for weak force. Physical laws are not symmetric with respect to reflection in space for weak force.
strangeness
Strangeness conserves, except for weak force.
no conservation
Physical laws are not symmetric with respect to scale. Physical laws are not symmetric with respect to uniform angular velocity.
symmetries
Conservation laws are about minimizations and symmetries. Symmetries require reference point, feature, and reference frame. Symmetry types depend on feature types. For example, rotating spheres with no features have no detectable spin. Particles with dipoles have detectable spin, which can be right or left. Particles must have mass, spin, or other feature to be detectable. Featureless objects or spaces have no symmetries. Symmetries can cancel large physical quantities. Physical theories have one symmetry for each conserved quantity (Noether) [1915].
energy
Energy conservation requires time symmetry: forward and backward in time are usually the same physically. By observing a physical process, observers cannot tell if time flows backwards or forwards.
Total closed-system energy is constant. However, energy can exchange between potential and kinetic energy. Kinetic energy minus potential energy {Lagrangian} measures energy exchange. The path integral of Lagrangian over time is the physical action. For cyclic processes, the system periodically returns to the same Lagrangian value, Lagrangian change is zero, and action is zero. For cyclic processes, the wave equations of motion are path integrals of Lagrangians over time set equal to zero.
momentum
Momentum conservation requires special-relativity constant-velocity reference-frame equivalence. When observing a physical process, observers have no preferred reference frame. The distance metric is the same for all constant-velocity observers (Lorentz invariance).
angular momentum
Angular momentum conservation requires right-left (parity) symmetry. When observing a physical process, observers cannot tell if it is right-handed or left-handed. Clockwise and counterclockwise rotations have same physics.
electric charge
Electric charge stays constant. Electric-charge conservation requires electromagnetism gauge invariance.
Physical Sciences>Physics>Dynamics>Conservation
5-Physics-Dynamics-Conservation
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Date Modified: 2022.0224