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.
Basic space-time symmetries keep physical laws the same under various conditions {invariance, physics}. Baryon number, spatial rotation, and space-time translation are always invariant.
Charge conjugation, parity, and time reversal combined are invariant for all physical laws. Charge conjugation and parity together are invariant, except for strange-particle decays in weak nuclear forces. Mass-strength and strong-force-strength differences in up and down and other quarks cause charge-conjugation symmetry breaking. Parity breaks down in weak nuclear forces. Time reversal breaks down in weak nuclear forces.
Heat and work are kinetic energy. Force fields cause potential energy. Total energy is sum of kinetic and potential energies, which can interconvert. Isolated-system total energy is constant {energy conservation, dynamics}| {conservation of energy, dynamics}. Energy is invariant through time-coordinate translations. Physical laws are symmetric with respect to time dimension, so physics does not change if time reverses direction. Physical laws remain true at all times. All physical interactions are the same if time reverses, charges reverse, and positions reverse. However, weak-force physical laws are not symmetric with respect to time.
cause
Isolated systems have no added forces and so no added potential energy. Isolated systems have no volume changes and so no added distances or potential energy. Object movements interchange potential energies and kinetic energies, no matter which space-time path objects take.
vacuum energy
Kinetic energy and potential energy exert pressure on background vacuum energy. Kinetic energy has particle motions that make internal pressure. Potential energy has fields that make pressure by causing particle self-energy. Motions and fields pressure space-time points through which they pass. Space-time points have energy flux. Kinetic energy and potential energy both contribute to vacuum energy in the same way. Only energy amount counts. As masses move, vacuum adjusts to keep potential constant. Potential, flux, or pressure is constant at all vacuum points, making a new conservation law.
relativity
Mass and energy can interchange in space-time. By equipartition, all partition kinetic energies must be equivalent. Energy conservation remains true under relativistic conditions.
In general relativity, accelerations are equivalent to forces, which cause accelerations. Accelerations are velocity changes. Velocity changes change kinetic energy. Objects change velocity as they change field position and potential energy. Kinetic and potential energies are equivalent in general relativity.
quantum mechanics
Quantum mechanically, mass and energy states are the same. Energy conservation remains true under quantum mechanics.
dark energy
Energy conservation remains true for dark energy, which is symmetric in time.
Momentum conservation {conservation of momentum} means that total momentum is constant, no matter which direction objects take through space. Momentum is invariant under spatial-coordinate translations. All directions are equivalent. Physical laws are symmetric with respect to space dimensions. Physics does not change if space directions reverse, rotate, or translate. Physical laws remain true at all space points.
System total momentum stays constant. For interacting objects, one object's momentum change balances other object's momentum change, because both objects interact over same time. For non-interacting objects, motion states and object masses do not change, so momenta do not change. Fields and their bosons carry or contain momentum and inertia.
Angular momentum conservation {conservation of angular momentum} means that total angular momentum is constant, no matter what rotations (spins or orbits) objects take, at any orientation. Angular momentum is invariant under rotations. Angular momentum is invariant under handedness change, right-handed or left-handed. All rotations are equivalent. Physical laws are symmetric with respect to rotation. Physics typically does not change if spin directions reverse or change orientation. Physical laws remain true for right-handed or left-handed arrangements.
System total angular momentum, from spins, orbits, and curved trajectories, stays constant. Using infinite radius, angular-momentum conservation is equivalent to momentum conservation. Angular-momentum conservation implies that system mass center stands still, so universe either does not rotate or does not move. Angular-momentum conservation implies that forces have equal and opposite reaction-forces and that masses have inertia.
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Date Modified: 2022.0225