Seonglae ChoContinuous Symmetry of the Action of a Physical System with force has a corresponding Conservation law
Symmetry indicates same physical principles against action (Noether Current’s derivative is 0)
- Symmetry against Space transition → Conservation of momentum → Inertia
- Symmetry against time transition → Conservation of Energy
- Symmetry against rotation - Conservation of Angular Momentum
This shows that the Conservation law is not absolute and inevitable, but rather a conditional property that is not absolute in all situations and depends on symmetry. In other words, it means that if symmetry is broken, conservation laws may not apply. This can be seen simply when interpreting Redshift, where the time translation symmetry is broken, and the energy conservation law does not seem to hold due to changes in wavelength.
Einstein explained the consistency of physical laws in General Relativity, clarified by Noether's work. This gives symmetry to spacetime transformations by fixing physical laws, including the speed of light, despite the foreign nature of spacetime. The conserved quantity for this symmetry of spacetime transformation is the Stress-energy tensor, and it is conserved without change rate as . In other words, in redshift, while time symmetry is broken, it is interpreted that energy is redistributed in the expanded spacetime that flexibly changes with spacetime symmetry.
Because the theory of relativity explains gravity as the curvature of spacetime itself, it requires modeling the entire curved spacetime gravitational field as a Stress–energy–momentum pseudotensor for the expression of gravitational energy.
