Conservation laws are the result of symmetries in nature.
VERN BENDER
The law of conservation of information means that information can not be created or destroyed. Conservation of information is quantum unitarity, the law that the quantum mechanical wavefunction constantly evolves coherently; no pure state ever becomes a mixed state.
Conservation laws include conservation of mass and energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge. Energy from sunlight becomes glucose during photosynthesis. Oxygen is combined with the carbon atoms left from the glucose molecule.
Locally, information is lost and generally unretrievable as it escapes the local system at light speed and goes elsewhere. In practice, information is lost because the universe is expanding. You can’t simply access all the information out there. Also, data is irretrievably lost when it passes beyond the edge of the observable universe and when wavefunctions collapse.
The deterministic evolution of the quantum state is called the principle of unitarity. The quantum state preserves information via the no-cloning theorem and the no-deleting theorem. No cloning, deletion, or hiding of information has convincingly been demonstrated for quantum systems. Conservation laws are the result of symmetries in nature. The laws of physics obey certain symmetries and defy others. The Universe is not always symmetric. Everything is symmetrical if a system is time-translation invariant, space-translation invariant, or rotationally invariant. When systems are symmetric, they are easily described and quantified. Non-symmetric systems are more complicated. The conservation laws go away when things are not symmetric.
A linear operator whose inverse is its adjoint is called unitary. These operators can be considered generalizations of complex numbers whose absolute value is one. When you die, your information goes elsewhere. Growing information is one of the objectives of our universe. At the quantum level, data is best understood as energy. For every continuous symmetry in nature, there is a fundamental conservation law. Time symmetry at the particle level corresponds to the conservation of energy.
The homogeneity of time leads to the invariance principle that the laws of physics remain the same at all times, which implies the law of energy conservation. The space-time intervals are known as invariants. Space and time are absolutes.
