Question

In nature, is total energy always conserved (yes or no)? Why?

Answer 1

Yes, In nature, total energy is always conserved. According to the law of conservation of energy during any process, chemical Or physical, total energy is same before and after the process. It implies that energy can neither be created nor be destroyed, it can only be transformed from one form to another form.

Conservation of total energy is the consequence of Noether's theorem, which states that laws of physics are invariant under Time transformation.

From a mathematical point of view it is understood as a consequence of Noether's theorem, developed by Emmy Noether in 1915. The theorem states every continuous symmetry of a physical theory has an associated conserved quantity; if the theory's symmetry is time invariance then the conserved quantity is called "energy". The energy conservation law is a consequence of the shift symmetry of time; energy conservation is implied by the empirical fact that the laws of physics do not change with time itself. Philosophically this can be stated as "nothing depends on time. In other words, if the physical system is invariant under the continuous symmetry of time translation then its energy (which is canonical conjugate quantity to time) is conserved. Conversely, systems which are not invariant under shifts in time (an example, systems with time dependent potential energy) do not exhibit conservation of energy – unless we consider them to exchange energy with another, external system so that the theory of the enlarged system becomes time invariant again. Conservation of energy for finite systems is valid in such physical theories as special relativity and quantum theory .