show that conservation of energy in an outcome of symmetry under time translation.
Answers
Answer:
Plants and animals (humans included) are interdependent on each other for many reasons. ... Here, plants consume decayed material from the soil for their nourishment and are consumed by plant-eating animals for their survival. The carnivores then consume the lower animals of the food chain for their nutrition and survival.
Explanation:
Time translation symmetry or temporal translation symmetry (TTS) is a mathematical transformation in physics that moves the times of events through a common interval. Time translation symmetry is the hypothesis that the laws of physics are unchanged, (i.e. invariant) under such a transformation. Time translation symmetry is a rigorous way to formulate the idea that the laws of physics are the same throughout history. Time translation symmetry is closely connected, via the Noether theorem, to conservation of energy.[1] In mathematics, the set of all time translations on a given system form a Lie group.
There are many symmetries in nature besides time translation, such as spatial translation or rotational symmetries. These symmetries can be broken and explain diverse phenomena such as crystals, superconductivity, and the Higgs mechanism.[2] However, it was thought until very recently that time translation symmetry could not be broken.[3] Time crystals, a state of matter first observed in 2017, break time translation symmetry.[4]