Noether Theorem
Hello Guys !!!
There are many laws that govern the universe and many basic laws such as gravity and conversation of energy that make us think them as the fundamental laws and that is true they govern a large part of the universe and many situations but there are many cases that they become wrong and some complications come like we have seen with gravity in case of negative matter and black holes.
This also makes for conversation of energy as this is not also always be true as the solution that we made with are so generals that they are mostly untrue so we need a better way of calculating the energy and its principles that are by Noether Theorem.
Why it was made
This was due to the fact that in general relativity the conversation of energy is not at all a basic law and not at least a fundamental law as we can see when a big object like star and galaxies moves away due to universe expansion then their light now increases there wavelength and due to this the energy is reduced and due to this the energy loos is not at all dated so where does the energy does make people think about it.
What is Noether's Theorem
The basic statement is for every continuous symmetry of the universe there exists a conserved quantity.
This only true for continuous and not all symmetry that we see that means something is continuously symmetric if it stays the same for any shift in coordinates.
This also depends upon the environment be the same as we can see the environment of symmetry be in a plain or in a spherical it become conserved.
This theorem helps us to find all the cases where the energy will not be conserved and deals with the ever-expanding universe and dark energy.
How to make more general Conservation of energy
This is mainly done by negating the increase in-universe size and gain in energy by dark energy by using Landau-Lifshitz-Pseduotensor.
We can see that Noether's mainly uses the principle of least action to be used by it.
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