Noethers Theorem

I was trying to explain this to someone else but I'm pretty sure I'm not correctly understanding it and confusing myself through analogy. I'm not even sure if I stated my question correctly. Basically the question came down to, 'what is energy?" Here is what I wrote, where am I wrong? I hate feeling like I'm using enough jargon to make incorrect statements sound plausible to someone who knows less than I do. Plus I assume this can be stated with much fewer words.

Values like energy and charge are conserved quantities due to a related symmetry (stay with me, I'll explain). The law of energy conservation states that energy is not created or destroyed, it is always maintained. Energy and mass are the same quantity, and all energy/mass is within spacetime. Energy can not exist outside of space or time. It is ultimately conserved because energy can not exist outside of spacetime and can not be destroyed within it.

We can say energy is conserved due to the invariance of time. Time invariance means that system isn't dependent on time. Energy can be dependent on time, but only within a localized area, which we could just say is part of a greater area, and so on. So if you look at the entire universe at different points in time, the amount of energy contained within it will always be the same. Time can change, the quantity of energy stays the same.

The laws of physics (really the laws of energy) are conserved with respect to time. Things don't just fall apart out of nowhere, energy doesn't magically appear, there is a continuously conserved quantity, which we call energy. This is why we can have cause and effect, this is why we can repeat an experiment and get the same results. Energy is ultimately a conserved quantity within the universe because it is not dependent on time. Energy travels through time and space, but changes to time do not affect it. If you do an experiment and repeat it again changing only the time, you get the same result. This gives the universe stability with respect to changes in time.

I don't feel like this is helping to describe energy much, but you have to forget your definition of energy and just think of it as a quantity (just a finite collection of something) within the universe that is conserved because it is invariant with respect to time. It's almost like being married and having friends that come and go. Over time you stay married but get new friends. If you try to work with friends, who are not stable, on some long term project you can't do much, because they vary with time. Your wife (assuming til death) is always going to be there and you can do things with her independent of time because she is always there, whether you look at your life at 30 or 80, she is there. Your wife is like energy, it's always there and you can manipulate it knowing that time itself won't affect it, it may change form but it will still be there.

You can use this quantity of energy to build an engine today, which you know will work a year from now (eliminating wear/tear, etc.). There isn't really an analogy for the friends which come and go, they aren't stable and can not be relied upon. In a very real sense, they are not there at all. They don't exist the way your wife does because she is invariant with respect to time. Your wife, or the quantity which is always there following the same rules, is energy. Everything else is non-existent. A universe with no wife but just friends who came and went wouldn't be stable enough to support life, much less galaxies or any structure intended to remain stable as time changes. Whatever energy is, we know time doesn't change it and that is why I'm sitting here typing to you and not annihilating because 10 seconds from the now the laws of the universe are going to change which would break apart my atoms. The stability of the universe over time is dependent upon a time invariant quantity, which we call energy. Basically time can 'flow' without messing everything up due only to it's relative movement.

Can I say that the lagrangian of a time invariant system conserves a quantity that we call energy? I never feel like i'm phrasing it right. But wait the [L] defines the energy so I can't use it to define itself, I don't know, I'm going to stop thinking.

TL:DR Energy is the conserved quantity of time invariance.. ?