Where, when, and why did the notion of conservation of energy become a law?
"Conservation of energy" has always been a law of Nature everywhere pretty much as far back as we can tell. But you mean the concept - where, when, and why has the concept become accepted as a true description of the way the Universe works.
It's an
empirical law. It is accorded the status of a "Law" because it has resisted every attempt to overturn it; and there have been some extremely creative attempts. Remember, empirical truths rest on the extent and ingenuity of the failed attempts to disprove them. This one has been so successful that it is safe to treat it as an axiom for almost all our calculations, but "accepted without proof" is not a good way of thinking about empirical truths.
There are a bunch of works on the history of these ideas listed in Wikipedia:
http://en.wikipedia.org/wiki/Conservation_of_energy#History_of_ideas
There are also lots of lessons like this one:
http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Conservation_of_energy.html
Couldn't we have just as easily put causation (and only allowing forward time travel to exist) as an axiom and then simply found "fixes" to any violations to this concept similar to conservation of energy axiom that we all appear to simply accept without proof ?
It is not possible to prove an empirical truth so all empirical truths have to be, literally, "accepted without proof". So it is not a useful characterization.
What we do is talk about the strength of an empirical truth, the amount of evidence that supports it, and, more importantly, the extent and ingenuity of the failed attempts to disprove it.
This leads to an idea of the likelyhood that the particular truth will turn out to be false
this time.
It's like tossing a coin and it always comes up heads - how long before you just accept that it is a double-headed coin and be done with it?
But bear in mind that Newton's
laws of motion, Newton's
law of gravitation, are called "Laws" even though we know they are untrue - exactly because they are extremely good anyway. Conservation of energy is a much much stronger law. It is difficult to overstate how strong it is - the limits appear when you deal with some of the models of quantum mechanics (where energy is strictly conserved at vertices in Feynman diagrams but may be violated within uncertainty limits for virtual particles) and general relativity (where energy is difficult to define).
You will need to look up "empiricism" to get more details about how empirical truths are arrived at...
