Relationship between the constancy of the laws of physics and conservation principles I have heard it said before in passing (I think it was on Star Talk Radio) that there is some specific relationship between the constancy of the laws of physics and conservation principles such as the conservation of momentum and conservation of energy. 
The claim, as I remember it, is that the principle of the conservation of momentum is 'equivalent' to saying that the laws of physics are constant throughout space.
Similarly, I heard it said that stating the principle of the conservation of energy is 'equivalent' to saying that the laws of physics are constant throughout all times.
In what way are these claims equivalent? In what way does one follow from the other. Or, am I misremembering some of the details of what was said?
Sorry if this question is a little bit vague. 
 A: You are referring to the theorem of Emmy Noether: "If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time". Any such symmetry refers to the constancy of the laws of nature under this symmetry transformation. For example, if you observe a system in a particular place and then observe exactly the same system in a different place (say, shifted or "translated" by a certain distance), then the behavior of the system should be the same, because the laws of nature do not depend on where exactly things happen (provided no specific differences like different gravity, etc.). Then, according to the Noether theorem, there would be a corresponding conservation law. In case of the space translation symmetry, what is conserved is momentum. In case of the time translation symmetry ( the system behaves tomorrow the same way as today - the laws of nature do not depend on time), the conserved quantity is energy. There are many other symmetries, each producing its own conserved quality, such as angular momentum, electric charge, and others.
https://en.m.wikipedia.org/wiki/Noether%27s_theorem
