Underpinnings of conservation of energy/mass

[Undacuva]

I understand the 1st law of thermodynamics developed as a generalization based on experimental observations, in that an exception has yet to be found in thousands of situations, so it is considered to hold true in all possible situations.
If that is how it developed, is there any other theory or formula which can only hold true if there is no exception to the conservation of energy/mass? If someone does actually prove an exception, what will be the implication (if any) for the rest of what we know about physics?

 

[jbriggs444]

I understand the 1st law of thermodynamics developed as a generalization based on experimental observations, in that an exception has yet to be found in thousands of situations, so it is considered to hold true in all possible situations.
If that is how it developed, is there any other theory or formula which can only hold true if there is no exception to the conservation of energy/mass? If someone does actually prove an exception, what will be the implication (if any) for the rest of what we know about physics?

Conservation of energy is also a mathematical consequence of Noether's Theorem and the assumption that the laws of physics are invariant over time (the same now as they were yesterday and will be tomorrow).

Similarly, conservation of momentum follows from the assumption that the laws of physics are invariant over position (same here as they are over there). Conservation of angular momentum follows from the assumption that the laws of physics are invariant with respect to direction (same if one looks one way or if one looks another).

Conservation of mass is not on an equally firm footing. Although energy is conserved, mass (if computed as the sum of the masses of the particles making up a system) is not precisely conserved. The classic example of mass non-conservation in this sense is in a nuclear bomb where the mass of a Uranium atom is greater than the sum of the masses of the remaining pieces after it splits.

 

[.Scott]

Conservation of Mass and Energy is a theory. You can use it to make predictions, and so far when such predictions are made, those predictions have proved out. This can be said for all good theories.

As Physics advances, what were held as good theories are sometimes found to be limited. For example, e=mc^2 put a wrinkle in the original conservation of energy theory. Newton's Laws took a hit with the discovery of relativity.