If someone could prove that matter and energy actually can be created or destroyed, what effect would it have on our science? How would it change our assumptions of the nature of matter and energy? Thanks!
As pointed out in my comment, there are questions of scale to be addressed. However, one thing can be stated: the model must lose time invariance, or some other key feature that physicists like.
There is a theorem, Nother's theorem, which states that in any Lagrangian system which has a symmetry group (which includes nearly all systems physics is interested in but excludes many systems such as those which include friction but ignore the heat generated) must have a conserved value. It can be shown with mathematics that the time invariance of physical laws (an event occurs in exactly the same way, regardless of what time it occurs at, as long as all other conditions besides time are met) enforces some concept of conservation of energy over all physical laws.
This means we have three clear paths, and who knows how many muddled paths in between:
- The world is defined by rules that are not Lagrangian. This opens up a whole can of worms, depending on which rules you choose to tweak. I don't know if either of us have the mathematical/physics background to discuss the particulars of any one property of the universe functioning this way.
- The world loses time invariance. This means, quite literally, that things that worked before may not work again. It opens doors for concepts like "there used to be magic in this world, but it fled, so we can never use it again." (from the link HDE 226868 provided, it looks like general relativity takes this tack)
- Physics lumps all non-Lagrangian or non time-invariant processes into its "noise" terms, and continues on merrily, solving problems, until one day someone finds a way to take advantage of all those pesky noise terms to find energy that physics didn't even know existed, and dominates all those who believe physics defines truth.