This is something that has bothered me for some time, and I can't seem to find any threads on here about it. In a lot of my undergraduate courses in physics, we talk about integrating something physical to infinity. For example, in electrostatics, we talk about the work needed to assemble a collection of charges that we "brought in from infinity." Or in quantum, we integrate to infinity all of the time to satisfy probability (e.g. the normalization condition). As my quantum professor always says, "we integrate over all space," which is usually a sphere with infinite radius. I know we have to make approximations all of the time in physics, and I am fine with that, but this is one that to me doesn't seem valid with all that we know about the universe. As far as I know, physicists don't think the universe is infinite in size. I have read, though, that the prevailing theory in cosmology is that the universe will probably expand forever. If that is the case, then I can see some validity in integrating space or time out to infinity. What do you guys think? I know this will probably make some of your eyes roll, because for all practical purposes, we can just do this math in order to get a very good approximation of something we are interested in. Another thing that just occurred to me, is that concepts such as infinite mass or density (e.g. with black holes) is "not physical," yet considering interactions between matter and energy at infinite separation is?