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Question: Where does space end? What, if anything, is after the end of space?
Your question pushes up against the limits of cosmology and astronomy. Cosmology is the mathematical theory of the Universe and its origin, while astronomy is the science of observing and measuring the objects that appear to us in outer space. Astrophysics is the science that allows these measurements to be interpreted. Concerning the end of space, first, since space in the Universe is currently believed to be expanding (as part of the Big Bang theory of the origin of the Universe), it is not possible to point to its end. In fact, space is understood to be expanding at an accelerating pace and so the act of pointing to the limits of space would not even be accomplished before that limit had been left far behind. In the practice of astronomy, the end of space is considered to be the furthest objects whose light we, the observers, can view using current technology. Since the technology of astronomy continues to develop, the limits of space in astronomy must increase as the observational range increases over time. Another important factor is the belief that the speed of light is fixed and the same at all times and places. This means that it takes light a certain finite time to travel through space. This, combined with current estimates of the age of the Universe, it can be said that there is light traveling though space that has not yet reached us. As this light comes to us, the Universe is seen to grow. One conclusion you could draw from all of these facts is that there is no end to space. If there were a current stable boundary of the universe, its detection could be approached by technological improvement only in a pattern of diminishing returns, as when you move in some direction by decreasing your steps by half with each step. For example, in refining existing techniques one makes improvements to existing technology, like increases in energy efficiency of an existing machine. In that pattern a goal will never be reached because, according to the 'diminishing returns' pattern, we would be approaching the goal ever more slowly. You might ask 'but why couldn't someone invent a new technique that would enable a big jump in our ability to observe great distances'. That could happen, but no one can predict that, and so it can't be taken into account until it happens. So, even if there was an end to space, and space wasn't expanding, we could never predict that we could observe it.As to the question of what would be 'out there' after the space of the Universe ends, this is currently not within scientific investigation. It can come up in various theoretical models, but since these are all mathematical, using variables that cannot presently be observed, I think an appropriate answer is that what is out there beyond space is a construction of mathematical variables.
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