Contact in an expanding universe: an instructive exercise in dynamic geometry

Physics

Scientific paper

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Scientific paper

The particular problem solved in this paper is that of calculating the time required to overtake a distant object receding under cosmic expansion, and the speed at which that object is passed. This is a rarely investigated problem leading to some interesting apparent paradoxes. We employ the problem to promote a deeper understanding of the dynamic geometry behind the expansion of space in three eras, especially for physics undergraduates. We do not utilize the standard cosmological formulae, but deliberately take a simpler approach, comprehensible to any student comfortable with differentials. This should offer an intuitive preparation for later courses in general relativity. The paper can be read straight through, or offered to a class in segments as problems to investigate. The overall intention is to leave students with a more tangible grasp of expanding space.

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