GR allows for the possibility of travel in time by the space-dragging effect of an infinitely long, dense, rotating cylinder. Q: Why does the cylinder have to be infinitely long? A: It doesn't, an extremely long cylinder will do - long enough to eliminate "edge effects". Q: Why even extremely long? Are we talking dozens/thousands/millions of light years? Would one light year be too short a cylinder? Ten thousand miles? My question is less about how long it needs to be and more about why it has to be so long? i.e. How the does vast length of the cylinder affect the um ... effect?
Not according to more recent results. It really does need to be an infinite cylinder. There's a theorem due to Hawking published well after Tippler's original paper on the "rotating cylinder" time machine that shows that compact geometries (which includes finite cylinders as any finite geometry will be compact) can't be time machines (generate closed timelike curves) unless they violate the weak energy condition (have parts that have negative mass). More precisely: This is Hawking's ``chronology protection'' result (Phys. Rev. D46 (1992) 603), which shows that creation of closed timelike curves from a compact region of spacetime requires that the weak energy condition be violated. My understanding is that Tippler's calculation that infinite rotating cylinders (which were easy to solve for mathematically) were time machines is correct, but the asumption that the finite solution also were time machines was not rigorously shown and is in fact incorrect. See the thread on Mallet's time machine where this came up. [add] Note that the thread on Mallet's time machine is about Mallet's time machine, not Tippler's. The utility of the thread will be in providing some more discussion of the specific chronology protection result due to Hawking which shows that Tippler's time machine can't work if it's finite. https://www.physicsforums.com/showthread.php?t=42834&highlight=time+machine+Mallet