The Gödel Metric
&quot;Nature abhors a time machine&quot; says Stephen Hawking.<p>The school of thought there is that closed timelike curves <i>could</i> be possible in  many theoretical ways. You can imagine funky cosmologies, ways of making wormholes, ways of making tachyons... when you get specific enough with any possibility, theory has shown it is impossible. But the problems with each possibility don&#x27;t seem to have a common theme. None of those reasons seem to lead to a fundamental proof prohibiting closed time-like curves. It seems instead that something (coincidence, nature&#x27;s desires, a proof yet undiscovered) is conspiring to prohibit all of them.<p>The Gödel Metric, for instance, is just a toy universe. It has a cylindrical topology (unlike ours), a negative cosmological constant (unlike ours) and finely tuned cosmological parameters that don&#x27;t match ours. Showing we don&#x27;t live in this universe is trivial. Showing we don&#x27;t live in that universe <i>simply because it has time travel</i> still eludes us.