Having read “A World Without Time” some years back, I seem to recall Kurt Godel “proving” (to Einstein’s satisfaction, anyway) that time is a closed loop and, since time and space are kinda the same thing, it should be possible to fly in a rocket ship from one part of the loop to another. Leave today and arrive last Thursday, or in the year 2525, with no fancy hyperdrives, worm-holes, etc. – just your garden-variety space ship. He supposedly even calculated how fast the ship would have to go and how much fuel it would take!
So–have I got the gist of that right? And if so, does it mean we maybe need to rethink some of the stuff my logical positivist friends and I have been laughing at all these years: ufo sightings, ladies talking on cell phones in silent movies, etc?
You don’t know what logical positivism is. It means that the Universe is knowable and, therefore, we only take things into consideration once we have sufficient evidence to conclude they’re real. (More simply, it holds that things which can’t be verified in some manner are nonsense, neither true nor false.) Unless and until we have that for these things, we don’t need to take them very seriously.
In short, the burden of proof is on the person making the claim, not the person refuting it.
Hope that helps a bit, although maybe the articles are too technical. I think here’s the important bit:
“[The Goedel metric’s] definition is somewhat artificial (the value of the cosmological constant must be carefully chosen […]), but this spacetime is regarded as an important pedagogical example.”
Kurt Godel proposed a possible set of laws for the universe, not inconsistent with what we know, in which time travel is possible:
He did not say that this is necessarily how the universe works. He said that there is a possible reformulation of physical laws in which time travel is possible. The general opinion is that this is a cute idea, but there is no proof whatsoever that this is how the universe works. This idea was not really considered likely by anyone, and it certainly wasn’t proved to Einstein’s satisfaction. Scientists frequently do this. They will come up with a reformulation of the laws of the universe in some interesting way. Sometimes the reformulation makes no testable predictions. Sometimes it makes a prediction that can be shown to be incorrect. Only very rarely does it make a correct prediction.
Figured it must be something like that ("…cute idea, but…no proof whatsoever"), but can’t say the author of “A World Without Time” gave that impression. When he says Godel actually calculated the amount of fuel, speed, etc., he should have added a caveat along the lines of “assuming Godel’s model of the universe is correct–which nobody thinks too likely.”
But I suppose you’ve gotta admit that drains off a bit of the excitement.
Well, it’s not really a ‘reformulation’ of the laws of physics – the Gödel metric is a solution of Einstein’s equations, i.e. a possible way for spacetime to be, which allows closed timelike curves, which are well known to be possible in general relativity (though usually somewhat pathological). IIRC, it describes a rotating universe, which I don’t think is consistent with current observation.
'Fraid not; the time dilation effect is proportional to “how deep the gravity well is” (in a mathematically well-defined sense.) Earth’s gravity well, even at the center of the Earth, simply isn’t deep enough to cause “infinite time dilation” like you want. You need a black hole for that; if you hover just outside the event horizon, you’ll live forever. Or at least until your spaceship’s fuel runs out and you fall in.