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Most works of fiction have quite imaginative views of time travel. Mighty machines that teleport in time instead of space. Gaping portals in space that take you to another time. Mystical beings with a special power to move freely in time, sometimes taking a mortal companion.

Physicists, on the other hand, sometimes have different ideas. Willem Stockum, for example, showed that general relativity is consistent with a type of time travel where you walk in a circle and end up in the past, no machines, portals, or mystical powers necessary. Okay, you might need to run depending on how big the closed time-like curve is. Gödel also studied this type of time travel.

My question is if a world's equator could be a closed time-like curve, making the first person to go around the world (via the equator) also the first time traveler.

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  • $\begingroup$ This sounds like an interesting question of theoretical physics. Since you also want a hard-science answer, have you considered posting it on Physics.SE? $\endgroup$
    – L.Dutch ♦
    Commented Feb 8, 2019 at 6:02
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    $\begingroup$ @L.Dutch I'm not sure how well received it would be there, since its talking about a fictional world. $\endgroup$
    – Christopher King
    Commented Feb 8, 2019 at 6:05
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    $\begingroup$ it would be funny to see a theoretical physicist with a 20-dimensional word sketched on his blackboard object that this question is about a fictional word.. :) but I see no issues in having it here on worldbuilding. Just wanted to be sure you considered the option. $\endgroup$
    – L.Dutch ♦
    Commented Feb 8, 2019 at 6:09
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    $\begingroup$ I made a few edits to your question. First, you didn't have the tag [time-travel] which seems kind of basic. To make room, I removed [alien-geometry] which I wasn't sure fit. But if you want it, swap something out for it. You said "fanatical" in the first line but I was pretty sure you mean "fantastic." That word is correct but most Americans use it to mean "super great" so I changed it to "imaginative." I made a couple other edits that might not be what you wanted. Please check them and make sure. Change back anything I got wrong. $\endgroup$
    – Cyn
    Commented Feb 8, 2019 at 18:10
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    $\begingroup$ @Cyn Yeah, the edits are good. $\endgroup$
    – Christopher King
    Commented Feb 8, 2019 at 18:21

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As far as I'm aware, closed time-loops of the sort you suggest (taking a fixed path through space and arriving back at a location prior to your departure without using faster-than-light travel) have only been proved for orbits around rotating infinitely long cylinders of infinite mass.

Therefore closed time-like curves are not a plausible feature of any sane planet. Closed curves can only be accessed introducing specific, weird categories of singularities. Which is to say, you need to hang out near something as extreme as a black hole AND add an array of further weird constraints. These are incompatible with anything like a planet as we understand it.

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  • $\begingroup$ Also, say the circumstances are meet to allow it. Your would miss earth, since it rotates around the sun, which moves on the milky way, and even the milky way moves. So how do you take into account the position you need to arrive at for a given time? $\endgroup$
    – Gustavo
    Commented Feb 13, 2019 at 21:22
  • $\begingroup$ Motion is relative. The closed-timelike loop is a loop centred on the causative gravity well. The perception of the path shape by a distant observer is irrelevant (although they would agreed that you orbited the object in a closed loop) $\endgroup$
    – Mark_Anderson
    Commented Feb 13, 2019 at 21:48

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