Gödel says the absence of a global time function
seems to imply an absurdity. For it enables one e.g., to travel into the near past of those places where he has himself lived.
But is it not true that, given sufficient knowledge of the topology of spacetime and velocities, a global time function could be created?
To illustrate simply. Three spacecraft could depart from Earth to various regions of space, and if they have enough information they could each operate adjusted clocks to show Earth-time. And if they travelled back to Earth their adjusted clocks would still be in sync when they arrived.
The possibility that this could be done is surely sufficient to say, in principle, that a global time function can exist, (and Gödel's absurdity would not).
Obviously obtaining the topology information is not simple, but possible, in principle, so the clock adjustments could be made.
I would appreciate any answers as to whether or not this could be done.
Additional note
Material supporting this view from a review of Einstein, Relativity & Absolute Simultaneity
The astronomer Van Flandern contributes a highly readable essay on "Global Positioning System and the twins' paradox", arguing that GPS is "a practical realization of Lorentz's 'universal time', wherein all clocks remain synchronized despite being in many different frames with high relative speeds". In essence, the GPS system considers one frame, the local gravitational field (read, Lorentzian ether), to be privileged: here alone clocks tick at universal time, lending a new, technology-infused meaning to Lorentzian relativity.
