Please set me straight about velocity based time travel

bobbarker00
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I just finished watching a hawkins program about time travel that theorized that the faster an object travels through space, the slower it moves through time. The example involved a trip to Alpha Centauri at 99.9% light speed. He claimed that although the trip would only take a few years to complete for the occupants on the ship, tens of thousands of years would have passed on earth.
I am not educated in physics, just a regular guy with a desire to learn, but I do have two questions about this concept that I would appreciate some clarification on-
1- Have I completely misunderstood the concepts outlined by this hypothetical?
2- If this concept is correct, let's say there are two vessels that left Earth at the same time to take the same trip to Alpha Centauri, one going 99.9% the speed of light and one going 1/2 the speed of light.
a. Would the vessel going closer to the speed of light arrive farther in the future?
b. Does that mean the vessel going slower wouldn't warp time to the same degree and therefore arrive earlier?
Again I'm sure that I have just completely misunderstood the concept, and I would appreciate being set straight on this matter.
Thanks in advance.
 
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There's no time travel involved. Different journeys through spacetime will take different times as measured by comoving clocks. If two people go from A to B to A at different speeds or routes, their clocks might differ when they get together again.

See the many threads on the 'twin paradox' in this forum.
 
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Thread 'Can this experiment break Lorentz symmetry?'

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Thread '1-Way Speed of Light'

Does the speed of light change in a gravitational field depending on whether the direction of travel is parallel to the field, or perpendicular to the field? And is it the same in both directions at each orientation? This question could be answered experimentally to some degree of accuracy. Experiment design: Place two identical clocks A and B on the circumference of a wheel at opposite ends of the diameter of length L. The wheel is positioned upright, i.e., perpendicular to the ground...
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Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
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