And you have it partially correct. Darby60 can indeed move forward in time at any rate up to but not including an infinite rate. Darby90 cannot move backwards in time for two reasons.
To be sure, to accomplish the following involves engineering - not physics - that is currently unobtainable. First, we are all moving forward in time because that is where the arrow of time points. Second, we are not all moving forward in time at the same rate. That rate is fully defined by the gravitational strength of field in which we find ourselves and our speed with respect to the laboratory or rest frame (in this case the Earth). If darby60 travels at .9999999999 c the gamma factor will be 70711. For every hour ticked off on darby60's clock inside his vehicle 70,711 hours will tick off in the laboratory frame.
Divide 30 years by 70711 hours and the result is .0000424262 years which translates to ~3 hours 45 minutes. It will take darby60 3 hrs 45 mins to travel 30 years into the future at the velocity. No law of physics has been violated and no unusual permutation of known physics needs to be called into play. In less than 4 hours darby60 will be 30 years into the future having aged only those ~4 hours. The question is, would he meet himself? No. There is no darby90 in the future. darby60+4 hours is the only darby to be had. He never traveled at the slow rate to arrive 30 years in the future.
Now the question is can darby90 travel back in time 30 years to meet darby60? The answer is probably not and at the present time, given the state of our understanding of General Relativity, the answer is a qualified no, he cannot travel back in time. The qualifier is every hypothesis H1 must be stated such that it can be nullified. That means, "Well we cannot do it today but there's always tomorrow. And tomorrow it is possible that someone will discover something new."
As of today, and yes I know this is a time travel forum, there is absolutely no viable theory of time travel to the past let alone a viable blueprint to build a time gadget. There are real physics papers that have been published and peer reviewed with positive feedback. But those are all, every one of them, gedankenexperiments that are completely hypothetical. They all depend on the experimental system's state to be in configurations that are either known to be even theoretically impossible (e.g., Tipler's Cylinder which is required to be infinitely long thus infinitely massive and rotating with an angular velocity very near the speed of light) violate the known laws of physics as we currently understand them or require other system states where the universe has to be configured in ways that simply do not match observation.
How close are we to having a viable time travel gadget, assuming it is even possible? 500 years? A 1000 years? Who knows. I can guarantee you that it won't be 2036, 11 years from now. Titor notwithstanding, GE is busy researching theoretical semiconductor science and quantum computing. I don't see any sign that they are building a time machine that by Titor's own description would instantly destroy the Earth if activated on the Earth leaving absolutely no life left except, maybe, marine species..
yes, I do not think our science has a working concept of time or gravity, which seem to be two sides of the same coin. If we do not understand what gravity waves or gravatons are, we also cannot understand what time actually is.
There is a physics book called "The End of Time: the next revolution of physics" its author proposes that everything is made of static frames. Each frame is like a snapshot of reality, or unique configuration. The arrow of time is the movie projector sequentially running through all these configuration spaces
x, 371 pages :
archive.org
So, if you were able to go against the arrow of time, what would you see? would you be going backwards through all the configuration spaces, as if the projector was running the movie in reverse?
My take is you cannot run backwards against the arrow of time because the universe is continuously expanding, and the expansion is carrying you with it as state time from the big bang gets stretched out into spatial time. The closest analogy is trying to walk down to the base of an escalator whose steps are moving upwards.
My assumption is the big bang did not destroy the singularity it originated from. The singularity is still there, and only parts of it expanded to form our "world". We measure time through spatial displacement. How do you do that in a singularity that has no space? You can measure the changes in the state of its energy levels. because only a stretching out of the singularity happened to create "new" space, you can map the singularity's state time to the universe's stretched out spatial time.
So, to go against the arrow of time, you have to first leave our universe and get out of the expansion. Then, you have to follow the state/spatial mapping outside the universe to an earlier point in the arrow of time and re-enter the expanding universe. At this point, you will appear to have travelled backwards in time. It's more like teleportation than running a movie in reverse.
The end of time book does not go into such teleportation. It only talks about configuration spaces.
How do you leave our universe? You create a small gravity bubble that behaves like a mini universe, which you ride in like a car, inside of the ethereal similarity the universe came from. There is some transition space in which you do not actually have to be at the center of the singularity, just on the outskirts of it.
And, the ethereal singularity has to be spinning to expand in the first place into new space. It has to be a Kerr black hole. So you have to be on the outskirts of its inner horizon, in your gravity bubble universe, on the expansion side.
Taken all together, this is the holographic principal in physics in action