Question:
Much of what I here spoken about time travel seems to relate more to historical time, in other words moving from the past to the present and then on to the future. The arrow of time as you said.

Where I’m having difficulty is trying to connect this to the time fluctuations experienced on board a moving space ship when it passes through gravitational waves.

I’m completely unqualified to answer your question (and in fact I don’t even have a sastifying answer), but I’ve spent some thinking about the exact same problem and I thought I would offer you the explanation I eventually came up with.

I think it comes down to the relativity of simultaneity. Let’s say a space ship is moving at 99% of c and you’re stationnary. When the ship passes you by (i.e. when you’re at the same position), you both set your clocks to 0. Now, say you wait a second in you reference frame. Then you will observe that time moves more slowly on the ship; its clock only indicates 0.14 s (if I’m not mistaken) instead of 1 s :

Your reference frame:
Your clock: 1 s
Ship’s clock: 0.14 s

But, see, the problem is that you’re implicitely assuming that you’re mesuring the time on both clocks at the same time. However, simultaneity is relative; there is not way to synchronize the two events — you looking at your clock and the ship looking at its clock — for both reference frame. Therefore, the people on the ship will NOT agree that when their clocks indicate 0.14 s, yours is at 1 s. Instead, they will find that:

Ship’s reference frame:
Ship’s clock: 0,14 s
Your clock: 0.0199 s

I came this far on my own, but then found out that Wikipedia already had a (much better) explanation:

http://en.wikipedia.org/wiki/Time_dilatation#Time_dilation_due_to_relative_velocity_symmetric_between_observers

Anyway, beyond this point, my thinking is still fuzzy. I’m currently of the opinion that I should try to understand the Lorentz transformation first and foremost, and see all the rest (time dilation, length contraction, relativity of simultaneity, etc.) as special cases or consequences. Every time I’ve tried to understand special relativity, I always end up hitting a wall because the concept seem to make no sense on their own… they always lead to the kind of problem you’ve brought up.

But I still hope I’ll understand it one day.

Great talk. Though there a question asked at the end that I also have had. I think I know what the guy was asking and I don’t think you answered it (or maybe you did and I’m just not understanding). If a space ship is moving at 99% of c and I am stationary, you say that a clock on the space ship with be moving slower, relative to my clock. But a person on the spaceship would observe themselves being stationary and me moving at 99% of c. Right? It seems like this argument privileges the space ship’s clock over my clock, and I thought that was wrong, based on special relativity. Of course I know I haven’t found a flaw with Einstein’s theory(!) so I wonder if you could explain where my thinking has gone haywire.

BTW I am really enjoying the book, but I’m not finished yet, so maybe you get to this point.

Thanks.