# starship-design: Increasingly less Fun with Spacetime

```(I've tried sending this letter some hours earlier, but it doesn't seem to
have reached SD)

Ken replied to Lee:

>In order to spell this out more clearly, I only used one "type" of FTL
>journey -- 500c from the current frame of the ship.  In both of the FTL
>legs, from Dwight's perspective, the time at Earth advances in a positive
>direction.  This way you can't say that the FTL is taking Dwight back in
>time and disallow it on those grounds alone.  The back-in-time leg was the
>sub-light journey that Dwight starts out with!  His journey away from Earth
>at 0.4c is the only vector in which time seems to "go backwards" at Earth.

??? As far as I understand time doesn't go backwards when you move, it just
goes slower.

>Now, this "back-in-time" behavior will happen with or without FTL.  This
>happens in the twin paradox when one twin turns around; the stationary twin
>"sees" the other twin travel backwards in time.

No, I don't think so:

(The numbers between braces show the clockrate)

With respect to the stationary twin, the moving twin's clock:

- ticks at the same rate as the stationary clock before it leaves Earth. (1)
- starts ticking slower during acceleration. (1->0.5)
- ticks slowly forwards during the period of no acceleration. (0.5)
- starts ticking faster when the ship decelerates. (0.5->1)
- ticks at the same rate as the stationary clock when the ship has a zero
relative velocity. (1)
- starts ticking slower during acceleration towards Earth. (1->0.5)
- ticks forwards at a slower rate during the period of no acceleration. (0.5)
- starts ticking faster when the ship decelerates. (0.5->1)
- has the same rate when his brother is back on Earth again. (1)

With respect to the moving twin, the other twin's clock:

- ticks at the same rate as the stationary clock before it leaves Earth. (1)
- starts ticking slower during acceleration. (1->0.5)
- ticks slowly forwards during the period of no acceleration. (0.5)
- suddenly increases speed very much as soon as deceleration starts. (0.5->3)
!The tick rate is much faster than a clock at rest!
- keeps ticking very fast during the deceleration, but slowly decreases
speeds until the moving twin has come to rest and then has the same
tick rate as Earth's clock. (3->1)
- starts ticking faster again when the twin accelerates towards Earth. (1->3)
- drops it ticking rate quite suddenly when acceleration stops. (3->0.5)
!The tick rate drops from going faster than normal to slower than normal!
- ticks slowly forwards during the period of no acceleration. (0.5)
- starts ticking faster when the twin decelerates (0.5->1)
- has the same rate when his brother is back on Earth again. (1)

So the stationary twin thinks his brother lived slower or equal all the time.
But the moving twin thinks his brother first lived slower, than started
living hyperfast, and finally slower again. However his brother lived
hyperfast more than he lived slower, so the net result is that his brother
lived faster.

>But this is not a true
>paradox, because by the time they catch up to each other, time has still
>advanced for both of them; you can never get a net-negative time without
>FTL.

It isn't a paradox at all, as long as you point out all the facts. (Which I
hope I did.)

Timothy

NB. I'm aware of unreal and real timedilation. In my previous messages I'm
not confusing light-travel-time with timedilation.

NB2. I believe Ken's multi-camera observing system is also called a freezed
frame or a snapshot. My whole explanation above is in such frames of reference.

```