Alcubierre warp drive

[acrosome]

Originally Posted by lwcamp

So, start at Sol and warp to Sirius. Entering and exiting warp are events with a space-like separation. In your frame of reference exiting warp is either simultaneous or after entering warp - not a problem yet. Now when you are at Sirius, change your velocity by a lot so you are in a new reference frame (perhaps using the hovering method described earlier). Get into a reference frame where exiting warp happened a lot earlier than entering warp. Now warp back to Sol. You arrive before you left. If you want to be contrary you could try to cause a paradox, such as trying to ambush yourself and blow your other-self up before he leaves so you could never get back to blow yourself up.

So, to do this, at some point you'd need the ability to acquire an immense real velocity? In other words, just what sort of reference frame would allow you to observe that exiting warp occurred before entering warp?

[lwcamp]

Originally Posted by acrosome

So, to do this, at some point you'd need the ability to acquire an immense real velocity? In other words, just what sort of reference frame would allow you to observe that exiting warp occurred before entering warp?

That depends on how long the warp seems to take and how far you warp. Suppose we warped from Earth to a star 100 light years away. Suppose the time it takes in years is 1/10000th the distance in light years, so our journey takes 3.65 days. Since I don't know the answer yet, I'm going to work out the math. Let our departure event occur at position x0 = -100 ly and time t0 = -0.01 y and our arrival event is x1=0, t1 = 0.

Now assume that we can change our velocity in essentially zero time. I will use primes (') to denote the coordinates measured in the reference frame with a changed velocity. This gives us
x1' = 0
t1' = 0
and
x0' = cosh(eta) x0 - sinh(eta) t0
t0' = cosh(eta) t0 - sinh(eta) x0
The parameter eta is called the rapidity, and corresponds to a speed v = tanh(eta) * c. The function cosh is the hyperbolic cosine
cosh(x) = (exp(x)+exp(-x))/2
sinh is the hyperbolic sine
sinh(x) = (exp(x)-exp(-x))/2
and tanh is the hyperbolic tangent
tanh(x) = sinh(x)/cosh(x)
exp(x) means raise the base of the natural logarithm (often denoted e) to the power x (or e^x).

Since I don't feel like doing algebra right now, I wrote a quick program in c++ to run the calculations. For a speed of 0.0009999997 c (eta = 0.001, v ~ 300 km/s) I find that x0' = -100.00004 ly and t0' = 0.09000001 y. Since it still takes pretty near 0.01 year to get back, we would arrive at a time coordinate of t2'=0.01 y (and, of course, a space coordinate of x2' = x0' to a very good approximation, although to be rigorous we would include the change in position due to our relative motion). This is 0.08 y before we left, or about a month. So in this example you get back a month before you left (rigorously, we would transform from x2',t2' coordinates back to x2,t2 coordinates if you wanted to find out how long you had been waiting for your former self to jump in the frame of reference of the earlier you, but for these small velocities it doesn't make much of a difference, you still get back a month before you left in both reference frames).

In fact, in this example a change in velocity of little more than 60 km/s gets you back just before you left.

Luke

[acrosome]

Originally Posted by lwcamp

In fact, in this example a change in velocity of little more than 60 km/s gets you back just before you left.

So on any rational scale you'd either need instantaneous acceleration or really long and fast tramlines to do this? Well, heck, THAT ain't gonna happen in my campaign, so I guess I won't have to worry about players screwing with causality...

If I'm willing to assume that the exotic matter problem has somehow been solved I assume that stable wormholes are also possible. And after all, I'd have to assume that for the Alcubierre drive, anyway. So, how would they differ, in practice?

I'll have to google Krasnikov tubes...

EDIT- I looked up Krasnikov tubes. Both they and wormholes seem to have immense potential for screwing with causality, don't they? The Alcubierre drive as you explained it, assuming that I understand it correctly, seems to be a bit more difficult to (mis)use in that manner.

[lwcamp]

Originally Posted by acrosome

So on any rational scale you'd either need instantaneous acceleration or really long and fast tramlines to do this? Well, heck, THAT ain't gonna happen in my campaign, so I guess I won't have to worry about players screwing with causality...

Not so much instantaneous acceleration as the acceleration time is included in the travel time use for the example (such as 2.65 days warping and 1 day accelerating before warping back).

You can always say that the same thing that prevents wormholes from forming time machines works for warping as well - as soon as you are in a configuration in which a time machine is just barely possible, you get a sort of perfect resonator for quantum fluctuations that follow the time travel path and meet themselves to build up and amplify themselves to destructive levels. This not only prevents time machines but discourages people from trying.

Originally Posted by acrosome

If I'm willing to assume that the exotic matter problem has somehow been solved I assume that stable wormholes are also possible. And after all, I'd have to assume that for the Alcubierre drive, anyway. So, how would they differ, in practice?

In practice, the main difference would be that a wormhole wouldn't leave a physical artifact threading through the usual space we are used to between stars - the connection would occur through a bridge space-time that is outside the space-time that we would normally travel through. Thus, you wouldn't have to worry about an orbiting solar power station or something striking the tramline.

Also, think about the implications of a spacecraft being able to bottle itself up in a basement universe, connected to this universe only via an umbilicus the diameter of a proton. It would seem to be a near-perfect defense, for example. You could save a lot of propellant by not decelerating at your destination planet - just turtle up and plow into it, then dig yourself out (although at proton size you are likely to zip through the entire planet, so maybe this isn't the best example).

Warp tramlines likely operate on schedules - to get around the issues of information not being able to propagate from the inside of the warp bubble to the space-time in front of it (resulting in a metric pileup and singular surface, which gives you the nasty radiation problems) what you do is have the equipment on the tramline synchronized to pulse at the right time to give the effect of a superluminal disturbance traveling down the line without actually having to transmit the information superluminally. So if you have arranged for this to happen once per day, for example, you can only take the warp line once per day. With a wormhole you can go through any old time.

When forging new routes to distant unexplored stars, wormholes can potentially lead to wait times much shorter than what you would expect from the difference in coordinate time of sending a light speed signal and the signal arriving at the new star (you do this by exploiting the time dilation of the projected end of the wormhole, and the fact that the other end, the end left at home, is at rest with respect to the projected end when viewed through the wormhole). If you can do the same trick with a warp tramline, it is not so obvious.

Originally Posted by acrosome

I'll have to google Krasnikov tubes...

EDIT- I looked up Krasnikov tubes. Both they and wormholes seem to have immense potential for screwing with causality, don't they? The Alcubierre drive as you explained it, assuming that I understand it correctly, seems to be a bit more difficult to (mis)use in that manner.

As far as I can see, they all have the same potential for messing with causality - the method involved is the same in all cases and so the math tends to work out the same. As mentioned before, you can prevent this by invoking the causality protection postulate that destroys potential time machines before they form.

As an aside, I am getting a significant amount of deja vu from this discussion - Rick Robinson't Rocketpunk Manifesto blog recently features an entry on the limits of realistic FTL and I participated in the extensive discussion in the comment section. You might find reading through the comments interesting - we cover a lot of the ground you have been asking about, and you might get additional insights into how to structure your setting
http://www.rocketpunk-manifesto.com/...est-cheat.html
You might want to just skip through the parts where people digress to talking about the metaphysics of duplication, Herbert's kludge of shields in Dune, and other side-tracks, of which there are many. For example, you could start at this comment
http://www.rocketpunk-manifesto.com/...13686130748261
and not miss much.

Luke