I’m not sure what you mean by “topologically-identified space”. Looking around, I suspect it’s the difference between a universe being spatially a 3-sphere Vs. a 3-torus, with only the 3-torus version having a preferred frame. Is this basically it?
If so, I don’t think this is relevant to whether you can have a space which simultaneously has a topology with a preferred reference frame and which satisfies Special Relativity. I only need one example.
If you had a working Alcubierre Drive, and wanted to use it as a time machine instead of a FTL drive, how would you configure it?
Be sure to cool it with baboon’s blood.
Thanks. I’ve seen this explained here many times, and I can never hear enough about the middle graf, the money graf.
But, as someone holding on to analogies with the skin of my teeth, in my 3-D physically perceived world, two objects on an expanding balloon do have greater distances between them at t+n. Their addresses on the map stay the same and their distances are always proportionally the same relative to tn-1, but separate they do.
Fucking analogies.
ETA: “…their distances are always proportionally the same relative to tn-1” is a pretty loaded, and wrong, sentence, I think. Is it? Spacetime can change non-homogenously, right?
I would dial in the desired date and time on the little LED display, hit the gas, and try to get to 88 mph before I run into the photo development booth.
Right, and I didn’t mean to imply otherwise. Strictly speaking, such a space does not globally satisfy SR, but it does satisfy it locally, which is almost always all that one’s interested in.
I see what you’re saying, but I’d like it if Dopers, when correcting other Dopers, not only point out the mistake, but also suggest a better option.
Maybe we have different definitions of Special Relativity. To me, it means the constancy of the speed of light (plus, I guess, space being isotropic and homogeneous), and everything that then follows from that. The lack of a locally preferred reference frame then falls out it as an effect, not a starting requirement. The lack of a preferred reference frame that can only be found using global measurements doesn’t follow from that, so it doesn’t really make sense (to me) to say it doesn’t globally satisfy Special Relativity.
Going back to my earlier post, is it actually the case that if the universe is spatially closed as a 3-sphere, it wouldn’t have a preferred reference frame? Or is that not even what you were saying? It’s hard to visualize, obviously, but visualizing 2+1 dimensions, with space a 2-sphere and time radial, I would think you’d still have a single preferred frame. From there to a 3-sphere plus time doesn’t seem that big of a leap.
Yes, yes. Everyone who slept through Philosphy 101 knows that the OP used the colloquial definition.
Have a cookie.
With the Universe as a 3-sphere, you could define something that behaved in some ways like a globally-preferred reference frame, but it would be really weird if you tried to interpret it that way. Basically, you’d be defining a reference frame for a higher-dimensional embedding space, not for our space itself.
Can you point me to something that talks about this?
This is a very important question, and deserves an answer from someone who knows more about this than I. But as far as I under stand it, the fact that the interior of the Alcubierre warp bubble is immune from time dilation doesn’t prevent the warp bubble as a whole from being used as a faster-than-light messaging system.
If you can communicate using a FTL messaging system between two observers who are both travelling slower than light but at significantly different velocities, then it could be possible for one observer to communicate with the past of the other one, and vice-versa. If you send the message back and forth at least once, you can end up communicating with your own past. The message you send could even be your own self, if the bubble is big enough.
Ursula K. Le Guin did not report this problem.
But the stock exchange…
The short answer to how to configure your warp-drive ship as a time machine is that your ship also needs to have conventional engines, and the top speed attainable by your regular engines times the top effective speed attainable by your FTL drive has to be greater than c^2. Then it’s just a matter of getting up to the right velocity using your conventional engines before engaging the warp drive.