What do you mean by “simultanously”? You’ve used it to refer to events which do not occur at the same place.
I think that you’ve shown that the distance between your departure point and Mars is six light years; you’ve done that by moving space around such that the point you departed from is in the vicinity of Alpha Centauri.
Space and time aren’t defined to be static in the way the math I understand requires it to be.
What do you mean by “simultanously”? You’ve used it to refer to events which do not occur at the same place.
The details are not significant. Simultaneously in the rest frame of earth. Whatever. Or send a timing signal from Mars to Earth at the same time as the radio message is emitted toward Alpha Centauri, then leave Earth when you receive the timing signal. You’ll still arrive before the radio message, even though you’ve given it a head start.
I think that you’ve shown that the distance between your departure point and Mars is six light years;
The distance between Earth and Mars is 225 million km on average, or 12.5 light minutes.
If you like, you can send your radio message from the same location as your departure point. First emit a (directional) radio signal from earth toward Alpha Centauri. Then depart in your spaceship, just making sure not to collide with the radio signal on your way there (go a different way, say by taking a pit stop at Vega). You’ll still get there before the light signal.
you’ve done that by moving space around such that the point you departed from is in the vicinity of Alpha Centauri.
In a sense, yes, that is exactly what an alcubierre drive is meant to do. The trajectory that starts at Earth, enters the bubble, sits there a while, exits the bubble and arrives at Alpha Centauri travels “locally” less than six light years. The bubble train might be analogised to a wormhole in that it establishes a shorter path between two otherwise distance places.
But unlike a wormhole, the Alcubierre drive doesn’t require you set up the path and destination in advance (unless Krasnikov is right, and there aren’t any tachyons), and it’s an effect confined to the vicinity—in space and time—of the ship using it. So in all meaningful senses it can reasonably be described as a faster than light drive, as opposed to a bridge, which is what a wormhole is.
That ‘directional radio signal’ is taking a longer path, as noted by the fact that a different directional radio signal (one that went with the traveler) would get there first.
Are you using a Euclidean definition of speed? Part of the insanity is that the payload, inside the bubble, can be at rest relative to the origin and/or destination, despite the distance changing.
Sanity check: before, during, and after the trip, shine a laser continuously ‘forward’, toward the destination. Turn off the bubble well short of arrivial. What pattern of red shifting should the destination expect to see?
Part of the insanity is that the payload, inside the bubble, can be at rest relative to the origin and/or destination, despite the distance changing.
I’m sure it only looks like insanity to people who haven’t studied general relativity.
The point is that an Alcubierre drive lets you get from here to Alpha Centauri (which I now discover is actually 4.4 light years away, since I finally decided to look it up just then) in less than 4.4 years. Whether it does that by temporarily making the distance shorter along a certain path is mostly irrelevant for the purpose of classifying it as a particular kind of starship drive.
The point which started the discussion is that you don’t get to look back and see yourself leave. (probably; I’m not certain how light behaves when there is more than one ‘straight line’ path, of different lengths, to the destination; that seems like is could happen if you took a dogleg around the most direct path.
The radio signal and the ship leave from points that are near each other in the space-time metric. In other words, simultaneous from a reference frame in which they are physically close.
You’ve moved space around, but only for a small local (space-time wise) area; you haven’t permanently moved the two stars closer together.
If the radio signal ever touches the bubble, it arrives before/with the non-light content of the bubble.
You’ve moved space around, but only for a small local (space-time wise) area; you haven’t permanently moved the two stars closer together.
The point of departure is now six years away from points that it was previously nearby.
Imagine a strip of topology rubber running the length of the trip; you start next to one end, but instead of moving along the strip, you compress it in front of you and stretch it behind you.
And in any case, you’ve moved a ‘cylinder’ of spacetime roughly 6 light years long. Just because you’ve expanded just as much as you’ve compacted doesn’t mean you’ve expanded the ‘same’ spacetime that you’ve compacted.
So go around the radio. Or use a laser beam or high energy particle beam (near-c, not c, obviously) if you’re worried about diffraction and aiming or refraction of your bubble.
When you get there and turn off the warp drive, space is now flat. (We’ll assuming no one else is making the journey recently / soon / nearby / whatever.) You’re saying the original point of departure is now near where you ended up. I say that’s a distinction that doesn’t matter, and all that’s relevant is that you were near one star, now you’re near another, and at no time were those stars near each other. And you got there faster than a photon / high energy particle / whatever could have, via the normal route.
What experimental result do you anticipate, that distinguishes between the “original departure point” having moved, versus my assertion that all points in space are distinguishable only by things like what matter / energy is occupying them (and the curvature that results)?
A suffienctly flexible braided rope, fixed to Earth and some point beyond the destination, with a splice in it at the point of departure: the splice will end up at the point of arrival, but the number of braids on either side will remain constant and no tension will be noted at either end.
A lack of time-dialation effects on the transported cargo-an atomic clock that made the round-trip would remain synced with one that didn’t, showing that it hadn’t moved.
I’m saying that the path you took is shorter than the naive one. There is no meaningful discussion of instant distance between two points/objects in general relativity; that’s a holdover from Euclidean geometry with time-variable additions.
Finally, the math.
What do you mean by “simultanously”? You’ve used it to refer to events which do not occur at the same place.
I think that you’ve shown that the distance between your departure point and Mars is six light years; you’ve done that by moving space around such that the point you departed from is in the vicinity of Alpha Centauri.
Space and time aren’t defined to be static in the way the math I understand requires it to be.
The details are not significant. Simultaneously in the rest frame of earth. Whatever. Or send a timing signal from Mars to Earth at the same time as the radio message is emitted toward Alpha Centauri, then leave Earth when you receive the timing signal. You’ll still arrive before the radio message, even though you’ve given it a head start.
The distance between Earth and Mars is 225 million km on average, or 12.5 light minutes.
If you like, you can send your radio message from the same location as your departure point. First emit a (directional) radio signal from earth toward Alpha Centauri. Then depart in your spaceship, just making sure not to collide with the radio signal on your way there (go a different way, say by taking a pit stop at Vega). You’ll still get there before the light signal.
In a sense, yes, that is exactly what an alcubierre drive is meant to do. The trajectory that starts at Earth, enters the bubble, sits there a while, exits the bubble and arrives at Alpha Centauri travels “locally” less than six light years. The bubble train might be analogised to a wormhole in that it establishes a shorter path between two otherwise distance places.
But unlike a wormhole, the Alcubierre drive doesn’t require you set up the path and destination in advance (unless Krasnikov is right, and there aren’t any tachyons), and it’s an effect confined to the vicinity—in space and time—of the ship using it. So in all meaningful senses it can reasonably be described as a faster than light drive, as opposed to a bridge, which is what a wormhole is.
That ‘directional radio signal’ is taking a longer path, as noted by the fact that a different directional radio signal (one that went with the traveler) would get there first.
Are you using a Euclidean definition of speed? Part of the insanity is that the payload, inside the bubble, can be at rest relative to the origin and/or destination, despite the distance changing.
Sanity check: before, during, and after the trip, shine a laser continuously ‘forward’, toward the destination. Turn off the bubble well short of arrivial. What pattern of red shifting should the destination expect to see?
I’m sure it only looks like insanity to people who haven’t studied general relativity.
The point is that an Alcubierre drive lets you get from here to Alpha Centauri (which I now discover is actually 4.4 light years away, since I finally decided to look it up just then) in less than 4.4 years. Whether it does that by temporarily making the distance shorter along a certain path is mostly irrelevant for the purpose of classifying it as a particular kind of starship drive.
The point which started the discussion is that you don’t get to look back and see yourself leave. (probably; I’m not certain how light behaves when there is more than one ‘straight line’ path, of different lengths, to the destination; that seems like is could happen if you took a dogleg around the most direct path.
The radio signal and the ship leave from points that are near each other in the space-time metric. In other words, simultaneous from a reference frame in which they are physically close.
You’ve moved space around, but only for a small local (space-time wise) area; you haven’t permanently moved the two stars closer together.
If the radio signal ever touches the bubble, it arrives before/with the non-light content of the bubble.
The point of departure is now six years away from points that it was previously nearby.
Imagine a strip of topology rubber running the length of the trip; you start next to one end, but instead of moving along the strip, you compress it in front of you and stretch it behind you.
And in any case, you’ve moved a ‘cylinder’ of spacetime roughly 6 light years long. Just because you’ve expanded just as much as you’ve compacted doesn’t mean you’ve expanded the ‘same’ spacetime that you’ve compacted.
So go around the radio. Or use a laser beam or high energy particle beam (near-c, not c, obviously) if you’re worried about diffraction and aiming or refraction of your bubble.
When you get there and turn off the warp drive, space is now flat. (We’ll assuming no one else is making the journey recently / soon / nearby / whatever.) You’re saying the original point of departure is now near where you ended up. I say that’s a distinction that doesn’t matter, and all that’s relevant is that you were near one star, now you’re near another, and at no time were those stars near each other. And you got there faster than a photon / high energy particle / whatever could have, via the normal route.
What experimental result do you anticipate, that distinguishes between the “original departure point” having moved, versus my assertion that all points in space are distinguishable only by things like what matter / energy is occupying them (and the curvature that results)?
A suffienctly flexible braided rope, fixed to Earth and some point beyond the destination, with a splice in it at the point of departure: the splice will end up at the point of arrival, but the number of braids on either side will remain constant and no tension will be noted at either end.
A lack of time-dialation effects on the transported cargo-an atomic clock that made the round-trip would remain synced with one that didn’t, showing that it hadn’t moved.
I’m saying that the path you took is shorter than the naive one. There is no meaningful discussion of instant distance between two points/objects in general relativity; that’s a holdover from Euclidean geometry with time-variable additions. Finally, the math.