Can Faster-Than-Light Travel Allow You to Return Before You Set Out?

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The discussion revolves around the concept of faster-than-light travel and its implications in spacetime, particularly whether one could return to their starting point before they set out. Participants explore the nature of spacetime intervals and the representation of such scenarios in spacetime diagrams.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants examine the implications of traveling faster than the speed of light, questioning the validity of spacetime diagrams in such contexts. They discuss the nature of spacelike intervals and how different inertial frames might affect the perception of time and travel.

Discussion Status

The conversation is ongoing, with participants offering insights into the complexities of spacetime and the challenges of visualizing these concepts. Some have suggested that the original poster's confusion may stem from the assumptions about inertial frames and spacelike intervals, while others are questioning how to accurately represent these ideas in a diagram.

Contextual Notes

There is a focus on the limitations of traditional spacetime diagrams when considering faster-than-light travel, as well as the implications of changing inertial frames. Participants are grappling with the definitions and assumptions that underpin their understanding of the problem.

ehrenfest
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Even if someone could travel faster than c, could he return before somewhere before he set out? Could she arrive at some intermediate destination before she set out? Draw a spacetime diagram representing this trip?

OK. Obviously the first question is no because in a spacetime diagram your wordline would just get closer and closer to the x-axis the faster you travel.

However, I am confused about the point of second and third questions. The second question is obviously no for the same reason, but what is it getting at? And how can you draw a spacetime diagram since it is impossible?
 
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It's not so obvious. If you can travel faster than c, then your origin and destination define a spacelike interval. That means that there is another inertial frame in which the origin is in the future of the destination. So the traveler could boost into that frame and then by traveling faster than c, could return to the origin before he left.
 
Wow. That's true. So my argument holds only when you stay in a single inertial reference frame. I am still confused about what the question wants me to draw. How do you represent that in a spacetime diagram?
 
Don't really know what they want you to draw, but from the viewpoint of the stay at home observer, it's pretty simple. He travels out on a spacelike line, then adjusts his frame and returns on another spacelike line joining him with a point t<0 on the observer's timeline. You can see that the restriction that he can only reach spacelike points with t>0 is artificial, by adjusting his frame he can reach any spacelike point.
 
Dick said:
Don't really know what they want you to draw, but from the viewpoint of the stay at home observer, it's pretty simple. He travels out on a spacelike line, then adjusts his frame and returns on another spacelike line joining him with a point t<0 on the observer's timeline. You can see that the restriction that he can only reach spacelike points with t>0 is artificial, by adjusting his frame he can reach any spacelike point.

Okay. He starts at rest in S. Let's say his (maximum) velocity is 3/2c. Then he travels 3/2c meters in a second and then stops. t is now 1 in S and some very small number for the traveller. How can you be sure that there are points with t < 0 that are accessibly to him? Is there a maximum distance he can travel before points with t<0 become inaccessible to him?
 
Because he's now spacelike separated from his origin. I thought we agreed there were frames in which his origin is in the future of his current location. Try a Lorentz transformation at his current position and see what's accessible at the origin. Though I'm not sure it's worth messing around with the numbers too much.
 

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