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Question Regarding Spacetime Coordinate Rotation in TIME: A TRAVELER'S GUIDE

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Question Regarding Spacetime Coordinate Rotation in TIME: A TRAVELER\'S GUIDE

Hi:

This is a question regarding a diagram in Clifford Pickover's book TIME: A TRAVELER'S GUIDE. If you don't have access to the book, it would be difficult for me to formulate the question such that you would know what I'm getting at. That being said...

In regard to Figure 11.1 (a spacetime diagram) in Chapter 11 of the book, Pickover indirectly describes what would happen if x' and t' (i.e., the "Alligator's Jaws")) were to rotate counterclockwise and clockwise, respectively, towards the 45-degree line. However, he doesn't seem to discuss what would happen if they were to rotate PAST the 45-degree line (i.e., if x' were to pass from 45 degrees to 90 degrees and if t' were to pass from 45 degrees to 0 degrees). So, what WOULD happen?

Also, he indirectly says that when x' and t' are both at 45 degrees, and the moving system is moving at the speed of light, time and space in the moving system have united and are indistinguishable. What's this supposed to mean? What would it feel like (i.e., if I was inside a spaceship moving at the speed of light, and I took a step forward inside the ship would I "go back in time" or something)? Also, couldn't it be argued that WE'RE always in a system that is moving at the speed of light relative to SOMETHING else (i.e., cosmic rays), despite the fact that time and space don't seem indistinguishable to us?

Thanks for any help!
 
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