Originally posted by DeepThought
The Wikipedia pages on mathematics have a habit of making these things appear about twenty times harder than they actually are. Part of my reason for pointing you in that direction was because I couldn't work out what you were trying to say.
One criticism, you have time as a complex coordinate, but if we have time for slower than light particles as r ...[text shortened]... f sub-luminal half tachyonic description can provide a realist solution to the apparent paradox.
Yeah, Wiki has a way of compressing a books worth of knowledge, (or several) into a few short pages,to succinctly tell you about what you are after. However, comprehending all the new terminology at once makes it difficult to digest in a head spinning passive word reading experience.
One criticism, you have time as a complex coordinate, but if we have time for slower than light particles as real and imaginary for faster than light particles then what does a complex value for time represent - something going both slower and faster than light? On the other hand quantum mechanics does involve this "spooky action at a distance". Maybe your dual half sub-luminal half tachyonic description can provide a realist solution to the apparent paradox.
I was trying to imply that once "c" is met or exceeded "Real Time" stops or freezes, hence "Real Speed" ceases to have a meaning. You may travel through "Imaginary Time" (a time dimension orthogonal to real time) where perhaps the Lorentz Transformation still applies, but works to extend "Imaginary Time" with increased imaginary velocity. When you accelerate below "c" Real time begins again( speeding up as you decelerate), but you are no longer in the Real time that you began, but in a Real Time parallel to it. As for the backwards time travel, its only relative to the "rest time" experienced in the the parallel real time frame you arrived in, it doesn't seem that it would be an "absolute" backwards time travel just more of an offset from the head of the time arrow of the newly arrived at frame.
Now, perhaps exceeding "c" is the difference to arriving "absolutely" backwards in time, just as acceleration to "c" in "Real time" acts to propel the traveler into the future, the Lorentz Transform gives an opposite effect (extension) when traveling above "c" in "Imaginary time". So I don't know, that's where I'm at.
Another thing to consider: How does assuming complex time in this way effect the derivation of general relativity...Maybe GR as written its not the full picture, and when accounted for backwards time travel can be accounted for in the new relationships?