Circular Geometry and Special Relativity

[vanderwallis]

In this thread, I am going to consider whether the theory of Special Relativity is " complete" so to speak. No, Im not talking about the fact that it does not cover for non-inertial reference frames and the gravitation problem - thats the business of General Relativity. Instead Im going to be considering things like faster than light motion and seeing whether special relativity actually offers any insight into this.
The tone I wish to convey is more of a curious student trying to explore this rather unchartered ( as far as I know) part of the theory, and I think it would be useful if we could discuss this and perhaps some of the more distinguished members could offer further insight into this.

I'll start by reminding you of the fundamental " postulate " of the theory ; that the speed of a body through space-time is always constant and equal to the speed of light. For a body at rest ( relative to some frame of reference) , all its motion is though time. Moving bodies have some of their motion through time diverted into motion through space ( keeping the motion through space-time constant and equal to c). I like to think of motion through space-time as a vector. Imagine the x - axis represents speed though space, and the y -axis speed through time. The length of the vector is always equal to c, but for a body at rest, the vector will point parallel to the y-axis, and for a photon it would point parallel to the x-axis. If we draw this vector from the origin and consider the locus of all possible points from rest to traveling at c, we get a quarter circle. The radius is equal to c and represents the constancy of motion through space-time.
But why should we stop at the quarter circle ? Why not draw a full circle ? This is where things get interesting. Because now we have a load of new points we can consider. Part of the circle now passes through the negative x- axis and negative y-axis so we have some new interesting situations we can consider.
We can now have objects that travel :
1. Positively through time , negatively through space.
( +ve y-axis , negative x-axis) - 2nd quadrant
2. Negatively through time, negatively through space.
( -ve y-axis , negative x-axis) - 3rd quadrant
3. Negatively through time, positively through space.
( -ve y-axis , positive x-axis) - 4th quadrant

For all these objects ( or bodies or whatever you want to call them ) , the motion through space-time is still c - remember constant radius).
So of what importance are these new situations ? What do they mean ?

What does it mean to travel positively through time and negatively through space ?!
- Just motion in the opposite direction as I see it ( not too amazing ! )

What about Negatively through time, positively through Space ?
- This is the 4th Quadrant. Think about the circle again, the vector that represents motion through space-time is below the x-axis while still keeping its length constant. When we think about it this way, we can see that the speed of motion through space actually decreases below c as we move the vector further down like the arm of a dial. This is quite puzzling if you think about it, and once and for all banishes the idea of " Tachyons" that travel through space faster than c . According to the circle, this is impossible - goodbye Tachyons !
So what is this telling us ? It tells us we can have objects in this Universe that appear to be normal in that they travel through space at speeds below c , BUT they travel back in time ( relative to the observer ). If certain properties depend on the direction of time then perhaps reversing the direction of time will reverse the properties ! What could these objects ( bodies) be ?

[Max™]

There are too many issues with the tachyonic concept in general as is, and objects with negative electrical charges "face" the past.

[MikeInfinity]

Thanks for your thoroughness.
Space is a system of associated points, Time is a succession of instances.

What does it mean to travel positively through time and negatively through space ?!

It wold mean to travel into the future yet remain in the same location.

What about Negatively through time, positively through Space ?

You could travel anywhere in space by simply going back in time at least 1 sec (or less but you must travel backwards).

[MikeInfinity]

I’m not a technical toe questor but I search for the general principals behind the particulars of a given subject. Like how the Wright Brothers weren’t scientist yet invented the airplane. My friends and I are attempting to build a simple time machine, a box that can turn a clock backwards or turn a burned cigarette back whole. These suppressed documents are invaluable to a student of science.... here are a few notes from the:

Possibility of Experimental Study of the Properties of Time by N. A. Kozyrev

http://www.rexresearch.com/articles/kozyrev.htm

I. Time possesses a quality, creating a difference in causes from effects, which can be evoked by directivity or pattern. This property determines the difference in the past from the future.

II. Causes and results are always separated by space. Therefore, between them there exists an arbitrarily small, but not equaling zero, spatial difference.

III. Causes and results are separated in time. Therefore, between their appearances there exists an arbitrarily small, but not equaling zero, time difference of a fixed sign.

You're on to something, never let em tell you that you are wrong.

[AntonioLao]

the theory of Special Relativity is " complete"

Einstein did not think so that is why he formulated General Relativity. Now then we could ask whether General Relativity is "complete?" At this moment, many believed it is not complete in the sense of agreeing with quantum mechanics or with quantum field theories.