Special Relativity shows Inversion of Spacetime

Martin Q

Temporal Novice
In the equations for transforming between reference frames (Lorentz Transformations) one might discard faster than light (FTL) (v > c) as the result yields an imaginary number. However, I considered the possibility that complex numbers themselves, represent Spacetime coordinates. It is almost a mathematically tautology that they do so. I even re-derived the transformations, and they result in the same formulae, as the imaginary components cancel out in the solving of the system of equations.

Now, if you consider space coordinates the real component and temporal coordinates the imaginary component, speeds slower than light (STL) (v < c) result in the same transformations as with using only real numbers for both space and time coordinates. However, FTL speeds result in space and time coordinates inverting spots (due to imaginary numbers appearing and cancelling each other out for the time coordinate). Moreover, the transformation results in a temporal coordinate shift that implies events in the future for FTL reference frame appear to be in the past for STL reference frames, and vice reversa. The implication is that FTL speeds result in travelling backwards in time relative to STL reference frames.

Naturally, it seems impossible to accelerate a massive object FTL, as its inertia also increases with its speed, yielding an inertia approaching infinity as its speed approached that of light. However, I am currently in the process of deriving Einstein's field equations for General Relativity with complex spacetime coordinates. I will update with my results. My hypothesis is that a massive objected may be accelerated through a singularity to reverse its direction of travel through time.

I will update you all when I have finished.

Opinions, criticisms, and resources are welcome.


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[QUOTE='Einstein]Have you ever thought that describing spacetime with equations might be the wrong path to knowledge?
[/QUOTE]Sure. However, any sort of model we propose in only an approximation of spacetime, related to our current degree of knowledge. Yet, if the model holds true, we must give it some merit. It ought to therefore be an approximation of the accurate path to knowledge, which we ought to traverse until it no longer holds true, at which point we can only search for a better model.

[QUOTE='Martin Q]In the equations for transforming between reference frames (Lorentz Transformations) one might discard faster than light (FTL) (v > c) as the result yields an imaginary number.
[/QUOTE]Imaginary numbers mean very real things (pun obviously intended) in the dynamics of any multivariate system.

Being a control systems engineer, I utilize the concept of frequency domain (the reciprocal or inverse of the time domain) to analyze any system's natural response (its transfer function) to stimulus (inputs).  The solutions to the primary dynamic modes of a system (e.g. solutions to their transfer function characteristic equation) can involve mathematical roots of even orders (e.g. exponents of 2, 4, 6, etc...).  And any 2nd order characteristic equation can result in complex conjugate roots that describe the system's dynamic response.  When a system has imaginary roots (an imaginary numerical portion in addition to its real-valued portion) this tells us that the response of that system can oscillate between at least two different states as time progresses.

This math that helps us analyze and develop control systems for physical systems is well known, well understood, and very applicable to the Massive SpaceTime universe we all inhabit.


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