hyperspace waves

probably in 2010 - I had first intuitive idea about hyperspace waves when looking on equations of special relativity
 
in 2012 I got back to this idea
          
Einstein told us in his special theory, that no real objects can travel faster than light. Well but what about "inertial frames"? These are not real objects at all! So they can travel at any speed! And Lorentz transformation works for these inertial frames as well, and it is very easy to realize, that for v>c real quantities are transformed to complex ones and vice versa. For many people this is boundary, they cannot cross in their thoughts. But this is not a problem for electrical engineer especialy from Prague. Electrical engineer works with  complex quantities every day. And if  real angular frequency of sine wave transforms to complex one, is that a problem for an electrical engineer? Of course not, insteadof sine function, he will get hyperbolic  sinus multiplied by imaginary unit. And hyperbolic sinus is sum of exponential function. The biggest problem here  was the multiplying by imaginary unit. So how to deal with that? Can be quantities like voltage or intensity purely imaginary? I was almost in the end, because I didn't know how to deal with that. There is a basic assumption that physical quantities are only real.  At least everybody tells that...

Well but in radio electronics, the subject I have mostly studied in the college, there are some exceptions to that rule like complex envelopes, complex spectrum etc. But these quantities  are not physical quantities, but mathematical objects, that make calculations and reasoning with related physical entities easier. So again how to deal with that problem?

 Fortunately I started to learn about  quaternions. I also quickly realized that they are connected also to quantum field theory (via Pauli matrices etc). Therefore I was strongly felt, that if I can express theory of relativity in quaternions, it could be later also unified with quantum theory. But I was fighting  with this approach, at the beginning, as I had no idea, how to convert 4-vectors to quaternions. But finally I have realized this. Space coordinates must be multiplied by "minus imaginary" unit. Finally I started to uncover hidden texture of space time. The  math is running on biquaternions! At the same time I also learned about octonions, which are closely related to biquaternions. 

Since I realized this late in 2012, I spent about next 3/4 of year I was making symbolical calculations with matrix representations of biquaternions in WxMaxima software. It was first time I used WxMaxima, so anyway I had  to solve almost everything myself like on paper (1). Unfortunately I was not yet familiar with  GIT software, so I have many not well organized files with calculations and interpretation of results. So the results are hard to interpret (2)


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