| complex circle
The plot of a complex number a + bi on the complex plane shares with an infinite number of other complex numbers such that their absolute value c = sqrt(a + b) are equal. The locus of all these infinite complex number is a complex circle. Although a real circle is one of the conic sections of 3-dimensional space, the complex circle is an abstract circle of 4-dimensional space and time. It is no coincidence that special and general relativity as well as quantum mechanics relied on complex circles for descriptions of reality. The formers used it to describe the large scale structures, while the latter, the small scale structures. It is worthwhile to repeat saying that both perspectives are quite successful and are supported by repeatedly verified empirical data.
However, their independent success could not possibly secure their joint success. Many theorists have tried to formulate a theory of quantum gravity, still without any foreseeable satisfactory conclusion. This failure might be due to the difficulty of linking a real circle to a complex circle.
The solution might be simply to forget about complex circles and work only with real circles and try redefining time with directional attributes. Directional time at the infinitesimal region suggests temporal quantization or quantum of spacetime since at this level space and time lose their separate identity. These real circles could then allow their descriptions by Hadamard matrices.
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Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
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