On conjugate complex time—I: complex time implies existence of tangential potential that can cause some equipotential effects of gravity
Section snippets
General ramifications of the complex time idea
I want to show in this note that El Naschie's idea of complex time (ICT) [1], [2], [3], which was discussed in [4], [5], can be understood geometrically and that existence of a second dimension of time (SDT) follows from the inverse Lorentz transformation of time rate (ILTTR). Moreover, the existence of SDT seems to imply the presence of a tangential gravitational potential, which is a very serious consequence. Therefore I will show in an accompanying paper that indeed there exists experimental
Second dimension of time
It is a well-known fact that the following (orthogonal) real ordinary differential equation [26]:determines two unique semicircles (positive and negative) which satisfy Eq. (1) where r is a constant radius. The form of Eq. (2) resembles that of the ILTTR which can be written in terms of time rates (all rates will appear in upper cases):where the rate T refers to the resting frame and T′ to the moving one. Since the ILTTR refers to rates of time flow (and
Some features of the complex time
Since in the light of Eqs. (4) time is not only a fourth dimension, but also distinct planar geometric structure, its imaginary character can thus be interpreted in the very geometric sense as not directly representable in the LBS, which agrees with the geometrical “picture” of the TBS as an abstract dual vector space to the LBS. As a matter of fact, in this very sense the imaginary unit i was once introduced into geometry [38], [39], [40]. As such the imaginary unit i should be distinguished
Spatial flow of time implies equipotential effects
The ICT may affect interpretation of gauge field theories. For if Eq. (4a) is the time-based vector representation of the ICT which, being formally equivalent to the ILTTR also admits a decomposition of time rate depending on speed, then the first dimension of time is motion-independent and therefore “static”. Let us consider massless particles like photons, at first. Since time rate relates to energy via frequency, then such a static component of a moving particle's decomposed energy should
Conclusions
We have seen that the conjectured spatial structure of time flow which is implied by the ICT could be derived from the ILTTR. Unlike those previous attempts at multidimensional time, however, the ICT does not really suggest any extraneous increase of the resting resultant time, but merely a possibility of decomposition of time into a static and a kinematic time component in the inertial reference frame. Such a decomposition of time, however, implies spatialized energy and therefore also the
Acknowledgments
Thanks to Slava G. Turyshev for additional information on runaway spacecrafts.
References (91)
On the nature of complex time, diffusion and the two-slit experiment
Chaos, Solitons & Fractals
(1995)On conjugate complex time and information in relativistic quantum theory
Chaos, Solitons & Fractals
(1995)Wick rotation, Cantorian spaces and the complex arrow of time in quantum physics
Chaos, Solitons & Fractals
(1996)- et al.
On El Naschie's complex time and gravitation
Chaos, Solitons & Fractals
(1997) A note on quantum gravity and cantorian spacetime
Chaos, Solitons & Fractals
(1997)Time symmetry breaking, duality and Cantorian space–time
Chaos, Solitons & Fractals
(1996)Experimental evidence against a three-dimensional time
Phys Lett A
(1983)On the possibility of a three-temporal Lorentz transformation
Phys Lett A
(1979)Theoretical proposal of a high-energy experiment fit to reveal a three-dimensional time
Phys Lett A
(1983)Introduction to nonlinear dynamics, general relativity and the quantum
Chaos, Solitons & Fractals
(1997)