Time, quasi-temporal change and imaginary numbers

Abstract

The thesis is mainly concerned with the argument for dynamic time. Accepting McTaggart s proof of the unreality of time, it is argued however, that any description of dynamic time involving static concepts must lead to a contradiction. It is shown that the contradiction arising from this proof is equivalent to the contradiction posed by Aristotle s definition of change: change is the possession of incompatible properties. A special case of such a change is quasi-temporal change, defined as the possession of incomparable properties at the same time. Furthermore it is claimed that change is a primitive entity. The Block Universe view that three-dimensional dynamic and four-dimensional static representations of the world are equivalent to each other is rejected because of the unknown nature of imaginary numbers describing the time-like dimension of spacetime. It is proposed that the imaginary number i is an mathematical embodiment of change, expressed in the form of quasi-temporal variable: i = [1,-1]. As such i is a scalar variable with two numbers, 1 and 1, assigned to it. To develop further this idea the Special Theory of Relativity and Hamilton s theory of the complex numbers are used. It is claimed that the natures of imaginary numbers the time-like dimension are the same. It is shown that this dimension can be given by two opposite displacements of light occurring at the same time. To use Hamilton s theory a pair of two times is proposed: normal time and dimensional time. The moments of these times are identified with the Hamilton s primary and secondary moments of time respectively. It is shown that Hamilton s theory is invariant upon such identification. This allows the extension of the argument forming the theory of the complex numbers. The second theme of the thesis is an argument for multiplicity of times. It is proposed that every being of a natural kind exists in its own time. Individual time is taken as a composition of topologically open time and topologically closed time. Such a composition allows an explanation of the convolution of change and permanence and also formulation of a new interpretation of Quantum Mechanics.