3.3.2 The Dynamic Creation of Dimensions

According to the above Duality of Time Postulate, the dynamic Universe is the succession of instantaneous discrete frames of space, that extend in the outward level of time that we normally encounter, but each frame is internally created in chronological sequence within the inward level that is the real flow of time. This is schematically demonstrated in Figure III.4, where space is conventionally shown in two dimensions, as the (x, y) plane, and we will mostly consider the x axis only for simplicity.

Figure III.4: Representing the inner and outer levels of time together as genuinely-complex time-time space. In the real flow of time, one frame of space is re-created in internal chronological sequence, that then appears as one instance of the imaginary time, as split-complex or hyperbolic numbers.

In reality, however, we can conceive of at least seven levels of time, which curl into the four dimensions of space-time: 3D+1, that are the three spatial and one temporal dimensions; since each spatial dimension is formed by two of the six inner levels of time, while the seventh is the outer normal time that we encounter.

This Duality of Time model brings back the same classical concept of aether but in a novel manner that does not require it to affect the speed of light, since it is now the background space itself, rather than something in the background. On the contrary, since space is dynamically created in time, we can now give a simple ontological reason for the constancy and invariance of the speed of light, which is so far considered as an axiom, that has been experimentally verified but not yet proven in any theoretical sense.

Moreover, we have shown in Chapter V of Volume II how this postulate can be applied to deduce the mass-energy equivalence relation (E=mc²) directly from fundamental classical principles. This should provide a conclusive evidence to the hypothesis because it has been shown that an exact derivation of this famous relation is not possible without the inner level of time.

Aether is therefore the flat space itself that is generated dynamically in the inner level, and not something in the background, while matter particles are some condensed or excited states of this dynamic aether.

Because they are always being re-created perpetually in the real flow of time, at the only real speed (of light) that is the speed of creation, all objects are essentially waves, but they are detected as particles in the outer (imaginary) time, as we shall see further below.

In the continuous creation of the Duality of Time hypothesis, the physical dimensions of space are sequentially being re-created in the inner levels of time, which makes the outward time genuinely imaginary with respect to the inner time, and thus easily expressed in terms of Euclidean geometry by using hyperbolic split-complex numbers H. This will also have deep implications on the various fields of mathematics, such as geometry and number theory, because complex numbers are now genuinely natural while the reals are one of their special approximation. This was discussed at length in Chapter V of the Ultimate Symmetry.

Without postulating the Duality of Time and the resulting continuous creation of space, this concept of imaginary time does not have any genuine reality or justification outside the mathematical formulation, because both the Galilean space and Minkowski space-time consider space and time to be coexisting together, i.e. they both are real. The fact that each frame of the inner time (which constitutes space) appears as one instance on the outward time is what justifies treating time as imaginary with relation to space, thus perpendicular to it. In this dynamic creation of space in the complex time, the outward time is discrete and imaginary, while space becomes continuous with relation to the outer time, but this is only relative to the dimension in which the observer is situated, so for example: the 2D plane is itself continuous with relation to its inner dimensions but it forms one discrete instance with relation to the flow of time in the encompassing 3D, which then appears internally continuous but discrete with regard to the encompassing outward time T.

Henceforth, the Duality of Time is expressed in terms of simple Euclidean geometry, but based on complex-time. This genuinely-complex time-time frame will allow expressing the (deceitfully continuous) non-Euclidean space-time in terms of this granular Euclidean complex-time space, whose granularity is expressed intrinsically by using the hyperbolic split-complex numbers (H), i.e. without invoking Riemannian geometry that is becomes an approximation of this complex-time geometry. This approximation, that lead to the non-Euclidean Minkowski space-time continuum of General Relativity, is necessary only when we consider the dimensions of space to be co-existing together in (and with) time, thus causing the deceptive continuity of physical existence.

Moreover, in this complex representation, Lorentz transformation becomes a rotation, as it was originally shown by Poincaré Poincaré (1906), but now this now applies to transformations between inertial and non-inertial frames alike, because the dynamic relation between the real and imaginary parts of time implies that the instantaneous velocity in the outer level of time is always zero, whether the object is accelerating or not!

This essential characteristic of the dynamic and granular complex time, that results from the Duality of Time Postulate, leads to the three principles of Relativity all at once. Therefore, in addition to making gravity a true quantum field theory, other fundamental interactions could be also represented in terms of this space-time geometry, but in lower dimensions.

The concept of imaginary time is already being used widely in various mathematical formulations in quantum physics and cosmology, without any actual justification apart from the fact that it is a quite convenient mathematical trick that is useful in solving many problems. As Hawking stated: “It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?” Hawking (1998).

Hawking, however, considers the imaginary time as something that is perpendicular to normal time that exists together with space, and that is how it is usually treated in physics and cosmology. According to the postulate of the Duality of Time, however, since space is now the real time, the normal time itself becomes genuinely imaginary.

Employing imaginary time is very useful because it provides a method for connecting Quantum Mechanics with statistical mechanics by using a Wick rotation, by 90 degrees. In this manner we can find a solution to dynamics problems in n dimensions, by transposing their descriptions in n+1 dimensions, i.e. by trading one dimension of space for one dimension of time, which means substituting a mathematical problem in Minkowski space-time into a related problem in Euclidean space.

Schroedinger equation and the heat equation are also related by Wick rotation. This method is also used in Feynman’s path integral, which was extended in 1966 by DeWitt into gauge invariant functional-integral DeWitt (1967). For this reason, there has been many attempts to describe quantum gravity in terms of Euclidean geometry, because in this way it is possible to avoid singularities which are unavoidable in General Relativity.

We conclude, therefore, that the Duality of Time does not replace or contradict the main exiting theories, but it exposes a deeper understanding of time that leads to metaphysical (non-background) Euclidean complex-time, which is absolutely Euclidean, and which approximates to the non-Euclidean, Minkowskian or de Sitter / anti- de Sitter, space when we suppose the background to be continuously existing with real physical dimensions. This approximation leads to General Relativity, and the current first and second quantizations, of energy and fields, but Quantum Gravity requires this third quantization, that is the true quantization of the space-time itself, and this cannot be achieved without taking into account the hidden symmetry of the new granular complex-time geometry.

Therefore, the correspondence principle is fulfilled by the Duality of Time Theory, because the semi-Riemannian geometry on the real space R is a special approximation of this complex-time geometry on the hyperbolic space H, so General Relativity is produced when we consider space and matter to be coexisting together in (and with) time, thus causing the deceptive continuity of physical existence. All the principles of Special and General Relativity can be derived mathematically from the Duality of Time postulate, in addition to exact derivation of the mass-energy equivalence relation that is not possible within the current theories without introducing some approximation or induction.