Multiple Time Dimensions, why not?

One of the biggest misconceptions deep-rooted in the human mind is the one-dimensionality of time. When physicists discover a theory that calls for multiple extra dimensions, such as the string theory, their first reaction is to assign those extra as spatial dimensions. They do so because they abhor the plurality of time ^a).

In order to give the reason for their invisibility, the physicists hypothesize that the extra dimensions are curled up into tiny loops ^b). However, as there are so many possibilities on how those extra-dimensions may be curled up, the outcomes of such string theory can reach billions.  It gives us a good reason to allow the Occam razor getting rid of this dire hypothesis without delay.

Internal symmetry

The second reason for the invisibility of the extra-dimensions is that they are time dimensions. A world with multiple space and time dimensions certainly complies with the principle of the relativity. We would have in our worlds no more bizarre things such as donut-like or Calabi-Yau tiny manifolds. As such, the world may preserve its internal symmetry in which changing [reversibly] the time dimension with the space dimension leaves the physical laws identical. 

It is evident that the physical laws' formulation in the world with many time dimensions would be exceedingly complicated. However, we may have a more natural way to solve the formulation by transforming all but one time dimensions into space dimensions. Having done that,  we get a simple system of higher-dimensional space with only one temporal dimension without altering the outcome of the result. 

To give an illustration, let us take the example of our space (or 3-brane as you wish ^c)) which we interpret as embedded in a 10-ambient spacetime. Under multiple time dimensions framework, such a system consists of three space dimensions and seven temporal dimensions. By transforming all temporal dimensions  (except the highest dimensional one) into space dimensions, we get a system having nine space dimensions and one temporal dimension  (a 9-brane embedded in the same 10-ambient spacetime). The physical laws' formulation in the latter system is much simpler than that in the first one ^d).

Under such a system we can also transform only some of the time dimensions into space dimensions and keep the remaining intact. As such, we would have various dimensional branes ranging from 3-brane to 9-brane embedding in the same 10-ambient spacetime without even changing the outcome of the result. 

These are the various dimensional branes which we encounter in the superstring theory. However, in most of the cases, each of those branes is assumed to have only one temporal dimension. As such, the physicists who deal with those branes have not any simple way to solve the respective formulation ^e). 

Even in dealing with the 9-brane, we may have no good solution. We may, in this case, extend the dimensions of the ambient spacetime higher and higher until we get the solution ^f). 

We may say that the higher the brane's dimensions are, the flatter it is.  This situation makes the mathematical formulation of the physical laws simpler.

Figure-1 diagrammatically shows how events which are not simultaneous at a particular time dimension t₁ become simultaneous at a higher time dimension t₂. It is as though space flatten out as the number of temporal dimensions becomes higher that makes the physical laws formulation more straightforward ^g).

Notes:

a)   Physicists wrongly regard the 4-spacetime as having three space dimensions and one temporal dimension which should be inherently multidimensional. The underlying of what we know as 4-spacetime is 4-dimensional time having a 3-dimensional cross-section (3-brane) in it.

b)   Kaluza and Klein first introduced Kaluzathe idea to unify the electromagnetic field with that of gravity by adding the curly fifth dimension to the classical four. Later on, the idea is extended for much higher dimensions in which the loop size of the extra dimensions is at the order of Planck size (10^-33 cm).

c)  We use the notations of space, hypersurface, hyper-interface or brane interchangeably.

d)   A system consisting of 3-space embedded in 10-dimensional ambient spacetime can be formulated as Hypercomplex function:

q = x₁ +x₂ + x₃ + ic₁t₁ + jc₂t₂ + kc₃t₃ +lc₄t₄ + mc₅t₅ + nc₆t₆ + oc₇t₇ 

under a coordinate patch consisting of three real x₁, x₂, x₃ and i, j, k, l, m, n, and o as independent imaginary numbers as the basis coordinate representing seven different time dimensions, c_i is the speed of light of the respective temporal dimensions t_i .

It is identical to Octonion :  

q = x + ic₁t₁ + jc₂t₂ + kc₃t₃ +lc₄t₄ + mc₅t₅ + nc₆t₆ + oc₇t₇ 

where x = x(x₁ , x₂ , x₃)

The physical laws prevailing in such a system would be extremely complicated. Under the internal symmetry, we can make it much simpler by changing the extra time dimensions into spatial ones transforming the system to get a system consisting of 9-space embedded in 10-dimensional ambient spacetime.

Its mathematical formulation then becomes a simple ordinary complex number:

q = x₁ +x₂ + x₃ + x₄ +x₅ + x₆ + x₇ + x₈ + x₉+ oc₇t₇

Denoting x = x (x₁, … x₉), we get a simple form:

q = x + oc₇t₇

e)   For example, if we have a system consisting of 6-brane embedded in 10-ambient spacetime (a system with 6 space dimensions and 4 time dimensions): 

q = x₁ +x₂ + x₃ + x₄ +x₅ + x₆ +lc₄t₄ + mc₅t₅ + nc₆t₆ + oc₇t₇ 

Usually we consider such a system having only one time dimension and disregard the other three: 

q = x₁ +x₂ + x₃ + x₄ +x₅ + x₆ +lc₄t₄ 

the solution of this formulation would be the only approximation of the former.

f)   The dimensions of macro-cosmos are assumed to be [quasi] infinite. It happened that we need only an ambient spacetime having 11 dimensions embedding a 10-brane  as in the case of supergravity theory.

g)   In such a diagram, simultaneous events would flatten their loci, an n-surface (hyperinterface, brane) embedded in (n+1) ambient spacetime; otherwise, the surface would not be flat. Figure-1B shows events which happen simultaneously at a certain time dimension t₂ while they do not happen simultaneously at a lower time dimension t₁ (Figure-1A).

Multiple Time Dimensions, why not?

Einstein's Biggest Blunder

Einstein always said that the biggest blunder he ever made in his life was his introduction of the cosmological constant in his general relativity theory. But in fact, it was not. The unawareness about his misconception on the nature of spacetime was instead his biggest blunder.

Let’s see what I mean by this. On the inextricability of the spacetime Einstein said1:” the non-divisibility of the four-dimensional continuum of events does not at all, however, involve the equivalence of the space coordinates with the time coordinate. On the contrary, we must remember that the time coordinate is defined physically wholly differently from the space coordinates“. With all due respects to Einstein, this is obviously nothing but a vicious-circle statement.

Multidimensional time

He rejected the belief on the division of the four-dimensional continuum into three-dimensional space and a one-dimensional time continuum. Indeed, we don’t have any problem with this, but what we concern most is that when we divide the four-dimensional continuum in two we will get a three-dimensional space taking place in between the four-dimensional time continuum. Hardly anybody is aware of such obvious logical fact. What we are used to perceiving the reality of one-dimensional time is, in fact, the resultant of these underlying four dimensions of time.

Indeed, the spacetime continuum as a whole should be both homogeneous and isotropic. It should have equivalent dimensions i.e. “pure” time dimensions, in the sense that they are undivided. As such, the spacetime is timeless; there is no past, now and future. It is also spaceless since the “now” is not yet present (a). There could be no matter or light to be created in such a proto-world, it is in total chaos.

The Slit Spacetime

The creation of material things can only be taking place if such a world is split. By splitting the four-dimensional world into two halves, a three-dimensional space (hypersurface) is created in between the two. The original time dimensions at such newborn space are transformed into different kind of dimensions (spatial dimensions) because of the effect of the hyper-interfacial tension (b) of this hypersurface (c). This spacetime’s split is analogous to the split of oil and water, a phenomenon we can observe in our daily life.

This split spacetime is what truly representing the actual world. Einstein and, alas, the mainstream physicists have erroneously taken this chaotic proto-world to represent the material world. No wonder they are obliged to set up light-cone frameworks at any point of such spacetime to preserve order and causality.

Einstein rejected from the outset the concept of absolute simultaneity. He developed his concept of relative simultaneity by giving a central theoretical role to the events and the propagation of light, in that it founds the concept of time upon the law of propagation of light.

But the notation of event is just another word of point coordinate, occurrence, happening or incident with no reference to the state of being or the existence of things. The good reference to define simultaneity is, therefore, not events measured through the propagation of light but the existence of fundamental (ephemeral) things such as those of quantum particles.

The simultaneity of particles’ creation and annihilation

So far we haven’t yet discussed how and why the spacetime is splitting. The special relativity theory has unified the fundamentals: space, time, energy and matter into two; the spacetime and energy. The general relativity reveals that the spacetime is not an independent reality as what we might think. The spacetime is not like the container independent to whatever fills it neither the energy something that fills the container. The grand unification of the relativity theory of those two leads us to conclude that energy is the only real and independent thing in nature while the spacetime is to fade away into merely the structural quality of energy.

Now, the energy by itself composes of positive and negative energies as formulated in the relativistic energy equation E2=m2c4+p2c2. Eventually, the energy as a whole breaks up into its opposite elements and splits accordingly the spacetime into two halves. The three-dimensional space is taking place in between the two as was discussed in the foregoing.

The interplays between the two opposite energies across through the 3-interface ignite quantum sparks (“quarks”) (d) which we perceive as the quantum particles. These “quarks” are short living (ephemeral) and appear to be persistent only because of the perpetual interplays between such opposite energies. We perceive these continuous interplays as perpetual creation and annihilation of quantum particles giving rise to the perception of the passage of time and the time direction: the past, now and future. The creations [and annihilation] of the quantum particles are taking place simultaneously giving rise to the universal now. The three-dimensional space and the universal now are the different aspects of the same thing.

This may answer to Einstein's worry about the nature of Now. Einstein himself denied the absolute character of simultaneity and thus the existence of the universal now. In the relativity theory that is currently conceptualized nothing corresponds to the experience of Now. Reporting a discussion, the philosopher Rudolf Carnap wrote3:”… Einstein explained that the experience of the Now means something special for man, something essentially different from the past and the future, but that this important difference does not and cannot occur within physics [… ] so he concluded that there is something essential about the Now which is just outside the realm of science”.

The reality of Now is nothing but space itself; it is not outside the realm of science. Referring the four-dimensionality of spacetime Minkowski did not explicitly deny the existence of space and concluded:” we should then have in the world no longer space, but an infinite number of spaces, analogously as there are in three-dimensional space number of planes. Three-dimensional geometry becomes a chapter in four-dimensional physics. Now you know why I said at the outset that space and time are to fade away into shadows, and only a world in itself will subsist” 2.

This space or spaces are not necessarily flat as in the case of Minkowski’s spacetime. This gives rise to local times along the different places along the curvature of the interface whose temporal dimension is different from that of the universal now. The current modern physics theories require higher and higher dimensions, in essence, are the endeavor to get the simultaneity of the existence of things (flat hypersurface) that might happen only at the higher temporal dimension. Only then the grand unification theory may be fully accomplished.

Notes:

1. Space and the universal now are different aspects of the same thing.

2. It is directly related to the nature of the gravitation constant.

3. We refer to concurrently space as hypersurface, 3-space, 3-surface, or 3-interface.

4. The notation of this “quark” (quantum spark) is more general than the conventional quark specifically representing the smallest element of the atomic nuclei.

References:

1. Einstein, Albert: The Meaning of Relativity, Princeton University Press, New Jersey, Fifth Edition, 1954

2. Einstein et al.: The principle of Relativity, Dover Publications, Inc., New York, 1952

3. Barbour, Julian: The End of Time, Phoenix, London, 2001

Einstein's Biggest Blunder