Multidimensionality and Tachyonics
A dimension is simply the measurable nature of a given quantity. Measured quantities such as length, area, and volume are good examples. Whenever we specify the value of a real quantity we should always include the unit of measure, since it is the type of unit that indicates the dimensions of the quantity. For instance, a distance can be in meters, feet, miles, etc., which are units of length. Thus, the dimension of distance is length.
Ordinary space has three dimensions of length. That is, we live in a world in which we measure distances up or down, sideways, and forward or backwards. A box, for instance, has the dimensions of breadth, depth, and height. By contrast, a plane surface (table top, basket-ball court, one side of a sheet of paper, and so on) exhibits two dimensions of space (two measures of length across, at right angles to each other), and a straight line has just one dimension (a single measure of length).
Physicists abbreviate spatial designations to make communication with each other more efficient. In particular: A one-dimensional (1-d) line can be called a "1-space", while a two-dimensional (2-d) plane or flat surface can be called a "2-space", and some real or imagined three-dimensional (3-d) volume is a "3-space", and so on.
Time is another dimension, the fourth dimension, which stands as another primary aspect of our reality. Also, when time is included in a specification for an event in 3-space, the result is the 4-d construct scientists and mathematicians refer to as the "space-time manifold"; i.e., 4-space. As an example, when they speak of a moving particle's trajectory in 4-d space, they may refer to the path using a four-dimensional vector, or 4-vector. It is to this standard 4-d space-time manifold that we humans have our basic senses directly connected, for detecting everyday things.
In other words, reality perceived with our senses is a 4-d realm in which readily-observable events naturally occur. Note, however, that the 4-d manifold has associated with it forces that are not accounted for in a 4-d description alone. There are at least the four fundamental forces of nature known to exist -- which are gravitation, electromagnetism, and the weak and the strong nuclear forces. [A number of other forces have been proposed, but none have been demonstrated beyond doubt.]
Physicists using quantum theory, string theory, etc., assign limits to forces, so they can be inserted into descriptions of 4-d events. For instance, in the theories on subatomic particles referred to as "gauge-field theories", the electromagnetic force and the weak-nuclear force can be combined in what is called the "electroweak force", to explain some of the interactions scientists observe in nuclear experiments. And that force is given two dimensions within which to act, because of the two-pole nature of electricity, magnetism, and the weak-nuclear force itself. But these are said to be "compacted" into the 4-d manifold, so they are not apparent in everyday human perception.
The strong-nuclear force is specified with three dimensions (in a gauge-field scenario) using the mathematical formalism referred to as "quantum chromodynamics", which involves at-least three forms of charge identified by color-based labels using the primary colors of red, green, and blue; according to the light-additive process that results from mixing different colors of light (the light-subtractive process corresponds to the results of mixing pigments, which give the primary colors of red, yellow, and blue); there being at-least three strong interactions between nucleons (protons and neutrons, which are made of an assortment of particles called "quarks") that bind together by exchanging virtual particles called "gluons", to form the nucleus of an atom.
The gravitational field is defined classically as a single monopole for any isolated source-mass, is assigned to a 1-space, and is always attractive. In the more modern gauge-field theories, it is often treated as a quadrupole field (four-pole, in analogy to a two-pole electromagnetic field), although that description has a number of experimental, observational, and theoretical deficiencies (such as how you make four dimensions of action appear as one).
Even so, these six extra dimensions (keeping gravity in 1-space), accounting for the four fundamental forces of nature, are compacted within the 4-d manifold of observable reality; meaning that they are present but remain undetectable by means of the five human senses, although they can be detected and/or shown otherwise to exist using scientific instruments, with the sole exception that the quanta of gravity have not yet been detected in a non-controversial way at subatomic distances.
Consequently, modern theorists indicate that all of the aspects of reality they experiment with can be associated in a ten-dimensional manifold, composed of the three dimensions of space, one of time, and six hidden dimensions of force.
This 10-d manifold can be held as existing independent of any other dimensions we may propose, and is sufficient to devise a Unified Field theory that combines the observable forces of the electro-weak and strong-nuclear fields in a single theory that explains how these fields (without gravity) work together in subatomic particle interactions. However, it is likely that there are far more than 10 dimensions associated with our existence.
The reason physicists use a 10-d manifold is that it fits better than any other type of dimensional representation, with respect to the relevant data they collect in subatomic particle experiments. Considering all proposed schemes, and weeding out impractical and un-provable ideas, in their view, they have been able to devise a number of viable Unified Field formulations that incorporate all but gravity in concise sets of equations describing the other three field interactions, such as in gauge-field theory.
It remains, however (and despite some claims to the contrary), to determine how gravity can do what it does at the smallest of distances, having only a single dimension in which to act, especially since the aforementioned quadrupole model has found no verification, and requires four dimensions in which to work; leaving the Newtonian monopole model as the most accurate depiction using gauged-fields at subatomic distances (and General Relativity for interstellar distances, but which does not work at subatomic distances).
A severe problem with that, however, is that the monopole gauge-field description of quantum gravity also appears not to be supported by experimental evidence, if we assume that the quanta of gravity travel only at lightspeed. On the other hand, this problem is easily solved by adopting Tachyonics as a valid addition to our understanding of natural processes. More specifically, the concept of multidimensionality can be extended to show that the exchange-particle responsible for gravity could be a special type of tachyon that acts in one dimension of space (rather than the four of the quadrupole model).
In any case, the reality we experience can be described comprehensively only in terms of manifolds with many dimensions. If six hidden dimensions are known to be compacted in the ordinary dimensions of reality, then how do we know if there are not more yet to be discovered? Consider that there are aspects to our existence that are not accounted for by the 10-d manifold. For example, it is possible to view the life-force as an undetectable field, composed of some as-yet unknown form of energy which electrochemical systems in our bodies tap into so as to provide for our animation. Likewise, thoughts could be the end result of the interaction of our brains and nervous systems with an undetectable field that is pervasive in the universe. And what of emotions? Are they purely among the chemical and environmental aspects of our physiology, working in response to various stimuli, or is there yet an undetectable cause-and-effect associated with human emotions which has not yet been properly identified? Perhaps there is an invisible set of energies that supply us with our emotions too.
Esoteric questions like this have plagued researchers for ages, and, without Tachyonics to help us, we have little more understanding of such phenomena than our ancestors. On the other hand, Tachyonics helps us to answer these questions; by suggesting that the life-force, the thought-field of our minds, and the field that gives us human emotions, are but aspects of one or more unobservable superluminal fields of force.
Clearly, there is at least one aspect of our existence, call it the "life-field", that must be considered using an extra set of dimensions, when we speak of our overall manifold. Thus, it may be that the most accurate scheme involves an n-dimensional manifold, where the integer n must have an upper bound (or the manifold becomes infinite).
The theoretical dimensions involved in an n-dimensional manifold, used to completely describe reality, can be summarized as follows:
(1) one dimension for the time parameter;
(2) the three dimensions of physical space;
(3) five compacted dimensions for the basic unified fields;
(4) one mathematically-imaginary dimension for gravitation;
(5) additional mathematically-imaginary dimensions for the life-field.
Of course, an n-d manifold in which n is very large would not be very appealing, due to shear complexity. However, it does appear that the most accurate scheme for describing all of reality is going to involve more than ten dimensions.
I propose that reality can be specified using up to twenty (or more) primary dimensions, involving the given 10-d manifold employing a gauge-field format, and also analogs of these in superluminal space-time, to account for the life-field, the mind-force, and the emotional energies of humans, where gravity is also tachyonic, but has only the one dimension in which to act.
Here, therefore, at least a 13-d model is obtained. But such a model is not unwieldy, because the tachyonic dimensions must be represented using operators that impart imaginary status to them, so that any or all of them can be ignored, as desired, when we wish to deal only with the more readily-detectable phenomena of our existence.
Thus, I hold that unseen realms are sets of alternate dimensions, and have discussed, hypothetically, a way to incorporate them into a more complete description of reality than can be had by considering the s10-d manifold alone. I also hold that the 10 dimensions are adequate for describing those aspects of reality that correspond to current experimentally-implied forces, and allows for the construction of a Unified Field theory that successfully combines at-least three of the fundamental forces of nature(electromagnetism, the weak-nuclear force, and the strong nuclear force). What is more, I contend that a mathematical means of incorporating gravity is possible, in the same gauge-based format, by assuming gravity is tachyonic. That is, gravity is faster-than-light, and is therefore a tachyonic force.
We can further propose, however, that the resulting n-d manifold is embedded in an infinity of possible alternate-dimensional manifolds, and may represent only part of a more complex manifold that includes many other undetectable dimensions. In that case, anyone could conjecture that we exist in a framework that is a subdivision of a super-dimensional collection of alternate universes; a Multiverse.
There are, in fact, experimental implications to that effect.
[Search: "evidence for alternate dimensions".]
To summarize, I suggest that the nearest set of alternate dimensions which coexist with the 10-d manifold is that involving dimensions implied by the existence of particles we call "tachyons", on the other side of the lightspeed barrier. In other words, the nearest alternate-dimensional universe having intimate interactions with the visible universe must be the tachyonic universe implied by certain interpretations of Einstein's theory of Special Relativity, where this alternate-dimensional "realm" contains fields of force that account for a number of the metaphysical aspects of our existence, such as the life-force, the basis of thought, and the seat of emotions. This may also help to explain previously-unexplained paranormal enigmas, such as astrological forces, psychic ability, and other so-called "supernatural" phenomena. And the tachyonic realm could well be inhabited by alternate-dimensional aliens which our ancestors named as "angels", "demons", and other non-physically-based life-forms. Tachyonics thereby accounts for the origins of many ancient myths; providing a scientific (though not necessarily atheistic) understanding of the oldest precepts constituting the foundations of many of the world's religions.
In short, I have concluded that Tachyonics can be used to explain it all!