Chapter XXII

 

HOW MANY DIMENSIONS?

 

"Beyond the stars inhabits other worlds."

- Einstein -

 

     By postulating the entrance of this Dark Energy in our Universe, there is, of course, another question that immediately arises in my mind:

     How many are the dimensions that surround us?

     There will not be three, for sure. At least, there is one more. If there are others, I will simple not know!

      The entrance of this uniform dark energy in our Universe should be postulated by a Fifth Dimension, ubiquitous, and always present, that involves us from all directions.

     If the Universe is becoming each time bigger and more and more quickly larger, it is because there is something on the 'outside’ that can constantly come in through this fifth dimension! This dimension is the hidden entrance of this energy, responsible for expanding the Universe at all points of space evenly.

     We can even say that it is a fifth essence that enters through a fifth dimension. A Magic Energy, which leaves out through one door but enters through all!

     Unless someone has a better idea, I am obliged to introduce this new concept, absolutely different and exotic, yet for us a little bit abstract and esoteric!

     This mantle which involves us must hide many secrets … the 'Bubbles of Oil' of the hyper-space!

     The idea of living in an imaginary Universe with more dimensions is not new. Many theories have tried to explore these concepts. The Theory of Strings was one of them. For this theory to be viable, our Universe should have more than three dimensions, at least ten. In this Universe, the extra dimensions would not be visible, or they would not be perceived by us, in that case, these dimensions should be extremely small, so that, they were consider to be rolled. This rolled and small size dimensions would be much more difficult to detect than the larger size and extended dimensions, which are evident, the so familiar three spatial dimensions.

     But our Universe may very well have much more dimensions than what it seems at first sight. And a new dimension will be, therefore, a new direction in space and time!

     The multi-dimensions of the Strings Theory had its initial inspiration from the theory of two mathematicians: Kaluza and Klein.

     In 1919, Kaluza sent a paper to Einstein with an explosive suggestion. Proposing that the space tissue could have more than the three common dimensions! Beyond those dimensions which we all know and that are provided by our physical senses and by our perceptions, there would be in our space tissue a fourth dimension!

     If our Universe had a total of five dimensions, four for space and one of time, it would be possible to get a combination of unification between the Theory of General Relativity and the Electromagnetic Theory of Maxwell in a single common formalism.

      Thinking that there may be more dimensions out there might be something with a peculiar sense, more or less bizarre. After all, what is the meaning of this new dimension?

      Our three known dimensions are defined by the three possible directions of movement allowed in a spatial area, which are what we usually call of: left-right dimension, front-back dimension, and up-down dimension. These are the three possible spatial movements, accompanied always by a dimension of time, which is, the future-past dimension.

     A new dimension implies and provides the existence of a direction independent of all the others, therefore, it can be consider as a new movement, a different way of experiencing and crossing the space and time!

     But even if the Universe contains an extra spatial dimension, such a direction will reflect a physical concept rather difficult to conceive and to understand in our intellect. There are certain concepts which can only be perceived through mental abstractions.

     On the other side, we cannot simply deny the existence of other possible dimensions. The concepts between what we believe that the world is and the concepts of what they really are, it will always be very speculative and controversial, subject of numerous descriptions and interpretations.

      There is a difference between what we can give as a definition of real and what is the exact essence of reality.

      Wised would be the modesty that would advocate a view more undefined rather than defined about the dimensions of the Universe. Our senses only serve to excite the reason, to provide us the good sense, to indicate and to testify, but they cannot see and know everything. The truth does not come from the physical senses, except a small part.

     Until the appearance of the Theory of Relativity it seems out of the question that the Universe which we live in had more than three dimensions. But with this new theory, this old concept of three spatial dimensions had to be reviewed and it was establish and considered that the new space-time consists of only four unique dimensions, since time can be converted into a spatial component and vice versa.

      Therefore, the geometry of Restricted Relativity applied to the old space-time is no longer Euclidean but instead of it, is now consider as Minkowskian; and in General Relativity, the geometry is no longer to be considered as Minkowskian, but Riemannian. The Math reveals itself, applied to new geometries and new dimensions.

     Before the suggestion of Kaluza it was assumed that Gravity and Electromagnetism were two distinct forces, unrelated, with no relationship between each other, and that there was not a single chance of connection between them. But the creativity of Kaluza, imagining the hypothesis of a Universe with one extra spatial dimension, was a remarkable event, since it suggests, for the very first time, that there might exist a deep relationship between Gravity and Electromagnetism. That these two forces have geometric properties and that this property, the extra dimension, joins them together; making possible the missing relation, associating and uniting them, undoubtedly, to the wrinkles of the fabric of space-time. Naturally, everything that defines the space and time must be attached to it, as such, there should be a unification between Gravity and Electromagnetism.

     The strange theory of Theodor Kaluza and Oscar Klein led to interesting results, if the space-time post by Einstein and Minkowski is added a fifth dimension, then, using their own field equations of theory of relativity, it is shown that the electromagnetic phenomena can be interpreted as having a geometric origin. In other words, the electromagnetic field and also the gravitational field are both geometricable! This means that these two concepts are not so distinct as they seem, that there is a possibility of unification, that these concepts cannot be attached with predefined and exact properties, but instead of it, the main properties of these fields should be classificate as undefined and adaptable to the very structure of space and time, being both very versatile and dynamic.

     Or more simply, if the gravitational structure of an object provides a relative space and time field, the same gravitational structure is composed by electromagnetic forces which share the same properties of relativity. What it is obtained from here is that:  both Gravity and Electromagnetism are geometricable are relative!

     Under the hypothesis of a subtle extra spatial dimension, Kaluza has proceed with his work, undertaken this mathematical analysis in which at the relativity equations is added a new dimension and came to a set of new equations. After a study of the resulting of these new equations, corresponding to the addition of a new dimension, Kaluza understood that these new equations were not other than the Maxwell equations to describe the Electromagnetic Force!

     This remarkable possibility, although it was an extremely beautiful idea, has been reflected in several subsequent detailed studies, but which were always in conflict and incompatible with the experimental data. It seemed that there was no way to confirm the existence of this new dimension.

     However, this concept has continued to inspire new physical theories, namely the M Theory, or Theory of Strings. But ten or eleven dimensions are much more difficult to conceive than the five dimensions of Kaluza-Klein.

     We also have a new theory emerging in the XX century, developed by the physicists Lisa Randall and Raman Sundrum, simply known as the Randall-Sundrum model. This theory also believes that we live on a hypersurface consisting of a space-time of five dimensions. It should be noted that this theory also uses all of the mathematical formalism developed by Einstein in his theory of General Relativity, only changing the dimensionality, which is five.

     If it is shown that this Dark Energy comes to us through a fifth dimension, then, there still maybe some time to reconsider a five dimensions theory for our Universe and to demonstrate, experimentally, the discovery of this hidden dimension.

     I remember a phrase I once read "Physics is first invented and then discovered. The hidden dimensions have been invented; they are only waiting to be discovered." - Carlos Romero -.

     In a heuristic and intuitive way I would say that this hidden dimension will not have to be necessarily smaller, rolled and coiled; or larger and extended. It’s not very likely that we will be able to specify the status of this new dimension, this one, it will simply be an involving dimension, ubiquitous and omnipresent.

     Maybe just this concept of a new dimension, could be capable to explain the transfer and entry of this Dark Energy in our Universe and only perhaps this new multidimensional space could contain and include the very own limits of space itself, the topography of the Universe, the frontiers of the Cosmos.

      If we conceive a horizon, a limit, a boundary for our Universe, we can always ask our self about what can exist beyond that frontier?

      A Cosmic Abysm?

     The question of the Topology of the Universe has shown a growing interest in Cosmology and raised several other possibilities and approaches. Some of these assumptions include a theoretical natural basis; others are focus in a pure mathematical and geometrical concept. Essentially what is asked is whether if the topology of the Universe is infinite or whether if it has a specific geometry and shape.

      It will not be very easy to conceive a geometric model that includes the boundaries of space and time for our Universe. Although it is more convenient for astronomers to work with two dimensional flat surfaces, the real surface of the Universe is much more complex and it is a property that we have not yet been able to measure. If we conceive a three-dimensional geometry, such as a spherical surface, this will result in a Universe with a curve surface, coiled on itself, which would mean that if we could walk continuously in the same direction we would turn back to the same point.

      But even if we could conceive the correct description of this space, the Geometry of the Cosmos, still so we would be limitating the space of the Universe in space. This means that we are imposing the limit of space in space!? … which will always leads us to a paradox that we can never define where the end of space is!

     Is it then possible that space could be infinite?

     I do not wish to annoy you but, doesn’t it seem to you that any specific limit or any type of topology that we can consider, it necessarily limitates space in space itself? So then, how many are the completely spatial dimensions of the Universe?

      Is it possible that we exist in a Universe with infinite dimension?

     The ‘Problem of the Infinite’ it is always an uncomfortable issue and a very inconvenient one!

      But these pernicious infinites, challengers of our reasoning, are present and persistent in several points of the History of the Universe.