MULTIPLE DIMENSIONS, A UNIVERSE OF LARGE, NOT SMALL ADDITIONAL DIMENSIONS
Introduction
We have learned so much about our universe and how our world operates through the science of physics. It only makes sense for us to rely on physics to provide hints and clues regarding where to look next. Or a direction to go in order to build upon what we already know and have learned. Our responsibility to the universe is to look hard at what we have learned. Asking questions to learn more and to understand better what we know is the first step to moving forward and moving outward into our universe.
In the year 1868, Georg Friedrich Bernhard Riemann's paper on 'N' dimensional space was published. Essentially, Riemann's paper mathematically showed that the geometry of our universe could have 'N' dimensions. Information regarding Planck length was not part of the physics known at this time. This infers that the conclusion in Riemann's 'N' dimensional space paper was for large overlapping dimensions. Large dimensions are significantly different from the seven dimensions of space down below the Planck length currently theorized in string theory. In other words, our universe does not have to be limited to the three dimensions in which we live. The universe could be any number of dimensions over and above three.
SIDE NOTE: Regarding the term "'N' dimensional space," any positive whole number can replace the 'N'. We live in 3 dimensions of space (3D space), but the math says 10 dimensions, 75 dimensions, or 500 million dimensions of space are possible. Also mentioned above was Planck length; this is the smallest length possible in our 3D universe, and it is way smaller than the size of the atom. Riemann's paper is the basis of the 10, 11, or 25 dimensions associated with string theory. However, the extra dimensions in string theory are curled up and exist in the space of the Planck length.
Theodor Kaluza, in 1921, theorized a unification of gravity with electricity and magnetism in five dimensions (four dimensions of space and one time). In his original theory, Kaluza looked at the extra dimension of space to be large, not small. After being given feedback on his original large dimension theory, Kaluza modified his theory and reduced the size of his extra dimension. He did not, however, reduce the size of his fourth dimension of space to below the Planck length. Kaluza's use of an extra dimension of space was primarily done as a mathematical tool to try and combine gravity with electricity and magnetism as a follow-up to Maxwell's unification of electricity and magnetism. Specifically, the presumption at the time was that the three forces, gravity, electricity, and magnetism, had to all be associated through one set of equations. The unification of forces via the extra dimension theorized by Kaluza ultimately had some problems, the biggest of which was no "evidence" of a large overlapping fourth dimension. Thus, Kaluza's theory fell out of favor.
However, over 100 years later, the question now is what evidence would a fourth dimension present to those living in three dimensions?
SIDE NOTE: There is information that in his original unification of electricity and magnetism, Maxwell used four dimensions of space and one of time. Did Kaluza follow Maxwell's initial use of five total dimensions? Additionally, work to extend Maxwell's equations into 'N' dimensional space has been published.
Some additional questions for future consideration regarding ‘N’ dimensional space:
Why not keep dimensions large rather than going small, as in string theory?
What concept, mathematics, or physics prevents large, overlapping dimensions?
Riemann’s original theory had ‘N’ dimensions of space, so why stop at four?
What in nature or physics requires unification beyond electricity and magnetism?
Why not expand our knowledge in theoretical physics into four-dimensional or higher spaces first and then see if the unification of forces is possible?
Discussion
Established mathematics and previous theories that looked at a universe with more than three dimensions of space show that a multi-dimensional universe is a familiar idea. String theory, the current unification theory, looks at a multi-dimensional universe. With string theory, the extra dimensions of space are confined to an unimaginably small space that is experimentally impossible to reach and verify. In other words, in general, a universe of multi-dimensional space is an accepted theory rather than a proven theory. So, why can't a multi-dimensional universe be composed of larger, overlapping dimensions rather than folded dimensions in the smallest known space? And does our current physics and knowledge provide foresight for a universe with large, overlapping multiple dimensions?
Large Overlapping Dimensions Overview
Presume that a one-dimensional space is embedded in a two-dimensional space. And the two-dimensional space is embedded in our three-dimensional space. This presumption is very straightforward, given that a two-dimensional space can be created by stacking one-dimensional spaces, and a three-dimensional space can be made by combining two-dimensional spaces. Additionally, two-dimensional spaces are used in mathematics and physics as a tool for extending concepts and theories into higher-dimensional space. Therefore, we can presume that our three-dimensional space is embedded in a four-dimensional space.
Gravity is a required physical characteristic of all mass in our three dimensions, and it envelopes all of space in our universe. Therefore, our three-dimensional gravity will also influence embedded two-dimensional space. Again, by extension, it is not unreasonable to presume that four-dimensional gravity will exist and have some influence on our three-dimensional space. With the presumption that our three dimensions of space are embedded in four-dimensional space, the expectation is that the force of four-dimensional gravity would look like what we call dark energy in our three-dimensional space.
Standard Model
In the standard model, there are three generations of elementary quarks. From the first generation of the "up" and "down" quarks comes the proton and neutron that comprise the nucleus of every atom in our universe. The second generation of quarks is exactly like the first generation of quarks; only they are far more massive and energetic. The stability of our three-dimensional proton composed of the first-generation up and down quarks is well known. Why would we think that a second quark generation proton does not exist as the "charm" and "strange" quarks are nothing more than heavier versions of the "up" and "down" quarks? Currently, the second and third generation of quarks exists for very, very short periods of time in our three-dimensional universe with no specific purpose. The question of concern is why would nature provide us with a second and third generation of quarks that do nothing?
The physics of our universe has shown us that nature is purposeful and that things happen for a reason. Keeping things consistent, why is there no second generation of protons and neutrons? The short answer for now in particle physics would be that these second-generation nucleons cannot exist in three dimensions as they are too heavy and, therefore, too energetic. However, the general expectation is a larger fourth dimension would allow for more energetic particles to exist. In other words, the second-generation nucleons could exist in a fourth dimension, which could mimic the dark matter we see here in our three-dimensional space.
Due to energy constraints, only three generations of quarks have been discovered. However, there is no physics or concepts that prohibit more generations of quarks and associated particles. In other words, much like Riemann's 'N' dimensions of space, there could also be 'N' generations of elementary particles.
Antimatter Asymmetry
One of the most significant questions associated with our universe and its physics is the lack of any antimatter in our universe. However, the existence of antimatter is accurate in that antimatter has been created through natural cosmological processes and experiments. The reality of the existence of antimatter, but the fact that none of it is significantly present in our universe, represents a huge issue concerning one of the basic principles of physics, symmetry.
So far, antimatter, for the most part, is nowhere to be found in our universe, creating a colossal symmetry issue. Adding multiple, larger, overlapping dimensions allows for antimatter to exist outside of our 3D universe but still be a part of our overall universe. A fourth-dimensional antimatter existence would maintain the symmetry in the overall universe, a simple solution to what is currently a significant problem that has no other known potential solutions.
Right-Handed Asymmetry
Antimatter asymmetry is not the only asymmetry within our universe. And our current physics has no solution, explanation, or ideas on how to handle the asymmetry. The second asymmetry, and arguably a more significant asymmetry, is "Right-Handed Asymmetry." This is a genuine issue within our universe and modern physics that is not discussed or considered.
A quick discussion regarding right and left-handed particles is in order. This will be a very down-and-dirty discussion. One of the quantum characteristics of elementary particles is "spin." There is much more associated with spin, but for this paper, we will only worry about right-handed and left-handed spin, which describes the direction of a particle's spin.
Within our universe, Neutrinos are by far the most abundant particles. There are millions upon millions of Neutrinos passing through our bodies every second of every day. All of the observed Neutrinos in our universe have left-handed spin. A Neutrino with right-handed spin does not exist in our universe. In other words, there is a right-handed spin asymmetry in our universe with the most abundant elementary particle in our universe.
The next left-handed interaction is of great importance in chemistry and particle physics. This interaction involves the weak nuclear interaction, also known as beta decay. The weak nuclear interaction changes neutrons into protons, and vice-versa, changing protons into neutrons. Once again, maintaining a short description for this paper, the weak nuclear interaction and beta decay is when a neutron decays into a proton and an electron. The weak nuclear interaction also includes a proton becoming a neutron with the addition of an electron. This is where the particle physics part comes in; the decay processes for protons and the change process for neutrons involve the W (plus and minus) and Z Bosons. The issue here is W and Z Bosons are only left-handed, and they only interact with left-handed spin protons, neutrons, and elementary particles. As for right-handed protons and neutrons, there is no specific information regarding what occurs with these particles.
The proton and neutron are the basic building blocks of all matter in our universe. Yet there is a distinct asymmetry associated with these building blocks for which there is no answer or understanding. The asymmetry related to the universe's "building blocks" goes much deeper than the elementary particles that make up the universe as we know it. The right-handed asymmetry also involves another set of building blocks on Earth: amino acids, the basic building blocks of all life here on Earth. Amino acids also come in right-handed and left-hand molecules. Only the left-handed amino acid molecules are the building blocks for the proteins in all of the life that we know.
To put all of this into perspective, all of the matter that we know of in the universe and all of the life that we know of here on Earth are all about left-handed interactions. In other words, as we know it, we live in a left-handed universe with no known reason or explanation for this. This lack of knowledge begs the question; does a right-handed antimatter universe exist in another dimension since it does not exist in our known universe? If it does, it would account for most of the missing symmetry in our known universe.
Large Overlapping Dimension Further Information
Information and evidence indicating the existence of large, overlapping dimensions within our current knowledge of physics and the universe goes beyond what was covered above. We know that our universe is expanding, which affects the vacuum energy density of space. Maintaining the same energy density in the vacuum of the universe's space requires an influx of energy into the universe's expanding space. Larger overlapping dimensions can account for and supply the vacuum energy necessary to maintain a constant energy density in expanding space.
Thinking Outside of the Box
Regarding the expanding space of our universe, a fourth dimension could cause this expansion. Additionally, the question of "What is the space of our universe expanding into?" routinely arises. The answer may be as easy as our 3D space grows into the 4D space it is a part of.
One of the principal endeavors of physics today is the unification of quantum physics with relativity through a "Grand Unification Theory" and then discovering the "Theory of Everything." Adding large overlapping dimensions increases the overall platform available to work and move forward on unification. Specifically, increases in the amount of energy, gravity, and particles available in more dimensions provide more opportunities for achieving unification. The same thought holds for a Theory of Everything. Increasing the physical attributes of the universe available to work with can increase the chances of finding a Theory of Everything.
One additional aspect of multiple overlapping dimensions is independence. That is, our three-dimensional space can be independent of other dimensions, thus allowing us to have the physics concepts unique to our space. Similarly, a 4th overlapping dimension of space can have its unique physics and concepts, some of which may "leak" into our three dimensions of space. As we expand and learn more about additional dimensions of space, there will be new frontiers and energy levels for us to learn. This additional knowledge through extra dimensions can also help us understand what we do not entirely understand in our three-dimensional physics.
Riemann's paper was proof for 'N' dimensions. Relating this to the standard model, nothing says there are only three generations of particles. It is not unreasonable to presume that there are more, possibly, 'N' generations of quarks and elementary particles corresponding with more dimensions of space. We cannot claim that because something has not been discovered, it does not exist. This is particularly true when established mathematics and previous theories have looked at multiple dimensions for solutions. Moreover, given that our current knowledge indicates there are more dimensions and potentially more generations of elementary particles, we need to look for these things until we can prove they do not exist.
Conclusion
When was the last significant discovery in physics? If we think about quantum physics and relativity, both were discovered over 100 years ago. Additionally, the discovery of both quantum physics and relativity came about from physics concepts already in place. Relativity was based on Maxwell's work with electricity and magnetism, while quantum physics came from Planck's work with black-body radiation. A universe of multiple dimensions is the leading theory being worked on today through string theory. So, a multi-dimensional theory is something that has been introduced previously. The current string theory looks at dimensions compacted into a small area of space. If it is possible for extra dimensions to be small, then symmetry would suggest that our universe could also be composed of extra, large, overlapping dimensions. Furthermore, there is nothing in today's physics that forbids large, overlapping dimensions.
This paper looked at part of our current knowledge base for physics and picked out some of the most direct pieces of evidence and information that point to our universe having multiple large dimensions of space above our three dimensions of space. Furthermore, past and present theories and mathematical papers have looked at multiple dimensions of space as being a part of our overall universe. Additionally, multiple large, overlapping dimensions are the most direct and easiest way to account for the asymmetries in our current physics and understanding of our three-dimensional universe. There is also direct visual evidence for multiple large, overlapping dimensions; consider the Klein bottle and other objects we see in three dimensions that can only be "opened" up in four dimensions of space.
There is a purpose to all things about the universe we live in. Therefore, the physics of the universe and everything we discover about the universe and in physics must have a purpose. If we do not have a physics purpose for everything discovered so far, then more must be discovered. Furthermore, a purpose to our universe and its physics also dictates that we do not have unanswered questions about anything we have found. If we have to rely on something unknown and not understood, we have a hole in our understanding of current physics and our universe. Today's physics provides hints and clues that point us in directions to look further. It is up to us to accept this challenge and move toward a greater understanding of our universe.
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