MULTIPLE DIMENSIONS, A UNIVERSE OF LARGE NOT SMALL DIMENSIONS
Abstract
We have learned so much about how our universe and our world operate through the science of physics. It only makes sense for us to rely on physics to provide us with 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 in order to learn more and to better understand what we know is the first step to moving forward and moving outward into our universe.
Introduction
In 1868 Georg Friedrich Bernhard Riemann's paper on 'N' dimensional space was published. Essentially, Riemann’s paper mathematically showed that it was possible for the geometry of our universe to have ‘N’ dimensions. Information regarding Planck length was not known at this time. This infers that the conclusion in Riemann’s ‘N’ dimensional space paper was for large overlapping dimensions. This is 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.
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 lowered the size of his extra dimension. He did not, however, lower 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 in order 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. Unification of forces via the extra dimension theorized by Kaluza ultimately had some problems, the biggest of which was there was no “evidence” of a large overlapping fourth dimension. Thus Kaluza’s theory fell out of favor.
However, 100 years later the question arises as to what evidence would a fourth dimension present to those living in three dimensions? A Side Note: There is information/indication 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? It should also be noted that work has been done to extend Maxwell’s equations into ‘N’ dimensional space.
Some additional questions for future consideration regarding ‘N’ dimensional space:
1. Why not keep dimensions large rather than going small as in string theory?
2. That concept, mathematics or physics prevents large, overlapping dimension?
3. Riemann’s original theory had ‘N’ dimensions of space, so why stop at four?
4. What in nature or physics requires unification beyond electricity and magnetism?
5. Why not expand our knowledge and/or theoretical physics into four dimensional or higher spaces first and then look to see if unification of forces is possible?
Discussion
Established mathematics as well as previous theories that looked at a universe with more than three-dimensions shows that a multi-dimensional universe is not a “new” idea. String theory, the current unification theory, looks at a multi-dimensional universe. With string theory, the extra dimensions are confined to an unimaginably small space that is experimentally impossible to reach and/or to verify the existence of such dimensions. In other words, in general a universe of multi-dimensional space is an excepted theory. So, why can’t a multi-dimensional universe be comprised of larger, overlapping dimensions, and does our current physics and knowledge provide any 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 which in turn is embedded in our three-dimensional space. This presumption is very straight forward given that a two-dimensional space can be created by stacking one-dimensional spaces and a three-dimensional space can be created by stacking two-dimensional spaces. Additionally, two-dimensional spaces are routinely used in mathematics and physics as a tool for extending concepts and theories into higher dimensional space. Therefore, by extension we can presume that our three-dimensional space is embedded in a four-dimensional space. Like Russian nesting dolls and this can go on beyond four-dimensions.
Gravity is a real physical part of all mass in our three-dimensions and it envelopes all of space and time in our universe. Therefore, our three-dimensional gravity will also have an influence on the embedded two-dimensions. 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 expectations is the influence 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 make up the nucleus of every atom in our universe. The second generation of quarks is exactly like the first generation of quarks, only a bit more massive and energetic. The stability of our three-dimension proton 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 this second generation of quarks, as well as the third generation, simply exists 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, that things happen for a reason. This observation and belief is in general the basis of “Unification.” Keeping things consistent, why is there not a second generation of proton and neutron? 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. But, 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 and their existence there 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 largest questions associated with our universe and its physics is the lack of any antimatter in our universe. However, the existence of antimatter is real in that it has been created through experiments and used in some experiments. The reality of the existence of antimatter, but the fact that none of it is present in our universe represents a very large issue with respect to one of the basics principles of physics, symmetry.
So far antimatter is nowhere to be found in our universe creating a huge symmetry issue. Adding multiple, larger, overlapping dimensions allows for a place for antimatter to exist outside of our universe and therefore maintaining antimatter 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
The antimatter asymmetry is not the only asymmetry within our universe and our current physics with no solution, no explanation and no ideas on how to handle the asymmetry. The second asymmetry, and arguably a more significant asymmetry is “Right-Handed Asymmetry.” This very real issue within our universe and physics is for the most part not discussed or considered.
A quick discussion regarding right and left-handed particles is in order here. 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 the purposes of this paper we will only worry about right-handed and left-handed spin, which is a description of the direction of a particle 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 has never been observed. 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 only interaction is one of great importance in chemistry and particle physics. This is the weak nuclear force also known as beta decay. The weak nuclear reaction/force changes neutrons into protons, and vice-versa, change protons into neutrons. Once again, maintaining a short down and dirty description for this paper, the weak nuclear force and/or beta decay is the process where a neutron decays into a proton and an electron. The weak nuclear force also includes a proton becoming a neutron with the addition of an electron. This is where the particle physics part comes in, the changing/decaying processes for protons and 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 and reactions or interactions, that is a physics family secret that is not discussed.
The proton and neutron are the basic building blocks of all matter in our universe. Yet there is a very distinct asymmetry associated with these building blocks for which there is no answer or understanding. The asymmetry associated with “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 are the basic building blocks of all life here on earth and they also come in right-handed and left-hand molecules. It turns out that only the left-handed amino acid molecules are used as 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 only universe and there is no known reason or explanation for this. This begs the question; does a right-handed antimatter universe exist in another dimension of the overall universe since it does not exist in our known universe? If it does, it would account for 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 of space. In order to maintain the same energy density in the vacuum of space there has to be an influx of energy. Larger overlapping dimensions can account for and/or supply the required influx of vacuum energy. This could be considered as being directly related to a fourth dimension accounting for the expansion or our universe.
One of the principle endeavors of physics today is unification of quantum physics with relativity through a “Grand Unification Theory” or a “Theory of Everything.” Adding large overlapping dimensions increases the overall platform available to work forward on unification. Specifically, increases in the amount of energy, gravity, and particles available in more dimensions provide more opportunities for achieving unification.
One additional possible aspect of multiple overlapping dimensions is independence. That is our three-dimensional space/universe can be independent from other dimensions thus allowing us to have physics concepts that are unique to our space. As we expand and learn more about additional dimensions of space we will be provided with new frontiers of space to learn about and new levels of energy to help us learn. This additional knowledge through additional dimensions can also help us understand what we currently do not completely understand in our own three-dimensional physics.
Riemann’s paper was proof for ‘N’ dimensions. Relating this to the standard model, there is nothing that 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 it 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 move forward looking for these things until we can prove they do not exist
Conclusion
When was the last major discovery in physics? If we think about quantum physics and relativity, both were discovered over 100 years ago. Additionally, both quantum physics and relativity were based on moving forward with physics concepts that were already in place. Relativity was based on Maxwell’s work with electricity and magnetism while quantum physics was based on Planck’s work with black body radiation. A universe of multiple dimensions is the main theory being worked on today, string theory. So a multi-dimensional theory is not something new. The current 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 comprised of large, overlapping dimensions. Furthermore, there is nothing in today’s physics that forbids large, overlapping dimensions.
This paper looked at our current knowledge base for physics and picked out some of the most direct pieces of evidence/information that point to our universe having multiple large dimensions. Furthermore, past and present theories and mathematical papers have done work in multiple dimensions showing multiple dimensions 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 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 also have purpose. If we do not have a physics purpose for any of the things discovered, then there is more to be discovered. Furthermore, a purpose to our universe and its physics also dictates that we do not have unanswered questions about anything we have discovered. If we have to rely on something that is unknown and not understood then we have a hole in our understanding of physics and our universe. Today’s physics provides us hints and clues that are pointing us in directions to look further. It is up to us to accept this challenge and move toward a greater understanding of more of our universe.
