Introduction: A Unifying Theory of Dimensional Geometry and Interaction
What If We Have Missed the Extra Dimensions of Universe Because We Don’t Understand How to Look for Them?
This is the introduction of the companion articles to my Unifying Theory of Dimensional Geometry and Interaction series on YouTube. The goal is to go more in-depth and technical on the topics I discussed in my videos. You can view the series in progress by viewing the playlist here: https://www.youtube.com/playlist?list=PLhloW30YwYviMcZ_o6qpaREx2ZQbDL2tr
This article focuses on expanding my introduction from 00:00–08:35
A Brief History of Extra Dimensions
The search for extra dimensions goes pretty far back, but it has been a persistent idea since Einstein’s Theory of General Relativity (GR) was published back in 1915. This is because, while the GR answered many cosmological conundrums (such as the orbit of Mercury and the gravitational red-shift of light), it left us with even more unanswered questions:
- Why does spacetime curve?
- What is spacetime curving into?
- How exactly are space and time connected?
- What do we do with all these “infinities” that show up in the equations?
- How can we reconcile gravity with quantum mechanics?
- WTF is up with black holes?
- and many more…
The first swing at trying to better reconcile the meaning of GR came from a chap called Theodor Kaluza who published a paper in 1921 that solved GR using five dimensions. The equations not only helped rationalize GR, but they also ended up reproducing the results from the Maxwell equations for electro-magnetism, often called the “Kaluza miracle.”
However, the scientific community HATED (HATES) the idea of extra dimensions, and Kaluza’s proposal came shortly after another extra-dimensional drama where quaternions (equations for 4D rotation) were used to describe electro-magnetism. That’s right, Maxwell's equations originally started out with quaternions. But from the pressure from the scientific community, those equations were “purified” of the implication of extra dimensions to what we know today.
The two main problems with extra-dimensions in the scientific community are:
- The math is harder, if the simpler version works well enough, why change it?
- “Where is it?!?!?” — Extra dimensions are hard to conceptualize, so postulating them is difficult when people can’t get their head around them.
In the hopes of addressing the second problem, Oscar Klien proposed a quantum interpretation in 1926. In this modification, the answer to “where is the extra dimension?” is that it is very very small, so we can’t see it. It’s a “quantum dimension.”
However, this created some larger math problems, akin to fitting a square peg in a quantum hole, as Oscar was trying to fit the theory into expectations, rather than the other way around.
So, extra-dimensions fell by the wayside. There was some life to the idea starting in 1937 with the introduction of S-Matrix theory, but that lingered along with small support until the surge of “String theory” in the 1980s. This has been referred to as the “Superstring revolution,” and it maintains a more robust following to this day, with advocates like Michio Kaku.
The problem with String Theory, and its many variations, is that it is… well… messy. It’s difficult to test, requires a lot of assumptions, and it is constantly being modified to address different issues. It’s the theoretical physics equivalent of a Frankenstein’s monster.
Most of all, however, is the lack of a “graviton.” For string theory to be correct (and lots of our current quantum field theories as well), we need to find and prove the existence of a graviton to finish a complete picture of “force carrying particles.” To date, we have not found it.
So… modern physics, with all its progress and breakthroughs, remains at a bottleneck around gravity. Without being able to explain it, or reconcile GR and quantum field theory/quantum mechanics, we know we don’t really understand what is going on.
This what I have set out to accomplish: Reconciling GR and the quantum world. While I am not the first (or second, or third…) to try doing with extra-dimensions, I do believe I have something unique to offer. I am going to propose a new way of thinking about dimensional geometry and interaction.
In my first video, which includes Chapter 1–4, I focus on showing how gravity can be explained with extra-dimensions and doesn’t require a “graviton” or “force-carrying” particle. More so, I hope this approach gives an idea of how I will be working my way “down” the size and force scale.
Unifying Theory, not Unified Theory
First, let me state that I am calling my theory “unifying” and not “unified” for a very important reason. This is NOT a proposed “Theory of Everything.” I think one of the big reasons we have failed to unify GR and Quantum Mechanics is that we keep trying to come up with a theory that explains absolutely everything, dust off our hands, drop the mic, and call it day.
One of the reasons I am so excited about the ideas I am proposing is that I believe it will open a whole new world of physics to explore. I think it is short sighted, to say the least, that this one problem, as difficult as it has been, is the one thing standing between us and a complete understanding of the Universe.
Getting to the Point: Extra-Dimensional Geometry
The purpose of this theory is to propose a new way of thinking about extra-dimensional geometry. The case I will make is that the reason we have failed to prove/validate extra dimensions thus far is that we have been thinking about them the wrong way. We have “burdened” the science and the math with too many assumptions about what we should expect from extra-dimensions that we have missed the observable and “obvious when you see it” evidence right in front of us.
At the end of the theory, I will show that every universal “force” we observe is just an effect of relativity and the dimensional “shape” of the Universe as a whole. This is very similar to the proposition of M-Theory. However, my approach to dimensional geometry is dramatically different. For example, my approach does not require lots of quantum dimensions, or “strings” for that matter.
Some of the arguments I will be making are:
- Modern geometry has failed to acknowledge additional angles and degrees of movement needed to understand extra-dimensions. Even though they, ironically, show up in many of the equations we already rely on.
- Modern theoretical physics has too quickly given up on foundational principles of physics, such as “conservation of energy,” in their quest to understand quantum mechanics and cosmology.
- The laws of physics don’t “break down” at a quantum level if you include extra dimensions of motion.
- Singularities and infinities are consequences of poorly applied geometry and calculus. This includes using hyperbola and projection to try and understand extra-dimensions, but then failing to reverse-engineer them or put the findings in context.
Where’s the Beef? Prove it.
So, the problem with extra-dimensional theories so far is that they are so hard to prove. That leads to the BIG question: Can I prove this one?
The answer is YES! And here is how I am going to go about it:
- First, I am going to go one step at a time from gravity (General Relativity) down to Strong and Weak force showing how the same approach can be used across the entire scale.
- Once I do that, I will produce a simplified version of the Standard Model that is unified with General Relativity.
- I will describe several real-world experiments that can be performed to validate or invalidate various assertions I make throughout this process. So far, sadly, they are all beyond my resources, but they are absolutely practical and possible, especially compared to massive endeavors like the Large Hadron Collider or Space X.
- Finally, I will produce a series of “new things we can discover” from this approach. These new discoveries will be the key to confirming my theory.
To hold you over, I will be doing some deep dives into the math around black holes. That won’t “prove” my theory, but it will show how my approach can neatly fit all current observations and even explain things like “Hawking Radiation” and resolve the “Information Paradox.”
So, Let’s Get Started…
I have published this article at the same time as my Chapter 1 article: Understanding Extra-Dimensional Concepts. I intend to publish an article to accompany each chapter of my video, but it will always come after the video. This is so I can use the feedback from the video to know what to focus on most (or correct) in the article.
Next Article: Chapter 1: How to Think About Extra-Dimensions in Physics
