Excerpts Note & Synopses
A sneak peek of ‘Einstein’s Intuition: Visualizing Nature in Eleven Dimensions’ is available here, which includes the preface and chapters one through four. Select a chapter or the synopses from the book excerpt menu at the top of this window or by clicking the links below.
|Preface||Chapter One||Chapter Two||Chapter Three||Chapter Four|
The full book is available in hardcover full color, softcover full color, iBook and audiobook here.
Humanity has always yearned to glimpse what lies just beyond the horizon, to touch that which is just out of reach. Our curiosity guides us to seek what lies beyond our senses and to make sense of a world contradictory in character. Great explorers of the past filled in the map of our world. Their charts enriched our conceptual access to the great beyond. But this was only the beginning. The world is only a small part of what needs to be mapped. The structure of reality, the Universe, the laws of physics, and the deep underlying character that supports it all needs to be mapped if we are ever to have intuitive answers to our biggest questions. Einstein was the last great champion of the quest to obtain this complete map. He took our barren notions of physical reality and filled in details that no one before him had imagined. He reached deep inside himself, touched the great beyond, and called the experience “lifting a corner of the great veil.” It is time for us to lift the remainder of that veil. It is time for us to discover the rest of Nature’s hidden structure and to learn how to simultaneously conceptualize eleven dimensions.
Part 1 – Returning to a Conceptual Approach
This chapter introduces the reader to the history of how our conceptual map of the cosmos has changed over time. Our earliest maps depicted the earth as a flat disk surrounded by a giant rotating sphere that was embedded with thousands of tiny points of light. With more observations the world switched from being described as flat to round. To account for the motions of the sun and moon three distinct spheres, three celestial levels, were added to the map. Then when the motions of the five visible planets were noticed the map of the heavens evolved into one with seven levels inside the original sphere of stars. Today all of these notions have been replaced by a map that places our world orbiting around an average star that is located in a rather average looking galaxy. The best current map we have of the cosmos (general relativity) was authored by Albert Einstein. His map revealed a character of spacetime that had never before been accounted for. But despite the improvements, Einstein’s map is still not complete. There are many observations that it does not explain or predict. In fact, the entire realm of the super-small entirely contradicts the rules of general relativity. Quantum mechanics is the set of mathematical equations that are used to statistically explain occurrences in that microscopic realm. These equations have not been combined into any useful or intuitive map. They have also not been reconciled with the requirements of Einstein’s map. Today we stand with an incomplete map in hand as we peer into the structure of Nature.
In order to continue our quest for the final map of physical reality we need to be willing to completely rewrite the foundational structure of that map. The foundations of every map are the assumptions within it that define the structure of space and time. All higher-order geometric rules, structures and interactions stem from those base assumptions. Since we have been unable to explain the mysteries of Nature through the lens of our current assumptions we need to revisit those assumptions and consider the possibility of a new structure underneath it all. We need to challenge our most basic assumptions about space and time.
To restructure our conception of physical reality we need to make sure that we understand what a dimension is. The dimensional parameters of a given map form the basis and structure for everything else that follows. This chapter discusses exactly what physicists mean by the word ‘dimension.’ It then explores the connectedness of spatial dimensions and explains how those descriptors are part of our map of physical reality. Next we examine the idea of curved spatial geometries, which leads us to the possibility of additional dimensions. The dimension(s) of time are also briefly introduced in this chapter.
This chapter introduces some very important clues that we will use to piece together our new foundational structure of physical reality. Some of the biggest mysteries of Nature come from the quantum nature of the microscopic realm. Quantum mechanics has taught us that there is a minimum discrete unit of both space and time. Fundamental electric and magnetic interactions are all based on discrete quantum units. Light even exists in quantum packets called photons. Somehow all of these quantum packets travel through the fabric of space as a mysterious wave but they also retain their quantum characteristics. All of this brings us to the suggestion that the foundation of our new map of physical reality must incorporate a quantized structure for the fabric of space and time.
Part 2 – The Framework of Quantum Space Theory
Chapter 5 – Absolute Volume
In this chapter, the reader is introduced to the basic framework of quantum space theory (qst). They learn how to conceptualize nine spatial dimensions simultaneously and discover how it is possible to move about from one location to another without changing x, y, z position. The three types of volume (interspatial, spatial, and superspatial) are introduced and the concept of two time dimensions is foreshadowed. This new geometry reveals many characteristics of spacetime that are ignored in the familiar four-dimensional descriptions. These additional geometric parameters are where the mysterious effects of quantum mechanics and general relativity come from. Elevating our comprehension of the structure of Nature (the map in our head) to include all of the eleven dimensions that make up physical reality has the effect of bringing us into sync with its actual form. In doing this we gain access to the intuitive solutions of the greatest mysteries of modern physics.
Chapter 6 – Space
The concept of space has always been elusive. Humans are accustomed to conceptualizing space as nothingness – what you have if you remove everything from a region. Yet we have always known that space is imbued with properties. For example, distance and volume still remain once we remove everything else from a region. This measurable quantity is not nothingness – but what exactly is it? What is it made of? What other properties does it have? How do we extract a definition of distance from the geometry of Nature? What are the geometric assumptions that lie beneath our answers to those questions? These questions and more are tackled in this chapter. Based on our new eleven-dimensional geometry we come to a conclusion on what distance really is, how the structure of space composes the four dimensions of Nature that we are familiar with, and why space only exists in a discrete sense.
Chapter 7 – Time
The notion that time passes at a universal rate in all locations throughout the universe seems obvious to us. 100 years after Einstein proved this idea to be false the majority of the world still thinks that traveling through time at different rates is something that is found only in science fiction movies. The surprise is that time travel is a scientific fact. This fact violates our familiar four-dimensional intuition, it comes with a glut of philosophical questions, but it is a fact nonetheless. Long ago physicists set out to account for this character of Nature. In this chapter we discover that from the eleven-dimensional vantage point this fact is not only intuitively explained, it is also required by the geometry of spacetime. The passage of time is defined uniquely at each location in the sea of spacetime. As the character of that sea changes, from one region to another, the rate at which time passes reflects these changes. All of this can be read from the key of our new eleven-dimensional map. It explains the arrow of time that we experience, and it resolves the philosophical conundrums of time travel.
Chapter 8 – The Speed of Spacetime
Many people know that physicists say that the fastest anything can go through space is the speed of light. People often respond to this statement by asserting that with better technology we will one day find a way to go faster than the speed of light. They fail to recognize that the speed of light is not a reflection of our technological capabilities. Instead it is more akin to saying that you cannot go further north than the North Pole. The geometry of spacetime dictates this condition. It is inscribed in the texture of physical reality. This chapter explores that texture and explains why this condition naturally follows from the eleven-dimensional geometry of Nature.
Chapter 9 – Warped Spacetime
Here, we dive into the mysteries of gravity. The magical force that pulls the moon toward the earth has, like an endless riddle, long echoed through the minds of humankind. Einstein connected gravity to a geometric distortion that extended into higher dimensions, but he never granted us with a full picture of these additional dimensions. Now that we have learned how to conceptualize these other dimensions, our map of the Universe naturally accounts for the effects we credit to gravity. Throughout this chapter we practice switching our intuition from the four-dimensional view we grew up with to the eleven-dimensional view of qst. As we do this we discover that gravity’s riddles readily transform into accessible conditions of the structure of Nature.
Chapter 10 – The Bucket
The ancient philosophical debate about the nature of acceleration versus time and position rests on whether or not an underlying reference frame exists in Nature. In this chapter we discover a unique solution to this bitter debate. We find that from within the eleven dimensions that define our universe, there is an underlying reference frame – one that we call absolute volume – but from the ultimate perspective (any higher-dimensional resolve) that reference frame is as fluid as the rest. The reason that time and position are measures that can only be defined in comparison to some other time or position, while acceleration needs no comparison to be defined, is a direct result of the quantized structure of spacetime. This condition is also required by the geometry of Nature.
Chapter 11 – Dimensional Analysis
This chapter reviews the dimensions that we have explored in this part of the book. It then introduces the curious concepts of spinors and the requirements of limited dimensional freedom that gravity sets in the universe. After explaining how these conditions are consequences of the quantized geometry we have been exploring we examine the philosophical requirements for extending the rules of that geometry. We discuss where these rules take us, and how they open the next great door of human imagination. It is here that the heartstrings of our personal life are connected to the external world and the infinite is found in the finite.
Part 3 – Physical Reality in Eleven Dimensions
Chapter 12 – The Questions of Quantum Mechanics
In order to understand how miraculous it is that we can solve the big mysteries of the small realms simply by changing our geometric assumptions about spacetime we need to be familiar with those mysteries. To that end this chapter discusses the enigmas of quantum mechanics: particle/wave duality, the non-locality of the universe, and the photoelectric effect. After each mystery is developed we then turn to view each of them from the eleven-dimensional perspective that we have been exploring. Every time we do this, the process becomes a little easier and the mysteries of advanced physics go from imposing frustrations to delightful and accessible parts of Nature’s geometry.
Chapter 13 – Beneath Quantum Mechanics
In this chapter we explore a deterministic explanation of the double slit experiment (Bohm’s interpretation), and come into possession of a clear ontology for the state vector.
Chapter 14 – Quantum Tunneling & Entanglement
This chapter is dedicated to an exploration of the mysteries of quantum tunneling and entanglement. We start from a conceptually historical approach and then reexamine the data from the geometric perspective of our new map. What we find is that although all of these effects are mind bending from our four-dimensional perspective, they are all natural and simple aspects of Nature when we frame it in eleven dimensions.
Chapter 15 – Black Holes and Elementary Particles
One of the most profound mysteries of our time may turn out to be centered on the question of what black holes are like inside their event horizons. By definition no light escapes a black hole to reveal its interior structure. For this reason, the insides of black holes have been assumed to be forever beyond our grasp. As it turns out, that limitation only exists when we frame physical reality as being four-dimensional. In this chapter, we discover exactly what a black hole is, what its full geometry looks like (even within its event horizon), and how black holes are related to entropy and the discrete pieces of space. We even learn how and why black holes form. All of these discoveries are automatic requirements of our new geometry.
Chapter 16 – The Constants of Nature
The physical quantities that appear over and over in all of our equations in physics, chemistry, biology and so on are often taken as brute unexplainable values. The anthropic principle is often used (in practice) to squelch questions about how these values came to be as they are. The universe, they say, acquired these values randomly and since only the combination that we have in this universe leads to the formation of life, the fact that we are here asking the questions shows the outcome of the universe’s initial dice roll. This is not a profound solution. Even a random mechanism capable of setting the values of the constants of Nature needs to be explained. In this chapter, we discover the explanation for how the constants of Nature have come to have the values that we measure. We also discover that there is a non-arbitrary scale within Nature. All of this drastically reduces the mathematical complexities of the equations we have become familiar with and it gives us a solid understanding as to why the universe is the way it is.
Chapter 17 – Deterministic Versus Stochastic Models
Is the universe deterministic or stochastic? Do things evolve strictly in accordance with cause and effect? Or is there a part of the universe that ultimately is not bound by cause and effect? This has been a timeless debate. Today’s physicists are divided on the matter because the two main branches of physics do not clearly come to full agreement on this issue. General relativity is deterministic. Most of quantum mechanics is also deterministic. The ad hoc interpretation of state reduction that we use today is decidedly stochastic. That is the only part of quantum mechanics that is stochastic. The interesting thing is that the predominant interpretation of state reduction is not the only consistent interpretation available. So the answer to our question boils down to our justification of the interpretation we select for quantum mechanics. But how do we decide which interpretation is correct? In this chapter we explore these issues. In the end we find that our new model depicts a universe that is fully deterministic. The seemingly stochastic equations of state reduction used in the standard interpretation are revealed as solutions that are based on only part of the dimensions in the universe. When the full dimensions of Nature are considered the system regains determinism. This means that every action has a cause. The philosophical impact this can have on how we choose to live our lives is quite prophetic. What this means is that the geometry of Nature is a very personal issue.
Chapter 18 – Emergent Reality
The complex structures around us are always emerging and evolving. Where do they come from? What determines their structure and formation? What does it all depend upon? And what drives the evolution of these systems? Understanding the emergence of form from the underlying geometric foundation of Nature is the focus of this chapter. We explore the concept of supervenience and discover that the KD map eliminates the present day problems with illogical infinites that quantum mechanics currently wrestles with in their maps.
Chapter 19 – The Hierarchy Problem
A popular question today asks why the force of gravity is so infinitesimally weaker than the other three forces. By comparison the strong nuclear force, the weak nuclear force and the electromagnetic force are roughly all the same strength. How is it that gravity is so different? Where does this difference come from? This question is called the hierarchy problem. In this chapter we learn that there is a difference in the origins between the three similar forces and gravity. Gravity is the effect of a small inelasticity in the quanta of space. This inelasticity is what sets up spacetime density gradients or the curvature of spacetime. The reason that the force of gravity is so very weak is that this inelasticity is many powers smaller than the degree of elasticity in the quanta. From this we discover that the four forces are all expressions of the interactive properties belonging to the geometry of Nature. Exposure of that full geometry brings unification.
Chapter 20 – Beyond Forces
If we were to look up and watch an astronaut orbit the earth in nothing but his spacesuit we would say that the force of gravity is what is responsible for her elliptical path. By doing this we are asserting that a force is acting on the astronaut. But when a force acts on an object that object is accelerated. Whenever someone is accelerated they can feel it. So does our astronaut feel some force pulling or pushing on her and accelerating her toward the earth? The answer is no. The astronaut is not being accelerated at all. Instead she is going straight through curved space. As it turns out, forces are often titles we give to our mischaracterizations of the world. We form expectations for how things should work based on the four dimensions we believe in. Then, when we observe occurrences that do not fit within that set, we make up ‘magical’ forces that exist over and above the rules we assumed in order to explain the observations we made. Therefore, forces are little more than shadows of the mistakes we made when we were originally framing the geometry of the universe. Once we see the universe in its full geometric form these forces dissolve and the mysterious effects of these “forces” are readily accessible. Nature’s true geometry should already include the effects we blame on forces.
Chapter 21 – Quantized Vortices
Expanding on Lord Kelvin’s beautiful idea we explore the rules of formation for vortices in a superfluid and discover that these sonons naturally match up with the fundamental particles of mass in our universe. The formation of these “superfluid smoke rings” offers us a new understanding of the Higgs mechanism and opens up the possibility of understanding even mass in terms of geometry.
Chapter 22 – Superfluidity
In this chapter we enrich our exploration of what it means to be a superfluid and we find that the mere assumption that the vacuum is a superfluid automatically leads to the expectation that its dynamics are controlled by the Schrödinger equation. We also explore how spacetime curvature can be explained in terms of analogue gravity.
Chapter 23 – Illuminating Dark Matter
Dark matter haloes surround galaxies increasing the amount of gravitational distortions in these outer regions. But no one has been able to explain where this extra gravitational energy comes from. What causes these haloes to form? Why don’t we find the culprits in our laboratories here on earth? How do we explain the structures we see in our largest telescopes? These are the questions we address in this chapter. What we discover is that the dark matter haloes surrounding galaxies are the effects of phase changes in the sea of spacetime. Since spacetime is particulate, just as water is, it can have different phases. These phases correspond to different geometric connectedness just as the phases of H2O do. When we account for the varying geometric arrangements of these space quanta with a dependency on temperature we naturally get the distortions that we have been attributing to dark matter.
Chapter 24 – Bohmian Mechanics
This chapter is for the mathematician that wants to dive into the set of equations that best express the intuitive geometry that we have been exploring throughout the book. (Although the full mathematical set has not been completed at this point.) The math is explained in words and equations. A discussion on the history of Bohmian mechanics, which is the foundational set of equations, is also included. Then a suggestion is given for the direction in which the final formalism will come from – a suggestion that is based on the insights our our new eleven-dimensional map.
Chapter 25 – Symmetry and Symmetry Breaking
The laws of physics don’t depend on where you are or which direction you are going. Why? Why do all our equations assert that the laws of Nature are time-reverse symmetric yet they all clearly seem to unfold with a preference in time? Is time ultimately symmetric or asymmetric? What other symmetries exist in Nature and why? These are the questions that are addressed and answered in this chapter. The characters we call symmetries in Nature all stem from the geometric structure that defines the fabric of spacetime. By understanding this structure we come to terms with the symmetries of Nature.
Chapter 26 – Entropy
The second law of thermodynamics states that if there ever exists a system that possesses less than its maximum entropy (disorderedness) then it will be extremely likely to have higher entropy both before and after that moment. This has been accepted as one of the most inviolate, ironclad tenants of our universe – yet it has never been explained. Why do systems tend toward disorderedness? Where does the law of entropy come from? In this chapter, we discover that the particulate nature of space leads to entropy because geometric mixing is an inherent part of all systems in spacetime. We also explore entropy to greater depths and discover its connection to evolution and the Big Bang.
Chapter 27 – Genesis
In this chapter we come to a topic that some have said lies ‘outside the realm of science.’ The first thing we discover is that they were wrong. The question of what caused the Big Bang, what got the whole thing started to begin, with turns out to be encased by the infinite cascades of dimensional hierarchy that is within the set of our KD map. This means that we can answer the question of ultimate origins. The answer turns out to be very elegant and perhaps a bit surprising. Nietzsche’s concept of eternal recurrence reemerges through this insight and this reemergence pulls humanity into the depths of this question in a whole new way.
Chapter 28 – Dark Energy
Now that the reader has had some practice seeing physical reality in eleven dimensions, it is time to address a mystery that is so captivating that I had a hard time saving it for last. This is the mystery of dark energy. The chapter begins by giving a history of the discoveries that led to our modern understanding of the expanding universe, and humanity’s struggle with identifying its cause, which we have cleverly named dark energy. The reader is given the chance to apply their new eleven-dimensional intuition to solve this mystery. To do this we must each address the question of expanded space – what does that really mean? Then we must discover what is really causing the light reaching our eyes from distant stars to be red-shifted. As we have come to expect, the solution is surprisingly clear and delightfully intuitive from our higher-dimensional vantage.
Chapter 29 – Intellectual Astronauts
This chapter warms the reader to the philosophical impact that this new geometry has on humanity. A new way of seeing the world around us has always changed the way we interact with it. The responsibility we have with each new improvement is the task of absorbing discovered truths and incorporating them into our daily lives. Here we find that our entire way of being, our most basic mode of existence (at least in the West) is based on assumptions that do not ultimately hold. Where do we go from here? The KD map has a lot to say about this and our personal lives.
Chapter 30 – The Wilderness of Intuition
Our curiosity often tricks us into falling for solutions that are made merely of smoke and mirrors when a more rigid solution is not available. The entities that profit most from the continued projection of that smoke have led a campaign to convince us that the truth we seek is not obtainable by science, that the quest of science is not capable of satisfying the deep yearning we have. This is, and has always been, a lie. Now that we possess a richer map of Nature, the apparentness of that lie stands out in the daylight for everyone to see. In this chapter we discuss how the process of the scientific quest is the most fulfilling and satisfying human experience. It throws us beyond ourselves and encourages us to intellectually and emotionally transcend any barriers that hold us back. The characters of science are the people with passion and vigor for life, the seekers, the explorers and the embracers of wonder. It is through the quest of science that our humanity is redefined and lifted to a new plane.