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OF QUANTUM MECHANICS

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The Theory of Gravity

CONCEPTUAL RELATIVITY

With No Math at All

(Formerly: Relativity in a Nutshell)

by Chongo in collaboration with José

An in-depth, conceptual explanation of the fundamental principles from which the Theory of Relativity is based, explained in the fewest number of words that it can be adequately explained, without resorting to mathematical notation. There is not a single mathematical symbol contained in the text (except the page numbers). The most basic foundations of classical science are described in a way that anyone, regardless of their educational background, can understand, and most of all, explained in such a way that one comes to understand just why they are – indeed, why they must be – true.

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TABLE OF CONTENTS

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Prologue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0

I. Special and General Relativity . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 4

I. Straight Lines and Tilting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

III. Truth and Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

IV. Opinion and Falsehood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

V. The Many Perspectives of Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

VI. The Dimensions of Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

VII. Motion According To Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

VII. Time’s Debut as a Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

IX. The Problem with Light and the Discovery of Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

X. Dimension and Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

XII. Time Being Identical to Space means Many Reference Frames . . . . . . . . . . . . . . . . . . . . . . . . . . 26

XII. The Crux of Relativity: What ‘Now’ Is – And Isn’t . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 30

XIII. Special Relativity’s Straight Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

XIV. The Conservation of Energy and Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

XV. Tilting a Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

XVI. Relativity’s Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . 48

XVII. Using Relativity for Explaining Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

XVIII. What Relativity Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

XIX. What Relativity Doesn’t Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Appendix A: Experiment Demonstrating Special Relativity’s ‘Tilting’ of a “Space”. . . . . . . . . . . . . . . . . . . . . . 83

Appendix B: Experiment to Reveal Our Physically Existent ‘True’ Individual “Space”. . . . . . . . . . . . . . . . . 93

Appendix C: The Shape of Space (‘True’ Space) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Glossary and Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

PREFACE

This is the story of the theory of gravity, the Theory of Relativity, described in a very simple manner, without mathematical notation of any kind. Understanding relativity provides the first step toward seeing why the universe is the way it is, by describing space and time and the motions of those ‘big’ (meaning bigger than an atom) things which lie within space and time better than any other body of ideas existing. (The motion of the smallest things, like individual elementary subatomic particles, is accurately described by another theory, the theory of energy: the Theory of Quantum Mechanics). The chapters that follow will explain how relativity is a most natural (meaning inescapable) property of a ‘real’, ‘working’ universe, as is the one in which we live. The relativity of (the inseparability of) space and time emerges, out of the very nature of a most naturally occurring 'miracle', which is the all-encompassing ‘miracle’ everywhere, always, that we call existence.

This story of Relativity is an adventure in abstract thought and a fundamental milestone in any genuine, objective pursuit of truth: one lacking any preconceived prejudice about what truth must be. This part of objective truth’s description will introduce you to what is very likely a completely new way for imagining the universe, and a completely new means for imagining the time and the space that are so very much a part of the universe. Relativity demonstrates how time is absolutely inseparable from space, how tics on a clock are no different in the least from gradients on a ruler, and thus how time is exactly the same thing that space is: simply another physical dimension.

In understanding the Theory of Relativity’s classical description of reality, we can uncover the beauty that lies beneath everything we observe. Seeing this beauty can serve to remove widespread and common myths and misunderstandings that have always left us, and indeed still leave so many to whom education in true physical science, is either unavailable, ineffective, or inaccurate, in the vague ambiguity of mystery. It is this ambiguous mystery that creates of those lacking an understanding of science so much opportunity for the sentimental assertions of dogma and tradition, as well the conclusions that these assertions yield, to shape their thoughts and guide their decisions, instead of letting proven scientific reason do so instead. Now, for the first time in human history, there is opportunity to escape the myths and misunderstandings that are so often the outcome of mystery’s illusion. We can do this using the concrete foundations of physical science for explaining all phenomena, ultimately, for even explaining existence itself. The veil of mystery that might seem to surround relativity and theoretical physics in general is a veil that is no more than a simple lack of common widespread understanding of science (physical theory). It is a lack of common understanding that is born of a common lack of ‘real’ opportunity to ever gain such understanding that ultimately serves to the common disadvantage of all.

Though we may ‘believe’ they are true, the presumed certainty of our simple intuitive descriptions of nature and the corresponding inaccurate and limited conventional model of it that we are ordinarily taught and by necessity must inescapably incorporate into our thinking in order to successfully interact with our environment have consistently and universally provided us with that which is not true about it, to satisfy the need we might have for knowing what is, in the face of the lack of an opportunity to ever realize what an understanding science can demonstrate. In the face of the mystery that a lack of opportunity for understanding leaves, our beliefs may be all that we can presume being true, because we have no other options available. However, for the sake of genuinely understanding nature (meaning in a way which is physically demonstrable), we are required to ‘believe’ nothing, because we can ‘know’ instead, by observing facts, in light of science’s rigorously tested explanations. Using science, we can verify whether something is true or not, because we can physically test whether it isn’t. Yes, the Theory of Relativity (just like the Theory of Quantum Mechanics too) can be physically tested: you can demonstrate its truth, by means of the apparent impossibility of ever proving it untrue. This is to say that science has indeed put relativity to many, many tests: those trying to prove it incorrect (when appropriately applied). Irrefutably, the Theory of Relativity (again, just like the Theory of Quantum Mechanics) has NEVER once failed ANY test that science has EVER subjected it to – NOT A SINGLE ONE – making it as true as anything in the universe can ever be, because no one has ever successfully demonstrated, or better stated, no one has ever even come close to demonstrating, its incorrectness – not even once.

Understanding the simple principles underlying what is a truly monumental advancement in human understanding, and most significantly, recognizing that understanding these simple principles and the conclusions that this advancement that relativity is yields are within anyone’s conceptual grasp, can serve to remove the seeming distance that isolates common understanding from what is truly, at its heart, a single fundamental idea: that time is a dimension, no different in any way at all from space. This single conclusion that relativity reveals tells us an enormous amount about the universe in which we live, and ultimately, when combined with another model, the Theory of Quantum Mechanics, leads to explaining why life is even here in the universe at all (see The Meaning of Existence, by Chongo in collaboration with José, Jan., 2008).

Understanding the model that science uses to accurately describe space, time, classical (‘big’) motion, and gravity can introduce anyone who simply wishes to know what is true in nature to what may be a completely new way to envision and imagine things in it. Understanding the principles upon which the most accurate description of time, space, classical motion, and gravity are based can lead us to discover how physical reality is simply a shape (an extremely complicated one) and why all motion is just the shape of the universe changing, as we, and everything living, roll down a one-way road called time, observing the contours of this shape, with each passing moment of our journey.

Using the conclusions made by physical science, namely, the Theory of Relativity, we can understand the continuity that space and time seem to be, understand accurately the motion of big things within space and time, and most significantly, understand a very simple yet absolutely inescapable phenomenon that we experience everywhere always called gravity, all of which being what the Theory of Relativity does so impeccably well. Learning real science begins with learning relativity – just as making science interesting to everyone should begin by studying relativity’s richness first too.

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EXCERPT:

The Theory of Relativity is the best working model there is for describing space, time, classical motion (that of ‘big’ things), and, most significantly, gravity. This ‘working’ explanation of space, time, the motion of ‘big’ things, and gravity, the Theory of Relativity (‘working’, by virtue of corresponding so precisely to observed large-scale reality), is based upon a single, very simply, and intuitively fundamental idea, namely that of ‘geometric tilting’. Embodied in the simple idea of how one thing can ‘tilt’ with respect to another, is all the conceptual foundation that is necessary for understanding what is an absolutely remarkable explanation for physical phenomena. From this very simple single principle of how one thing, a ‘surface’, can ‘tilt’ with respect to another thing, another surface, emerges what is irrefutably the very best working description of space, time, the motion of ‘big’ things, and again, most significantly, gravity, that modern science has ever known – the absolute best. (There exists only a single other model of gravity, a model specified by String Theory, but this model yields general relativity when large aggregations are considered, which would therefore make the Theory of Relativity simply String Theory’s generalization [and hence make relativity to this extent just as valid as String Theory may someday be demonstrated to be].)

Imagining relativity requires that we understand the single geometric principle of how a two-dimensional surface can tilt, with respect to another two-dimensional surface, in the three dimensions that are required for containing two such distinctly tilted surface areas. Imagining conceptually one surface tilting with respect to another surface leads to conceptually imagining the fundamental idea upon which the Theory of Relativity is based: that of how a three-dimensional volume of space can tilt (special relativity, and in the case of general relativity ‘bend’, bending being a more complex form of tilting), with respect to another three-dimensional volume of space, in the four dimensions that are required for containing two such distinctly tilted three-dimensional volumes. By understanding this single simple idea, that of geometric tilting, we have all the conceptual foundation that is necessary to understand anything we wish to understand, about a truly remarkable body of ideas called “general relativity”, or more formally, the Theory of Relativity. Using the simple notion of geometric tilting, we can begin to look at space, time, motion, and gravity in what may very likely be an altogether new way, and a way that cannot help but be a much, much richer way than we ever looked at them or ever imagined looking at them before, and most importantly, in a much ‘truer’ way than before as well.

To understand exactly what it is that geometric tilting explains – and hence understand its tremendous significance in the realm of science – it is appropriate to understand a single phenomenon; this phenomenon being the very phenomenon that gave rise to the notion of tilting as a way of explaining it, and hence of explaining what had yet to ever be explained before by means of “conventional, common-sense” thinking. Tilting explains ‘perfectly’, or better stated, explains most ‘accurately’, just how the speed of light never changes (based upon accurately explaining why it never does) as a consequence of motion (i.e. ‘pushing’ light [its emitter] to make it go faster [or moving a detector with respect to the light]). That is, tilting explains in a very logical manner precisely how the speed of light remains the same, regardless of moving the source emitting the light, or of moving that which detects the light. In explaining how (and why) the speed of light never changes, tilting explains how the laws of nature (of physics) never change with motion either. Relativity does this by explaining how everything in the universe can be both at rest and moving, at the same time (i.e. concurrently). And, relativity explains another thing: gravity. Not only does tilting explain how the speed of light and the laws of nature along with that speed never change, tilting also surprisingly leads to explaining yet another ‘seemingly’ unrelated phenomena, namely that of gravity. Yes, the Theory of Relativity, by explaining how the speed of light never changes, leads to a very, very accurate explanation of gravity – the most accurate, testable explanation yet imagined by science (it has yet to ever fail). The Theory of Relativity (general relativity) is absolutely the best physically testable description of gravity that has ever existed (as well as a description that is wholly consistent with a macro-generalization of String Theory’s model of the “graviton” particle).

Now, first, before proceeding to explaining how the Theory of Relativity’s tilting, by explaining how the speed of light never changes, ultimately explains gravity, it is first necessary to understand precisely what a theory ‘is’, according to physical science’s definition of the term (we will return to tilting later). Physical science’s definition of the term theory may not and very likely will not agree in the least with how a dictionary defines it because the dictionary’s definition may be based upon a ‘common’ understanding of the term, to the exclusion of physical science’s definition; in which case we must ignore altogether the dictionary’s definition or it will only serve to confuse. This is because should we happen to misunderstand precisely (meaning in a definite way: exclusive of any ambiguity) what a theory is for physical science, then we might, mistakenly, yet very, very, very easily, misunderstand relativity, believing it to be either more than, or less than, what it really is, which is a model of reality that works better than any other model there is for describing ‘big’ nature, particularly gravity (while recognizing that for energy, unquestionably, relativity does not apply at the quantum level). So, to the end of explaining relativity in a conceptual way, we begin by explaining first, precisely what, according to physical science, a theory is – which might be very different from what we might imagine it being. The next chapter is dedicated to dispelling the common and widespread misunderstandings that so many have regarding precisely what a theory really is – and perhaps even more importantly, those regarding precisely what a theory really is not.

By understanding first what a theory is and isn’t, we can begin to understand an even more fundamental idea, the very idea that science, ideally, pursues, and the fundamental idea that gave rise to the concept of a ‘theory’ for a means of best specifying it, namely, that idea we designate by the seemingly vague term of ‘truth’. Theory is the word that science uses for specifying just how close we can really come to specifying what is true in nature. According to science, it is, for very, very sound reasons, absolutely impossible to ever come any closer to specifying just what is true in nature than through a genuine scientific theory, which is a body of ideas (i.e. principles and concepts as well as the conclusions that arise from them) that accurately predicts physical phenomena in a precise physically testable way. This is what relativity is, a theory: as close as we can come to specifying truth, for the time and space of gravity.

© 2008 C. Tucker (Chongo)

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DEDICATION

This book is dedicated to the memory of a committed thinker, physicist, mathematician, a very conscientious human being, a scientist, a world-class rock climber, a skilled outdoorsman, as well my tutor, collaborator, and best friend, José. His understanding of nature led to my ultimate understanding of it which will hopefully, eventually lead to many other people’s understanding of it too.

We can all thank José.