Summary of the contents of “Pondering Relativity: An Illustrated Guide for Building and Understanding of Einstein’s Relativity.”

When first introduced by physicist Albert Einstein in 1905 and later expanded in 1915, the theories of relativity were controversial and not universally accepted. Since then, many scientific studies have confirmed the theories’ predictions. Today, relativity is central to our understanding of the Universe. This book introduces the concepts of relativity for the non-scientist using coordinated illustrations that help visualize how relativity works. The illustrations are sequenced throughout the book in a way that helps build and reinforce understanding gradually.

Overview

This book describes relativity in the simplest of terms with illustrations to help visualize and understand its principles.

The concepts of relativity are not as difficult to understand and appreciate as traditional thinking would have us believe. In fact, the principles of relativity can be understood at a conceptual level without any math at all. And high school algebra can suffice for exploring the basic workings of Special Relativity, the first and easiest of Einstein’s theories of relativity. The biggest difficulty in understanding relativity is that its effects only become obvious under conditions not normally experienced in everyday life. This makes it hard to appreciate how relativity works. It is therefore beneficial to study relativity using imagined situations that expand everyday experiences to incorporate conditions under which the effects of relativity are evident and can be envisioned.

This book aims to do that, building an understanding of relativity using illustrations and examples that allow the reader to envision the conditions under which relativity can be experienced. It presents the basic concepts of relativity beginning with the observational foundations that drove Einstein to propose it. It makes the case for Einstein’s initial theory of relativity, called the Special Theory of Relativity, by showing how it resolves inconsistencies between how we traditionally measure motion and the measurements made of the speed of light. The book then builds on this foundation to define and explain the more complete and comprehensive theory of relativity, called the General Theory of Relativity. General Relativity expands Einstein’s initial theory to also explain how acceleration and gravity affect the shape of space and the passage of time. After describing and depicting the Special and General Theories of Relativity, implications for how the Universe works are explored. Mental exercises and illustrations for remembering and internalizing the principles of relativity are presented in Appendix C.

As noted, this book uses diagrams to graphically show how relativity works. The diagrams work together to gradually build an appreciation of relativity principles. They help develop an internal visual picture of relativity and thus make relativity easier to understand. However, while the diagrams help with visualizing and understanding relativity, they are only a visual approximation to how relativity actually works. The diagrams depict relativity principles on the flat, two-dimensional pages of this book, while relativity really works in a four-dimensional space-time. Four-dimensional space-time is what Einstein says results from combining three-dimensional space (that has three directions you can go: forward-back, right-left, and up-down) with time. This is an important part of relativity and is discussed in detail in this book. The simple two-dimensional diagrams help with visualizing and understanding how relativity works, while the actual four-dimensional geometries are too complex to accurately represent in pictures.

Target Audience

This book is written for anyone who would like to understand the principles of relativity. A basic understanding of high school math is helpful but not necessary.

This book is written for non-scientists. The concepts are presented in their simplest form with pictures and illustrations to help achieve understanding. No math is needed, although a few simple formulas are presented for those interested, just to give deeper insights into the workings of relativity. For example, simple algebraic formulas are provided to show why it is not possible to travel faster than the speed of light. It is not necessary to understand the formulas in order to appreciate the basic concepts of relativity. The reader is able to skip them entirely, if desired.

There is no reason that anyone who has an interest should avoid learning about relativity. Relativity is something that anyone with a high school education can understand, at least at a conceptual level, and enjoy. Illustrations and simplified descriptions are provided to help grasp otherwise complex principles that define relativity. The goal is to develop an understanding of the concepts of relativity, building from basic human experience and common sense. For those interested in a more in-depth discussion of relativity, references for further reading are provided. Also Appendices A and B provide some very basic (high school level) mathematical descriptions and Appendix C includes exercises to help remember the concepts.

Pondering Framework

The concepts and principles of relativity are presented using illustrative figures, consistent perspectives and simple graphics. This approach facilitates visualizing and learning, and supports ongoing pondering as a way to build a deeper and more enduring understanding of relativity.

This book is a “pondering book.” It is meant to develop understanding through a “pondering” process in which the concepts of relativity are internalized by ongoing and repeated visualization. This is important because the concepts of relativity require adopting a new way of seeing the world that (initially, at least) seems inconsistent with everyday experience. This seeming inconsistency is because we experience the world from an Earth-bound human perspective. The human experience does not include near light speed motion, under which the workings of relativity would be self-evident. In order to provide a perspective where the effects of relativity can be shown, this book extrapolates from common everyday situations to imagine conditions under which the principles of relativity can be visualized. Numerous illustrations with explanations are provided to help in this process.

Finally, this book presents the concepts and foundations of relativity from a learning perspective. Material is organized and presented in a logically structured way that builds an understanding of foundational concepts before developing more difficult ones. The illustrations reinforce the material and help readers visualize and internalize the concepts, building on our human-scale experience and backgrounds. Simple coordinated figures are provided throughout the book as an aid for building understanding in a logical sequence. Each chapter begins with a list and summary of major points covered therein.

The contents of this book are organized for gradual learning and building an understanding of relativity.

The summary below provides an overview of the contents of this book. It summarizes the main points covered in each chapter. It also offers a good review of the material and a reference for remembering the larger context of material presented. Readers can refer back to this table as needed to see the larger context and review prior material, and to support the pondering process.

Overview of the Contents of this Book

Introduction

• Overview. This book describes Special and General Relativity in simple terms with many illustrations to help visualize and understand the concepts.
• Target audience. This book is written for anyone who would like to understand the principles of relativity. A basic understanding of high school math is helpful but not required.
• Pondering framework. The concepts and principles of relativity are presented using graphics and visual components, building from consistent perspectives. This approach facilitates learning and supports ongoing pondering as a way to develop a deeper and more enduring understanding.
• What you will learn. The main points of each chapter of this book are summarized in this section. This summary introduces the organization and contents of this book. It also provides a contextual foundation for structuring your understanding of relativity as a tool for subsequent review.

What is Light?

The nature of light. Knowledge of how light behaves is central for understanding relativity. This chapter describes important characteristics of light. It describes what light is made of and presents key aspects of light’s behavior that form the foundation for understanding relativity.

• The size of the Universe. This section describes how we use light to measure the size of the Universe.
• Unexpected observations. Some unexpected discoveries about light that led Einstein to develop his theories of relativity are discussed.
• The color of light. This section describes how the color of light is determined. We can tell a lot about the effects of relativity from its effects on the color of light.
• The electromagnetic radiation spectrum. This section explains how light is really just a portion of the larger spectrum of electromagnetic radiation, including radiation associated, for example, with radar, radio, and x-rays.

There is No Up or Down in Space, or Anywhere Else

• The aether. Many scientists before and at the time of Einstein believed that there was an invisible structure that defined space and against which all motion could be judged and measured. This structure was called the “aether.” The acceptance of relativity led scientists to abandon the idea that there is a space-defining aether.
• The nature of motion. Motion of any object can only be defined and measured relative to the position and motion of other objects. This is called Galilean Relativity because it was the Italian Renaissance scientist Galileo Galilei who first proposed it. Galilean Relativity forms a central principle underlying Einstein’s Special Theory of Relativity.
• Incompatibility between relativity and the aether. Einstein’s theories of relativity were incompatible with the existence of an aether. This disagreement put Einstein at odds with many of his colleagues. The eventual acceptance of Einstein’s theories ultimately led to the abandonment of belief in a space-defining aether.
• The velocity of motion is relative too. The understanding that an object’s motion must be measured relative to other objects led Einstein to realize that velocity (the time-distance relationship between objects) depends on what object is chosen as a reference for measuring the motion. This formed the foundation for the Special Theory of Relativity.

The Special Theory of Relativity

• How Special Relativity works. This section describes how the behavior of light and Galilean Relativity combine to form the basis of Einstein’s Special Theory of Relativity. Illustrations show how the Special Theory of Relativity provides a new way of understanding time and space. It graphically shows why under Special Relativity, time slows and space compresses when objects move “uniformly” relative to one another, and why “moving clocks run slow.”
• Why Special Relativity is called “special.” This section answers the question, what is so “special” about Special Relativity?
• Observer perspective is the key. The perspective of the observers in considering properties of moving objects is central in defining the effects of Special Relativity. This section explains why.

Clocks

• Clocks. Clocks are central to understanding relativity. This chapter asks the questions: what is a clock and how are clocks related to time and relativity?
• Light-clocks. Hypothetical clocks called light-clocks use the movement of light to measure time and provide significant insight into how relativity works. Light-clocks are introduced in this chapter and used throughout the rest of the book to make relativity understandable.
• Clocks and time. Questions of whether hypothetical light-clocks correlate with the “real” clocks available to scientists and people are addressed in this section.

Time and Space

• Time slowing. The relationship between relative motion – the movement of objects relative to each other – and the slowing of time as defined by Special Relativity is described more completely in this section.
• Space compression. When time is slowed due to the effects of Special Relativity there is a commensurate compression of space that is experienced. This relationship is presented, explained and illustrated.
• Bi-directional application. There is no preferred frame-of-reference when considering the effects of Special Relativity. For example, when two objects are moving relative to each other, either object can be considered to be the fixed reference for measuring Special Relativity’s effects.

Shortcomings of Special Relativity and the Equivalence Principle

• Shortcomings of Special Relativity. Accelerations, such as the centrifugal force in spinning objects, limit the applicability of Special Relativity and
  establish a beginning point for understanding General Relativity. This section describes why.
• The nature of acceleration and gravity. This section describes how acceleration and gravity work together and why they are really the same force.
• The Equivalence Principle. This section describes how “inertial mass” (that makes objects keep moving) and “gravitational mass” (that gives large objects like the Earth gravity) are equivalent and therefore why acceleration and gravity have similar effects on time and space.

General Relativity: Reality in Four Dimensions

• Doubling down boldly. The Special Theory of Relativity defined new ways of understanding space and time that went against and beyond previous conventions of understanding. But compared to General Relativity these advances were minor. Einstein was truly “doubling down boldly” when he proposed General Relativity.
• General Relativity requires a new kind of geometry. The everyday mathematics and geometry we use to describe three-dimensional space are not adequate for describing General Relativity. This section explains how Einstein had to find a new mathematical geometry that could work for his four-dimensional Theory of General Relativity.
• Space and time do not exist separately. One of the most fundamental outcomes of Einstein’s theories of relativity is that space and time are not separate things.
• Space-time becomes distorted under conditions of gravitation. Gravity affects how things move through space-time by affecting the shape of space-time.
• Acceleration and gravity are equivalent but different. Gravity and acceleration are equivalent – they feel the same, are related to mass in a similar way, and can be combined like when banking a bicycle during a turn. However, they also have some important differences – being in an accelerating rocket ship is not the same as standing on Earth’s surface.
• Motion and space-time distortions cause changes to light’s appearance. Relative motion changes the frequency (color) of light. Acceleration causes the color of light to keep changing as the speed of motion keeps changing. Gravity has a similar effect. Illustrations are included to help explain.
• Extreme gravitational conditions create extreme time slowing and space compression. Under extreme gravitational conditions, time can slow to the point of stopping and space can become so compressed that light cannot escape its hold. This happens around “black holes” described in this section.

What Relativity Says About the Universe: Part 1 – Time, Space and Aging

• Time and aging. Does relativity affect how fast we grow old? Einstein’s twin paradox used a space-traveling example to answer this question. The twin paradox is presented in this section.
• The universal speed limit. Why are relative speeds faster than the speed of light, called speed “c,” not possible? This section shows why.
• Simultaneous events and causality. Given the effect of relative motion on time, is there really such a thing as simultaneous events? Can relativity upset the order of events such that results can occur before the events that caused them? If not, why not? This section answers these questions with real world examples.
• The relationship between event ordering, the slowing of time and the compression of space. This section graphically shows how relative motion that affects the ordering of events does this by compressing space and slowing time. It’s obvious when you see it.

What Relativity Says About the Universe: Part 2 – How the Universe Is Made

• Moving through space-time. This section explores how the universal speed limit (speed “c”) and the one-way nature of time (always going from past to future) combine to limit our movements within space-time.
• Relativity limits information access. Just as important as the limits that relativity puts on our movements through space-time are limits relativity places on what we can know. This section shows why.
• Time it takes for light to travel across space. Is it really true that it takes light many years to reach us from distant stars and galaxies? Well no, but why not? This section explains.
• Exceeding the universal speed limit. Really, isn’t there anything that can go faster than speed “c”? Well OK, yes there is, but what is it? This section describes the few situations in which faster than speed “c” movement is at least implied and may be possible.
• The appearance of compressed space or actual compressed space? Do things actually become shorter with the compression of space or is it just the appearance of things (and space) shortening? The answer is both yes and no. This is described in this section.
• How objects bend space-time. How is it that massive objects are able to bend space-time? How do things far away from the Earth know that the Earth is “pulling” on them? How does gravity extend across space-time? This section answers these questions.
• The structure of space-time. This section explores the question: what is space-time made of? Is space-time really empty?
• E=mc². Energy (E) and mass (m) are interchangeable as defined in Einstein’s famous equation, E=mc². This famous interrelationship between mass and energy defines important characteristics of how the Universe is put together and works. So what does E=mc² have to do with relativity? This section explores the ramifications of Einstein’s famous equation.
• Limits of relativity’s scope and competence. Are there limits to what relativity can tell us about the Universe? Yes, this section describes them.

Where’s the Proof?

• The questioning scientific community. This section describes how the scientific community responded to Einstein’s theories: at first skeptical and eventually congratulatory.
• Verification of Einstein’s predictions. Einstein made three major predictions that he said would validate his theories. This section describes them.
• Modern experiments have measured the effects of relativity. This section discusses the results of recent scientific studies conducted to test Einstein’s theories. Measurements verifying relativity’s predictions about the effects of relative motion and gravity on time and space are described. The very recent discovery and measurement of gravity waves moving through space are also presented.
• Putting relativity into practice. Beyond theory and experiment, the proof is in the pudding. That is, does relativity work in the real world? This section describes how our knowledge of relativity makes modern technology and conveniences possible.

Science and Religion

• The goal of science. The work that scientists do along with the deeper meanings and perspectives that accrue from an understanding of science and relativity are discussed.
• Science and Religion. How can our growing understanding of science inform our religious beliefs? How can religion inform and motivate scientific progress? What can dogma-based religions do to keep up with science? This section discusses these important questions and suggests a way forward.
• God’s DNA. Science teaches us that the Universe began in a giant “Big Bang” 13.8 billion years ago and has been expanding and evolving ever since. This section discusses that evolution, our growing understanding of how the Universe works, and asks the God question.
• Beyond DNA. With the creation of humans, a new kind of evolution that occurs outside of biological structures has begun.
• The Universe and God. Scientific discoveries about the Universe and its evolution invariably raise questions about Creation and God. This section discusses these questions in relation to science.
• Closing thoughts. The main goals of this book are noted.

As noted, this book is organized so that earlier chapters provide a foundation for later material. Each chapter contains information that is expanded and built upon in later chapters. Graphical illustrations are included throughout. They are simplifications of the concepts intended to help in visualizing how relativity works. The graphic depictions and illustrations are repeated and expanded throughout the book as a way to help reinforce understanding. These illustrations are simple two-dimensional diagrams that help visualize how relativity works without trying to capture the deeper understanding that Einstein described with advanced mathematics and differential geometry.

Finally, it takes time to become comfortable with the concepts of relativity. You may follow all the arguments and logic as you read this book but still not feel entirely comfortable in your understanding of relativity. This is normal. Even professors that teach relativity admit that it differs from their common sense and normal experience, and is therefore difficult to fully appreciate at a human level. Nevertheless, with repeated pondering, the concepts of relativity will become more readily appreciated. You will gain a level of comfort with relativity as you read this book since the concepts are reinforced and reviewed throughout. Subsequent pondering will further build a more solid understanding.

For those interested, three appendices are provided to give a deeper understanding of relativity. The first two appendices offer a glimpse at the mathematical underpinnings of Special Relativity. These are presented using high school level math for ease of understanding. The third appendix includes some mental exercises that can help in remembering the concepts of relativity. These appendices are summarized below.

Overview of the Contents of the Appendices

Appendix A. Pythagorean Illustration

• Special Relativity can be visualized at a basic level using the Pythagorean theorem. Appendix A provides this insight. It shows how a simple application of the Pythagorean theorem (from high school geometry) can be used to derive the formulas for time slowing and space compression as defined by the Special Theory of Relativity.

Appendix B. Calculations for the Addition of Relative Velocities

• Mathematical calculations for some of the examples from the book are provided for those interested. These examples use simple algebra to show why it is not possible to exceed the speed of light according to Special Relativity.
• The Lorentz transformations used by Einstein to develop Special Relativity are described and related to the formulas for adding velocities across multiple frames-of-reference.

Appendix C. How to Remember

• The main lessons of this book are summarized to help in reviewing Special and General Relativity and for remembering the scientific contexts from which they were derived.
• Exercises to help see how relativity works are presented as an aid for remembering the relativity concepts.

These appendices are included to: (1) provide a glimpse into the underlying mathematical foundations of relativity, for those who are interested; and (2) offer some fun exercises that will help build a deeper intuitive understanding of how Special and General Relativity work.

 

Selected Illustrations from the Book

The way the book makes relativity understandable is with simple coordinated illustrations that help the reader visualize and see how relativity works. These illustrations are coordinated throughout the book to build understanding gradually as readers learn, ponder and enjoy relativity. The illustrations are very simple and basic in their construction with descriptive labels making the relativity concepts and principles obvious. In addition to making it easy to see how relativity works this also supports ongoing review and pondering. Here are a few example illustrations from the book.

(Figure 2-3.) Illustration showing how we know that the speed of light is always the same.

(Figure 4-3.) Since the speed of light is always the same, then time must go slower on moving platforms with a commensurate compression of space. This illustration uses a moving train to illustrate, as Einstein did.

(Figure 7-1.) If all motion is relative then one could say that it is the Universe that is spinning around the object (the bucket). But then, how to account for the acceleration forces felt in the bucket? This mystery led Einstein to expand his Theory of Special Relativity to develop the more complete Theory of General Relativity.

(Figure 7-5.) Figure showing how acceleration and gravity are equivalent.

(Figure 8-1.) Illustration showing how adding dimensions affects perceived geometry in unexpected ways. This is similar to going from our accustomed three dimensions of space to four-dimensional space-time.

(Figure 8-4.) Illustration using a two-dimensional analogy to help see how the bending of four-dimensional space-time explains the otherwise mysterious “pull of gravity”.

(Figure 8-7.) Illustration that compares inertial and acceleration frames-of–reference with and without nearby gravitational sources.

(Figure 9-6.) Why can’t we go faster than the speed of light? This figure shows how adding velocities will NOT result in exceeding the speed of light when the effects of Special Relativity are considered.

(Figure 9-10.) Relative motion can change the order that events happen.

(Figure 9-11.) Illustration showing why it is NOT possible for Special Relativity to change the order of events such that results occur before the events that caused them.

(Figure 9-15.) Illustration of why objects in motion appear to shorten due to the effects of Special Relativity.

(Figure 11-4.) How the apparent shift in position of a star’s appearance demonstrated that space-time is bent by gravity near large massive objects.

(Figure C-3.) Exercise for imagining (and practicing) the effects of Special Relativity in everyday life.

These and other simple figures are included throughout the book to make it easy to visualize how relativity works and to understand relativity at a conceptual level.

I hope you enjoy pondering my book and enjoy the excitement of understanding relativity.

Questions that are Answered by the Book

After making the workings of Special and General Relativity obvious and understandable you will find sections that provide illustrated answers to the following questions:

• Will relative motion make us age more slowly?
• Why can’t we go faster than the speed of light?
• Can relativity make results happen before the events that caused them?
• How does motion make time slow and space compress?
• What does relativity say about how we move through space-time?
• How does relativity limit what we can know about?
• How much time does it take for light to travel across space?
• Isn’t there anything that can exceed speed “c”?
• Is it the appearance of space compressing or actual compressing? What is really happening?
• How can objects bend space-time? How does space-time know there is a massive object nearby and it needs to bend?
• What is space-time made of?
• What does E-mc2 have to do with relativity?
• If the Universe is expanding, isn’t there a point where space is moving away at a speed that is faster than the speed of light? How does that work?
• Are there limits to relativity’s scope and what it can tell us about the Universe?
• What does the wave-particle duality of light say about reality?

I hope you enjoy pondering my book and enjoy the excitement of understanding relativity.

Human factors and ergonomic principles are important for designing information presentation to optimize understanding consistent with human learning and memory predispositions. This can make the difference between confusion and deep learning for long-term retention. Human factors engineers, for example, know how to: (1) make complex information understandable through consistent presentation frameworks; (2) enhance internalization of information by providing for reinforcing review; (3) make complex concepts visually intuitive; and (4) provide a strong structural framework to help novice learners, who don’t already have background knowledge of the topic.

These principles have guided me in the writing of Pondering Relativity: An illustrated guide for Building an Understanding of Einstein’s Relativity (described below). Specifically, my book applies the following Human factors and ergonomic approaches and techniques:

• Extensive visualization – Graphic illustrations are used throughout to augment text and create clear and simple visual representations of relativity concepts.
• Explicit perspective – Illustrations and associated text always make cognitive perspectives and orientations obvious with clear labels and visual cues.
• Consistent framework – Presentation frames of reference are kept consistent throughout the book so that readers’ orientation is quickly and easily aligned.
• Gradual learning structure – Builds from simple to complex in a building block fashion that establishes foundational understanding before more difficult topics are introduced.
• Integrated review built in – Presents basic principles and concepts followed by interpretation for how the Universe works. This creates a learning framework that automatically reviews material as relativity principles are discussed in the larger context of how the Universe works.
• Virtual exercises that allow readers to experience relativity – Since our Earth-bound existence does not provide conditions sufficient for experiencing the effects of relativity directly, exercises are provided to expand normal daily activities into virtual relativity classrooms for practicing and experiencing how relativity works.
• Self-reinforcing graphics – Key graphic elements are repeated within illustrations throughout the book to reinforce key foundational concepts and support the learning and internalizing process.
• Multiple levels of understanding supported – Readers are able to appreciate relativity at different levels from simple concepts to optional basic mathematical underpinnings.
• Pondering framework – Supports a pondering process in which readers can experience relativity on a personal level through ongoing and repeated visualization to internalize concepts presented.