Time for Everyone and Time for Everything Arieh Ben-Naim
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1 Time for Everyone And Time for Everything Arieh Ben-Naim Preface Acknowledgments Chapter 1. Time in the Bible Appendix 1: A visit to Ma’alot Ahaz in Neot Kedumim, Israel Chapter 2. What is Time? My private collection of clocks and watches Appendix 2: A visit to the L. A. Mayer Museum of Islamic Art Chapter 3. Velocity and Frequency Appendix 3: A visit to the National Physics Laboratory (NPL) Chapter 4. History of Time Appendix 4: A visit to the British Museum, and Science museum, London Chapter 5. History of Thinking about Time Appendix 5: A visit to Stonehenge, England Chapter 6. History of timekeeping and measurement of time Appendix 6: It’s Russian Time, it’s Konstantin Chaykin’s Time Chapter 7. Time in Physics Appendix 7: A visit to Fabergé Museum, Saint Petersburg, Russia Chapter 8. Perception of Time A visit to the Vienna Museum of Clocks and Watches Appendix 8: A visit to Hermitage Museum 2 Chapter 9. Time, Causality, and Conditional Probability Appendix 9: A visit to Newgrange, County Meath, Ireland Chapter 10. Confusing absolute “always” and “never” with practical “always” and “never,” respectively Appendix 10: A visit to the Royal Observatory Greenwich (ROG) Chapter 11. Time’s Arrow, Entropy, and the Second Law of Thermodynamics Appendix 11: Visit to some Antiques shops Chapter 12. Time for Fun Appendix 12: A visit Kaunas; a gamut of emotions; Time for Sorrow and Time for Hope Appendix A: A qualitative presentation of the concept of logarithm Appendix B: The concept of a limit, and the velocity at a point in time Appendix C: Periodic Processes Appendix D: Zeno Paradox Appendix E: Time Dilation and Lorentz Transformation Appendix F: Solution to the urn problem Appendix G: A few notes on 20Q games. Preface While writing my book on “Entropy for Smart Kids and their Curious Parents,” I felt an urgent need to write a book on “Time for Smart Kids,” compelled to do so from a mistake by authors who write about Entropy intertwining it with Time. The truth is, Time and Entropy are totally unrelated concepts. By establishing a connection between Time and Entropy numerous authors have led their readers to the wrong path. They have not only misled but also confused readers on each of these two concepts. 3 The association of Time and Entropy is implicitly contained in Clausius’ and Boltzmann’s formulation of the Second Law. It was expressed explicitly by Eddington who “invented” the concept of the Arrow of Time, relating it to the Entropy and the Second Law. This totally unfounded association between the two concepts has lingered on. In fact, numerous books propagated further this faulty association (e.g. Hawking, Carroll, Muller, Rovelli, and many others) culminating in the most absurd assertion that entropy equals time’s arrow. (“Equal,” with equality sign “=” !) Although I have already written about this misconstrued association in my recent book (2018a), I decided to devote two chapters in the present book to discuss the reasons and plausible causes for this association, and to point out how, and why some authors have gone astray. Notwithstanding the importance of debunking the myth about the association of entropy and time, I think that Time is a fascinating topic on its own. Time is a concept everyone is familiar with, and yet no one can define it. Time perception has multi-faceted aspects and dimensions. Time measurement has a long and interesting history, and the history of thinking about time is extremely interesting. All these combined compelled me to write this book. The book is addressed to everyone from the lay reader, to students, and to teachers and well-established researchers. There are no prerequisites for reading this book. Some mathematical details are provided in the Appendices. The book consists of twelve chapters, each dealing with a different aspect of time. Normally, a book on time should start with some possible definitions. However, in the case of time there is no definition therefore, I decided to discuss in Chapter 1 some aspects of time as they appear in the Bible. It is only in Chapter 2 where I pose the question: What is time? I am presenting some answers given by physicists and philosophers throughout the history, but ultimately time is left undefined. Some 4 authors offer their reader a “definition” of time, some even promise a “precise definition.” However, if you read throughout the book you will not find any definition. What you will most likely find is a misconstrued association of entropy with time. This will be discussed this in Chapter 11. Chapter 3 is devoted to defining and discussing two important concepts associated with time; velocity and frequency. In Chapter 4, I discuss what people call “History of Time,” and I will show that basically the is no “history of Time.” In most books in the “history of Time,” authors usually discuss the “History of Thinking About Time.” this topic is discussed in Chapter 5. In Chapter 6 I will discuss the history of measuring time, which in my personal opinion is the most fascinating one. In the course of writing this book, I have traveled far and wide in order to learn more about how mankind developed devices to measure time, dating back from prehistoric times to modern times. Chapter 7 is devoted to time in Physics, sometimes referred to as “Physics of Time.” Time is an essential and indispensable parameter in any science dealing with changes. It is supposed to be an objective quantity although there is always some uncertainty about the meaning of time. Chapter 8 is about the subjective aspects of time, how we perceive time, and how these perceptions of time change with age, mood, and personality. Chapter 9 discusses the connection between time, cause and effect, and conditional probability. Chapters 10 and 11 are devoted mainly to debunking the myth that time is associated with entropy and the Second Law. Finally, the last chapter 12, which is the lighter part of the book, contains some famous quotations on time, some jokes, exercises, and some personal comments and views about time and how it is used in the English language. 5 As I have written in my previous books, I exhort the readers of this book to read it as critically as possible, and should you find anything wrong or have any questions, I urge you to write to me. While writing this book from 2017 to 2018, I became deeply engrossed not only in the methods in which clocks and watches were developed to measure time. Slowly, I realize that I had grown fascinated with timepieces. In my numerous trips, I also visited some museums which had impressive and wide array of antique clocks and watches on display. I eagerly snapped photos of them like there were no tomorrows. Only a small fraction of these photos I could include in this book. My fascination and interest in timepieces knew no time boundaries, the old and the new simply left a lasting impression on me. I visited such sites such as Stonehenge in the UK, and Newgrange in Ireland which both seem to be the earliest monuments left by prehistoric people who probably have developed interest in timekeeping. Acknowledgments TENTATIVE I am grateful to Ron Aharon, Robert Engel, Robert Goldberg, Jose Angel Sordo Gonzalo, Douglas Hemmick, Shannon Hunter, Richard Henchman, Mike Rainbolt and Erik Szabo for reading parts or all of the manuscript and offering useful comments. ADD: Margarita, Konstantin, Mac, Andy, Hanoch, Unna, Azriel, Alexey, Sergey, Daumantas, As always, I am very grateful for the graceful help from my wife, Ruby, and for her unwavering involvement in every stage of the writing, typing, editing, re-editing, and polishing of the book. Chapter 1. Time in the Bible I will start by assuming that you, the reader, knows the definition of the following words: “day,” “night,” “morning” and “evening.” I also assume that you know what 6 week, month, and year mean. Before you continue reading the quotation below I suggest that you write a short “definition” of these terms, or at the very least remember what these terms mean no matter how familiar you might be with them. I do not expect that you will really “define” these term, just try to explain to yourself, in either your mind or in writing, what you mean when you say: “day,” “night” and morning. Now, read carefully and critically the following verses from the book of Genesis1: Genesis Chapter 1. 1:1 In the beginning God created the heaven and the earth. 1:2 And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. 1:3 And God said, Let there be light: and there was light. 1:4 And God saw the light, that it was good: and God divided the light from the darkness. 1:5 And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day. 1:6 And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters… (1:7 And God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament: and it was so.) 1:8 And God called the firmament Heaven. And the evening and the morning were the second day. 1:9 And God said, Let the waters under the heaven… 1:13 And the evening and the morning were the third day.