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More About This Textbook
Overview
Albert Einstein was admired for his unique intellect and loved for his great humanity.
This unassuming man greeted passersby in his walks along the streets near his home in Princeton, he answered letters from children, and he counseled statesmen.
He warned President Roosevelt of the danger that the Axis powers might be able to make nuclear weapons, and urged an American effort to develop that capability first.
After the war he was outspoken about what he saw as the need for the world community to think and act in new ways to avoid nuclear suicide.
Already in 1917, during World War I, he wrote, "How is it that this culture-loving era could be so monstrously amoral? More and more I come to value charity and love of one's fellow being above everything else."
The same Einstein replied to a group of sailors who had written to tell him how their mascot, a cat, came to be named 'Professor Albert Einstein,' as follows: "I am sending my heartiest greetings to my namesake, and also from our own tomcat who was very interested in the story and even a little jealous."
His reputation for casual dress and untamed hair was well known. Once, being asked about his socks, which did not match, he explained it all. How wrong it would be, he said, "if the containers were of a higher quality than the contents."
In the bibliography at the end of this book are listed a number of books of a biographical nature. They are highly recommended.
About Modern Physics
Physics used to be about things that we could see, or at least imagine. Falling and flying objects, things heating and cooling, magnets pushing or pulling, light beams that bend and focus, and later things like radio waves that we could not see but that behaved like things that we could see.
Then, as physicists began to probe more deeply, they found that radio waves did not behave like objects that were familiar. When you chased after them, or ran out to meet them, the effect differed fundamentally from the effect of chasing or running out to greet a running child. The difference had to do with the extremely great speed.
So began the era of "modern physics," that took science into realms that were outside our direct experience. As the theories that physicists had built were applied to things so small, or so fast, that we could no longer easily compare their predictions with familiar experiences, physics changed. Relativity deals with things that move incredibly fast. The math is not what is so difficult about Special Relativity; introductory high school algebra does quite well. Nor did nature spring upon us intricate and complicated new basic principles.
The difficulty in understanding Relativity lies largely in trying to imagine things that are outside our experience and that behave in ways our intuition suggests are wrong.
For that challenge there is help: a good teacher, or a good book, giving good explanations, good examples, good illustrations.
Author Bio: Walter Scheider is the recipient of the Presidential Award for the teaching of Science.
He is a graduate of Harvard University, where he also received his PhD. For seventeen years he was a research scientist at the University of Michigan, working on the binding kinetics of small molecules to proteins. He taught physics there, and for twenty years afterwards in the public schools of Ann Arbor, Michigan.
He is principal author of articles in the Proceedings of the National Academy of Sciences, the Journal of Physical Chemistry, the Annals of the New York Academy of Sciences, the Biophysical Journal, The Physics Teacher, and The Science Teacher.
His program was a nationally designated Exemplary Program of Physics Teaching. He is the recipient of the Lawrence A Conrey Award for Contribution to Science Education, and was twice named to Who's Who Among America's Teachers.
Author Comments:
Is there anything new in "A serious but not ponderous book about Relativity?"
Of course not. Special Relativity, at least as far as the non-specialist reader is concerned, is a well travelled subject. Many new books appear every few years on this nearly century old subject.
It is in the way it is done, in the insights that are left with the reader, in the thoroughness of presentation, in the readability, and last, but not least, in the skill with which the narrative connects with the reader's mind, that any one such book stands out.
I have been flattered by readers' comments on the writing and on the style.
But beyond style is spirit and perspective. There is such a thing as being always meticulously correct, and yet not taking oneself too terribly seriously. You will laugh with me about the tale of Timus Ybatu's contested mile run, and yet you will retain, from that example from fantasy, indelibly, the message contained in it about the relation of times measured by observers differently positioned.
If you are a non-physicist with a year of high school algebra, you are equipped to handle the math in this book. Necessary concepts that go beyond that are introduced from basic relations. For example, you may have not studied mathematical transformations. To understand relativity, transformation is a key concept. So there is a chapter on what a transformation is, from the bottom up, before the Lorentz transformation is used.
The question of math in a book for the general reader is important.
Why math?
Because without math, it is almost impossible to define the meaning of terms precisely. With only words, the reader infers meanings to words from their common usage in spoken English, although the scientific use of these words may be quite different. Only when terms are defined can they be used beyond the particular sentences in which they appear in a book on relativity. Misunderstanding flourishes in the reading of the no-math books, even while the authors write such books in the hope that the absence of math will make the subject easier to understand.
The popular books are necessarily weak in conveying understanding with precision. On the other hand, the more mathematical books on relativity, including the texts, tend to suffer from the excessive reliance on mathematical formalism to tell the story. The lack of talk between author and reader in these books leaves the reader with results that have been arrived at mathematically without the necessary explanation and discussion that almost all of us need.
And so, it is not how much math, but in what context and to what purpose is the math present? Math needs to be there to make things precise and well defined, embedded in a wealth of verbal explanation to give significance to the concepts, but never to carry the burden of description alone, or to crowd out the conversation between author and reader.
For the non-expert its has been a hard choice to make, between the popular books which, no matter how well done, are forced to pull assertions about relativity out of the blue, and the texts, which drag those same assertions out of a maze of mathematics. In both cases, the reader is left having to accept some of the most counter-intuitive conclusions of relativity on the say-so of experts. The reader whom this book is designed to serve wants something better.
I have enjoyed teaching relativity to my students. Mostly they are not physicists and never will be, but they have brains. I have taught, not just lectured on the subject. I have had hundreds of conversations with students and others who are not physicists but have brains, and over more than fifteen years have learned what helps and what doesn't help in the way of explanations, examples, illustrations. It is amazing how hungry so many ordinary citizens are for some understanding of this most fascinating aspect of the world around us. And how absolutely willing they are to have someone to talk to on a level well above the snippets on the news media and the pablum of the popularized books.
While relativity books for the generalist are ground out yearly, I believe no one until now has provided the "non-physicist with brain" a book worthy of that reader, without becoming ponderous.
This book began as a set of notes that I duplicated for my students because I found nothing appropriate for them on the bookstore shelves. Gradually these notes grew into this book. If there had not been a gaping hole in the available repertoire, I surely would not have gone to the trouble of doing this. I hope you enjoy reading it as much as I enjoyed creating a "serious but not ponderous book about Relativity."
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Read an Excerpt
"One day in May 1905, Einstein stopped in to see his friend and colleague from the Bern patent office, Michele Besso, to discuss a question 'which was difficult for me to understand...' He had been puzzling, like many others, over the apparent contradiction between an unexpected implication of Maxwell's Laws of Electro-magnetic Fields, and a 250 year-old basic principle inherent in Newton's Laws of Motion. Einstein thought both these fundamentals of physics to be so compelling that he was stumped to see how to reconcile them. 'Trying a lot of discussions with him [Besso], I could suddenly comprehend the matter ...' Albert Einstein had the crazy idea of resolving the conflict by dumping our most basic ideas about time: [the idea] that at any instant of time there is a NOW that is common to everybody and everything in the universe, and [the idea] that the progression of time is absolute, unaffected by anything else that happens. It was the most drastic, most unbelievable, most unlikely way to solve the conundrum."
"...One has to ask what led Einstein to this way of dealing with the apparent contradiction.
"... Nowadays Relativity is universally accepted because of the large volume of experimental verification of its many predictions. But, after all, this mass of experimental evidence was not available to him then, and so Einstein must have been driven by other arguments. The experimental facts that he had to work with consisted largely of those that delineated the apparent incompatibility of the Maxwell equations with Galilean Relativity. His biographer, Abraham Pais, comments that, 'Einstein was driven to the special theory of relativity mostly by aesthetic arguments, that is, arguments of simplicity.'
"Simplicity means that a little bit of law goes a long way. It means that a few basic principles, in themselves not complicated, take care of most, or all, the regulation needed to make the world what it is. It means that the most basic laws are simple and sweeping in their generality. Nature is observed to govern not with random and capricious exercise of power, as well she could. For some reason, she is not only dependable and consistent, but also parsimonious. She rules with a few laws of immense scope. Her basic laws are simple in design, even if their consequences may be complex and varied.
"And so we should not be surprised to find Einstein charting his way through Maxwell's conundrum using the criteria of simplicity and elegance, sorting and sifting possibilities in his mind with an incisiveness that was perhaps more the key to his genius than his mathematical skill, which after all was shared by many. 'I soon learned to scent out that which was able to lead to fundamentals and to turn aside from everything else, from the multitude of things that clutter up the mind and divert it from the essential,' he wrote later.
"It is astounding, at first glance, to think that abandoning absolute time and fixed space would be part of an argument of simplicity. [So, let us look more closely at the conundrum from which he sought an escape:]
"One of the powerful generalizations that followed inescapably from Newton's Laws of Motion is that nature makes rules only about changes in the velocity of objects, not about their velocity itself. Nature provides us no rule from which to determine a value to assign to an object's velocity. This is the essential content of Galilean relativity. No one seriously questioned Galilean Relativity. It was, after all, a statement about the Laws of Mechanics, and everyone was certain what those Laws were.
"Maxwell's laws of the electromagnetic field appeared to defy this principle of relativity. Maxwell's equations imply a particular value for the velocity of light, and do not have the generous indifference to laboratory movement inherent in Galilean relativity.
"[The easy explanation would have been if Galilean relativity simply did not apply to Maxwell's Laws.] This possibility attracted the quibblers, the nit pickers. Are Maxwell's equations Laws of Mechanics, or are they not? True, they deal with the motion of things, but isn't it possible that light and other electromagnetic waves are so fundamentally different from moving 'objects' that Galilean Relativity does not apply to them? If so, then Maxwell's law of the propagation of light may just fall through a loophole in classical relativity.
"Einstein didn't buy this argument for a moment.
"Here is his opinion: 'Even though classical mechanics does not supply us with a sufficiently broad basis for the theoretical presentation of all physical phenomena, still we must grant it a considerable measure of 'truth,' since it supplies us with the actual motions of the heavenly bodies with a delicacy of detail little short of wonderful. The principle of (classical) relativity must therefore apply with great accuracy in the domain of mechanics. But that a principle of such broad generality should hold with such exactness in one domain of phenomena, and yet should be invalid for another, is a priori not very probable.'
"Here, then, was the conflict. Einstein, at this point, accepted that in closing the loophole in Galilean relativity, he had exiled Maxwell's equations from the kingdom of classical relativity. It appears, Einstein conceded, that one must either abandon the 'simple law of the propagation of light in vacuo,' or one must abandon the (classical) principle of relativity. 'Those of you who have carefully followed the [foregoing] discussion are almost sure to expect that we should retain the principle of relativity, which appeals so convincingly to the intellect because it is so natural and simple,' he added.
"Einstein had painted himself into a corner. He had committed himself forcefully to the widened principle of relativity, which would have forced him to yield on Maxwell's Laws. Yet he felt almost as strongly about what he called the law of propagation of light. We end this chapter not knowing how he will extricate himself from this conundrum."
Table of Contents
Part I. The Detectives
Ch 1. "Questions that children are taught not to ask"
Ch 2. "Because it is so natural and simple"
Ch 3. Maxwell's Conundrum
Ch 4. Einstein
Ch 5. Relativity, Look-back Time, and other confusions
Part II. The Phenomena
Ch 6. Clocks and Meter Sticks: What to Keep and What to Toss? -- Some Corollaries
Ch 7. The Phenomena: Time
Ch 8. The Phenomena: Length and Other Kinds of Distance
Ch 9. The Phenomena: Invariance of Space-time Interval
Ch 10. The Phenomena: Relativistic Mass and the Speed Limit
Ch 11. The Phenomena: Energy and its equivalence to Mass
Ch 12. The Lorentz Transformation
Ch 13. The Phenomena: Bullet in the Rocket: Velocity Addition
Ch 14. The Phenomena: Simultaneity
Part III. Stars, Particles, and Spacetime
Ch 15. Transformations
Ch 16. Graphing the Lorentz Transformation: Minkowski Diagrams
Ch 17. Equations of Motion in Four Dimensional SpaceTime
More problems
Bibliography
Appendix I. Maxwell's Laws and the Speed of Light
Appendix II. Proof of the Equality of Axis Angles in Minkowski Diagrams.