Physics Over Easy

Breakfasts with Beth and Physics

Leonid V Azároff

• Publisher: WSPC
• Year: 2010
• ISBN:
  9789814338578
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Astronomy & Astrophysics

During a sequence of meals, the author relates the principal features of physics in easy-to-understand conversations with his wife Beth. Beginning with the studies of motion by Galileo and Newton through to the revolutionary theories of relativity and quantum mechanics in the 20th century, all important aspects of electricity, energy, magnetism, gravity and the structure of matter and atoms are explained and illustrated.

The second edition similarly recounts the more recent application of these theories to nanoparticles, Bose–Einstein condensates, quantum entanglement and quantum computers. By including accurate measurements of the Cosmic Microwave Background and supernovae in near and distant galaxies, an understanding of how the universe was formed in an Inflationary Big Bang is now possible. We've also gained a much better picture of the life of stars and how they may turn into red giants, white dwarfs, black holes, neutron stars or pulsars.

Read the book and share with us your thoughts on our Facebook site at http://www.facebook.com/worldscientific or Twitter account at http://twitter.com/worldscientific.

Contents:

• What Keeps Us Going?
• Breakfast of Hard-Boiled Eggs with Inertia
• Breakfast of Eggs Bene-Bricked
• Breakfast of Apple-Gravity Pancakes
• Breakfast of Cereal and Calories
• Breakfast of Hot Cakes with Energy
• Breakfast of French Toast
• Breakfast of Cold Cuts
• Breakfast of Blueberry Muffins
• Breakfast of Apple Fritters and Love
• Breakfast of Eggs and Crisp Bacon
• Breakfast of Oat Meal with Light Cream
• Breakfast of Lox and Bagels
• Breakfast of Farina
• Breakfast of Danish Pastry
• Breakfast of Waffles
• Breakfast of O. J., Donuts, and Coffee
• Breakfast of Rice Krispies
• Breakfast of Corn Fritters
• Dinner at Home
• Lunch at the Beach
• Lunch at Venetian Bay
• Breakfast at the Beach
• Dinner Under the Stars
• After Dinner at Home

Readership: General readers curious about science.

Chapter One:
Breakfast of Hard-Boiled Eggs with Inertia

How It All Began — with Rolling Balls

Our Breakfast discussions of physics began one morning when I observed: “I am really enjoying my review and discovery of many tidbits of information about the early physicists.”

This naturally prompted Beth to ask “Who was the first physicist?” (Her boundless curiosity prompts Beth to pose many such questions, as will be soon apparent.)

“Galileo Galilei was the first physicist, although he himself did not realize that. You see,” I added, “scholars were not labeled ‘scientists’ or ‘physicists’ until the middle of the nineteenth century when the Master of Trinity and occasional Vice Chancellor of the University of Cambridge, William Whewell, first proposed such a name.”

“But surely there were others who had studied the topics we now call physics long before Galileo,” Beth protested. “How about the many advanced civilizations of the Egyptians, or Greeks, or Mayans, or Aztecs, or those in Asia and elsewhere?”

“We can find the remains of ancient structures in the Americas, in Asia, and in Africa, and we know about the many simple tools that the early builders had already discovered and utilized.” I responded. “But, surprisingly, the earliest records we have of scientific analyses go back to the teachings by ancient scholars in what we now call Greece and Turkey. The sole exception was the systematic observation of heavenly bodies, but this was more an art than a science. Also, its end use was directed at predicting the fortunes of rulers, not toward understanding the workings of nature.

What did take place back then, however, has direct bearing on Galileo’s life. Beginning about 2,500 years ago, some of the people living along the shores of the cerulean seas surrounding what we now call the Near East began to speculate out loud about their ideas on what made up their environment. Maybe because they did not call themselves scientists, they had no trouble attracting others to listen to these ideas and to join in their efforts.”

“Lee, are you suggesting that, if professors did not call themselves professors, they would get more students to listen?”

“It’s an interesting possibility. In any case, ‘schools’ developed gradually under the tutelage of individual Greek scholars. One of the earliest, Pythagoras, now called the father of natural philosophy, is best remembered for deducing that the sum of the squares of the two short sides of a right triangle just equals the square of the long side, called the hypotenuse. Less well known is his claim that the earth must be spherical, at a time when everyone else was convinced that the earth was perfectly flat. Pythagoras did not base his conclusion on an observation that boats reaching the horizon gradually disappear from view (Fig. 1) but rather on the premise that a sphere was the most aesthetically pleasing shape a body could have. For this reason alone, a perfect earth should be a sphere! To protect themselves from popular anger at such an unorthodox idea, however, the Pythagoreans formed a secret society, swearing not to divulge their conclusions to outsiders.”

“Were they more concerned about being ridiculed or about their personal safety?” Beth continued.

“I don’t really know. It may be that forming a secret society was just a matter of intellectual snobbery.” I responded before going on.

“You doubtlessly remember from your course in logic that the rules for rigorous reasoning were systematically spelled out by the most brilliant Greek philosopher, Aristotle. He then applied these rules to the analysis of a broad range of topics of possible interest to humans. In doing this, he never felt a need to subject his conclusions to any test other than that the arguments leading up to them obey these rules of logic. What puzzles me, however, is how the same people who required such rigorous proofs for their theorems in geometry could have been so cavalier in their acceptance of untested ideas about everything else?”

Fig. 1. As a boat passes over the horizon (defined by the straight line of vision of an observer), the spherical shape of the earth causes a boat to ‘sink’ out of view, in the same way as the sun does at sunset.

“I believe that Aristotle’s writings included the description of human behavior.” Beth noted. “That would make him the very first psychologist as well.”

“Aristotle had fixed ideas about a lot of things, including how bodies on earth move. First he distinguished between what he called ‘natural’ motion and ‘violent’ motion. Natural motion was supposedly based on the ‘nature’ of an object. An object whose nature was of the earth, for example, a stone, would tend to return to the earth when lifted up and released. The larger or heavier the stone, the more rapidly would it seek to return. Similarly, smoke rises from a burning log because smoke is of air and so it seeks to return to the air. Such natural motion could take place in a straight line up or down, as was the case for most natural motion on earth.”

“What about a leaf?” Beth asked. “It floats rather than falls to the earth in a straight line.”

“According to Aristotle, a leaf’s nature is mostly of earth but also partly of air. It should fall to the ground like a stone, but much more slowly.”

“How did he handle the motion of the planets and the stars?” Beth wanted to know next. “They don’t travel in straight lines toward or away from the earth.”

“Here again Aristotle provided a neat answer. Celestial objects move in circles. Since circular motion has neither a beginning nor an end, it can go on forever.”

“Like circular conversations?”

“That’s probably why we call them circular. But let me continue. To move a stone in a horizontal direction, a ‘violent’ motion had to be imposed on it. Such violent motion could be imparted by a rapidly moving stream to a log floating on it, or by the wind to a falling leaf or to the sails of a ship. When the external agent imposing such violent motion is removed, the object returns to its natural state. The stone falls back to the earth and the log and boat float in place without further lateral motion.”

“Wait a minute,” Beth interjected. “When a stone is thrown sideways, the hand imparts a violent motion to it. But how did he deal with the fact that the stone keeps moving sideways after the hand releases it?”

“Here is just one example of Aristotle’s genius: as the stone moves forward, he reasoned, it must push the air ahead of itself out of the way and leave a pocket devoid of air behind it. The compressed air, therefore, rushes toward the back of the stone to fill this void. In doing this, it propels the stone forward! Gradually, the stone strives to return to its natural state and falls back to the earth, from whence it came. How do you like that as a neatly logical explanation?”

“O.K. Can we agree that Galileo may be called the very first physicist but that others earlier laid down some of the groundwork?” Beth asked as she plopped two eggs into boiling water in a saucepan. “Now let’s get back to where we started. Tell me more about Galileo and what he did to distinguish himself.”

“Galileo was born into an impecuneous but noble family in Pisa, Italy on February 15, 1564. His father had a deep interest in the mathematical aspect of music but urged his most talented son to pursue a financially more rewarding career in medicine. So the young Galileo enrolled at the University of Pisa to prepare himself for a life as a physician. Like his father before him, however, Galileo found the study of mathematics far more interesting. He dropped out of the medical program to indulge his scientific curiosity and, fortunately, the rectors of the University of Pisa recognized his scientific promise and appointed him an instructor in mathematics. They did this even though Galileo held no formal degrees in mathematics or in any other field. This enabled him to stay on for three additional years while he did his seminal work on the motion of freely falling bodies there.”

“What had Galileo done that so impressed his elders?” Beth wanted to know.

“Already while pursuing his medical studies, Galileo was frustrated by the inadequacies of Aristotle’s teachings. One day while attending a church service in Pisa, Galileo was fascinated by the regularity of the back-and-forth swinging of the chandelier suspended from the ceiling by a long chain. Timing the duration of each swing against his own pulse beats, he found each swing to last exactly as long as the one before it. Later, at home, he duplicated this observation by suspending various weights from strings of different lengths. He found that he could change the duration of each swing by changing the length of the string or the weight of the suspended object. Aristotelean logic could not explain this. Neither could Galileo come up with a very satisfactory explanation. This did not prevent him from inventing a pulsometer, however, which is the forerunner of the metronomes that would annoy music students for many years to follow.”

“Isn’t a swinging candelabrum simply a pendulum?” Beth interjected. “And what distinguished Galileo from Aristotle? Was it the fact that he was not satisfied just speculating about the pendulum’s regularity and instead carried out actual experiments?”

“That’s part of the distinction and a most important part.” I responded “But another, even more important distinction was Galileo’s ability to generalize his experimental observations into a general law of nature. To see how that happened, let me describe for you how he corrected the misconception about freely falling objects that persists among some people even to the present day.”

“You mean the one derived from Aristotle’s conclusion that what goes up must also come down?” Beth asked mischievously as she plopped another pair of eggs into the saucepan.

“Not exactly. Aristotle taught that the speed of a falling object depended on its weight — the heavier the object, the faster it should fall toward the earth. To test this hypothesis, Galileo did not climb atop the leaning tower of Pisa, as some legends suggest. He realized that comparing the descent of two different objects would be fraught with innumerable difficulties: they have to be released at exactly the same time. The times of their release and their arrival below must be clocked precisely. Additionally, an allowance would need to be made for the resistance of the air through which they were falling. We are all familiar with the effect that streamlining has on the speeds of cars, boats, etc., and Galileo was not unaware of the role that air would play in free fall. He also lacked a stop watch or any time piece, for that matter, with which he could measure sufficiently accurately the speed of an object’s descent.”

“I hope that you make this clear in your textbook, Lee. It’s hard for a reader in the twentieth century to realize that there was a time without watches or the many other things that we take so for granted.”

“I try to do this by describing how Galileo overcame these limitations. First of all, he had a set of very smooth boards made up which contained V-shaped grooves so that he could roll a ball along the groove in a perfectly straight line. (The groove also minimized contact with the rolling ball, that is, the effect of friction.) By inclining a board at different angles, Galileo could vary the speed of a ball’s descent in a controlled manner. To measure that speed, he arranged little tripping devices that rang a bell as the rolling ball passed by. Finally, he controlled the flow of water from a reservoir into a small container by putting his finger over the outlet tube of the reservoir. When the ball tripped the first bell, he released the water and, when the second bell rang, he shut it off again. Careful weighing of the water in the container then provided an accurate measure of the amount of time elapsed between the two consecutive events. To be sure that his measurements were reliable, Galileo repeated each trial a number of times. Most importantly, he kept accurate records of all his measurements.”

“I know all about the importance of keeping accurate records,” Beth exclaimed. “But what, exactly, did Galileo learn from watching balls roll down an inclined plane?”

“The first thing that Galileo discovered as he timed the descent of his freely rolling balls was that their speed did not depend on their weight, as Aristotle had incorrectly claimed. In fact, he found that the speed of all balls, regardless of their size or weight, increased in a very regular way: the further they rolled, the faster they rolled. This increase in speed is called acceleration, by the way.

As importantly, Galileo noted that the acceleration of every ball remained constant regardless of what the angle was at which he inclined the board! To check this out further, he measured the speeds during different intervals of a particular roll and again observed that the acceleration, that is, the rate at which the speed increased, was the same regardless of how fast the ball was rolling at the start of any measurement. The only thing that varied a ball’s acceleration was the inclination angle of the board. The steeper the board, the faster the ball descended.”

“I realize that this can’t be actually done in practice” Beth interrupted, “but what would the acceleration be if the board were absolutely vertical?”

“That is a very pertinent question,” I responded. “Should the board be raised to a vertical position, the constant acceleration measured by Galileo would become the same as the constant acceleration of a freely falling body!

In fact, this is what distinguishes Galileo from Aristotle. Instead of being satisfied with a logical explanation of his observations, Galileo asked, what would the result have been in an ideal experiment? How would the different size balls behave if they did not have to roll on actual boards? In this way, Galileo was able to extend his observations of rolling balls to the free fall of any object regardless of its size of shape, as long as it could be imagined falling through a vacuum that offered no air resistance.”

“Did Galileo know about vacuums?” Beth inquired.

“The idea of a vacuum goes back to the Ancient Greeks, but how well Galileo understood what a vacuum is or whether one actually exists anywhere in the world, I really don’t know.” I replied. “Galileo did understand that a leaf or piece of paper falls to the ground with a different acceleration than a stone because a leaf encounters more air resistance than a stone.”

“Well, are you suggesting that the shape of a freely falling object affects its rate of descent?” Beth persisted. “I thought that you said a moment ago that the acceleration of any object in free fall was the same regardless of its size or its shape...

Table of contents

• Cover
• Half title
• Title
• Copyright
• Dedication
• Contents
• Preface to the Second Edition
• Introduction: What Keeps Us Going?
• Chapter One: Breakfast of Hard-Boiled Eggs with Inertia
• Chapter Two: Breakfast of Eggs Bene-Bricked
• Chapter Three: Breakfast of Apple-Gravity Pancakes
• Chapter Four: Breakfast of Cereal and Calories
• Chapter Five: Breakfast of Hot Cakes with Energy
• Chapter Six: Breakfast of French Toast
• Chapter Seven: Breakfast of Cold Cuts
• Chapter Eight: Breakfast of Blueberry Muffins
• Chapter Nine: Breakfast of Apple Fritters and Love
• Chapter Ten: Breakfast of Eggs and Crisp Bacon
• Chapter Eleven: Breakfast of Oat Meal with Light Cream
• Chapter Twelve: Breakfast of Lox and Bagels
• Chapter Thirteen: Breakfast of Farina
• Chapter Fourteen: Breakfast of Danish Pastry
• Chapter Fifteen: Breakfast of Waffles
• Chapter Sixteen: Breakfast of O. J., Donuts, and Coffee
• Chapter Seventeen: Breakfast of Rice Krispies
• Chapter Eighteen: Breakfast of Corn Fritters
• Chapter Ninteen: Dinner at Home
• Chapter Twenty: Lunch at the Beach
• Chapter Twenty-One: Lunch at Venetian Bay
• Chapter Twenty-Two: Breakfast at the Beach
• Chapter Twenty-Three: Dinner Under the Stars
• Chapter Twenty-Four: After Dinner at Home
• Glossary of Physics Terms
• Acknowledgments
• Index