Fizyx for Felines: A Physics Textbook for the Curious Cat

Chapter 0

Posted in Uncategorized by skonabrittain on 29 January, 2010

The introductory chapter is named after my own cats, because their names are mentioned in it. Future chapters will be named after famous scientists’ cats, some real and some imaginary (but all complex, of course).
A photo of Femto Chan is featured. (I wanted it to be a photo of Atto Chan, because her diminutive size makes Gravitation appear to be even larger, but she is the least cooperative, whereas Femto Chan is the most prone to restfulness. Zepto Chan is the most cooperative but, despite his name, he is also the largest. If you don’t understand what his name indicates about his size, you will after reading Chapter 0.)
    






Chapter 0 – Brittain’s Cats


Introduction

This terror, then, this darkness of the mind,
Not sunrise with its flaring spokes of light,
Nor glittering arrows of morning can disperse,
But only Nature’s aspect and her law,

Lucretius
(c. 99 – c. 55 BCE)
Roman poet
De Natura Rerum (On the Nature of the Universe)
Nature and Nature’s laws
lay hid in night:
God said, Let Newton be!
and all was light.

Alexander Pope
(1688-1744)
English poet
epitaph for Sir Isaac Newton
In the
night
all cats
are gray.

Miguel de Cervantes
(1547–1616)
Spanish poet
Don Quixote

Although you may have never studied physics before, you make use of it every day. Whenever you pounce on a mouse, or fall head first and land on your feet, or use a cat-flap door, or even just bask in a pool of sunlight, you are using your knowledge of physics, albeit probably subconsciously.

Physics is the study of the physical universe. Physicists seek explanations for the physical phenomena we observe and then try to cohere the explanations into simple elegant laws, with the aid of mathematics. These laws are then tested by applying them to other situations, and extending them into other areas, with the goal of making them as general as possible.

Most of the observable phenomena physicists study can be thought of in terms of change: change of position,which is motion; change of form; change of temperature; change of color; and so forth. One type of law that is particularly appealing to physicists is the conservation law. In studying change, physicists are actually more interested in what is not changing, what quantity remains the same amidst all the changes. Such a quantity is said to be conserved. In the first chapter of this text, we will see that momentum and energy are two such quantities. Their conservation laws are among the most important laws throughout the field of physics.

Physicists prefer that the number of basic laws be minimized and that they appear as simple as possible. They accomplish this elegance with the aid of mathematics. Sometimes they need to use very high-powered mathematics so that they can express many things in one apparently simple equation. For example, much of Einstein’s Theory of General Relativity can be summarized with the second-rank tensor equation Gμν = 8πTμν. (If not knowing what a tensor is is making you feel tenser, relax – you won’t see another one in this book. It takes a book the size of Misner, Thorne & Wheeler’s Gravitation, which truly embodies its name, to explain that simple-looking equation1. See Figure 0-1.)




Femto Chan asleep on Gravitation

Figure 0-1. Studying tensors reduces tension



Because the physical world is so complicated, physicists often make mathematically simplifying assumptions. For example, to study the motion of a ball, we assume that it is a perfect sphere. Or at first, even more preposterously, we assume that all its mass is concentrated at a single dimensionless point in space.

Initially, physicists focused on describing motions on a scale at which we normally observe phenomena – the scale of balls, mice, etc. Later, they found that these relatively simple laws of classical mechanics could be applied to telescopically large objects, such as planets, and to microscopically small objects, such as molecules. However, as they delved into an even smaller arena, at the atomic scale and below, the laws no longer held up, and they developed a new area of physics, quantum mechanics, to explain atomic phenomena.

The same situation occurs for other extreme realms. At normal experiential speeds, even at the swift speeds obtainable by cheetahs, classical mechanics reigns. But at speeds approaching the speed of light, classical mechanics breaks down and must be replaced by relativistic mechanics.

When the laws of quantum mechanics or relativistic mechanics are applied to everyday objects, they reduce to the laws of classical mechanics. Thus, although it is now known that some of the classical mechanics laws are not complete, correct descriptions, they are excellent approximations, correct to as many significant figures as we generally care about. In other words, classical physics works on an everyday scale. So rather than labeling it as either wrong or incomplete, physicists refer to it as an effective theory.

This text will cover the various areas of physics in roughly historical order, mainly because this is also the simple-to-complex order. Classical mechanics is also known as Newtonian mechanics, because of Isaac Newton’s pivotal role in its development. Thus, we will begin with a study of Newtonian mechanics, in which you will see that Newton’s cats also played pivotal roles.

Measurement

The key to testing abstract physicals laws is, of course, measurement of concrete physical quantities. There are two different systems of measurement in widespread use in physics. The best one is the metric system, where length is measured in meters (and the derived quantities – centimeters for smaller lengths and kilometers for larger ones) and mass is measured in grams (or often kilograms).

The whole world uses this metric system, except for only three countries: Burma, the Southeast Asian home to Burmese cats, the friendliest domestic species; Liberia, the western African home to lions and other big cats; and the United States, home to the author and her cats. However, due to the preeminence of American scientists, many readers will be more familiar with the alternate system, where length is measured in feet and mass is confused2 with weight, which is measured in pounds. Fortunately, at least both systems measure time in the same units, with seconds being the basic unit.

Actually, there used to be two standard metric systems used by scientists: MKS, which stands for Meters, Kilograms and Seconds; and CGS, which stands for Centimeters, Grams and Seconds. The latter was obviously better suited for applications involving felines and the former for human applications. But the difference was just a matter of scale, and it was very easy to switch between them, as all the quantities are related by simple powers of ten.

These two systems coexisted on equal footing until 1875, when, on a glorious spring day in Paris, seventeen countries, including the United States, ratified the "Treaty of the Meter", creating the General Conference on Weights and Measures (CGPM, which stands for Conférence Général des Poids et Mésures). In 1960, CGPM established our modern metric system, the International System of Units (SI), with the basic units for length and mass being the meter and the kilogram, respectively.

For each type of quantity, there is one basic unit term, and the smaller and larger unit terms are obtained from it by using standard prefixes3. For example, kilo- means a thousand, so a kilometer is 1000 meters, a kilosecond is 1000 seconds, and a kilowatt is 1000 watts.4 The current SI prefixes are included here in a table so that you can easily reference them from anywhere in the text.


Figure 0-2.
Table of SI prefixes

Prefix Symbol Factor Prefix Symbol Factor
deka da 101   deci d 10-1
hector h 102   centi c 10-2
kilo k 103   milli m 10-3
mega M 106   micro µ 10-6
giga G 109   nano n 10-9
tera T 1012   pico p 10-12
peta P 1015   femto f 10-15
exa E 1018   atto a 10-18
zeta Z 1021   zepto z 10-21
yotta Y 1024   yocto y 10-24

As technology allows us to access further and deeper, new prefixes are added. When the SI was adopted, only the first six rows of this table were included. In 1964, the CGPM added the left side of the next two rows, and 11 years later, it added their corresponding diminutives. The last two rows were added in 1991.

Personal Note

Incidentally, the author’s children, the youngest of whom was born the year "zepto-" & "yocto-" were added, have been familiar with the right half of this table since they were very young, thanks to the family pets named Nano Chan, Pico Chan, Femto Chan, Atto Chan and Zepto Chan5. Perhaps, by the time you are reading this, there will also be a Yocto Chan in the family. But this is unlikely because, in an attempt to avoid needing terms beyond the reach of the CGPM, all the current female Chans have been spayed.

 



1 – For those of you dying of curiosity, that deceptively simple equation stands for 10 equations that relate the curvature of spacetime to the matter and energy in it, which are way beyond the scope of this text. <return-to-text>

2 – This confusion will be elucidated in Chapter 1. <return-to-text>

3 – There is just one exception to this rule: the name of the basic unit for mass, kilogram, already has a prefix incorporated into it, so the SI prefixes are instead applied to its root, the "gram". <return-to-text>

4 – Note that computer scientists have misappropriated some of these decimal-based prefixes for their binary situations. Thus, a kilobyte should always mean 1000 bytes but often instead means 1024 (i.e. 210) bytes. This has led to confusion on an international scale, which has recently been somewhat alleviated by the December 1998 International Electrotechnical Commission’s approval of a related set of prefixes for binary factors. In that system, 1024 bytes is one kibibyte (1 Kibyte); kibi is an abbreviation of kilobinary and is symbolized Ki. We hope you have not been too distracted by the thought of biting some kibbles to follow this discussion. <return-to-text>

5 – The name "Chan" is pronounced not as the Chinese "Chan" but rather as the Irish "Sean" because it is a contraction of the French "chat noir". <return-to-text>


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  1. Femto Chan said, on 2 February, 2010 at 07:13

    I love this book! I also love that big black book that says Gravitation and smells like catnip. When Fizyx for Felines gets published, I promise to read it, too, if you also smear catnip on it It’s hard for me to read it online because the text keeps jumping around erratically when I pounce on the mouse. That’s all for now – it’s time for my next nap. Purr…


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