| Author: |
Benjamin Crowell
|
| Published in: | Benjamin Crowell |
| Release Year: | 2006 |
| ISBN: |
xxxxxxxxx
|
| Pages: | 178 |
| Edition: | First Edition |
| File Size: | 14 MB |
| File Type: | |
| Language: | English |
Description of Conceptual Physics
Even before history began, people must already have noticed certain facts about the sky. The sun and moon both rise in the east and set in the west. Another fact that can be settled to a fair degree of accuracy using the naked eye is that the apparent sizes of the sun and moon don’t change noticeably. (There is an optical illusion that makes the moon appear bigger when it’s near the horizon, but you can easily verify that it’s nothing more than an illusion, by checking its angular size against some standard, such as your pinkie held at arm’s length.) If the sun and moon were varying their distances from us, they would appear to get bigger and smaller, and since they don’t appear to change in size, it appears, at least approximately,
that they always stay at the same distance from us.
From observations like these, the ancients constructed a scientific model, in which the sun and moon traveled around the earth in perfect circles. Of course, we now know that the earth isn’t the center of the universe, but that doesn’t mean the model wasn’t useful. That’s the way science always works. Science never aims to reveal the ultimate reality. Science only tries to make models of reality that have predictive power.
Our modern approach to understanding physics revolves around the concepts of symmetry and conservation laws, both of which are demonstrated by this example.
The sun and moon were believed to move in circles, and a circle is a very symmetric shape. If you rotate a circle about its center, like a spinning wheel, it doesn’t change. Therefore, we say that the circle is symmetric with respect to rotation about its center. The ancients thought it was beautiful that the universe seemed to have this type of symmetry built-in, and became very attached to the idea.
A conservation law is a statement that some number stays the same with the passage of time. In our example, the distance between the sun and the earth is conserved, and so is the distance between the moon and the earth. (The ancient Greeks were even able to determine that earth-moon distance.)
In our example, the symmetry and the conservation law both give the same information. Either statement can be satisfied only by a circular orbit. That isn’t a coincidence. Physicist Emmy Noether showed on very general mathematical grounds that for physical theories of a certain type, every symmetry leads to a corresponding conservation law. Although the precise formulation of Noether’s theorem, and its proof, are too mathematical for this book, we’ll see many examples like this in which the physical content of the
theorem is fairly straightforward.
The Conceptual Physics idea of perfectly circular orbits seems very beautiful and intuitively appealing. It came as a great disappointment, therefore, when the astronomer Johannes Kepler discovered, by the painstaking study of precise observations, that orbits such as the moons were actually ellipses, not circles. This is the sort of thing that led the biologist Huxley to say, “The great tragedy of science is the slaying of a beautiful theory by an ugly fact.” The lesson of this story, then, is that symmetries are important and beautiful, but we can’t decide which symmetries are right based only on common sense or aesthetics; their validity can only be determined based on observations and experiments.
As a more modern example, consider the symmetry between right and left. For example, we observe that a top spinning clockwise has exactly the same behavior as a top spinning counterclockwise. This kind of observation led physicists to believe, for hundreds of years, that the laws of physics were perfectly symmetric with respect to right and left. The symmetry appealed to physicists’ common sense. However, experiments by Wu et al. in 1957 showed that this symmetry was violated in certain types of nuclear reactions. Physicists were thus forced to change their opinions about what constituted common sense. 1.2 Conservation of Mass
that they always stay at the same distance from us.
From observations like these, the ancients constructed a scientific model, in which the sun and moon traveled around the earth in perfect circles. Of course, we now know that the earth isn’t the center of the universe, but that doesn’t mean the model wasn’t useful. That’s the way science always works. Science never aims to reveal the ultimate reality. Science only tries to make models of reality that have predictive power.
Our modern approach to understanding physics revolves around the concepts of symmetry and conservation laws, both of which are demonstrated by this example.
The sun and moon were believed to move in circles, and a circle is a very symmetric shape. If you rotate a circle about its center, like a spinning wheel, it doesn’t change. Therefore, we say that the circle is symmetric with respect to rotation about its center. The ancients thought it was beautiful that the universe seemed to have this type of symmetry built-in, and became very attached to the idea.
A conservation law is a statement that some number stays the same with the passage of time. In our example, the distance between the sun and the earth is conserved, and so is the distance between the moon and the earth. (The ancient Greeks were even able to determine that earth-moon distance.)
In our example, the symmetry and the conservation law both give the same information. Either statement can be satisfied only by a circular orbit. That isn’t a coincidence. Physicist Emmy Noether showed on very general mathematical grounds that for physical theories of a certain type, every symmetry leads to a corresponding conservation law. Although the precise formulation of Noether’s theorem, and its proof, are too mathematical for this book, we’ll see many examples like this in which the physical content of the
theorem is fairly straightforward.
The Conceptual Physics idea of perfectly circular orbits seems very beautiful and intuitively appealing. It came as a great disappointment, therefore, when the astronomer Johannes Kepler discovered, by the painstaking study of precise observations, that orbits such as the moons were actually ellipses, not circles. This is the sort of thing that led the biologist Huxley to say, “The great tragedy of science is the slaying of a beautiful theory by an ugly fact.” The lesson of this story, then, is that symmetries are important and beautiful, but we can’t decide which symmetries are right based only on common sense or aesthetics; their validity can only be determined based on observations and experiments.
As a more modern example, consider the symmetry between right and left. For example, we observe that a top spinning clockwise has exactly the same behavior as a top spinning counterclockwise. This kind of observation led physicists to believe, for hundreds of years, that the laws of physics were perfectly symmetric with respect to right and left. The symmetry appealed to physicists’ common sense. However, experiments by Wu et al. in 1957 showed that this symmetry was violated in certain types of nuclear reactions. Physicists were thus forced to change their opinions about what constituted common sense. 1.2 Conservation of Mass
Content of Conceptual Physics
1 Conservation of Mass and Energy 7
2 Conservation of Momentum 37
3 Conservation of Angular Momentum 61
4 Relativity 69
5 Electricity 91
6 Fields 109
7 The Ray Model of Light 127
8 Waves 155
2 Conservation of Momentum 37
3 Conservation of Angular Momentum 61
4 Relativity 69
5 Electricity 91
6 Fields 109
7 The Ray Model of Light 127
8 Waves 155
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