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RELATIVITY AND QUANTUM PHYSICS FOR BEGINNERS
By Steven L. Manly, Steven Fournier
Steerforth PressCopyright © 2009 Steven L. Manly
All rights reserved.
Science and the Human Bias
Humans seek to understand the universe!
Religion is based on faith. Art is based on aesthetics. While both religion and art can provide insight into the human condition, the methodology of science is unique in that it bows to observations. Ideas that are not consistent with what we see in nature under controlled and repeatable circumstances are thrown out!
"Faith" is a fine invention When Gentlemen can see, But Microscopes are prudent In an Emergency. —Emily Dickinson
In science a person looks at something and makes a hypothesis (or theory) about how it works. Then they design an experiment to test the hypothesis. After doing the experiment, the person modifies or discards the theory depending on the results of the experiment. This process repeats, and our scientific understanding of the phenomenon evolves.
Communication, honesty, and reproducibility of observations lie at the core of what makes science work. Experimental results must be conveyed to others unambiguously and in detail so that others can reproduce the experiment.
This paper describes the measurement of the energy dependence of elliptic flow for charged particles in Au+Au collisions using the PHOBOS detector at the Relativistic Heavy lon Collider (RHIC). Data taken at collision energies of [square root of SNN] = 19.6, 62.4, 130 and 200 GeV are shown over a wide range in pseudorapidity. These results, when plotted as a function of η' = |η| - Ybeam, scale with approximate linearity throughout η', implying no sharp changes in the dynamics of particle production as a function of pseudorapidity or increasing beam energy.
There's no room for ambiguity and confusion in scientific communications. This leads to a precise, layered, specialized language—or lingo—in each area of science.
Also, this desire for unambiguous clarity, along with the basic quantitative nature of many measurements, leads to the heavy use of mathematics in science.
Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency. —René Descartes
Music communicates ... but it evokes different feelings in different people.
Mathematics and very precise language allow scientists to communicate with as little confusion as possible.
There's more to it than clarity. Mathematics and layers of concepts often lead to the ability to ask questions and have insights that are not possible otherwise.
Natural human tendencies
In spite of scientists' attempts to make un-ambiguous measurements, human judgment and intuition often comes into play.
Scientists sometimes stop looking for errors in an experiment or data analysis when they get the answer they expect to find, yet they look very hard for problems if they see something unexpected.
An expert is a man who has made all the mistakes which can be made in a very narrow field. —Niels Bohr
The limitation of experience
Our senses, intuition, and tendency to interpret data are tuned to times and distances and speeds and sizes that are commonly encountered. This is what we know. Our expectations are biased toward the realm of our experience. Every time we create a new technology that allows us to see farther, smaller, or faster things we are forced to expand our minds to encom-pass the unexpected.
Anthropocentric and geocentric ideas
Humans have always wanted to feel important and have tended to like ideas that place them at the center of the universe. Religions often play to this desire.
Nature doesn't seem to have the same hang-up.
The methodology of science tends to push us beyond the human bias.
Experimental results are shared and experiments are repeated. This leads to the constructive and frank inter-change of ideas and the correction of earlier mistakes.
A hypothesis with a human bias is fair to propose. After all, perhaps we are special!
But, in science, that hypothesis (just like any other) must be supported by experimental data if it is to survive. Scientists tend to prefer simpler explanations when given a choice and all other things are equal.
As strange as it may seem, aesthetics does have a place in science. Science has an artistic side. A critical part of the methodology of science is known as Ockham's razor—when choosing between different theories that describe the data, the simplest is often the best.
Numquam ponenda est pluralitas sine necessitate. (Plurality is never to be posited without necessity.) —William of Ockham
The progression of Man's view of earth's place in the cosmos is a good example of science overcoming the human bias.
The most widely held view of cosmology through the Middle Ages was that catalogued by the Egyptian astronomer Ptolemy in his book Almagest, written in AD 150. The Ptolemaic universe contained many elements proposed long before his time by others, such as Aristotle and followers of Pythagoras. In Ptolemy's view, the sun, moon, stars, and five known planets move around the earth on a complex system of nested, rotating transparent (or crystalline) spheres and circles within circles. Because the planets, sun, and moon each have unique motions in the sky relative to the stars, the complicated multishell and circle-within-circle arrangement was necessary in order for the model to agree with observations of the heavenly bodies.
Then came along a Prussian astronomer (born in what is now Poland), named Nicolaus Copernicus 1473–1543), and he ...
As he neared death, Copernicus published De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres), which presented a heliocentric (sun-centered) view of the universe that was eventually shown to be simpler than Ptolemy's cosmology.
A man born shortly after the death of Copernicus, Danish astronomer Tycho Brahe, made very careful measurements of the motion of the heavenly bodies—much more accurate and precise than were available before. Brahe created a cosmological model where the sun and the moon moved in circles about the earth while the planets moved in circles about the sun.
Armed with Brahe's data, a German astronomer and mathematician named Johannes Kepler—who had been an assistant to Brahe and "appropriated" his data upon Brahe's death—pursued his study of Brahe's data and his own observations and discovered that a heliocentric system with the planets having slightly elliptical orbits was best able to describe the data. He developed three laws of planetary motion that eventually were explained by Isaac Newton and his theory of gravity.
The final blow against the Ptolemaic/geocentric universe came in 1610, when an Italian named Galileo Galilei used a new device—a telescope—to observe the phases of Venus. The exhibition of phases by Venus was strong evidence that Venus orbited the sun.
The search for simplicity and consistency in experimental observations coupled with more and better observations allowed mankind to overthrow deeply held convictions about the structure of the universe.
The struggle against the human bias continues to this day. As we have expanded our horizons to see things vastly smaller/faster/larger/farther than ever before, we have been forced to confront preconceptions born of the human experience and create wholly new ways of looking at the world around us. There is nothing quite as strange and exciting as the reality show of our universe.
This book describes the crazy, revolutionary theories of relativity and quantum physics and shows how these ideas have led to amazing advances in our understanding of the universe.CHAPTER 2
Surviving a Trip to the Mall
Headed to the mall for the perfect accessory or that new pair of running shoes? To get there and find that perfect thing, you'll need a fundamental concept of space and time.
Most institutions demand unqualified faith; but the institution of science makes skepticism a virtue. —Robert K. Merton, Social Theory and Social Structure (1962)
The methodology of science relies on people making observations of nature and relating those observations to others. To do that scientists need to have a concept of space and time.
The concept of space and time is not just for scientists. Shopping, playing soccer, hunting deer, working, even ... er ... surfing require that people have a concept of space and time.
Space is the fabric in which we measure where things and events are located.
Time is the fabric in which we measure when things and events are located.
According to modern astronomers, space is finite. This is a very comforting thought—particularly for people who cannot remember where they left things. —Woody Allen
Time is but the stream I go a-fishing in. —Henry David Thoreau
Time goes, you say? Ah no! Alas, time stays, we go. —Henry Austin Dobson
As you can see, life would be awfully boring without change. Fortunately, the universe around us is not static. In fact, the only constant is change, and change requires the concept of time. Time is the ruler against which change is measured.
The only thing that stays the same is change. —Melissa Etheridge, "Change"
The only reason for time is so that everything doesn't happen at once. —Albert Einstein
All of us share a basic concept of space and time, which is integral to how we view the world.
It takes three numbers to specify the position of something in everyday life. Suppose you go to the grocery store looking for corn nuts and you have trouble finding them. Finally you ask the manager for help. In order to lead you to the com nuts, the manager has to specify the aisle, how far down the aisle you should go, and the shelf on which you should look. That's three numbers, one corresponding to each spatial dimension in which we live. The room that you are sitting in has a length, width, and height—three numbers.
How long a minute is, depends on which side of the bathroom door you're on. —Zall's Second Law
We might live in a universe with more than three spatial dimensions in spite of the fact that we can only perceive three dimensions. How can this be? Imagine being an ant on a large beach ball or a sailor on the ocean. In both cases, the relevant world seems flat and two dimensional. Yet we know both the sailor and ant are moving on a large three-dimensional object. It might be the case that the universe has more to it than meets the eye.
Space is to place as eternity is to time. —Joseph Joubert
Three spatial dimensions moving lockstep through time. This is our shared view of the world. Let's be very clear about what this means. If we handed out synchronized watches to ten different people in a room and asked them to leave, go about their business, but return in exactly one hour, each person would return to the room at the same time, regardless of what they did during that hour. Time is absolute. It moves along at the same rate no matter who you are or what you are doing.
Today is the tomorrow we worried about yesterday. —Unknown source
To be sure, we perceive time to pass at different rates depending on whether we are having fun or are bored or in pain or in ecstasy. But if we look at a clock, time passes at the same rate for everyone—no matter whether he or she is happy, sad, or indifferent.
If you want to learn about space and time, a great place to begin is in the study of motion. Speed is a measure of how far something goes (in space) in a given amount of time. Since speed is a quantity that involves both space and time, our well-defined human intuition about space and time leads us to have particular expectations about speeds.
To learn about speed, imagine taking a trip to the mall and sitting at a cafe watching people on a moving sidewalk. They look at you rather strangely when you pull out the radar gun and start to make speed measurements.
What can you learn by watching people and recording speeds?
You see that a person moves past you on the moving sidewalk at a speed equal to that of his walking speed plus the speed of the sidewalk.
The result from the mall sidewalk radar gun experiment should not be too surprising. In everyday life, velocities add. You see this all around you every day. Want another example? Imagine you are going to the mall in a car that is moving with a speed of 30 miles per hour. Suppose you approach another car from behind that is moving only 25 miles per hour. The fact that velocities add means that your car approaches the other car with a relative speed of 5 miles per hour.
If you are driving a car or shooting at a running deer or playing a sport your brain is processing relative velocities constantly. Hunters and football quarterbacks "lead" their targets. The concept of relative velocities that everyone uses is exactly what you measured at the mall in the sidewalk thought experiment. It makes sense to us. It works.
Nobody in football should be called a genius. A genius is a guy like Norman Einstein. —Joe Theismann, former NFL quarterback
I want to rush for 1,000 or 1,500 yards, whichever comes first. —George Rogers, former NFL running backCHAPTER 3
Nature's Relatively Strange Reality Show
After the mall security chaps decide that your radar gun experiments by the moving sidewalk are freaking out the shoppers, you take your inquisitive nature and radar gun out to the mall parking lot. Measuring the speed of passing cars quickly becomes boring. So you decide to see if you can measure the speed of the light emitted by the cars' headlights.
It turns out that a radar gun can't measure the speed of light. But don't let that bother you for the moment. Suppose that you can measure the speed of the light emitted by a car headlights. What do you see?
If the car is not moving, you observe the car emitting light that moves at a speed of 670,616,630,000 miles per hour. You measure the same speed no matter what direction the car is pointed.
For comparison, consider this: F-16 fighter jets can travel at a top speed of approximately 1,500 miles per hour.
When you measure the speed of the light emitted by a stationary car and one that is zooming by at a high speed, you get the same value—c.
Light is so fast that it travels a distance roughly equal to the distance between New York and San Francisco one hundred times in each second.
This is the same thing as saying two people walking at the same speed in the mall continue to move at the same speed even after one of them steps onto the moving sidewalk without changing their stride! This violates the common human intuition about relative velocities. It makes no sense.
Believe it or not, the fact that light moves at the same speed no matter how you or the source of the light move with respect to each other was not discovered in a mall parking lot by bored science geeks.
The "something fast" that Michelson and Morley used for their experiment—their moving sidewalk—was the earth itself. Earth moves around the sun at a speed of approximately 30 kilometers per second and the solar system moves around the center of the Milky Way galaxy at a speed of roughly 250 kilometers per second and so forth. They compared the speed of light along the direction of Earth's motion to the speed perpendicular to the direction of earth's motion through space.
See this? It happens with strings, too. The waves traveling on this string are interfering. They add together when they pass through each other.
Albert Michelson was the first American awarded the Nobel Prize in Physics. The award was presented to him in 1907.
Nature has many examples of waves. They all operate more or less like the "wave" that crowds do in big sporting events. In the human wave in a stadium, each person moves up and down with a very particular timing. The wavelike form that travels around the stadium comes about because each person moves a moment after the person to one side and a moment before the person to the other side. This organized and carefully timed movement of many individuals leads to something more than incoherent individual movements. The end result is the wave shape moving around the stadium. In water waves, the water molecules move up and down. In sound waves in air, the air molecules wiggle to and fro. In waves traveling on a guitar string, the string vibrates up and down.
Light is also a wave—though it is a bit strange in that there is no waving material. In light, electric and magnetic fields do the waving. More on this later.
Scientists are humans. They don't like give up their long-held beliefs any more easily than anyone else. For years after the results of the Michelson-Morley experiment were known, physicists struggled to reconcile the experiment with the intuitive vision of relative velocities.
I have no special talents. I am only passionately curious. —Albert Einstein, in a letter to Carl Seelig
Brilliant and influential people often have the skill of being able to see things and ask questions that seem obvious and simple afterward. Albert Einstein was particularly gifted in this way.
For those who do not think, it is best at least to rearrange their prejudices once in a while. —Luther Burbank
Excerpted from RELATIVITY AND QUANTUM PHYSICS FOR BEGINNERS by Steven L. Manly, Steven Fournier. Copyright © 2009 Steven L. Manly. Excerpted by permission of Steerforth Press.
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