Exploring Quantum Physics through Hands-on Projects E-Book

David Prutchi

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 471

Veröffentlichungsjahr: 2012

Beschreibung

Build an intuitive understanding of the principles behind quantum mechanics through practical construction and replication of original experiments With easy-to-acquire, low-cost materials and basic knowledge of algebra and trigonometry, Exploring Quantum Physics through Hands-on Projects takes readers step by step through the process of re-creating scientific experiments that played an essential role in the creation and development of quantum mechanics. Presented in near chronological order--from discoveries of the early twentieth century to new material on entanglement--this book includes question- and experiment-filled chapters on: * Light as a Wave * Light as Particles * Atoms and Radioactivity * The Principle of Quantum Physics * Wave/Particle Duality * The Uncertainty Principle * Schrödinger (and his Zombie Cat) * Entanglement From simple measurements of Planck's constant to testing violations of Bell's inequalities using entangled photons, Exploring Quantum Physics through Hands-on Projects not only immerses readers in the process of quantum mechanics, it provides insight into the history of the field--how the theories and discoveries apply to our world not only today, but also tomorrow. By immersing readers in groundbreaking experiments that can be performed at home, school, or in the lab, this first-ever, hands-on book successfully demystifies the world of quantum physics for all who seek to explore it--from science enthusiasts and undergrad physics students to practicing physicists and engineers.

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Dedication

Introduction

Prologue

Your Quantum Physics Lab

Important Disclaimer and Warnings

Legal Disclaimer

Safety and General Precautions

Acknowledgments

About the Authors

Chapter 1: Light as a Wave

Newton’s View: Light Consists of Particles

Young’s Interference of Light

Automatic Scanning of Interference Patterns

The Final Nail in the Coffin For Newton’s Theory of Light

Light as an Electromagnetic Wave

Polarization

Optics with 3-cm Wavelength “Light”

Real-World Behaviors

Double-Slit Interference with Microwaves

The Doppler Effect

Experiments and Questions

Chapter 2: Light as Particles

The Seed of Quantum Physics: Planck’s Formula

The Photoelectric Effect

Can We Detect Individual Photons?

Low-Cost PMT Power Supplies

Listening to Individual Photons

Where Does this Leave Us?

Experiments and Questions

Chapter 3: Atoms and Radioactivity

The Need for Vacuum

The Mechanical Vacuum Pump

The Vacuum Gauge

A Very-High-Voltage Power Supply

A Vacuum Tube Lego® Set

Phosphor Screens

The Electron Gun

The Discovery of the Electron

Cathode-Ray Tubes

Thomson’s First 1897 Experiment—Negative Charge and Rays are Joined Together

Thomson’s Second Experiment—Electrostatic Deflection of Cathode Rays

Thomson and the Modern CRT

Thomson’s Third Experiment—Mass-to-Charge Ratio of the Electron

Measuring e/m with our CRT

A Magical Measurement of e/m

Thomson’s “Plum Pudding” Model of the Atom

Geiger–Müller Counter

α, β, and γ

The Nature of Beta Radiation

The Ionizing Power of Alpha

What are Alpha Particles?

Rutherford’s Alpha-Scattering Experiment

Rutherford’s Planetary model of the Atom

Experiments and Questions

Chapter 4: The Principle of Quantum Physics

Emission Spectroscopy

Bohr’s Spark of Genius

Orbitals and Not Orbits

Quantization-The Core of Quantum Physics

Experiments and Questions

Chapter 5: Wave–Particle Duality

Gamma-Ray Spectrum Analysis

What is the Nature of Light?

Two-Slit Interference with Single Photons

Imaging Single Photons

The Answer: Complementarity

Matter Waves

Matter Waves and the Bohr Atom

Experimental Confirmation of De Brogile’s Matter Waves

Two-Slit Interference with Single Electrons

A Simple TEM

Blurring the Line Between Quantum and Classical

Particle-Wave Duality in the Macroscopic World

Experiments and Questions

Chapter 6: The Uncertainty Principle

Wavefunctions

The Uncertainty Principle

Experimental Demonstration of the Uncertainty Principle

Time–Energy Uncertainty

Fourier Analysis

Bye, Bye Clockwork Universe

Experiments and Questions

Chapter 7: Schrödinger (and His Zombie Cat)

Real-World Particle in a Box

Quantum Tunneling

Quantum Tunneling Time

Superposition and Schrödinger’s Cat

Many-Worlds Interpretation

Schrödinger’s Cat in the Lab

Beam Splitters

Who Rolls the Dice?

The Mach-Zehnder Interferometer

“Which-Way” Experiments

The Quantum Eraser

Experiments and Questions

Chapter 8: Entanglement

Bell’s Inequalities

An Entangled-Photon Source

Detecting Entangled Photons

High-Purity Single-Photon Source

Testing Bell’s Inequality

Closing the Loopholes

The Age of Quantum Information

A Quantum Random-Number Generator

Quantum Information

Quantum Teleportation

Faster-than-Light Communication?

Quantum Cryptography

Quantum Computing and Technologies for the Future

Experiments and Questions

References

Sources for Materials and Components

Abbreviations

Index

EXPLORING QUANTUM PHYSICS THROUGH HANDS-ON PROJECTS

Copyright © 2012 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New JerseyPublished simultaneously in Canada

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Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

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Library of Congress Cataloging-in-Publication Data:

Prutchi, David.Exploring Quantum Physics Through Hands-On Projects/David Prutchi and Shanni R. Prutchi.p. cm.Includes index.ISBN 978-1-118-14066-6 (pbk.)1. Quantum theory—Popular works. 2. Quantum theory—Experiments. 3. Science projects.I. Prutchi, Shanni R. II. Title.QC174.12.P785 2011535’.15—dc232011030360

In memory of Zeide Simon.Dedicated to Saba Shlomo, Savta Ruthi, Babbe Rosmari,Dorith, Hannah, and Abigail.

Introduction

Tell me and I forget. Teach me and I remember. Involve me and I learn.

—Benjamin Franklin

Physics developed steadily after the introduction of Isaac Newton’s ideas in the 1600s and had made great progress by the nineteenth century. People really felt the impact of this knowledge when the Industrial Revolution was made possible by the application of everything that scientists had learned about mechanical forces, gravity, electricity, magnetism, heat, light, and sound.

By the late nineteenth century, scientists felt that all of this understanding of physics formed a framework that could describe the world very deeply and thoroughly. Still, there were some nagging inconsistencies between theoretical calculations and experimental data, which were acknowledged by Lord Kelvin (who formulated the First and Second Laws of Thermodynamics) in his 1900 lecture titled “Nineteenth-Century Clouds over the Dynamical Theory of Heat and Light.” The two “dark clouds” to which he was alluding were the unsatisfactory explanations that the physics of the time could give for the constancy of the speed of light, as well as for the glow produced by a hot body.

What is now known as “modern physics” was born from the two major physical theories that were developed during the twentieth century to resolve these two “dark clouds”: for the former, the Theory of Relativity; for the latter, quantum mechanics.

Quantum mechanics makes statements that are even weirder than those of relativity. In the odd world of quantum physics—at least as explained through the extreme thought experiments of its original founders—objects can be in two places at the same time, cats can be both simultaneously dead and alive, and everything that looks continuous to us is really pixelated into tiny, discrete chunks.

In spite of its strangeness, a working knowledge of relativity requires no more than basic algebra and geometry. After all, relativity is just a more fundamental, up-to-date, and accurate version of the classical physics founded by Newton. On the other hand, quantum mechanics is much more difficult to understand. Richard Feynman, a physicist who won the Nobel Prize for his work on quantum physics, didn’t believe that anyone really understands what the theory tells us. In his words: “I think I can safely say that nobody understands Quantum Mechanics.”

Nevertheless, quantum mechanics works so well that it has enabled the development of lasers, transistors, chips, and displays used in the electronic gadgets that are so important to our modern lives. Because of this, quantum physics ought to be an important part of everyone’s education. However, the math is so complex, and our most intuitive notions about reality are so shockingly wrong, that understanding of this subject has remained largely confined to a select group of physicists and engineers. Unfortunately, this has also led to many popularizations that grossly misguide readers and give them completely false notions about the concepts and implications of quantum mechanics.

In this book we will try a different approach. The idea is to build an intuitive understanding of the principles behind quantum mechanics through hands-on construction and replication of the original experiments that led to our current view of the quantum world. We have developed the experimental setups in such a way that they can be constructed easily and at low cost. In addition, we have worked and re-worked the math, so that it is accessible to anyone with knowledge of high school algebra, basic trigonometry, and, if possible, a little bit of calculus. We want to point out that in spite of the many simplifications that we make, we strive to present a conceptually correct view of quantum physics to those who are not conversant in its highly specialized jargon and formalism.

Our approach comes from the belief that there is a huge difference between knowing about something and actually understanding it. We believe that if one is to understand anything about quantum mechanics, one must first develop a “gut feeling” about the quantum world, to get past the mystical veil that so tightly wraps its inner workings. We are hands-on tinkerers, so we follow Benjamin Franklin’s approach toward education: “Tell me and I forget. Teach me and I remember. Involve me and I learn.”

Our hope is that the do-it-yourself approach will demystify quantum physics, and help you navigate away from sensationalistic, speculative, or outright false accounts of this incredibly beautiful field.

Quantum effects tend to vanish as the size of an object increases. For this reason, quantum experiments are practical only for very small objects, such as photons (bits of light), electrons, protons, and other subatomic particles.* In this book, we will show you how to adapt commonly available electronic components, hardware store supplies, and other relatively low-cost items that can be purchased online to reproduce some of the most ground-breaking experiments ever done in physics!

Throughout the book, we will slowly build up a quantum picture of the world. The first chapter will have you become familiar with the way nineteenth century physicists understood light. Despite the advent of quantum mechanics, nineteenth century optics is still used today to make camera lenses, glasses, telescopes, and microscopes. However, the misbehavior of classical optics under very specific circumstances was one of the two clouds looming on Lord Kelvin’s horizon. Understanding the classical view of light is key to appreciating why quantum mechanics would stir such a revolution in physics. In the first chapter, we will perform the experiments that seemed to confirm the correctness of the classical understanding of light’s nature, but we’ll also look at some of the problems raised by these same experiments.

In the second chapter, we will replicate the experiments that produced the data that could not be reconciled with the theoretical explanations of classical physics. We will study the sweeping explanations proposed by Max Planck and Albert Einstein to resolve this issue.

The third chapter will get us into atomic physics and radioactivity. We will build equipment to perform the experiments that gave us our current view of atoms and that brought chemistry into the modern era.

Next, in chapter 4, we will look at quantization—the core principle behind quantum mechanics—and at some of the ways in which it successfully tackles one of Lord Kelvin’s “dark clouds.”

In the experiments of chapter 5, we will take advantage of technology that was unavailable to the pioneers of quantum mechanics to show that both light and material objects can behave with the characteristics of both waves and particles. This is where quantum physics starts to get really weird, allowing particles to behave as if they are in two places simultaneously!

Chapter 6 will introduce Heisenberg’s Uncertainty Principle—the concept that we cannot measure the exact position and momentum of an object at the same time. We will see that this is not due to imprecise measurements. Technology is advanced enough to hypothetically yield correct measurements. Rather, the blurring of these magnitudes is a fundamental property of nature with truly mind-boggling implications about our view of reality.

In chapter 7, we will talk about Dr. Schrödinger and his famous pet. We won’t be conducting any experiments with dead or alive (or zombie) cats, but we will build some hands-on demonstrations that show Schrödinger’s legendary thought experiment in action.

Last, chapter 8 looks at demonstrations of the existence of entanglement. This quantum property is so uncanny that it caused Einstein to mock it by calling it “spooky action at a distance.” Entanglement was proven only in the 1980s, but its deep implications are already causing radical changes in the way in which we view our world. We will also look at technologies that are being developed as a consequence of understanding the role of information in quantum mechanics, and will end the book by peeking at how entanglement is quickly making strides into areas that until recently were purely the domain of science fiction, enabling quantum teleportation, unbreakable cryptography, and quantum computing.

* The difficulty of studying quantum effects on even slightly larger objects, such as atoms or molecules, is so great that only a few labs around the world are equipped to handle this difficult task.

PROLOGUE

YOUR QUANTUM PHYSICS LAB

This book assumes that you have some experience in electronic prototype construction. The circuits actually work, and the schematics are completely readable. It will be easy for you to understand them if you know some circuit design. However, the tested, modular circuits, components, and software are easy to use to build practical instrumentation, even if you view them as “black boxes,” and do not explore their theoretical basis.

Of course, there are some basic electronic instruments that you will need in order to build, test, and use the equipment that we describe in this book. At the very least, you should equip your lab with the following:

Soldering pen, pen rest with wet sponge, solder wire, and solder wick. Preferably, you should use a 70-W soldering station in which you can adjust the temperature between 220–480°C.

Assorted tools, including a sharp diagonal wire cutter, wire stripper, various screwdrivers, hobby knife, needle-nose pliers, etc.

Two handheld, autoranging, 4

1

/

2

-digit, digital multimeters (DMMs). We suggest that you purchase two identical units. Tektronix and Fluke multimeters are recommended, but any of their 4

1

/

2

-digit look-alikes (sold for around $35) are okay.

High-voltage probe (>40 kV) compatible with your multimeter.

Dual-channel, 60-MHz oscilloscope with FFT module. We recommend a second-hand Tektronix TDS210 with FFT module. However, there are many look-alikes that will work equally well. As a lower-cost alternative, you can consider connecting your PC to a USB dual-channel, 60-MHz oscilloscope adapter.

Adjustable, metered, dual-output, linear, bench power supply. You want a unit capable of delivering two outputs adjustable between 0 and at least 20 VDC at 2 A each. A used Tektronix PS280 would be ideal.

The following are really helpful, but not absolutely necessary:

High-voltage DC power supply. Ideally, you want to acquire a well-regulated power supply with selectable polarity (that is, you can choose whether the output referenced to ground will be positive or negative) and a range of 0–2,000 V with at least 1-mA current capability. A used HP 6516A would be great.

Function generator. Doesn’t need to be fancy. Something that will produce sine, triangular, and square waves at frequencies of up to at least 1 MHz will do.

10-MHz pulse generator. Nothing excessive. We recommend something like a Global Specialties model 4010.

Spare PC with at least 2-GHz Pentium 4 processor and 2-GB RAM. You should install student editions of Excel and MATLAB to log, plot, and analyze the experimental data that you will obtain.

Since the prime subject in quantum physics is the photon (a particle of light), you will need a few lasers. Fortunately, laser pointers have dropped dramatically in price, placing in our hands wonderful, well-behaved “photon sources” that just a few years ago would have been out of the reach of anyone but the most advanced labs in the world. We recommend that you equip your lab with the following lasers:

IR diode laser, 980-nm wavelength, 30-mW power.

Helium-neon (HeNe) laser, 632-nm wavelength (red), 5-mW power.

Red laser pointer, 670-nm wavelength, 5-mW power.

Green laser pointer, 532-nm wavelength, 5-mW power.

Violet laser, 405-nm wavelength, 100-mW power.

Many of the setups require mechanical construction. We have tried to keep this to a minimum by using off-the-shelf parts, but you will need to do some drilling and shaping. Most of the enclosures are made of aluminum, so you should have a handheld drill with a full set of drill bits. You will also need a good hacksaw, tin snips, and a nibbler, as well as an assortment of tools to tap holes, bend metal rods, and assemble parts together.

In addition, you should start a well-organized “junk box” to keep your electronic and optical components. We use plastic stacking shoe boxes that are neatly labeled to keep our parts organized. Useful parts that you may want to collect from old equipment or surplus sales include:

Capacitors, resistors, inductors, and other passive electronic components.

Aluminum boxes, power supplies, power adapters, power cords, fuses, rocker switches, panel lights, panel meters, prototyping boards, and other parts to build and enclose instruments.

High-voltage diodes and capacitors from microwave ovens, old TVs, and CRT monitors.

Strong magnets from damaged hard drives.

Old oscilloscope CRT screens, even if the CRTs are dead.

High-speed op-amps, comparators, and other linear ICs.

Light-emitting diodes (LEDs) of different colors.

Laser LEDs and laser modules from CD, DVD, and Blu ray™ players/recorders, and laser pointers.

Lenses and high-quality mirrors, such as those found in old cameras, binoculars, and projectors.

High-voltage flyback transformers from old color TVs and CRT monitors.

Items containing small amounts of radioactive materials such as ionization-type smoke detectors, old-style lantern mantles, and old luminescent watch hands.

Polarizers from camera lenses, sunglasses, and 3D movie glasses.

Lastly, a word about where to find bargain components and instruments—storefront surplus stores (at least those dealing with electronics and science) are a disappearing breed. Most surplus is traded today on eBay® and other Internet auction sites (e.g., www.ebid.net, www.LabX.com, etc.) The best finds on eBay usually come from estate sales, as well as from people who specialize in buying surplus lots from the government or hi-tech companies that are going out of business. Before bidding on anything, check on the reputation of the seller, and read the item description very thoroughly. From our experience, we can tell you that “unable to test” most often means “broken and not repairable.” Especially when buying online, caveat emptor!

A few interesting brick-and-mortar surplus stores are still around.* They have a presence on the Internet, but you will find the most interesting pieces by rummaging through their shelves. If you travel around, try to take a detour and visit the following:

Apex Electronics in the vicinity of Los Angeles, California: You will find racks and racks full of electronics equipment, as well as a yard full of junk (including rocket parts). Plan to spend a full day browsing or leave empty-handed and confused!

The Black Hole of Los Alamos in Los Alamos, New Mexico: It is similar in character to Apex, but is heavily loaded with atomic research surplus from the Los Alamos National Lab.

Fair Radio Sales in Lima, Ohio: You will find racks and pallets full of unclassified surplus equipment. It is quite far from the major cities in Ohio, but the drive is worthwhile, since it contains many wonderful one-of-a-kind items that don’t make it into their catalog.

Murphy’s Surplus Warehouse near San Diego, California: You will find some of the best surplus military equipment to be found! Definitely a worthwhile place to visit.

Skycraft Parts & Surplus, very close to Disney in Orlando, Florida: Very cool store. Worthwhile visiting, especially if you have had it with Mickey Mouse and his friends! It is full of otherwise unobtainable stuff, much of it surplus directly from NASA’s Kennedy Space Center.

Surplus Sales of Nebraska in Omaha, Nebraska: This is a place that we haven’t visited, but we often purchase very unique equipment from them via their Web site. We can just imagine what unadvertised jewels their warehouse may contain!

Whether you are a student, hobbyist, or practicing engineer, we hope that this book will help you find how easy it is to understand the principles of quantum physics by building and experimenting with sophisticated setups at a small fraction of the comparable commercial cost.

For additional information, updated software, and more information on the projects detailed in this book please visit our Web site at: www.prutchi.com.

* For readers in Europe, Army Radio Sales in London, United Kingdom, has an excellent selection of useful items. Unfortunately however, they are a mail-only business. You cannot visit their warehouse.

IMPORTANT DISCLAIMER AND WARNINGS

LEGAL DISCLAIMER

The projects in this book are presented solely for educational purposes. The construction of any and all experimental systems must be supervised by an engineer, experienced and skilled with respect to such subject matter and materials, who will assume full responsibility for the safe use of such systems.

The authors and publisher do not make any representations as to the completeness or the accuracy of the information contained herein, and disclaim any liability for damages or injuries, whether caused by or arising from the lack of completeness, inaccuracies of the information, misinterpretations of the directions, misapplication of the circuits and information, or otherwise. The authors and publisher expressly disclaim any implied warranties of merchantability and of fitness of use for any particular purpose, even if a particular purpose is indicated in the book.

References to manufacturers’ products made in this book do not constitute an endorsement of these products, but are included for the purpose of illustration and clarification. It is not the authors’ intent to make any technical data presented in this book supersede information provided by individual manufacturers. In the same way, any citation of government and industry regulations and standards that may be included in this book are solely for the purpose of reference and should not be used as a basis for design or testing.

Since some of the equipment and circuitry described in this book may relate to or be covered by U.S. or other patents, the authors disclaim any liability for the infringement of such patents by the making, using, or selling of such equipment or circuitry, and suggest that anyone interested in such projects seek proper legal counsel.

Finally, the authors and publisher are not responsible to the reader or third parties for any claim of special or consequential damages, in accordance to the previous disclaimer.

SAFETY AND GENERAL PRECAUTIONS

Many of the projects presented in this book involve power supplies that pose severe electrical shock hazards. In addition, some of the projects involve sources of laser, microwave, or ionizing radiation that may present hazards to the user, especially to sensitive tissues, such as those of the eyes. It must be stressed to the builder the need to exercise safety precautions involving proper handling, building, and labeling of potentially dangerous equipment. The builder and users of equipment described in this book assume full responsibility for the safe use of such devices.

Warnings Related to the Use of High-Voltage Power Supplies

High-voltage power supplies present a serious risk of personal injury if not used in a safe manner or by unqualified personnel. Needless to say, you need to exercise utmost care when conducting an experiment that uses high voltage. However, you also need to be careful after turning off the power supply, because many power supplies and the devices to which they connect can store energy, so that even with the unit unplugged from the wall a lethal hazard can still exist.

Always remove metal objects such as rings, jewelry, and watches before working with high voltage. Keep one hand in a pocket or closed behind your back and we recommend you wear rubber-soled shoes. Always prove to yourself that there is no voltage present anywhere in the high-voltage equipment on which you are working. Never rely on just one switch to power down a high-voltage supply. Turn the power switch off and disconnect the cord from the wall outlet. Be sure no one will inadvertently reconnect the power while you are working on the device. When working with power supplies of several hundred volts or higher, be especially aware that fully discharged capacitors can “self-charge” through the phenomenon of dielectric absorption.

Lastly, never work with high voltage alone, and never leave a high-voltage experiment unattended!

Warnings Related to the Use of Lasers

Lasers produce a very intense beam of light. Even low-power laser pointers can cause permanent damage if pointed directly at the eye! The coherence and low divergence of laser light means it can be focused by the eye into an extremely small spot on the retina, resulting in localized burning and permanent damage in just an instant. Certain wave-lengths of laser light can cause cataracts. Infrared and UV lasers are particularly dangerous, since the body’s “blink reflex,” which can protect an eye from excessively bright light, works only if the light is visible.

Before turning on a laser, always be sure that it is pointed away from yourself and others. Never look directly into a laser, and never direct a laser at another person. Follow the same rules for direct reflections of laser light from reflective surfaces.

Warnings Related to Exposure to Ultraviolet Light

Ultraviolet light can cause permanent eye damage. Do not look directly at UV radiation, even for brief periods. If it is necessary to view a UV source, do so through UV-filtered glasses or goggles to avoid damage to the eyes. Take appropriate precautions with pets and other living organisms that might suffer injury or damage due to UV exposure.

In addition, please note that light from violet LEDs and lasers may contain substantial amounts of UV light that is absorbed largely in the lens of the eye and may cause cataracts.

Warnings Related to Microwave Exposure

Although the microwaves generated by the Gunnplexers that we will describe in the book are weak, the output is sufficiently concentrated that it could cause eye damage at very close range. Never look into the open end of a Gunnplexer while it operates at a distance under 50 cm.

Warnings Related to the Use of Sources of Ionizing Radiation

The radioactive sources recommended for use in the experiments described in this book are professionally manufactured, sealed sources that are exempt from U.S. Nuclear Regulatory Commission and state licensing. They present no special storage or disposal requirements. The activities of these sources are sufficient to conduct nuclear science experiments using standard Geiger–Müller (GM) counters or scintillation detectors, yet low enough not to present any radiation hazard. Nevertheless, we recommend using lead shields when shipping or storing multiple gamma sources to reduce radiation levels.

Make sure that the radioactive source disks are never breached or damaged. The major hazard with a breached sealed source is that radioactive materials could enter the body by inhalation, skin absorption, or ingestion. Immediately place a damaged source inside a zippered plastic bag and dispose of it according to the manufacturer’s instructions.

Everyday items such as smoke detectors, old lantern mantles, and watches with radium-painted dials are radioactive sources that must be treated with respect. Most of these items are no longer manufactured, as exposure to the radioactive material was a health threat to the employees who made them. These everyday items were not designed for instructional or experimental use, and may therefore be hazardous when used for purposes other than originally intended.

Another potential source of radiation in the experiments described in this book comes from the use of vacuum electron tubes powered at over 15,000 V. Detectable levels of X-rays may be produced, depending on the conditions in which these are operated. Caution must be exercised by the experimenter to ensure adequate safety.

Warnings Related to the Use of Vacuum Tubes

Vacuum tubes, especially large ones, present a safety hazard if the tube breaks. Flying glass and electrodes can travel great distances when a tube implodes. This is a particular danger when large tubes, such as CRTs, are used. Treat all glassware under vacuum with respect. Safety glasses should be worn at all times to protect your eyes from flying glass should the glassware break and implode. Before each use, check all vacuum glassware for scratches, cracks, chips, or other mechanical defects that could lead to failure.

Warnings Related to the Use of Rare-Earth Magnets

Some of the projects in this book involve the use of rare-earth magnets (e.g., neodymium and samarium-cobalt magnets), which produce very intense magnetic fields at close distances. The chief hazard with these magnets is that they are strong enough to cause injuries to body parts pinched between two magnets, or a magnet and a metal surface. In addition, magnets allowed to get too near each other can strike each other with enough force to chip and shatter the brittle material, and the flying chips can cause injuries.

Warnings Related to the Use of Chemicals

Some of the experiments described in this book involve the use of hazardous chemicals. Please read the original supplier’s MSDS (material safety data sheet), and make sure that you understand how to properly handle each material regarding its toxicity, health effects, first aid, reactivity, storage, disposal, protective equipment, and spill-handling procedures.

Warnings Related to the Authors’ Attempts at Humor

Throughout this book, the authors sometimes attempt to use humor to explain certain concepts in a light-hearted manner. However, the authors are not professional comedians, and thus cannot assure the desired effect. Be assured, however, that the authors do not intend to offend any dead, alive, zombie, or otherwise undecided cats.

ACKNOWLEDGMENTS

We are deeply indebted to George J. Telecki, publisher at Wiley-Interscience, for giving us the opportunity to publish our work. We also thank Wiley’s editorial staff, and the copy editor Mary Safford Curioli, for their invaluable help in preparing this book.

We would also like to thank and acknowledge the anonymous reviewers who provided precious suggestions and insights that helped refine the scope of this book.

We are especially grateful to Elana Resnick for working with us to verify the experimental setups and for helping us write the Instructor’s Guide for this book.

Most of all, we want to thank Dorith (Mom), Hannah, and Abigail for their patience and encouragement while we fought over writing style and grammar, made a mess in the garage while building equipment, spoke physics at the dinner table, and got everyone irritated and irradiated along the way.

ABOUT THE AUTHORS

David Prutchi received his Ph.D. in Engineering from Tel-Aviv University in 1994, and then conducted postdoctoral research at Washington University. His area of expertise is the development of active implantable medical devices, and he is currently the Vice President of Engineering at Impulse Dynamics. He is an adept do-it-yourselfer, dedicated to bringing cutting-edge experimental physics within grasp of fellow science buffs.

Dr. Prutchi has published over 30 papers and holds over 70 patents. He is the lead author of the book Design and Development of Medical Electronic Instrumentation: A Practical Perspective of the Design, Construction and Test of Medical Devices, which was published by John Wiley & Sons.

Shanni R. Prutchi is a high-school junior at Jack M. Barrack Hebrew Academy in Bryn-Mawr, Pennsylvania. As an avid science and engineering enthusiast, she conducts research with her father in the areas of radio-astronomy and quantum physics.

The authors’ Web site is www.prutchi.com

CHAPTER 1

LIGHT AS A WAVE

Before we get into quantum physics, let’s understand the classical view of light. As early as 100 C.E., Ptolemy—a Roman citizen of Egypt—studied the properties of light, including reflection, refraction, and color. His work is considered the foundation of the field of optics. Ptolemy was intrigued by the way that light bends as it passes from air into water. Just drop a pencil into a glass of water and see for yourself!

As shown in Figure 1a, the pencil half under the water looks bent: light from the submerged part of the stick changes direction as it reaches the surface, creating the illusion of the bent stick. This effect is known as refraction, and the angle at which the light bends depends on a property of a material known as its refractive index.

Figure 1 Refraction of light: (a) A pencil dipped in water appears distorted because refraction causes light to bend when it passes from one substance into another, in this case from air to water. (b) A laser pointer clearly demonstrates Snell’s law of diffraction.

In the 1600s, Dutch mathematician Willebrord Snellius figured out that the degree of refraction depends on the ratio of the two materials’ different refractive indices. Most materials have a refractive index greater than 1, which means that as light enters the material from air, the angle of the ray in the material will become closer to perpendicular to the surface than it was before it entered. This is known as Snell’s Law, which states that the ratio of the sines of the angles of incidence and refraction (θ1, θ 2) is equal to the inverse ratio of the indices of refraction (n1n2):

Try it out yourself with a small laser pointer! As shown in Figure 1b, partially fill a small aquarium with water. Disperse some milk in the water to make it a bit cloudy, which will make the laser beam visible. Use smoke from a smoldering match or candle to make the laser beam visible in the air above.

NEWTON’S VIEW: LIGHT CONSISTS OF PARTICLES

In 1704, Sir Isaac Newton proposed that light consists of little particles of mass. In his view, this could explain reflection, because an elastic, frictionless ball bounces off a smooth surface just like light bounces off a mirror—that is, the angle of incidence equals the angle of reflection.

Remember that Newton was very interested in the way masses attract each other through the force of gravity. In his view, this force was responsible for refraction at the boundary between air and water. Newton imagined that matter is made up of particles of some kind, and that air would have a lower density of these particles than water. This is not far from what we know today—we would call Newton’s particles “molecules” and “atoms.” Newton then proposed that there would be an attractive force, similar to gravity, between the light particles and the matter particles.

Now, when a light particle travels within a medium, such as air or water, it is surrounded on all sides by the same number of matter particles. Newton explained that the attractive forces acting on a light particle would cancel each other out, allowing the light to travel in a straight line. However, near the air–water boundary, the light particle would feel more attracted by water than by air, given the water’s higher density of “matter particles.” Newton proposed that as the light particle moves into the water, it experiences an attractive force toward the water, which increases the light particle’s velocity component in the direction of the water, but not in the direction parallel to the water.

This velocity increase in the direction perpendicular to the air–water boundary would deflect the light closer to perpendicular to the surface, which is exactly what is observed in experiments. Newton thus claimed that the velocity of light particles is different in different transparent materials, believing that light would travel faster in water than in air. (We now know this is not the case, but we’ll get to that in a minute.)

Newton didn’t equate gravity with the attractive force between matter particles and light particles. He needed this force to be equal for all light particles crossing the boundary between two materials to explain how a prism separates white light into the colors of the rainbow. Newton proposed that the mass of a light particle depended on its color. In his view, red light particles would be more massive than violet light particles. Because of their increased inertia, red light particles would thus be deflected less when crossing the boundary between materials.

Newton’s greatness conferred credibility to his theory, but it was not the only one around. Dutch physicist Christiaan Huygens had proposed an earlier, competing theory: light consists of waves. This was supported by the observation that two intersecting beams of light did not bounce off each other as would be expected if they were composed of particles. However, Huygens could not explain color, and the wave versus particle debate for the nature of light raged until decisive experiments were carried out in the nineteenth century.

YOUNG’S INTERFERENCE OF LIGHT

Around 1801, Thomas Young discovered interference of light. This phenomenon is only possible with waves, providing conclusive evidence that light is a wave. In Young’s experiments, light sent through two separate slits results in a pattern that is very similar to the one produced by the interference of water waves shown in Figure 2.

Figure 2 Water waves from two sources interfere with each other to form a characteristic pattern: (a) A ripple tank is a shallow glass tank of water used to demonstrate the basic properties of waves. In it, a shaking paddle produces waves that travel toward a barrier with two slits. (b) Plane waves strike two narrow gaps, each of which produces circular waves beyond the barrier, and the result is an interference pattern.

Let’s spend some time experimenting with water waves before we go on to reproducing Young’s experiments on the interference of light. Start by building a ripple tank, as shown in Figure 3, out of a glass baking pan (for example, a Pyrex® rectangular pan), some wood, two rubber bands, and a vibrating motor made for pagers and cellular phones.

Figure 3 In our home-built ripple tank, a wooden stand supports a glass baking pan a distance away from a white sheet of paper. (a) With a light shining from above, ripples on a shallow layer of water in the pan are projected as shadows on the paper. (b) A small vibrating motor attached to a suspended beam just touching the water surface produces plane waves with which we can conduct experiments on wave reflection, refraction, and interference. For the sake of clarity, these pictures don’t show the steel wool padding that we use to absorb reflections at the tank walls.

The waves in the shallow layer of water are better observed by illuminating them from above to cast shadows through the glass bottom onto a white sheet of paper 50 cm below the tank. Use a spotlight, not a floodlight for illumination. Even better, use a strobe light (like the ones used by party DJs) to “freeze” the waves in place. Fill the pan with water to a depth of around 5 mm, and then fit pieces of metal sponge around the edges of the tank to reduce unwanted wave reflections from the pan’s walls. Test the setup by dimming the room lights and lightly dipping a pencil into the water to create ripples.

To generate continuous plane waves, attach the vibrating motor to a wooden beam. Use rubber bands to suspend the beam from a support beam, and adjust the height of the vibrating beam so that it just touches the water surface. Power the motor from a 1.5-V D cell through a 100 Ω potentiometer (e.g., Clarostat 43C1-100).

Next, set up two straight barriers with a short one between them, along a line parallel to the vibrating beam. Make the gaps between barriers about 1-cm wide. Turn the potentiometer to generate straight waves with a wavelength of about 1 cm. Try different separations between the slits, and see if your data agree with the equation:

where d is the fringe separation (e.g., between the central fringe and the first fringe to its side), λ is wavelength, s is the distance between the slits, and r is the distance from the 2-slit barrier to the point where the fringes are observed.

Thomas Young did essentially the same thing using colored light instead of water waves. We will use inexpensive laser pointers and a simple double slit to replicate the experiment that Young performed to support the theory of the wave nature of light (Figure 4). Instead of making a double-slit slide,* we use one made by Industrial Fiber-optics. Their model IF-508 diffraction mosaic is a low-cost ($6) precision array of double slits and gratings for performing laser double- and multiple-slit diffraction experiments. The mosaic is mounted in a 35-mm slide holder and contains four double slits and three multiple-slit arrays on an opaque background with clear apertures. Double-slit separations range from 45 to 100 μm in width. The gratings are 25, 50, and 100 lines/mm.

Interestingly, Young found that the separation between fringes is related to the distance between the slits exactly through the same equation as the water analog:

where s is the distance between slits, λ is the wavelength of the light, d is the separation between fringes (the distance between central maximum and each of the first bright fringes to its side), and r is the distance from the slits to the screen.

AUTOMATIC SCANNING OF INTERFERENCE PATTERNS

Accurately measuring interference patterns from projections on a screen is rather tedious. However, you can build a simple device that makes it possible to display interference patterns on an oscilloscope, making it easy to measure not only the distance between fringes, but also their amplitude.

As shown in Figure 5, the idea is to use a rotating mirror and a fast-light sensor to convert the interference pattern into an equivalent time-domain signal that can be displayed by a conventional oscilloscope. For the light sensor, we used a TAOS TSL254R-LF light-to-voltage converter. This device is an inexpensive component that incorporates a light-sensitive diode and amplifier on a single chip. It is very easy to use. It requires a supply voltage in the range of 2.7 to 5.5 V (we use two 1.5-V AA batteries in series), and produces an output voltage that is directly proportional to the light intensity. We placed the light sensor behind a narrow slit built from two single-edge razor blades.

Figure 5 A simple scanner makes it easy to measure interference and diffraction patterns with an oscilloscope. (a) Simplified diagram of the basic concept. A small DC motor spins a mirror to scan the pattern onto a narrow-view light sensor, transforming the pattern’s distribution along space into a signal that varies with time. An oscilloscope synchronized to the motor displays the pattern. (b) For the light sensor we used a TAOS TSL254R-LF light-to-voltage converter placed behind a narrow slit made from two razor blades. (c) We used a motor and polygon mirror from a broken bar-code scanner to build our setup.

As shown in Figure 5c, we built the optical stand from 1-in. × 1-in. cross-section, T-slotted aluminum extrusions made by 80/20, Inc. These are meant for building office cubicles and machine frames, so they are widely available (e.g., from McMaster-Carr) and inexpensive. In spite of this, they are very rugged and sufficiently straight to perform optical experiments. Our motor and mirror came from a discarded supermarket bar-code scanner. However, you could rig a small front-surface mirror to the shaft of a small 2,000 to 4,000 rpm DC motor. The TSL254R-LF’s response time (2 μs rise/fall time) is appropriate for these speeds. The advantage of a bar-code scanner motor is that it usually comes installed with a polygonal mirror and speed controller. Having more mirror surfaces per revolution reduces flicker if you are using an analog oscilloscope. The integrated controller maintains a constant rotation speed, which allows you to calibrate the system to produce a constant space-to-time relationship. Figure 6 shows a typical oscilloscope trace obtained with our system for a 10-μm slit spacing with a 630-nm red laser.

THE FINAL NAIL IN THE COFFIN FOR NEWTON’S THEORY OF LIGHT

Diffraction, reflection, and color are also explained by Young’s wave theory. However, interference is the calling card of waves, so Young’s experiments convinced many in the early 1800s that light is indeed a wave. In spite of this, Newton’s reputation was so strong, that his particle model of light retained adherents until 1850, when French physicist Jean Foucault provided final, decisive proof that Newton’s particle theory of light must be wrong. Remember that Newton’s theory required the speed of light to be higher in water than in air? Well, Foucault experimentally showed the exact opposite. As shown in Figure 7, Foucault used a steam turbine to spin a mirror at the rate of 800 rps. He bounced a light beam off the rotating mirror; the beam was then reflected by a stationary mirror 9 m away. By the time the light returned to the rotating mirror, the mirror had rotated a little, causing the light to be deflected a certain amount away from the source.

Figure 7 In 1850, Jean Foucault used this setup to measure the speed of light in (a) air and (b) water. He found that light travels more slowly in water than in air, contrary to the prediction of Newton’s particle theory of light.

Foucault then placed a water-filled tube with transparent windows along the light path between the mirrors. If, as Newton affirmed, light travels faster in water than in air, the deflection angle would be smaller and the beam would arrive closer to the source.† Instead, Foucault found that introducing water in the optical path further delayed the beam, indicating that light travels more slowly in water than in air, contrary to the prediction of Newton’s particle theory of light.

LIGHT AS AN ELECTROMAGNETIC WAVE

Later, in the 1860s, Scottish physicist James Clerk Maxwell identified light as an electromagnetic wave. Maxwell had derived a wave form of the electric and magnetic equations, revealing a wave-like nature of electric and magnetic fields that vary with time.

Figure 8 An oscillating electric field generates an oscillating magnetic field; the magnetic field in turn generates an oscillating electric field, and so on. Together these oscillating fields form an electromagnetic wave with wavelength λ that propagates at the speed of light c.

Because the speed of Maxwell’s electromagnetic waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself must be an electromagnetic wave. This fact was later confirmed experimentally by Heinrich Hertz in 1887. Today, we use the electromagnetic spectrum at all wavelengths—from the enormously long waves that we use to transmit AC power, through the radio wavelengths that are the foundation of our wireless society, to the extremely short wavelengths of gamma radiation (Figure 9).

Figure 9 The electromagnetic spectrum. Maxwell concluded that light itself must be an electromagnetic wave. This fact was later confirmed experimentally by Hertz in 1887.

We understand that the only difference between visible light and the rest of the spectrum is that it is the range of electromagnetic waves to which our eyes are sensitive.

POLARIZATION

Polarization is an important characteristic of light that Maxwell’s electromagnetic theory was finally able to explain. Notice in Figure 8 that the electric field is shown to oscillate in one plane, while the magnetic field oscillates on a perpendicular plane. The wave travels along the line formed by the intersection of those planes. The electromagnetic wave shown in this figure is said to be “vertically polarized,” because the electric field oscillates vertically in the frame of reference we have chosen.

Light from most natural sources contains waves with electric fields oriented at random angles around its direction of travel. A wave of a specific polarization can be obtained from randomly polarized light by using a polarizer.

A polarizer can be made of an array of very fine wires arranged parallel to one another. The metal wires offer high conductivity for electric fields parallel to the wires, essentially “shortening them out” and producing heat. Because of the nonconducting spaces between the wires, no current can flow perpendicularly to them. As such, electric fields perpendicular to the wires can pass unimpeded. In other words, the wire grid, when placed in a randomly-polarized beam, drains the energy out of one component of the electric field and lets its perpendicular component pass with no attenuation at all. Thus, the light emerging from the polarizer has an electric field that vibrates in a direction perpendicular to the wires.

Although the wire-grid polarizer is easy to understand, it is useful only up to certain frequencies, because the wires have to be a fraction of the wavelength apart. This is difficult and expensive to do for short wavelengths, such as those of visible light. In 1938, E. H. Land invented the H-Polaroid sheet, which acts as a chemical version of the wire grid. Instead of long thin wires, it uses long thin polyvinyl alcohol molecules that contain many iodine atoms. These long, straight molecules are aligned almost perfectly parallel to one another. Because of the conductivity provided by the iodine atoms, the electric vibration component parallel to the molecules is absorbed. The component perpendicular to the molecules passes on through with little absorption.

As you will see throughout this book, understanding polarization is very important when experimenting with quantum physics, so we would like for you to gain an intuitive feel for this interesting property of waves.

OPTICS WITH 3-CM WAVELENGTH “LIGHT”

Let’s start by experimenting with a polarizer that is actually made out of wires, such as the one shown in Figure 10. However, we’ll need a source of electromagnetic waves with sufficiently large wavelength. Fortunately, it is easy to generate and detect microwaves with a wavelength of around 3 cm, making it possible to experiment with “optical” components scaled up to very convenient dimensions. Using a 3-cm microwave wavelength transforms the scale of the experiment. Measurements that would require specialized equipment at optical wavelengths to deal with submicrometer dimensions are easily accomplished with a simple ruler at 3-cm wavelengths.

Figure 10 A parallel-wire polarizer absorbs electric field lines that are parallel to the wires. Only the perpendicular electrical field component of light is allowed to pass, producing light that is polarized perpendicularly to the direction of the wires.

As shown in Figure 11, a simple microwave transmitter can be built using a Gunnplexer,3,4 which is a self-contained microwave module based on a specialized diode invented by John B. Gunn in the early 1960s. When a DC voltage is applied to the Gunn diode, current flows through it in bursts at regular intervals in the 10- to 100-GHz (1010 to 1011 Hz) range. These oscillations cause a wave to be radiated from the Gunnplexer’s output slot.

Figure 11 Schematic diagram for the Gunnplexer microwave transmitter/receiver. Two identical units can be built, but one simplified transmitter and one simplified receiver can also be used in these experiments.

You can find a Gunnplexer to use by taking apart a surplus microwave door opener or speed radar gun. The typical power output of Gunnplexers for these applications is in the 5- to 10-mW range, and they commonly operate in either the so-called X-band (at 10.5 GHz) or K-band (24.15 GHz). For the receiver, you will need a second Gunnplexer built to operate in the same frequency range as your transmitter Gunnplexer, but this time you will use the microwave detector diode that is part of these modules.

As shown in Figure 12, we used surplus MO87728-M01 Gunnplexers, but almost any other model should work just as well. Aluminum die-cast boxes made by Bud Industries (model AN-1317) made nice enclosures for the transceivers. We bought the metallized-plastic horn antennas from Advanced Receiver Research.

Figure 12 These are the X-band 10.5-GHz transmitter/receivers that we built from surplus Gunnplexer modules. Polarized microwaves with a wavelength of approximately 3 cm are launched from the horn antenna when the Gunn diode is powered. The “Mixer” diode in a second Gunnplexer is used to detect microwaves. It produces an output voltage proportional to the intensity of a properly polarized microwave signal.

A word of caution regarding the use of Gunnplexers: although the microwaves generated by Gunnplexers will not cook you, the output is sufficiently concentrated that it could cause eye damage at very close range. It is wise to never look at close range into the open end of a Gunnplexer while it operates.

Now to our experiments. Place the Gunnplexers about a meter apart and point the antennas at each other. Connect a digital voltmeter to the detector diode of your receiving Gunnplexer (the “mixer” output). Turn on the transmitter. The highest voltage across the mixer diode should appear when the Gunnplexers are oriented in the same plane. This is because Gunnplexers are polarized transmitters and receivers of microwaves. The electric field of the transmitted wave oscillates in the same orientation as the Gunn diode, and the detector is sensitive to fields in the same orientation as the mixer diode. In our setup, we measure around 0.8 V output from the receiver when the horn antennas are placed right against each other. The signal drops down to 40 mV at a distance of 65 cm. You may note that the output voltage from the detector is negative with respect to ground. This is normal, and happens because of the way in which the mixer diode is internally connected within the Gunnplexer.

Next, you can build a polarizer by arranging copper wires in an array, just as in the idealized diagram of Figure 10