Introducing Quantum Theory E-Book

J.P. McEvoy

• Herausgeber: Icon Books
• Kategorie: Wissenschaft und neue Technologien
• Serie: Graphic Guides
• Sprache: Englisch

Seitenzahl: 127

Veröffentlichungsjahr: 2014

Beschreibung

Quantum theory confronts us with bizarre paradoxes which contradict the logic of classical physics. At the subatomic level, one particle seems to know what the others are doing, and according to Heisenberg's "uncertainty principle", there is a limit on how accurately nature can be observed. And yet the theory is amazingly accurate and widely applied, explaining all of chemistry and most of physics. Introducing Quantum Theory takes us on a step-by-step tour with the key figures, including Planck, Einstein, Bohr, Heisenberg and Schrodinger. Each contributed at least one crucial concept to the theory. The puzzle of the wave-particle duality is here, along with descriptions of the two questions raised against Bohr's "Copenhagen Interpretation" - the famous "dead and alive cat" and the EPR paradox. Both remain unresolved.

Leseprobe

Published by Icon Books Ltd, Omnibus Business Centre, 39–41 North Road, London N7 9DP email: [email protected]

ISBN: 978-184831-757-4

Text and illustrations copyright © 2013 Icon Books Ltd

The author and artist have asserted their moral rights.

Originating editor: Richard Appignanesi

No part of this book may be reproduced in any form, or by any means, without prior permission in writing from the publisher.

Contents

Cover

Title Page

Copyright

What is Quantum Theory?

Classical Physicists

It’s All Proven (and Classical). . .

“Fill in the Sixth Decimal Place”

The Fundamental Assumptions of Classical Physics

The Solvay Conference 1927 – Formulation of Quantum Theory

The First Law of Thermodynamics

Rudolf Clausius: Two Laws

The Existence of Atoms

Averaging Diatomic Molecules

Ludwig Boltzmann and Statistical Mechanics

Thermal Equilibrium and Fluctuations

The Thirty Years War (1900–30) – Quantum Physics Versus Classical Physics

Black-Body Radiation

Paradoxical Results

What Went Wrong?

The Ultraviolet Catastrophe

Enter Max Planck

Pre-Atomic Model of Matter

Planck’s Predicament

Chopping Up the Energy

A Quantum of Energy

The Photoelectric Effect

A Classical Interpretation

Enter Albert Einstein

A Small Flat at Kramergasse 49, in Bern

Einstein’s Explanation of the Photoelectric Effect

Millikan: Hard-headed Classical Physicist

Bright Line Light Spectra

Emission Spectra

Absorption Spectra (Dark Lines)

Fraunhofer Lines

The Discovery of Helium

Hydrogen – Test Case for Atomic Structure

Balmer: the Swiss School Teacher

Hydrogen Frequencies From Balmer’s Formula

Discovery of the Electron

Christmas Pudding Atom

Rutherford’s Nuclear Atom

Size of the Nucleus

Arrival of the Quantum Hero, Niels Bohr

Bohr Meets Nicholson: Quantized Angular Momentum

First: Linear Momentum

Second: Angular Momentum

The Bohr Quantum Postulates

Mixing Classical and Quantum Physics

Bohr Derives the Balmer Formula

A Closer Look at Spectra . . . and More Lines

Another Quantum Number Added, k

The Zeeman Effect . . . and Still More Lines

Three Quantum Numbers, n, k, m

Wolfgang Pauli: the Anomalous Zeeman Effect, Electron Spin and the Exclusion Principle

The Pauli Effect

Pauli’s “Hidden Rotation” and the Spinning Electron

Pauli’s Exclusion Principle

Closed Shells and Inert Gases

The Wave/Particle Duality

Properties of Waves

Wave Speed

Diffraction and Interference

Einstein . . . a Lone Voice

A French Prince Discovers Matter Waves

An Associated Wave

Dramatic Conclusions

An Astounding Thesis

Confirmation of Matter Waves

Electron Waves in Atoms

Visualizing the Atom: the “Old Quantum Theory”

Triple Birth of the New Quantum Theory

Heisenberg, Genius and Mountain-Climber

Heisenberg’s Picture of the Atom

Max Bom and Matrix Mechanics

Pauli Shows Matrix Mechanics is Correct

Erwin Schrödinger – Genius and Lover

Schrödinger’s Equation

Fourier Wave Analysis of Periodic Functions

Visualizing Schrödinger’s Atom

The Balmer Formula, the Zeeman Effect and All That

Schrödinger: a Return to Classical Physics?

Who Needs Particles Anyway?

Two Theories, One Explanation

Schrödinger Meets Heisenberg

Max Born: the Probability Interpretation of ψ

Two Kinds of Probability

Schrödinger’s Cat. . . The Quantum Measurement Problem

Consciousness and the Collapsing Wave Function

Paul Adrian Maurice Dirac: Genius and Recluse

Dirac’s Version of Quantum Mechanics

Dirac’s Transformation Theory

The Beginning of Quantum Electrodynamics

The Dirac Equation and Electron Spin

The Prediction of Anti-Matter

The Uncertainty Principle

Heisenberg’s Gamma-Ray Microscope

The Breakdown of Determinism

Complementarity

The Copenhagen Interpretation

Como, Italy, September 1927

The Solvay Conference, October 1927

Einstein’s Box of Light

A Sleepless Night

The EPR Paradox

The Locality Principle

Bohr and Non-Locality

Bell’s Inequality Theorem

An Undiscovered World

Quantum Theory and the New Millennium

John Archibald Wheeler, Quantum Physicist

A Final Word

Further Reading

Acknowledgements

Index

What is Quantum Theory?

Quantum theory is the most successful set of ideas ever devised by human beings. It explains the periodic chart of the elements and why chemical reactions take place. It gives accurate predictions about the operation of lasers and microchips, the stability of DNA and how alpha particles tunnel out of the nucleus.

QUANTUM THEORY IS NON-INTUITIVE AND DEFIES COMMON SENSE. RECENTLY, ITS CONCEPTS HAVE BEEN LIKENED TO EASTERN PHILOSOPHY AND USED TO PROBE THE SECRETS OF CONSCIOUSNESS, FREE WILL AND THE PARANORMAL. THIS BOOK ANSWERS THE QUESTION: WHERE DID QUANTUM THEORY COME FROM? QUANTUM THEORY HAS NEVER FAILED. QUANTUM THEORY IS ESSENTIALLY MATHEMATICAL. . . ITS STRUCTURE HAS REVOLUTIONISED HOW THE PHYSICAL WORLD IS VIEWED.

Niels Bohr’s presentation of quantum theory in 1927 remains today’s orthodoxy. But Einstein’s thought experiments in the 1930s questioned the theory’s fundamental validity and are still debated today. Could he be right again? Is there something missing? Let’s begin at the beginning . . .

Introducing Quantum Theory

YOU KNOW, IT’S EASIER TO EXPLAIN QUANTUM THEORY TO AN ABSOLUTE BEGINNER THAN TO A CLASSICAL PHYSICIST. YOU’RE KIDDING. WHAT’S THEIR PROBLEM, THESE CLASSICAL GUYS, WITH THE MODERN THEORY?

The problem is this. Just before the turn of the century, physicists were so absolutely certain of their ideas about the nature of matter and radiation that any new concept which contradicted their classical picture would be given little consideration.

Not only was the mathematical formalism of Isaac Newton (1642–1727) and James Clerk Maxwell (1831–79) impeccable, but predictions based on their theories had been confirmed by careful detailed experiments for 4 many years. The Age of Reason had become the age of certainty!

Classical Physicists

What is the definition of “classical”?

By classical is meant those late 19th century physicists nourished on an academic diet of Newton’s mechanics and Maxwell’s electromagnetism – the two most successful syntheses of physical phenomena in the history of thought.

WITH A SIMPLE INNCLINED PLAVE AND A METAL SPHERE, I DEMONSTRATED THAT THE GREAT ARISTOTLE’S PHYSICS WAS FLAWED. OH, STOP SHOWING OFF!

Testing theories by observation had been the hallmark of good physics since Galileo (1564–1642). He showed how to devise experiments, make measurements and compare the results with the predictions of mathematical laws.

The interplay of theory and experiment is still the best way to proceed in the world of acceptable science.

It’s All Proven (and Classical). . .

During the 18th and 19th centuries, Newton’s laws of motion had been scrutinized and confirmed by reliable tests.

MY GRAVITATION LAW HAS BEEN USED TO PREDICT MEASURED MOVEMENTS OF THE PLANETS WITH GREAT ACCURACY.

I PREDICTED THE EXISTENCE OF INVISIBLE “LIGHT” WAVES IN MY ELECTROMAGNETIC WAVE THEORY OF 1865, AND HEINRICH HERTZ (1857–94) DETECTED THE SIGNALS IN 1888 IN HIS BERLIN LABORATORY. NOW THEY’RE CALLED RADIO WAVES.

THESE WAVES REFLECT AND REFRACT JUST LIKE LIGHT. MAXWELL WAS RIGHT.

No wonder these classical physicists were confident in what they knew!

“Fill in the Sixth Decimal Place”

A classical physicist from Glasgow University, the influential Lord Kelvin (1824–1907), spoke of only two dark clouds on the Newtonian horizon.

HOW WAS I TO KNOW THAT ONE OF THESE CLOUDS WOULD DISAPPEAR ONLY WITH THE ADVENT OF RELATIVITY – AND THE OTHER WOULD LEAD TO QUANTAM THEORY?

In June 1894, the American Nobel Laureate, Albert Michelson (1852–1931), thought he was paraphrasing Kelvin in a remark which he regretted for the rest of his life.

ALL THAT REMAINS TO DO IN PHYSICS IS FILL IN THE SIXTH DECIMAL PLACE. (I CAN’T BELIEVE I SAID THAT!)

The Fundamental Assumptions of Classical Physics

Classical physicists had built up a whole series of assumptions which focused their thinking and made the acceptance of new ideas very difficult. Here’s a list of what they were sure of about the material world . . .

1) The universe was like a giant machine set in a framework of absolute time and space. Complicated movement could be understood as a simple movement of the machine’s inner parts, even if these parts can’t be visualized.

2) The Newtonian synthesis implied that all motion had a cause. If a body exhibited motion, one could always figure out what was producing the motion. This is simply cause and effect, which nobody really questioned.

3) If the state of motion was known at one point – say the present – it could be determined at any other point in the future or even the past. Nothing was uncertain, only a consequence of some earlier cause. This was determinism.

4) The properties of light are completely described by Maxwell’s electromagnetic wave theory and confirmed by the interference patterns observed in a simple double-slit experiment by Thomas Young in 1802.

5) There are two physical models to represent energy in motion: one a particle, represented by an impenetrable sphere like a billiard ball, and the other a wave, like that which rides towards the shore on the surface of the ocean. They are mutually exclusive, i.e. energy must be either one or the other.

6) It was possible to measure to any degree of accuracy the properties of a system, like its temperature or speed. Simply reduce the intensity of the observer’s probing or correct for it with a theoretical adjustment. Atomic systems were thought to be no exception.

Classical physicists believed all these statements to be absolutely true. But all six assumptions would eventually prove to be in doubt. The first to know this were the group of physicists who met at the Metropole Hotel in Brussels on 24 October 1927.

The Solvay Conference 1927 – Formulation of Quantum Theory

A few years before the outbreak of World War I, the Belgian industrialist Ernest Solvay (1838–1922) sponsored the first of a series of international physics meetings in Brussels. Attendance at these meetings was by special invitation, and participants – usually limited to about 30 – were asked to concentrate on a pre-arranged topic.

The first five meetings held between 1911 and 1927 chronicled in a most remarkable way the development of 20th century physics. The 1927 gathering was devoted to quantum theory and attended by no less than nine theoretical physicists who had made fundamental contributions to the theory. Each of the nine would eventually be awarded a Nobel Prize for his contribution.

IT IS COMPARABLE TO SEEING US POSING TOGETHER TO COMMEEMORATE THE DEVELOPMENT OF CLASSICAL PHYSICS.

This photograph of the 1927 Solvay Conference is a good starting point for introducing the principal players in the development of the most modern of all physical theories. Future generations will marvel at the compressed time scale and geographical proximity which brought these giants of quantum physics together in 1927.There is hardly any period in the history of science in which so much has been clarified by so few in so short a time.

Look at the sad-eyed Max Planck (1858–1947) in the front row next to Marie Curie (1867–1934). With his hat and cigar, Planck appears drained of vitality, exhausted after years of trying to refute his own revolutionary ideas about matter and radiation.

I STARTED IT ALL IN 1900 BY POSTULATING THAT MATTER CAN ABSORB AND ADMIT ELECTROMAGNETIC RADIATION (I.E. LIGHT) ONLY IN ENERGY BUNDLES CALLED QUANTA WHOSE SIZE IS PROPORTIONAL TO THE FREQUENCY OF THE RADIATION.

A few years later in 1905, a young patent clerk in Switzerland named Albert Einstein (1879–1955) generalized Planck’s notion.

That’s Einstein in the front row centre, sitting stiffly in his formal attire. He had been brooding for over twenty years about the quantum problem without any real insights since his early 1905 paper. All the while, he continued to contribute to the theory’s development and endorsed original ideas of others with uncanny confidence. His greatest work – the General Theory of Relativity – which had made him an international celebrity, was already a decade behind him.

I SHOWED THAT LIGHT ALWAYS EXISTS AS QUANTA, WHICH IS, OF COURSE, WHY MATTER ABSORBS AND EMITS IT AS SUCH. TOO BAD PLANCK NEVER BELIEVED ME!

IN MY LECTURE, I REVIEWED THE PROBABILISIC INTERRETATION OF QUANTUM THEORY TO THE APPARENT SATISFACTION OF MOSTLY EVERYONE, EXCEPT EINSTEIN.

In Brussels, Einstein had debated the bizarre conclusions of the quantum theory with its most respected and determined proponent, the “great Dane” Niels Bohr (1885–1962). Bohr – more than anyone else – would become associated with the struggle to interpret and understand the theory. At the far right of the photo, in the middle row, he is relaxed and confident – the 42 year old professor at the peak of his powers.

In the back row behind Einstein, Erwin Schrödinger (1887–1961) looks conspicuously casual in his sports jacket and bow tie. To his left but one are the “young Turks”, Wolfgang Pauli (1900–58) and Werner Heisenberg (1901–76) – still in their twenties – and in front of them, Paul Dirac (1902–84), Louis de Broglie (1892–1987), Max Born (1882–1970) and Bohr. These men are today immortalized by their association with the fundamental properties of the microscopic world: the Schrödinger wave equation; the Pauli exclusion principle; the Heisenberg uncertainty relation, the Bohr Atom . . . and so forth.

They were all there–from Planck, the oldest at 69 years, who started it all in 1900 – to Dirac, the youngest at 25 years, who completed the theory in 1928.

The day after this photograph was taken – 30 October 1927 – with the historic exchanges between Bohr and Einstein still buzzing in their minds, the conferees boarded trains at the Brussels Central Station to return to Berlin, Paris, Cambridge, Göttingen, Copenhagen, Vienna and Zürich.

They were taking with them the most bizarre set of ideas ever concocted by scientists. Secretly, most of them probably agreed with Einstein that this madness called the quantum theory was just a step along the way to a more complete theory and would be overthrown for something better, something more consistent with common sense.

But how did the quantum theory come about? What experiments compelled these most careful of men to ignore the tenets of classical physics and propose ideas about nature that violated common sense?

Before we study these experimental paradoxes, we need some background in thermodynamics and statistics which are fundamental to the development of quantum theory.

What is Thermodynamics? The word means the movement of heat, which always flows from a body of higher temperature to a body of lower temperature, until the temperatures of the two bodies are the same. This is called thermal equilibrium.

Heat is correctly described as a form of vibration . . .

THIS SEAT IS WARM. DID YOU LEAVE SOMETHING THERMAL BEHIND? NO, IT’S JUST THAT THE MOLECULES IN THE SEAT ARE STILL VIBRATING AT THE SAME RATE AS MY BODY – WHICH IS APPARENTLY FASTER THAN YOURS – SO THE SEAT FEELS WATM TO YOU.

The First Law of Thermodynamics

Mechanical models to explain the flow of heat developed quickly in 19th century Britain, building on the achievements of James Watt (1736–1819), a Scot who had built a working steam engine.

Soon after, the son of a Manchester brewer, James Prescott Joule (1818–89), showed that a quantity of heat can be equated to a certain amount of mechanical work.

THIS NEW MECHANICAL EQUIVALENT OF HEAT WAS THE BEGINNING OF THE STUDY OF THERMODYNAMICS.

Then somebody said . . . “since heat can be converted into work, it must be a form of energy” (the Greek word energy means “containing work”). But it wasn’t until 1847 that a respectable academic scientist, Hermann von Helmholtz (1821–94), stated . . .

WHENEVER A CERTAIN AMOUNT OF ENERGY DISAPPEARS IN ONE PLACE, AN EQUIVALENT AMOUNT MUST APPEAR ELSEWHERE IN THE SAME SYSTEM.

This is called the law of the conservation of energy. It remains a foundation of modern physics, unaffected by modern theories.

Rudolf Clausius: Two Laws

In 1850, the German physicist Rudolf Clausius (1822–88) published a paper in which he called the energy conservation law The First Law of Thermodynamics. At the same time, he argued that there was a second principle of thermodynamics in which there is always some degradation of the total energy in the system, some non-useful heat in a thermodynamic process.

Clausius introduced a new concept called entropy – defined in terms of the heat transferred from one body to another.

I SHOWED THAT THE TOTAL ENTROPY OF A SYSTEM INCREASES WHEN HEAT FLOWS FROM A HOT