Forces of the Quantum Vacuum:An Introduction to Casimir Physics

William M R Simpson, Ulf Leonhardt

• Publisher: WSPC
• Year: 2015
• eBook ISBN:
  9789814644778
• Topic: Physical Sciences
• Subtopic: Electromagnetism

Forces of the Quantum Vacuum presents a number of theoretical approaches to Casimir, van der Waals and Casimir–Polder forces that have been fruitfully employed in mainstream research, and also reviews the experimental evidence for Casimir forces. Beginning with basic ideas in quantum mechanics and building its way to a sophisticated form of macroscopic QED, the book provides an inspiring training manual for graduate students to develop in a natural progression the ideas needed for modern theoretical research on Casimir forces.

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Chapter 1

Normal mode quantum electrodynamics: the quantum vacuum and its consequences

STEFAN YOSHI BUHMANN

Besides, who ever thought any quality to be a heterogeneous aggregate, such as light is discovered to be? But to determine more absolutely what light is, after what manner refracted, and by what modes or actions it produceth in our minds the phantasms of colours, is not so easy.

– Issac Newton, New Theory about Light and Colours (1671)

§1.WAVE-PARTICLE DUALITY — WHAT IS LIGHT (LIKE)?

As stated by the United Nations in their proclamation of an International Year of Light in 2015, ‘light plays a vital role in our daily lives and is an imperative cross-cutting discipline of science in the 21st century’ [1]. But what exactly is this important entity?

Light exhibits a whole range of interesting properties (like colour, energy, momentum, speed, polarisation and behaviours (like reflection, refraction, diffraction, interference, absorption, emission). Some of them are accessible by our immediate sensory experience while others can only be revealed via careful experimentation. A possible, but unsatisfactory definition of light would state that it is nothing more or less than an object which has these properties and shows these behaviours. However, this descriptive characterisation in terms of seemingly unrelated attributes does not explain anything, nor does it provide us with any intuition.

1.1Light as a particle

As a first step towards greater insight into the nature of light, we could ask the alternative question: What is light like? Does it behave like anything else that we know of from our everyday experience? Newton tried to find an answer to this question by studying refraction in prisms [2]. He concluded that light is like a stream of corpuscles: tiny, not necessarily indivisible particles which travel along straight trajectories at finite speed [3]. The particle analogue is able to explain how obstacles give rise to a shadow and how light is reflected (as the corpuscles bounce off a mirror) and refracted (as they change direction upon being attracted towards a medium).

1.2Light as a wave

Newton’s contemporary Huygens put forward a very different analogy. He stated that light is like a wave: a continuous oscillation moving through space [4]. According to the principle now bearing his name, the propagation of such a wave can be understood by regarding it as made up from spherical waves. In this way, reflection and refraction can be understood by thinking of spherical waves emanating from an illuminated surface. As with Newton’s particle analogy, the wave model provides us with an intuition of how light may behave in a given situation.

However, as Newton objected, waves can go around corners whereas light seemingly doesn’t. Or does it? As Young demonstrated with his famous double-slit experiment [5], light does exhibit the typical wave behaviour of diffraction and interference. Two coherently illuminated slits in a screen are the sources of two spherical light waves. Their superposition gives rise to an oscillatory pattern in the space behind the slits. This wave behaviour is analogous to the patterns of ripples created by two stones dropped into the surface of a lake.

1.3The photon

It seemed as though the argument was settled in favour of Huygens’ wave analogy. But this was not the end of the story. Based on observations of the photoelectric effect, Einstein concluded that light consists of discrete quanta of fixed energy which can only be emitted or absorbed as a whole [6]. It appears Newton was partly correct.

So is light like a particle or is it like a wave? The answer is light is a bit of both—and much more. In short, one could say that light is emitted and absorbed like a particle, but propagates like a wave. This integration of the two diametrically opposing descriptions of light as discrete particles on the one hand, and as a continuous wave on the other, has surprising consequences. To see this, let us return to Young’s double-slit experiment and imagine what happens when we gradually reduce the light coming through the slits. We will begin to see that the continuous wave pattern formed behind the slits is actually composed of discrete spots. One can even reduce the light source so much that single light quanta, or particles, pass through the slits one at a time [7]. If we record them on a screen, each of them will leave a single bright spot. Yet after recording many such events, these spots will mysteriously form the continuous interference pattern of the wave model again. How do the light particles accomplish this? They are all mutually independent and each may only leave a single bright spot, which has to contribute to the overall interference pa...

Table of contents

• Cover page
• Title Page
• Copyright
• Dedication
• Contents
• Foreword
• Introduction
• CHAPTER 1 Normal mode quantum electrodynamics: the quantum vacuum and its consequences
• CHAPTER 2 Van der Waals and Casimir–Polder dispersion forces
• CHAPTER 3 The Casimir stress in real materials
• CHAPTER 4 Macroscopic QED and vacuum forces
• CHAPTER 5 Measuring Casimir phenomena
• CHAPTER 6 Casimir forces at the cutting edge
• Further reading
• Appendix: Regularisation techniques
• Index
• About the authors