Understanding the particle nature of light and its consequences requires quantization of light. Quantization is a process of transforming a continuous system to a discrete system. In physical sciences, quantization is carried out for entities and quantities that are inherently discrete in nature. This refers to the graininess in the actual physical state (here, electromagnetic field) whose macroscopic ensemble manifestation (wave nature) is a large-number approximation. The microscopic grainy dynamics gives rise to delicate and tiny perturbations at the level of a single grain that sum up to produce large effects at the macroscopic level (continuous domain). Thus, quantization describes the physical state at the scale of a single grain while the continuous domain describes the average dynamics (macroscopic manifestation), which wipes out the properties of single grains. As an example, quantization of an electromagnetic field yields grainy particles called photons, the existence of which has been verified experimentally. These grains have well-defined quantized quantities such as energy. In this chapter, we discuss the grainy nature of light and its quantized quantities (energy, angular momentum, etc.) associated with the grains (photons) of light.
Understanding the particle nature of light and its consequences requires quantization of light. Quantization is a process of transforming a continuous system to a discrete system. In physical sciences, quantization is carried out for entities and quantities that are inherently discrete in nature. This refers to the graininess in the actual physical state (here, electromagnetic field) whose macroscopic ensemble manifestation (wave nature) is a large-number approximation. The microscopic grainy dynamics gives rise to delicate and tiny perturbations at the level of a single grain that sum up to produce large effects at the macroscopic level (continuous domain). Thus, quantization describes the physical state at the scale of a single grain while the continuous domain describes the average dynamics (macroscopic manifestation), which wipes out the properties of single grains. As an example, quantization of an electromagnetic field yields grainy particles called photons, the existence of which has been verified experimentally. These grains have well-defined quantized quantities such as energy. In this chapter, we discuss the grainy nature of light and its quantized quantities (energy, angular momentum, etc.) associated with the grains (photons) of light.
It is evident from the previous chapter that certain quantities that appear continuous at the macroscopic scale does actually exist in a discrete form at the microscopic scale. So, quantization of these entities makes sense and reveals a plethora of information at such length scales. In this book, our key concern lies with the properties of light, and rightfully so, we will explore different states of the optical radiation field. We will learn that light exists in many states that makes it so unique. Experimental evidence shows that light behaves as a particle at the microscopic scale (subject to specific conditions), although it behaves like a wave at the macroscopic scale. In this chapter, we will dwell deep and discuss many characteristics related to the particle nature of light. Specifically, we will consider two important states of light, the Fock and coherent states. These states can be regarded as the most fundamental states of light that enable complex interpretation of quantum features in the radiation field.
Quantum field theory describes the particle nature of electromagnetic radiation using the "photon," but has never explained why a fundamental particle exhibits such perfect wave behavior. This paper provides a complete alternative explanation: the photoelectric effect, Compton scattering, and antibunching experiments — landmark experiments considered proof of photon particle nature — require no photon concept. Quantization is not a property of light itself, but of the discrete energy level structure governing how bound electrons emit and absorb energy. Light remains a continuous transverse wave; discreteness results from electrons as "prisoners" in atomic "cages" that can only transition between specific energy steps. Waves propagate continuously and are emitted and absorbed in quantized form — the photon is not a particle, but the name of an energy-exchange event.
Introduction It is believed that the basic physical building blocks forming the world we live in may be categorized into particles of matter and carriers of force between matter. All known elementary constituents of matter and transmitters of force are quantized. For example, energy, momentum, and angular momentum take on discrete quantized values. The electron is an example of an elementary particle of matter, and the photon is an example of a transmitter of force. Neutrons, protons, and atoms are composite particles made up of elementary particles of matter and transmitters of force. These composite particles are also quantized. Because classical mechanics is unable to explain quantization, we must learn quantum mechanics in order to understand the microscopic properties of atoms – which, for example, make up solids such as crystalline semiconductors. Historically, the laws of quantum mechanics have been established by experiment. The most important early experiments involved light. Long before it was realized that light waves are quantized into particles called photons, key experiments on the wave properties of light were performed. For example, it was established that the color of visible light is associated with different wavelengths of light. Table 2.1 shows the range of wavelengths corresponding to different colors. The connection between optical and electrical phenomena was established by Maxwell in 1864. This extended the concept of light to include the complete electromagnetic spectrum. A great deal of effort was, and continues to be, spent gathering information on the behavior of light.
In chapter 2, following the Maxwell description, we discuss vector potential, the continuity equation, and energy and momentum corresponding to optical fields. Based on the Maxwell depiction, quantization of electromagnetic fields is obtained. Quantized electromagnetic fields, such as Fock states, coherent states, squeezed states, and Schrödinger cat states, provide a general understanding of the quantum nature of the field. Thereby, we build the necessary foundation-level knowledge required to understand electromagnetic fields in the quantum domain.
At the conceptual level, the quantization procedure replaces the pure particle description of classical mechanics by a particle-wave treatment satisfying the requirements of the fundamental wave–particle dualism. Technically, one can always start from a generalized wave equation and use it as a basis to discuss wave-front propagation in the form of rays following classical particle trajectories, see Sections 2.2.1 and 3.1. Consequently, any wave theory inherently contains that aspect of the wave–particle dualism. Especially, Maxwell's equations of electrodynamic theory include both wave and particle aspects of electromagnetic fields. Hence, it could be that there are no additional “quantum,” i.e., wave–particle dualistic aspects. However, as we discuss in this chapter, Maxwell's equations can be expressed in the framework of Hamilton's formulation of particle mechanics. This then suggests that in addition to the approximate ray-like behavior, electromagnetic fields do have a supplementary level of particle-like properties. Due to the fundamental axiom of wave–particle dualism, the additional particle-like aspects of electromagnetic fields must then also have a wave counterpart that can be axiomatically introduced via the canonical quantization scheme described in Section 3.2.3. Since the spatial dependency in Maxwell's equation contains wave–particle dualism already at the classical level, it is clear that the new level of quantization cannot be a simple real-space feature but has to involve some other space describing the structure of the electromagnetic fields. In fact, this quantization yields several very concrete implications such as quantization of the light energy, elementary fluctuations in the light-field amplitude and intensity, and more.
For over a century, physics has treated time as a continuous background parameter while quantizing everything else—fields, energy, and angular momentum. This paper argues that the assignment of discreteness has been reversed: Light is not quantized; energy is not quantized. The record is quantized—and the record is what generates time. Within the Emergence as Regime Formation framework, temporal advance arises through irreversible record formation governed by the Future Contraction Postulate: Δt = −kₜ Δ ln Ω where Ω represents generative capacity—the number of realizable configurations remaining to a system. Each irreversible recording event reduces Ω and generates a finite increment of physical time. The paper demonstrates that experimental phenomena commonly interpreted as evidence for quantized light—including the photoelectric effect, Compton scattering, blackbody radiation, photon anti-bunching, and Hong–Ou–Mandel interference—are fully consistent with a framework in which: • The electromagnetic field remains continuous• Sources and detectors undergo discrete irreversible recording events• Apparent field quantization arises from projecting continuous processes onto a discrete lattice of records Explicit derivations of photon anti-bunching statistics and the Hong–Ou–Mandel interference dip are provided without invoking Fock space or field quantization. The results reproduce the standard quantitative predictions of quantum optics while relocating the source of discreteness from the field to the recording process. This relocation dissolves several foundational puzzles in physics, including: • Wave–particle duality• The quantum measurement problem• The emergence of classicality• The arrow of time• The “problem of time” in quantum gravity Within the broader Emergence as Regime Formation program, the same recording dynamics generate quantum mechanics, gauge theory, and gravitational structure as regime limits of a single continuity equation with irreversible recording.