The Formation of Photons from Continuous and Expanding Electromagnetic Fields

Understanding the process of photon formation from continuous and expanding electromagnetic (EM) fields is essential for comprehending the quantum nature of light. In this article, we will explore how an integral field of EM radiation transitions into discrete photons as it propagates from a source. We will delve into the principles of EM field quantization and the association between photons and the detectors that interact with them.

The Role of EM Fields

While the momentum of an EM wave can be derived from Maxwell's equations, the concept of quantizing the field fundamentally changes our understanding of its behavior on a macroscopic and microscopic scale. The Poynting vector, which describes the power flow of an EM field, plays a crucial role in this transition.

From Continuous to Quantized Fields

Close to the source of radiation, the energy is propagated as an integral field rather than divided into individual photons. As we move away from the emission point, the wavefronts become large enough to be divided into discrete wavefronts, eventually forming photons. This process is not instantaneous but occurs at a specific distance from the source, where the field's energy is sufficient to create these discrete units of radiation.

The Formation Distance of Photons

In a vacuum, the distance at which photons form can be calculated based on the wavelength and the number of energy quanta. The surface area of the wavefront of each photon is given by:

So frac{lambda^2}{16 pi}

The diameter of the elementary wavefront is then:

do frac{lambda}{2 pi}

At a distance from the source where this transition occurs, the entire wavefront has an area equivalent to n squares with a side length of frac{lambda}{2 pi}.

Calculating the Photon Formation Distance

For a spherical wavefront in vacuum, the radius R where individual photons form can be calculated as:

R frac{lambda}{pi} sqrt{frac{n}{pi}}

With n being the number of quanta calculated by dividing the total energy E emitted in a cycle by the energy of a photon at that frequency:

n frac{E}{h u}

Once the number of quanta n is known, we can calculate the radius R where individual photons are formed.

The Concept of Photons

A photon can be understood as the interaction between the expanding spherical EM field and a detector or observer. This process of quantization arises because the detector is composed of atoms, each with its own oscillating electric fields. These oscillations lead to incremental interactions with the EM field, hence the concept of a quantum, meaning a minimum quantity.

A photon is not an object but a measurement of kinetic EM radiant energy. This understanding explains why there are no gaps between photons in a continuous EM wave; the wave itself is continuous, but the interactions are quantized. As a result, the distance of the radiation source from the detector does not affect the formation or existence of photons; it is the interaction with the detector that defines their presence.