Scale invariance, or its absence, in the context of electromagnetism refers to the behavior of electromagnetic phenomena under changes in length scales. In physics, scale invariance implies that the laws or equations governing a system remain unchanged when you scale up or down the system's size.
In classical electromagnetism, described by Maxwell's equations, scale invariance is not present. This means that the behavior of electromagnetic fields and interactions depends on the specific length scale involved. For example, the strength of the electric field generated by a point charge decreases with distance according to the inverse square law. If you double the distance, the electric field becomes four times weaker. This behavior indicates a lack of scale invariance because the laws governing electromagnetism change when the length scale is altered.
However, in the framework of quantum electrodynamics (QED), which is the quantum mechanical description of electromagnetism, there is an interesting feature known as asymptotic freedom. At very high energies or very short distances (small length scales), the strength of the electromagnetic interaction weakens. This phenomenon arises due to the behavior of the coupling constant in QED, which describes the strength of the electromagnetic interaction. As the energy scale increases, the coupling constant becomes smaller, leading to weaker interactions.
Asymptotic freedom in QED is an example of scale non-invariance in a specific context. It means that the behavior of electromagnetic interactions changes depending on the energy or length scale involved. At low energies or large length scales, the electromagnetic force is strong, as observed in everyday life. However, at extremely high energies or small length scales, the force weakens significantly. This property of scale non-invariance is a consequence of the quantum nature of electromagnetism and is a significant feature of quantum field theories like QED.