How Introducing the Gauge Field Led to the Discovery of the Electromagnetic Force

The key idea is that electromagnetism naturally emerges when we enforce local gauge symmetry on a quantum system.

Everything works fine in 3D world, but when you elevate to space-time 4D which is a must when we explore the universe deeper, gauge symmetry without introducing some adjusting part is broken.

Hence gauge field has to be introduced

Next, why this gauge field, also is exactly the electromagnetic potential, represents the photon? The key insight is the deep connection between symmetry and forces! Respect to Emmy Noether Again!