This deep learning is not Google’s deep learning, AI but how we grasp deep learning.

Such as Path G’s interpretation of gauge invariance is intuitive; Quantum Sense’s approach to the Schrödinger equation focuses on problem-solving; and at a high level, I observed that ARRB suggests that physics and mathematics serve primarily to translate collected or observed data into equations that facilitate deduction and computation. This perspective is highly logical. Furthermore, it highlights a recurring issue in academia, where professors often present dry and unengaging theories without conveying a profound understanding of the historical reasoning of the foundational thinkers in the field.

One case is to learn “Quantizing the field led to photon excitations”, chatGPT answers:

The idea that particles are excitations of fields emerged from the development of quantum field theory (QFT) in the early 20th century. The first person to conceptualize this was Paul Dirac, followed by contributions from Heisenberg, Pauli, Feynman, and others. Here’s how the discovery unfolded:

5. Quantum Field Theory of Everything: 1950s – Present

Once the idea was established in electrodynamics, it was extended to:

• Weak and strong nuclear forces (Yang-Mills theory, 1950s).
• The Higgs field (Higgs, 1964) explains how particles get mass.
• The Standard Model (1970s) fully describes all known fundamental particles as field excitations.

The Higgs boson discovery in 2012 was the final confirmation that fields are real, and particles are just their excitations.

The key insight that led to the discovery of photons as excitations of the electromagnetic field comes from treating the field like a collection of harmonic oscillators and then applying quantum mechanics to it

Step 4: How This Explains Photon Properties

1. Particle-Like Behavior
   Since these excitations are discrete, they behave like individual particles in interactions (e.g., photoelectric effect, Compton scattering).
2. Wave-Like Behavior
   The field still exists everywhere, and different modes can interfere, explaining wave properties like diffraction.
3. Vacuum Fluctuations
   The lowest state is not empty, because even when no photons exist, there is still the zero-point energy of the quantum oscillators.

Then it leads to question: Describing Classical Waves in the Field Perspective, then further to how EM field is described in differential forms (bivector) and the Maxwell equations be reduced to only one equation concisely, then it leads to photon discovery, further to abelian and non-abelian gauge theory, to Yang-Mills Theory…