When Einstein discovered relativity, we embrace 4D, even it’s very bizarre for most people to grasp the fourth dimension – time.

But once we are equipped with this 4D view based math, those difficult problem such as space contraction, time dilation are essentially to reach to one realization that every object in the universe is moving at constant speed – light speed in 4D. How simple and clear!

Maxwell Equations contains 8 equations to describe magnetism, in 4D can be concisely expressed by two equations using tensor.

Quantum Fields: In the framework of quantum field theory (QFT), every type of elementary particle is associated with its respective quantum field. For example, the electron is associated with the electron field, and photons (the quanta of the electromagnetic field) are associated with the electromagnetic field. In this sense, particles are excitations of their respective fields. So, while charged particles like electrons can interact with the electromagnetic field (and are sources for it), they are not described by the electromagnetic field tensor itself.

The idea of unifying different forces of nature using higher dimensions has been a topic of interest for over a century. One of the early attempts to unify gravity (described by General Relativity) with electromagnetism is known as Kaluza-Klein theory, which posits that our universe might have additional spatial dimensions beyond the familiar three.

Here’s a brief overview:

Kaluza-Klein Theory (5D approach):

• The idea was first proposed by Theodor Kaluza in 1919 and later refined by Oskar Klein in 1926.
• Kaluza proposed that by adding a fifth dimension to the equations of General Relativity, the equations could describe both gravity and electromagnetism.
• When the five-dimensional equations are “reduced” back to four dimensions (by assuming the fifth dimension is compact and small), the four-dimensional equations manifest as Einstein’s equations of General Relativity plus Maxwell’s equations of electromagnetism. Additionally, there is a scalar field that emerges from the compactification process.
• Klein provided a physical interpretation of the fifth dimension. He suggested that this extra dimension might be “curled up” or compactified to a size so small that it’s undetectable, which is why we don’t perceive it in our everyday experiences.

Challenges and Modern Developments:

1. Quantum Mechanics: Kaluza-Klein theory was developed before the advent of quantum mechanics. When quantum mechanics is considered, the simple picture of Kaluza-Klein theory gets much more complex.
2. Other Forces: The Standard Model of particle physics, which was developed much later, revealed two other forces: the weak and strong nuclear forces. The Kaluza-Klein theory in its original form does not account for these forces.
3. String Theory: Modern attempts to unify forces, like string theory, often use higher dimensions (sometimes 10, 11, or even more). Some of these ideas are descendants of Kaluza-Klein theory. In string theory, these extra dimensions can be compactified in various complex ways, leading to a vast landscape of potential solutions.