The chain of dimensional strikes (dimensionality reduction) in physics is essentially a top-down degradation from the highest-dimensional frameworks of the universe.

With every step down in dimensionality, the theory gets closer to human observation and our everyday understanding of reality.

But the tragic irony is this: even when these theories degrade all the way down to the bottom layer—classical physics—99% of people still don’t truly understand them. This essentially dooms the vast majority of us to ignorance.

So, are you part of the 1%? Let’s trace the tech tree of the universe.

Layer 1: M-Theory (Brane Theory) Link to heading

  • Dimensions: 11D
  • The Downgrade (Dimensional Reduction): Branes are essentially condensed from multiple strings. If you roll a brane into a closed loop, compress it into a line, or use other mathematical projection methods on this dimension, it degrades into String Theory.

Layer 2: String Theory Link to heading

  • Dimensions: 10D
  • The Downgrade: 10D = 3D Space + 1D Time + 6D Calabi–Yau Manifold (named after Eugenio Calabi and Shing-Tung Yau).

This 6D real-number space is actually a 3D complex-number space—a microscopic, high-energy realm completely invisible to ordinary mortals. Its geometric properties dictate the fundamental particle types and physical constants of our universe. Every distinct Calabi-Yau manifold corresponds to a completely different universe.

When we apply dimensional reduction here, we simply ignore this compactified 6D space, leaving us with the familiar 4D low-energy world we live in.

Sidenote: This 6D space is indivisible. It is a highly complex geometric structure where different geometric topologies output different physical constants. Have you ever wondered where the source code for the speed of light or cosmic constants is written? How do particles know what rules to follow? It’s determined by the geometric, topological “shapes” hidden inside these dimensions. They act like the DNA of particles, operating at the Planck scale—a magnitude so incomprehensibly small that no microscope will ever see it.

Layer 3: General Relativity Link to heading

  • Dimensions: 4D
  • The Downgrade: At the low-energy limit, String Theory degrades into General Relativity. The closed-string vibration modes in String Theory perfectly correspond to the graviton. This elegant connection ensures that the spacetime curvature described by General Relativity can be naturally derived from the quantum vibrations of strings. When spacetime is entirely flat and devoid of gravity, General Relativity degrades into Special Relativity.

Layer 3.5: Special Relativity Link to heading

  • Dimensions: 4D
  • The Downgrade: When an object’s speed is far below the speed of light, Special Relativity degrades into Newtonian Mechanics.

Layer 4: Newtonian Mechanics Link to heading

  • Dimensions: 3+1D Slices
  • Reality Check: Do you really understand Newtonian Mechanics? (Do you truly grasp the implications of an absolute spacetime perspective?)

Let’s rewind. When Layer 2 (String Theory) undergoes dimensional reduction, what we see at the low-energy limit is a continuous, unbroken surface (the smooth spacetime of General Relativity). But at the high-energy limit, what we see is a chaotic cluster of dancing strings (particles).

As the string length approaches zero, the vibrations degrade into point particles. This unlocks an alternative candidate for Layer 3: Quantum Field Theory.

Layer 3 (Alternative): Quantum Field Theory (QFT) Link to heading

  • Dimensions: 4D
  • QFT is generally understood as the combination of Quantum Yang-Mills Theory (gauge boson fields) + the Higgs mechanism + Fermion field theory. Under certain conditions, QFT degrades into Quantum Electrodynamics.

Layer 3.5: Quantum Electrodynamics (QED) & 1954 Yang-Mills Theory Link to heading

  • Dimensions: 4D
  • The Downgrade: In the low-energy and non-relativistic limit, QED degrades into Maxwell’s equations. Naturally, Yang-Mills theory—which is fundamentally an extension of Maxwell’s work—can also degrade back into Maxwell’s equations.

Layer 4: Maxwell’s Equations Link to heading

  • Dimensions: 3+1D Slices
  • (This is the stuff undergrads usually pretend to understand to pass exams, and almost entirely forget after graduation).

The Unsung Heroes and the Math Problem Link to heading

As most physics buffs know, the “Yang” in Yang-Mills refers to Chen-Ning Yang.

Looking at the two dimensional reduction trees above, it’s obvious that Professor Yang is a god-tier grandmaster on par with Einstein. But… unfortunately, history is complicated.

The original 1954 version of the Yang-Mills theory predicted that force-carrying particles had zero mass. However, 20 years prior, Hideki Yukawa had already proven that mesons do have mass. Because of this glaring contradiction, the Yang-Mills theory was instantly shelved. The kicker? Yang himself couldn’t explain why this discrepancy existed, even though the partial differential equations were mathematically beautiful.

Applying classical Yang-Mills to Quantum Field Theory is a mathematically agonizing process. It wasn’t until the early 1970s, when scientists invented a series of advanced mathematical tools, that the physics community began to believe Yang-Mills was actually right. This led to the establishment of the quark model and the prediction of gluons, which replaced Yukawa’s macro-level mesons. By 1979, particle colliders discovered massless gluons, thoroughly “resurrecting” Yang-Mills and placing the crown on its head.

But here is the catch: The older version of Yang-Mills describes fields in a “classical” universe—smooth, continuous, and deterministic. Quantizing classical field equations is an absolute nightmare. The physicists who resurrected the theory essentially created “dark magic” math tools to make it computable at the quantum scale, but these tools are built on unproven mathematical structures.

To this day, constructing a rigorous mathematical foundation for quantized Yang-Mills theory remains incomplete. It is famously considered the hardest of the Clay Mathematics Institute’s million-dollar Millennium Prize Problems.

Einstein vs. The Mathematicians Link to heading

From a similar perspective, I personally feel incredibly bad for David Hilbert.

Single-handedly, Hilbert derived the complete mathematical solutions for General Relativity and laid the mathematical foundation for Quantum Mechanics (Hilbert Space). He is an absolute titan among titans in the mathematics community, yet the general public has no idea who he is.

Einstein, on the other hand, was not an exceptional mathematician. Instead, he relied on his razor-sharp physical intuition and insight. He effectively adopted an “open-source, grab-and-use” approach to mathematics, beating Henri Poincaré and Hilbert to the punch to claim the ultimate prize of relativity.

Perhaps this limitation in raw mathematical ability is exactly why Einstein spent the second half of his life failing to formulate a Grand Unified Theory.

When you compare Einstein to Sir Isaac Newton—a man who literally had to invent a new mathematical tool (Calculus) just to propose his own physical framework—I honestly think Einstein has to take a backseat.