Why Do We Need This Theory?

“We live in a fragmented world. Different laws, different theories, like isolated islands, lacking bridges between them.”

← Back to Home | Next: Reading Guide →

Special Note on Scientific Nature

To the Rigorous Reader:

The “GLS Theory” presented here is an exploratory theoretical framework aimed at constructing a unified perspective compatible with existing physical laws.

We are well aware that the cornerstones of physics are experimental verification and mathematical rigor. In this article, for the sake of accessibility, we may use words like “is,” but in a scientific context, they should be understood as “is modeled as” or “is equivalent to.”

Furthermore, the domains of physical quantities are usually clearly defined within specific theoretical frameworks (e.g., Newtonian mechanics vs. Quantum mechanics). This theory attempts to explore the fusion of these domain boundaries, so in certain transition regions, the definitions of concepts may undergo a “phase transition”-like generalization. We invite readers to maintain an open but critical scientific attitude.

The Puzzles of Physics

Imagine you are a detective investigating a complex case. You have many clues:

• 📍 Clue A (General Relativity): Tells you gravity can be described geometrically
• 📍 Clue B (Quantum Mechanics): Tells you the microscopic world follows the principle of superposition of probability amplitudes
• 📍 Clue C (Thermodynamics): Tells you macroscopic time has a direction, entropy always increases
• 📍 Clue D (Information Theory): Tells you information has physical reality
• 📍 Clue E (Cosmology): Tells you the universe is expanding

Each clue seems reasonable, but when you try to piece them together, you find they have tensions in their fundamental assumptions:

Puzzle 1: Conflict Between Gravity and Quantum Mechanics

General Relativity is based on differential manifolds, assuming spacetime is smooth, continuous, deterministic.

Quantum Mechanics is based on Hilbert space, allowing discrete energy levels and probability superposition.

Question: At the center of a black hole, or at the moment of the Big Bang, gravity is extremely strong and scales are extremely small—both theories apply. But they give completely different answers. It’s like two witnesses giving completely contradictory descriptions of the same event. We need a more underlying framework to reconcile them.

Puzzle 2: Multiple Faces of Time

Relativity: Time is part of geometry (coordinate time/proper time).

Quantum Mechanics: Time usually acts as an external parameter (evolution parameter).

Thermodynamics: Time shows directionality through entropy increase (arrow of time).

Question: What is time really? Is it geometry, a parameter, or an arrow? Or are all three, and we just haven’t found a way to unify them?

Puzzle 3: Mysterious Connection Between Entropy and Gravity

In the 1970s, physicists Bekenstein and Hawking discovered: Black holes have temperature and entropy. Moreover, a black hole’s entropy is proportional to its surface area, not volume.

$$S_{\text{BH}}=\frac{A}{4G\hslash }$$

This implies that gravitational systems might have holographic properties. Usually, entropy should be proportional to volume (the larger the room, the more possibilities for disorder). But black hole entropy is proportional to surface area, as if all information is encoded on the surface.

Question: Why is entropy related to area? Does this imply that spacetime geometry itself is made of information?

Puzzle 4: Why Does the Universe Follow These Laws?

We have Einstein’s equations, Yang-Mills equations, Dirac equations… These equations are all very successful and can precisely predict experimental results.

But, why does the universe follow these equations?

Question: Is there a deeper reason that makes these laws not “made” but necessarily emergent from some more fundamental structure?

The Dream of Unification

Physicists have always dreamed of finding a “Theory of Everything” that can unify all these fragmented theories.

Historical Unification Achievements

Humanity has had several great unifications:

1. Newton (17th century): Unified planetary motion in the heavens and apple falling on earth
2. Maxwell (19th century): Unified electricity and magnetism
3. Einstein (20th century): Unified time and space, as well as mass and energy
4. Standard Model (20th century): Unified electromagnetic, weak nuclear, and strong nuclear forces

Each unification brought profound insights and new technologies.

Current Attempts

Now, physicists are trying to unify gravity and quantum mechanics. Main candidate theories include:

• String Theory: Believes fundamental particles are tiny vibrating strings
• Loop Quantum Gravity: Believes spacetime itself is a discrete network
• Causal Dynamical Triangulation: Uses simple triangles to piece together spacetime

But these theories all face challenges: either the mathematics is too complex, lack experimental evidence, or cannot give clear predictions.

The Perspective of GLS Theory

GLS unified theory takes a path based on information geometry.

Not Seeking “New Symmetries”

Traditional unified theories usually seek a larger symmetry group (like Grand Unified Theory).

But GLS theory proposes: Perhaps the problem is not about finding larger symmetries, but about re-examining the domains of fundamental concepts.

Unifying “Ontology,” Not “Symmetry”

The core hypothesis of GLS theory is:

Time, causality, geometry, information—might not be four independent concepts, but four projections of the same reality.

Like a cube, viewed from different angles, the projections are different shapes:

• Viewed from the front, it’s a square
• Viewed from the side, it’s also a square
• Viewed from above at an angle, it’s a hexagon

But there is only one cube.

Similarly, we attempt to establish the following correspondences:

• Scattering Perspective: S-matrix, phase, delay time
• Geometric Perspective: metric, curvature, geodesics
• Information Perspective: entropy, relative entropy, Fisher metric
• Causal Perspective: partial order, diamonds, Markov property

Core Formula: Unified Time Scale Identity

GLS theory constructs a mathematical equation as a bridge connecting different physical quantities:

$$\kappa (\omega )=\frac{{\phi }^{\prime }(\omega )}{\pi }={\rho }_{\text{rel}}(\omega )=\frac{1}{2\pi }\text{tr}Q(\omega )$$

This equation reveals the numerical equivalence of the following physical quantities under specific conditions:

• $\kappa (\omega )$: Scattering time delay
• ${\phi }^{\prime }(\omega )/\pi$: Phase derivative
• ${\rho }_{\text{rel}}(\omega )$: Relative density of states
• $\text{tr}Q(\omega )/2\pi$: Wigner-Smith group delay

This means that, in mathematical structure, they can be viewed as different manifestations of the same underlying object.

Theoretical Implications

If this unified framework is valid, it might provide us with new explanatory paths:

1. Possibility of Deriving Gravity from Entropy

Inspired by the work of Jacobson and Verlinde, we explore whether it is possible to not assume Einstein’s equations, but to derive them as a consequence of the Maximal Entanglement Entropy Principle.

If we assume generalized entropy on small causal diamonds takes an extremum, Einstein’s equation $G_{ab}+\Lambda g_{ab}=8\pi G{T}_{ab}$ might emerge as a thermodynamic equation of state.

2. Variational Structure Unifying Physical Laws

We attempt to construct a unified variational principle: Universe Consistency Variational Principle.

$$\delta \mathcal{I}[\mathfrak{U}]=0$$

In this framework, different physical laws (like Maxwell’s equations, Dirac equations) might correspond to constraints at different levels.

3. Self-Consistency of Observers and Physical Structure

Traditional physics often treats observers as external entities.

GLS theory attempts to incorporate observers into the physical description, proposing that observers might be self-referential subsystems within the physical structure.

This means consciousness might not be independent of physical laws, but a property of complex self-referential systems.

4. Connecting Discrete and Continuous

GLS theory suggests that discrete structures (like Quantum Cellular Automata) and continuous structures (like differential manifolds) might be descriptions of the same physical reality at different scales.

Discrete $\stackrel{\text{continuous limit}}{\to }$ Continuous

This is similar to fluid mechanics, where discrete molecular motion manifests as continuous fluid equations at the macroscopic level.

Goals of This Tutorial

The goal of this tutorial series is not to make you memorize a bunch of formulas, but:

🎯 Goal 1: Change Your Worldview

Help you see:

• Time is not a flowing river, but a dimension of geometry
• Causality is not a mysterious “force,” but mathematical partial order
• Boundaries are not irrelevant “container shells,” but the source of reality
• The universe is not chaotic, but deeply unified

🎯 Goal 2: Build Intuition

Through analogies, diagrams, and comparisons, help you intuitively understand these profound concepts, not just memorize formulas.

🎯 Goal 3: Provide Multiple Paths

Readers with different backgrounds can choose different paths:

• Physics background: Start with mathematical tools and variational principles
• Philosophy background: Start with ontology and conceptual unification
• Engineering background: Start with measurable quantities and applications
• Complete beginner: Start with everyday experience and analogies

What’s Next?

If you’re already excited and ready to begin this adventure, then:

📚 Step 1: Reading Guide

First read the Reading Guide to find the learning path that suits you best.

🗺️ Step 2: Concept Map

Browse the Concept Map for a bird’s eye view of the core concepts of the entire theory.

🚀 Step 3: Start Learning

Based on your interests and background, choose an entry point:

• Complete beginner → Fundamental Concepts Start from everyday experience
• Have physics background → Core Ideas Go straight to unified ideas
• Want to see formulas → Mathematical Tools Understand mathematical framework
• Want to see the big picture → Final Unification See the ultimate answer

Summary in One Paragraph

Physics faces profound puzzles: gravity and quantum mechanics are incompatible, time has multiple faces, entropy and gravity are mysteriously connected, and we don’t know why the universe follows these laws.

GLS unified theory provides a completely new perspective: Not seeking larger symmetries, but recognizing that time, causality, geometry, and information are four projections of the same reality.

The core insight is condensed in the Unified Time Scale Identity: scattering delay = phase derivative = density of states = group delay.

Starting from this unification, gravity, quantum field theory, cosmology, and even consciousness can all emerge as different levels of the same “universe consistency variational principle.”

This is not just theoretical unification, but ontological unification: all things share the same source, only projections differ.

Ready to begin this intellectual adventure?

← Back to Home | Next: Reading Guide →