Why Particle Physics Replaced "Energy" with "Information"

Abstract: Classical and introductory physics formulate physical interactions in terms of forces, potential energy, and energy conservation. However, in modern quantum field theory and quantum gravity, energy is recognized as an observer-dependent bookkeeping device that is not globally conserved in expanding general relativistic spacetimes. Here, we explore the conceptual revolution that recast fundamental physical interactions as local information exchange protocols. By analyzing gauge invariance as a phase synchronization requirement, Feynman propagators as quantum data packets, and Landauer’s principle, we demonstrate why information is a physical, thermodynamic primitive ($E \ge k_B T \ln 2$). We further examine how bulk spacetime geometry and gravitational attraction emerge directly from quantum entanglement entropy through the AdS/CFT correspondence and the $ER = EPR$ conjecture. These principles reveal that the physical universe is fundamentally computational, with forces and spacetime geometry serving as emergent manifestations of quantum information flow.

"It from bit. Otherwise put, every 'it' — every particle, every field of force, even the spacetime continuum itself — derives its function, its meaning, its very existence entirely from binary choices, bits."
— John Archibald Wheeler (1989)[^1]

When we first study high school physics, the universe is presented as an arena of forces and energy. A ball rolls down a hill because it converts gravitational potential energy into kinetic energy. Opposite electric charges attract because of the electrostatic force between them. Energy appears to be the ultimate cosmic currency — an indestructible, measurable fluid that flows between systems.

Yet, if you step into a contemporary seminar on quantum field theory (QFT), high-energy particle physics, or quantum gravity, a curious linguistic shift occurs. Physicists rarely speak about forces pushing objects. Instead, they talk about gauge connections, quantum channels, local phase consistency, correlation functions, entanglement entropy, and quantum information bounds.

Why did modern physics move from thinking of interactions as "energy and force transfers" to viewing them as information exchange?

In this deep dive, we explore: 1. The Flaw of Energy: Why energy is merely a bookkeeping tool rather than fundamental reality. 2. Gauge Theory: How fundamental forces arise simply by demanding that local observers can maintain distinct quantum information. 3. Feynman Propagators: Why particle interactions are quantum message-passing protocols. 4. Thermodynamics & Landauer’s Principle: How information became a measurable physical quantity ($E \ge k_B T \ln 2$). 5. Holography, AdS/CFT, and $ER = EPR$: How spacetime geometry and gravity are woven out of quantum entanglement. 6. Interactive Visualizers: Hands-on tools to explore gauge phase synchronization, Landauer's bound, and entanglement-built spacetime.

1. The Bookkeeper's Illusion: What Is Energy, Really?

In 1918, mathematician Emmy Noether proved one of the deepest theorems in all of science[^2]:

\[\text{Continuous Symmetry of Action } S \iff \text{Conserved Physical Current}\]

Specifically: - Spatial translation symmetry (physics is the same here as it is 1 meter to the left) $\implies$ Conservation of Linear Momentum $\mathbf{p}$. - Rotational symmetry (physics does not depend on the direction you face) $\implies$ Conservation of Angular Momentum $\mathbf{L}$. - Time translation symmetry (the laws of physics today are the same as tomorrow) $\implies$ Conservation of Energy $E$.

flowchart TD
    Symmetry["Spacetime Symmetries of the Action S"]

    Symmetry --> Time["Time Invariance: t → t + δt"]
    Symmetry --> Space["Space Invariance: x → x + δx"]
    Symmetry --> Angle["Rotation Invariance: θ → θ + δθ"]
    Symmetry --> Phase["Internal Phase Invariance: ψ → e^(iα) ψ"]

    Time --> Energy["Conserved: Energy (Hamiltonian H)"]
    Space --> Momentum["Conserved: Linear Momentum p"]
    Angle --> AngMom["Conserved: Angular Momentum L"]
    Phase --> Charge["Conserved: Electric / Gauge Charge Q"]

    style Symmetry fill:#1e293b,stroke:#475569,stroke-width:2px,color:#fff
    style Time fill:#2563eb,stroke:#1d4ed8,stroke-width:2px,color:#fff
    style Phase fill:#8b5cf6,stroke:#6d28d9,stroke-width:2px,color:#fff
    style Energy fill:#10b981,stroke:#047857,stroke-width:2px,color:#fff
    style Charge fill:#f59e0b,stroke:#d97706,stroke-width:2px,color:#fff

Why Energy Fails as a Fundamental Primitive

Observer Dependence: In special relativity, energy is merely the temporal component of a four-momentum vector $p^\mu = (E/c, p_x, p_y, p_z)$. Change your relative velocity, and the energy value changes completely.
Breakdown in General Relativity: In an expanding universe governed by the FLRW metric, spacetime is not time-translation invariant. As photons travel across expanding space, their wavelengths stretch (cosmological redshift). Energy is not globally conserved in general relativity.
Energy is a Scalar Quantity with No Structural Context: Knowing a system has $100\text{ Joules}$ tells you nothing about whether it is organized into a living cell, a supercomputer, or a hot puff of thermal steam.

To understand how particles interact and what structures can exist, we need to know how quantum states distinguish themselves from one another. That is the domain of Information.

2. The Great Breakthrough: Forces as Local Information Synchronization

In quantum mechanics, a matter particle (like an electron or quark) is described by a complex wave function or field $\psi(x)$:

\[\psi(x) = R(x) e^{i \theta(x)}\]

The probability density of finding the particle at position $x$ is:

\[P(x) = |\psi(x)|^2 = \psi^*(x) \psi(x) = R(x)^2\]

Notice that if you multiply $\psi(x)$ by a global phase factor $e^{i \alpha}$ (where $\alpha$ is a constant number across the entire universe), the probability distribution does not change at all:

\[\psi'(x) = e^{i \alpha} \psi(x) \implies |\psi'(x)|^2 = (e^{-i \alpha}\psi^*(x))(e^{i \alpha}\psi(x)) = |\psi(x)|^2\]

Global Phase Transformation (Instantaneous across all space):
Point A:  θ_A  ───(+α)───>  θ_A + α
Point B:  θ_B  ───(+α)───>  θ_B + α
(Requires instantaneous coordination across the universe — violates relativity!)

The Conflict with Special Relativity

Special relativity states that no physical influence can propagate faster than the speed of light $c$. How could an electron in your laboratory instantly "agree" on a global reference phase $\alpha$ with an electron in the Andromeda Galaxy?

It cannot. Physics must be locally symmetric. You must have the freedom to rotate the quantum phase independently at every point in space and time:

\[\psi(x) \to \psi'(x) = e^{i \alpha(x)} \psi(x)\]

Now, consider what happens when we calculate the kinetic energy or motion of the electron using the derivative $\partial_\mu \psi(x)$:

\[\partial_\mu \psi'(x) = \partial_\mu \left( e^{i \alpha(x)} \psi(x) \right) = e^{i \alpha(x)} \partial_\mu \psi(x) + i (\partial_\mu \alpha(x)) e^{i \alpha(x)} \psi(x)\]

The extra derivative term $i (\partial_\mu \alpha(x))$ ruins the invariance of the physics! The particle's equation of motion breaks down unless we introduce a compensating field $A_\mu(x)$ that dynamically cancels this phase discrepancy.

flowchart TD
    Demand["Demand: Local Freedom of Quantum Phase θ(x)<br/>Each point can choose its own reference clock"]

    DerivBreak["Ordinary derivative ∂_μ ψ breaks down<br/>Mismatch across neighboring spacetime points"]

    Introduce["Introduce a Gauge Connection Field A_μ(x)<br/>Transmits phase comparison information between points"]

    Dcov["Construct Covariant Derivative: D_μ = ∂_μ - i q A_μ"]

    ForceBorn["Gauge Boson Emerges (Photon, Gluon, W/Z)<br/>What we called 'Force' is the Phase Synchronization Channel!"]

    Demand --> DerivBreak --> Introduce --> Dcov --> ForceBorn

    style Demand fill:#1e293b,stroke:#3b82f6,stroke-width:2px,color:#fff
    style DerivBreak fill:#b91c1c,stroke:#ef4444,stroke-width:2px,color:#fff
    style Introduce fill:#f59e0b,stroke:#d97706,stroke-width:2px,color:#fff
    style Dcov fill:#0284c7,stroke:#0369a1,stroke-width:2px,color:#fff
    style ForceBorn fill:#10b981,stroke:#047857,stroke-width:2px,color:#fff

By replacing the ordinary derivative $\partial_\mu$ with the gauge covariant derivative (formulated for non-Abelian fields by Chen-Ning Yang and Robert Mills in 1954[^3]):

\[D_\mu = \partial_\mu - i q A_\mu(x)\]

where $A_\mu(x)$ transforms as $A_\mu'(x) = A_\mu(x) + \frac{1}{q} \partial_\mu \alpha(x)$, the entire equation becomes perfectly invariant!

The Profound Conclusion:
The electromagnetic field (the photon), the strong force (gluons), and the weak force ($W^\pm, Z^0$) exist solely as information-carrying gauge connections. Their purpose in the mathematics of nature is to transmit the local phase choices of matter fields across spacetime so that local observers remain mathematically consistent.

3. Quantum Field Theory: Feynman Diagrams as Data Packets

In classical physics, two repelling electrons are said to sit in an invisible static "potential well" $V(r) = \frac{k e^2}{r}$.

In Quantum Electrodynamics (QED), there is no static force at all. Instead, the interaction is described by a scattering amplitude $\mathcal{M}$ computed via Feynman diagrams[^4]:

        e⁻ (p₁) ─────────────────●───────────────── e⁻ (p₃)
                                 │
                                 │ Virtual Photon γ
                                 │ Four-momentum q = p₁ - p₃
                                 │ Propagator: D_μν(q) = -i η_μν / (q² + iε)
                                 │
        e⁻ (p₂) ─────────────────●───────────────── e⁻ (p₄)

The interaction is a discrete exchange of quantum numbers and 4-momentum: 1. Electron 1 undergoes a local quantum transition at vertex 1, emitting a virtual gauge boson. 2. The boson acts as a quantum propagator carrying momentum $q^\mu = (\Delta E, \Delta \mathbf{p})$, polarization, and phase information across space. 3. Electron 2 absorbs the boson at vertex 2, updating its own momentum state.

When you sum over millions of these quantum message exchanges, the coarse-grained macroscopic average reproduces Coulomb's inverse-square force:

\[\langle \text{Scattering Amplitude} \rangle \xrightarrow{\text{non-relativistic limit}} V(r) = \frac{e^2}{4 \pi \epsilon_0 r}\]

What we experience as "energy and force" is the statistical thermodynamic limit of countless discrete quantum data exchanges.

4. Landauer’s Principle: Information Has Physical Mass and Energy

For decades, information was regarded as an abstract mathematical concept formulated by Claude Shannon for telecommunications:

\[H = - \sum_{i} p_i \log_2 p_i\]

In 1961, physicist Rolf Landauer at IBM demonstrated that information is intrinsically physical[^5].

                  Landauer's Principle of Computation

       Known Bit: 0 (State A)   ───────┐
                                       ├──> Merged into Reset State (0)
       Known Bit: 1 (State B)   ───────┘

       2 Microstates Compressed into 1 Microstate
       Entropy Loss in Information Register: ΔS_info = - k_B ln 2
       Entropy Transferred to Environment:   ΔS_env  ≥ + k_B ln 2
       Minimum Heat Dissipated:              ΔQ = T ΔS_env ≥ k_B T ln 2

The Landauer Bound

Whenever a physical computer or quantum system erases or overwrites $1 \text{ bit}$ of information, the phase space of physical microstates shrinks by a factor of 2. By the Second Law of Thermodynamics, that entropy must be dumped into the thermal environment:

\[\Delta E \ge k_B T \ln 2\]

At room temperature ($T = 300\text{ K}$):

\[\Delta E_{\text{min}} \approx 1.3806 \times 10^{-23} \times 300 \times 0.6931 \approx 2.87 \times 10^{-21}\text{ Joules} \approx 0.0179\text{ eV}\]

Concept	Classical Mechanics (18th-19th Century)	Quantum Information Physics (21st Century)
Primary Currency	Mechanical Energy $E = T + V$	Quantum Information / Entanglement $S = -\text{Tr}(\rho \ln \rho)$
Origin of Forces	Pushes and pulls across distance	Local gauge invariance & phase synchronization
Interaction Medium	Continuous scalar/vector potential	Quantum channels & gauge bosons
Black Hole Content	Mass $M$ and singularity	Surface information storage ($S = A / 4 G \hbar$)
Spacetime Origin	Fixed, immutable background stage	Emergent quantum entanglement network ($ER = EPR$)
Limiting Principle	Conservation of Energy ($\Delta E = 0$)	Bekenstein Information Bound ($I \le \frac{2\pi R E}{\hbar c \ln 2}$)

5. Holography, AdS/CFT, and $ER = EPR$: Spacetime is Entanglement

The ultimate culmination of the "information replaces energy" revolution occurred at the intersection of quantum gravity and string theory.

1. The Bekenstein-Hawking Black Hole Entropy

When Jacob Bekenstein[^6] and Stephen Hawking[^7] studied black holes, they discovered something shocking. If you drop a massive object of energy $E$ into a black hole, the black hole's capacity to store information increases not with its volume, but with its surface area:

\[S_{\text{BH}} = \frac{k_B c^3 A}{4 G \hbar} = \frac{k_B A}{4 \ell_P^2}\]

where $\ell_P = \sqrt{\frac{G \hbar}{c^3}} \approx 1.616 \times 10^{-35}\text{ m}$ is the Planck length.

       1 Planck Area Pixel = 1 Bit of Quantum Information
              ┌───┬───┬───┬───┬───┬───┐
              │ 0 │ 1 │ 1 │ 0 │ 1 │ 0 │
              ├───┼───┼───┼───┼───┼───┤
              │ 1 │ 0 │ 0 │ 1 │ 0 │ 1 │   Black Hole Horizon Surface (Area A)
              ├───┼───┼───┼───┼───┼───┤   Stores N = A / 4ℓ_P² Qubits
              │ 0 │ 1 │ 1 │ 1 │ 0 │ 0 │
              └───┴───┴───┴───┴───┴───┘

The maximum amount of information you can cram into any region of space before it collapses into a black hole is strictly proportional to the boundary area $A$. This is the Holographic Principle.

2. The Ryu-Takayanagi Formula

In 1997, Juan Maldacena formulated the AdS/CFT correspondence (holographic duality)[^8]: a gravitational theory in $(d+1)$-dimensional curved spacetime is mathematically identical to a quantum field theory with no gravity living on its $d$-dimensional boundary.

Shinsei Ryu and Tadashi Takayanagi proved that the geometric distance and curved spacetime in the interior (the gravitational bulk) is literally calculated by the quantum entanglement entropy $S_A$ of the boundary qubits[^9]:

\[S_A = \frac{\text{Area}(\gamma_A)}{4 G_N \hbar}\]

where $\gamma_A$ is the minimal surface in the bulk anchored to region $A$.

3. $ER = EPR$ (Maldacena & Susskind)

In 2013, Juan Maldacena and Leonard Susskind proposed the groundbreaking $ER = EPR$ conjecture[^10]: - $EPR$: Einstein-Podolsky-Rosen quantum entanglement between particles. - $ER$: Einstein-Rosen bridges (spacetime wormholes) connecting two regions.

       EPR Entanglement ──────────(ER = EPR)──────────► ER Wormhole
   Particle A ──●                      Spatial Bulk            ●── Particle B
      │        ( Entangled Qubits )         │                  │
      └─────────────────────────────────────┴──────────────────┘
                 Geometry IS Entanglement Threading

If you take two entangled particles and maximize their entanglement, the geometry connecting them is a microscopic wormhole. If you disentangle them, the geometric connection snaps. Spacetime is not a container where particles interact; spacetime itself is woven out of quantum entanglement.

AdS/CFT Holographic Dictionary:
Boundary:  Pure Quantum Entanglement S(A:B) ──(Information Correlation)──
                     ↕ (Holographic Dual)
Bulk:      Smooth Spacetime Geodesic Distance / Wormhole Bridge

3. $ER = EPR$: Einstein-Rosen Wormholes Equal Einstein-Podolsky-Rosen Entanglement

In 2013, Juan Maldacena and Leonard Susskind proposed the $ER = EPR$ hypothesis: - EPR (1935): Quantum entanglement between two particles ($|\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$). - ER (1935): Einstein-Rosen bridges (spacetime wormholes).

graph LR
    subgraph Microscopic["Quantum Information Layer (EPR)"]
        QubitA["Qubit State A"] <===>|Quantum Entanglement Correlations| QubitB["Qubit State B"]
    end

    subgraph Macroscopic["Emergent Geometry & Gravity (ER)"]
        SpaceA["Spacetime Region A"] <===>|Smooth Wormhole / Geodesic Metric| SpaceB["Spacetime Region B"]
    end

    Microscopic <===>|ER = EPR Duality| Macroscopic

    style QubitA fill:#3b82f6,stroke:#1d4ed8,stroke-width:2px,color:#fff
    style QubitB fill:#3b82f6,stroke:#1d4ed8,stroke-width:2px,color:#fff
    style SpaceA fill:#10b981,stroke:#047857,stroke-width:2px,color:#fff
    style SpaceB fill:#10b981,stroke:#047857,stroke-width:2px,color:#fff

If you take two black holes and maximize the quantum entanglement between their constituent microstates, a smooth spatial tunnel (wormhole) opens between them. If you disentangle the particles (erasing the mutual quantum information), the wormhole snaps and space literally ceases to exist between the two regions!

In the words of Mark Van Raamsdonk:

"Spacetime geometry is the geometric manifestation of quantum entanglement."

6. Interactive Exploratorium

Explore these core concepts interactively with the widgets below.

Adjust the local phase $\alpha(x)$ at Point 2. Observe how the ordinary gradient breaks down (mismatch), and watch how the gauge connection field $A_\mu(x)$ synchronizes the phase information to restore physical invariance.

Point 1 Phase (θ₁): 0°

Point 2 Phase Shift (α(x)): 90°

Enable Gauge Connection A_μ

Loading gauge connection status...

Calculate the fundamental thermodynamic energy cost required to process and erase information at various temperatures — from the cosmic microwave background ($2.73\text{ K}$) to room temperature and supercomputers.

Information Erased ($N$ bits):

Temperature ($T$ in Kelvin):

Minimum Heat Energy Dissipated

2.87 × 10⁻¹⁵ J

Equivalent Electron Volts

17.9 keV

Entropy Discharged to Cosmos

9.57 × 10⁻¹⁸ J/K

7. Summary: The Great Shift in Physics

To summarize why modern fundamental physics prefers the language of information over energy:

Information Is Invariant and Universal: While energy changes under velocity boosts and fails to be conserved globally in general relativity, quantum information (von Neumann entropy, entanglement fidelity, and channel capacity) is coordinate-independent.
Forces Are Information Channels: The Standard Model gauge fields (photons, gluons, $W/Z$) do not "exert forces" in the classical sense; they are gauge connections that maintain local quantum phase consistency across spacetime.
Spacetime Itself Emerges from Qubits: Modern quantum gravity and holography (AdS/CFT, Ryu-Takayanagi, $ER=EPR$) demonstrate that smooth geometric distances, gravitational attraction, and black hole horizons are macroscopic manifestations of microscopic quantum entanglement.

Energy is the measure of work a system can perform, but Information is the code of reality itself.

Data and Code Availability

Interactive Visualizers: The phase synchronization visualizer and Landauer's bound calculator are implemented in pure vanilla JavaScript/HTML5 Canvas, executed entirely client-side.
Source Code: All markdown documents, equations, and interactive models are open source on GitHub: kamingfung/kamingfung.github.io.
Physical Constants: Calculations utilize CODATA recommended values for Boltzmann constant $k_B$, elementary charge $e$, and speed of light $c$[^11].

References

[^1]: Wheeler, J. A. Information, physics, quantum: The search for links. Proc. 3rd Int. Symp. Foundations of Quantum Mechanics, Tokyo, 354–368 (1989). [^2]: Noether, E. Invariante Variationsprobleme. Nachr. D. Ges. Wiss. Göttingen, Math.-Phys. Kl. 1918, 235–257 (1918). https://doi.org/10.1007/BF02392404 [^3]: Yang, C. N. & Mills, R. L. Conservation of isotopic spin and isotopic gauge invariance. Phys. Rev. 96, 191–195 (1954). https://doi.org/10.1103/PhysRev.96.191 [^4]: Feynman, R. P. Space-time approach to quantum electrodynamics. Phys. Rev. 76, 769–789 (1949). https://doi.org/10.1103/PhysRev.76.769 [^5]: Landauer, R. Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961). https://doi.org/10.1147/rd.53.0183 [^6]: Bekenstein, J. D. Black holes and entropy. Phys. Rev. D 7, 2333–2346 (1973). https://doi.org/10.1103/PhysRevD.7.2333 [^7]: Hawking, S. W. Particle creation by black holes. Commun. Math. Phys. 43, 199–220 (1975). https://doi.org/10.1007/BF02345020 [^8]: Maldacena, J. The large-N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231–252 (1998). https://doi.org/10.4310/ATMP.1998.v2.n2.a1 [^9]: Ryu, S. & Takayanagi, T. Holographic derivation of entanglement entropy from AdS/CFT. Phys. Rev. Lett. 96, 181602 (2006). https://doi.org/10.1103/PhysRevLett.96.181602 [^10]: Maldacena, J. & Susskind, L. Cool horizons for entangled black holes. Fortschr. Phys. 61, 781–811 (2013). https://doi.org/10.1002/prop.201300020 [^11]: Tiesinga, E., Mohr, P. J., Newell, D. B. & Taylor, B. N. CODATA recommended values of the fundamental physical constants: 2018. Rev. Mod. Phys. 93, 025010 (2021). https://doi.org/10.1103/RevModPhys.93.025010