Explore how spacetime dynamics emerge from fundamental information processes governed by entropy principles, unifying quantum, thermodynamic, and gravitational phenomena within a single mathematical framework.
At the most fundamental level, reality consists not of matter or energy, but of quantum information. Every physical process, from an apple falling to a star exploding, can be understood as a transformation of information.
The total quantum information content of a system can be expressed as: I_{\text{total}} = S_{\text{vN}}(\rho_{\text{global}}) - \frac{1}{2}\sum_{i,j} S_{\text{vN}}(\rho_{i,j})
Spacetime geometry emerges from the entanglement structure of the underlying quantum information substrate. The relationship between entanglement entropy and spatial distance is mathematically formalized.
The emergent distance between regions can be expressed as: d(A, B) = \frac{\alpha \ell_p}{\ln[S_{\text{max}}/S_{\text{ent}}(A:B)]}
The Information-Entropy Framework provides natural explanations for several long-standing puzzles in physics:
Why time flows in only one direction despite time-symmetric physical laws
How the universe began in an extraordinarily ordered state
What drives the accelerating expansion of the universe
How to reconcile quantum mechanics with general relativity
The Information-Entropy Framework is built upon five fundamental principles that together provide a comprehensive mathematical foundation for understanding spacetime dynamics.
At the most fundamental level, reality consists of quantum information rather than matter or energy. Every physical process can be understood as a transformation of information.
Spacetime geometry emerges from the entanglement structure of the underlying quantum information substrate. The relationship between entanglement entropy and spatial distance is mathematically formalized.
A scale-invariant coupling function determines how entropy production at different scales contributes to spacetime dynamics, effectively unifying quantum, thermodynamic, and gravitational phenomena.
Different forms of entropy (quantum entanglement, thermodynamic, gravitational, cosmic horizon) operate across different scales but are fundamentally connected as manifestations of a single underlying information-theoretic quantity.
A hierarchy of scales from the Planck scale to the cosmic horizon scale defines how information organizes and transforms across different levels of reality.
These five principles are deeply interconnected, forming a cohesive framework that explains how quantum information gives rise to the spacetime we observe. The framework demonstrates that the distribution and transformation of quantum information across different scales produces the observed properties of spacetime, including its emergence, dynamics, and expansion.
Through the derivation of a scale-invariant coupling function, the framework establishes how entropy production at different scales contributes to cosmic evolution, effectively unifying quantum, thermodynamic, and gravitational phenomena within a single mathematical framework. This approach resolves several long-standing puzzles in physics including the arrow of time, the origin of dark energy, and the extraordinarily low entropy of the early universe.
The Information-Entropy Framework is built upon a rigorous mathematical foundation that connects quantum information, entropy, and spacetime dynamics through a series of key equations and formulations.
At the most fundamental level, reality consists of quantum information. This equation quantifies the total information content of a quantum system, accounting for global and local entropies.
Where S_{\text{vN}} is the von Neumann entropy and \rho represents density matrices
Spacetime geometry emerges from the entanglement structure of the underlying quantum information substrate. These equations formalize how quantum entanglement translates into spatial distance and how decoherence drives the emergence of classical spacetime.
Where d(A, B) is the emergent distance between regions A and B, S_{\text{ent}}(A:B) is the entanglement entropy, S_{\text{max}} is the maximum possible entropy, \ell_p is the Planck length, and \alpha is a dimensionless constant
Where \Gamma_{\text{decoherence}} is the decoherence rate with units of [time]⁻¹, k_B is Boltzmann's constant, and \frac{dS_{\text{ent}}}{dt} is the rate of entanglement entropy production
The scale-invariant coupling function determines how entropy production at different scales contributes to spacetime dynamics.
Where \alpha = \frac{d-2}{2}, \beta = \pi, and \gamma = 2
This equation provides a direct mathematical link between entropy dynamics and cosmic expansion, demonstrating that the universe's expansion is driven by the fundamental increase of entropy across all scales, weighted by the scale-invariant coupling function.
Where \frac{\ddot{a}}{a} is the cosmic acceleration, the first two terms represent standard contributions, and the integral represents entropy production across all scales
The mathematical framework presented here provides a consistent and unified description of physical phenomena across all scales. It demonstrates how quantum information processes at the Planck scale give rise to the classical spacetime and gravitational dynamics we observe at macroscopic scales.
The framework makes specific, quantitatively testable predictions across multiple observational domains, providing clear paths to empirical validation. It shows that recursive cosmological structures naturally emerge as a consequence of fundamental entropy principles rather than serving as a foundational assumption.
The Information-Entropy Framework provides natural explanations for several long-standing puzzles in physics, including the arrow of time, dark energy, and black hole thermodynamics.
In the pre-geometric phase, time has no preferred direction. As spacetime geometry emerges from quantum information through entropy-producing processes, the direction of time aligns with the direction of increasing entropy.
The rate of proper time experienced by any observer is related to the local entropy production rate:
Where \gamma is a small coupling constant and S_0 is a characteristic entropy production rate.
The origin of the universe's initial low entropy state is explained as a natural consequence of the emergence of our spacetime from quantum information configurations.
The quantum vacuum represents an extremely ordered state of information, with patterns of entanglement that determine the geometric properties of the emergent spacetime.
This approach resolves the puzzle of why the universe began in an extraordinarily ordered state when disorder is overwhelmingly more probable in conventional frameworks.
Our framework provides a natural explanation for dark energy as a consequence of cosmic-scale entropy dynamics. The effective cosmological constant emerges from the entropy of the cosmic horizon:
This integral yields a value of \Lambda_{\text{eff}} \approx 10^{-52} \text{ m}^{-2}, consistent with observations without fine-tuning.
Our framework provides a natural resolution to the cosmological constant problem—why the observed value of dark energy is approximately 120 orders of magnitude smaller than quantum field theory predicts.
In our approach, dark energy is not a vacuum energy but emerges from cosmic-scale entropy dynamics. The apparent value of the cosmological constant is:
This integral naturally yields a value consistent with observations without fine-tuning, because the scale-invariant coupling function suppresses contributions from small-scale quantum fluctuations while enhancing those from cosmic-scale entropy processes.
Current composition of the universe according to observational data
In our framework, black holes emerge as extreme entropy-generating structures in spacetime. Rather than postulating black holes as universal generators, we show that they arise naturally from the tendency of complex information systems to maximize entropy production.
The entropy of a black hole follows the Bekenstein-Hawking formula:
Where A is the area of the event horizon. We predict specific quantum corrections to this formula:
Where \alpha_1 = -1/90\pi and \alpha_2 = 1/1440\pi^2 are derived from quantum gravity calculations.
The information-theoretic properties of black holes make them natural candidates for dimensional translation points where information undergoes significant reorganization.
This reorganization might, as an emergent property, give rise to new spacetime structures that could potentially be interpreted as "child universes."
However, in our framework, this recursive cosmological structure emerges as a consequence of fundamental entropy principles rather than serving as a foundational assumption. The framework provides a mathematical description of how information is processed at the event horizon and how this processing relates to the global structure of spacetime.
The Information-Entropy Framework makes specific, quantitatively testable predictions across multiple observational domains, providing clear paths to empirical validation:
Specific patterns in the CMB polarization that reflect the quantum information structure of the early universe.
A slow evolution of the effective cosmological constant over cosmic time, potentially testable with next-generation dark energy surveys.
Specific quantum corrections to black hole entropy that could be tested through gravitational wave observations of black hole mergers.