GSC Model: Derivations from First Principles

A collaborative workspace for deriving new physical insights from the Ground State Configuration (GSC) model through emergent gravity and informational dynamics.

1. Black Hole Phenomena

Black holes represent the ultimate laboratory for any theory of quantum gravity. The GSC model's core tenets—that information is fundamental and spacetime is emergent—should provide a powerful framework for resolving long-standing paradoxes.

1.1. The Information Paradox

The GSC Model Approach: In the GSC model, information is never destroyed. It undergoes a transformation from being locally accessible to being encoded in the non-local correlational structure of the multiverse. This happens via a continuous process of causal history imprinting during infall.

Proposed Derivation Steps:

  1. Modeling the State in the GSC Hilbert Space:

    The full Hilbert space is a tensor product of the local branch and the multiverse: $\mathcal{H}_{GSC} = \mathcal{H}_{local} \otimes \mathcal{H}_{multi}$. An infalling electron begins in a state largely unentangled with the multiverse:

    $$|\psi_{e}\rangle_{initial} = |\psi_{local}\rangle \otimes |\psi_{multi}^{0}\rangle$$
  2. Continuous Information Transfer via Relativistic Branching:

    As the electron falls, it continues to interact with the local quantum vacuum. This interaction, governed by an interaction Hamiltonian $H_{int}(t)$, causes a continuous branching of its causal history into the multiverse. This is not a single event, but a gradual process where the electron's state evolves unitarily:

    $$|\Psi(t)\rangle = \mathcal{T} e^{-i \int_{t_0}^{t_f} H_{int}(t') dt'} |\Psi(t_0)\rangle$$

    The operator $\mathcal{T} e^{-i \int H_{int}(t') dt'}$ represents the time-ordered evolution that progressively entangles the local state with $\mathcal{H}_{multi}$.

  3. Conservation of Informational Freedom during Infall:

    The total information, $S_{total}$, is conserved. As the electron falls, its ability to be in a superposition of states locally diminishes ($S_{local} \to 0$). This loss of local freedom is precisely compensated by an increase in its entanglement with the multiverse ($S_{multi}$ increases), as its causal history is imprinted across many branches.

    $$\frac{dS_{local}}{dt} = -\frac{dS_{multi}}{dt}$$

    The process concludes when no "superpositional invariance" remains—the particle has fully decohered with the local system and its information is now entirely non-local.

  4. Hawking Radiation and the Concept of Multiversal Time:

    The imprinted causal history is not static. The parameter tracking the evolution of this branching and entanglement can be understood as a form of "multiversal time." Hawking radiation is the mechanism by which this process runs in reverse: quantum fluctuations at the horizon couple to the imprinted history, slowly untangling it and leaking the information back into $\mathcal{H}_{local}$ as correlated radiation.

  5. Deriving the Page Curve:

    The Page Curve emerges naturally from this model. The "turn" of the curve happens at the Page time—the point where the rate of information being returned to our universe via Hawking radiation (the untangling of causal histories) becomes greater than the rate of information being imprinted by new infalling matter. The entropy of the radiation $S(\rho_{rad})$ must then decrease, ensuring the total process is unitary.

    $$S(\rho_{rad}) = -\text{Tr}(\rho_{rad} \log \rho_{rad})$$

1.2. Decomposing Black Hole Mass: Local vs. Multiversal Components

Problem Statement: An observer at infinity measures the total mass-energy of a black hole ($M_{ADM}$). In the GSC model, this mass should have two distinct origins: (1) the mass-energy of local matter currently undergoing informational transfer, and (2) the effective mass-energy of information already encoded into the multiverse structure, which is felt gravitationally as an entropic force.

The GSC Model Approach: We can decompose the total mass into a local component ($M_{local}$) and a multiversal component ($M_{multi}$) by relating mass directly to the informational entropy of the system.

Proposed Derivation Steps:

  1. The Mass-Information Equivalence Postulate:

    We postulate that mass-energy is a manifestation of information. The total mass $M$ of a system is proportional to its total informational content (entropy) $S$. Let $\alpha$ be a fundamental constant linking information to mass, with units of mass/entropy.

    $$M = \alpha S$$
  2. Decomposition of Mass:

    The total mass of the black hole, $M_{total}$, can be decomposed into two parts based on the state of the information within it:

    • $M_{local}$: The mass from information that is still local and has not been fully imprinted into the multiverse. This is proportional to $S_{local}$.
    • $M_{multi}$: The effective mass from information that is fully encoded in the multiverse entanglement structure. This is proportional to $S_{multi}$.

    The total mass is the sum of these components:

    $$M_{total} = M_{local} + M_{multi} = \alpha S_{local} + \alpha S_{multi}$$
  3. Evolution of Mass Components:

    The evolution of the black hole's mass composition can now be described. For a **young, accreting black hole**, it is actively consuming local matter, so $S_{local}$ is large, and $M_{local}$ is a significant fraction of the total mass. For an **old, isolated black hole**, most of its initial information has been fully imprinted. Therefore, $S_{local} \to 0$ and its mass is almost entirely multiversal: $M_{total} \approx M_{multi}$.

  4. Testable Prediction:

    This decomposition could have observational consequences. The gravity generated by $M_{local}$ should behave like standard stress-energy, while the gravity from $M_{multi}$ is an entropic force. This could lead to subtle deviations from General Relativity in the spacetime near a black hole, depending on its age and accretion history. These deviations might be detectable in the gravitational wave signals from binary black hole mergers, particularly in the ringdown phase.

2. Cosmological Puzzles

Here we will explore the GSC model's potential to explain the origin and evolution of the universe.

2.1. Cosmic Inflation without an Inflaton

  • Problem: Explain the rapid exponential expansion of the early universe.
  • GSC Approach: Model inflation as an informational phase transition.
  • [Start derivation here...]

2.2. Baryon Asymmetry

  • Problem: Explain the observed dominance of matter over antimatter.
  • GSC Approach: Investigate asymmetries in the GSC's fundamental "computational rules."
  • [Start derivation here...]

3. Quantum Foundations

This section will focus on deriving the foundational principles of quantum mechanics itself from the GSC model.

3.1. The Measurement Problem & The Born Rule

  • Problem: Explain why quantum systems "collapse" into a single state upon measurement, with probabilities given by $|\psi|^2$.
  • GSC Approach: Model measurement as an irreversible entanglement with a complex macroscopic system.
  • [Start derivation here...]