This aligns with and extends the logic of It-from-Bit (Wheeler), the Holographic Principle ('t Hooft, Susskind), and qubit-geometrization (Bao, Preskill, etc.), but we go further to propose:
"Reality is emergent from informational transitions."
2. Formal Definition
Let I\mathcal{I} be the fundamental informational state space of the universe. A single unit of information is a binary choice (bit), but in the quantum context, it generalizes to a qubit. We define cosmic information as follows:
Definition:
Let \Sigma be a topological manifold representing an informational layer. Then the information content I()\mathcal{I}(\Sigma) is the minimum number of distinguishable quantum states required to fully specify the geometry and physical field configurations on \Sigma, modulo gauge redundancy.
Mathematically:
I()=log2dim(Heff())\mathcal{I}(\Sigma) = \log_2 \, \dim \left( \mathcal{H}_{\text{eff}}(\Sigma) \right)
Where:
Heff\mathcal{H}_{\text{eff}} is the effective Hilbert space of physical (non-gauge) states encoding the geometry + matter field configuration.
The logarithm base 2 reflects the bit-unit of informational measure.
If geometry is entangled with quantum states, this becomes a quantum conditional entropy:
Icond=S(geometrymatter)\mathcal{I}_{\text{cond}} = S(\rho_{\text{geometry}} | \rho_{\text{matter}})
3. Measurement of Information in Physical Systems
