Formal Derivation of Emergent Spacetime to the Bruhat-Tits Tree

In the paper's words

The fundamental incompatibility between the continuous spacetime of general relativity and the background-dependent time of quantum mechanics suggests that time is not a fundamental constituent of reality. This paper addresses the ontological crisis of time by formally deriving macroscopic spacetime and the invariant speed of light directly from the discrete properties of the Bruhat-Tits tree. Our methodology maps the timeless adjacency operator of this tree to a dynamic time-evolution operator using the Page-Wootters mechanism within a rigged Hilbert space, validated through computational simulations of graph excitations.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Tensor networks placed on the tree accurately reproduce holographic entanglement entropy (Heydeman et al., 2016).

   from 1.5 Literature

2. This architecture perfectly reproduces the Ryu-Takayanagi formula for entanglement entropy (Hung et al., 2019).

   from 2.5 Holographic Tensor

How it is done

1. This paper addresses the ontological crisis of time by formally deriving macroscopic spacetime and the invariant speed of light directly from the discrete properties of the Bruhat-Tits tree.

   from Addressing

2. We must formally map the timeless graph to this epistemic parameter using a specific discrete model.

   from 1.3 The Epistemic/Mental

3. Recent breakthroughs have formally formulated the p-adic AdS/CFT correspondence (Gubser et al., 2017).

   from 1.5 Literature

4. Instead, its dimensionless upper bound is a derived property of the underlying combinatorial structure of the Bruhat-Tits tree, while its physical dimension emerges strictly from the observer’s thermodynamic coarse-graining.

   from 1.7 Research Questions

What would falsify it

1. To recover observable physics, observers must define an internal, epistemic clock.

   from 2.6 The

2. The flow defines the epistemic boundary between the fundamental graph and the observable universe.

   from 3.3

3. Signatures of Discrete Cutoffs The breakdown of Lorentz invariance should be observable.

   from 6.6 Observational

Where the claim stops

1. It does not yet account for quantum fluctuations of the graph itself.

   from 7.6 Limitations of the Current

2. Quantum mechanics assumes a fixed, external background time parameter to govern unitary evolution.

   from 1.1 The Crisis of Time in

3. However, these models primarily operate in Euclidean signature and lack dynamic time.

   from 1.5 Literature

Where to read

1. Addressing259 words · 1 min
2. 1.0 Introduction699 words · 3 min
3. 2.0 Theoretical627 words · 3 min
4. 3.0639 words · 3 min
5. 4.0 Formal Results611 words · 3 min
6. 5.0623 words · 3 min
7. 6.0 Discussion:580 words · 3 min
8. 7.0 Conclusion510 words · 2 min
9. Appendices232 words · 1 min