Quasiparticles as Rational Functions: Extending ODR to Condensed Matter

In the paper's words

The Ontological Distribution of Reality (ODR) framework identifies a particle with its Compton count N_C = m/m_P ∈ Q^+, a dimensionless rational number whose prime factorization assigns it a fixed vertex on the Bruhat–Tits tree. This paper extends that framework to address a natural objection: what of quasiparticles — phonons, magnons, Cooper pairs, and dressed electrons — whose effective mass depends on the host material? We argue that a quasiparticle is not an invariant vertex but a context-dependent edge traversal: a rational function N_C^*(α) = f(N_C^bare, N_C^lattice, dots) of the background Compton counts.

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

Numbers it reports

1. Its "frequency" is a statistical average (the Wien peak in frequency is approximately 160 GHz at 2.725 K), not a sharp eigenfrequency [established].

   from 4.2 Frequency Stability

2. This prediction has held for the ~90 years since Landau's Fermi liquid theory, and it is the paper's central claim.

   from 7. Conclusion

3. In the ODR framework, a particle is a persistent ratio — a combinatorial coordinate on the BT tree, stripped of spatial extension, existing only as a prime-factorized relationship to the Planck scale [speculative — ODR v3.0].

   from 3.3 ODR / Bruhat–Tits Tree: Invariant Rational Number

4. The electron is not a "thing" that has mass $m_e$; it is the ratio $N_C \approx 4.185 \times 10^{-23}$.

   from 3.3 ODR / Bruhat–Tits Tree: Invariant Rational Number

How it is done

1. The distinction is: QFT renormalization: The bare mass is a UV-divergent parameter; the dressed (physical) mass is what we measure.

   from 5.4 Distinction from Bare-Dressed Renormalization

2. Bruhat–Tits Theory: A New Approach .

   from Bibliography

What would falsify it

1. The characterization of quasiparticles as non-invariant rational functions would be disconfirmed if: A quasiparticle were found whose effective mass $m^*$ is independent of the host material, temperature, and external fields — i.e., if $m^*$ were a universal constant.

   from 5.6 Falsifiability

2. We exemine three test cases: electron effective mass in semiconductors, phonon dispersion, and the CMB as a thermodynamic ensemble, and provide falsifiability conditions for the core claim.

   from Abstract

3. Section 5 formalizes the quasiparticle as a rational function and provides falsifiability conditions.

   from 1. Introduction

Where the claim stops

1. For the electron, the cyclic Compton frequency is approximately $1.236 \times 10^{20}$ Hz.

   from 2.1 Quantum Field Theory: Intrinsic Oscillation

2. However, this is understood in modern QFT as an interference artifact between positive- and negative-energy solutions that vanishes under second quantization — it is not a physical oscillation of the particle [established — standard QFT interpretation].

   from 2.1 Quantum Field Theory: Intrinsic Oscillation

3. They behave mathematically like elementary particles — carrying momentum, spin, and obeying quantum statistics — but are emergent: they do not exist outside the bulk material.

   from 3.2 Condensed Matter: Quasiparticle as Emergent Excitation

Where to read

1. Abstract158 words · 1 min
2. 1. Introduction255 words · 1 min
3. 2. The Compton Frequency Across Disciplines262 words · 1 min
4. 3. What Is a Particle? Three Frameworks271 words · 1 min
5. 4. Particle vs. CMB: A Question of Ontological Priority312 words · 1 min
6. 5. Quasiparticles in the ODR Framework645 words · 3 min
7. 6. Discussion239 words · 1 min
8. 7. Conclusion133 words · 1 min
9. Declarations61 words · 1 min