Why Physics Theories Cannot All Be Linked Together

In the paper's words

Physics is fragmented by persistent bifurcations—general relativity versus quantum mechanics, continuum versus discrete descriptions, the Heisenberg cut, and the status of the observer. These schisms impose concrete costs: collider, fusion, and quantum‑hardware programmes proceed without a shared observable that can bridge the frameworks underlying their design choices. This work asks whether a master calibration—a family of partial translation maps that composes consistently across all frameworks—can exist, and what combinatorial and error‑budget burden such a calibration imposes.

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

Numbers it reports

1. A genericity projection with independent square‑constraint success probability $p=0.9$ yields a master‑calibration success probability of $6.34\times10^{-168}$ and a maximal family size of $n_{\max}=7$ at a 1 % success threshold.

   from Abstract

2. In microwave metrology, a thru‑free multiline calibration eliminates the need for a thru standard in TRL‑type vector‑network‑analyzer calibration by using an arbitrary transmissive two‑port device plus a reflect standard; both methods yield the same normalized error terms because the eigenvalue formulation does not require a thru definition, and measurements over 1–150 GHz confirm excellent agreement [8].

   from 2. Background and Related Work

3. Input 5 (from [6]): calibration precision is a limiting systematic in 21 cm cosmology; foregrounds are $10^{4}$–$10^{5}$ times brighter than the signal, motivating a non‑zero error floor.

   from 4. Analysis

4. Uniform per‑edge error floor – a minimum translation error $\varepsilon_{\min}=10^{-2}$ is taken from the systematic limit identified in 21 cm cosmology, where foregrounds are $10^{4}$–$10^{5}$ times brighter than the signal [6].

   from Limitations

5. Error‑floor realism The per‑edge error floor $\varepsilon_{\min}=10^{-2}$ is motivated by the systematic limit identified in 21 cm cosmology, where foregrounds are $10^{4}$–$10^{5}$ times brighter than the signal [6].

   from 7. Practical Implications and Engineering Pathways

6. The European Particle Physics Strategy Update aggregates community proposals for collider projects and quantifies the scientific reach of a shared observable, reporting expected measurement precisions of about 1 % for oblique parameters and a projected $10^{12}$ $Z$ bosons at circular colliders [1].

   from 1. Introduction

How it is done

1. A three‑framework loop with edge errors $10^{-3}$, $2\times10^{-3}$, and $5\times10^{-4}$ gives a closure‑error bound of $3.4965\times10^{-3}$.

   from Abstract

2. C5 – Three‑framework closure bound $\Delta_{\gamma}\le3.4965\times10^{-3}$ for edge errors $10^{-3}$, $2\times10^{-3}$, and $5\times10^{-4}$ (Section 4, Derivation 3).

   from 1. Introduction

3. The European Particle Physics Strategy Update takes a bottom‑up approach in which the community submits proposals for near‑, mid‑ and longer‑term projects, and its precision‑physics conclusions quantify what a shared observable would buy: precise $Z$‑boson measurements at future $e^{+}e^{-}$ colliders, in particular $10^{12}$ $Z$ bosons at circular colliders, oblique parameters measured with $\sim1\%$ precision (about a factor 10 better than current precision), and a rich Higgs‑coupling programme tied to the naturalness problem [1].

   from 2. Background and Related Work

4. For composable translations $\tau_{ij}$ and $\tau_{jk}$, the composed error obeys the first‑order bound $$\varepsilon_{ij\circ jk}\le\varepsilon_{ij}+\varepsilon_{jk}+\varepsilon_{ij}\,\varepsilon_{jk}.$$ Definition 3.3 (Composition failure).

   from 3.3 Composition and closure

What would falsify it

1. A concrete falsification test follows directly from Result R3.

   from Falsifiability criteria

2. Observation of $\Delta_{\gamma}\gt 3.5\times10^{-3}$ would falsify the first‑order composition model and, by extension, the combinatorial success probability $P_{\mathrm{master}}$ derived under independence.

   from Falsifiability criteria

3. A second falsification avenue concerns the combinatorial bound on family size.

   from Falsifiability criteria

Where the claim stops

1. The analytical framework developed in Sections 4–5 quantifies three intertwined obstacles to a master‑calibration effort: (i) a combinatorial overload of square‑constraint equations relative to the number of available pairwise maps, (ii) a first‑order closure‑error budget that quickly exceeds realistic tolerances, and (iii) an exponential decay of the joint success probability under the independence assumption for constraint satisfaction.

   from 6. Discussion

2. The quantitative conclusions rest on a set of explicit assumptions: Independence of square constraints – each of the $\binom{N}{3}=3654$ independent composition constraints is assumed to succeed with probability $p=0.9$ independently of all others (Input 8).

   from Limitations

3. One‑schism‑per‑pair allocation – the pairwise‑capacity argument (Derivation 2) assumes that each of the 29 schisms must be assigned to a distinct unordered pair of the candidate $n=7$ domains.

   from Limitations

Where to read

1. Abstract226 words · 1 min
2. 1. Introduction735 words · 3 min
3. 2. Background and Related Work748 words · 3 min
4. 3. Methods462 words · 2 min
5. 4. Analysis632 words · 3 min
6. 5. Results113 words · 1 min
7. Appendix A. Divergence report21 words · 1 min
8. Appendix B. Claim attribution202 words · 1 min
9. 6. Discussion817 words · 4 min
10. 7. Practical Implications and Engineering Pathways767 words · 3 min
11. 10. Conclusion158 words · 1 min
12. Provenance and AI Involvement225 words · 1 min