DOI: 10.5281/zenodo.17726160
title: Einstein Audit for Faster‑Than‑Light Hidden Sectors (MIN): Causality Indices, Delta N_eff Guardrail, PTA Coherence & Ringdown GR Tests

description: Short description.

The Einstein Audit for Faster‑Than‑Light (FTL) Hidden Sectors is an analysis‑only toolkit that turns classic FTL thought experiments into a concrete constraint space tied to real observables. We define population‑level causality indices from the tachyon antitelephone geometry, compress the FTL sector into a universal small parameter \epsilon_{\text{FTL}}^2 = \langle(W-1)^2\rangle, and combine this with a ΔN_eff guardrail auditor, a PTA Probability of Consistency Index (PCI), and a pooled ringdown deviation parameter ε to form an “Einstein distance’’ D_E. The condition D_E \le 1 becomes a no‑free‑FTL‑lunch inequality that bounds the RMS FTL excess, paradox wedge occupancy, and any FTL channel capacity allowed by current or future cosmology and gravitational‑wave data. The pack ships templates, minimal Python runners, and a LaTeX mini‑note so others can reproduce or stress‑test the audit.

 

2.3 Long description 

 

Einstein Audit for Faster‑Than‑Light Hidden Sectors (MIN)

 

Status: testable framework / analysis‑only mini‑kit. This deposit does not claim real faster‑than‑light travel or violations of General Relativity (GR). Instead, it provides a reproducible “Einstein audit’’ that tells you how much room is left for any FTL‑like hidden sector, given cosmology and gravitational‑wave constraints.

Core idea

Tachyon antitelephone thought experiments show how superluminal signaling can generate closed causal loops. Here we turn that kinematic geometry into population‑level causality indices and connect them directly to ΔN_eff, pulsar timing arrays (PTAs), and black‑hole ringdowns.

 





Causality layer.

We define a paradox strength P(\beta,W) for each pair of relative speed \beta=v/c and FTL factor W=w/c, and identify a paradox wedge in the (\beta,W) plane where closed loops are possible. From a distribution \rho(\beta,W) over the hidden‑sector kinematics we build:

 





Q[\rho]: wedge occupancy (probability that a random configuration lies in the paradox wedge),




J[\rho]: mean‑square paradox severity,




C[\rho]=\sqrt{J/Q}: conditional RMS paradox strength. 

In the near‑light regime W=1+\delta with \delta\ll 1, all of these collapse to a single universal parameter \epsilon_{\text{FTL}}^2=\langle\delta^2\rangle: Q\simeq\frac{1}{2}\epsilon_{\text{FTL}}^2, J\simeq\frac{1}{6}\epsilon_{\text{FTL}}^2, and C\to 1/\sqrt{3}.



 




ΔN_eff guardrail.

The hidden sector’s stochastic GW background is modeled as a smooth broken power law (SBPL) \Omega_{\rm gw}(f). A runnable ΔN_eff auditor (template JSON + Python snippet) maps the SBPL parameters into an extra‑radiation contribution

\Delta N_{\rm eff} = \frac{8}{7}\!\left(\frac{11}{4}\right)^{4/3}\! \int \Omega_{\rm gw}(f)\,d\ln f

and reports Ω_gw at 3 mHz and 25 Hz. We define an energy fraction \varepsilon_{\rm energy} = \Delta N_{\rm eff}/\Delta N_{\rm eff}^{\max} with a default guardrail \Delta N_{\rm eff}^{\max}=0.3.




PTA and ringdown gates.

Cross‑PTA agreement enters through a Probability of Consistency Index (PCI) computed from NG15/EPTA/PPTA “knee’’ posterior draws under a common prior (one‑column CSV templates included). Ringdown deviations from GR are summarized by a pooled parameter \varepsilon\pm\sigma_\varepsilon derived from per‑event QNM deviation posteriors (template CSV included).




Einstein distance and no‑free‑FTL inequality.

The pack combines these ingredients into a three‑component Einstein constraint vector

\vec X = \Big(S/S_0,\ 1-\mathrm{PCI},\ \varepsilon/\sigma_\varepsilon\Big),

where S=\varepsilon_{\rm energy}J is the causality–cosmology action and S_0 is a reference scale (default S_0=1/6). The Einstein distance is

D_E = \|\vec X\|.

The condition D_E\le 1 defines a unit “Einstein ball’’ of models that are jointly compatible with the ΔN_eff guardrail, PTA coherence, and GR‑consistent ringdowns. In the small‑excess limit this yields a no‑free‑FTL‑lunch inequality for the universal parameter,

\epsilon_{\text{FTL}}^2 \le \frac{\sqrt{1-(1-\mathrm{PCI})^2-(\varepsilon/\sigma_\varepsilon)^2}}{\varepsilon_{\rm energy}},

which directly bounds the RMS FTL excess, wedge occupancy Q\simeq\frac{1}{2}\epsilon_{\text{FTL}}^2, and paradox severity J\simeq\frac{1}{6}\epsilon_{\text{FTL}}^2.




Information‑capacity bound.

A compact Monte Carlo pack (capacity CSV + notes) provides a toy FTL channel whose capacity obeys C(\varepsilon)\sim \varepsilon\log(1/\varepsilon) as the wedge occupancy \varepsilon\to0. Given the Einstein‑limited occupancy Q_{\max}, the toolkit returns an “Einstein capacity bound’’ C_{\rm FTL}^{\max} on the per‑use information capacity of any FTL‑like hidden sector that remains inside the Einstein ball.



What this is and is not

This is an analysis‑only, pre‑theory framework. It does not claim evidence for FTL signals or violations of General Relativity. Instead, it offers a concrete way to ask: if some exotic hidden sector allowed FTL‑like signaling, how large could its RMS excess \epsilon_{\text{FTL}} and channel capacity be without conflicting with ΔN_eff, PTA, and ringdown constraints? As real PTA posteriors, ΔN_eff limits, and ringdown tests improve, the Einstein ball shrinks and the allowed region in (\varepsilon_{\rm energy}, \epsilon_{\text{FTL}}) space becomes correspondingly smaller.

Files in this MIN pack

This MIN version is intentionally minimal and analysis‑only—no real PTA or ringdown data are included. It ships:





\texttt{FTL_Chronon_Toy_Framework.tex}: LaTeX mini‑note with the full formalism and inequalities.




\texttt{DeltaNeff_Audit_TEMPLATE_MIN_…json} + \texttt{DeltaNeff_Audit_RUN_MIN_…py}: SBPL → ΔN_eff guardrail auditor and multiband Ω_gw checkpoints.




\texttt{NG15/EPTA/PPTA_knee_COMMON_PRIOR_TEMPLATE_MIN_…csv} + \texttt{pci_from_knee_samples_MIN_…py}: PTA PCI template and demo PCI runner.




\texttt{ringdown_with_errors_TEMPLATE_MIN_…csv}: ringdown ε pooling template. 




\texttt{FTL_Thought_Experiment_Pack/}: core antitelephone formulas, wedge threshold CSVs, and worldline diagrams. 




\texttt{capacity_bound_vs_epsilon.csv} + \texttt{MONTE_CARLO_NOTES.txt}: information‑capacity bound curve and derivation notes.




\texttt{README_Last_Mile_MIN_…md}: step‑by‑step instructions for running the audit and interpreting the Einstein distance.



Researchers can drop in real PTA knee posterior CSVs and ringdown ε estimates, run the provided scripts, and obtain concrete bounds on \epsilon_{\text{FTL}}, Q_{\max}, J_{\max}, and C_{\rm FTL}^{\max} under their chosen ΔN_eff guardrail and Einstein‑distance threshold.
description: In More Basic Terms

This project starts from a simple science‑fiction question: what if something in the Universe could send signals faster than light? According to Einstein’s relativity, that kind of “FTL” signaling would usually create time‑loop paradoxes — situations where a message arrives before it is sent. That is why physicists normally say FTL is impossible.

Instead of trying to build a warp drive, this work does something different: it turns that thought experiment into a reality‑check tool. We imagine a hidden sector of the Universe that might have FTL‑like behaviour, and we ask a very strict question: how strong could that sector be, and how fast could it be, without already contradicting what we see in cosmology and gravitational‑wave data?

The toolkit does this in three steps. First, it measures how badly an FTL sector would damage cause‑and‑effect — how often time‑loop paradoxes would occur, and how strong they would be on average. Second, it connects that “causality damage” to the energy the sector would add to the early Universe, which shows up as extra radiation (the famous quantity called Delta N_eff) and as a faint background of gravitational waves. Third, it folds in two more powerful tests from astronomy: how consistent different pulsar‑timing experiments are with each other, and how closely black‑hole ringdowns agree with Einstein’s predictions.

All of this information is combined into a single score called the Einstein distance. If the distance is small, the model behaves very much like ordinary Einstein gravity; if the distance is large, the model is in strong conflict with what we observe. From this, the work derives a simple “no free FTL lunch” rule: you cannot crank FTL speeds up arbitrarily without either burning too much energy in the early Universe or spoiling the excellent agreement of pulsar timing and black‑hole observations with Einstein’s theory.

This is not evidence that FTL really exists, and it does not claim that Einstein has been proven wrong. What it does is give researchers a new, quantitative ruler for judging wild FTL ideas against real data. Instead of saying “FTL is fantasy” or “FTL would change everything” in vague terms, this framework says: if an FTL‑like hidden sector exists, here is exactly how big it could be, how often it could produce paradox‑causing configurations, and how much information it could possibly carry, while still passing today’s tests.

The potential impact is long‑term. As cosmological measurements, pulsar timing arrays, and black‑hole observations become more precise, the allowed room for any FTL‑like sector will shrink. If future data remain perfectly Einstein‑like, this tool will help show just how strongly FTL scenarios are ruled out. If, on the other hand, future data reveal clear and reproducible anomalies, this same tool could help decide whether they really look like an FTL‑type signal or something more ordinary. In that sense, the work is part of the “infrastructure” for any future revolution: it turns faster‑than‑light speculation into something that can be audited, bounded, and eventually confirmed or excluded using the sky itself.
description: Press / Public Summary

Can faster‑than‑light messages exist without breaking the Universe?

Einstein’s theory tells us that nothing can send information faster than light. If you try, you usually get a time‑travel paradox: a message that arrives before it is sent. People often stop there and say “so FTL is impossible” — but very few works try to make this argument precise and test it directly against what we see in the sky.

This project doesn’t claim to have found faster‑than‑light signals. Instead, it builds a kind of audit tool for any future FTL‑like idea. It starts from the classic Einstein‑style thought experiments, where super‑fast signals create closed time loops, and turns them into hard numbers:

– how often would paradox‑causing configurations happen in a hypothetical FTL sector?

– how “strong” would those causality violations be on average?

We then connect that “causality damage” to the early Universe’s energy budget and to the faint hum of gravitational waves that present and future observatories are trying to measure.

The result is a single score called the Einstein distance. If the Einstein distance is small, the hidden sector behaves almost perfectly like standard Einstein gravity. If it is large, the model collides with what we already know from cosmology, pulsar timing arrays, and black‑hole “ringdown” signals after mergers. From this we derive a simple “no free faster‑than‑light lunch” rule: you cannot crank up FTL speeds, or use FTL to send lots of information, without paying a visible price in the early‑Universe radiation content or in precision gravitational‑wave tests.

In practical terms, this framework moves FTL from pure science‑fiction into something the cosmos can rule on. Today, the available data already limit how big and how energetic any FTL‑like hidden sector could be. Tomorrow, as measurements of the cosmic radiation budget, pulsar timing, and black‑hole spectroscopy sharpen, the allowed room will shrink even more. If the data continue to agree with Einstein, this tool will help show that FTL‑type sectors are essentially squeezed out. If, however, future observations reveal clear, reproducible deviations, the same tool will help decide whether they look like genuine FTL‑style effects or something more conventional.

The potential impact is conceptual rather than technological. We are not announcing warp drives or time machines. What we are doing is changing the question: instead of “Is faster‑than‑light travel possible?” we ask “Exactly how much faster‑than‑light behaviour is still compatible with everything we know about the Universe?” That shift — from speculation to a precise, testable bound — is what could slowly change textbooks and the narrative about FTL: from a simple “never” to a tightly quantified “only this much, if at all, and here is how we would know.”



 





“We’re not claiming to have found faster‑than‑light signals — we’re providing the first systematic way to audit any such claim against the entire Universe.”




“Our Einstein Audit turns a science‑fiction idea into a number you can compare to real cosmology and gravitational‑wave data.”




“If the cosmos stays perfectly Einstein‑like, this tool will show just how little room is left for any hidden faster‑than‑light sector.”