A guided walk through the core ideas. No prerequisites needed.
Coherence is how collectively a group of things behaves. A marching band moving in lockstep: high coherence. A crowd wandering in a plaza: low coherence. Dense matter in a crystal lattice — every atom locked in step: high coherence. Sparse gas drifting between stars: low coherence. Synchronism asks whether one equation can quantify this transition across all of physics.
7 short sections on this one page, lettered A–G — about 10 minutes in all. (The “Step 2 of 6” above is this page's place in the Beginner path; the letters are only for the sections inside this page. The sections appear one at a time: use the Next button below each section, or the progress bar, to move between them.)
New here? This ~10-minute intro is the fastest path to understanding the framework. Want a more structured journey? Learning Paths offers Beginner / Intermediate / Advanced routes with 6–8 steps each.
Section Aρ (presence)
Start with Presence
A single electron floating in a vacuum — almost nothing around it to interact with. Now: the core of a neutron star, where matter is packed 10¹⁴× denser than lead and everything is interacting with everything. That difference is what Synchronism calls presence (ρ). At its simplest, presence is density — how much stuff is packed into a given space. But which stuff counts? Only the neighbors close enough to actually influence the system — everything beyond some horizon might as well not exist. Synchronism calls that horizon the MRH (Markov Relevancy Horizon — “Markov” is the mathematician’s word for “only the current neighbors matter, not the history”): the bubble of nearest neighbors that matter. Everything outside the bubble can be ignored. (The formal version, if you want it: the minimal set of degrees of freedom whose transitions materially influence coherence — same idea, stated precisely.) A single atom doesn’t “feel” the Andromeda galaxy — it only responds to what’s immediately around it; Andromeda is outside its MRH. See the Glossary for the full definition. Synchronism starts here: presence, measured within that bubble, is the universal input.
Section BC = 0 (sparse) → C = 1 (collective)
The Coherence Function
Feed that density into: C(ρ) = tanh(γ · ln(ρ/ρ_crit + 1)).
What tanh does, in plain words: it is an S-shaped curve, like a dimmer switch — flat at first, then rising,
then levelling off near 1. Feed it a small number and it outputs nearly 0; feed it a large number and it outputs nearly 1, with no abrupt jump.
Out comes a number between 0 and 1. Zero means sparse and independent — few neighbors, each element acting on its own.
One means dense and collective — everything interacting, behavior dominated by the crowd.
(Note: in this framework C measures density-driven collective ordering, not quantum phase coherence — quantum systems like superconductors land at low C.)
Try it: Coherence Explorer — drag two sliders and watch C(ρ) change in real time. Best hands-on intro on the site.
Expert note (physicist terminology)BEC/superconductors land at low γ (≈6×10⁻⁴ for BCS) because large Ncorr sits in the denominator: γ = 2/√Ncorr. A very small γ means a nearly flat S-curve — so C stays close to 0 at any physically accessible density, despite these systems being quantum-coherent. This is a documented inversion in the framework (see γ Calculator caveats): the formula assigns the flattest curves to the most-correlated systems, opposite to what real phase transitions do.
Section COriginal idea: γ = 2/√N_corr — failed where tested
The γ Parameter — the original idea, and what happened to it
γ sets how sharply the dial turns. The original idea was γ = 2/√N_corr, where N_corr is how many
particles move together as a unit: one electron alone gives γ = 2, a crystal of 10²⁴ atoms gives γ ≈ 10⁻¹².
That formula did not survive testing. Where it made a checkable prediction, the sign came out backwards
(predicted correlation +0.55, measured −0.55), and N_corr had to be defined differently in every field to make
it work. When γ is simply fitted to galaxy data it comes out near 0.5 — the value at which the equation turns
into MOND's. So read γ = 2/√N_corr as the starting hypothesis, not as how things work.
Try it: γ Calculator — click any preset (Ideal Gas, Water, BEC) to see γ and its regime.
Section Dγ ≈ 1: a crossover band where fitted values cluster (Reparametrization)
Where γ ≈ 1
Roughly the quantum-classical boundary: a crossover zone where the dial turns
gradually, not a phase transition (tanh is smooth, so nothing snaps here). When γ was fitted
phenomenon by phenomenon across 1,703 chemical phenomena, most fitted values landed near this band.
Those γ values were fitted, not predicted — the formula above failed — so the clustering is an
observation about where fits landed, with a template-bias caveat and no mechanism. Neither this
placement nor the old consciousness-threshold placement follows from the equation.
Section Ea₀ ≈ cH₀/(2π): a coincidence, not a derivation
Scale Up: Galaxies
Apply the same equation to galaxies. Stars in a galaxy are individual uncorrelated
classical particles (N_corr = 1, γ = 2). The critical density ρ_crit = A × V_flat² connects
to rotation velocity. MOND — Modified Newtonian Dynamics, the long-standing rival proposal that gravity itself changes below a threshold acceleration, rather than invoking dark matter — has an acceleration constant a₀, and a₀ = cH₀/(2π) falls out of the same constants —
but this is a dimensional coincidence (the only scale buildable from c and H₀), not a first-principles
derivation; the 2π is unexplained and the match is off by ~13%. See Honest Assessment.
In plain words: the number happens to match a combination of the speed of light (c) and the universe's
expansion rate (H₀, the Hubble constant). That may be luck; nobody has derived it.
Section FMeasurement = MRH crossing
Scale Down: Quantum Measurement
What if "wave function collapse" isn't a special event? What if it's just a system
crossing the MRH — the Markov Relevancy Horizon — where correlations decay below the noise floor?
No observer needed. No consciousness required. Just a boundary crossing.
("Noise floor", in everyday terms: a whisper in a loud room is still there, but nobody can pick it out
from the background. The proposal is that a quantum correlation fades the same way — it is not destroyed,
it just drops below what the surroundings can tell apart from noise.)
(See "Two Reframes" for the CRT analogy that makes this intuitive.)
Section GHonest about limits
Where It Fails
Melting points: 53% error. Critical exponents: 2× off. Superconductor Tc: 6.5× wrong.
Not every application of C(ρ) works. The function captures density→coherence well,
but can't replace domain-specific physics where crystal structure, spin-orbit coupling,
or multi-body effects dominate.