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 counter 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 Continue 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 5–9 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.
What ln does, in plain words: it squashes huge ranges, so 10×, 100× and 1000× the reference density become evenly spaced steps (about 2.3, 4.6 and 6.9). That lets one dimmer switch cover densities that differ by many factors of ten.
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 CIn short: the formula for γ failed. The γ the framework chose loses to MOND, an older rival theory. When we tuned γ until it matched galaxies, the equation turned into MOND, so it added nothing new there.
The γ Parameter — the original idea, and what happened to it
C is the dial. γ is a setting on it: how early the dial starts to turn as density rises. It was meant to set how sharply the dial turns, but no γ makes this curve sharp. 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). In plain words: the formula said galaxies with fewer stars moving
together should sit further above the standard galaxy rotation relation, and the real galaxies did the reverse; the
±0.55 is the correlation between the formula's γ and how far each galaxy sits from that relation. N_corr also 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 (MOND: a 40-year-old rival idea that says gravity itself gets stronger than Newton predicts in very weak
fields, instead of adding dark matter, a proposed invisible substance that has never been directly detected and is inferred only from its gravitational pull; section E says more). So read γ = 2/√N_corr as the starting hypothesis, not as how things work.
γ in three lines, since the page meets it three times: (1) proposed γ = 2/√N_corr: failed. (2) Galaxies, with stars
as uncorrelated units, γ = 2 (the framework's own original choice): loses to MOND on real rotation curves (only just, once whole galaxies rather than
individual data points are counted). (3) γ fitted freely ≈ 0.5: this is exactly MOND's own formula, so it matches MOND
by construction. That is neither a win nor a loss; it means nothing new survives.
In everyday terms: "predicted" means the number was fixed before looking at the data; "fitted" means a knob was
turned until the curve matched. A fitted match is not evidence, and here the tuned knob simply lands on an older,
already-known theory (MOND). Matching MOND tells you the idea can reproduce MOND, not that it adds anything. MOND wrote this
shape down in 1983, so matching it after tuning adds nothing new.
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
material by material in ~1,700 chemistry sessions (a session counter, not a count of distinct 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 EA number measured in galaxies sits suspiciously close to a number from the expansion of the universe. Nobody knows why, and this framework does not explain it either.
Scale Up: Galaxies
Apply the same equation to galaxies. Stars in a galaxy are individual uncorrelated
classical particles (N_corr = 1, γ = 2: the framework's original guess, which loses to MOND, not the fitted γ ≈ 0.5; see the γ status above). The critical density ρ_crit = A × V_flat² (V_flat is the steady top speed of stars far from a galaxy's centre; A is a
fitted constant, about 0.029 in these units, not derived from anything) 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. Its value happens to match a combination
of the speed of light and the universe's expansion rate. That may be luck; nobody has derived it.
For the curious: where a₀ ≈ cH₀/(2π) comes fromVerdict first: probably a coincidence, and not evidence for this framework. Why: c and H₀ (the Hubble
constant) can only be combined into an acceleration one way, cH₀, so any formula of the form cH₀ × (a number) will
land near MOND's a₀ for some number. Here the number is 1/(2π), which nothing derives; with it the match is off by
~13%. Milgrom noticed that a₀ is close to cH₀ in 1983, so the closeness was known before this framework. See Honest Assessment.
Section FMeasurement = MRH crossing (an interpretation; same predictions as standard QM)
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.)
Status, in one line: an interpretation, not a failed or a winning prediction. Read as "looking doesn't disturb
anything", it is contradicted by experiment (the quantum Zeno effect: watching a system very frequently can freeze it in
place, a real measured effect, Itano et al. 1990); read as "measuring resets the system", it
gives exactly standard quantum mechanics. It would become testable only if the framework named a scan period, and
it hasn't.
Section GHonest about limits
Where It Fails
Melting points: 53% error. Critical exponents (the numbers that describe how sharply a property changes
near a phase transition): listed as 2× off, though the function as written has none, so that entry records a failed
framing rather than a measured number. Superconductor Tc (the temperature below which a material superconducts):
6.5× wrong (607 K predicted for YBCO, 93 K actual).
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.