Time-Gel · Lab · Protocol simulator

Ice Clock Simulator Model

What would a clock inside freezing supercooled water show if Time-Gel were true? Move the parameters and compare the freezing cell (A) with its two controls: heat-matched (B1) and entropy-matched, no crystal (B2). Companion to Information Looking for Its Owner. Every number here comes from the model, not from a measurement.

01 // Reading

Rate (primary): clock slows only while entropy is produced. Stock (rival): clock stays slow while ice exists.

02 // Water and cycle

Supercooling

Freezing time Thin layer: about a minute.

Ice held frozen

Melting time

Melt bath above 0 °C

Share of entropy made inside the cell The rest is made in the wall and bath, where the clock cannot see it. Open

03 // Theory and clock

ρ_crit (rate) Atomic-clock bound today: ≳ 10³³ s⁻¹m⁻³.

ρ_crit,rec (stock) No bound exists yet.

Clock instability ε 10⁻⁵: internal gamma source (decay constant). 10⁻¹⁸: optical clock (cannot sit inside the cell).

Number of cycles

04 // Result

One cycle: frozen fraction and clock lag

Lag of the cell's clock behind an outside clock, accumulated over one cycle. Each curve is scaled to its own maximum so the shapes can be compared; true sizes are in the cards above.

Whole run: A − B2 difference against clock noise

The decisive comparison is A − B2: same entropy, crystal versus no crystal. Under the rate reading it stays at zero; only the stock reading lifts it. A curve outside the grey band would be detectable.

05 // Assumptions

Flow law, weak-field limit: dτ/dt ≈ 1 − ρ_I/(2ρ_crit); gravity cancels between cells. Model
Rate reading: ρ_I = σ/k_B. Entropy generated per m³ of supercooled water frozen: ρL·ΔT/(T_mT). Melting from a bath at +ΔT_m: ρL·ΔT_m/(T_m(T_m+ΔT_m)).
B1 heater dumps the same heat as A into the bath during freezing: entropy Q/T, about T_m/ΔT times A. B2 heater is set to A's entropy over the whole cycle, melting included.
Stock reading: ρ_rec = Lρ_ice/(k_BT ln 2) times the frozen fraction f(t).
Recalescence: a fraction c_pΔT/L freezes within 10 ms; the rest grows linearly over the freezing time.
Detection: the mean fractional rate difference over the run must exceed ε. Achievable bound: ρ_crit > (lag per cycle)·ρ_crit/(ε·cycle time).
Order-of-magnitude model. It shows what the protocol can and cannot see; it is not a result. Interpretation