Theory of Reality · measured scale experiment

Dye, water & fields in 3D + time

Follow a 3D dyed vortex through water. Rotate the volume to see sunlight reflect from water, compare a detailed 2D slice, and test electric and magnetic responses over time.

3D VOLUME · 10 × 10 × 10 mmDrag to orbit · pinch to zoom · tilt to see sunlight on the surface

t = 0.00 s

Orbit · pinch / scroll to zoom · sun glint follows viewing angle

Dye retained100.0%

Peak water speed0.0 mm/s

Vortex circulation0.0 mm²/s

Drop count0

Sunlight on water

Sun elevation 32°Sun direction 217°Sun brightness 1.0×Surface micro-ripples 0.06

Flat surface R at view angle—

Flat surface transmission—

The bright sun image on the 3D water surface follows your viewing angle. It uses unpolarized Fresnel reflectance and Snell refraction into water (visible-light index n ≈ 1.333). The micro-ripple slider perturbs reflected rays; transmitted rays refract through the mean flat surface. It does not solve water-surface waves. The percentages below are for a flat surface; local ripples vary the angle. Sun intensity is displayed with camera-like tone mapping.

RGB light reference

650 nm · 461 THz530 nm · 566 THz450 nm · 666 THz

The diagram below uses a fixed 22° incidence angle as a separate RGB reference; it does not track the sun sliders. It illustrates Fresnel reflection and Beer–Lambert transmission through the center of the active dye field. Wave motion is slowed, wavelength ratios are kept. The water image is a dye concentration map, not atom-by-atom light scattering. The field controls couple to the 3D mode; the 2D comparison uses its earlier hydrodynamic solver. The RGB absorption coefficients are illustrative; no ink spectrum has been supplied.

Electromagnetic inputs

Electric field E100 V/mMagnetic field B0.05 TMagnetic gradient dB/dx0 T/mConductivity σ0.055 µS/cmElectric oscillation (not light)0 Hz (DC)

Current density—

|J × B|—

Polarization P—

Magnetization M—

Diamagnetic |f|—

Heating rate—

Flow / raw field accel—

Electrodes supply E along x; B points along z. Uniform forces are balanced by pressure in this closed water volume. The acceleration ratio compares raw force scales, before pressure balance. A field gradient with electric current can create flow. In homogeneous water a diamagnetic gradient force shifts pressure; its raw value below is not the remaining flow force. Conductivity changes with dissolved ions; the default is ultrapure water at 25 °C. Material values: εr ≈ 78.5 and χ ≈ −9 × 10⁻⁶ (SI).

Set up the drop

Drop diameter 3.0 mmFall height 30 mmRetained circulation 6.0%Density excess 0.00%Playback rate 1.00×

Starts just after coalescence. Impact is encoded as initial dye and a vortex ring in 3D or a vortex pair in the 2D slice. The retained circulation slider sets an uncalibrated fraction of impact speed × drop diameter. It determines how fast the curls develop; it is not an experimental fit. Playback rate is a target; the simulation clock can lag on slower devices.

Numbers before animation

Impact speed—

Reynolds / Weber—

Ohnesorge—

Schmidt—

Molecular diffusion in 10 s—

Grid spacing—

At this scale, molecular diffusion alone moves dye only about 0.09 mm in 10 s. Visible curling and stirring come mostly from the moving water. Thin structures below one grid cell are numerically unresolved; their visible blur includes numerical diffusion, not just molecular diffusion.

One spacetime event

Coordinates are (ct, x, y, z). The six independent electromagnetic components belong to F_μν; magnetism is not itself another spatial axis.

Time history stores the dye centroid and fields. If you suspect another dimension, a measurable prediction must differ from this spacetime model.

What is solved

∇·u = 0
ρ(∂t u + u·∇u) = −∇p + ρν∇²u + f_density + J×B + χ∇(B²)/(2μ₀)
∂t c + ∇·(u c) = D∇²c
J = σ(E + u×B),   P = ε₀(εᵣ−1)E

3D mode: a 20³ staggered incompressible Navier–Stokes grid with conservative dye transport, viscosity, Boussinesq density force, and quasi-static J×B plus diamagnetic gradient force. The 2D mode retains the higher-resolution vertical section of incompressible Navier–Stokes on a staggered 80 × 120 grid, with pressure projection and water viscosity. A conservative slope-limited flux transports dye in both modes. Molecular diffusion uses D = 4.0 × 10⁻¹⁰ m²/s, a measured Rhodamine 6G proxy. The optional density excess adds downward buoyancy.

The initial circulation is Γ = retention × √(2gh) × diameter. The retention fraction is a transparent, uncalibrated closure for unresolved impact and surface tension. The fluid surface is held flat: this model does not solve a free surface, atomistic H₂O, frequency-dependent dielectric relaxation, electrode double layers, induced magnetic fields, or sub-grid turbulence. The initial 3D ring shape and circulation are uncalibrated model closures. Normal velocity is zero at the computational cell’s outer edges, modelling a water-filled cell rather than water suspended by air.

Research used to set scale and behavior: measured vortex formation and impact regimes · free-surface vortex experiment · aqueous fluorescent dye diffusivity · water properties. Differences from a particular dye, concentration, drop shape, and impact setup will change the actual plume. · IAPWS visible-light refractive index · Fresnel and Snell optics · IAPWS water permittivity · NIST ultrapure water conductivity · electromagnetic spacetime tensor · measured water diamagnetism.