Experiment · Brownian motion · Controlled comparison
A smaller spread. But how much smaller?
Double the particle radius without changing the liquid, temperature, observation time or random draws. Then distinguish what you changed from what changed as a consequence.
The worked comparison uses 290.15 K, viscosity 1.35 mPa·s, and radii 0.5 and 1 micrometre, with explicitly modern SI constants. It is a synthetic model calculation, not historical measurements.
BM-01 · One controlled variation
Change one thing. Keep the question clear.
Static worked comparison
Same seed (common random numbers): isolates the effect of the change; these are not independent trials. The same recording grid, tracer count, selected coordinate and model are retained. A physical setup change creates a new run; a measurement change reads the existing recording.
Starting is explicit. It reconstructs the pinned baseline in a worker before enabling changes. Pinning a new baseline accepts the current completed setup as the starting point for your next question.
Static worked comparison, calculated when this site was built.
What was held fixed?
| Input | Unit | Baseline | Variant | Role |
|---|---|---|---|---|
| Temperature | K | 290.15 | 290.15 | Held fixed (locked) |
| Viscosity | mPa·s | 1.35 | 1.35 | Held fixed (locked) |
| Particle radius | μm | 0.5 | 1 | Physically changed |
| Trial seed | — | 1905 | 1905 | Held fixed (locked) |
| Tracer count | — | 400 | 400 | Held fixed (locked) |
| Recording resolution | s | 0.02 | 0.02 | Held fixed (locked) |
| Recording length | s | 10 | 10 | Held fixed (locked) |
| Observation interval | s | 1 | 1 | Held fixed (locked) |
| Selected dimension | — | 1 | 1 | Held fixed (locked) |
| Selected axis | — | 0 | 0 | Held fixed (locked) |
| Statistic | — | rms | rms | Held fixed (locked) |
What changed as a consequence?
| Quantity | Unit | Baseline | Variant | Ratio | Difference |
|---|---|---|---|---|---|
| Model diffusion coefficient | μm²/s | 0.31485 | 0.15742 | 0.5 | -0.15742 |
| Model coordinate RMS displacement | μm | 0.79353 | 0.56111 | 0.70711 | -0.23242 |
| Sample coordinate RMS displacement | μm | 0.84428 | 0.59699 | 0.70711 | -0.24728 |
| Sample signed mean | μm | 0.0025034 | 0.0017702 | 0.70711 | -0.00073323 |
| Sample coordinate mean square | μm² | 0.7128 | 0.3564 | 0.5 | -0.3564 |
| Model interval-dependent apparent speed | μm/s | 0.79353 | 0.56111 | 0.70711 | -0.23242 |
Inspect the two accepted identities
Baseline
Instance: comparison-_R_15fiv5uiv5b_; run: comparison-_R_15fiv5uiv5b_/run/1; snapshot: 1; accepted input revision: 1.
Model: bm01-host-preview-v1; constants: modern-si-2019; stream: philox-box-muller-host-v1; allocation: bm-01.latent.v1; executable: source:sha256:06f140ad57b373415f0056e72c0a61cee543139245eb0f242333675672ccd7b2.
Host calculation; no WASM artifact is claimed.
Variant
Instance: comparison-_R_15fiv5uiv5b_-worked-variant; run: comparison-_R_15fiv5uiv5b_-worked-variant/run/1; snapshot: 1; accepted input revision: 1.
Model: bm01-host-preview-v1; constants: modern-si-2019; stream: philox-box-muller-host-v1; allocation: bm-01.latent.v1; executable: source:sha256:06f140ad57b373415f0056e72c0a61cee543139245eb0f242333675672ccd7b2.
Host calculation; no WASM artifact is claimed.
Read the generated comparison statement
Physically changed: Particle radius from 0.5 μm to 1 μm. Held fixed: Temperature 290.15 K, Viscosity 1.35 mPa·s, Trial seed 1905, Tracer count 400, Recording resolution 0.02 s, Recording length 10 s, Observation interval 1 s, Selected dimension 1, Selected axis 0, Statistic rms. Re-described: nothing. Changed as a consequence (variant / baseline readouts): Model diffusion coefficient (ratio 0.5); Model coordinate RMS displacement (ratio 0.70711); Sample coordinate RMS displacement (ratio 0.70711); Sample signed mean (ratio 0.70711); Sample coordinate mean square (ratio 0.5); Model interval-dependent apparent speed (ratio 0.70711).
Why halving diffusivity does not halve displacement
Within this diffusion model, doubling radius or viscosity halves the diffusion coefficient. The coordinate RMS displacement scales with the square root of that coefficient, so its ratio is about 0.70711, not 0.5, at the same elapsed time.
Using common random numbers makes the corresponding sampled paths scale together. This isolates the setup change; it does not provide two independent experiments. This comparison does not offer independent-seed confidence intervals.
Changing the observation interval asks a different question of the same recording. Four times the time gives twice the model coordinate RMS; the finite sample can differ. The apparent speed depends on the chosen interval and is undefined at zero time.
Return to the displacement argumentOpen the completed variant settings in the full tracer lab
Keep this comparison and your explanation
Optional and private. Save the completed evidence, its exact settings and replay recipe, and your own explanation. Your words are not analyzed or assessed. The notebook remains on this device unless you export it.
No prediction was recorded before this request. You can still save the evidence and your explanation.
Up to 10,000 characters per text field and 64 KiB per complete entry; the notebook has a total device-storage budget. Nothing is silently shortened. Replaying is a separate explicit action in the notebook.
Open your notebook and saved comparisons