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Sandbox Physics

Neutrinos · D12 · The inverse problem

IceCube: From Sensor Hits to a Track

Generate a teaching event in an ice array, hide its true direction, and fit the sensor times. Change scattering and absorption to see when a bright event becomes harder to reconstruct.

Interactive modelIceCube: From Sensor Hits to a Track
Hit sensors—\text{—}
Recorded photoelectrons—\text{—}
Fitted polar angle—\text{—}
Fitted azimuth—\text{—}
Timing residual RMS—\text{—}
Angular error · truth comparison—\text{—}

TEACHING SIMULATION · RECORDED DATA

Inspect the measurement

Preparing a reproducible teaching record…

Read a sample of the record
Scientific reference ↗Read the worldwide history →2026 Nobel Prize in Physics →

Physics tutorial

Fit the recorded times, then inspect the residuals

BackgroundCoordinates are local Cartesian metres: z points upward, x and y are horizontal. Polar angle is measured from positive z; azimuth turns from x toward y. The reference point is assumed known, as in a constrained calibration exercise.

Why it mattersHow much direction information survives absorption and scattering?

Start with the essentials

Focus question
How much direction information survives absorption and scattering?
One-sentence intuition
A fitted direction is an inference from the frozen hit record. More collected charge does not by itself prove a better or unbiased fit.

Core mathematical model

Earliest direct light in homogeneous ice

ti=t0+li+din2−1ct_i=t_0+\frac{l_i+d_i\sqrt{n^2-1}}{c}

For an infinite track at vacuum light speed, l is the sensor displacement along the track and d the perpendicular distance. A nondispersive index 1.32 is assumed, so phase and group speeds coincide.

Fit with an unknown time origin

u^=arg⁡min⁡u∑i(ti−tgeo,i(u)−t^0)2\widehat{\mathbf u}=\arg\min_{\mathbf u}\sum_i(t_i-t_{\mathrm{geo},i}(\mathbf u)-\widehat t_0)^2

The time offset is profiled as the mean difference for each trial direction. A global coarse angular grid is refined locally. Late scattered photons can bias this deliberately simple direct-light fit; RMS is a residual diagnostic, not angular uncertainty.

Common difficulties

Fit the recorded times, then inspect the residuals

Typical misconceptionThe fitted charged-particle direction is the exact neutrino direction.

Better mental modelInteraction kinematics are omitted. This is a charged-track timing exercise with a known anchor, not an event classifier, neutrino-energy measurement or full IceCube reconstruction.

Run the experiment

  1. 01

    Blind reconstruction

    Generate an event with truth hidden. Fit recorded hits, then reveal truth.

    What to observe: The fitted arrow and angular error are calculated after fitting; the fitter never reads the generated direction.
  2. 02

    Break the propagation model

    Choose Strong scattering. Fit the new event and compare timing residuals.

    What to observe: Early unscattered photons may still carry direction information, but delayed first hits can bias the fit.
  3. 03

    Lose photons

    Choose Strong absorption and compare hit count and residuals across several generated events.

    What to observe: Fewer sensors constrain the fit. This display does not supply a calibrated confidence interval or guarantee a monotonic error increase in every random event.