Q017 · Mirror / absorber / neutron counts

Gravitational Quantum Bouncer

Lift an absorber above a horizontal mirror. Record neutrons at each height and compare a four-state mixture with a prepared ground state. Change the flight time to see why the transmission edge is not an energy level.

Recorded trials $\text{—}$

Transmission at probe $\text{—}$

01 / CHANGE THE BOUNDARY. ASK WHAT GETS THROUGH.

Lift the ceiling. Count the survivors.

Scan the gap and save. Repeat with only the ground state. Then speed up the neutrons: the energy levels stay put, but the measured edge moves.

Horizontal flight above a hard mirror · absorber over the full mirror · vertical gap greatly enlarged · detector after the mirror

Absorber height

h/\mathrm{\mu m}

20

Ready. Each scan setting uses 200 independent incident particles.

TRY A CONTRAST

Gravity

g/(\mathrm{m/s^2})

9.81

Horizontal speed

v_x/(\mathrm{m/s})

5

Overlap loss rate

\Gamma/\mathrm{s^{-1}}

160

Vertical preparation

Sampling settings

Sampling seed

s_0

1729

Moving the probe preserves readings. Changing the device or preparation starts a fresh sample; save first. Nothing runs by itself.

Ultracold neutrons above an ideal hard mirror in uniform gravity. Four incoherent prepared vertical states; a declared overlap-loss model removes population during horizontal flight. Absorber-induced state distortion, roughness scattering and mode mixing are omitted. Density is continuous in height; turning heights are not shelves for particles.

02 / FIRST THE COUNTS. THEN THE CURVE.

The gap opens gradually.

Model reference

$h/\mathrm{\mu m}$ · Blue: current records. Amber: last saved other sample. Dashed: optional model. Drag to inspect; the slider supports keyboard input.

AT THIS PROBE SETTING

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No recorded particles yet.

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95% pointwise Wilson interval. No simultaneous-band or optional-stopping guarantee.

LATEST 60 RAW OUTCOMES

Blue: transmitted. Gray: reflected or absorbed. No hidden trajectory is recorded.

03 / WHAT CAN THESE RECORDS TELL US?

An observed edge is not an energy level.

Model only: each bar shows its contribution before and after the absorber. Absorption changes populations, not the energy markers.

FIRST OBSERVED HALF-TRANSMISSION CROSSING

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Independent model comparison

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MODEL INSPECTION · NO NEW RECORDS

Discrete energies. Continuous height.

$z/\mathrm{\mu m}$ · Drag the absorber. Gray: incoming density. Blue: surviving unnormalized density per incident neutron. Orange markers: classical turning heights.

$E_n/\mathrm{peV}$ · Numerical hard-mirror eigenstates. The incoming state mixture has only the first four modes.

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04 / KEEP THE EVIDENCE

Save before changing the experiment.

Eight frozen samples. Restoring inspects the original records; acquiring again starts a new run. CSV contains individual outcomes, scan membership and original settings.

Physical model, units and sources

\ell=0.12\,\mathrm m,\quad\psi(0)=0,\quad V(z)=m_ngz

The ground-state scale uses the neutron mass and SI constants. A 360-point finite-difference solution extends to eighteen gravity lengths. The absorber is a diagonal phenomenological loss channel proportional to each unperturbed mode’s probability above the gap; it does not impose a second hard wall. Coherent mixing, distorted eigenstates, real roughness, energy-dependent material absorption, loading efficiency and neutron decay are omitted. Preparation is ideal and the detector has unit efficiency. Geometry magnification is anisotropic; vertical position is a probability distribution, never a hidden ballistic track.

Nesvizhevsky et al. · mirror, absorber and transmitted neutrons · Voronin et al. · absorbing waveguide and limits of a simple loss model

Start with the essentials

Focus question: How tall must a slit be for a neutron to get through?
One-sentence intuition: A discrete energy spectrum still has a continuous position distribution.

Core mathematical model

Gravity length

z_0=\left(\frac{\hbar^2}{2m_n^2g}\right)^{1/3}

About 5.87 micrometers at Earth gravity.

Hard-mirror states

\psi_n(z)\propto\operatorname{Ai}(z/z_0-a_n),\quad E_n=m_ngz_0a_n

The positive Airy zeros set energies. The probability density extends beyond the classical turning height.

Declared absorber model

S(h)=\sum_n w_n\exp\!\left[-\Gamma\frac{\ell}{v_x}\int_h^\infty|\psi_n(z)|^2\,dz\right]

A phenomenological diagonal loss channel, not a solution of a rough absorbing waveguide. The mirror length is twelve centimeters.

Common difficulties

What was measured?

Typical misconceptionNeutrons occupy discrete height shelves.

Better mental modelEnergies are discrete; each state has a continuous density. The detector records only survival through an absorber.

Idealization

Typical misconceptionAgreement here certifies a real device.

Better mental modelUltracold neutrons above an ideal hard mirror in uniform gravity. Four incoherent prepared vertical states; a declared overlap-loss model removes population during horizontal flight. Absorber-induced state distortion, roughness scattering and mode mixing are omitted. Density is continuous in height; turning heights are not shelves for particles.

Run the experiment

01
Predict
Choose the four-state mixture. Predict whether a wider slit can lower the transmission.
What to observe: Keep the reference curve hidden until after recording.
02
Scan and preserve
Scan heights and save. Prepare only the ground state and repeat.
What to observe: Frozen samples retain the settings that produced them.
03
Expose the limitation
Increase horizontal speed at the same height. The state energies remain fixed, but less flight time means less loss.
What to observe: A half-transmission height is an operational statistic, not an energy measurement.