Ten thousand muons
cross every square
metre of this ground
every minute.
They come from the top of the atmosphere, they pass through rock, and they scatter. The plan was to measure that scattering and turn it into a picture of what the muons went through.
The software got built. The instrument did not. What follows descends through how muon tomography is meant to work, and ends with what the simulation found — that this specification, at this scale, does not close.
A cosmic ray hits the upper atmosphere and shatters into a shower of particles. The muons in that shower are the only ones that reach the ground.
A proton arriving from outside the solar system strikes an air nucleus. The collision produces pions and kaons, which decay in flight into muons. Each muon carries gigaelectronvolts of energy, travels at 99.97% of the speed of light, and lives long enough — through time dilation — to cross the atmosphere before it decays.
Nothing built stops them. A muon crosses concrete, granite, steel and lead, losing a little energy and picking up a small deflection on the way.
At sea level the flux is steady and comes mostly from overhead: the intensity follows a cosine-squared falloff with zenith angle. That steadiness is what makes the measurement possible — the signal is free, constant, and impossible for a subject to switch off.
This is the depth where every other method has already given up.
Industrial X-ray and gamma radiography manage a few centimetres of dense matter, and they need a source and an exclusion zone. Ground-penetrating radar attenuates in wet or conductive soil beyond two to five metres. Core drilling is destructive, localised, and runs to tens of thousands of euros per borehole — and it only tells you about the hole.
Bar lengths are penetration depth on a shared scale. The muon bar is the whole width because nothing else on this chart comes close. The penetration is real — muons do cross all of it. Turning that into a useful image is the part this design did not manage: at distance the coincidence rate falls as the inverse square, and the contrast goes with it.
Two panels, 9.5 kilograms each, to be carried to the structure and set either side of it.
Each panel was specified to carry four tracking planes of 64 X and 64 Y scintillator strips, read out by silicon photomultipliers, with an FPGA time-to-digital converter resolving each hit to 75 picoseconds. Three things in that sentence do not survive arithmetic. The station draws 12.5 watts, which on a 150 Wh pack is twelve hours — not the day the documents claimed. The timing architecture needs 4,096 carry primitives against roughly 200 available in the chosen device. And the mass budget omits the 28 kg of lead the same design requires for its momentum measurement.
Inside dense material a muon is deflected. How far it bends depends on what it hit.
Coulomb scattering scales with density and atomic number, so a void barely bends a track while a steel reinforcing bar bends it sharply. That single number — the deflection angle — is the measurement, and the contrast it offers is real: lead scatters 20.6 times more strongly than concrete. What defeats the design is how many deflections can be collected. At close range they accumulate in hours. At the standoffs the survey-time table assumed, in days.
Thousands of fitted deflections become one volume: a density map of what the muons crossed, with nothing drilled and nothing irradiated.
Every requirement was plausible.
None of them compose.
The left column was written first. The instrument software was then built to test it, and the right column is what it measured. No number on the left is unreasonable by itself — 75 ps TDCs exist, 10 kg instruments exist, 12 h of battery life is ordinary. The failure is that they were specified independently and never multiplied together.
| Parameter | Specified | Measured |
|---|---|---|
| Resolution | 2.1 mrad | 15.15 mrad |
| Lever arm | 600 mm station separation | 140 mm plane spacing |
| Acceptance | 23.8–28.8 % | 18.0 % |
| Lead CNR | 5.92 · 27.60 | 1.41 |
| Voxel at 1 m | 10 mm | ~15 mm |
| Endurance | > 24 h on 150 Wh | 12.0 h at 12.5 W |
| Mass | < 9.5 kg per station | omits 28.4 kg of lead |
| Timing fabric | 128 ch · 75 ps | 4,096 CARRY4 needed, ~200 available |
| Pier survey at 3 m | 6–8 h | ~29 days |
- The lever arm is the root cause. A direction is fitted within a station, from the two planes measuring one coordinate — 140 mm apart, not the 600 mm between stations. That substitution alone is worth 7.2×, and every quantity derived from angle inherits it.
- The rate law was extrapolated rather than re-derived. The survey-time table was built at benchtop scale and applied at metres, where the governing variable is standoff squared. Reaching 6–8 h at 3 m would need roughly 100 m² of active area.
- The budgets were never added up. Twenty-four hours of endurance, 9.5 kg of mass and a passive lead momentum spectrometer are pairwise incompatible. Any two can hold. Not all three.
- What is not in question. Muon tomography works and is sold commercially — nuclear waste characterisation, mineral exploration, volcanology, cargo screening. The finding is about this specification at this scale.
What the physics does allow is smaller: sub-metre targets at 0.3–0.7 m standoff, where the rate is high and 15 mrad is enough to resolve 8–10 mm. That is a real instrument, and the direction a continuation should take. The first step is not another document — it is one SiPM on a bench, which is the only thing that fixes the largest unmeasured input in every number above.