Muon Decay Experiment — SACE Stage 2 Physics

Phase 1 — Mt Washington Summit

Altitude 1910 m. Muons arrive at roughly 568 per hour.

Scintillator

Elapsed 00:00

Muons detected 0

Queue 0

Collect data for at least 5 minutes

CRO Traces

Read the time of the decay spike from the active trace and enter it below.

Waiting for the first muon…

Confirmed traces (0)

Stop collecting and confirm all queued traces to continue.

Phase 2 — Sea Level

A second identical detector at sea level, running for the same duration as Phase 1. Played back at 20× speed. Muons are counted automatically — no input required.

Scintillator

Sim time 00:00

Muons detected 0

Speed 20×

Passing CRO Traces

Traces flash past — we only count how many arrive, not when they decay.

Detector waiting…

Playback in progress…

Phase 3 — Classical Survival Prediction

For each muon detected at Mt Washington, we drew a line starting at 1910 m and extending downward by the distance that muon should travel before decay, assuming it moves at 0.994 c. Count how many lines reach sea level.

How is distance calculated?

All muons travel at approximately 0.994 c. Once we know the time t between detection and decay, the distance travelled before decay is simply

d = 0.994 × 3 × 10⁸ m/s × t

A muon that decays after 2.2 μs (the mean lifetime) travels only about 660 m — nowhere near the 1910 m needed to reach sea level from Mt Washington. A muon would need to live for ≈ 6.38 μs to make it all the way down, which is almost three mean lifetimes.

Count how many of your Phase 1 muons reach sea level according to this classical picture. Compare that number to the count measured at sea level in Phase 2.

Compare your numbers

Phase 1 — muons detected at Mt Washington —

Phase 2 — muons detected at sea level —

Your classical prediction (from graph)

Enter your count above, then continue.

Phase 4 — Effective Distance

Classical physics predicted only a handful of muons should reach sea level, yet the sea-level detector counted hundreds. Something in our calculation is wrong. If we accept the sea-level count as correct, what distance do the muons behave as if they travelled?

The measurements

Muons at Mt Washington —

Muons at sea level —

Survival fraction (N_sea / N_mtn) —

Mean decay time ⟨t⟩ (from Phase 1) —

Finding the effective distance

At the summit we recorded — muons with a mean decay time of — μs. Classically, the probability of a muon surviving long enough to travel a distance d is:

P(survive) = e^{−d / (v · ⟨t⟩)}

The sea-level detector actually measured a survival fraction of —. Solving for d:

d_eff = −v · ⟨t⟩ · lnN_seaN_mtn

Try the slider: find the value of d for which the predicted survival fraction matches the one we measured. That is the distance the muons behave as though they had travelled.

Effective distance d

d = m

predicted survival = —

measured survival = —

The ratio

L / d_eff = —

In the muon's reference frame the mountain is moving — and moving rulers contract. The muon "sees" only a distance L / γ, where γ is the Lorentz factor. The ratio above is the Lorentz factor you have extracted from your own measurements.