# Proof: The mean neutron lifetime measured in beam experiments is more than 1 second shorter than the lifetime obtained from ultracold-neutron bottle experiments

- **Generated:** 2026-03-28
- **Verdict:** DISPROVED
- **Audit trail:** [proof_audit.md](proof_audit.md) | [proof.py](proof.py)

## Key Findings

- The beam experiment world average for the neutron lifetime is **887.7 +/- 2.2 seconds** (B1).
- The bottle (ultracold neutron) experiment world average is **878.5 +/- 0.8 seconds** (B1).
- The difference (beam minus bottle) is **+9.2 seconds** (A1) — beam experiments measure a **longer** lifetime, not a shorter one.
- The claim asserts the opposite direction: that beam is shorter. This is **false** by approximately 10 seconds.

## Claim Interpretation

**Natural language:** "The mean neutron lifetime measured in beam experiments is more than 1 second shorter than the lifetime obtained from ultracold-neutron bottle experiments."

**Formal interpretation:** The claim asserts that (beam lifetime) - (bottle lifetime) < -1.0 seconds. That is, the beam value must be at least 1 second below the bottle value for the claim to hold. The operator "<" with threshold -1.0 is the conservative formalization — if the beam lifetime equals or exceeds the bottle lifetime, the claim is clearly false.

In reality, the beam lifetime exceeds the bottle lifetime by about 9 seconds, making (beam - bottle) approximately +9.2 — far above the threshold of -1.0. The claim has the direction of the well-known "neutron lifetime puzzle" exactly backwards.

## Evidence Summary

| ID | Fact | Verified |
|----|------|----------|
| B1 | U.S. DOE: beam lifetime 887.7 +/- 2.2 s, bottle lifetime 878.5 +/- 0.8 s | Yes |
| B2 | Quanta Magazine: beam ~14 min 48 s, bottle ~14 min 39 s, gap ~9 s | Yes |
| A1 | Computed difference (beam - bottle) from DOE values | Computed: +9.2 seconds (beam is longer) |
| A2 | Computed difference (beam - bottle) from Quanta values | Computed: +9.0 seconds (beam is longer) |
| A3 | Claim evaluation: is (beam - bottle) < -1.0? | Computed: False |

*Source: proof.py JSON summary*

## Proof Logic

The U.S. Department of Energy reports that one method (beam) measures the neutron lifetime as 887.7 seconds and another method (bottle) measures it as 878.5 seconds (B1). Computing the difference: 887.7 - 878.5 = +9.2 seconds (A1). The positive sign means beam experiments yield a **longer** lifetime, not a shorter one.

This is independently corroborated by Quanta Magazine, which reports that "the gap between the world-average bottle and beam measurements has only grown slightly — to nine seconds" (B2), with beam being the longer measurement. The DOE-derived difference of 9.2 seconds and the Quanta-reported gap of 9 seconds agree within 0.2 seconds.

The claim states that beam is "more than 1 second shorter" than bottle. Formally, this requires (beam - bottle) < -1.0. Since the actual value is +9.2, the claim is false — the direction is reversed. Beam experiments consistently measure a longer neutron lifetime than bottle experiments, not a shorter one.

## Counter-Evidence Search

1. **Alternative definitions of "beam experiment"?** — Searched for non-standard definitions. All sources consistently define beam experiments as measuring proton decay products from cold neutron beams (~888 s) and bottle experiments as trapping ultracold neutrons (~879 s). No alternative definitions found.

2. **Any beam result below the bottle average?** — Checked PDG 2024 data and recent publications. The most recent beam measurement (YUE 2013) is 887.7 +/- 1.2 s. No beam experiment has ever produced a result below the bottle average. The discrepancy has persisted since the 2000s.

3. **Could "shorter" mean something else?** — Linguistic analysis confirms "shorter" unambiguously refers to the numerical lifetime value, not experiment duration.

*Source: proof.py JSON summary*

## Conclusion

**DISPROVED.** The claim that beam experiments measure a neutron lifetime more than 1 second shorter than bottle experiments is false. The actual relationship is the opposite: beam experiments yield 887.7 s compared to 878.5 s for bottle experiments — a difference of +9.2 seconds, with beam being the *longer* measurement. This is the well-known "neutron lifetime puzzle," and the claim has its direction reversed. All citations were fully verified against their source pages.

Note: 1 citation comes from an unclassified source (Quanta Magazine, tier 2). However, the disproof does not depend on it — the U.S. DOE source (tier 5, government) alone establishes the result.

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Generated by [proof-engine](https://github.com/yaniv-golan/proof-engine) v0.10.0 on 2026-03-28.
