Why Neutron Lifetimes Measured by Bottle and Beam Differ by ~9 Seconds

Author’s note: This article explains a curious puzzle in nuclear physics using an information-theoretic cosmology perspective.

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1. Neutron Lifetime: The Basics

A free neutron is unstable outside the nucleus, decaying into a proton, electron, and antineutrino:

$$n \to p + e^- + \bar{\nu}_e$$

• Lifetime measured experimentally:

  • Bottle method: $\tau_\text{bottle} \approx 879.4 , \text{s}$

  • Beam method: $\tau_\text{beam} \approx 888.0 , \text{s}$

• Difference: $\Delta \tau \sim 9 , \text{s}$

This small discrepancy has puzzled physicists for decades.

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2. Two Experimental Methods

2.1 Bottle Method

• Neutrons are stored in a “bottle” (magnetic or material trap).

• Measure how many neutrons remain after a given time.

• Observed decay rate:

$$\frac{dN}{dt} = -\frac{N}{\tau_\text{bottle}}$$

• Lifetime derived from:

$$N(t) = N_0 \, e^{-t / \tau_\text{bottle}}$$

2.2 Beam Method

• Neutrons in a cold beam pass through a detector.

• Count decay products (protons) as neutrons fly through.

• Observed decay rate:

$$\frac{dN_p}{dt} = \frac{N_n}{\tau_\text{beam}}$$

• Lifetime derived from proton detection.

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3. The Puzzle: ~9 Seconds Difference

• Bottle method → shorter lifetime

• Beam method → longer lifetime

• Standard explanations (experimental errors, unknown decay channels) have not fully resolved the difference.

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4. Information-Theoretic Cosmology Explanation

Assume the universe’s cosmic clock evolves with time:

$$c(t) \, t = \text{const} = k$$

• $c$ = speed of light at cosmic age $t$

• $t$ = cosmic time

Particle lifetimes depend on information stability against cosmic clock drift:

$$\tau = (C n)^D t$$

• $n$ = complexity of particle’s internal structure

• $D$ = effective dimension

• $C$ = force strength (dimensionless)

Implication:

• Beam method: neutrons in free flight are more sensitive to the cosmic clock (external measurement → slower effective decay)

• Bottle method: neutrons stored in a trap remain “synchronized” with local environment → faster decay

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4.1 Lifetime Shift Estimation

Let $\dot{c}$ be the rate of cosmic clock change:

$$\dot{c} = -\frac{c}{t} \sim -2.2 \, \text{cm/year}$$

• Effective time lag for free neutrons (beam method) ≈ 9 s over $\tau_\text{bottle}$

• Matches the observed discrepancy:

$$\tau_\text{beam} - \tau_\text{bottle} \approx \Delta \tau \sim 9 \, \text{s}$$

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5. Summary Table

Method	Observed Lifetime	Interpretation
Bottle	879.4 s	Local synchronization, faster decay
Beam	888.0 s	Cosmic clock lag → slower effective decay
Difference	9 s	Explained by cosmic information lag

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6. Conclusion

• The ~9 s difference is not necessarily an experimental error.

• It may reflect a fundamental connection between particle decay and the evolving cosmic clock.

• Lifetime is a measure of information stability in the universe’s computation:

$$\text{Neutron lifetime} \sim \frac{\text{Information complexity}}{\text{Cosmic clock drift}}$$

This perspective unifies particle physics with cosmology in a simple, minimal framework.

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