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Using Neutrinos to test the Time-Energy Uncertainty Relation in an Extreme Regime

We discuss a direct test of the relation of time and energy in the very long-lived decay of tritium (H3) (meanlife τ~ 18 yrs) with the width Γ~ 10^{-24} eV [set by the time-energy uncertainty (TEU)], using the newfound possibility of resonance reactions H3 \leftrightarrow He3 with ΔE/E ~ 5x10^{-29}. The TEU is a keystone of quantum mechanics, but probed for the first time in this extreme time-energy regime. Forestalling an apparent deviation from the TEU, we discuss the ramifications and a possible generalization of the TEU as ΔE Δt > (\hbar/2)[1+(Δt/T)^n] where Δt = τis the time of measurement (the lifetime of the state), T=L/c the time for light to cross the Universe ~ 3x10^{18} s, and n a parameter subject to future measurements. (by R. S. Raghavan.)