Experimental Test of a Time-Temperature Formulation of the Uncertainty Principle Via Nanoparticle Fluorescence

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The uncertainty in the measured fluorescence decay lifetimes of 30 nm particles of YAG:Cc was used to evaluate the predictions of a novel form of the Heisenberg uncertainty principle suggested by de Sabbata and Sivaram, ΔT Δt ≥ h/k. The worst-case uncertainty in temperature of ≈ 4.5 °K (as derived from the relationship between temperature and lifetime) and the measured uncertainty in decay lifetime, ≈ 0.45 ns, yielded an “internal” estimate of ΔT Δt = 2.0 × 10⁻⁹ °K s, which is ≈ 263 times larger than ħ/k = 7.6 × 10⁻¹² °K s. An “external” estimate of ΔT Δt = 4.5 × 10¹¹ °K s (which is = 6 times ħ/k) is derived from the independently measured uncertainty in the temperature of the sample and the experimentally determined uncertainty in lifetime. These results could be low by a factor of 5.6 if signal averaging must be taken into account. If valid, the findings are consistent with the predictions of this version of the uncertainty principle and they imply the existence of a type of “thermal quantum limit.”