Experimental Test of a Time-Temperature Formulation of the Uncertainty Principle
A novel form of the Heisenberg uncertainty principle, as introduced by de Sabbata and Sivaram, ∆T∆t ≥ ħ/k, was tested using laser-induced fluorescence of 30 nm particles of YAG:Ce. The temperature-dependent fluorescence decay lifetimes of this material were measured at thermal equilibrium over the range from ≈ 285 to 350 °K. The 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 ∆T∆t ≥ 2.0 × l0−9 °K s, which is ≈ 263 times larger than ħ/k = 7.6 × l0−12 °K s. An “external” estimate of ∆T∆t ≥ 4.5 × 10−11 (which is ≈ times ħ/k) is derived from the measured uncertainty in the temperature of the sample and the measured uncertainty in lifetime. These results could be argued to increase by a factor of 5.6 if signal averaging is taken into account. If our approach is valid, then the findings are not inconsistent with the limitations predicted by this formulation of a time-temperature uncertainty principle and they imply the existence of a type of thermal quantum limit. The approach might thus open a path towards improved precision in the determination of the Boltzmann constant based on thermal squeezing techniques.
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