Experimental Test of a Time-Temperature Formulation of the Uncertainty Principle

  • G. T. Gillies
  • S. W. Allison
Part of the NATO Science Series book series (NAII, volume 141)


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.


Uncertainty Principle Dopant Atom Charge Transfer State Decay Time Constant Decay Lifetime 
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  1. [1]
    Heffner H 1962 Proc. IRE 50 1604CrossRefGoogle Scholar
  2. [2]
    Yoneya T 1989 Mod. Phys. Lett. A 4 1587MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    Abe S and Suzuki N 1990 Phys. Rev. A 41 4608MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    Unnikrishnan C S and Gillies G T 2003 Rep. Prog. Phys. invited for submissionGoogle Scholar
  5. [5]
    de Sabbata V and Sivaram C 1992 Found. Phys. Lett. 5 183MathSciNetCrossRefGoogle Scholar
  6. [6]
    de Sabbata V 1994 Nuov. Cim. A 107 363ADSCrossRefGoogle Scholar
  7. [7]
    Gillies G T, Unnikrishnan C S, Pfister O and Ritter R C 2003 Phys. Rev. Lett. in preparationGoogle Scholar
  8. [8]
    Kobayashi T 1995 Phys. Lett. A 207 320MathSciNetADSMATHCrossRefGoogle Scholar
  9. [9]
    Kobayashi T 1996 Phys. Len. A 210 241ADSMATHCrossRefGoogle Scholar
  10. [10]
    Kobayashi T 2001 Nuov. Cim. B 116 493ADSGoogle Scholar
  11. [11]
    Ford G W and O’Connell R F 2002 Am. J. Phys. 70 319ADSCrossRefGoogle Scholar
  12. [12]
    Fonger W H and Struck C W 1970 J. Chem. Phys. 52 6364ADSCrossRefGoogle Scholar
  13. [13]
    Grattan K T V and Zhang Z Y 1995 Fiber Optic Fluorescence Thermometry ( London: Chapman and Hall )Google Scholar
  14. [14]
    Struck C W and Fonger W H 1971 J. Appl. Phys. 42 4515ADSCrossRefGoogle Scholar
  15. [15]
    Blackmore J S 1969 Solid State Physics ( Philadelphia: Saunders ) pp 78–81Google Scholar
  16. [16]
    Einstein A 1907 Ann. Phys. 22 180MATHGoogle Scholar
  17. [17]
    Debye P 1912 Ann. Phys. 39 789MATHCrossRefGoogle Scholar
  18. [18]
    Born M and von Karmen T 1912 Z Physik. 13 297MATHGoogle Scholar
  19. [19]
    Allison S W, Gillies G T, Rondinone A J and Cates M R 2002 Nanotechnology submittedGoogle Scholar
  20. [20]
    Allison S W and Gillies G T 1997 Rev. Sci. Instrum. 68 2615ADSCrossRefGoogle Scholar
  21. [21]
    Dowell L J, 1989 Investigation and Development of Phosphor Thermometry Ph.D. Dissertation, University of VirginiaGoogle Scholar
  22. [22]
    Gillies G T, Allison S W and Tissue B M 2002 Nanotechnology 13 484ADSCrossRefGoogle Scholar
  23. [23]
    Allison S W, Cates M R and Gillies G T 2002 Rev. Sci. Instrum. 73 1832ADSCrossRefGoogle Scholar
  24. [24]
    Ramsey N F 1987 IEEE Trans. Instrum. Meas. 36 155Google Scholar
  25. [25]
    Ramsey N F 1992 J. Phys. II (Paris) 2 573Google Scholar
  26. [26]
    Ramsey N F 1995 Physica Scripta T59 26CrossRefGoogle Scholar
  27. [27]
    Aharonov Y and Reznik B 2000 Phys. Rev. Lett. 84 1368MathSciNetADSMATHCrossRefGoogle Scholar
  28. [28]
    Mohr P J and Taylor B N 2000 Rev. Mod. Phys. 72 351ADSMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • G. T. Gillies
    • 1
  • S. W. Allison
    • 2
  1. 1.Department of PhysicsUniversity of VirginiaCharlottesvilleUSA
  2. 2.Engineering Technology DivisionOak Ridge National LaboratoryOak RidgeUSA

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