Skip to main content
Springer Nature Link
Log in

Probabilistic Nature of a Field with Time as a Dynamical Variable

  • Conference paper
  • First Online:
Quantum Interaction (QI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10106))

Included in the following conference series:

  • 813 Accesses

Abstract

Taking time as a dynamical variable, we study a wave with 4-vector amplitude that has vibrations of matter in space and time. By analyzing its Hamiltonian density equation, we find that the system is quantized. It obeys the Klein-Gordon equation and thus also the Schrödinger equation. Only a probability can be assigned for the detection of a particle. This quantized field has physical structures that resemble a zero-spin quantum field. The possibility to apply our formalism outside quantum physics is briefly discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Unlike the ‘intrinsic time’ [23, 24] suggested as a dynamical variable of the studied system (e.g. position of a clock’s dial or position of a classical free particle [26]) that can function to measure time, the ‘internal time’ defined here is an intrinsic property of matter that has vibration in time.

References

  1. Rovelli, C.: Quantum Gravity. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  2. Anderson, E.: Problem of time in quantum gravity. Annalen der Physik 524, 757 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Munoz, J., Ruschhaupt, A., Campo, A. (eds.): Time in Quantum Mechanics - Vol 2. Lecture Notes in Physics, vol. 789, p. 97. Springer, Heidelberg (2009)

    Book  Google Scholar 

  4. Yearsley, J., Downs, D., Halliwell, J., Hashagen, A.: Quantum arrival and dwell times via idealized clocks. Phys. Rev. A 84, 022109 (2011)

    Article  Google Scholar 

  5. Ordonez, G., Hatano, N.: Existence and nonexistence of an intrinsic tunneling time. Phys. Rev. A 79, 042102 (2009)

    Article  Google Scholar 

  6. Kiukas, J., Ruschhaupt, A., Werner, R.: Tunneling times with covariant measurements. Found. Phys. 39, 829 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Madrid, R.: Time as a dynamical variable in quantum decay. Phys. A 913, 217 (2013)

    Google Scholar 

  8. Pauli, W.: General Principles of Quantum Mechanics. Springer, Heidelberg (1980)

    Book  Google Scholar 

  9. Muga, J., Leavens, C.: Arrival time in quantum mechanics. Phys. Rep. 338, 353 (2000)

    Article  MathSciNet  Google Scholar 

  10. Aharonov, Y., Bohm, D.: Time in the quantum theory and the uncertainty relation for time and energy. Phys. Rev. 122, 1649 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  11. Holevo, A.: Probabilistic and Statistical Aspects of Quantum Theory. North-Holland, Amsterdam (1982)

    MATH  Google Scholar 

  12. Aharonov, Y., Oppenheim, J., Popescu, S., Reznik, B., Unruh, W.: Measurement of time of arrival in quantum mechanics. Phys. Rev. A 57, 4130 (1998)

    Article  MathSciNet  Google Scholar 

  13. Olkhovsky, V., Recami, E.: Time as a quantum observable. Int. J. Mod. Phys. A 22, 5063 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wang, Z., Xiong, C.: How to introduce time operator. Ann. Phys. (N.Y.) 322, 2304 (2007)

    Google Scholar 

  15. Galapon, E.: Post Paulis theorem emerging perspective on time in quantum mechanics. In: Muga, G., Ruschhaupt, A., Campo, A. (eds.) Time in Quantum Mechanics - Vol. 2. Lecture Notes in Physics, vol. 789. Springer, Heidelberg (2009). doi:10.1007/978-3-642-03174-8_3. And references therein

    Google Scholar 

  16. Brunetti, R., Fredenhagen, K., Hoge, M.: Time in quantum physics: from an external parameter to an intrinsic observable. Found. Phys. 40, 1368 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hegerfeldt, G., Muga, J.: Symmetries and time operators. J. Phys. A Math. Theor. 43, 505303 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Strauss, Y., Silman, J., Machnes, S., Horwitz, L.: Study of a self-adjoint operator indicating the direction of time within standard quantum mechanics. C. R. Math. 349, 1117 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Arsenovic, D., Buric, N., Davidovic, D., Prvanovic, S.: Dynamical time versus system time in quantum mechanics. Chin. Phys. B 21, 070302 (2012)

    Article  Google Scholar 

  20. Lee, T.D.: Can time be a discrete dynamical variable? Phys. Lett. B 122, 217 (1983)

    Article  Google Scholar 

  21. Lee, T.D.: Difference equations and conservation laws. J. Stat. Phys. 46, 843 (1987)

    Article  MathSciNet  Google Scholar 

  22. Yau, H.Y.: Emerged quantum field of a deterministic system with vibrations in space and time. Conf. Proc. 1508, 514 (2012)

    Google Scholar 

  23. Busch, P.: On the energy-time uncertainty relation. Part I: dynamical time and time indeterminacy. Found. Phys. 20, 1 (1990)

    Article  Google Scholar 

  24. Busch, P.: On the energy-time uncertainty relation. Part II: pragmatic time versus energy indeterminacy. Found. Phys. 20, 33 (1990)

    Article  Google Scholar 

  25. Hilgevoord, J.: Time in quantum mechanics: a story of confusion. Stud. Hist. Phil. Mod. Phys. 36, 29 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  26. Butterfield, J.: On Time in Quantum Physics - The Blackwell Companion to the Philosophy of Time. Wiley-Blackwell, Oxford (2013)

    Google Scholar 

  27. Jammer, M.: Concepts of Mass in Contemporary Physics and Philosophy. Princeton University Press, Princeton (2009)

    Book  Google Scholar 

  28. Salecker, H., Wigner, E.: Quantum limitations of the measurement of space-time distances. Phys. Rev. 109, 571 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  29. Karolyhazy, F.: Sixty-Two Years of Uncertainty. Plenum, New York (1990). Ed. by Miller, A.I

    Google Scholar 

  30. Kudaka, S., Matsumoto, S.: Uncertainty principle for proper time and mass. J. Math. Phys. 40, 1237 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  31. Aharonov, Y., Reznik, B.: Weighing a closed system and the time-energy uncertainty principle. Phys. Rev. Lett. 84, 1368 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  32. Briggs, J.: A derivation of the time-energy uncertainty relation. J. Phys. Conf. Ser. 99, 012002 (2008)

    Article  Google Scholar 

  33. Greenberger, D.: Conceptual problems related to time and mass in quantum theory. arXiv:1011.3709. [quant-ph]

  34. Feynman, R.: The theory of positrons. Phys. Rev. 76, 749 (1949)

    Article  MATH  Google Scholar 

  35. de Barros, A., Oas, G.: Some examples of contextuality in physics: implications to quantum cognition. Contextuality Quantum Phys. Psychol. 6, 153 (2015). Ed. by Dzhafarov, E., Jordan, S., Zhang, R., Cervantes, V

    Article  Google Scholar 

  36. Khrennikov, A.: Quantum-like brain: interference of minds. Biosystems 84, 225 (2006)

    Article  Google Scholar 

  37. Khrennikov, A.: Quantum-like model of processing of information in the brain based on classical electromagnetic field. Biosystems 105, 250 (2011)

    Article  Google Scholar 

  38. de Barros, A.: Quantum-like model of behavioral response computation using neural oscillators. Biosystems 110, 171 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FDNL Research, 119 Poplar Avenue, San Bruno, California, 94066, USA

    Hou Y. Yau

Authors
  1. Hou Y. Yau
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hou Y. Yau .

Editor information

Editors and Affiliations

  1. San Francisco State University, San Francisco, California, USA

    Jose Acacio de Barros

  2. University of Oxford, Oxford, United Kingdom

    Bob Coecke

  3. City University of London, London, United Kingdom

    Emmanuel Pothos

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Yau, H.Y. (2017). Probabilistic Nature of a Field with Time as a Dynamical Variable. In: de Barros, J., Coecke, B., Pothos, E. (eds) Quantum Interaction. QI 2016. Lecture Notes in Computer Science(), vol 10106. Springer, Cham. https://doi.org/10.1007/978-3-319-52289-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-52289-0_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52288-3

  • Online ISBN: 978-3-319-52289-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics