Skip to main content

On Negative Probabilities and Path Integrals

  • Chapter
  • First Online:
Trajectory Analysis in Health Care
  • 701 Accesses

Abstract

This principle of superposition is basic to wave behaviors and the analysis of harmonic systems. For individuals, measured behaviors may provide specific values at given times, but cumulatively, all individuals generally fall on a normalized distribution of values. Feynman challenged researchers to think beyond the conventional use of positive probabilities. This approach has not been used in statistics or epidemiology. Nevertheless, it has immediate implications to applied research interventions with positive and negative health conditions and behaviors, especially within the context of Wright’s path coefficients. Behavioral trajectories are impacted by coupled systems such that negative probability “accounting adjustments” might apply for events and non-events.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

ATP:

Adenosine triphosphate

pCO2 :

Percentage carbon dioxide

pO2 :

Percentage oxygen

References

  • Bartlett, M. S. (1945). Negative probability. Mathematical Proceedings of the Cambridge Philosophical Society, 41(1), 71–73.

    Article  Google Scholar 

  • Bohm, D. (1987). Hidden variables and the implicate order. In B. J. Hiley & F. D. Peat (Eds.), Quantum implications: Essays in honour of David Bohm (pp. 33–45). London: Routledge & Kegan Paul.

    Google Scholar 

  • Bonhoeffer, D. (1933 [1995]). Christ the center. In Kelly, G.B. & Nelson, F.B. (eds.), A testament to freedom: The essential writings of Dietrich Bonhoeffer, pp. 110–123. New York: HarperOne.

    Google Scholar 

  • Bracewell, R. (1965). The Fourier transform and its applications. New York: McGraw-Hill.

    Google Scholar 

  • Bracewell, R. (1989). The Fourier transform. Scientific American, 260(6), 86–95.

    Article  CAS  PubMed  Google Scholar 

  • Carson, D. A. (1998). An infectious origin of extraskeletal calcification. Proceedings of the National Academy of Sciences of the United States of America, 95, 7846–7847.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Croskerry, P. (2003). The importance of cognitive errors in diagnosis and strategies to minimize them. Academic Medicine, 78, 775–780.

    Article  PubMed  Google Scholar 

  • Davies, P., Demetrius, L. A., & Tuszynski, J. A. (2012). Implications of quantum metabolism and natural selection for the origin of cancer cells and tumor progression. AIP Advances, 2, 011101. 2158-3226/2012/2(1)/011101/14.

    Article  PubMed Central  Google Scholar 

  • Dirac, P. A. M. (1942). Bakerian lecture: The physical interpretation of quantum mechanics. Proceedings of the Royal Society A, Mathematical, Physical and Engineering Sciences, 180(980), 1–40.

    Article  CAS  Google Scholar 

  • Eigen, M., & Schuster, P. (1979). The hypercycle: A principle of natural self organization. Berlin: Springer.

    Book  Google Scholar 

  • Feynman, R. P. (1948). Space-time approach to non-relativistic quantum mechanics. Reviews of Modern Physics, 20(2), 367–387.

    Article  Google Scholar 

  • Feynman, R. P. (1987). Negative probability. In B. J. Hiley & F. D. Peat (Eds.), Quantum implications: Essays in honour of David Bohm (pp. 235–248). London: Routledge & Kegan Paul.

    Google Scholar 

  • Feynman, R. P., & Hibbs, A. R. (1965). Quantum mechanics and path integrals. New York: McGraw-Hill.

    Google Scholar 

  • Granada, A., Hennig, R. M., Ronacher, B., Kramer, A., & Herzel, H. (2009). Phase response curves: Elucidating the dynamics of coupled oscillators. Methods in Enzymology, 454, 1–27.

    Article  CAS  PubMed  Google Scholar 

  • Hashimoto, S., Ochs, R. L., Rosen, F., Quach, J., McCabe, G., Solan, J., et al. (1998). Chondrocyte-derived apoptotic bodies and calcification of articular cartilage. Proceedings of the National Academy of Sciences of United States of America, 95, 3094–3099.

    Article  CAS  Google Scholar 

  • Hayflick, L. (2007). Entropy explains aging, genetic determinism explains longevity, and undefined terminology explains misunderstanding both. PLoS Genetics, 3(12), e220. doi:10.1371/journal.pgen.0030220.

    Article  PubMed  PubMed Central  Google Scholar 

  • Hiley, B. J. (2012). Process, distinction, groupoids and Clifford algebras: an alternative view of the quantum formalism. arXiv.1211.2107v1 [quant-ph] 9 Nov 2012.

    Google Scholar 

  • Hoesel, B., & Schmid, J. A. (2013). The complexity of NF-κB signaling in inflammation and cancer. Molecular Cancer, 12, 86. doi:10.1186/1476-4598-12-86.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hollar, D., Rowland, J., (2015). Promoting health literacy for people with disabilities and clinicians through a teamwork model. Journal of Family Strengths, 15(2), Article 5. http://digitalcommons.library.tmc.edu/jfs/vol15/iss2/5.

  • Kahneman, D. (2002). Maps of bounded rationality: A perspective on intuitive judgment and choice (Nobel lecture on economic Sciences). Stockholm: The Nobel Foundation.

    Google Scholar 

  • Kohn, L. T., Corrigan, J. M., & Donalson, M. S. (Eds.). (1999). To err is human: Building a safer health system. Washington, D.C.: Institute of Medicine, National Academy Press.

    Google Scholar 

  • Lay, J. E. (1963). Thermodynamics: a macroscopic-microscopic treatment. Columbus, OH: Charles E. Merrill Books, Inc.

    Google Scholar 

  • Loy, G. (2007). Musimathics: The mathematical foundations of music (Vol. 2). Cambridge, MA: MIT Press.

    Google Scholar 

  • Makary, M. A., & Daniel, M. (2016). Medical error – The third leading cause of death in the US. BMJ, 353, i2139. doi:10.1136/bmj.i2139. (Published 3 May 2016).

    Article  PubMed  Google Scholar 

  • Margulis, L. (1998). Symbiotic planet. New York: Basic Books.

    Google Scholar 

  • McMenamin, M. A. S., & McMenamin, D. L. S. (1990). The emergence of animals: The Cambrian breakthrough. New York: Columbia University Press.

    Google Scholar 

  • Mintz, B., & Illmensee, K. (1975). Normal genetically mosaic mice produced from malignant teratocarcinoma cells. Proceedings of the National Academy of Sciences of United States of America, 72, 3585–3589.

    Article  CAS  Google Scholar 

  • Nicholls, D. G. (1982). Bioenergetics: An introduction to the chemiosmotic theory. New York: Academic Press.

    Google Scholar 

  • Redelmeier, D. A. (2005). The cognitive psychology of missed diagnoses. Annals of Internal Medicine, 142, 115–120.

    Article  Google Scholar 

  • Stevens, L. C. (1960). Embryoid potency of embryoid bodies derived from a transplantable testicular teratoma of the mouse. Developmental Biology, 2, 285–297.

    Article  CAS  PubMed  Google Scholar 

  • Thomas, R. D. K., Shearman, R. M., & Stewart, G. W. (2000). Evolutionary exploitation of design options by the first animals with hard skeletons. Science, 288, 1239–1242.

    Article  CAS  Google Scholar 

  • Tinbergen, N. (1963). On aims and methods of ethology. Zeitschrift für Tierpsychologie, 20, 410–433.

    Article  Google Scholar 

  • Wallerstein, G., & Elgar, S. (1992). Shock waves in stellar atmospheres and breaking waves on an ocean beach. Science, 256, 1531–1536.

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Cite this chapter

Hollar, D.W. (2018). On Negative Probabilities and Path Integrals. In: Trajectory Analysis in Health Care. Springer, Cham. https://doi.org/10.1007/978-3-319-59626-6_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-59626-6_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59625-9

  • Online ISBN: 978-3-319-59626-6

  • eBook Packages: MedicineMedicine (R0)

Publish with us

Policies and ethics