Abstract
The epoch-making idea of the quantum as a fundamental property of Nature was introduced by Max Planck in 1900. Quantum mechanics is undoubtedly one of the most important and experimentally accurate scientific theory in the history of science. Accuracy is defined by the degree to which a theoretical value is close to the measured experimental value. Precision, in contrast, defines the degree to which an experiment, when it is repeated, produces a series of measured values to within a level of precision, namely, to within a certain error. Its range of applications and mathematical depth are unmatched, and quantum mechanics continues to yield novel and unexpected results—in technology as well as in all scientific fields, including physics and mathematics. Paradoxically enough, in spite of all its empirical and mathematical success quantum mechanics—due to its strange and enigmatic conceptual framework—has, until now, defied all attempts to reach a satisfactory understanding of its inner workings.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Accuracy is defined by the degree to which a theoretical value is close to the measured experimental value. Precision, in contrast, defines the degree to which an experiment, when it is repeated, produces a series of measured values to within a level of precision, namely, to within a certain error.
- 2.
The “trans-empirical quantum principle” is stated in Sect. 3.9 and discussed in detail in Chap. 3.
References
Peres, A.: Quantum Theory: Concepts and Methods. Kluwer, Holland (1998)
Aspect, A.: Bell’s inequality test: more ideal than ever. Nature 398(189), 1408–1427 (1999)
Baaquie, B.E.: Quantum Finance. Cambridge University Press, Cambridge (2004)
Ballentine, L.E.: Quantum Mechanics: A Modern Development. World Scientific, Singapore (1998)
Baaquie, B.E.: Path Integrals in Quantum Mechanics, Quantum Field Theory and Superstrings. Cambridge University Press, Cambridge (2013)
Bell, J.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge (2004)
Odom, B., Hanneke, D., D’Urso, B., Gabrielse, G.: New measurement of the electron magnetic moment using a one-electron quantum cyclotron. Phys. Rev. Lett. 97, 030801 (2006)
DeWitt, B.S., Graham, N.: The Many-Worlds Interpretation of Quantum Mechanics. Princeton University Press, Princeton (1973)
Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969)
Dirac, P.A.M.: The Principles of Quantum Mechanics. Oxford University Press, Oxford (1999)
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)
Wigner, E.P.: The problem of measurement. Am. J. Phys. 31, 6–15 (1963)
Feynman, R.P.: The Character of Physical Law. Penguin Books, Baltimore (2007)
Feynman, R.P., Hibbs, A.R.: Quantum Mechanics and Path Integrals. McGraw Hill, New York (1960)
Gottfried, K., Yan, T.-M.: Quantum Mechanics. Springer, Germany (2003)
Greenstein, G., Zajonc, A.G.: The Quantum Challenge, 2nd edn. Jones and Bartlett, Boston (2006)
Heisenberg, W.: The Physical Principals of the Quantum Theory. Dover, New York (1949)
Heisenberg, W.: Physics and Philosophy: The Revolution in Modern Science. Prometheus Books, New York (1999)
Isham, C.J.: Lectures on Quantum Theory. Imperial College Press, London (1995)
Klyachko, A.A., Can, M.A., Binicioğlu, S., Shumovsky, A.S.: Simple test for hidden variables in spin-1 systems. Phys. Rev. Lett. 101, 020403 (2008)
Kochen, S., Specker, E.P.: The problem of hidden variables in quantum mechanics. J. Math. Mech. 17 (1967)
Kurzyński, P., Ramanathan, R., Kaszlikowski, D.: Entropic test of quantum contextuality. Phys. Rev. Lett. 109, 020404 (2012)
Lawden, D.F.: The Mathematical Principles of Quantum Mechanics. Dover, New york (2005)
Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics. Addison-Wesley, Reading (1964)
Mackey, G.W.: Mathematical Foundations of Quantum Mechanics. Dover, New York (2004)
Major, F.G., Gheorghe, V.N., Werth, G.: Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement. Springer, Germany (2010)
Nielsen, M.A., Chang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Muga, G.: Time in Quantum Mechanics. Springer, Berlin (2008)
Muller, H., Peter, A., Chew, S.: A precision measurement of the gravitational redshift by the interference of matter waves. Nature 463(3), 926–929 (1983)
Newton, R.G.: The Truth of Science: Physical Theories and Reality. Harvard University Press, Cambridge (1997)
Healy, R.: The Philosophy of Quantum Mechanics. Cambridge University Press, Cambridge (2008)
Ramanathan, R., Soeda, A.A., Kurzyński, P., Kaszlikowsk, D.: Generalized monogamy of contextual inequalities from the no-disturbance principle. Phys. Rev. Lett. 109, 050404 (2012)
Schlosshauer, M.A.: Decoherence: and the Quantum-to-Classical Transition. Springer, Germany (2010)
Stapp, H.P.: The Copenhagen interpretation. Am. J. Phys. 40 (1963)
Streater, R.F.: Classical and quantum probability. J. Math. Phys. 41, 3556–3603 (2000)
von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1983)
Yu, S., Oh, C.H.: State-independent proof of Kochen-Specker theorem with 13 rays. Phys. Rev. Lett. 108, 030402 (2012)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Baaquie, B.E. (2013). Synopsis. In: The Theoretical Foundations of Quantum Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6224-8_1
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6224-8_1
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-6223-1
Online ISBN: 978-1-4614-6224-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)