A Formulation of Quantum Theory Based on Two Physical Principles

ABSTRACT

We demonstrate two points: 1) the formalism of quantum mechanics can be understood simply as a structure for the expression of the physical notion that not all observables can have values simultaneously; 2) the specific uncertainty relations can be derived (rigorously) by combination of the invariance principle with a general uncertainty relation based only on the existence of unspecified pairs of conjugate observables. For this purpose, we present a formulation of quantum mechanics based strictly on the invariance principle and a “weak” statement of the uncertainty principle that asserts only the existence of incompatible (conjugate) observables without specifying which observables are incompatible. We go on to show that the invariance principle can be used to develop the equations of motion of the theory, including the Klein-Gordon and Schrodinger equations.

We demonstrate two points: 1) the formalism of quantum mechanics can be understood simply as a structure for the expression of the physical notion that not all observables can have values simultaneously; 2) the specific uncertainty relations can be derived (rigorously) by combination of the invariance principle with a general uncertainty relation based only on the existence of unspecified pairs of conjugate observables. For this purpose, we present a formulation of quantum mechanics based strictly on the invariance principle and a “weak” statement of the uncertainty principle that asserts only the existence of incompatible (conjugate) observables without specifying which observables are incompatible. We go on to show that the invariance principle can be used to develop the equations of motion of the theory, including the Klein-Gordon and Schrodinger equations.

Cite this paper

Deck, R. (2015) A Formulation of Quantum Theory Based on Two Physical Principles.*Journal of Modern Physics*, **6**, 434-447. doi: 10.4236/jmp.2015.64047.

Deck, R. (2015) A Formulation of Quantum Theory Based on Two Physical Principles.

References

[1] Deck, R.T. (2010) A Logical Development of Quantum Mechanics from Physical Principles. CreateSpace 2010.

[2] Eisberg, R. and Resnick, R. (1985) Quantum Physics. 2nd Edition, John Wiley & Sons, New York.

[3] Merzbacher, E. (1970) Quantum Mechanics. 2nd Edition, John Wiley & Sons, New York.

[4] Liboff, R.L. (1992) Introductory Quantum Mechanics. 2nd Edition, Addison-Wesley, New York, 66-80.

[5] Dirac, P.A.M. (1958) The Principles of Quantum Mechanics. 4th Edition, Clarenden Press, Oxford.

[6] Goswami, A. Quantum Mechanics. 125.

[7] Deck, R.T. and Ozturk, N. (1994) Foundations of Physics Letters, 7, 419-436.

http://dx.doi.org/10.1007/BF02189245

[8] Sposito, G. (1970) An Introduction to Quantum Physics. John Wiley & Sons, Inc., New York, 178.

[1] Deck, R.T. (2010) A Logical Development of Quantum Mechanics from Physical Principles. CreateSpace 2010.

[2] Eisberg, R. and Resnick, R. (1985) Quantum Physics. 2nd Edition, John Wiley & Sons, New York.

[3] Merzbacher, E. (1970) Quantum Mechanics. 2nd Edition, John Wiley & Sons, New York.

[4] Liboff, R.L. (1992) Introductory Quantum Mechanics. 2nd Edition, Addison-Wesley, New York, 66-80.

[5] Dirac, P.A.M. (1958) The Principles of Quantum Mechanics. 4th Edition, Clarenden Press, Oxford.

[6] Goswami, A. Quantum Mechanics. 125.

[7] Deck, R.T. and Ozturk, N. (1994) Foundations of Physics Letters, 7, 419-436.

http://dx.doi.org/10.1007/BF02189245

[8] Sposito, G. (1970) An Introduction to Quantum Physics. John Wiley & Sons, Inc., New York, 178.