A model for the solution of the quantum measurement problem

Biswaranjan Dikshit


The basic idea of quantum mechanics is that the property of any system can be in a state of superposition of various possibilities (or eigen states). This state of superposition is also known as wave function and it evolves linearly with time in a deterministic way in accordance with the Schrodinger equation. However, when a measurement is carried out on the system to determine the value of that property (say position), the system instantaneously transforms to one of the eigen states and thus we get only a single value as outcome of the measurement. Quantum measurement problem seeks to find the cause and exact mechanism governing this transformation. In an attempt to solve the above problem, in this paper, we will first define what the wave function represents in real world and will identify the root cause behind the stochastic nature of events. Then, we will develop a model to explain the mechanism of collapse of the quantum mechanical wave function in response to a measurement. In the process of development of model, we will explain Schrodinger cat paradox and will show how Born’s rule for probability becomes a natural consequence of measurement process.


Quantum measurement problem; Born’s rule; Schrodinger cat paradox; Biased will theory

Full Text:



N. David Mermin. Could Feynman Have Said This?. Physics Today, 57 (5), 10. 2004.

David Deutsch. Quantum theory of probability and decisions. Proc. R. Soc. Lond. A, 455,3129-3137. 1999

Edward Farhi, Jeffrey Goldstone and Sam Gutmann, How Probability Arises in QuantumMechanics. Annals of physics, 192, 368-382. 1989.

J B Hartle. Quantum mechanics of Individual systems. American Journal of Physics, 36(8), 704-712. 1968

Meir Hemmo and Itamar Pitowsky. Quantum probability and many worlds. Studies in History and Philosophy of Modern Physics, 38, 333-350. 2007.

David J. Baker. Measurement outcomes and probability in Everettian quantum mechanics. Studies in History and Philosophy of Modern Physics, 38, 153-169. 2007.

Adrian Kent. Against Many-Worlds Interpretations. Int. J. Mod. Phys. A, 5, 1745-1762. 1990.

Andres Cassinello and Jose Luis Sanchez-Gomez. On the probabilistic postulate of quantum mechanics. Foundations of Physics, 26 (10), 1357-1374. 1996.

Carlton M. Caves and Rudiger Schack. Properties of the frequency operator do not imply the quantum probability postulate. Annals of Physics, 315, 123–146. 2005.

Euan J. Squires. On an alleged “proof” of the quantum probability law. Physics letters A, 145 (2-3), 67-68. 1990.

A Einstein, B Podolsky and N Rosen. Can Quantum-Mechanical Description of Physical reality be considered complete?. Physical Review, 47, 777-780. 1935.

J S Bell, “On the Einstein Podolsky Rosen paradox”, Physics, 1 (3), 195-200 (1964)

Alain Aspect, Philippe Grangier and Gerard Roger. Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedanken experiment: A new violation of Bell’s inequalities. Physical Review Letters, 49 (2), 91-94. 1982.

Alain Aspect, Jean Dalibard and Gerard Roger. Experimental test of Bell’s inequalities using time varying analyzers. Physical Review Letters, 49 (25), 1804-1807. 1982.

Alain Aspect. Bell’s inequality test: more ideal than ever. Nature, 398, 189-190. 1999.

W Tittel, J Brendel, H Zbinden and N Gisin. Violation of Bell inequalities by photons more than 10 km apart. Physical Review Letters, 81 (17), 3563-3566. 1998.

Z Y Ou and L Mandel. Violation of Bell’s inequality and classical probability in a two- photon correlation experiment. Physical Review Letters, 61 (1), 50-53. 1988.

Y H Shih and C O Alley. New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion. Physical Review Letters, 61 (26), 2921-2924. 1988.

Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter and Anton Zeilinger. Violation of Bell’s inequality under strict Einstein Locality conditions. Physical Review Letters, 81 (23), 5039-5043. 1998.

Roger Colbeck and Renato Renner. No extension of quantum theory can have improved predictive power. Nature communications, 2:411, 1-5. 2011.

Zeeya Merali. Quantum Mechanics Braces for the ultimate test. Science, 331, 1380-1382. 2011.

David Bohm. A suggested Interpretation of the Quantum theory in terms of “Hidden” variables. I. Physical Review, 85 (2), 166-179. 1952.

Marco Genovese. Research on hidden variable theories: A review of recent progresses. Physics Reports, 413, 319-396. 2005.

A J Leggett. Nonlocal Hidden-Variable Theories and Quantum mechanics: An incompatibility theorem. Foundations of Physics, 33 (10), 1469-1493. 2003.

Nicolas Gisin. Impossibility of covariant deterministic nonlocal hidden-variable extensions of quantum theory. Physical review A, 83, 020102(R). 2011.

Simon Groblacher, Tomasz Paterek, Rainer Kaltenbaek, Caslav Brikner, Marek Zukowski, Markus Aspelmeyer and Anton Zeilinger. An experimental test of non-local realism. Nature, 446, 871-875. 2007.

Tomasz Paterek, Alessandro Fedrizz, Simon Groblacher, Thomas Jennewein, Marek Zukowski, Markus Aspelmeyer and Anton Zeilinger. Experimental test of Nonlocal Realistic theories without the Rotational Symmetry assumption. Physical Review Letters, 99, 210406, 1-4. 2007.

G C Ghirardi, A Rimini and T weber. Unified dynamics for microscopic and macroscopic systems. Physical Review D, 34 (2), 470-491. 1986.

Gian Carlo Ghirardi, Philip Pearle and Alberto Rimini. Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles. Physical Review A, 42 (1), 78-89. 1990.

Wojciech Hubert Zurek. Decoherence, einselection, and the quantum origins of the classical. Reviews of Modern Physics, 75 (3), 715-775. 2003.

Wojciech H. Zurek. Decoherence and the transition from quantum to classical. Physics Today, 44 (10), 36-44. 1991.

E. Joos. Elements of environmental decoherence. In P. Blanchard, D. Giulini, E. Joos, C. Kiefer, I.-O. Stamatescu (Eds.), Decoherence: Theoretical, experimental, and conceptual problems (pp. 1–17). New York: Springer, 1999

Stephen L Adler. Why decoherence has not solved the measurement problem: a response to P. W. Anderson. Studies in history and Philosophy of Modern physics, 34, 135-142. 2003.

Biswaranjan Dikshit. A simple proof of Born’s rule for statistical interpretation of quantum mechanics. Journal for Foundations and Applications of Physics, 4 (1), 24-30. 2017.

E Schrodinger. Indeterminism and Free will. Nature, 138, 13-14. 1936.

John Conway and Simon Kochen. The free will theorem. Foundations of Physics, 36 (10), 1441-1473. 2006.

John H. Conway and Simon Kochen. The strong free will theorem. Notices of the AMS, 56 (2), 226-232. 2009.

Biswaranjan Dikshit. Origin of Quantum Mechanical Results and Life: A Clue from Quantum Biology. NeuroQuantology, 16 (4), 26-33. 2018.

Zeeya Merali. Solving Biology's Mysteries Using Quantum Mechanics. Discover, December 29. 2014

http://discovermagazine.com/2014/dec/17-this-quantum-life )

Johnjoe McFadden and Jim Al-Khalili. A quantum mechanical model of adaptive mutation. Biosystems, 50, 203 – 211. 1999.

DOI: http://dx.doi.org/10.23756/sp.v7i2.482


  • There are currently no refbacks.

Copyright (c) 2019 Biswaranjan Dikshit

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Science & Philosophy - Journal of Epistemology, Science and Philosophy. ISSN 2282-7757; eISSN  2282-7765.