Quantum Structures and the Nature of Reality pp 103-140 | Cite as

# Against “Paradoxes”: A New Quantum Philosophy for Quantum Mechanics

## Abstract

It is a commonplace that XXth century physics has produced powerful new theories, such as Relativity and quantum mechanics, that upset the world view provided by XIXth century physics. But every physicist knows how difficult it may be to explain the basic aspects of these theories to people having a non-physical professional training. The main reason of this is that both Relativity and quantum mechanics are based on fundamental ideas that are not hard to grasp in themselves, but deeply contrast the primary categories on which our everyday thinking is based, so that it is impossible to place relativistic and quantum results within the framework suggested by ordinary intuition and common sense. Yet, despite this similarity, there are some relevant differences between the difficulties arising in Relativity and in quantum mechanics. In order to understand this point better, let us focus our attention on Special Relativity first (analogous arguments can be forwarded by considering General Relativity). Here, the strange links between space and time following from the even more strange assumption that the velocity of light is independent of the motion of the observer conflict with the very simple conception of space and time implicit in our daily practice (and explicitly stated in classical Physics, think of Newton’s “absolute space” and “absolute time”): but this conflict regards geometrical space-time models, not the very roots of our language, hence our thought. Then, let us consider quantum mechanics. Here it is a basic notion that properties of physical systems are *nonobjective*, in the sense that a property cannot be thought of as existing if a measurement of it is not performed. As Mermin [30] writes,

“it is a fundamental quantum doctrine that a measurement does not, in general, reveal a preexisting value of the measured property”.

## Keywords

Quantum Mechanic Physical Object Quantum Logic Intuitionistic Logic Testable Property## Preview

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## References

- [1]
- [2]
**Bell**, J.S., “On the Problem of hidden variables in quantum me-chanics”,*Rev. Mod. Phys*,**38**, 1966, p. 447.zbMATHCrossRefGoogle Scholar - [3]
- [4]
**Bohm, D. and Aharonov, Y**., “Discussion of experimental Proofs for the paradox of Einstein, Rosen, and Podolsky”,*Phys. Rev*,**108**, 1957, p. 1070.MathSciNetCrossRefGoogle Scholar - [5]
**Bohr**, N., “Can Quantum Mechanical Description of Reality be Considered Complete?”,*Phys. Rev*,**48**, 1935, p. 696.zbMATHCrossRefGoogle Scholar - [6]
**Braithwaite**, R.B.,*Scientific Explanation*, Cambridge University Press, Cambridge, 1953.zbMATHGoogle Scholar - [7]
**Busch, P., Lahti, P.J., and Mittelstaedt, P**.,*The Quantum Theory of measurement*, Springer, Berlin, 1991.Google Scholar - [8]
**Dalla Pozza, C. and Garola, C**., “A Pragmatic Interpretation of Intuitionistic Propositional logic”,*Erkenntnis*,**43**, 1995, p. 81.MathSciNetCrossRefGoogle Scholar - [9]
**Einstein, A., Podolsky, B., and Rosen, N**., “Can quantum mechanical description of reality be considered complete?”,*Phys. Rev*,**47**, 1935, p. 777.zbMATHCrossRefGoogle Scholar - [10]
**Finkelstein, D**., “Matter, space and logic”, in:**Hooker, C. A**. (ed.),*The Logico-Algebraic Approach to quantum mechanics*,*Vol II*, Reidel, Dordrecht, 1979.Google Scholar - [11]
**Finkelstein, D**., “The physics of logic”, in:**Hooker, C. A**. (ed.),*The Logico-Algebraic Approach to quantum mechanics*,*Vol II*, Reidel, Dordrecht, 1979.Google Scholar - [12]
**Furry, W.H**., “Note on the quantum mechanical theory of measurement”,*Phys. Rev*,**49**, 1936, p. 393.zbMATHCrossRefGoogle Scholar - [13]
**Furry, W.H**., “Remarks on measurements in quantum theory”,*Phys. Rev*,**49**, 1936, p. 476.zbMATHCrossRefGoogle Scholar - [14]
**Garola, C**., “Embedding of posets into lattices in quantum logic”,*Int. Journ. of Theor. Phys*,**24**, 1985, p. 423.MathSciNetzbMATHCrossRefGoogle Scholar - [15]
**Garola, C**., “classical foundations of quantum logic”,*Int. Journ. of Theor. Phys*,**30**, 1991, p. 1.MathSciNetzbMATHCrossRefGoogle Scholar - [16]
**Garola, C**., “Semantic incompleteness of quantum physics”,*Int. Journ. of Theor. Phys*,**31**, 1992, p. 809.MathSciNetzbMATHCrossRefGoogle Scholar - [17]
**Garola, C**., “Truth versus testability in quantum logic”,*Erkenntnis*,**37**, 1992, p. 197.MathSciNetCrossRefGoogle Scholar - [18]
**Garola, C**., “Reconciling local realism and quantum physics: a critique to Bell”,*Teoreticheskaya i Matematicheskaya Fizika*,**99**, 1994, p. 285.MathSciNetGoogle Scholar - [19]
**Garola, C**., “Criticizing Bell: Local realism and quantum physics reconciled”,*Int. Journ. of Theor. Phys*,**34**, 1995, p. 269.Google Scholar - [20]
**Garola, C**., “An operational Critique to Bell’s Theorem”, in:**Garola, C. and Rossi, A**. (eds.),*The Foundations of quantum mechanics. Historical Analysis and Open Questions*, Kluwer Academic Publishers, Dordrecht, 1995.CrossRefGoogle Scholar - [21]
**Garola, C**., “Pragmatic versus semantic contextuality in quantum physics”,*Int. Journ. of Theor. Phys*,**34**, 1995, p. 1383.MathSciNetzbMATHCrossRefGoogle Scholar - [22]
**Garola, C. and Solombrino, L**., “The theoretical apparatus of semantic realism: A new language for classical and quantum physics”,*Found. of Phys*,**26**, 1996, p. 1121.MathSciNetCrossRefGoogle Scholar - [23]
**Garola, C. and Solombrino, L**., “Semantic realism versus EPRlike paradoxes: the Furry, Bohm-Aharonov and Bell paradoxes”,*Found. of Phys*,**26**, 1996, p. 1329.MathSciNetCrossRefGoogle Scholar - [24]
**Greenberger, D.M., Horne, M.A., Shimony A., and Zeilinger, A**., “Bell’s theorem without Inequalities”,*Am. Journ. of Phys*,**58**, 1990, p. 1131.MathSciNetCrossRefGoogle Scholar - [25]
- [26]
**Kochen, S. and Specker, E.P**., “The problem of hidden variables in quantum mechanics”,*Journ. of Math. Mech*,**17**, 1967, p. 59.MathSciNetzbMATHGoogle Scholar - [27]
**Jauch, J.M**.,*Foundations of quantum mechanics*, Addison-Wesley, Reading (Mass. ), 1968.zbMATHGoogle Scholar - [28]
**Ludwig, G**.,*Foundations of quantum mechanics I*, Springer Verlag, New York, 1983.zbMATHCrossRefGoogle Scholar - [29]
**Mackey, G.W**.,*The Mathematical Foundations of quantum mechanics*, Benjamin, New York, 1963.zbMATHGoogle Scholar - [30]
**Mermin, N.D**., “Hidden variables and the two theorems of John Bell”,*Reviews of Modern Physics*,**65**, 1993, p. 803.MathSciNetCrossRefGoogle Scholar - [31]
- [32]
- [33]
**Putnam, H**., “Is logic empirical?”, in:**Hooker, C.A**. (ed.),*The Logico-Algebraic Approach to quantum mechanics*,*Vol II*, Reidel, Dordrecht, 1979.Google Scholar - [34]
- [35]
- [36]
**Sellerl, F**., “Even local probabilities lead to the paradox”, in:**Sellerl, F**. (ed.),*quantum mechanics Versus Local Realism*, Plenum Press, New York, 1988.Google Scholar - [37]
- [38]
**Tarski, A**., “The semantic conception of truth and the foundations of semantics”, in:**Linsky, L**. (ed.),*Semantics and the Philosophy of Language*, University of Illinois Press, Urbana, 1952.Google Scholar - [39]
**Wigner, E.P**., “On hidden variables and quantum mechanical probabilities”,*Am. Journ. of Phys*,**38**, 1970, p. 1005.CrossRefGoogle Scholar