## Abstract

Standard quantum mechanics undeniably violates the notion of separability that classical physics accustomed us to consider as valid. By relating the phenomenon of quantum nonseparability to the all-important concept of potentiality, we effectively provide a coherent picture of the puzzling entangled correlations among spatially separated systems. We further argue that the generalized phenomenon of quantum nonseparability implies contextuality for the production of well-defined events in the quantum domain, whereas contextuality entails in turn a structural-relational conception of quantal objects, viewed as carriers of dispositional properties. It is finally suggested that contextuality, if considered as a conditionalization preparation procedure of the object to be measured, naturally leads to a separable concept of reality whose elements are experienced as distinct, well-localized objects having determinate properties. In this connection, we find it necessary to distinguish the meaning of the term reality from the criterion of reality for us. The implications of the latter considerations for the notion of objectivity in quantum mechanics are also discussed.

### Similar content being viewed by others

## Notes

In this work we shall make no detailed reference to alternative interpretations of ordinary quantum mechanics as, for instance, Bohm’s ontological or causal interpretation.

In a paper related to the Einstein–Podolsky–Rosen argument, Schrödinger remarked with respect to this distinctive feature of nonfactorizability as follows: ‘‘When two systems, of which we know the states by their respective representations, enter into temporary physical interaction due to known forces between them, and then after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own… I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought’’ (Schrödinger 1935/1983, p. 161).

For instance, the entangled correlations between spatially separated systems can not be explained by assuming a direct causal influence between the correlated events or even by presupposing the existence of o probabilistic common cause among them in Reichenbach’ s sense. Butterfield (1989) and van Fraassen (1989) have shown that such assumptions lead to Bell’s inequality, whereas, as well known, the latter is violated by quantum mechanics. See in addition, however, Belnap and Szabó (1996) for the notion of a

*common*cause in relation to quantum correlations occurring in the Greenberger–Horne–Zeilinger (GHZ) situation.The following account of Heisenberg is characteristic of the significance of the notion of potentiality as a clarifying interpretative concept for quantum theory. He writes: “The probability function … contains statements about possibilities or better tendencies (‘potentia’ in Aristotelian philosophy), and these statements … do not depend on any observer … The physicists then speak of a ‘pure case’ … [Consequently,] it is no longer the objective events but rather the probabilities for the occurrence of certain events that can be stated in mathematical formulae. It is no longer the actual happening itself but rather the possibility of its happening—the potentia—that is subject to strict natural laws … If we … assume that even in the future exact science will include in its foundation the concept of probability or possibility—the notion of potentia—then a number of problems from the philosophy of earlier ages appear in a new light, and conversely, the understanding of quantum theory can be deepened by a study of these earlier approaches to the question” (Heisenberg 1958, p. 53; 1974, pp. 16, 17).

See, for instance, Heisenberg (1958, pp. 42, 185); Popper (1980, Chap. 9; 1990, Chap. 1); Shimony (1993, Vol. 2, Chap. 11). Margenau (1950, pp. 335–337, 452–454) has also used the concept of ‘latency’ to characterize the indefinite quantities of a quantum-mechanical state that take on specified values when an act of measurement forces them out of indetermination.

It should be analogously underlined that the pure quantum-mechanical state does not constitute a mere expression of our knowledge of a particular microphysical situation, as frequently nowadays construed, thus acquiring an epistemic status (e.g., Fuchs and Peres 2000). The quantum state designates an economic and effective embodiment of

*all possible manifestations*of the quantum-mechanical potentialities pertaining to a system; it encapsulates all facts*concerning the behavior*of the system; it codifies not only what may be ‘actual’ in relation to the system, upon specified experimental conditions, but also what may be ‘potentially possible’, although it does not literally represent any concrete features of the system itself. The latter element, however, does not abolish the character of quantum state as a bearer of*empirical content*, since the quantum state modulates as a whole the characteristics or statistical distributions of realizable events. Furthermore, the statistical distribution of any such event—associated to a certain preparation procedure of a quantum state—is a stable, reproducible feature. Thus, the*generator*of these statistical regularities, namely, the quantum state associated with preparation, can be considered as an*objective*feature of the world (for details, see Sects. 3 and 4).The probabilistic dependence of measurement outcomes between spatially separated systems forming an entangled quantum whole corresponds, as an expression of the violation of the separability principle, to the violation of what has been coined in the Bell-literature as Jarrett’s (1984) ‘completeness condition’, or equivalently, Shimony’s (1986) ‘outcome independence’ condition. A detailed description of these conditions would fall outside the scope of the present work. A review of them may be found in Howard (1997).

A recent generalized version of the so-called no-signaling theorem is given by Scherer and Busch (1993).

It should be pointed out that Bohr already on the basis of his complementarity principle introduced the concept of a ‘quantum phenomenon’ to refer “exclusively to observations obtained under specified circumstances, including an account of the whole experiment” (Bohr 1963, p. 73). This feature of context-dependence is also present in Bohm’s ontological interpretation of quantum theory by clearly putting forward that “quantum properties cannot be said to belong to the observed system alone and, more generally, that such properties have no meaning apart from the total context which is relevant in any particular situation. In this sense, this includes the overall experimental arrangement so that we can say that measurement is context dependent” (Bohm and Hiley 1993, p. 108).

Note that the so-called invariant or state-independent, and therefore, context-independent properties—like ‘rest-mass’, ‘charge’ and ‘spin’—of elementary objects-systems can only characterize a certain class of objects; they can only specify a certain sort of particles, e.g., electrons, protons, neutrons, etc. They are not sufficient, however, for determining a member of the class as an individual object, distinct from other members within the same class, that is, from other objects having the same state-independent properties. Thus, an ‘electron’, for instance, could not be of the particle-kind of ‘electrons’ without fixed, state-independent properties of ‘mass’ and ‘spin’, but these in no way suffice for distinguishing it from other similar particles or for ‘individuating’ it in any particular physical situation. For a detailed treatment of this point, see, for example, Castellani (1999).

In standard quantum mechanics, it is not possible to establish a causal connection between a property A(t) at time t and the same property A(t′′) at a later time t′′, both pertaining to an object-system S, if S had been subjected at a time value t′, t < t′ < t′′, to a measurement of a property B incompatible with A. Because the successive measurement of any incompatible property of this kind would provide an uncontrollable material change of the state of S. Thus, a complete causal determination of all possible properties of a quantum object, most notably, coordinates of position and their conjugate momenta, allowing the object, henceforth, to traverse well-defined trajectories in space-time is not possible.

It is tempting to think that a similar sort of context-dependence already arises in relativity theory. For instance, if we attempt to make context-independent attributions of simultaneity to spatially distant events—where the context is now determined by the observer’s frame of reference—then we will come into conflict with the experimental record. However, given the relativization of simultaneity—or the relativization of properties like length, time duration, mass, etc.—to a reference frame of motion, there is nothing in relativity theory that precludes a complete description of the way nature is. Within the domain of relativity theory, the whole of physical reality can be described from the viewpoint of any reference frame, whereas, in quantum mechanics such a description is inherently incomplete.

It is worthy to note in this association that the impossibility of preparing the same initial contextual state in mutually exclusive measurement arrangements constitutes a sufficient condition for preventing derivability of the Bell inequality without invoking nonlocality (e.g., De Baere 1996).

It has been shown by Ivanovic (1981), Wooters and Fields (1989), see also, Brukner and Zeilinger (1999), that the total information content of a quantum system represented by a density matrix (pure or mixed) is optimally obtainable from a complete set of mutually exclusive (complementary) measurements corresponding to the system’s complete set of mutually complementary observables.

## References

Aspect, A., Grainger, G., & Roger, G. (1982). Experimental test of Bell’s inequalities using time-varying analyzers.

*Physical Review Letters, 49*, 1804–1807.Atmanspacher, H. (1994). Objectification as an endo–exo transition. In H. Atmanspacher, & G.J. Dalenoort (Eds.),

*Inside versus outside*(pp. 15–32). Berlin: Springer.Baere, W. De. (1996). Quantum nonreproducibility at the individual level as a resolution of quantum paradoxes. In A. Mann, & M. Revzen (Eds.),

*The dilemma of Einstein, Podolsky and Rosen – 60 years later*(pp. 95–108). Bristol: Institute of Physics Publishing.Belnap, N., & Szabó, L. E. (1996). Branching space-time analysis of the GHZ theorem.

*Foundations of Physics, 26*, 989–1002.Blank, J., Exner, P., & Havlicek, M. (1994).

*Hilbert space operators in quantum physics*. New York: American Institute of Physics.Bohm, D., & Hiley, B. (1993).

*The undivided universe. An ontological interpretation of quantum theory*. London: Routledge.Bohr, N. (1963).

*Essays 1958–1962 on atomic physics and human knowledge*. New York: Wiley.Brukner, C., & Zeilinger, R. (1999). Operationally invariant information in quantum measurements.

*Physical Review Letters,*83, 3354–3357.Butterfield, J. (1989). A space-time approach to the Bell inequality. In J. Cushing, & E. McMullin (Eds.),

*Philosophical consequences of quantum theory: Reflections on Bell’s theorem*(pp. 114–144). Notre Dame: University of Notre Dame Press.Castellani, E. (1999). Galilean particles: An example of constitution of objects. In E. Castellani (Ed.),

*Interpreting bodies*(pp. 181–196). Princeton: Princeton University Press.Cassirer, E. (1936/1956).

*Determinism and indeterminism in modern physics*. New Haven: Yale University Press.Einstein, A. (1948/1971). Quantum mechanics and reality. In M. Born (Ed.),

*The Born-Einstein letters*(pp. 168–173). London: Macmillan.Esfeld, M. (2004). Quantum entanglement and a metaphysics of relations.

*Studies in the History and Philosophy of Modern Physics,*35, 601–617.Espagnat, B. De. (1995).

*Veiled reality*. Reading: Addison-Wesley.Fine, A. (1986).

*The shaky game: Einstein, realism and the quantum theory*. Chicago: University of Chicago Press.Fine, A. (1987). With complacency or concern: Solving the quantum measurement problem. In R. Kargon, & P. Achinstein (Eds.),

*Kelvin’s Baltimore lectures and modern theoretical physics*(pp. 491–506). Cambridge: MA, MIT Press.Fuchs, C., & Peres, A. (2000). Quantum theory needs no interpretation.

*Physics Today,*3, 70–71.Greenberger, D., Horn, M., Shimony, A., & Zeilinger, A. (1990). Bell’s theorem without inequalities.

*American Journal of Physics,*58, 1131–1143.Healey, R. (1991). Holism and nonseparability.

*The Journal of Philosophy,*LXXXVIII, 393–421.Heisenberg, W. (1958).

*Physics and philosophy*. New York: Harper & Row.Heisenberg, W. (1974).

*Across the frontiers*. New York: Harper & Row.Howard, D. (1989). Holism, separability and the metaphysical implications of the Bell experiments. In J. Cushing, & E. McMullin (Eds.),

*Philosophical consequences of quantum theory: Reflections on Bell’s theorem*(pp. 224–253). Notre Dame: University of Notre Dame Press.Howard, D. (1994). What makes a classical concept classical? In J. Faye, & H. Folse (Eds.),

*Niels Bohr and contemporary philosophy*(pp. 201–229). New York: Kluwer.Howard, D. (1997). Space-time and separability: Problems of identity and individuation in fundamental physics. In R. Cohen, M. Horne, & J. Stachel (Eds.),

*Potentiality, entanglement and passion-at-a distance*(pp. 113–141). Dordrecht: Kluwer.Ihmig, K. (1999). Ernst Cassirer and the structural conception of objects in modern science: The importance of the “Erlanger Programm”.

*Science in Context, 12*, 513–529.Ivanovic, I. D. (1981). Geometrical description of quantal state determination.

*Journal of Physics A, 14*, 3241–3245.Jarrett, J. P. (1984). On the physical significance of the locality conditions in the Bell arguments.

*Noûs, 18*, 569–589.Jauch, J. (1968).

*Foundations of quantum mechanics*. Reading: MA, Addison-Wesley.Karakostas, V. (2003). The nature of physical reality in the light of quantum nonseparability.

*12th international congress of logic, methodology and philosophy of science*, Oviedo, Volume of Abstracts, pp. 329–330.Karakostas, V. (2004). Forms of quantum nonseparability and related philosophical consequences.

*Journal for General Philosophy of Science, 35*, 283–312.Kochen, S., & Specker, E. (1967). The problem of hidden variables in quantum mechanics.

*Journal of Mathematics and Mechanics, 17*, 59–87.Landsman, N. (1995). Observation and superselection in quantum mechanics.

*Studies in History and Philosophy of Modern Physics, 26*, 45–73.Luders, G. (1951). Ueber die Zustandsänderung durch den Messprozess.

*Annalen der Physik, 8*, 322–328.Margenau, H. (1950).

*The nature of physical reality*. New York: McGraw Hill.Mermin, N. D. (1995). Limits to quantum mechanics as a source of magic tricks: Retrodiction and the Bell–Kochen–Specker theorem.

*Physical Review Letters, 74*, 831–834.Mermin, N. D. (1998). What is quantum mechanics trying to tell us?

*American Journal of Physics, 66*, 753–767.Popper, K. R. (1980).

*The logic of scientific discovery*. London: Hutchinson.Popper, K. R. (1990).

*A world of propensities*. Bristol: Thoemmes.Primas, H. (1993). The Cartesian cut, the Heisenberg cut, and disentangled observers. In K.V. Laurikainen, & C. Montonen (Eds.),

*Symposia on the foundations of modern physics*(pp. 245–269). Singapore: World Scientific.Rovelli, C. (1996). Relational quantum mechanics.

*International Journal of Theoretical Physics, 35*, 1637–1678.Scheibe, E. (1973).

*The logical analysis of quantum mechanics*. Oxford: Pergamon Press.Scherer, H., & Busch, P. (1993). Problem of signal transmission via quantum correlations and Einstein incompleteness in quantum mechanics.

*Physical Review A, 47*, 1647–1651.Schrödinger, E. (1935/1983). The present situation in quantum mechanics.

*Naturwissenschaften*, 22, 807–812, 823–828, 844–849. Reprinted in J. Wheeler, & W. Zurek (Eds.),*Quantum theory and measurement*(pp. 152–167). Princeton: Princeton University Press.Shimony, A. (1986). Events and processes in the quantum world. In R. Penrose, & C. Isham (Eds.),

*Quantum concepts in space and time*(pp. 182–203). Oxford: Oxford University Press.Shimony, A. (1993).

*Search for a naturalistic world view, Vol. 2, Natural science and metaphysics*. Cambridge: Cambridge University Press.Tittel, W., Brendel, J., Zbinden, H., & Gisin, N. (1998). Violation of Bell inequalities by photons more than 10 km apart.

*Physical Review Letters, 81*, 3563–3566.Van Fraassen, B. C. (1989). The charybdis of realism: Epistemological implications of Bell’s inequality. In J. Cushing, & E. McMullin (Eds.),

*Philosophical consequences of quantum theory: Reflections on Bell’s theorem*(pp. 97–113). Notre Dame: University of Notre Dame Press.Wooters, W., & Fields, B. (1989). Optimal state-determination by mutually unbiased measurements.

*Annals of Physics, 191*, 363–381.

## Author information

### Authors and Affiliations

### Corresponding author

## Rights and permissions

## About this article

### Cite this article

Karakostas, V. Nonseparability, Potentiality, and the Context-Dependence of Quantum Objects.
*J Gen Philos Sci* **38**, 279–297 (2007). https://doi.org/10.1007/s10838-007-9050-9

Received:

Revised:

Accepted:

Published:

Issue Date:

DOI: https://doi.org/10.1007/s10838-007-9050-9