Abstract
Friends of the so-called nomological interpretation of the wave function claim that the wave function does not represent a physical substance, nor does it represent a property of physical things; rather, it is law-like in nature. In this paper we critically assess this claim, exploring both its motivations and its drawbacks and reviewing some of the recent debates in the literature concerning such an interpretation.
This paper corresponds with some few amendments and incorporations to the talk the authors gave at the XII Ontology Congress in San Sebastian, Spain, the 6th of October of 2016.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
For particles with spin, the GE is slightly more complicated and takes the form:
$$ \frac{dQ_k}{dt}=\frac{\mathrm{\hslash}}{{\mathrm{m}}_k}\operatorname{Im}\left(\frac{\Psi^{\ast}\left(Q,t\right)\cdot {\overrightarrow{\nabla}}_{q_k}\Psi \left(Q,t\right)}{\Psi^{\ast}\left(Q,t\right)\cdot \Psi \left(Q,t\right)}\right) $$where the dot represents an appropriate product between spinor wave functions.
- 2.
This is the view actually endorsed, for instance, by David Bohm in the seminal paper of Bohmian mechanics (see Bohm 1952). Given the peculiarities of the wave function field that we will comment on in the next section, Bohm and Hiley (1993) finally interpret the wave function (or a functional thereof) as a field of active information.
- 3.
- 4.
The argument in favour of the reality of configuration space is reinforced by the fact that, in non-relativistic quantum mechanics, the recourse to configuration space (or to spaces of higher dimensionality) is inevitable. By this, we mean that all the information encoded by the wave function in configuration space cannot be encoded by separable properties of points of 3-dimensional space (that is by a finite number of fields all defined in 3-dimensional space). The idea is that some information concerning the correlation of entangled systems cannot be represented in a separable way in 3-dimensional space.
- 5.
It is worth recalling that none of the 3N dimensions of configuration space can be identified with any of the 3 dimensions of ordinary space.
- 6.
- 7.
See, for instance, Goldstein and Zanghì (2013, p. 97, n. 2).
- 8.
In Bohmian mechanics, one naturally works with the wave function in the representation of positions and from this follows the prominence of configuration space. However, in other quantum theories, the quantum state is defined as a ray of Hilbert space and its interpretation as a field would be even more problematic.
- 9.
For an excellent and extended discussion of this point, see Rivat (2016, Section 5).
- 10.
See Dürr et al. (1992, 860ss) for the definition of the effective wave function of a system and an argument to the conclusion that effective wave functions obey the Schrödinger dynamics.
- 11.
See Dürr et al. (1997: Section 13).
- 12.
See DeWitt (1967).
- 13.
Despite both G(t) and Ψ(t) being time-dependent parameters in a law, there are important disanalogies between these two cases. First, the wave function may well be much more complicated than G(t). Second, G(t) is a spatially constant parameter that only determines the strength of the gravitational force but not its form. In the case of the wave function, however, it has a non-trivial spatial dependence and the specific form of the law of motion of the Bohmian particles cannot be grasped without knowing Ψ(t). As a consequence, while it does not make sense to claim that G(t) defines the law of gravitation, it is more plausible to consider—together with DGZ—that Ψ(t) defines the law of motion of the Bohmian particles.
- 14.
Recall Goldstein and Zanghì’s remark, already quoted, that “if the wave is nomological, specifying the wave function amounts to specifying the theory.” (Goldstein and Zanghì 2013, p. 102).
- 15.
This is not quite the same determinism as the determinism one normally ascribes to Bohmian mechanics. The latter can be expressed in brief like this: Given the positions of all the particles at some time t 0, and the universal wave function Ψ(t 0), the full history of the universe is mathematically determined. The determinism of the dispositions described here should be expressed instead as: Given all the positions at a moment t 0, and the universal wave function Ψ(t 0), the velocities of all the particles at t 0 (i.e., the manifestation of the global disposition) are determined.
- 16.
An exception to this is classical gravity, which is universal (both on the active and passive side) and impossible to shield or thwart. Precisely this universality is what suggested to Einstein that it might not be a force at all, which led to the geometrization of gravity in General Relativity. In General Relativity gravity is still universal and impossible to shield, if we understand it as the disposition of all massive/energetic substances to curve spacetime in the fashion prescribed by Einstein’s equations.
References
Albert, D. (1996). Elementary quantum metaphysics. In J. T. Cushing, A. Fine, & S. Goldstein (Eds.), Bohmian mechanics and quantum theory: An appraisal (pp. 277–284). Dordrecht: Kluwer Academic Publishing.
Armstrong, D. (1983). What is a law of nature? Cambridge: Cambridge University Press.
Belot, G. (2012). Quantum states for primitive ontologists. European Journal for Philosophy of Science, 2(1), 67–83.
Bird, A. (2007). Nature’s metaphysics: Laws and properties. Oxford: Oxford University Press.
Bohm, D. (1952). A suggested interpretation of the quantum theory in terms of ‘hidden’ variables I and II. Physical Review, 85, 166–193.
Bohm, D., & Hiley, B. J. (1993). The undivided universe: An ontological interpretation of quantum theory. London: Routledge & Kegan Paul.
DeWitt, B. S. (1967). Quantum theory of gravity. I. The canonical theory. Physical Review, 160, 1113–1148.
Dretske, F. I. (1977). Laws of nature. Philosophy of Science, 44(2), 248–268.
Dürr, D., Goldstein, S., & Zanghi, N. (1992). Quantum equilibrium and the origin of the origin of absolute uncertainty. Journal of Statistical Physics, 67, 843–907.
Dürr, D., Goldstein, S., & Zanghi, N. (1997). Bohmian mechanics and the meaning of the wave function. In R. S. Cohen, M. Horne, & J. Stachel (Eds.), Experimental metaphysics: Quantum mechanical studies for Abner Shimony (pp. 25–38). Berlin: Springer.
Earman, J. (1989). World enough and space-time: Absolute vs. relational theories of space and time. Cambridge, MA/London: MIT Press.
Esfeld, M., Lazarovici, D., Hubert, M., & Dürr, D. (2014). The ontology of Bohmian mechanics. British Journal for the Philosophy of Science, 65, 773–796.
Goldstein, S., & Zanghi, N. (2013). Reality and the role of the wave function in quantum theory. In A. Ney & D. Albert (Eds.), The wavefunction: Essays on the metaphysics of quantum mechanics (pp. 91–109). Oxford: Oxford University Press.
Lange, M. (2009). Laws and lawmakers: Science, metaphysics, and the laws of nature. Oxford: Oxford University Press.
Maudlin, T. (2007). The metaphysics within physics. New York: Oxford University Press.
Rivat, S. (2016). On the metaphysics of quantum mechanics: Why the wave function is not a field. Unpublished manuscript available at: http://philosophy.columbia.edu/files/philosophy/content/Sebastien_Rivat_On_the_metaphysics_of_quantum_mechanics_-_why_the_wave_function_is_not_a_field.pdf
Suárez, M. (2015). Bohmian dispositions. Synthese, 192, 3203–3228.
Wallace, D., & Timpson, C. (2010). Quantum mechanics on spacetime I: Spacetime state realism. British Journal for the Philosophy of Science, 61(4), 697–727.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Solé, A., Hoefer, C. (2019). The Nomological Interpretation of the Wave Function. In: Cordero, A. (eds) Philosophers Look at Quantum Mechanics. Synthese Library, vol 406. Springer, Cham. https://doi.org/10.1007/978-3-030-15659-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-15659-6_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-15658-9
Online ISBN: 978-3-030-15659-6
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)