Abstract
This paper explores the idea that the wave-function is the unique fundamental concrete physical stuff of the world itself. The paper focuses on two suggestions: (a) First-quantized non-relativistic quantum mechanics is a not a theory of the 3-dimensional motions of particles, but of the 3N-dimensional undulations of a concrete physical field –the wave-function itself – where N is a very large number that corresponds, on the old way of thinking, to the number of elementary particles in the universe. (b) This particularly radical coming-apart of the geometry (on the one hand) and the fundamental arena (on the other) is what’s at the bottom of everything that’s exceedingly and paradigmatically strange about quantum mechanics.
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Notes
- 1.
Maybe a quick disclaimer is in order, at this point, about the metaphysics of lawhood: Nothing that I’m going to say here has any implications whatever – in so far as I am aware – about the dispute between Humean and Necessatarian ideas about the nature of laws. My own experience (mind you) is that many of the topics we will be talking about here, and many of the important questions about the foundations of physics in general, turn out to be a little easier to get one’s head around if one has a Humean conception of laws in the back of one’s mind – but none what I say here is going to in any way require or entail or depend on a conception like that.
- 2.
This (of course) is almost certainly impossible – that’s why we need quantum mechanics! But imagining otherwise will do no harm – for the moment – in so far as our purposes here are concerned.
- 3.
- 4.
Carlo Rovelli (as we will see in section 3 of this essay) has been thinking along lines like these, for some years now, about the General Theory of Relativity. Carlo sometimes speaks as if he aims to do away, at the fundamental level, with even so much as a differentiable manifold. But what I think he actually means to deny is not that there is a fundamental differential manifold, but (rather) that that manifold has a certain particular metaphysical status. What I think he actually means to deny (that is) is not that the world has some ultimate and fundamental set of topological possibilities, but (rather) that those possibilities inhere in, and are parasitic on, some ultimate and fundamental substance. Marco Dees’ unpublished doctoral dissertation The Causal Structure of Space-Time (on the other hand) aims to go genuinely further. Dees aims to treat the fundamental arena as a completely unstructured set of points, and proposes that not only geometrical and affine structure, but topological and differential structure as well, be understood as by-products of the dynamics. My own suspicion – for reasons that should become clear in section 2 of this essay – is that Dees’ very imaginative and ambitious program is likely to prove very difficult to actually carry through.
- 5.
And it happens that a project like that has in fact been underway for something on the order of 20 years now. For progress reports, see my Time and Chance, and chapters 1 and 2 of my After Physics.
- 6.
Or rather, on the particular version of the GRW theory that I am thinking about here – the original version, in which the wave-function is not supplemented with any further “primitive ontology”, the one which is usually referred to in the literature nowadays as GRW0.
- 7.
Various strategies have been proposed – strategies that go under the collective name of Primitive Ontology – for somehow hanging on to the claim that the fundamental space of the world is (notwithstanding everything) 3-dimensional. The interested reader can find detailed accounts of these strategies a number of the essays in Albert & Ney (2013); arguments against these strategies can be found in chapter 7 my book After Physics (Albert 2016).
- 8.
Note that earlier on, when we were dealing with a classical point-like ‘item’, we needed a fundamental, pre-dynamical, geometrical structure in order to even write down our dynamical laws. That’s what footnote 18 was about. But now that we are dealing with a quantum-mechanical, field-like wave-function, the thought is that a fundamental differential manifold, with no affine or geometrical structure at all, will suffice. That’s what section 2 was about.
- 9.
It might be thought that the transition to Quantum Mechanics introduces new and potentially worrisome issues here. It might be thought (in particular) that the non-local influences that we encounter in a theory like GRW – the ones (that is) associated with Bell’s Theorem – will bring other or additional or conflicting geometrical structure into the picture with them. But a little reflection will show that what’s non-local about those influences is not that they depend on some other or additional or conflicting conception of distance, but (rather, and precisely) that they do not depend on any conception of distance at all.
- 10.
Once upon a time (in papers like “Elementary Quantum Metaphysics,” which dates back to the late 1990’s) I used to say that the world of a theory like GRW, or Bohmian Mechanics, was only approximately 3-dimensional and Euclidian – that it was only 3-dimensional and Euclidian in so far as one was careful not to look too closely. And this now strikes me as a very bad way to have put it. What one does discover – if one looks at the world closely enough to see that it is quantum-mechanical rather than classical – is that the topology of the fundamental arena (on the one hand) and the topology induced by the emergent geometry (on the other) come apart. But it is no less the case in a quantum-mechanical world than it was in any classical one that the only conception of distance that has any physically significant role to play is the three-dimensional Euclidian one. The geometry of a non-relativistic first-quantized quantum-mechanical world (then) is not in any sense, and not by any measure, one whit less Euclidian and 3-dimensional than the geometry of a Newtonian world is.
References
Albert, D. Z. (2016). After physics. Cambridge, MA: Harvard University Press.
Brown, H. (2005). Physical relativity. Oxford: Oxford University Press.
Dees, M. (unpublished manuscript). The causal theory of space-time.
Foster, J. (1982). The case for idealism. New York: Routledge & Keegan Paul.
Ney, A., & Albert, D. Z. (Eds.). (2013). The wave function. New York: Oxford University Press.
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Albert, D. (2019). Preliminary Considerations on the Emergence of Space and Time. 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_6
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