Abstract
Microphysicalism seems the undisputed paradigm not only in solid-state physics and condensed matter physics, but also within many other branches of science that use computer simulations: The reduced description on the micro level seems epistemically favorable. This chapter investigates whether this view can be defended even in those cases where an ontological reduction is not under dispute. It will be argued that only when the mathematical models exhibit scale separation, is the reduced description on the level of the constituents a fruitful approach.
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Notes
- 1.
The term ‘scale separation’ is borrowed from the theory of critical phenomena, but applied more generally in this paper.
- 2.
Hoyningen-Huene distinguishes further types of reduction which for the purpose of this paper that focuses on mathematically formulated models and theories are not of relevance.
- 3.
It should be noted that when paradigm cases of reduction like thermodynamics are contested it is often the bridge rules that are problematic.
- 4.
This feature will only become relevant in the latter sections of this paper, when I briefly touch on the applicability of my approach beyond many-body systems.
- 5.
Note that this phase transition is not adequately described within the semiclassical approach as the emission of normal light due to spontaneous emission necessitates a quantum mechanical treatment of light.
- 6.
The Navier-Stokes equations can be derived from the micro-level description given by Liouville’s equation that gives the time evolution of the phase space distribution function. The derivation of the Navier-Stokes equation from even more fundamental laws, is, however, not the concern of this paper.
- 7.
There have been, however, recent advances in direct numerical simulations of the Navier-Stokes equations in the turbulent regime. However, the investigated Reynolds number today are below those investigated in laboratory experiments and it takes weeks or month of CPU. Also boundaries pose a severe challenge to the direct numerical simulations of the Navier-Stokes equations (see Pope 2000).
- 8.
Note that here I only claim that this reduction is successful in so far as it allows quantitative predictions of certain macro-variables. I do not address the question as to whether the micro-model offers an encompassing explanation, as discussed, for example, in Batterman (2001).
- 9.
This is the reason why, strictly speaking, the renormalization procedure works only at the critical point. The more remote the system is from the critical point, the more dominant become finite fluctuations of the correlation length that spoils the self-similarity.
- 10.
Thanks to Chris Pincock for pointing out this aspect.
- 11.
- 12.
Compare Hüttemann (2004) for a critical discussion on the ontological priority of the micro level.
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Hillerbrand, R. (2015). Explanation Via Micro-reduction: On the Role of Scale Separation for Quantitative Modelling. In: Falkenburg, B., Morrison, M. (eds) Why More Is Different. The Frontiers Collection. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43911-1_5
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