Abstract
Quantum laser theory proceeds in a way that seems at variance with the mechanistic model of explanation. First, as is typical for a complex systems theory, the detailed behavior of the component parts plays a surprisingly subordinate role. In particular, the so-called “enslaving principle” seems to defy a mechanistic reading. Moreover, being quantum objects, the “parts” of a laser are neither located in space nor describable as separate entities. I want to show that, despite these apparent obstacles, quantum laser theory constitutes a good example of a mechanistic explanation in a quantum physical setting, provided that one broadens the notion of mechanism. One may feel that such adjustments are ad hoc and question-begging. However, I will argue that the necessary adjustments are far more natural and less drastic than one may expect. Among other things I suggest that the structural similarities between semiclassical and quantum laser theory support a mechanistic reading of the latter.
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Notes
- 1.
This fact is also the reason why the laser is a paradigmatic example of a self-organizing system.
- 2.
See Kuhlmann and Glennan (2014) for a more comprehensive discussion of why quantum mechanics seems to undermine mechanistic explanations, and why in fact it doesn’t.
- 3.
I work in the so-called ‘Heisenberg picture’. As is well-known quantum mechanics can be formulated in different mathematically and physically equivalent ways. The two best-known representations or ‘pictures’ are the Schrödinger picture and the Heisenberg picture. Quantum mechanics is mostly formulated in the Schrödinger picture, where the state is time-dependent while the observables for position and momentum are time-independent. In the Heisenberg picture, on the other hand, observables carry the time-dependence, whereas the states are time-independent. Mathematically, the Heisenberg picture is related to the Schrödinger picture by a mere basis change, and thus physically both pictures lead to the same measurable quantities, of course. In some respects, the Heisenberg picture is more natural than the Schrödinger picture (in particular, for relativistic theories) since it is somewhat odd to treat the position operator, for instance, as time-independent. Moreover, the Heisenberg picture is formally closer to classical mechanics than the Schrödinger picture. For this reason it is advantageous to use the Heisenberg picture if one intends to compare the quantum and the classical case, which I want to do for the laser.
- 4.
Note that the first and the last part of the above row of equations are just definitions, indicated by “≡”.
- 5.
See Haken (1985), p. 236ff.
- 6.
The fluctuations comprise thermal and quantum fluctuations, giving rise to additional statistical correlations between the atoms and the field. Bakasov and Denardo (1992) show in some detail that there are some corrections due to the “internal quantum nature” of laser light, which they call “internal quantum fluctuations”.
- 7.
One can make a few simplifications (single laser mode, coupling constant independent of λ and μ) which ease the ensuing calculations. However, in the present context they are not helpful for a better understanding because they require further explanation and justification and widen the gap with realistic situations. For this reason I use the equations on p. 246 in Haken (1985), but without the simplifications introduced on p. 123, and that means with additional indices, which are still there on pp. 121ff.
- 8.
- 9.
In the 1970s Hermann Haken established the interdisciplinary approach of synergetics by transferring certain general insights that he had gained in his work on laser theory (see Haken 1983). Synergetics is one of a few very closely related theories of self-organization in open systems far from thermodynamic equilibrium.
- 10.
The predominance of one particular mode throughout the entire laser defines a ground state that no longer exhibits the symmetry of the underlying fundamental laws. These laws thus have a hidden symmetry that is no longer visible in the actual state of affairs, i.e., it is “spontaneously broken”.
- 11.
Moreover, in semiclassical laser theory, not everything is correct. For instance, below a certain threshold, lasers emit conventional lamp light. Semiclassical laser theory cannot accommodate this fact.
- 12.
Cartwright (1983) exploits this similarity in a different way. According to her reading, the quantum physical and the semiclassical approach offer two different theoretical treatments, while they tell the same causal story. And since we thus have different theoretical treatments of the same phenomenon, the success of these explanations yields no evidence in favour of a realistic interpretation of the respective theories. Morrison (1994) objects to Cartwright’s claim that the fate of the theoretical treatments is a supposedly unique causal story, saying that it is not unique. A closer survey of laser theory reveals that “there are also a variety of causal mechanisms [my emphasis, MK] associated with damping and line broadening” (Morrison 1994). Consequently, one has to look for something else that the different approaches share. Morrison argues that capacities, as introduced in Cartwright (1989), may do the job. However, as she then shows, there is also an insurmountable obstacle for telling a unique causal story in terms of capacities, if one understands capacities as entities in their own right. Against such a Cartwrightian reification of capacities, Morrison argues that, if one wants to describe laser theory in terms of capacities, there is no way around characterizing them in relational terms. Eventually, this could give us a unique causal story, albeit without any additional ontological implications about capacities as entities in their own right. While I think that Morrison’s reasoning is generally correct, I think there is an alternative to saying that capacities can only be characterized in relational terms. I claim that the causal story of laser light is best caught in terms of mechanisms. In the context of mechanisms, it is much more obvious that we don’t need, and should not reify causal powers, because the crucial thing is the interactive, i.e., causal organization of the system’s parts.
- 13.
This is what Batterman (2002) claims: “There are many aspects of the semiclassical limit of quantum mechanics that cannot be explained purely in quantum mechanical terms, though they are in some sense quantum mechanical” (p. 109). […] “It is indeed remarkable how these quantum mechanical features require reference to classical properties for their full explanation. Once again, these features are all contained in the Schrodinger equation—at least in the asymptotics of its combined long-time and semiclassical limits—yet, their interpretation requires reference to classical mechanics” (p. 110).
- 14.
Bokulich (2008) refrains from some of the stronger claims by Batterman arguing that “one can take a structure to explain without taking that structure to exist, and one can maintain that even though there may be a purely quantum mechanical explanation for a phenomenon, that explanation—without reference to classical structures—is in some sense deficient” (p. 219); […] semiclassical explanations are deeper than fully quantum mechanical explanations, insofar as they provide more information about the dynamical structure of the system in question than the quantum calculations do” (p. 232). However, in the present context even these weaker claims are not needed.
- 15.
In Kuhlmann (2011) I deal with the general question of whether complex systems explanations can be understood as mechanistic explanations.
- 16.
The Ginzburg-Landau theory was initially a phenomenological theory that analyzed the occurrence of superconducting phase transitions by general thermodynamic arguments without using a microscopic underpinning (as later supplied by the Bardeen-Cooper-Schrieffer theory). See Morrison (2012) for a detailed discussion of the philosophical implications concerning emergence in particular.
- 17.
See Kuhlmann and Glennan (2014) for a more general and comprehensive discussion of whether quantum physics undermines the mechanistic program.
- 18.
As it is very common in ontology, I use the expression ‘entity’ as the most neutral ontological term, covering everything that exists from conventional things like dogs to properties and states-of-affairs. I only mention this because, in MDC’s account of mechanisms, the term ‘entities’ is used more specifically in the sense of things or ‘substances’.
- 19.
Falkenburg (2007, Chap. 6) explores the part-whole relation for quantum systems in more detail. She argues that the sum rules for conserved quantities such as mass-energy, charge, and spin are crucial for determining what we should rate as the constituents/parts of matter. On the basis of this criterion she draws a positive conclusion regarding the question of whether even the quanta of interaction fields such as the gluons in the quark model can feature as parts of quantum systems.
- 20.
I want to mention briefly that in current ontology there is a popular approach, namely trope ontology, which analyses things as bundles of copresent properties (understood as tropes, i.e., particularized properties). And many trope ontologists argue that properties should be seen as parts, although they can occupy, as constituents of one bundle, the same spacetime region.
- 21.
As an aside, Bechtel and Richardson (2010) distinction of decomposition and localization already implies that successful decomposition does not automatically lead to localized components.
- 22.
See Healey (2013) for similar considerations, but with a diverging aim.
- 23.
See Kuhlmann (2011) for detailed examples.
- 24.
States comprise those properties that can change in time, like position, momentum, and spin (e.g., up or down for electrons). Besides these changing properties, there are permanent properties, such as mass, charge, and spin quantum number (e.g., electrons have the spin quantum number ½, which allows for two possible quantized measurement results, up or down, for any given spin direction).
- 25.
A pure state is represented by a vector in a Hilbert space. The contrast with a pure state is a mixed state, which can no longer be represented by a single vector. A mixed state can describe a probabilistic mixture of pure states.
- 26.
See Hüttemann (2005), who offers a very convincing study of the extent to which emergence occurs in QM, and correspondingly, ‘microexplanations’ fail vis-à-vis QM. Although Hüttemann’s focus differs from that of the present investigation, his arguments are nevertheless relevant, with suitable adjustments.
- 27.
Note that this doesn’t preclude the possibility of emergence in the sense of a failure of synchronic microexplanations.
- 28.
Recently, Reutlinger (2014) has argued that renormalization group methods also yield non-causal explanations—and a fortiori non-mechanistic ones—not because of the irrelevance of micro-details, but because the mathematical operations involved are not meant to represent any causal relations.
- 29.
See Sterrett (2010) for a philosophical analysis of the role of dimensional analysis in science.
- 30.
So can EPR style correlations also be explained by quantum mechanics? Imagine someone performs spin measurements on separated electron pairs that were emitted from a common source. Further imagine that our observer realizes that there are certain regularities in the results of two spin measurement devices. Each time she gets a spin up result in measurement device 1, she gets spin down in measurement device 2, and vice versa. Naturally, our observer assumes that there is a common cause for the correlations. By analogy, if you have pairs of gloves and each pair gets separated into two distant boxes, you always find a right glove in box 2, if you found a left glove in box 1. However, one finds that the electron pairs are correlated in a more intricate way: if you rotate the orientation of the spin measurement devices, you find the same kind of spin correlations again, even if you rotate by 90°. Since an electron cannot have a definite spin with respect to two mutually perpendicular orientations at the same time, the common cause explanation breaks down for the correlated spins of our electron pairs. In contrast, with quantum mechanics, it is possible to derive EPR style correlations from the basic axioms, namely from the unitary time evolution of states given by the Schrödinger equation and the resulting principle of superposition. But does this mean that EPR style correlations are explained? One could argue that in the framework of standard quantum mechanics, EPR style correlations are explained in a covering-law fashion. However, there is no explanation for why they come about, no causal story, and in particular no mechanistic story. Only particular interpretations or modifications of QM, such as Bohmian QM or the many worlds interpretation, may supply something like a mechanistic explanation.
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Kuhlmann, M. (2015). A Mechanistic Reading of Quantum Laser Theory. 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_13
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