#bohmian

Recently, we've been talking about emergence - more explicitly about emergent phenomena in many body systems. But what if the concept of emergence would not only apply 'within' quantum mechanics but also 'outside' the theory? What if quantum mechanics itself is an emergent theory from a classical-type underlying 'reality'? This is exactly the approach of an interpretation of quantum mechanics, called emergent quantum mechanics (EmQM).

Where is EmQM located in the 'zoo' of interpretations?

The 'zoo' of interpretations and alternative theories of quantum mechanics can be classified by their answers to the violation of Bell's inequalities. Bell's Theorem is a theory-independent result and therefore must hold for any possible approach which reproduces the results of standard quantum mechanics. Roughly speaking, the theorem's consequences are that one either has to give up the traditional understanding of realism, or the idea of locality. E.g. Rovelli's approach and QBism belong to the camp which gives up traditional realism and adheres to locality, whereas Bohmian Mechanics sticks to realism and therefore embraces nonlocality. In general, hidden variable theories belong to this 'realist' camp.

EmQM suspects a locally deterministic theory from which standard quantum mechanics emerges. Walleczek and Groessing (p. 2, [1]) suppose that instead of "absolute quantum randomness" there might be "quantum interconnectedness" - indicating the presence of some kind of nonlocality, e.g. nonlocal causality. Hence, this approach seems to belong to the above called 'realist' camp, in which a traditional understanding of realism is embraced and the price to pay is nonlocality, more neatly called "quantum interconnectedness".

Why EmQM?

Walleczek and Groessing [1] argue that a metaphysical fundament is needed in order to unify general relativity and quantum mechanics. Since general relativity is strictly deterministic and standard quantum mechanics inherently indeterministic, the metaphysical fundament of each theory starkly opposes each other such that the lack of unification seems inevitable. However, setting a microscopically causal fundament for both branches of physics, as well as the focus onto emergent phenomena, might yield a solution. For instance, the theory of quantum gravity already relies on the idea of emergent spacetime - together with EmQM it may be possible to lay a metaphysical framework of 'all physics'. Nevertheless it might be questionable, in my view, how this is supposed to work with an approach as EmQM in which nonlocality is a cornerstone, i.e. possibly causing trouble with causality as we know it from relativity.

EmQM and Bohmian Mechanics

Since EmQm and Bohmian Mechanics (BM) belong to the same, 'realist' camp, both seem to be related. Both claim to describe the underlying 'reality' beneath standard quantum mechanics. Both approaches share the belief that standard textbook quantum mechanics does not have descriptive character regarding the nature of reality, even though the theory is empirically successful. Then, standard quantum mechanics is regarded as an 'effective' theory.

However, two approaches can be well compared by regarding how they attempt to reproduce standard quantum mechanics. One main aspect in this respect is the appearance of randomness. Both approaches claim to be fundamentally deterministic and therefore have to explain why we experience the randomness of standard quantum mechanics in our laboratories. Bohmians do this by introducing so called "absolute uncertainty" [3], which is a consequence of the quantum equilibrium hypothesis. Effectively, this means that a universe in which Bohmian Mechanics governs the dynamics, it is impossible to gain knowledge about the configuration of a system beyond the probability distribution determined by the wave function ρ=|ψ|^2. Hence, the complete configuration of point particles, their positions and velocities do exist, but there is no experimental access to it. This limited knowledge is supposed to be the source of randomness and uncertainty that we encounter in standard quantum mechanics:

"This absolute uncertainty is in precise agreement with Heisenberg's uncertainty principle. But while Heisenberg used uncertainty to argue for the meaninglessness of particle trajectories, we find that, with Bohmian mechanics, absolute uncertainty arises as a necessity, emerging as a remarkably clean and simple consequence of the existence of trajectories." (p.864 [3])

Instead of making use of a (more or less ad-hoc) hypothesis, the appearance of randomness in EmQM seems a bit more natural: Only because the underlying dynamics is supposed to be deterministic, this does not imply pre-determination. This is something one can already observe in purely classical systems: The more complex a system is, the more uncertain is the outcome (often referred as "deterministic chaos"). A minor change in the boundary conditions can cause a huge change in the result. Thus, the central point is emergence:

"Critical in this context is that emergent phenomena are subject to unpredictability as a consequence of the intrinsically self-referential nature of the governing dynamics [...]." (p.5 [1])

In comparison, BM formulates its theory in a rather rigid manner. It formulates postulates from which the theory can be deduced. The issue with this is that these postulates have kind of an ad-hoc character. In my view, EmQM circumvents these problems by being less strict/definite. This approach does not seem to have a fixed formalism yet (at least I haven't found analyses on the same level of rigor as there are for BM), while the research seems to be more focused on exploring how emergence can enter the picture - as e.g. 't Hooft does in [2], where he describes explicit examples of possibly emergent symmetries. (Disclaimer: maybe my impression is incorrect, since I have only superficial knowledge about EmQM.)

Regardless of this point, both approaches seem to be interconnected in the end. Walleczek and Groessing (p.2 [1]) claim that a future EmQM would include BM. Hence, in my view, it might be possible that EmQM might support BM in the sense that it lifts the necessity of possibly ad-hoc appearing postulates as formulated in BM. Thus, any theory of quantum mechanics (orthodox or unorthodox) might not only yield emergent phenomena within the theory but quantum mechanics might unravel itsel as an emergent 'phenomenon'.

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References:

[1] Walleczek, Groessing, Is the World Local or Nonlocal? Towards an Emergent Quantum Mechanics in the 21st Century, arXiv:1603.02862, 2016

[2] 't Hooft, Emergent Quantum Mechanics and Emergent Symmetries, arXiv:0707.4568, 2007