Completely Top–down Hierarchical Structure In Quantum Mechanics

Completely Top–down Hierarchical Structure In Quantum Mechanics

Aharonov, Y.Cohen, E.Tollaksen, J.

Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest “atoms”? In this paper we answer these questions in the negative for a specific class of systems and measurements. After a general introduction of the topic, we present the main idea with a simple two-particle example, where strong correlations arise between two apparently empty boxes. This leads to surprising effects within atomic and electromagnetic systems.

A general construction based on pre- and postselected ensembles is then suggested, wherein the N-body correlation can be genuinely perceived as a global property, as long as one is limited to performing measurements which we term “strictly local.” We conclude that under certain boundary conditions, higher-order correlations within quantum mechanical systems can determine lower-order ones, but not vice versa. Surprisingly, the lower-order correlations provide no information whatsoever regarding the higher-order correlations. This supports a top–down structure in many-body quantum mechanics.

The above is definitely unwieldy for many of us laypersons, but I feel I have a minimally better grasp after reading this commentary by George Ellis, who made at least one appearance in the old flaws with mechanistic thinking thread on SF ->

Top-down causation and quantum physics

G. Ellis

The nature of emergence of complexity out of the underlying physics is a key issue in understanding the world around us (1). Genuine emergence can be claimed (2⇓–4) to depend on top-down causation, which enables higher emergent levels to direct the outcomes of causation at lower levels to fulfill higher-level causal requirements; for example, the needs of heart physiology at the systems level determine gene expression at the cellular level via gene regulatory networks (5) (Fig. 1). However, the idea of top-down causation has been denied by a number of commentators (e.g., refs. 6 and 7). The paper by Aharonov et al. (8) makes a strong contribution to this debate by giving quantum physics examples where top-down causation manifestly occurs. This physics result has strong implications for the philosophical debate about whether strong emergence is possible. Indeed, it gives specific examples where it occurs in a remarkably strong form.

Now, the word “causation” is regarded with suspicion by many philosophers of science, so to characterize what is happening one can perhaps rather use a number of different descriptions such as “whole–part constraint” or “top-down realization.” The key point remains the same, that higher levels can influence lower-level outcomes in many ways, and hence explain how strong emergence is possible. This occurs across science in general, and in physics in particular (3, 4). The latter point is key because of the alleged causal completeness of physics, which supposition underlies supervenience arguments against strong emergence (6) and the supposed possibility of overdetermination of lower-level outcomes (figure 1 of ref. 8). However, if top-down action occurs in physics in general, and in quantum physics—the bottom level of the hierarchy of emergence (Fig. 1)—in particular, such claims are undermined

There are, however, two further issues to mention. First, top-down causation is usually based in multiple realizability at lower levels, leading to equivalence classes of lower-level elements’ being the true causal factors at that level. This is very clear, for example, in the case of digital computers (chapter 2 of ref. 4). The question is how the reults of Aharonov et al. (8) relate to this issue of existence of lower-level equivalence classes.

Second, they comment at the end that their results might throw light on the issue of how the classical world emerges from the quantum. I rather doubt that this will be the case. Their philosophically important conclusions regarding emergence arise from the rather restrictive measurement protocol proposed in the paper. My view is that enlightenment on the quantum–classical issue will rather come from further study of the nature of heat baths (15) and their relation to wave function collapse (14).

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See also this paper by Michael Bitbol:

Downward Causation without Foundations

Downward causation looks impossible as a concept, but is well established as a fact. A top-down flux of causation going from an emergent level of processes (say biological or mental) to the fundamental level of processes (say physical) that is supposed to underpin it, sounds like a paradox. Yet this paradox seems to be forced upon us when we want to make sense of many phenomena ranging from psychosomatics to the mutual interaction between organismic and cellular life, for instance when we want to express certain facts of experience in which a change in our mental state has an immediate impact on our physiological state. My conviction is that what is likely to be paradoxical here is neither experience nor even its verbal expression in terms of downward causation, but the standard metaphysical interpretations that are superimposed onto them.The metaphysical conception to be dispelled when downward causation is at stake is a dualist and foundationalist picture: a picture according to which downward causation only makes sense if there are at least two (ontologically) distinct levels of processes, with their own specific entities and properties able to influence each other by way of efficient causality. This is also a picture in which, conversely, if there exists only one fundamental level of being and process, then the very concept of inter-level causation is pointless. To counterweight this popular picture, I will advocate in this article the idea that the phrases ‘downward causation’and ‘upward causation’ are loose ways of describing two modalities of action exerted on a process, which nothing prevents one from construing as non-dual. Acting globally (or coarsely, at a large scale) yields consequences that can be detected by experiments bearing on local levels. Conversely, intervening at the smallest accessible scale yields consequences that can be detected by experiments bearing on the larger scale. On the basis of this account, I will conclude that:

(i) Downward and upward causation are neither illusory nor inherently existent, but rather indexed by a certain level of intervention. Accordingly, downward and upward causation are not substantial concepts, but rather relational concepts throughout.

(ii) The relevant relations do not take place between otherwise self-subsistent entities.They contribute to the very definition of their terms. These defining relations are primarily the relations between the agents and the targets of their actions; and secondarily the relations between various domains of acting and experimenting

Completely Top–down Hierarchical Structure In Quantum Mechanics

Aharonov, Y.Cohen, E.Tollaksen, J.

Here is one of the better minds on the subject:

 Which way does causation proceed? The pattern in the material world seems to be upward: particles to molecules to organisms to brains to mental processes. In contrast, the principles of quantum mechanics allow us to see a pattern of downward causation. These new ideas describe sets of multiple levels in which each level influences the levels below it through generation and selection. Top-down causation makes exciting sense of the world: - Ian Thompson

https://philpeople.org/profiles/ian-j-thompson/news

Top-down causation and emergence: Some comments on mechanisms

George Ellis

Both bottom-up and top-down causation occur in the hierarchy of structure and causation. A key feature is multiple realizability of higher level functions, and consequent existence of equivalence classes of lower level variables that correspond to the same higher level state. Five essentially different classes of top-down influence can be identified, and their existence demonstrated by many real-world examples. They are: algorithmic top-down causation; top-down causation via non-adaptive information control, top-down causation via adaptive selection, top-down causation via adaptive information control and intelligent top-down causation (the effect of the human mind on the physical world). Through the mind, abstract entities such as mathematical structures have causal power. The causal slack enabling top-down action to take place lies in the structuring of the system so as to attain higher level functions; in the way the nature of lower level elements is changed by context, and in micro-indeterminism combined with adaptive selection. Understanding top-down causation can have important effects on society. Two cases will be mentioned: medical/healthcare issues, and education—in particular, teaching reading and writing. In both cases, an ongoing battle between bottom-up and top-down approaches has important consequences for society.