A strongly emergent system is a physical system whose properties are not reducible to causal relationships and interactions between the elements of this system. That is, the whole is not the sum of its parts. However, are there real examples of strongly emergent systems?
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1$\begingroup$ Thermodynamics emerges from statistical mechanics, its variables can be mathematically stated by averages in statistical mechanics, but are a completely new set. Would you call it strongly emergent? $\endgroup$– anna vCommented Mar 13, 2022 at 9:24
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$\begingroup$ @anna v No, this is a weak emergence. $\endgroup$– Arman ArmenpressCommented Mar 13, 2022 at 9:39
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$\begingroup$ "Strong emergence is the notion of emergence that is most common in philosophical discussions of emergence, and is the notion invoked by the British emergentists of the 1920s." consc.net/papers/emergence.pdf . Then this discussion is not on topic for the site, it is a philosophical question. certainly not a physics topic. I expect biological systems which emerge from the underlying atomic substructure would be strongly emergent . $\endgroup$– anna vCommented Mar 13, 2022 at 10:51
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2$\begingroup$ As far as anyone knows, all physical phenomena on "ordinary" length scales (really, from the size of a proton to the size of the observable Universe) can be explained in terms of the Standard Model plus general relativity, at least in principle. There are many cases where this link is not known explicitly (the vast majority of cases are like that in fact). But there are no cases where someone has observed a phenomenon that provably cannot be reduced to complicated interactions between fundamental particles. However, reducing things down to the Standard Model is rarely necessary or useful. $\endgroup$– AndrewCommented Mar 13, 2022 at 13:58
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2 Answers
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A strong piece of evidence that all physical phenomena are in principle reducible to constituent interactions is: For all symmetries and conservation laws (such as energy and momentum) that are strictly satisfied by the known microscopic interactions, no macroscopic violation is known in any physical system, however complex. This includes biological organisms, which have had billions of years of opportunity (and a strong incentive) to find a way to "cheat" conservation of energy, say, but have not done so.
It is generally impossible in practice to predict specific behaviors of complex systems, but it is very plausible that these behaviors are nevertheless mathematically determined by constituent interactions and that it is "merely" too difficult to solve the equations (and obtain accurate initial conditions). An important and successful test of this view is: When, fortuitously, some property of the underlying interactions is readily mathematically composable (i.e., tractable reductive reasoning can constrain the overall system behavior in some way) -- as with symmetries and conservation laws -- the resulting constraints do match observations.
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$\begingroup$ So you are saying that there is no Heisenberg uncertainty and that we are simply too dump to understand the physics behind? $\endgroup$– trikPuCommented Mar 13, 2022 at 17:39
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1$\begingroup$ @trikPu By "mathematically determined", I don't necessarily mean that systems are deterministic, but that macroscopic behaviors have whatever degree of predictability follows mathematically from the microscopic interactions. When there is intrinsic uncertainty, then overall system behaviors follow the expected distribution. $\endgroup$– nanomanCommented Mar 13, 2022 at 17:47
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In order to answer this you need to fill out the meaning of the word 'reducible'. A concept such as 'a heap' can be applied to a heap of coins, yet a single coin is not a little heap, nor does it have a property 'heapness' in addition to its other properties.
A more thought-provoking example is afforded by computer programming languages. Is a language such as Python or Java 'reducible' to assembler code or logic gates? Arguably the answer is either 'no', or if it is 'yes' then we deduce that the term 'reducible' is being used in a way that does not give much insight into the phenomenon in question (the high-level language). The concept does not capture the relations between levels of description. For more on this you might find this discussion helpful:
Does physics explain why the laws and behaviors observed in biology are as they are?
Finally, in quantum entanglement we have a whole which is not the sum of its parts, in the sense that the state of the whole simply cannot be expressed as if the parts each had self-contained properties. It is hard to cash out the term 'reducible' in such a way that it says entangled systems are entirely reducible. So if that is the case then any entangled pair of particles is a counter-example which was asked about.
answered Mar 13, 2022 at 9:16
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$\begingroup$ Thanks for the answer. In my opinion, part of your answer refers to weak emergence, that is, if all the information about each element of the system, about all their interactions and about the very structure of the system is known, it is quite possible to accurately describe the emergent properties of the whole. For strongly emergent systems, this is not possible, since even complete information about elements and interactions cannot model an emergent property. As for entangled particles: an entangled pair is one quantum object, it does not consist of two separate parts even in principle. $\endgroup$ Commented Mar 13, 2022 at 9:38
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$\begingroup$ @ArmanArmenpress what is your distinction between a "system with strong emergence" and a "system which does not consist of two separate parts even in principle"? If I have an entangled pair I certainly can separate them and look at just one of the particles, but I will not have full information about the system $\endgroup$ Commented Mar 13, 2022 at 17:51
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$\begingroup$ @By Symmetry It's not the same thing. In the case of strong emergence, the macroscopic emergent description, even in principle, cannot be reduced to a microscopic one. If you model all the microscopic degrees of freedom of a system, you don't get the same emergent macroscopic property. As for entanglement: it is one thing to consider a part of an object, another thing to consider the whole object. If the emergent object is not something that can be divided into parts, then the question is off. $\endgroup$ Commented Mar 13, 2022 at 18:02