Quantum theory as an inferential system

John O. Campbell

April 2017

In a number of previous blog posts, books (1; 2) and papers (3; 4) I have developed the notion that due to a number of new findings a wonderfully unifying scientific interpretation may now be possible. This interpretation focuses on ‘inferential systems’ which may operate throughout nature and which accumulate the knowledge required for the existence of complex systems. Such inferential systems are typified by internal probabilistic models which are updated by evidence. The internal models code an executable strategy for existence which manifests as type of generalized phenotype or, in Dawkins’ terms, vehicles. In turn these phenotypes or vehicles collect evidence concerning the success of the coded strategy, evidence that is used to update the internal model in a Bayesian manner and accumulate a catalogue of knowledge that specifies a strategy for existence.

This paradigm is non-controversial in its application to many complex systems which emerge from physical reality including biology (5), neural-based behaviour (6; 7) and cultural evolution (8). Indeed, the consensus understanding within each of these fields is consistent with the inferential system model (9). It is however a greater challenge for this paradigm to explain physical systems. While some physical theories or interpretations conform to the paradigm (10; 11), they are, yet, far from consensus.

However, a recent research program conducted by Philipp Hohn derives quantum theories, our most fundamental physical theories, from informational or Bayesian postulates (12; 13) and thus demonstrates how quantum theory may arise through the actions of an inferential system. His papers develop quantum theory within the context of an ‘observer’ who interrogates natural systems with binary questions that may be answered using experimental evidence. The statistics over all possible answers to these experimental questions forms the ‘state space’ of the system. 

The culmination of Hohn’s program is the demonstration, given some reasonable constraints on the observer’s ability to acquire information, that the internal model or ‘catalogue of knowledge’ (13) that the observer will develop by evolving their model using the principles of Bayesian inference is quantum theory.  In other words, the evidence-based inferential system he describes will infer quantum theory from the evidence it receives. 

Unfortunately, quantum theory is only now emerging from over a century of conceptual confusion whose lingering effects tend to place Hohn’s findings in an ambiguous context. Some of the key scientists who developed quantum theory, including Niels Bohr, interpreted this theory as inconsistent with our usual understanding of scientific theories. They made two key speculative interpretations which have long haunted the theory: 

1) The words ‘measurement’ in the quantum postulates refers to human activities and therefore the fundamental theory involves humans and/or human consciousness.

2) Quantum theory does not describe the actual world but is rather a kind of abstract or Platonic description which at best only indirectly describes the real world.

  

The first of these casts a shadow on Hohn’s findings as his conclusion may appear somewhat trivial, in the sense that it is historically obvious that science has inferred its understanding of quantum phenomena from the evidence and that this inferential process has resulted in the catalogue of knowledge known as quantum theory. From this perspective Hohn’s conclusions appear little more than an account of how quantum theory was inferred by scientists. This perspective hinges on Hohn’s ‘observers’ being interpreted as human, scientific observers.

On the other hand, Hohn’s conclusion may be interpreted in a more profound light where ‘observers’ are not constrained to scientific observers but rather may be any entity operationally capable of gathering and processing empirical evidence. In this sense, an observer is any entity which acts as a quantum phenomenon and thus extends the appropriate title ‘observer’ to all quantum entities. 

This ambiguity between the anthropocentric status of ‘observer’ or ‘measurement’ has dogged quantum theory from its beginnings. However modern developments seem to have come down in favor of the broadly-based understanding that the use of these words in quantum theory does not constrain them to human ‘observers’ or only to ‘measurements’ performed by humans. As Wojciech Zurek notes (14):

The dividing line between what is and what is known to be has been blurred forever. While abolishing this boundary, quantum theory has simultaneously deprived the “conscious observer” of a monopoly on acquiring and storing information: Any correlation is a registration, any quantum state is a record of some other quantum state. 

A human presence or consciousness is not required for the world to operate in a quantum manner. All quantum states may be considered observers.

Hohn however, appears to endorse Bohr’s anthropocentric interpretation of this issue. He quotes approvingly Bohr’s statement that (15): 

There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature...

Perhaps the best that can be said is that Bohr’s statement contradicts principles considered central to science in its denial that science is fundamentally a description of actual reality. Bohr was entirely spot on in the sense that so far science has only developed an abstract theory concerning quantum phenomena. Science has not yet discovered the details of the actual reality which quantum theory describes but we should expect this to eventually become known. Claims of the completeness of quantum theory are premature; as Einstein noted, quantum theory is obviously incomplete. What physics says about Nature has value only to the extent that its descriptions share mutual information with how Nature is and the purpose of physics or any other science is to maximize this mutual information.

It is evident that there is a very long way yet to go on this path towards maximization. Our ignorance is immense. This path may even be of an infinite length. Any claim of complete understanding is hopelessly premature and only presents obstacles to further understanding which we can expect to be developed a little further along the path.

We should understand that ‘measurement’ of quantum phenomena is not an experience unique to humans. Quantum entities ‘measure’ each other all the time. Measurements conducted by humans are merely set-ups for us to view naturally-occurring quantum interactions; interactions which occur all the time, whether humans are watching or not.

This confusion may be at least partially resolved by an understanding that models of phenomena occur at many different levels within nature. Those models which are constructed by humans participating in science attempt to model other aspects of nature and many of these ‘aspects of nature’ involve models of their own. Thus, scientific models often describe other models. For example, the science of genetics describes the genetic models found in organisms and due to the centrality of genetics within biology this model is crucial to our understanding of most aspects of biology. The point I would like to stress is that the actual genetic models are not the creation of scientists but rather are models coded in DNA and existing within organisms. They are what nature is. On the other hand, the scientifically constructed model of genetics is a description of nature’s models written in DNA; the scientific models are models of models and have value only to the extent that they accurately describe or share mutual information with nature’s actual models.

The same relationship may be found in neuroscience; mental models are not the product of scientists rather they are models coded in neurons within brains. The scientifically constructed models which attempt to model mental models are likewise models of models. As the great neuroscientist, Karl Friston noted (6):

Our capacity to construct conceptual and mathematical models is central to scientific explanations of the world around us. Neuroscience is unique because it entails models of this model making procedure itself. There is something quite remarkable about the fact that our inferences about the world, both perceptual and scientific, can be applied to the very process of making those inferences: Many people now regard the brain as an inference machine that conforms to the same principles that govern the interrogation of scientific data.

During the decade since Friston wrote the above he has expanded this paradigm to biology and perhaps to existence in general (16).

If we take Hohn’s demonstration at face value and accept that his ‘observer’ may be any entity capable of receiving and processing quantum information then we may extend this paradigm to quantum physics and view scientifically constructed models of quantum phenomena as scientific models of nature’s models. 

The second lingering speculation concerning quantum theory, that it does not describe what nature actually is, also cast a shadow on Hohn’s findings. Since the inception of quantum theory, a debate has raged between those who view quantum theory as ‘epistemology’ (a description of what we can know about reality) and those who view it as ‘ontology’ or how nature actually is. 

Einstein championed the view that science describes ontology and that the ultimate aim of science is to describe what nature is.  

Bohr was less constrained by this traditional view of science as naturalism. For example, he promoted the idea of vitalism (the belief that life contains non-physical phenomena) in biology long after almost all biologists had firmly rejected that notion. As the biologist, Ernst Mayr wrote (17): 

we might note in passing a rather peculiar twentieth-century phenomenon-the development of vitalistic beliefs among physicists. Niels Bohr was apparently the first to suggest that special laws not found in inanimate nature might operate in organisms. He thought of these laws as analogous to the laws of physics except for their being restricted to organisms.

The development of quantum theory was deeply tainted with non-naturalistic explanations, leading E.T. Jaynes to quip that the theory’s accepted norm was ‘A standard of logic that would be considered a psychiatric disorder in other fields’ (18) . As the historian of science, Juan Miguel Marin, observes (19):

Not only was consciousness introduced hypothetically at the birth of quantum physics, but the term ‘mystical’ was also used by its founders to argue in favour and against such an introduction. In private conversations, at least as early as the 1927 Solvay Congress, the founders discussed ideas about quantum theory, ‘mysticism’ and consciousness. It was also around this time that Einstein accused Bohr of introducing ‘mysticism’ into physics.

This debate may be mitigated by an insistence that scientific theories are models of nature which strive to maximize the mutual information they share with nature. Scientific theories are what we can say about how nature is. This ‘ontic’ or naturalistic position gains support from some recent papers (20; 21) which claim to decide conclusively that quantum theory is a description of what nature is (21):

This means that we can deduce the quantum state from a knowledge of the ontic state. Hence, if these assumptions are correct, we can claim that the quantum state is a real thing (it is written into the underlying variables that describe reality).

If we reject mysticism and accept the position that the quantum state describes how nature actually is, then we can interpret Hohn’s paradigm in a more significant manner. His ‘observers’ may be interpreted as any quantum entity that can interact or acquire information at the quantum level.  This information acquisition involves a probabilistic model or state function of the information expected to be received. As the quantum entity acquires information or evidence it updates its probabilistic model in a Bayesian manner. As a result of this evidence-based evolution the wave function may be seen as a knowledge repository or catalogue which contains knowledge capable of making highly accurate predictions. This knowledge catalogue is the quantum entity’s ‘worldview’ and is equivalent to quantum theory. It is in this sense that our scientific quantum theory shares mutual information with nature operating at the quantum level.

In this view quantum entities are but another instance of nature’s many inferential systems and scientific quantum theory is but a human model which encapsulates one of nature’s many models. We may understand quantum phenomena within a naturalistic framework where it forms a level of existence within a nested hierarchy of levels that include biology, neural based behaviour and culture.  Each level is engaged in a common process which provides a unified view of existence over many levels of scientific subject matter. This common process is the inference of knowledge from information, a process by which knowledge evolves to explore the many strategies for existence found in nature.

References

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3. Bayesian Methods and Universal Darwinism. Campbell, John O. s.l. : http://arxiv.org/abs/1001.0068, 2009. AIP Conf. Proc. 1193, 40 (2009), DOI:10.1063/1.3275642. pp. 40-47.

4. Universal Darwinism as a process of Bayesian inference. Campbell, John O. s.l. : Front. Syst. Neurosci., 2016, System Neuroscience. doi: 10.3389/fnsys.2016.00049.

5. Darwin, Charles. The Origin of Species. sixth edition. New York : The New American Library - 1958, 1872. pp. 391 -392.

6. Free Energy and the brain. Friston, Karl and Klass, Stephan. 2007, Synthese, 159, pp. 417-458.

7. The visual system’s internal model of the world. Lee, Tai Sing. Proceedings of the IEEE. Institute of Electrical and Electronics Engineers, Vols. 103(8), 1359–1378.

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10. Smolin, Lee. The life of the cosmos. s.l. : Oxford University Press, 1998.

11. Quantum Darwinism. Zurek, Wojciech H. s.l. : http://www.nature.com/nphys/journal/v5/n3/abs/nphys1202.html, 2009, Nature Physics, vol. 5, pp. 181-188.

12. Quantum theory from rules on information acquisition. Hohn, Philipp Andres. s.l. : Entropy, 2017, Vols. 19(3), 98; .

13. Quantum theory from questions. Hohn, Philipp Andres and Wever, Christopher S.P. s.l. : PhysRevA.95.012102, 2017.

14. Decoherence and the Transition form Quantum to Classical - Revisited. Zurek, Wojciech H. s.l. : http://arxiv.org/ftp/quant-ph/papers/0306/0306072.pdf, 2003.

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17. Mayr, Ernst. This is Biology: The science of the living world. s.l. : Harvard University Press, 1998. ISBN 9780674884694.

18. Jaynes, Edwin T. Clearing up the mysteries - the original goal. [book auth.] John Skillings. Maximum Entropy and Bayesian Methods. s.l. : http://bayes.wustl.edu/etj/articles/cmystery.pdf, 1989.

19. 'Mysticism' in quantum mechanics: the forgotten controversy. Marin, Juan Miguel. 2009, European Journal of Physics, pp. 807 - 822.

20. On the reality of quantum states. Pusey, Matthew F., Barrett, Jonathan and Randolph, Terry. 2012, Nature Physics 8 , pp. 475 - 478.

21. Are quantum states real? Hardy, Lucien. s.l. : http://arxiv.org/abs/1205.1439, 2013, International Journal of Modern Physics B.