Modeling Quasi-Quantum Social Processes

Exploring Synergies across Theoretical Domains


David L. Sallach

Apply quantum models to social domains?  What strategies?

1.  Analogy
Analogical thought has been essential to scientific theory.  The discovery of the role of symmetry (and conservation) originated from an analogy with double-entry bookkeeping.  The evolution of field theory in physics repeatedly reconceptualized prior field formulations.  But analogy can only be a starting point;  to be effective, such qualitative insights need to be formalized.  For the social domain, this will necessarily require cross-domain structure mapping.

2.  Reduction
Reductionism in the natural sciences it has made repeated and vital contributions but, in the social sciences, it does not have a good track record.  Wilson, Hameroff, Penrose and others seek to build up from quantum chemistry to neurostructures.  However, the brain is wet, noisy and operates on a scale that is 10-20 orders of magnitude larger than quantum decoherence (Tegmark 2000; Joos 2003:107-109), so progress based upon reductionism is likely to be slow.  

3.  Formality
The quantum formalism has been successfully applied in areas such as computation and information retrieval.  It is possible that quantum algorithms may be useful within the social sciences when no substantive linkages have been made.  However, such an approach must be applied carefully, with the formalisms actually fitting the requirements of the social domain.  As cosmologists have identified the 'quasi-classical' domain as emergent from a thoroughly quantum universe, social scientists may posit and explore a quasi-quantum (QQ) social domain.  

4.  Convergence
Integrating across domains (e.g., the complexity, computational & social sciences), and enhancing the explanatory capacities of each strand, there is the potential for unique kinds of theoretical breakthroughs.  Of course, a Popperian strategy holds that all such innovations are falsifiable and resist refutation.

Balance
A key consideration is to know and be explicit about the assumptions one is making.  It will also be valuable to address the implications that each approach may have for the others.

The link between the first and third strategies (analolgy and formality) may be of greatest interest for a QQ social domain.  More specifically, if analogical components are mapped to the quantum formalism, it will give expression to the former and substance to the latter.  Of course, such a translation is unlikely to be simple and obvious, but it provides a process through which applicable concepts can be applied and aligned.

Competing quantum interpretations

The quantum formalism is effective at an operational level, and many working physicists are content with that.  In contrast, quantum interpretation is unresolved ... a playground of philosophers.  Still, coherent interpretation may be important in addressing new domains.

1.  Collapse (Bohr, Heisenberg, von Neumann)
Superposition is resolved through waveform collapse resulting from measurement.  Difficulties:  1) bifurcates quantum and classical worlds,  2) overly subjective (why do physical processes differ based on whether they are observed or not?), and 3) fails to address cosmology.

2.  Hidden Variables / Pilot Wave (de Broglie, Bohm, Bell)
Explains quantum paradoxes by positing hidden (unobserved) variables that produce quantum effects.  Difficulties:  Undocumentable, overly convenient, violates Occam's razor.

3.  Branching/Multiverse (Everett, Deutsch)
Precludes paradox by positing that every alternative that can happen, does, either by creating a new universe (Everett) or passing into a pre-existent one (Deutsch).  Difficulties:  ontologically extravagent, vague on cross-scale interactions.

4.  Decoherence/Consistent Histories (Gell-Mann, Hartle, Griffiths, Omnes, Joos, Zeh, Zurek)
Eliminates paradoxes and anomalies by restricting analysis to consistent (commuting) histories.  Difficulties:  may narrow and constrain results.

Quantum interpretation and cosmology

W.P. Grygiel:  The main objective of all interpretational efforts is to develop an appropriate framework or logically consistent discourse valid for both microscopic (quantum) and (classical) macroscopic regimes.

J.S. Bell (1981), Quantum Mechanics for Cosmologists
     Cosmologists ... must find the usual interpretive rules of quantum mechanics a bit frustrating:  '... a measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured ...'.
     It would seem that the theory is exclusively concerned with the 'results of measurement' and has nothing to say about anything else.  When the 'system' in question is the whole world, where is the measurer to be found?  Inside, rather than outside, presumably.  What exactly qualifies some subsystems to play this role?  Was the world wave function waiting to jump for thousands of millions of years until a single-celled living creature appeared?  Or did it have to wait a little longer for some more highly qualified measurer -- with a Ph.D.?  

Gell-Mann and Hartle (1990), Quantum Cosmology
     In the quasi-classical domain, probabilities (approximately obeying the rules of probability theory) can be assigned only to sets of histories that approximately decohere.  Decoherence needs a sufficiently coarse-grained description of alternative histories of the universe.
     If quantum mechanics is the underlying framework of physics, then there must be a description of the universe as a whole and everything in it in quantum mechanical terms.  In a theory of the whole, there can be no fundamental division into observer and observed.

Cosmological and Social Domains
Note that like the cosmological domain, the social domain:  1) exists at a quasi-classical scale, and  2) makes data available through observation but not through controlled experiment.  However, the social domain also appears to manifest quantum effects, especially in the realm of intentionality:  goals, strategies, plans, beliefs, commitments, desires, attachments, trust, emotions, etc.

Consistent histories

1.  Sample Spaces
Define a quantum [social] sample space of events.  A sampling space is the complete ensemble of mutually exclusive possibilities (events) one and only one of which actually occurs at any one time.  In any single quantum [social] sample space, the ordinary rules of probability are valid.  Associated with a sample space 𝔖 is an event algebra 𝔏 consisting of subsets of events of the sample space.

2.  Histories
Given a sample space, a probability distribution assigns a non-negative probability Pr(𝔢) to each event.  Aggregations of elements of the sample space are referred to as histories, where a history is thought of as a sequence of events at successive times.  Each full quantum history can be treated as a separate event in a new sampling space that consists of all the histories within the family.  The term “family of histories” is also used to denote a coarser sample space of histories that generates a particular Boolean algebra.

3.  Pre-probabilities
The ket |(Subscript[Ψ, 1])⟩, a quantum property at time (Subscript[𝓉, 1]), should not be considered a physical property but, rather, a pre-probability.  |(Subscript[Ψ, 1])⟩ should be thought of as a mathematical construct suitable for calculating certain probabilities, thus, a pre-probability.  It is useful as long as one does not try to combine the results for incompatible bases into a single description.  [Cf., Popper's propensity model.]

4.  MQS States
A Macroscopic Quantum Superposition (MQS) state corresponds to quantum situations that are macroscopically distinct.  There is nothing 'wrong' with MQS states from the viewpoint of fundamental quantum theory.  If one supposes that the usual Hilbert space structure of quantum mechanics is the appropriate sort of mathematics for describing the world, then MQS states will be present in the theory.  Families of histories containing MQS states may be useful for understanding where the reasoning underlying a paradox has gone astray.

5.  Consistent Families
     A consistent family of histories must meet certain conditions, specifically, the sample space must consist of a collection of mutually orthogonal projectors that add up to the history identity, and the chain operators for different members of the sample space must be mutually orthogonal.  
     Consider two histories of Great Britain:  one a political history which discusses the monarchs, the other an intellectual history focusing on the developments of British science.  Which is the correct history of Great Britain?  That is not the proper way to compare them.  Instead, there are certain questions that can be answered by one history rather than the other.
     
6.  Dependent Events
A quantum event--a property of a system at a single time--can be dependent upon a quantum event at some different time.  Then B depends on A, or A is the base of B.  Sometimes this contextuality can be removed by refining the history of the sample space, but in other cases it is irreducible either because a refinement is prevented by non-commuting projectors, or because it would result in a violation of consistency conditions.

7.  Density Matrices
Density matrices are employed to give a partial description of a quantum system.  They often function as pre-probabilities that can be used to generate probability distributions in different bases, and averages of different observables, but do not correspond to an actual physical [social] property.  Since, when using consistent histories, one assigns probabilities to histories and not to single states, the connection between probability and state is blurred (Grygiel).

8.  Quantum Reasoning
     When using a single quantum framework, quantum reasoning is (at least formally) identical to classical reasoning and, thus, it is important to be aware of the framework that is being used to construct a quantum description.  Each framework has its own sample space with its own probabilities and a corresponding event algebra.
     A framework is a Boolean of commuting projectors based upon a suitable sample space.  The sample space is a collection of mutually orthogonal projectors that sum to the identity, and thus form a decomposition of the identity.  
     Initial data can be expressed using a density matrix thought of as a pre-probability.  In order to draw conclusions from initial data, they must be embedded in an appropriate sample space.  A useful approach is to begin with a relatively coarse sample space and then refine it in different ways, depending upon the sorts of questions one is interested in.  When one refines a sample space, the probability associated with each of the elements of the original space is divided up among their replacement in proportion to their weights.
     Quantum dynamics are stochastic:  even given a precise state of the system at one time, various alternatives can occur at other times, amd the theory only provides probabilities for these alternatives.  Stochastic dynamics requires both the specification of an appropriate sample space, or family of histories, and also a rule [or rules] for assigning probabilities to histories.  Instead of starting with a single well-defined temporal development that can answer all questions, one has to start with the physical [social] questions themselves and use these questions to generate an appropriate framework in which they make sense.

Mapping Quantum Structures to the Social Domain

Discrete entities:  "a matter of life and death"

Superposition:  the first principle of quantum theory (Dirac), inherent in social intentionality
			Can be represented as a complex orientation field that combines emotion with cognition/concept/semantics.





Entanglement:  in social reality, it is multi-faceted:
 Family, group, tribe, network, ethnicity, language, religion, nation, civilization, and their interwining

({{Structure, Quantum, Social, Shared Characteristics}, {Unit, Quantum, Lifeform, Discrete form}, {Superposition, Physical, Intentional, Possibilistic}, {Entanglement, Cross-system quantum effects, Diversity of forms, Coevolution through interaction}, {Diffusion, Experimental histories, Social and cultural histories, Chains of divergence and convergence}, {Perspective, Basis, Endogenous orientation, Focal interest}})

David Bohm (1951):  "... thought processes and quantum systems are analogous in that they cannot be analyzed too much in terms of distinct elements, because the 'intrinsic' nature of each element is not a property existing separately from and independently of other elements but is, instead, a property that arises partially from its relation with other elements. ... "

"We suggest that … the behavior of our thought processes may perhaps reflect in an indirect way some of the quantum-mechanical aspects of the matter of which we are composed."

Erwin Schödinger (1926;1952):  \ (pp. 9-10)

" … the wave function is believed to embody facts.  It is the marvelous tool that is supposed to embody all facts concerning behavior of the system, not only the values of those observables that have sharp values, but also the statistics of those that have not ... The wave functions are mental material for building analytical pictures of real objects [entities] in one's mind; and performing thought [computational] experiments on them; the results of these thought experiments are obtained by ample use of mathematics and are then compared with the results of real experiments."(pp. 80-82)

Symmetry Analysis

Symmetry analysis constitutes the most important (indeed one might say the only) widely applicable method for finding analytical solutions of non-linear problems.

Deeply scientific issues are often associated with peeling away symmetries or searching for new symmetries of complex systems in order to reach a deeper understanding.

It is often possible to obtain more insight into the functional form of the result by applying symmetry arguments.  This always needs the introduction of additional information [such as theoretical relationships].

Symmetry analysis has both algebraic and statistical aspects.  It will require close attention to the scale of the social proceses, and grain of the corresponding data.

It has the potential to constitute a new and more effective form of social analysis.

It seems unlikely that this research program could be adequately addressed without a tool like Mathematica, and the community that supports it.

References

Arfi, Badredine. 2005. "Resolving the trust predicament:  A quantum game-theoretic approach." Theory and Decision 59:127-174.

Bohm, David.  1951.  Quantum Theory.  New York:  Dover.

Cantwell, Brian J.  2002.  Introduction to Symmetry Analysis.  New York:  Cambridge University Press.

DiTeodoro, Antonio & Victor M. Villalba.  2008.  Asympototic symmetries in cosmological models.  International Journal of Theoretical Physics 47:1885-1890.

Gell-Mann, Murray.  1990.  Quantum mechanics in the light of quantum cosmology.  Pp. 425-458 in W.H. Zurek, ed., Complexity, Entropy and the Physics of Information.  Redwood City, CA:  Addison-Wesley.

Griffiths, Robert B.  2002.  Consistent Quantum Theory.  New York:  Cambridge University Press.

Grygiel, Wojciech P.  2007.  Consistent quantum histories:  Towards a universal language of physics.  Concepts of Physics 4:71-98.

Kiefer, C.  2003.  Consistent histories and decoherence.  Pp. 227-258 in E. Joos, H.D. Zeh, C. Kiefer, D. Giulini, J. Kupsch & I.-O. Stamatescu, eds., Decoherence and the Appearance of a Classical World in Quantum Theory.  New York:  Springer.

Omnes, Roland.  1999.  Understanding Quantum Mechanics.  Princeton, NJ:  Princeton University Press.

Przibram, K., ed. & M.J. Klein, tr.  1967.  Letters on Wave Mechanics.  New York:  Philosophical Library.

Tegmark, M.  2000.  Importance of quantum decoherence in brain processes.  Physics Review E61:4194-4206.

Viana, Marlos.  2008.  Symmetry Studies:  An Introduction to the Analysis of Structured Data in Applications.  New York:  Cambridge University Press.