Category Archives: quantum probability theory


eJournal:, ISSN 2567-6458, 2.January 2019
Author: Gerd Doeben-Henisch


This is a continuation from the post QUANTUM THEORY (QT). BASIC PROPERTIES, where basic properties of quantum theory (QT) according to ch.27 of Griffiths (2003) have been reported. Before we dig deeper into the QT matter here a remark why we should do this at all because the main topic of the blog is the Actor-Actor Interaction (AAI) paradigm dealing with actors including a subset of actors which have the complexity of biological systems at least as complex as exemplars of the kind of human sapiens.


As Griffiths (2003) points out in his chapter 1 and chapter 27 quantum theory deals with objects which are not perceivable by the normal human sensory apparatus. It needs special measurement procedures and instrumentation to measure events related to quantum objects. Therefore the level of analysis in quantum theory is quite ‘low’ compared to the complexity hierarchies of biological systems.

Baars and Edelman (2012) address the question of the relationship of QT and biological phenomena, especially those connected to the phenomenon of human consciousness, explicitly. Their conclusion is very clear: “Current quantum-level proposals do not explain the prominent empirical features of consciousness”. (Baars and Edelman (2012):p.286)

Behind this short statement we have to accept the deep insights of modern (evolutionary and micro) biology that a main characteristics of biological systems has to be seen in their ability to overcome the fluctuating and unstable quantum properties by a more and more complex machinery which posses its own logic and its own specific dynamics.

Therefore the level of analysis for the behavior of biological systems is usually ‘far above’ the level of quantum theory.

Why then at all bother with QT in the case of the AAI paradigm?

If one looks to the AAI paradigm then one detects the concept of the actor story (AS) which assumes that reality can be conceived — and then be described – as a ‘process’ which can be analyzed as a ‘sequence of states’ characterized by decidable ‘facts’ which can ‘change in time’. A ‘change’ can occur either by some changing time measured by ‘time points’ generated by a ‘time machine’ called ‘clock’ or by some ‘inherent change’ observable as a change in some ‘facts’.

Restricting the description of the transitions of such a sequence of states to properties of classical probability theory, one detects severe limits of the descriptive power of a CPT description compared to what has to be done in an AAI analysis. (see for this the post BACKGROUND INFORMATION 27.Dec.2018: The AAI-paradigm and Quantum Logic. The Limits of Classic Probability). The limits result from the fact that actors within the AAI paradigm are in many cases ‘not static’ and ‘not deterministic’ systems which can change their structures and behavior functions in a way that the basic assumptions of CPT are no longer valid.

It remains the question whether a probability theory PT which is based on quantum theory QT is in some sense ‘better adapted’ to the AAI paradigm than Classical PT.

This question is the main perspective guiding the further encounter with QT.

See next.















  • Bernard J. Baars and David B. Edelman. Consciousness, biology, and quantum hypotheses. Physics of Life Review, 9(3):285 – 294, 2012. D O I: 10.1016/j.plrev.2012.07.001. Epub. URL
  • R.B. Griffiths. Consistent Quantum Theory. Cambridge University Press, New York, 2003


BACKGROUND INFORMATION 27.Dec.2018: The AAI-paradigm and Quantum Logic. Basic Concepts. Part 1

eJournal:, ISSN 2567-6458
Author: Gerd Doeben-Henisch

Some corrections: 28.Dec.2018

As mentioned in a preceding post the AAI paradigm has to be reconsidered in the light of the quantum logic (QL) paradigm. Here some first concepts which have to be considered (see for the following text chapter two of the book: Jerome R. Busemeyer and Peter D. Bruza, Quantum Models of Cognition and Decision, Cambridge University Press, Cambridge (UK), 2012).

The paradigms of ‘quantum logic’ as well as ‘quantum probability theory’ arose in the field of physics, but as it became clear later these formalisms can be applied to other domains than physics too.

The basic application domain is a appears as a paradigm – real or virtual – in which one can distinguish ‘events‘ which can ‘occur‘ along a time-line as part of a bigger state. The ‘frequency‘ of the occurrences of the different events can be ‘counted’ as a function of the presupposed time-line. The frequency can be represented by a ‘number‘. The frequency can be a ‘total frequency’ for the ‘whole time-line’ or a ‘relative frequency’ with regard to some part of a ‘partition of the time-line’. Having relative frequencies these can possibly ‘change‘ from part to part.

The basic application domain can be mapped into a formalism which ‘explains’ the ‘probability’ of the occurrences of the events in the application domain. Such a formalism is an ‘abstraction’ or an ‘idealization‘ of a certain type of an application domain.

The two main types of formalisms dealt with in the mentioned book of Busemeyer and Bruza (2012) are called ‘classical probability theory’ and ‘quantum probability theory’.

The classical theory of probability (CTP)has been formalized as a theory in the book by A.N. Kolmogorov, Foundations of the Theory of Probability. Chelsea Publ. Company, New York, 2nd edition, 1956 (originally published in German 1933). The quantum logic version of the theory of probability (QLTP) has been formalized as a theory in the book John von Neumann, Mathematische Grundlagen der Quantenmechanik, published by Julius Springer, Berlin, 1932 (a later English version has been published 1956).

In the CTP the possible elementary events are members of a set E which is mapped into the set of positive real numbers R+. The probability of an event A is written as P(A)=r (with r in R*). The probability of the whole set E is assumed as P(E) = 1. The relationship between the formal theory CTP and the application domain is given by a mapping of the abstract concept of probability P(A) to the relation between the number of repetitions of some mechanism of event-generation n and the number of occurrences m of a certain event A written as n/m. If the number of repetitions is ‘big enough’, then – according to Kolmogorov — the relation ‘n/m’ will differ only slightly from the theoretical probability P(A) (cf. Kolmogorov (1956):p.4)

The expression ‘mechanism of event-generation‘ is very specific; in general we have a sequence of states along a time-line and some specific event A can occur in one of these states or not. If event A occurs then the number m of occurrences m is incremented while the number of repetitions n corresponds to the number of time points which are associated with a state of a possible occurrence counted since a time point declared as a ‘starting point‘ for the observation. Because time points in an application domain are related to machines called ‘clocks‘ the ‘duration‘ of a state is related to the ‘partition’ of a time unit like ‘second [s]’ realized by the used clock. Thus depending from the used clock can the number of repetitions become very large. Compared to the human perception can this clock-based number of repetitions be ‘misleading’ because a human observer has seen perhaps only two occurrences of the event A while the clock measured some number n* far beyond two. This short remark reveals that the relationship between an abstract term of ‘probability’ and an application domain is far from trivial. Basically it is completely unclear what theoretical probability means in the empirical world without an elaborated description of the relationship between the formal theory and the sequences of events in the real world.

See next.