A while ago I wrote a blog post suggesting that quantum logic should be applied more generally than to quantum physical systems ... that it should be applied to complex classical systems in some cases as well, if they are so complex that their states are unobservable to a certain observer.

This, I suggested, would require making the choice of logic observer-dependent: i.e., the system T might best be modeled by system S using quantum logic, but by system R using classical logic.

I didn't at the time see how to make this speculation rigorous but I've now found a related literature that helps a lot.

And by refining my previous idea, I've come up with an argument that possibly human consciousness may be effectively modeled using quantum logic, whether or not the human brain is a quantum system.

I may write a paper on this stuff at some point (in which process I'll probably figure out nicer ways to express the ideas), but wanted to write it down now while it's fresh in my mind.

Atmanspacher's Idea

Diederik Aerts and Liane Gabora have written some very nice papers related to this topic ... and I read their stuff years ago but didn't quite see how to connect it to my relevant intuitions.

What I discovered just recently was the related work of Harald Atmanspacher, which ties in more directly with the way I was thinking about these issues. (Some relevant papers by both of these guys are linked to at the end of this post.)

Put simply, Atmanspacher's view is that: In any case where two properties of a system cannot be simultaneously measured with high accuracy, you have a situation that should be modeled using quantum logic.

I.e., quantum logic should be applied to any case where there are incompatible observables ... whether or not this is due to quantum microphysics.

Making the Choice of Logic Observer-Dependent

My twist on Atmaspacher's idea is to suggest that quantum logic should be applied, by a cognitive system, to any situation that has two aspects which (perhaps by quantum microphysics, or perhaps simply due to its limitations as a cognitive system) the cognitive system cannot model simultaneously.

That is: If T has two aspects, and S cannot model these two aspects of T simultaneously without becoming non-S, then from the perspective of S, these aspects of T should be modeled using quantum logic rather than classical logic.

Note that S in this argument is not a specific physical system at a particular point in time, but rather a category of instantaneous physical systems, which are being considered as instantiations of a single abstract "system" (for example, "Ben Goertzel" is a category of instantaneous physical systems).

So, my suggestion is that whether T should be reasoned about by quantum or classical logic, must be determined by relativizing the reasoning to some category of instantaneous physical systems.

Possible Implications for Quantum Consciousness

What spurred me to start digging into these issues just now was a conversation with Stuart Hameroff, who believes consciousness to be a quantum phenomenon.

My suggestion is: It could be that a quantum model of human consciousness is the right one, even if the underlying physics of the brain is basically "classical" (and I don't claim to know for sure whether it is or not).

(Note that I referred above to a classical model of "human consciousness", not of consciousness in general -- I tend toward panpsychism, meaning I think everything is conscious and different systems just manifest universal consciousness in different ways.)

As a natural consequence of the above argument, I would suggest that each of us individually, due to our own processing limitations, cannot view ourselves in all aspects simultaneously.

If this is true, then perhaps we should model ourselves using quantum logic.

Being panpsychist I would not identify this with consciousness, but I would say that systems which are sufficiently complex that they implicitly model themselves using quantum logic, in predicting and analyzing their own dynamics, presumably have a distinctive character to the way they manifest universal consciousness.

Can We Tell the Cause of the Incompatibility?

An interesting question is: if I, as a cognitive system, am confronted with incompatible observables ... in what sense can I tell what the cause of this incompatibility is?

Can I tell a case where the incompatibility is caused by my own cognitive limitations, from a case where it is caused by fundamental indeterminacy such as is sometimes hypothesized to occur in quantum microphysics?

It would seem there is no direct way to make this determination, but we can induce general theories from observations of other system aspects, which lead us to hypotheses regarding the causes of an incompatibility.

Some Nice Quotes on Quantum Modeling of Classical Systems

These quotes come from

Andrei Khrennikov:

“I propose to consider any system which produces quantum statistics as quantum (”quantum-like”). A possible test is based on the interference of probabilities. I was mainly interested in using such an approach to ”quantumness” to extend the domain of applications of quantum mathematical formalism and especially to apply it to cognitive sciences. There were done experiments on interference of probabilities for ensembles of students and a nontrivial interference was really found. … Yes, we might expect nonclassical statistics, but there was no reason to get the quantum one, i.e., cos-interference. But we got it!”

Diederik Aeerts & Liane Gabora:

"While some of the properties of quantum mechanics are essentially linked to the nature of the microworld, others are connected to fundamental structures of the world at large and could therefore in principle also appear in other domains than the micro-world."

Diederik Aeerts:

"The emergence of quantal macrostates does not necessarily require the reference to corresponding quantal microstates"

Harald Atmanspacher, Hans Primas & Peter beim Graben:

"A generalized version of the formal scheme of ordinary quantum theory, in which particular features of ordinary quantum theory are not contained, should be used in some non-physical contexts."

"Complementary observables can arise in classical dynamic systems with incompatible partitions of the phase space."

A Few Relevant References

Atmanspacher:

"Weak quantum theory"

"Complementarity in Bistable Perception"

Aerts:

At

see

- Aerts, D. (1982). Example of a macroscopical situation that violates Bell inequalities. Lettere al Nuovo Cimento, 34, pp. 107-111.
- Aerts, D. (1991). A mechanistic classical laboratory situation violating the Bell inequalities with 2sqrt(2), exactly 'in the same way' as its violations by the EPR experiments. Helvetica Physica Acta, 64, pp. 1-23.
- Aerts, D. and Gabora, L. (2005). A theory of concepts and their combinations I: The structure of the sets of contexts and properties. Kybernetes, 34, pp. 167-191.
- Aerts, D. and Gabora, L. (2005). A theory of concepts and their combinations II: A Hilbert space representation. Kybernetes, 34, pp. 192-221