Bayesian component of the web of reality

Given that Zurek's work may offer a new plateau in our understanding of objective reality we might take a closer look at his accomplishments. In particular his derivation of Born's Rule, the rule providing probabilities concerning the outcome of interactions, gives us a new understanding of the place of probability within reality.

Bayesian probability, one of the two main schools of probability and the one we will focus on, considers probability as a measure of a state of knowledge.[i] It extends Aristotelian logic, where variables are either true or false, to a logic of probability where variables may have continuous real values between 0 and 1 (false and true). It has been proven, given a desiderata of rationality and consistency, that Bayesian probability is the only mathematical system able to extend logic into probability.

As E.T. Jaynes remarked :

So, thanks to Cox, it was now a theorem that any set of rules for conducting inference, in which we represent degrees of plausibility by real numbers, is necessarily either equivalent to the Laplace-Jeffreys rules, or inconsistent.[ii]

Keeping in mind that probability, in this sense, is the science of rational inference, that is making valid inferences from evidence, we can examine Zurek's accomplishment in deriving quantum probabilities from the rest of quantum theory.

It is hard to overstate Zurek's accomplishment in deriving the quantum axioms concerning prediction from those concerning the wave function. Physically his finding implies that the measurable outcomes are modelled by the wave function of the entangled system composed of quantum entity and environment prior to decoherence. The predictive model has two components:

1) The property of the quantum system that will be revealed during the information transfer to the environment will correspond to a 'pointer basis'. These properties are roughly classical in nature and do not include weird superposed quantum properties. The nature of the environmental entities with which the quantum system is entangled will influence the composite wave function so that it models a specific property that will be the subject of the information transferred during decoherence. That property might be position or it might be momentum or something else dependent on the environment.

2) The model predicts the possible values of the information concerning the specified property that will be transferred along with the specific probabilities for each value.

Combined these two components provide an exquisitely accurate predictive model. Zurek's work demonstrates that this model is not a creation of science rather it is a model inherent in nature which science has discovered.[iii]

The predicted probabilities, in a very Bayesian sense, describes the information concerning the quantum entity that will be received or 'known' in the environment of our objective reality. Once an information transfer takes place through the process of decoherence the predictive model inherent in the wave function is updated as required in axiom 3).

As by definition our objective reality consists precisely of this web of interactions this is the only information or knowledge available to any of the participating entities. At bottom all information is this type of quantum information and it is dispensed to its environment in accord with quantum theory entailing probability.

Quantum theory considered in this context provides a model for what we or any other entity in the quantum web can expect to 'know' about any other fundamental entity in the web. This knowledge is described as a probability distribution over a number of outcomes. It is heavily influenced by prior information; the quantum state at some previous known 'initial condition' and pertinent features of the environment (contained in the Hamiltonian).

A predictive model is inherent in the wave function of the entangled quantum entity plus environment system which provides probabilities for outcomes.

Quantum theory claims to supply the most accurate predictions of expected outcomes that are in principal possible. To date this claim is supported by the evidence. In other words when a measurement, an interaction or a computation is made the 'surprise' or discrepancy between the outcome and the theory's prediction is the minimum possible.

Once information is transferred to the environment through the process of decoherence the predictive model is updated in accordance with axiom 3.

A simple model of a generic knowledge mechanism is illustrated above and is important to our discussion as it will be used repeatedly below to illustrate emergent levels of complexity that have evolved over the course of time.

Although our web of interactions is fundamentally a web of quantum interactions it has, over the history of the universe, evolved emergent structures of great complexity, which will be discussed in detail below. These structures may also be understood in terms of information or knowledge but the information involved with these structures is still quantum information that may be processed and from which inferences may be drawn.

As an example, one might certainly balk at the idea that sensory information gathered by biological organisms has much to do with quantum interactions. However when we consider that the eye functions by receiving a sample of light from its environment and that the interaction between these photons from the environment and molecules such as rhodopsin in the retina is a quantum interaction involving only the transfer of quantum information we can see that it is precisely these interactions that are the source of any information subsequently available to the organism. The eye, the organism's brain and its behavioural reactions function to process this information, draw inferences from it and behave appropriately in response to it. None of these functions however are the source of new information. Likewise hearing depends on the detection of pressure waves. Pressure is transmitted through a quantum interaction where information regarding momentum is transferred to the environment in a quantum manner.

Perhaps an even more dramatic example involves photosynthesis, the biological process through which the sun's light is converted to a biologically useable form of chemical energy. Photosynthesis is a fundamental process in the web of life but complete details of its operation have long eluded researchers; specifically how this biological process can be 95% efficient while the best solar panel technology can produce only about 20% efficiency. Recent research indicates the answer may be that nature employs a quantum computation to decide on the most efficient chemical pathways to employ for each photon of light received.[iv] In this process, crucially important to life, a great portion of the underlying quantum information is harnesses to improve efficiency.

We might now see the web of reality as a web of information flow. The information that one entity can have of another and that composes the web is bound by the laws of physics and is probabilistic in nature.

[i] Wikipedia article, Bayesian Probability, http://en.wikipedia.org/wiki/Bayesian_probability, as viewed January 6, 2008

[ii] Jaynes, E. T., 1986, `Bayesian Methods: General Background (174Kb),' in Maximum-Entropy and Bayesian Methods in Applied Statistics, J. H. Justice (ed.), Cambridge Univ. Press, Cambridge

[iii] Zurek W, 2007, Relative States and the Environment: Einselection, Envariance, Quantum Darwinism and the Existential Interpretation, arXiv:0707.2832v1, http://arxiv.org/PS_cache/arxiv/pdf/0707/0707.2832v1.pdf

[iv] Sension Roseanne (2007), Biophysics: Quantum paths to photosynthesis, Nature 446, 740-741 (12 April 2007)