Objective Bayesian Reality 3

Our best physical theories, often called the standard model of particle physics, tell us that the objective web of reality is held together by only three types of interactions, the bonds of the three forces of nature: gravity, the electro-weak and the strong force. A main thrust of current physical research is attempting to reduce these three theories to a single 'theory of everything' that operated in undivided splendour near the time of the Big Bang, when things were simpler. Leading candidates in this search are String Theory and Loop Quantum Gravity.

It is clear that the success of these new theories will be dependent on accounting for phenomena occurring at the plank scale, that is about 10^-35 meters. When we consider that the diameter of a proton is about 10^-14 meters we see that there is a greater relative difference in scale between the Plank scale and that of 'fundamental' particles than there is between that of fundamental particles and phenomena in our experience. We might expect that as much emergent phenomena occurs below the scale of 'fundamental particles as occurs at scales above it.

Indeed some physical theories of reality at the Plank scale propose that 'fundamental' particles themselves, such as the photon may be emergent phenomena.[i] We are thus faced with perhaps an infinite regress of 'fundamental' realities. It looks like it might be 'turtles' all the way down. In spite of that daunting consideration, we may still be amply rewarded by appreciating boundaries on those aspects of reality that may have the ability to influence us or to interact directly with us.

The small number of interactions described by our physical theories are the only interactions known to exist at the particle physics level. In this sense the Logical Positivists have been exonerated; anything that does not interact by these forces is in principal unknown and unknowable to the web of reality we inhabit and from this vantage point may be said to have no existence nor produce any effects that are in principal detectable.

All physical interactions may be viewed as quantum interactions and the theories describing them are the most accurate and powerful in all of science.[1] Thus quantum interactions are at the core of our objective reality, are the gateway through which all of it participants must pass and form a boundary around the extent of reality that can be objectively known. If we are to understand the nature of our objective web we must start with an understanding of quantum mechanics.

Until recently this has not been possible. We have had extremely accurate theories of the quantum for nearly a hundred years but unfortunately although these theories were useful for calculations they shed no light on the nature of the quantum process. As one of the great creators of quantum theory, Richard Feynman said: ‘‘I think I can safely say that nobody understands quantum mechanics.”.[ii]

Fortunately this century long impasse has recently been skirted. The work of Wojciech Zurek, of the Los Alamos National Laboratory, and collaborators has revealed in detail the processes of quantum decoherence, the process central to understanding the mysteries of the quantum.[iii]

Quantum theory may be erected from a number of axioms. Usually it is a good sign for ease of understanding if a scientific theory can be constructed from a few simple axioms using only the assistance of logic. In these cases we need only understand the axioms and all the rest is implied.

With Newtonian classical mechanics this is surely the case. If we take Newton's three easily understood laws of motion as axioms, much of the resulting easily understood classical mechanics can be derived using logic alone. Unfortunately this has not been the case with quantum theory. The axioms underlying it do not seem to relate to anything understandable. Worse, they seem contradictory. We will list a set of axioms for quantum theory and comment on the problems of understanding they entail.

1) For every physical system there is a corresponding mathematical object called a state vector in Hilbert space that has no physical embodiment. This state vector is the most complete source of information that exists concerning the physical system.

How do we understand this? The most complete information we can have of a physical system is a non-physical mathematical object? Sounds like something outside of our web of reality whose existence is in principle unknowable.

2) The state vector evolves in time according to a continuous, deterministic mathematical function except when a measurement occurs and then it jumps to the state described in 4) and 5) below.

This axiom is a little more promising in that the undisturbed state evolves in a mathematically tractable manner. The jump part seems somewhat contradictory; smooth, continuous evolution and then a jump?

3) Once a measurement is made the state vector assumes a state such that the same measurement immediately reapplied to this state has 100% probability of achieving the previous measured result.

More promising yet, this axiom tells us that although there is a jump involved when we measure a quantum system this jump is not arbitrary and that the system's evolution picks up after the jump at the state revealed by the measurement and resumes its smooth evolution from there.

4) The outcome of any measurement on a physical system can be predicted by performing a specific mathematical operation on its state vector.

Not good for understanding. Predictions can only be made by performing a seemingly arbitrary mathematical operation on the mathematical object that is the source of all knowledge we can have of the quantum system.

5) The outcome of any measurement process on a physical system can only be predicted as a probability for obtaining that result. The procedure for obtaining this probability is known as Born's rule.

Not good either. Predictions can only be made in the form of probabilities and these probabilities must be calculated using another seemingly arbitrary mathematical rule.

The first step we can take to achieve clarity is to replace the word 'measurement' with 'interaction' in all the axioms above. As guided by our analysis of objective reality we must conclude that interactions conducted by humans and labelled by us 'measurements' are indistinguishable from other types of interactions taking place within the web of objective reality.

1) The source of a quantum system's effects that can be experience by any entity within the web of reality is a non-physical mathematical object.

2) The effects experienced by any entity within the web of reality concerning a quantum system can only be predicted by the application of two seemingly arbitrary mathematical procedures.

Zurek's work rigorously explains both. The first, as might be expected, is the nub of the conundrum. Zurek shows that we should not expect the quantum world to be part of the objective web of existence that we inhabit, only the effects of quantum systems that can pass through the filter of decoherence should be included in this reality. Quantum systems participate in reality only through those interactions. When analysed in detail these interactions or quantum decoherences consist of a transfer of information between the quantum system and the web of objective reality. Not all information concerning the quantum system is transferable. In fact the vast majority is not transferable. The relatively tiny amount of information that can be transferred is selected from the huge range of quantum possibilities and numerous copies of this information are deposited in the environment by a Darwinian process that Zurek coins Quantum Darwinism.

Second Zurek has succeeded in showing that the two seemingly arbitrary mathematical procedures specified by the last two axioms required to predict the nature of quantum systems' interactions are inherent in the first three axioms. In other words once we concede that much of quantum systems exist outside of our web of objective reality, in a manner described by the first three axioms, the nature of their interactions within our reality follows.

In this manner Zurek's work leads us to a new tighter definition of objective ontological reality. It is the sum of the interactions between the fundamental entities composing the universe. Information or influence from anything outside this web that might, in some weak sense, be said 'to exist' cannot in principal be detected within this reality.

Over time this web of interactions, in spite of the 2nd law of thermodynamics, has found emergent paths to forms of greater complexity including atomic physics, chemistry, biology and culture. These forms are fundamentally composed of the objective web and are participants within objective reality.

[1] Gravity is not usually considered a quantum theory but it has been shown that a quantum formulation is equivalent to General Relativity in the classical limit. This is the same limit in which General Relativity has been shown to be valid. It is in trying to extend the theory of Gravity to non-classical situations, including extreme energies and time and space resolutions on the plank scale, that both formulations fail. As noted in Wikipedia's article on the graviton: 'In this framework, the gravitational interaction is mediated by gravitons, instead of being described in terms of curved spacetime as in general relativity. In the classical limit, both approaches give identical results, which are required to conform to Newton's law of gravitation.'

[i] Alioscia Hamma, Fotini Markopoulou, Isabeau Premont-Schwarz, Simone Severini (2009), Lieb-Robinson bounds and the speed of light from topological order. Journal-ref: Phys.Rev.Lett.102:017204,2009

[ii] As viewed on Wiki Quotes, 11-14-08. http://en.wikiquote.org/wiki/Richard_Feynman

[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