Signalled Diffusion Book IV: Real Numbers vs Complex Numbers

Book IV of my Signalled Diffusion project can be down loaded from this post. The introduction to Book IV is reproduced below.  The books so far are listed below along with their links:

BOOK I:     Foundations

BOOK II:    Exponentiating Diffusion

BOOK III:  Drift-Diffusion

BOOK IV:  Real Number vs Complex number Diffusion.

BOOK V:    Complex Drift-Diffusion

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Introduction

Richard Dawkins and Brian Cox set the scene

The general consensus among scientists and layman alike is that quantum mechanics seems a strange and unintelligible way for the physical world to work; in particular it seems outrageous that this world should appear to do more than one thing at a time in that particles seemingly move in multiple directions at once. Further confounding our common sense physical expectations are those well-known apparently random discontinuous leaps of the system state vector when an attempt is made to measure a physical variable. Evangelical atheist Richard Dawkins puts his explanation on this state affairs:   

Physics appears to be a complicated subject, because the ideas of physics are difficult for us to understand. Our brains were designed to understand hunting and gathering, mating and child-rearing; a world of medium sized objects moving in three dimensions at moderate speeds. We are ill-equipped to comprehend the very small, the very large; things whose duration is measured in picaseconds or gigayears; particles that don't have position; forces and fields that we cannot see or touch, which we only know of only because they effect things that we can see and touch.

According to this we are creatures only “designed” (I’m sure that’s not meant literally!) for biosphere survival and therefore have no right to expect to understand the deeper mysteries of the cosmos. There is no reason why, for a jumped up primate, the cosmos should be anthropomorphically comprehensible and meaningful. The cosmos hasn’t been put there for this purpose; in fact you might hear Dawkins say that the cosmos is unlikely to have been put there for any purpose or reason at all; for Richard Dawkins it’s a fundamentally absurd cosmos and you can’t expect human beings to plumb the depths of this absurdity.  The cosmos is what it is without purpose; take it or leave it.

In regard to the specific enigma of quantum mechanics it is perhaps no surprise that parallel universe theory is a popular interpretation of quantum mechanics; it is one way of restoring the notion that reality isn’t ambiguous and in fact follows a single deterministic path of evolution; here the thought is that apparent quantum ambiguity is a sign there is a lot more unambiguous solid reality out there of which human consciousness is simply unaware. The parallel universe idea seems to provide two clarifications for the price of one: a) The totality of parallel universes is both unambiguous and deterministic b) the random leaping is just a perspective effect of us observers, confined as we are to just one of the parallel universes and only able to see just one of the many possible universes that ride side by side.

The intuitive agreeableness of the parallel universes interpretation of quantum mechanics is hinted at by Brian Cox in a BBC article entitled Brian Cox: 'Multiverse' makes sense (See also here):

“That there’s an infinite number of universes sounds more complicated than there being one,” Prof Cox told the programme.

“But actually, it’s a simpler version of quantum mechanics. It’s quantum mechanics without wave function collapse… the idea that by observing something you force a system to make a choice.”*¹

Accepting the many worlds interpretation of quantum mechanics means also having to accept that things can exist in several states at the same time.

But this leads to another question: Why do we perceive only one world, not many?

The suggestion here is that the many worlds interpretation makes sense because it cuts out the asymmetrical contingency inherent in the idea that the reduction of the quantum state vector entails the cosmos making an arbitrary selection singled out from among the many possible choices. In the light of Richard Dawkins views one might question why the cosmos should make even some sense by conforming to the aesthetics of symmetry. But if we run with the symmetry idea as per Brian Cox then symmetry considerations suggest that all possibilities ought to be out there somewhere, thus doing away with any seemingly arbitrary and contingent treatment being preferentially given to a very limited range of possibilities. Max Tegmark has gone even further with the elimination of arbitrary contingency in favour of the hyper-symmetry of his mathematical universe. In Tegmark’s mathematical universe Tegmark extends reification to all possible mathematical constructions; in short nothing, absolutely nothing, is subject to special and seemingly arbitrary selection. However, in Tegmark’s model there remains the tricky philosophical issue of why there is something rather than nothing; in the selection of something rather than nothing we have another awkward asymmetry. There have been some attempts at addressing the counter intuitive ideas that it is possible to get something from nothing by redefining “nothing” in terms of the quantum void. But this could equally be construed as effectively redefining “something” in terms of the quantum void! All in all how you answer these difficult questions is probably very much influenced by your a priori world view preferences and what makes sense to you.

What purports to make sense is a very subjective affair: For someone like Richard Dawkins the cosmos need not make any sense at all. But if we are to appeal to just what makes sense then I have to confess that to me the “many worlds” view, apart from perhaps the vague aesthetic appeal of symmetry, doesn’t make much sense. Moreover, as Brian admits the problem with the many worlds suggestion is the question of why is it only one world is visible to us? Therein, I believe, is the observational clue to the problem’s solution – there is, in fact, only one real world and that world is highly skewed in favour of order*. This suggestion makes more aesthetic sense to me than does “many worlds”.  Making sense of things is how we attempt to join the dots of experience into a coherent narrative or a world view synthesis. But because world views are a very complex product of very complex and differing life experience, it is not very easy to submit them to the formal scientific process of prediction and test. Accordingly, world view synthesis must be carried out with caution and with epistemic humility; fundamentalists and evangelicals of all flavours please take note. Although as far as world view synthesis is concerned some people like Brian Cox clearly have a different mind-set to myself in this respect, it would be very wrong to think the worst of them; like so many of us Brian Cox is simply doing his best to bring intelligibility to the world; if he has a clear conscience we have no grounds to condemn him.

This book attempts to make sense of quantum theory by taking real number diffusion as far as possible before quantisation (which is achieved by introducing “i” into the diffusion constant) with the aim of using this approach to unpack the meaning of quantum mechanics. In the final chapter of this book I propose my own qualitative sense making narrative, narrative which I’ve wrapped round quantum theory in an attempt to render it humanly intelligible.  In my opinion positing quantum theory as just a variation on real number diffusion brings us to a very anthropomorphic understanding of quantum mechanics and relativity; the very opposite of the opinion expressed by Richard Dawkins. In fact may I express my intuition in advance of any clearer analysis that to me the cosmos looks suspiciously like the interior of a huge cognitive system as it seeks and selects solutions to general purpose goals. In this study goal seeking, or “purpose”, is an important sense making construct and trumps, say, the aesthetics of symmetry, especially if the latter is empty of meaning. I touch on some of these matters in more detail in the epilogue.

1* This a priori bias toward order is clearly a necessary condition for perceiving observers. And I would question whether it is entirely coherent to talk about a world without conscious cognating observers. 

Sir Kenneth Clark on Symmetry (Again)

It is an irony that the "Many Worlds" view majors on symmetry and closed
 endedness.  It achieves this trick by expanding the limits of existence so far as to 
eliminate uncertainty and the unknown: All things have a certainty of occurring within
 a mathematically defined envelope, an envelope which although infinite, which
nevertheless has known boundaries (but at infinity!)

ADDENDUM 12/09/19

Here's Sean Carroll on his enthusiasm for the multiverse. I've taken these quotes from a post on Uncommon Descent. Some of his views are in many ways  the opposite of mine although the second quote below may prove more amenable to my way of thinking.  (See here for more on Sean Carroll's views)

The Many-Worlds formulation of quantum mechanics removes once and for all any mystery about the measurement process and collapse of the wave function. We don’t need special rules about making an observation: all that happens is that the wave function keeps chugging along in accordance with the Schrödinger equation. And there’s nothing special about what constitutes ‘a measurement’ or ‘an observer’ – a measurement is any interaction that causes a quantum system to become entangled with the environment, creating a branching into separate worlds, and an observer is any system that brings about such an interaction. Consciousness, in particular, has nothing to do with it. The ‘observer’ could be an earthworm, a microscope or a rock. There’s not even anything special about macroscopic systems, other than the fact that they can’t help but interact and become entangled with the environment. The price we pay for such a powerful and simple unification of quantum dynamics is a large number of separate worlds.

Sean Carroll, “Splitting the Universe: Hugh Everett blew up quantum mechanics with his Many-Worlds theory in the 1950s. Physics is only just catching up” at Aeon

In my own research, I’ve gone even farther, arguing that the quest for quantum gravity is being held back by physicists’ traditional strategy of taking a classical theory (such as Albert Einstein’s general relativity) and ‘quantising’ it. Presumably nature doesn’t work like that; it’s just quantum from the start. What we should do, instead, is start from a purely quantum wave function, and ask whether we can pinpoint individual ‘worlds’ within it that look like the curved spacetime of general relativity. Preliminary results are promising, with emergent geometry being defined by the amount of quantum entanglement between different parts of the wave function. Don’t quantise gravity; find gravity within quantum mechanics.

That approach fits very naturally into the Many-Worlds perspective, while not making much sense in other approaches to quantum foundations. Niels Bohr might have won the public-relations race in the 20th century, but Hugh Everett appears ready to pull ahead in the 21st.

Sean Carroll, “Splitting the Universe: Hugh Everett blew up quantum mechanics with his Many-Worlds theory in the 1950s. Physics is only just catching up” at Aeon