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 V: Complex Drift-Diffusion
***
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!)
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
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