vol 2: Synopsis
part III: Modern physics
page 20: The wave function of the universe
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The 'wave function' of the universe
Quantum mechanics is our best description of the physical universe. We begin from elementary events and show how these events are assembled into larger and larger events, culminating in the total event which we call the universe. The quantum mechanical description of the whole system is sometimes (for historical reasons) called the wave function(s) of the universe. This class of functions exists in transfinite function space.
The title of this chapter is a bow to the historical usage of quantum mechanics. Wave function is not a good term, however. It might be better to say the transformations of the universe. Both a function and a transformation are mappings. However, mathematical convention defines a function as a many-one mapping. In other words, functions tend to simplify things by compressing complex elements in their domains into simpler elements in their ranges. A transformation, on the other hand, may be many-many.
We can picture our world as sequences of events each of which can be decomposed into smaller events. Thus a party is made from the interactions of a roomful of people, talking, eating, drinking and so on. A particular conversation may be broken down into a series of utterances, each of which is an event. These events, though distinct, weld into a seamless whole which we call a party. A party itself is part of life, and each of our lives is part of the history of the human race, and so on.
Quantum physics reveals that there exist 'smallest' or elementary events, whose size is measured by Max Planck's 'quantum of action'. Such an event is the emission or absorption of a photon from an atom, or the the change of an electron spin from 'up' to 'down'. Planck's constant is an extremely small number, so that even the simplest event in human space comprises a huge number of elementary events.
Quantum mechanics assigns to each such event a Hilbert space, in which the event is represented by the transformation of a vector by an operator. An example is the transformation of a vector representing an electron with spin 'up' to a vector representing an electron with spin 'down'. More complex events are modelled in more complex Hilbert spaces.
We imagine that the total transformation of the universe embraces all elementary events through all time. The evidence we have to date suggests that the universe, and hence the transformation of the universe, has no end. The total transformation of the universe is an infinite open set of events. The Hilbert space of the transformation of the universe has a similar size to Cantors transfinite number space.
We imagine the quantum transformations of the universe as a hidden process which manipulates the probabilities of various events in observable space. They play a similar role to angels, the soul, or god in older models of the invisible controllers of human fate.
Books
| de Witt, Bryce S and Neill Graham (eds) , and Hugh Everett III, J A Wheeler, B S DeWitt, L N Cooper, D van Vechten, N Graham (contributors), The Many-Worlds Interpretation of Quantum Mechanics, Princeton UP 1973 Jacket: 'A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book is developed. The volume contains Dr Everett's short paper from 1957, "'Relative State' Formulation of Quantum Mechanics", and a far longer exposition of his interpretation, entitled "The Theory of the Universal Wave Function", never before published. In addition, other papers by De Witt, Graham and Cooper and van Vechtem provide further dicussion of the same theme. Together they constitute virtually the entire world output of scholarly commentary on the Everett interpretation.' Amazon back |
| Deutsch, David, The Fabric of Reality: The Science of Parallel Universes - and its Implications, Allen Lane Penguin Press 1997 Jacket: 'Quantum physics, evolution, computation and knowledge - these four strands of scientific theory and philosophy have, until now, remained incomplete explanations of the way the universe works. ... Oxford scholar DD shows how they are so closely intertwined that we cannot properly understand any one of them without reference to the other three. ...' Amazon back |
| Hofstadter, Douglas R, Goedel Escher Bach: An Eternal Golden Braid, Basic/Harvester 1979 An illustrated essay on the philosophy of mathematics. Formal systems, recursion, self reference and meaning explored with a dazzling array of examples in music, dialogue, text and graphics. Amazon back |
| Holland, Peter R, The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics, Cambridge University Press 1993 Jacket: 'This book presents the first comprehensive exposition of the interpretation of quantum mechancs pioneered by Louis de Broglie and David Bohm. ... Developing the theme that a material system such as an electron is guided by a surrounding quantum wave, a detailed examination of the classic phenomena of quantum theory is presented ... . ... The theory provides a novel and satisfactory framework for analysing the classical limit of quantum mechanics and Heisenberg's relations, and implies a theory of measurement without wavefunction collapse. It also suggests a strikingly novel view of relativistic quantum theory, including the Dirac equation, quantum field theory and the wavefunction of the universe.' Amazon back |
| Smolin, Lee, The Life of the Cosmos, Oxford University Pres 1997 Jacket: 'Smolin posits that a process of self-organisation like that of biological evolution shapes the universe, as it developes and eventually reproduces through black holes, each of which may result in a big bang and a new universe. Natural selection may guide the appearance of the laws of physics, favouring those universes which best reproduce. ... Smolin is one of the leading cosmologists at work today, and he writes with an expertise and a force of argument that will command attention throughout the world of physics.' Amazon back |
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