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Books > Science & Mathematics > Mathematics > Applied mathematics > Chaos theory
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Randomness And Undecidability In Physics (Hardcover)
Loot Price: R1,757
Discovery Miles 17 570
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Randomness And Undecidability In Physics (Hardcover)
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Recent findings in the computer sciences, discrete mathematics,
formal logics and metamathematics have opened up a royal road for
the investigation of undecidability and randomness in physics. A
translation of these formal concepts yields a fresh look into
diverse features of physical modelling such as quantum
complementarity and the measurement problem, but also stipulates
questions related to the necessity of the assumption of
continua.Conversely, any computer may be perceived as a physical
system: not only in the immediate sense of the physical properties
of its hardware. Computers are a medium to virtual realities. The
foreseeable importance of such virtual realities stimulates the
investigation of an "inner description", a "virtual physics" of
these universes of computation. Indeed, one may consider our own
universe as just one particular realisation of an enormous number
of virtual realities, most of them awaiting discovery.One motive of
this book is the recognition that what is often referred to as
"randomness" in physics might actually be a signature of
undecidability for systems whose evolution is computable on a
step-by-step basis. To give a flavour of the type of questions
envisaged: Consider an arbitrary algorithmic system which is
computable on a step-by-step basis. Then it is in general
impossible to specify a second algorithmic procedure, including
itself, which, by experimental input-output analysis, is capable of
finding the deterministic law of the first system. But even if such
a law is specified beforehand, it is in general impossible to
predict the system behaviour in the "distant future". In other
words: no "speedup" or "computational shortcut" is available. In
this approach, classical paradoxes can be formally translated into
no-go theorems concerning intrinsic physical perception.It is
suggested that complementarity can be modelled by experiments on
finite automata, where measurements of one observable of the
automaton destroys the possibility to measure another observable of
the same automaton and it vice versa.Besides undecidability, a
great part of the book is dedicated to a formal definition of
randomness and entropy measures based on algorithmic information
theory.
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