Newsgroups: sci.physics.particle,sci.physics,alt.consciousness,comp.ai.philosophy
From: price@price.demon.co.uk (Michael Clive Price)
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Subject: Re: Information Theory and QM
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Christian Cieslar writes:
> But anyhow there is a collapse of the wavefunction in our real world,
> and it is essential to the whole QM.
> Otherwise you would have to say: There are no particles just waves.

You've probably made Ron Maimon's day!

Ignoring the interpretation question of wave or particle, you are not
correct to say that QM needs collapse.  It doesn't.  Our fragile egos
often require it, but the universe has no need.
********************************
Q3   What is many-worlds?
     --------------------
AKA as the Everett, relative-state, many-histories or many-universes
interpretation or metatheory of quantum theory.  Dr Hugh Everett, III,
its originator, called it the "relative-state metatheory" or the "theory
of the universal wavefunction" [1], but it is generally called "many-
worlds" nowadays, after DeWitt [4a],[5].

Many-worlds comprises of two assumptions and some consequences.  The
assumptions are quite modest:
1)   The metaphysical assumption: That the wavefunction does not merely
     encode the all the information about an object, but has an
     observer-independent objective existence and actually *is* the
     object.  For a non-relativistic N-particle system the wavefunction
     is a complex-valued field in a 3-N dimensional space.

2)   The physical assumption:  The wavefunction obeys some standard
     linear deterministic wave equation at all times.  The observer
     plays no special role in the theory and, consequently, there is no
     collapse of the wavefunction.  For non-relativistic systems the
     Schrodinger wave equation is a good approximation to reality.  (See
     "Is many-worlds a relativistic theory?" for how the more general
     case is handled with quantum field theory or third quantisation.)

The rest of the theory is just working out consequences of the above
assumptions.  Measurement and observation are modelled by applying the
wave equation to the joint subject-object system.  Some consequences
are:
1)   That each measurement causes a decomposition or decoherence of the
     universal wavefunction into non-interacting and mostly non-
     interfering branches, histories or worlds.  The histories form a
     branching tree which encompasses all the possible outcomes of each
     interaction.  (See "Why do worlds split?" and "When do worlds
     split?")  Every historical what-if compatible with the initial
     conditions and physical law is realised.

2)   That the conventional statistical Born interpretation of the
     amplitudes in quantum theory is *derived* from within the theory
     rather than having to be *assumed* as an additional axiom.  (See
     "How do probabilities emerge within many-worlds?")

Many-worlds is a re-formulation of quantum theory [1], published in 1957
by Dr Hugh Everett III [2], which treats the process of observation or
measurement entirely within the wave-mechanics of quantum theory, rather
than an input an as additional assumption, as in the Copenhagen
interpretation.  Everett considered the wavefunction a real object. 
Many-worlds is a return to the classical, pre-quantum view of the
universe in which all the mathematical entities of a physical theory are
real.  For example the electromagnetic fields of James Clark Maxwell or
the atoms of Dalton were considered as real objects in classical
physics.  Everett treats the wavefunction in a similar fashion.  Everett
also assumed that the wavefunction obeyed the same wave equation during
observation or measurement as at all other times.  This is the central
assumption of many-worlds: that the wave equation is obeyed universally
and at all times.

Everett discovered that the new, simpler theory - which he named the
"relative state" formulation - predicts that interactions between two
(or more) macrosystems typically split the joint system into a
superposition of products of relative states.  The states of the
macrosystems are henceforth correlated with, or dependent upon, each
other.  Each element of the superposition - each a product of subsystem
states - evolves independently of the other elements in the
superposition.  The states of the macrosystems are, by becoming
correlated or entangled with each other, impossible to understand in
isolation from each other and must be viewed as one composite system. 
It is no longer possible to speak the state of one (sub)system in
isolation from the other (sub)systems.  Instead we are forced to deal
with the states of subsystems relative to each other.  Specifying the
state of one subsystem leads to a unique specification of the state (the
"relative state") of the other subsystems.

If one of the systems is an observer and the interaction an observation
then the effect of the observation is split the observer into a number
of copies, each copy observing just one of the possible results of a
measurement and unaware of the other results and all its observer-
copies.  Interactions between systems and their environments, including
communication between different observers in the same world, transmits
the correlations inducing local splitting or decoherence of branches of
the universal wavefunction [7a], [7b], [10].  Thus the entire world is
split, quite rapidly, into a host of mutually unobservable but equally
real worlds.

According to many-worlds all the possible outcomes of a quantum
interaction are realised.  The wavefunction, instead of collapsing at
the moment of observation, carries on evolving in a deterministic
fashion, embracing all possibilities embedded within it.  All outcomes
exist simultaneously but do not interfere further with each other, each
world having split into mutually unobservable but equally real worlds.


Q26  Can wavefunctions collapse?
     ---------------------------
Many-Worlds predicts/retrodicts that wavefunctions appear to collapse
(See "Does the EPR experiment prohibit locality?"), when measurement-
like interactions and processes occur via a process called decoherence
[7a], [7b], [10], but claims that they do not *actually* collapse but
continue to evolve according to the usual wave-equation.   If a
*mechanism* for collapse could be found then there would be no need for
many-worlds.  The reason why we doubt that collapse takes place is
because no one has ever been able to devise a physical mechanism that
could trigger it.

The Copenhagen interpretation posits that observers collapse
wavefunctions, but is unable to define "observer".  (See "What is the
Copenhagen interpretation?" and "Is there any alternative theory?") 
Without a definition of observer there can be no mechanism triggered by
their presence.

Another popular view is that irreversible processes trigger collapse. 
Certainly wavefunctions *appear* to collapse whenever irreversible
processes are involved in measurement or amplification and most
macroscopic, day-to-day events are irreversible.  The problem is, as
with positing observers as a cause of collapse, that any irreversible
process is composed of a large number of sub-processes that are each
individually reversible.  To invoke irreversibility as a *mechanism* for
collapse we would have to show that new *fundamental* physics comes into
play for complex systems, which is quite absent at the reversible
atom/molecular level.  Atoms and molecules are empirically observed to
obey some type of wave equation.  We have no evidence for an extra
mechanism operating on more complex systems.  As far as we can determine
complex systems are described by the quantum-operation of their simpler
components interacting together.  (Note:  chaos, complexity theory, etc,
do not introduce new fundamental physics.  They still operate within the
reductionistic paradigm - despite what many popularisers say.)

Other people have attempted to construct non-linear theories so that
microscopic systems are approximately linear and obey the wave equation,
whilst macroscopic systems are grossly non-linear and generates
collapse.  Unfortunately all these efforts have made additional
predictions which, when tested, have failed.  (See "Is physics linear?")

(Another reason for doubting that any collapse actually takes place is
that the collapse would have to propagate instantaneously, or in some
space-like fashion, otherwise the same particle could be observed more
than once at different locations.  Not fatal, but unpleasant and
difficult to reconcile with relativity and some conservation laws.)

The simplest conclusion, which is to be preferred by Ockham's razor, is
that wavefunctions just *don't* collapse and that all branches of the
wavefunction exist.

[1]  Hugh Everett III _The Theory of the Universal Wavefunction,
     Princeton thesis_ (1956?)
     The original and most comprehensive paper on many-worlds. 
     Investigates and recasts the foundations of quantum theory in
     information theoretic terms, before moving on to consider the
     nature of interactions, observation, entropy, irreversible
     processes, classical objects etc.  138 pages.  Only published in
     [5].
[2]  Hugh Everett III _"Relative State" Formulation of Quantum
     Mechanics_ Reviews of Modern Physics Vol 29 #3 454-462, (July
     1957)  A condensation of [1] focusing on observation.
[3]  John A Wheeler _Assessment of Everett's "Relative State"
     Formulation of Quantum Theory_, Reviews of Modern Physics Vol
     29 #3 463-465 (July 1957)  Wheeler was Everett's PhD
     supervisor.
[4a] Bryce S DeWitt _Quantum Mechanics and Reality_ Physics Today,
     Vol 23 #9 30-40 (September 1970)  One of the earlier, and more
     accurate, popularisations of Everett's work.  The April 1971
     issue has reader feedback and DeWitt's responses.
[4b] Bryce S DeWitt _The Many-Universes Interpretation of Quantum
     Mechanics_ in _Proceedings of the International School of Physics
     "Enrico Fermi" Course IL: Foundations of Quantum Mechanics_
     Academic Press (1972)
[5]  Bryce S DeWitt, R Neill Graham eds _The many-worlds
     Interpretation of Quantum Mechanics_, Contains
     [1],[2],[3],[4a],[4b] plus other material.  Princeton Series
     in Physics, Princeton University Press (1973) ISBN 0-691-
     08126-3 (hard cover), 0-691-88131-X (paper back)  The
     definitive guide to many-worlds, if you can get hold of a
     copy, but now (1994) only available xeroxed from microfilm
     (ISBN 0-7837-1942-6) from Books On Demand, 300 N Zeeb Road,
     Ann Arbor, MI 48106-1346, USA.  Tel: +01-313 761 4700 or 800
     521 0600.

[7a] Wojciech H Zurek _Decoherence and the Transition from the
     Quantum to the Classical_, Physics Today, 36-44 (October
     1991). The role of thermodynamics and the properties of large
     ergodic systems (like the environment) are related to the
     decoherence or loss of interference effects between superposed
     macrostates.
[7b] Wojciech H Zurek _Preferred States, Predictability, Classicality,
     and the Environment-Induced Decoherence_  Progress of Theoretical
     Physics, Vol 89 #2 281-312 (1993)  A fuller expansion of [7a]

[10] Murray Gell-Mann, James B Hartle _Quantum Mechanics in the Light
     of Quantum Cosmology_ Proceedings of the 3rd International
     Symposium on the Foundations of Quantum Mechanics (1989) 321-343. 
     They accept the Everett's decoherence analysis, and have extended
     it further.

Michael Price                        price@price.demon.co.uk
