Frans_Jozef

Friday, March 24th, 2006, 04:03 PM

Michael Clive Price's faq on the concept of multiple universes.

What is many-worlds? (http://forums.skadi.net/)

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]. (http://forums.skadi.net/) Many-worlds comprises of two assumptions and some consequences. The assumptions are quite modest: (http://forums.skadi.net/)

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.

(http://forums.skadi.net/)

2) The physical assumption: The wavefunction obeys the empirically derived standard linear deterministic wave equations 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 (http://forums.skadi.net/)"Is many-worlds a relativistic theory?" (http://www.hedweb.com/manworld.htm#relativistic) 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. Measurements and observations by a subject on an object 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. (See "What is decoherence?" (http://www.hedweb.com/manworld.htm#decoherence)) The histories form a branching tree which encompasses all the possible outcomes of each interaction. (See "Why do worlds split?" (http://www.hedweb.com/manworld.htm#split) and "When do worlds split?" (http://www.hedweb.com/manworld.htm#do)) 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?" (http://www.hedweb.com/manworld.htm#probabilities))

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 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, after the subsystems have jointly interacted, 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. (See "What is a relative state?" (http://www.hedweb.com/manworld.htm#relative))

If one of the systems is an observer and the interaction an observation then the effect of the observation is to 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 that induce local splitting or decoherence into non- interfering branches of the universal wavefunction. 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 single prior world having split into mutually unobservable but equally real worlds.

http://www.hedweb.com/manworld.htm

What is many-worlds? (http://forums.skadi.net/)

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]. (http://forums.skadi.net/) Many-worlds comprises of two assumptions and some consequences. The assumptions are quite modest: (http://forums.skadi.net/)

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.

(http://forums.skadi.net/)

2) The physical assumption: The wavefunction obeys the empirically derived standard linear deterministic wave equations 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 (http://forums.skadi.net/)"Is many-worlds a relativistic theory?" (http://www.hedweb.com/manworld.htm#relativistic) 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. Measurements and observations by a subject on an object 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. (See "What is decoherence?" (http://www.hedweb.com/manworld.htm#decoherence)) The histories form a branching tree which encompasses all the possible outcomes of each interaction. (See "Why do worlds split?" (http://www.hedweb.com/manworld.htm#split) and "When do worlds split?" (http://www.hedweb.com/manworld.htm#do)) 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?" (http://www.hedweb.com/manworld.htm#probabilities))

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 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, after the subsystems have jointly interacted, 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. (See "What is a relative state?" (http://www.hedweb.com/manworld.htm#relative))

If one of the systems is an observer and the interaction an observation then the effect of the observation is to 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 that induce local splitting or decoherence into non- interfering branches of the universal wavefunction. 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 single prior world having split into mutually unobservable but equally real worlds.

http://www.hedweb.com/manworld.htm