On the Many-Worlds-Interpretation
Comments on the Everett FAQ
An analysis of Everett's original paper is given in a separate entry
in this FAQ, called ''Circularity in Everett's measurement theory''.
The main conclusion is that Everett's analysis simply derives the
projection postulate by having assumed it, without any discussion,
in disguise. Thus his ''interpretation'' explains nothing.
The commentary below is a very old entry (from 1999, with a few later
amendments) regarding a particular, low quality but popular, version of
Everett's ''many worlds'' interpretation. My response here (in contrast
to the analysis mentioned above) is at the same superficial level.
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The Everett FAQ by Michael Clive Price, available at
http://www.hedweb.com/manworld.htm
claims to show ``how quantum paradoxes are resolved by the
"many-worlds" interpretation or metatheory of quantum mechanics.''
The following quotes refer to the version I downloaded on
Sept. 29, 1999.
My comments show that quantum paradoxes are not resolved by the version
of the "many-worlds" interpretation of quantum mechanics promoted by
the Everett FAQ; instead, the latter is full of home-made puzzles and
ambiguities.
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Q1 Who believes in many-worlds?
many-worlds is most popular amongst scientists
who may rather loosely be described as string theorists or
quantum gravitists/cosmologists. It is less popular
amongst the wider scientific community who mostly
remain in ignorance of it.
The paper
http://arxiv.org/PS_cache/quant-ph/pdf/0101/0101077v1.pdf
contains results of a poll at a quantum computation conference.
"Which interpretation of quantum mechanics is closest to your own?
(a) Copenhagen or consistent histories
(including postulate of explicit collapse): 4
(b) Modified dynamics
(Schroedinger equation modified to give explicit collapse): 4
(c) Many worlds/consistent histories (no collapse): 30
(d) Bohm (an ontological interpretation where an auxiliary
''pilot wave'' allows particles to have well-defined positions
and velocities): 2
(e) None of the above/undecided: 50
This very uninformative questionnaire is used to support the MWI.
The dominant statistical interpretation is not even mentioned (and
might figure under either (c) or (e)).
The consistent history interpretation has nothing to do with Everett's
MWI, but both are classified together in the single choice (c).
No collapse does not imply either of many worlds or consistent
histories, but this seems to be suggested by the choices.
In any case, this gives an upper bound of 30/90 = 33% on supporters of
MWI in the particular sample taken, while the only deducible lower
bound is 0%.
A slightly earlier (1977) poll recorded in
http://arxiv.org/pdf/quant-ph/9709032v1
gives the table
Copenhagen 13
Many Worlds 8
Bohm 4
Consistent Histories 4
Modified dynamics (GRW/DRM) 1
None of the above/undecided 18
giving a percentage of 8/48=17% supporters of MWI.
Q5 What is a measurement?
A measurement is an interaction, usually irreversible,
between subsystems that correlates the value of a
quantity in one subsystem with the value of a quantity in
the other subsystem.
But how can an interaction be irreversible if the evolution of the
wave function is unitary?
Q6 Why do worlds split? What is decoherence?
Any system complex enough to be described by
thermodynamics and exhibit irreversible behaviour is a
system complex enough to exclude, for all practical
purposes, any possibility of future interference between
its decoherent branches. An irreversible process is one in,
or linked to, a system with a large number of internal,
unconstrained degrees of freedom. Once the irreversible
process has started then alterations of the values of the
many degrees of freedom leaves an imprint which can't
be removed.
But how many particles needs a system to deserve being called complex?
What happens with a system with one particle less, why should it be
different? In a mathematically consistent interpretation, one may not
use concepts like `for all practical purposes' unless one specifies
exactly what that should mean.
In a
high dimension space almost all vectors are orthogonal,
without any significant degree of overlap. Thus vectors
for complex systems, with a large number of degrees of
freedom, naturally decompose into mutually orthogonal
components which, because they can never significantly
interfere again, are unaware of each other.
they decompose only into nearly mutually orthogonal components.
How close must the angle be to 90 degrees before we may say that
irreversibility (and hence measurement) has taken place?
Clearly, Nature must have such a criterion to know when it should split.
Without such a demarkation, the concept of measurement is vague and
no explanation of how Nature works has been given. The same problems
as in the Copenhagen interpretation remain, namely the ambiguity of
what constitutes a measurement...
Q7 When do worlds split?
The precise moment/location of the split is not sharply
defined due to the subjective nature of irreversibility, but
can be considered complete when much more than kT of
energy has been released in an uncontrolled fashion into
the environment. At this stage the event has become
irreversible.
How can irreversibility be subjective if it defines what a measurement
is and when worlds split? It would imply that when worlds split is also
a subjective matter. But then it is observer-dependent, the very thing
the interpretation is trying to avoid.
Decoherence occurs when irreversible
macro-level events take place and the macrostate
description of an object admits no single description. (A
macrostate, in brief, is the description of an object in
terms of accessible external characteristics.)
Again, this requires the observer to define accessible external
characteristics.
Q8 When does Schrodinger's cat split?
As the cyanide/no-cyanide interacts with the cat the cat
is split into two states (dead or alive). From the surviving
cat's point of view it occupies a different world from its
deceased copy. The onlooker is split into two copies only
when the box is opened and they are altered by the states
of the cat.
Indeed, this confirms that splitting is a subjective process not
affecting the world at large. Otherwise the number of worlds could not
depend on the point of view? Or is it to be understood as follows:
As the cyanide/no-cyanide interacts with the cat the world is split
into two, one containig a dead cat and the other one that is alive?
And each of these two worlds splits again as the onlooker opens the box?
But then we have 4 worlds, two of which corresponding to nonexistent
possibilities (e.g., the world with the dead cat which is found alive
on opening the box). Thus only one split should have occured, and the
`explanation' is nonsense.
Q11 How many worlds are there?
The thermodynamic Planck-Boltzmann relationship, S =
k*log(W), counts the branches of the wavefunction at
each splitting, at the lowest, maximally refined level of
Gell-Mann's many-histories tree. (See "What is
many-histories?") The bottom or maximally divided
level consists of microstates which can be counted by the
formula W = exp (S/k), where S = entropy, k =
Boltzmann's constant (approx 10^-23 Joules/Kelvin) and
W = number of worlds or macrostates.
This is funny since it implies a fractional number of worlds unless the
ensemble of worlds is microcanonical. But then each world is equally
probable, and we must be puzzled why we are in a world where the
unlikely happens rarely...
The entropy formula employed only counts the number of energetically
accessible energy eigenstates (not the number of all possible states
at a given energy, which is infinite), and is applicable only to a
bounded volume of matter in equilibrium.
But the many worlds interpretation must consider the whole universe
as the physical system, and the latter is neither in equilibrium nor
(most likely) bounded.
Q14 Is many-worlds a relativistic theory?
First quantisation: the wavefunction of an N particle
system is a complex field which evolves in 3N
dimensions as the solution to either the many-particle
Schrodinger, Dirac or Klein-Gordon or some other wave
equation. External forces applied to the particles are
represented or modelled via a potential, which appears in
the wave equation as a classical, background field.
many-particle Dirac or Klein-Gordon equation??
Unfortunately no one so far has found an N particle Dirac or
Klein-Gordon equation that approximates reality...
Many-worlds has
no problems incorporating QFT, since a theory (QFT) is
not altered by a metatheory (many-worlds), which makes
statements about the theory.
This is funny, too, conflicting with the asserted deterministic
nature of MWI since there is no deterministic QFT of interacting
fields. All QFT has to offer is the S-matrix that defines
probability amplitudes...
Q17 Why don't worlds fuse, as well as split?
Do splitting worlds imply irreversible physics?
The laws of physics are
reversible (or CPT invariant, more precisely) and fully
compatible with the irreversibility of thermodynamics,
which is solely due to the boundary conditions (the state
of universe at some chosen moment) imposed by the Big
Bang or whatever we chose to regard as the initial
conditions.
According to the Liouville equation (that follows from the
Schr"odinger equation assumed valid in MWI), the state of the
universe at any chosen moment evolves unitarily and hence
reversibly. Irreversibility can be introduced only as an approximation
in a coarse grained sense which corresponds to choosing time and
space scales to avoid the Poincare recurrence theorem.
A metatheory such as MWI that depends on such uncontrolled
approximations in its most basic tenets cannot be very fundamental...
Q22 Does many-worlds violate conservation of energy?
energy is conserved
within each world and also across the totality of worlds.
But in an irreversible world, energy is not conserved but dissipates.
The presence of such arguments that flatly contradict other statements
shows that MWI is a smokescreen without a consistent mathematics behind.
Q23 How do probabilities emerge within many-worlds?
Strictly speaking Everett did not prove that the usual
statistical laws of the Born interpretation would hold
true for all observers in all worlds. He merely showed
that no other statistical laws could hold true and asserted
the vanishing of the Hilbert space "volume" or norm of
the set of "maverick" worlds.
And he cannot prove it since statistics makes no sense in MWI as
everything that can happen, happens. Consider measuring a sequence of
orthogonal idempotent observables e_0, e_1, ... in a state psi with
= 0.001 for all i. After each measurement, the world
splits into two, corresponding to the two eigenvalues 0, 1 of e_i.
After N measurements we have 2^N worlds, half of them having e_0=0,
and half of them having e_0=1. But there should be only one thousendth
of the latter...
The formal proof involves a weighting of the world according to
probabilities. But these weights have no influence on what happens
in a world. How to distinguish a world with weight 0.9999 from one
with weight 1e-100000000000? The only way is that the latter world
contains lots of improbable historical imprints while the former
does not. But this leaves us to explain why we happen to
perceive a world of large weight throughout our entire life...
The emergence of Born-style probabilities as a
consequence of the mathematical formalism of the
theory, without any extra interpretative assumptions, is
another reason why the Everett metatheory should not be
regarded as just an interpretation.
As the previous argument shows, Born-style probabilities emerge
at best in a formal way, but not with a natural interpretation
as probabilities.
Q25 Why am I in this world and not another?
Why does the universe appear random?
The Copenhagen interpretation posits that observers
collapse wavefunctions, but is unable to define
"observer".
Without a definition of observer there can be no
mechanism triggered by their presence.
Actually it posits that measurements collapse wavefunctions, but is
unable to define "measurement". Without a definition of measurement
there can be no mechanism triggered by its presence.
Another popular view is that irreversible processes
trigger collapse. Certainly wavefunctions appear to
collapse whenever irreversible processes are involved.
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.
The same two arguments apply against splitting, with the conclusion
that there is no mechanism for splitting worlds since neither
measurement nor irreversibility can be clearly demarcated.
Q26 Can wavefunctions collapse?
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.
An even simpler conclusion, which is to be preferred by
Ockham's razor, is that wavefunctions neither collapse nor branch.
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Some recent papers on the arxiv about Many Worlds Interpretations:
hep-th/0403008
gr-qc/9703089
gr-qc/9309012
gr-qc/9704039
quant-ph/0312157
quant-ph/0312136
quant-ph/0303114
quant-ph/0303050
quant-ph/0211104
quant-ph/0209055
quant-ph/0112081
quant-ph/0112077
quant-ph/0111072
quant-ph/0111047
quant-ph/0108070
quant-ph/0001057
quant-ph/9910108
quant-ph/9904004
quant-ph/9709032
quant-ph/9703008
quant-ph/9609006
and some related papers:
gr-qc/9901024
gr-qc/9810078
gr-qc/9412067
gr-qc/9208001
quant-ph/9805065
quant-ph/9704006
quant-ph/9603008
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The above just criticises the Many Worlds interpretation, but
does not hint at what interpretation is better.
For my constructive views on the interpretation problem, see:
A. Neumaier,
Ensembles and experiments in classical and quantum physics,
Int. J. Mod. Phys. B 17 (2003), 2937-2980.
quant-ph/0303047,
http://www.mat.univie.ac.at/~neum/papers/physpapers.html#ensembles
and the links in the FAQ entry
Quantum mechanics without mysteries
http://www.mat.univie.ac.at/~neum/physfaq/topics/born.html
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A theoretical physics FAQ
http://www.mat.univie.ac.at/~neum/physics-faq.txt
Physics links by Arnold Neumaier
http://www.mat.univie.ac.at/~neum/physics.html