Noesis
The Journal of
the Mega Society
Number 96
August 1994
EditorRick Rosner
5139 Balboa Blvd #303
Encino CA 913163430
(818) 9869177
IN THIS ISSUE
FREQUENTLY ASKED QUESTIONS ABOUT
THE
MANYWORLDS OR RELATIVE STATE FORMULATION
OF
QUANTUM MECHANICS
ANSWERS COMPILED BY MICHAEL CLIVE PRICE
1 What are the
problems with quantum
theory?
2 What is the
Copenhagen interpretation?
3 What is
manyworlds?
4 What is a
"world"?
5 What is a measurement?
6 Why do worlds
split?
7 When do worlds
split?
8a What is
sumoverhistories?
8b What is
manyhistories?
9 How many worlds
are there?
10 Is manyworlds a
local theory?
11 Is manyworlds a
deterministic theory?
12 Is manyworlds a
relativistic theory?
13 Is manyworlds
(just) an interpretation?
14 What are the
alternatives?
15 Is manyworlds
testable?
16 Could previously separate worlds diverge
rather than split?
17 What is
manyminds?
18 Does manyworlds
violate Ockham's Razor?
19 Does the
multiplication of worlds violate conservation of energy?
20 How do
probabilities emerge within
manyworlds?
21 Does manyworlds
allow freewill?
22 Why am I in this
world and not another?
23 Can wavefunctions
collapse?
24 Is physics
linear?
25 Can we determine
what other worlds there are?
26 Who was Everett?
27 Who believes in manyworlds?
30 Does the EPR
experiment prohibit locality?
31 References and
further reading
Q1 What are the problems with quantum theory?
Quantum theory is the most
successful description of microscopic systems like atoms and molecules ever, yet often it is not applied
to larger, classical systems, like
observers or the entire
universe. Many scientists and philosophers are unhappy with the theory because it seems to
require a fundamental quantumclassical divide.
Einstein, for example, and despite his early contributions to the
subject, was never reconciled with
assigning the act of
observation a physical significance,
which QM requires. This contradicts the
reductionist ethos that, amongst other things, observations should emerge only as a consequence of an underlying physical theory and not be
present in the axioms, as they
are in the Copenhagen interpretation.
Yet the Copenhagen interpretation is the most popular interpretation of quantum mechanics. (See "What is the Copenhagen
interpretation?")
Q2 What is the Copenhagen
interpretation?
An unobserved system, according to the Copenhagen
interpretation of quantum theory, evolves in a deterministic way determined by
a wave equation. An observed system changes
in a random fashion, instantaneously, with the probability of any particular
outcome given by the Born formula, determined by the wavefunction. This is known as the collapse of the wavefunction. The problems with this approach are: (1) The collapse is an instantaneous process
across an extended region
("nonlocal"). This is in
conflict with
relativity, which states that
no processes can be transmitted faster than the speed of light. (Nevertheless it has been shown that no information can be transmitted faster
than light by the
collapse process). (2) The idea of an observer having an effect on microphysics is repugnant
to reductionism and
smacks of a return to prescientific notions of vitalism. Copenhagenism is a return to the old
vitalist notions that
life is somehow different from other matter,
operating by different laws
from inanimate matter. The collapse is
triggered by an observer, yet no definition of what an "observer" is
available, in terms of an atomic scale description, even in principle.
For these reasons
the view has generally been adopted that the wavefunction associated with an object is not a real "thing", but merely represents
our *knowledge* of the
object. This approach was developed by
Bohr and others, mainly at Copenhagen in the late 1920s. When we perform
an measurement or
observation of an object we acquire new information
and so adjust the wavefunction as we would boundary
conditions in classical physics to reflect this new information. This stance means that
we can't answer questions
about what's actually happening, all we can answer is what will be the probability of a particular
result if we perform a
measurement. This makes a lot of people very unhappy since
it provides no model for
the object.
It should
be added that there are
other, less popular,
interpretations of quantum theory, but they
all have their own drawbacks, which are widely reckoned more severe. Generally speaking they try to find a mechanism that describes the collapse process
or add extra physical objects to the theory, in addition to the wavefunction. In this sense
they are more complex. (See "Is there any alternative theory?")
Q3 What is manyworlds?
AKA as the Everett, relativestate, manyhistories or
manyuniverses interpretation. Dr Hugh
Everett III, its originator,
called it the relativestate metatheory or the theory of the universal wavefunction [1], but, after DeWitt [4a],[5], it is generally
called manyworlds nowadays.
Manyworlds comprises
of two assumptions and some
consequences. The assumptions are quite
modest: 1) The metaphysical assumption:
That the wavefunction does not merely encode the information about an object, but has
an observer independent objective existence.
For an Nparticle system the wavefunction is a complexvalued field in a 3N
dimensional space. In quantum field
theory the state vector spans a space of an indeterminate number of dimensions.
2) The physical
assumption: The wavefunction obeys some
standard deterministic
wave equation at all times. The observer
plays no special role in the theory and,
consequently, there is no collapse of the wavefunction. Measurement and observation are modelled by applying the wave equation to the joint subjectobject system. For nonrelativistic systems the Schrodinger
wave equation is a good
approximation to reality. (See "Is manyworlds a relativistic
theory?" for the more general case.)
The rest of the theory is working out consequences of the above assumptions. Some consequences
are: 1) That each measurement
causes a decomposition or decoherence of the universal wavefunction into noninteracting and
noninterfering branches or worlds.
History forms a branching tree which encompasses all the possible outcomes of each
interaction. (See "Why do worlds
split?" and "When do worlds split?") Every historical whatif 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
manyworlds?")
Manyworlds is a reformulation of quantum theory [1],
published in 1957 by Dr Hugh Everett III [2], which treats the process of
observation or measurement
entirely within the wavemechanics of quantum
theory, rather than an
input an as additional assumption, as in the Copenhagen interpretation. Everett considered the wavefunction a real object. (Manyworlds is a return to the classical,
prequantum 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 manyworlds: 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 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, by becoming correlated or entangled, meaning that it no longer
possible to speak the
state of one system in isolation
from the other subsystems. Instead we
are forced to only speak of the relative states of the subsystems, with respect to the other
subsystems. Specifying the state of one
subsystem leads to the state of the other subsystems. In this sense
the states of the subsystems are determined only relative to each other, hence Everett's original designation of his theory.
If one of the systems is an observer and the interaction an
observation then observer has been split into a number of copies, each copy observing just one of the possible results of a measurement and unaware of the other results and its own
observercopies. Interactions between systems and their
environments, including
communication between different observers in the same worlds, transmits the
correlations, inducing local splitting or decoherence of branches of the
universal wavefunction
[7],[10]. Thus the entire world is split, quite rapidly,
into a host of mutually unobservable but equally real worlds.
According to manyworlds 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 within
it. All outcomes exist simultaneously but do not interact further with each other, each world having
split into mutually unobservable but equally real worlds or branches of the universal wavefunction.
Q4 What is a "world"?
Loosely speaking a "world" is a complex, partially
closed
set of interacting subsystems which don't
significantly interfere with other elements
in a quantum superposition. Any complex system and its coupled environment, with a large number of internal degrees of freedom,
counts as a world. An observer, with internal irreversible
processes, counts as a complex
system. In terms of the wavefunction, a world is a decohered
branch of the universal wavefunction,
which represents a single macrostate.
The worlds all exist simultaneously
in a non interacting linear superposition.
Sometimes
"worlds" are called "universes", but more usually
this is reserved the totality of worlds, or "histories" (GellMann/Hartle's phrase, see "What is
manyhistories?").
Q5 What is a measurement?
A measurement
is an interaction between
subsystems that
triggers an amplification process, typically within an object (which we often designate as the measuring apparatus) with many internal degrees of freedom,
leading to a change in the higherlevel structure of the object (which
might be the recording apparatus). The
trigger is sensitive to some (often microphysical)
parameter of the one of the subsystems, which we designate the measured system. Eg the detection of a charged particle
by a Geiger counter leads to the generation of a "click". The absence of a charged particle
does not generate a click. The measured system is the charged particle. The interaction is with those elements
of the charged particle's wavefunction that passes *between* the charged detector plates,
triggering the amplification process (an irreversible electron cascade or
avalanche), which is ultimately converted to a click.
A measurement,
by this definition, does not require the presence of an observer.
Q6 Why do worlds split?
Worlds, or branches of the universal wavefunction, split when different components of a quantum
superposition "decohere" from each other [7], [10]. Decoherence refers to the loss of coherency
or absence of interference effects between the elements
of the superposition. For two components
or worlds to interfere with
each other all the atoms, subatomic particle, photons etc in
each world have to be in the same
state, in the same
place. For small systems this is quite possible. In the double slit experiment, for instance, it only requires that the divergent paths of the diffracted particle
overlap again at some point, because only the single particle
has been split. For more complex systems overlapping becomes harder
because all the constituents particles have to
overlap with their
counterparts
simultaneously.
In QM jargon we say that
the components (or vectors in the underlying
Hilbert space) have become permanently orthogonal due to the complexity of the systems increasing the dimensionality of the
Hilbert space. In a high dimension space almost all vectors are orthogonal. Each time a new degree of freedom
is activated the dimensionality of the space which the different components move through increases. Thus vectors for complex systems, with a large number of degrees of freedom,
naturally decompose into mutually orthogonal
components which, because they
never interfere again, are unaware
of each other. From the point of view of
the complex systems they have split into different, mutually unobservable
worlds.
Q7 When do worlds split?
Worlds irrevocably "split" at the sites of measurementlike interactions associated with thermodynamically irreversible
processes. An irreversible process will
always produce decoherence which splits worlds.
(see "Why do worlds split?", [7], [10])
In the example of a Geiger counter and a charged particle
(see "What is a measurement?")
after the particle has passed the
counter one world contains the clicked
counter and that
portion of the particle's wavefunction which passed though the
detector. The other world contains
the unclicked counter with
the particle's wavefunction with a "shadow" cast by
the counter in the particle's wavefunction. The Geiger counter split when the
amplification process became irreversible.
The splitting is local (ie originally in the region of the Geiger counter in our
example) and is transmitted causally to more distant systems (see "Is
manyworlds a local theory?" and "Does the EPR experiment prohibit
locality?"). 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. (The event has become irreversible.)
Consider
Schrodinger's Cat. A cat is placed in a
sealed box with a
device that releases a
lethal does of cyanide if a radioactive decay
is detected. After a while an observer
opens the box to see if the cat is alive or dead. According
to the CI the cat was neither
alive nor dead until the
box was opened, whereupon the wavefunction
of the cat collapsed into one of the two alternatives. The paradox, according to Schrodinger, is
that the cat presumably
knew if it was alive *before* the box was opened. According to manyworlds the device was split
into two states (cyanide released or not) by the radioactive decay. As the device/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 unlucky
and late copy. The external observer is split into two
copies only when the box
is opened and is altered by the state of the cat.
In the language of thermodynamics the decay of the atom and the
amplification of its detection by a Geiger counter, the release of the cyanide
and the death of the cat are all irreversible events. These events have caused the decoherence (see
"Why do worlds split?") of the different
branches of the wavefunction
of the cat + device + box. Decoherence
[7] occurs when irreversible macrolevel
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.
The advantage of linking the definition of worlds and the
splitting process with
thermodynamics is the splitting process is irreversible and
forwardtimebranching, following the increase with entropy. Like
all irreversible processes, though, there are exceptions even at the coarse grained level and worlds will occasionally
fuse. A necessary, although not
necessarily sufficient,
precondition for fusing is for all records, memories etc that
discriminate between the
prefused worlds or histories be lost.
Q8a What is sumoverhistories?
The sumoverhistories or the path integral formalism was
developed by Feynman in the 1940s [F] as an alternative interpretation of quantum mechanics, alongside Schrodinger's wave picture
and Heisenberg's matrix mechanics, for calculating transition amplitudes. All three approaches are mathematically
equivalent, but the PI formalism offers some interesting
insights into manyworlds. In the PI
picture the single particle wavefunction at (x',t') is built up of
contributions of all possible
paths from (x,t), where each path's contribution weighted by a (phase) factor
of exp(i*Action[path]/hbar) * wavefunction
at (x,t). The Action[path] is the
timeintegral of the lagrangian (roughly:
the kinetic minus the potential energy) along
the path from (x,t) to (x',t'). The
final expression is thus
sum or integral over all paths, irrespective of any classical dynamical
constraints. For Nparticle
systems the principle is
the same, except that the paths are over a 3N space.
Feynman developed his PI formalism further for his work on quantum electrodynamics,
QED, with his Feynman
diagrams, in parallel with
Schwinger and Tomonoga who developed a less
visualisable form of QED. Dyson showed
that these approaches
were all equivalent.
It is quite natural
when analysing systems from the PI point of view to think
of the particle continually
splitting apart and fusing together
to explore every possible
intermediate
configuration between the
specified start and end
states. For this reason the technique is often referred
to as "sumoverhistories".
Since we do not occupy a privileged moment in history it is natural to wonder if alternative histories are contributing
equally to transition amplitudes in the future, and therefore that they all have equal reality. Perhaps
we shouldn't be surprised
that Feynman,
therefore, is on record as believing
in manyworlds. (See "Who believes in manyworlds?") What is surprising is that
Everett developed his manyworlds theory entirely from the Schrodinger viewpoint without any detectable influence from Feynman's work, despite sharing the same thesis supervisor, John A Wheeler.
[F] Richard P Feynman, Spacetime approach to nonrelativistic quantum mechanics, Reviews
of Modern Physics, Vol 20 267 (1948)
Q8b What is manyhistories?
There is considerable
linkage between
thermodynamics and manyworlds, explored in the "decoherence" views
of Zurek [7] and GellMann and Hartle
[10], Everett [1] and others [4b].
GellMann and Hartle
have extended the role of decoherence in
defining the Everett worlds, or histories in their nomenclature. They
call their approach the "manyhistories" approach, where each "coarsegrained or classical
history" is associated
with a unique timeordered
sequence of sets of irreversible events, including
measurements, records,
observations and the like. (Finegrained histories effectively
relax the irreversible criterion.) Physically the manyhistories approach is isomorphic to Everett's manyworlds,
although GellMann and Hartle
choose not to accept Everett's metaphysical stance that each history corresponds to an element of reality.
The worlds split or "decohere" from each other
when irreversible events occur. (See
"Why do worlds split?" and "When do worlds split?".) Correspondingly manyhistories defines a
multiplyconnected hierarchy of classical histories where each classical
history is a "child" of any parent history which has only a subset of the child defining
irreversible events and a parent of any history which has a superset of such events. Climbing up the tree from child to parent moves to progressively coarser
grained consistent histories until eventually the top is reached where the
history has *no* defining events (and thus consistent with everything!). This is Everett's universal wavefunction. The bottom of the coarsegrained tree terminates with the maximally refined set of
decohering histories. The classical
histories each have a probability assigned to them and
probabilities are additive in the sense
that the sum of the
probabilities associated
a set classical histories is equal to the probability associated with the unique parent history defined by the
set. (Below the maximally refined
classical histories are the fine grained or quantum histories, where
probabilities are no longer additive and different histories significantly interfere with each other. The bottom level consists of complete microstates, which fully specified states.)
Q9 How many worlds are there?
It so
happens that we can use
the thermodynamic PlanckBoltzmann
relationship to count the branches at each splitting, at the lowest, maximally
refined level of
GellMann's manyhistories tree (See "What is manyhistories?"). The bottom level consists of microstates which can be counted by
the formula W = exp (S/k), where S = entropy, k = Boltzmann's constant (approx
10^{22} Joules/Kelvin) and W = number of worlds or macrostates. The number of coarser
grained worlds is lower, but still increasing
with entropy by the same ratio, ie the number of worlds a
single worlds splits into at the site of an irreversible event is exp(dS/k),
where dS = entropy of the defining event.
Because k is very small
a great many worlds split off at each macroscopic event.
Q10 Is manyworlds a local theory?
The simplest way to see that the manyworlds metatheory is
local is to note that
it requires that the
wavefunction obey some
relativistic wave equation, the exact form of which is currently unknown, but
which is presumed to be locally Lorentz invariant at all times and
everywhere. This is equivalent to
imposing the requirement that
locality is enforced at all times
and everywhere. Ergo manyworlds is a
local theory.
Another way of seeing this is examine how macrostates
evolve. Macrostates descriptions of
objects evolve in a local fashion. Worlds split as the macrostate description
locally divides inside the light cone of the triggering event. Thus the splitting is a local process,
transmitted causally at light or sublight speeds. (See "Does the EPR experiment prohibit
locality?" for more details and "When do worlds split?")
Q11 Is manyworlds a deterministic
theory?
Yes, manyworlds is a deterministic theory, since the wavefunction obeys a deterministic wave
equation at all times. All possible outcomes of a measurement or interaction are embedded
within the universal
wavefunction although
each observer, split by acts of observation, is only aware
of single outcomes due to the linearity of the wave equation. The world appears indeterministic, with the usual probabilistic collapse of the
wavefunction, but at the
objective level which includes all outcomes determinism is
restored.
Some people are under
the impression that the
only motivation for
many worlds is a desire
to return to a deterministic theory of physics.
This is not true. As Everett
pointed out, the objection with
the standard Copenhagen
interpretation is not the indeterminism per se, but that indeterminism occurs only with the intervention of an observer, when the wavefunction collapses.
Q12 Is manyworlds a relativistic
theory?
It is trivial to relativise manyworlds because all
relativistic theories of physics are still quantum theories with linear wavefunctions. There are three or more stages to developing
a fully quantum
relativistic theory. Simplifying
slightly gives:
First quantisation: the wavefunction is a complex
field which evolves in 3N dimensions which represent N particles. The wavefunction
is a solution of either
the manyparticle Schrodinger, Dirac or
KleinGordon equation or some other wave
equation.
Second quantisation: AKA quantum field theory, which handles
the creation and destruction of particles by quantising
fields as well as particles. (Each particle type corresponds to a field, in
QFT. Eg the electromagnetic field's particle
is the photon, but the number of particles involved is
indeterminate.) Again manyworlds has no
problems handling QFT. The wavefunction of a collection of particles
and fields exists in a Fock space, where the number of dimensions varies from
component to component.
Third quantisation.
The gravitational metric is quantised, along with
(perhaps) the topology of spacetime.
The physics of this is incomplete, but there is no reason for thinking
that manyworlds can't
be extended to cover this as well. (One of the original motivations of Everett's scheme was to provide
a system for quantizing the gravitational field within quantum cosmology to yield a complete description of the
universe.)
Q13 Is manyworlds (just) an
interpretation?
No, for four reasons:
First, manyworlds has testable implications (see "Is
manyworlds testable?") and interpretations, generally, do not have
testable differences from each other.
Second, the mathematical structure of manyworlds is not isomorphic to other formulations of
quantum mechanics like
the Copenhagen interpretation or Bohm's hidden
variables. The Copenhagen interpretation
does not contain those elements
of the wavefunction that correspond to the other
worlds. Bohm's hidden variables contain particles,
in addition to the wavefunction. Therefore neither theory is isomorphic to each other or manyworlds and are not,
therefore, merely rival "interpretations".
Third, there is no scientific, reductionistic alternative to many worlds. All the other theories fail for logical reasons. (See "Is there any alternative theory?")
Four, the interpretative side of manyworlds, like the subjective probabilistic elements,
are derived from within
the theory, rather than
added in by assumption, as in the conventional approach. (See "How do probabilities emerge within manyworlds?")
ManyWorlds should
really be described as a
theory or, more precisely, a metatheory, as Everett pointed out, since it makes
statements that are
applicable across a range
of theories. Manyworlds is the
unavoidable implication of any quantum theory which obeys some
type of wave equation,
linear with respect to
the wavefunction it
operates on.
Q14 What are the alternatives?
There is no other quantum theory, besides manyworlds, that is scientific and free of internal inconsistencies, that I am aware of. Briefly here are the defects of the most popular alternatives:
1) Copenhagen
Interpretation. Postulates that the observer obeys different physics than the nonobserver. (A return to vitalism.) The definition of observer varies from one
adherent to another, if present at all.
The status of the wavefunction
is also ambiguous. If the wavefunction is real
the theory is nonlocal (not fatal, but unpleasant), if not real then the theory supplies no model of reality. (See "What are the problems with quantum theory?")
2) Hidden Variables [B]. Explicitly
nonlocal. Bohm accepts that all the branches of the
universal wavefunction
exist. Like Everett Bohm held that the wavefunction
is real complexvalued field which never
collapses. In addition he postulated that there were particles
that move under the influence of a nonlocal
"quantum potential" derived from the wavefunction, in addition to the
classical potential. The action of the
quantumpotential is such
that the particles
are affected by only one of the branches of the wavefunction. (Bohm derives what is essentially
a decoherence argument to show
this, see section 7,#I [B]).
The implicit, unstated assumption made by Bohm is that only the single branch of wavefunction associated with particles
can contain selfaware observers, whereas Everett makes
no such
assumption. Most of Bohm's adherents do not seem
to understand (or even
be aware of) Everett's
criticism, section VI [1], that
the hidden variable particles
are not observable since the wavefunction
alone is sufficient to account for all observations. The particles can,
therefore, be discarded, along with the guiding
quantumpotential, yielding a theory isomorphic to manyworlds, without affecting
any experimental results.
[B] David J Bohm A suggested
interpretation of the quantum theory in terms of "hidden variables" I and II,
Physical Review Vol 85 #2 166193 (1952)
3) Quantum
Logic. Undoubtedly the most extreme of all attempts
to solve the QM measurement problem. Apart from abandoning
one or other of the classical tenets of logic these theories are all unfinished
(presumably because of internal inconsistencies). Also
it is unclear why different types
of logic apply on different
scales.
4) Extended
Probability [M]. A bold theory in which
the concept of probability is "extended" to include complex values [Y].
Whilst quite daring, I am not sure
if this is logically permissable, being in conflict with the relative frequency notion
of probability, in which case it suffers from the same criticism as quantum logic. Also
it is unclear, to me
anyway, how the resultant notion of "complex
probability" differs from the "probability amplitude" and thus
why we are justified in collapsing the complex
probability as if it were a classical probability.
[M] W Muckenheim A review of extended
probabilities Physics Reports Vol 133 339 (1986)
[Y] Saul Youssef __
hepth 9307019
5) Transactional model [C]. Explicitly
nonlocal. An imaginative theory, based on the FeynmanWheeler absorberemitter model of EM, in which advanced
and retarded probability amplitudes combine into an atemporal
"transaction" to form the Born
probability density. It requires that the input and output states, as
defined by an observer, act as emitters and absorbers respectively, but not any internal states
(inside the "black box"), and, consequently, suffers from the
familiar measurement
problem of the Copenhagen interpretation.
If the internal states *did* act as emitters/absorbers then the wavefunction would collapse, for example,
around one of the double slits (an internal state) in the double slit
experiment, destroying the observed interference fringes. In transaction terminology a transaction
forms between the first
single slit and one of the double slits and another transaction forms between the same double slit and the point of
screen where the photon lands.
[C] John G Cramer, The transactional interpretation of quantum
mechanics Reviews of Modern Physics Vol 58 #3 647687 (1986)
6) manyminds. Despite its superficial similarities
with manyworlds this
is actually a very unphysical, nonoperational theory. (See "What is manyminds?")
7) Nonlinear
theories in general. So far no nonlinear theory has any
accepted experimental support,
whereas many have failed experiment.
(See "Is physics linear?")
Q15 Is manyworlds testable?
Yes, it is. There are
two forms of tests: retrodictions (theory follows data) and predictions (data follows
theory).
A) A retrodiction occurs when already gathered
data is accounted for by
a later theoretical advance
in a more convincing fashion. The advantage of a retrodiction over a
prediction is that the data more likely to be free of experimenter bias. An example of a retrodiction is the
perihelion shift of Mercury which Newtonian mechanics plus gravity was unable, totally, to
account for whilst Einstein's general relativity made short work of it.
Manyworlds retrodicts all the peculiar properties of the (apparent) wavefunction collapse in terms of
decoherence. (See "Can wavefunctions
collapse?", "When do worlds split?" & "Why do worlds
split?") No other quantum theory
has yet accounted for this behaviour scientifically. (See "What are the alternatives?")
B) A prediction occurs when a theory suggests
new phenomena.
ManyWorlds predicts that
the Everettworlds do not interact with
each other, because of the presumed linearity of the wave equation. However worlds *do* interfere with each other, and this enables
the theory to be tested. (Interfere and
interact mean different things in quantum mechanics. See a guide
to QM.)
According to manyworlds worlds split with the operation of every
thermodynamically irreversible process.
The operation of our minds are irreversible, carried along for the ride, and divide with the worlds. Normally, therefore, this splitting is
undetectable to us. To detect the
splitting we need to set an up experiment where a mind is split but the world
*isn't*. We need a reversible mind.
The general consensus
in the literature [11], [16] is that
the experiment to detect other worlds will doable by about mid21st
century. That date is predicted from two trendlines, both of
which are widely accepted in their own respective fields. To detect the other worlds you need a
reversible machine intelligence. This
requires two things:
reversible nanotechnology and AI.
1) Reversible nanoelectronics. This is an straightline extrapolation based upon the log(energy) / logic
operation figures, which are projected to drop below kT in about 2020. This trend has held good for 50 years. An operation that dissipates much less than
kT of energy is reversible. (This implies that frictive or dissipative forces are absent.) If more than kT of energy is released then, ultimately, new
degrees of freedom
are activated in the environment and the change becomes
irreversible.
2) AI. Complexity of human brain = approx 10^{17}
bits/sec, based on the
number of neurons (approx 10^{10}) per human brain, average number of synapses per neuron
(approx 10^{4}) and the average
firing rate (approx 10^{3} Hz).
Straight line projection
of log(cost) / logic operation says that
human level, selfaware machine intelligences will be
commercially available by about 20302040.
Uncertainty due to
present humanlevel complexity, but the trend has held good for 40 years.
Assuming
that we have a
reversible machine intelligence to hand then the experiment consists of the
machine making three measurements
of the spin of an electron (or polarisation of a photon). (1) First it measures the spin along the zaxis. It records either spin "up" or spin
"down" and notes this in its memory. This measurements acts just to prepare the electron in a
definite state. (2) Second it measures the spin along the xaxis and records either
spin "left" or
spin "right" and notes *this* in its memory. The
machine now reverses the
entire xaxis measurement, including reversibly erasing its memory of the second measurement. (3) Third the machine takes a spin measurement along the zaxis. Again the machine makes a note of the
result.
According to the Copenhagen interpretation the original (1) and final (3) zaxis
spin measurements have only a 50% chance of agreeing
because the intervention of the xaxis measurement by the conscious observer (the machine) caused
the collapse of the electron's wavefunction. According to manyworlds the first and third
measurements will
*always* agree, because
there was no intermediate
wavefunction
collapse. The machine was split into two
states or different
worlds, by the second measurement;
one where it observed the electron with
spin "left";
one where it observed the electron with
spin "right". Hence when the
machine reversed the second measurement these two worlds merged
back together, restoring the original
state of the electron 100% of the time.
Q16 Could previously
separate worlds diverge rather than split?
This is definitely not permissable in manyworlds. Worlds do not exist in a quantum
superposition independently of each other before they decohere or split.
The splitting is a physical process, grounded in the dynamical evolution
of the wave vector, not a matter of philosophical/mental
convenience (see "Why do worlds split?" and "When do worlds
split?") If you try to treat the
worlds as preexisting and separate
then the maths all comes out wrong. Also
the divergence theory stops being deterministic, in
contradiction to the wave equations which are deterministic, since we have a
AAAAAAAAAAAAAAABBBBBBBBBBBBBBB ===========> time
Worlds
diverge
AAAAAAAAAAAAAAACCCCCCCCCCCCCCC
situation, rather than:
BBBBBBBBBBBBBBB
B
AAAAAAAAAAAAAA Worlds
splitting
C
CCCCCCCCCCCCCCC
Additionally the divergence
model has to explain why:
AAAAAAAAAAAAAAABBBBBBBBBBBBBBB
AAAAAAAAAAAAAAABBBBBBBBBBBBBBB
doesn't happen! This
false divergence model, at the mental level, seems favoured by adherents of
manyminds. (See "What is
manyminds?")
Q17 What is manyminds?
Manyminds proposes, as an extra
fundamental axiom, that
an infinity of separate
minds or mental states be associated
with each single brain
state. When the single physical brain
state is split into a quantum superposition by a measurement the associated minds are thought of as diverging rather than splitting. The motivation for this brainmind dichotomy seems purely to avoid talk
of minds splitting and talk instead about the divergence of preexisting separate mental states. There is no physical basis for this
interpretation, which is incapable of an operational definition. Indeed the divergence model
for physical systems is specifically not permitted in manyworlds. Manyminds seems to be proposing that minds follow different rules than
matter. (See "Could previously separate worlds diverge
rather than
split?")
In manyminds the role of the conscious observer is accorded
special status, with its fundamental axiom about
infinities of minds, and as such
is philosophically opposed
to manyworlds, which seeks to remove
the observer from any privileged role in physics. (Manyminds was co invented by David Albert,
who has, apparently,
since abandoned
it. See Scientific American July 1992 page 80 and contrast with April 94.)
The two theories should
not be confused.
Q18 Does manyworlds violate
Ockham's Razor?
William of Ockham, 12851349(?) English philosopher and one of the founders of
logic, proposed a maxim
for judging theories which says that
hypotheses should not be multiplied
beyond necessity. This is known as
Ockham's razor and is interpreted, today, as meaning that
to account for any set of facts the simplest theories are
to be preferred over more complex
ones. Manyworlds is viewed as
unnecessarily complex,
by some, by requiring the existence of a
multitude of worlds to explain
what we see, at any time, in just one world.
This is to mistake
what is meant by "complex". Here's an example. Analysis of starlight reveals
that starlight is very similar to faint sunlight, with spectroscopic absorption and emission lines. Assuming
the universality of physical law
we are led to conclude that
other stars and worlds are scattered, in great
numbers, across the cosmos. The theory that "the stars are distant
suns" is the simplest theory and so to be preferred by Ockham's Razor
to other geocentric theories.
Similarly manyworlds
is the simplest and most economical theory because it proposes
that same laws
of physics apply to animate observers as inanimate objects. The multitude of worlds predicted by the
theory is not a weakness
for manyworlds, any more than
stars are for astronomy, since the noninteracting worlds emerge from a simpler
theory.
(As an historical aside it is worth noting that Ockham's razor was also falsely used to argue in favour
of the older
heliocentric theories *against* Galileo's notion of the vastness of the
cosmos. The notion of vast empty interstellar spaces was too
uneconomical to be believable. Again they
were confusing the notion of vastness with
complexity [15].)
Q19 Does the multiplication of
worlds violate conservation of energy?
First, the law
conservation of energy is based
on observations within
each world. All observations within each world are consistent with conservation of energy,
therefore energy is conserved.
Second, and more precisely, conservation of energy, in QM,
is formulated in terms weighted averages or of expectation values. Conservation of energy is expressed
by saying that the time
derivative of the expectation
of the energy operator vanishes. This
statement can be scaled up to includes
the whole
universe. Each world has an approximate
energy, but the energy of the total wavefunction
(of any subset of) involves summing over each world, weighted with its probability measure. This weighted sum is a constant. So
energy is conserved within
each world and across the totality of worlds.
One way of viewing this result  that observed conserved quantities
are conserved across the totality of worlds  is to note that new worlds are not created by
the action of the wave equation, rather existing worlds are split into
successively smaller and smaller
slices, as measured in
the Hilbert space.
Q20 How do probabilities emerge within manyworlds?
Everett demonstrated [1],[2] that observations in each world obey all conventional
statistical laws predicted by the
probabilistic Born
interpretation by showing that the Hilbert space's inner
product or norm supplies
a unique measure or "volume" to each
world or set of worlds. The norm of the
set of worlds where experiments contradict the Born interpretation (nonrandom or maverick worlds) vanishes in the limit as the number of probabilistic
trials goes to the limit. Vectors with zero norm, where probability breaks down, don't exist (see below), thus we, as
observers, observe the familiar predictions of quantum theory expressed
as probabilistic events.
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
would hold true and asserted the vanishing
of the Hilbert space volume of the set of nonrandom worlds.
DeWitt (with Graham) later published a longer
*derivation* of Everett's assertion
[4a],[4b]. What Everett asserted
and DeWitt derived is that the collective norm of all the
maverick worlds, as the number of trials goes to infinity, vanishes. Since the only vector in a Hilbert space with vanishing norm is the null
vector (a defining axiom of a Hilbert space) this is equivalent to saying that nonrandomness
is never realised. Thus all worlds obey the usual Born predictions of quantum theory.
In more detail the steps are:
1) Construct the tensor product of N identical systems
in state psi> (repeated indices summed):
PSI_N>
= psi_1>*psi_2>*...... psi_N> where
psi_j>
= jth system prepared in state psi>
=
i_j><i_jpsi> (ie the amplitude of the ith eigenstate is independent
of which system
it
is in) so that
PSI_N>
= i_1>i_2>...i_N><i_1psi><i_2psi>...<i_Npsi>
2) Quantify the
deviation from the "expected" Bornmean for each component of PSI_N> with respect to the above
i_1>i_2>...i_N> basis by counting the number of occurrences
of the ith eigenstate/N. Call this number RF(i). Define the Borndeviation as D = sum(i)( (RF(i)  <ipsi>^{2})^{2}
).
Thus D,
loosely speaking, for each N length sequence expresses
how "nonrandom"
a particular
sequence
is although, of course, no finite sequence is excluded from happening since the
concept
of nonrandom becomes precise only as N goes to infinity [H].
3) Sort out terms in the expansion of
PSI_N> according to whether D is less/equal
to (.LE.) or greater than (.GT.) E, where E is a real, positive constant. Collecting terms together we get:
PSI_N>
= N,"D.GT.E"> + N,"D.LE.E">
worlds worlds
for
which for which
D
> E D <= E
4) What DeWitt showed
was that:
<N,"D.GT.E"N,"D.GT.E">
< 1/(NE) (proof in appendix of 4b)
Thus as
N goes to infinity then the righthand side vanishes for all positive values of
E.
(This
mirrors the classical "frequentist" position on probability which
states that if i occurs
with probability p(i) then the
proportion of N trials with
success i approaches p(i)/N as N goes
to
infinity [H]. This has the immediate benefit that sum(i) = 1.)
The norm of N,"D.LE.E">,
by
contrast, approaches 1 as N goes to infinity.
5) The norm of the
collection of nonrandom
worlds vanishes and therefore must be identified with
the same complex multiple of the null vector.
6) Since (by
assumption) the state vector faithfully models
reality then the null
vector cannot represent
any element of reality since it can be added to (or
subtracted from) any other state vector without
altering
the other state vector.
7) Ergo the nonrandom worlds are not realised, without making any additional
physical assumptions.
The emergence of Bornstyle
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. (See "Is manyworlds (just) an
interpretation?") The
interpretative elements are forced
my the mathematical structure inherent in the axioms.
[H] JB Hartle, Quantum Mechanics of Individual Systems, American Journal of
Physics Vol 36 #8 704712 (1968) Hartle has investigated the N goes to
infinity in more detail and more generally.
He shows that the relative frequency operator
obeys RF(i) psi_1>psi_2>.... = <ipsi>^{2}
psi_1>psi_2>....
Q21 Does manyworlds allow freewill?
ManyWorlds, whilst deterministic on the objective universal
level, is
indeterministic on the subjective level
so the situation is
certainly no better or
worse for freewill than in the Copenhagen view. Traditional Copenhagen indeterministic
quantum mechanics only
slightly weakens the case for freewill. In quantum terms each neuron is an essentially
classical object. Consequently quantum
noise in the brain is at such
a low level that it probably doesn't often
alter, except very rarely, the critical
mechanistic behaviour of sufficient
neurons to cause a decision to be different
than we might otherwise expect. The consensus view amongst experts is that freewill is the consequence  insofar as it is not an illusion,
which is a perfectly
acceptable way of viewing it  of the mechanistic operation of our brains, the
firing of neurons, discharging of synapses etc and fully compatible with the determinism of classical
physics.
Nevertheless,
some people find that with all possible
decisions being realised
in different worlds that the prima facia situation for free will looks quite
difficult. Does this multiplicity of
outcomes destroy freewill? If both sides of a choice are selected in different worlds why bother to spend
time weighing the evidence before selecting?
The answer is that whilst all decisions are realised, some
are realised more often than others  or to put to more
precisely each branch has its own weighting or measure which enforces the usual laws
of quantum statistics.
The measure
is supplied by the mathematical structure of
Hilbert spaces. Every Hilbert space has
a norm, constructed from the inner product,  which we can think
of as analogous to a volume  which weights each world or collection of
worlds. A world of zero volume is never realised. Worlds in which the conventional statistical
predictions consistently break down have zero volume and so are never realised. (See "How do probabilities emerge within manyworlds?")
Thus our actions, as expressions
of our will, correlate with
the weights associated with worlds. This, of course, matches our subjective
experience of being able to exercise our will, form moral judgements and be held responsible for our actions.
Q22 Why am I in this world and not
another? or Why the universe appears random,
but isn't.
Consider,
for a moment, this analogy:
Suppose
Fred has his brain divided in two and transplanted into different
cloned bodies (this is a gedanken operation!).
Let's further suppose
that each half brain is
regenerates to full functionality and we name the
resultant individuals Fredleft
and Fredright. Fredleft can ask, why did I end up as Fredleft?
Similarly Fredright can ask, why did I end up as
Fredright? The only answer possible
is that there was *no*
reason. From Fred's point of view it is a
subjectively *random* choice which individual Fred ends up
as. To the surgeon the whole process is deterministic. To Fred it seems random.
Same with manyworlds. There was no reason "why" you ended up in
this world, rather than
another. It was a subjectively random choice, an artifact
of your consciousness being split. The
universe is, in effect, performing
umpteen splitbrain operations on us all the time. The randomness apparent in nature is a consequence of
the splitting of worlds.
(See "How do probabilities emerge within manyworlds?" for how
the subjective randomness is
moderated by the usual
probabilistic laws of QM.)
Q23 Can wavefunctions
collapse?
ManyWorlds predicts/retrodicts that wavefunctions
appear to collapse (see "The EPR experiment"), when measurementlike interactions and processes occur
via a process called decoherence [7], [10], but claims that they do not *actually* collapse. If a *mechanism* for collapse could be found then there would be no
need for manyworlds. 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 there can be no
mechanism.
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, daytoday 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 subprocesses 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
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 same quantumoperation of their simpler
components. (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
nonlinear theories so that microscopic systems are
approximately linear and obey the wave equation but macroscopic systems are
grossly nonlinear and
generates collapse. Unfortunately all
these efforts have made additional predictions which, when tested, have failed.
(Another reason
for doubting that any
collapse actually takes
place is that the
collapse would have to propagate instantaneously or in some spacelike fashion, otherwise
the same particle
would be observed more than
one at different
locations. Not fatal, but unpleasant and
difficult to reconcile with
relativity.)
The simplest conclusion
is that wavefunctions
just *don't* collapse
and that all branches
of the wavefunction
exist.
Q24 Is physics linear? or Could we ever communicate with the other worlds? or Why do I only ever experience one world?
According to our present knowledge of physics whilst it is possible to detect the presence of
other nearby worlds, through
the existence of interference effects, it is impossible travel to or communicate with them. Mathematically this corresponds to an
empirically verified property of all quantum theories called linearity which
says that the worlds
can interfere with each
other with respect to a
external, unsplit, observer or system (whence they are manifest as diffraction or interference
patterns) but they
can't influence each
other in the sense that an experimenter can arrange to communicate with their own, already splitoff,
quantum copies.
Specifically the wave equation is linear, with respect to the wavefunction or state vector, which means that given any two solutions of the wavefunction with identical boundary conditions
then any linear combination of the solutions
is also a solution itself. Since each component of a linear solution evolves with complete indifference as to the
presence or absence of the other terms then we can conclude that no experiment in one world can
have any effect on
another experiment in another world.
Hence no communication is possible
between quantum worlds.
Linearity (of the wavefunction)
has been verified hold true to better
than 1 part
in 10^{27} [W] and some scientists believe that it is absolutely
true for various theoretical reasons. If slight nonlinear effects
were ever discovered then the
possibility of communication with/travel
to the other worlds would be opened up.
[W] Steven Weinberg, Annals of Physics, Vol 194 #2 336386
(1989) and Dreams of a Final Theory
(1992)
Q25 Can we determine what other
worlds there are? or Is the form of the Universal Wavefunction knowable?
To calculate the form of the universal wavefunction requires not only a knowledge of its dynamics (which we have a good approximation to, at the moment)
but also of the
boundary conditions. To actually
calculate the form of the universal wavefunction,
and hence make inferences
about *all* the embedded worlds, we would need to know the boundary conditions
as well. We are presently restricted to making inferences about those worlds with which have shared
a common history up to some
point, which have left traces
(records, fossils, etc) still discernable today. This restricts us to a subset of the extant
worlds which have shared the same boundary conditions with us. The further we probe back in time the less we know of the boundary
conditions and therefore the less
we can know of the universal wavefunction.
This limits us to drawing
conclusions about a restricted subset of the worlds  all the worlds which are
consistent with our
known history up to a some common moment, before they diverging. The
flow of historical events is, according to chaos/complexity theory/thermodynamics, very sensitive to
amplification of quantumscale uncertainty and this
sensitivity is a futuredirected oneway process. We can make very reliable deductions
about the past from the knowledge
future/present but we can't predict the future from knowledge the past/present. Thermodynamics implies that the future is harder
to predict than the
past is to retrodict. Books get written
about this "arrow of time" problem but we'll just have to accept this
as given.
The fossil and historical records say that dinosaurs and Adolf Hitler once existed but have
little to say about future.
Consider
the effects of that most quantum of activities, Brownian motion, on the
conception of individuals and the knockon effects
on the course of history. Mutation
itself, one of the sources
of evolutionary diversity,
is a quantum event. For an example of
the biological/evolutionary implications see Stephen Jay Gould's book
"Wonderful Life" for an exploration of the thesis that the path of evolution is driven
by chance. According to Gould
evolutionary history forms an enormously diverse tree of possible histories  all very
improbable  with our
path being selected by chance. According
to many worlds all these other possibilities are realised. Thus
there are worlds in which Hitler won WWII and worlds in which the dinosaurs
never died out. We can be as certain of
this as we are that
Hitler and the dinosaurs once existed in our own past.
Whether or not we can ever determine the totality of the
universal wavefunction
is an open question. If Steven Hawking's
work on the no
boundarycondition condition is ultimately successful, or it emerges from some
theory of everything,
and many think it will, then
the actual form of the *total* wavefunction
could, in principle, we determined from a
complete knowledge
physical law itself.
Q26 Who was Everett?
Hugh Everett III (19301982) did his undergraduate study in chemical
engineering at the Catholic University of America. Studying von Neumann's and Bohm's textbooks
as part of his graduate studies, under Wheeler, in mathematical
physics at Princeton University in the 1950s he became dissatisfied (like many others) with the collapse of the wavefunction. He developed, during discussions with Charles Misner and Aage Peterson (Bohr' assistant, then visiting
Princeton), his "relative state" formulation. Wheeler encouraged
his work and preprints
were circulated in January 1956 to a number of physicists. A condensed version of his thesis was
published as a paper to "The Role of Gravity in Physics" conference
held at the University of N Carolina, Chapel Hill, N Carolina in January 1957.
Everett was discouraged
by the lack of response from others, particularly Bohr, whom he flew to Copenhagen to meet but
got the complete brushoff from. Leaving physics after completing his
Ph.D, Everett worked as
a defense analyst at the Weapons Systems Evaluation Group, Pentagon. At some point he became
a private contractor, apparently quite successfully for he became a
multimillionaire. In 1968 Everett worked for the Lambda Corp. His published papers during this period cover things like optimising resource allocation
and, in particular, maximising enemy kill rates during nuclearweapon
campaigns.
Later (from 1968 onwards) Bryce S DeWitt, one of the 1957 Chapel Hill
conference organisers, but better
known as one of the founders of quantum gravity, successfully popularised Everett's relative
state formulation as the "manyworlds interpretation" in a series of articles [4a],[4b],[5].
Sometime in 19769
Everett visited Austin, Texas, at Wheeler or DeWitt's invitation, to give some talks on
QM. The strict nosmoking rule in the
auditorium was relaxed for Everett (a chain smoker); the only exception ever. Everett, apparently,
had a very intense and agitated manner, and spoke with a very acute style, correctly
anticipating and cutting off questions after a few words. Oh yes, a bit of trivia, he drove a Cadillac with horns.
With
the steady growth of
interest in manyworlds in the late 1970s Everett planned returning to physics to do more work on the subject of measurement in quantum theory, but died
of a heart attack in 1982. Survived by his wife.
Q27 Who believes in manyworlds?
A poll conducted by
"political scientist" L David Raub, reported by Tipler [T], of 72 of
the "leading cosmologists and other quantum field theorists" about
the "ManyWorlds Interpretation" gives the following
breakdown.
1) Yes, I think MWI is true 58%
2) No, I don't
accept MWI 18%
3) Maybe it's true but I'm not yet convinced 13%
4) I have no opinion
one way or the other 11%
Amongst the "Yes, I think
MWI is true" crowd
listed are Stephen Hawking and Nobel Laureates Murray GellMann and Richard Feynman. GellMann and Hawking recorded reservations with the name
"manyworlds", but not with
the content. Nobel Laureate Steven
Weinberg is also
mentioned as a manyworlder, although the suggestion is, not when the poll was conducted,
presumably before 1988 (when Feynman died).
The only
"No, I don't accept
MWI" listed by name is Penrose.
[T] Frank J Tipler, The Physics of Immortality, pages 1701
Q30 Does the EPR experiment prohibit
locality? or Quantum mechanics without
operators
The EPR experiment is widely regarded
as the definitive gedanken experiment for demonstrating that quantum mechanics is nonlocal
or incomplete. We shall see that it implies neither.
The EPR experiment was devised, in 1935, by Einstein,
Podolsky and Rosen to demonstrate that
quantum mechanics was incomplete [E].
Bell, in 1964, demonstrated that
any hidden variables
theory, to replicate the predictions of QM, must be nonlocal [B]. QM predicts strong correlations between separated systems, stronger
than any local hidden variables theory can
offer. Bell encoded this statistical
prediction in the form of some famous inequalities that apply to any type of EPR experiment. Eberhard,
in the late 1970s, extended Bell's inequalities to cover any local theory, with or without hidden variables. Thus the EPR experiment plays a central role in sorting and testing variants of
QM. All the experiments attempting
to test EPR/Bell's inequality
to date (including
Aspect's in the 1980s [As]) are in line with
the predictions of standard
QM  hidden variables
are ruled out. Here is the paradox of the EPR experiment. It seems to imply that any physical theory must
involve fasterthanlight "things"
going on to maintain
these "spooky" actionatadistance correlations and yet still be
compatible with
relativity, which seems to forbid
FTL.
Let's examine the EPR experiment in more detail.
So
what did EPR propose? The original
proposal was formulated in terms of correlations between the positions and momenta of two oncecoupled particles. Here I shall
describe it in terms of the spin (a type
of angular momentum intrinsic to the particle) of two
electrons. [In this treatment I shall ignore the fact that electrons always form
antisymmetric combinations. This does
not alter the results but does simplify the maths.] Two initially coupled electrons, with opposed
spins that sum to zero,
move apart
from each other across a distance of perhaps many light years, before being separately detected, say, by me on Earth and you on Alpha Centauri with our respective measuring
apparatuses. The EPR paradox results from noting that if we choose the same (parallel) spin axes to measure along then we will observe the two electrons' spins to
be antiparallel (ie when we communicate we find that the spin on our electrons are correlated and opposed). However if we choose measurement spin axes that are perpendicular to each other
then there is no correlation between
electron spins. Last minute alterations in a
detector's alignment can create or destroy correlations across great
distances. This implies, according to some
theorists, that fasterthanlight influences
maintain correlations between separated
systems in some circumstances
and not others.
Now let's see how manyworlds escapes from this dilemma.
The initial state of the wavefunction of you, me and the electrons and the rest of
the universe may be written:
psi>
= me> electrons> you>
rest of universe>
on in on
Earth deep Alpha
space Centauri
or more compactly, ignoring the rest of the universe, as:
psi>
= me,electrons,you>
And
electrons>
= (+,>  ,+>)/sqrt(2)
represents
a pair electrons, with
the first electron travelling towards Earth
and
the
second electron travelling towards Alpha Centauri.
+>
represents an electron with
spin in the +z direction
>
represents an electron with
spin in the z direction
It is an empirically established fact, which we just have to
accept, that we can
relate spin states in one direction to spin states in other directions like so (where "i" is the sqrt(1)):
left> = (+>  >)/sqrt(2) (electron with spin in x direction)
right>
= (+> + >)/sqrt(2) (electron with spin in +x direction)
up> = (+> + >i)/sqrt(2) (electron with spin in +y direction)
down> = (+>  >i)/sqrt(2) (electron with spin in y direction)
and inverting:
+> = (right> + left>)/sqrt(2) = (up> + down>)/sqrt(2)
> = (right>  left>)/sqrt(2) = (down>  up>)i/sqrt(2)
(In fancy jargon we say that the spin operator in different directions form noncommuting observables. I shall
eschew such
obfuscations.)
Working
through the algebra we
find that for pairs of
electrons:
+,>
 ,+> = left,right>
 right,left>
= up,down>i  down,up>i
me> represents me on Earth with
my detection apparatus. I shall assume that
we are capable of either measuring spin in the x or y direction, which are both
perpendicular the line of flight of the electrons. After having measured the state of the electron my
state is described as one of either:
me[l]>
represents me + apparatus + records having measured xaxis
spin and recorded the x axis
spin as "left"
me[r]>
ditto with the xaxis
spin as "right"
me[u]>
ditto with the yaxis
spin as "up"
me[d]>
ditto with the yaxis
spin as "down"
Similarly for you>
on Alpha Centauri. Notice that it is irrelevant *how* we have measured the electron's spin. The details of the measurement process are irrelevant. To model
the process it is sufficient
to assume that there is a way, which we have
further assumed does not disturb the
electron. (The latter assumption may be
relaxed without
altering the results.)
To establish familiarity with the notation let's take the state of the initial wavefunction as:
psi>_1
= me,left,up,you>
/ \
/ \
first
electron in left second electron
in up state
state
heading towards heading
towards you on
me on Earth Alpha
Centauri
After the electrons arrive at their detectors, I measure the spin along the xaxis and you along the yaxis. The wavefunction
evolves into psi>_2:
local
psi>_1
============> psi>_2 = me[l],left,up,you[u]>
observation
which represents me having recorded my electron on Earth with spin left
and you having recorded your electron on Alpha Centauri with spin up. The index in []s indicates the value of the
record. This may be held in the
observer's memory,
notebooks or elsewhere in the local environment (not necessarily in a readable
form). If we communicate our readings to
each other the wavefunctions evolves into
psi>_3:
remote
psi>_2
============> psi>_3 = me[l,u],left,up,you[u,l]>
communication
where the second index in []s represents the remote reading entering
the observers' local records. Notice that the results both agree with each other.
Eg my record of your reading agrees
with your reading.
That's
the notation established. Now let's see
what happens in the more general case where, again,:
electrons>
= (+,>  ,+>)/sqrt(2).
First we'll consider
the case where you and I have previously
arranged to measure the our respective electron
spins along the same xaxis.
Initially the wavefunction
of the system of electrons and two experimenters
is:
psi>_1
=
me,electrons,you>
=
me>(left,right>
 right,left>)you>
/sqrt(2)
= me,left,right,you>
/sqrt(2)  me,right,left,you>
/sqrt(2)
After the we each perform
our measurements we
get:
psi>_2
=
me[l],left,right,you[r]>
/sqrt(2)  me[r],right,left,you[l]>
/sqrt(2)
The observers (you and me) have been split (on Earth and Alpha Centauri) into relative
states (or local worlds) which correlate with
the state of the electron. If we now
communicate over interstellar modem (this will take a few years since you and I are separated
by light years, but no matter) then, for example, the world corresponding to
the 2nd term in the above
expansion contains me having
seen my electron with
spin right also contains
you having seen your electron with
spin left. So
we jointly agree, in both worlds, that spin has been conserved.
Now suppose
that we had prearranged to measure the spins along different axes.
Suppose I measure the xdirection spin and you
the ydirection spin. Now things get a bit more complex. To analyse what happens we need to decompose the two electrons along their respective spin axes.
psi>_1
= me,electrons,you>
=
me>(+,>  ,+>)you>/sqrt(2)
=
me> (
(right>+left>)i(down>up>)

(right>left>)(down>+up>)
)
you> /2*sqrt(2)
=
me> (
right>(down>up>)i
+
left>
(down>up>)i

right>(down>+up>)
+
left>
(down>+up>)
)
you> /2*sqrt(2)
=
me> (
right,down> (i1)  right,up> (1+i)
+
left,up> (1i) + left,down> (1+I)
)
you> /2*sqrt(2)
= (
+
me,right,down,you> (i1)

me,right,up,you> (i+1)
+
me,left,up,you> (1i)
+
me,left,down,you> (1+I)
)
/2*sqrt(2)
So
after you and I make our local observations we get:
psi>_2
=
(
+
me[r],right,down,you[d]> (i1)

me[r],right,up,you[u]> (I+1)
+
me[l],left,up,you[u]> (1I)
+
me[l],left,down,you[d]> (1+I)
)
/2*sqrt(2)
Each term realises
a possible outcome of
the joint measurements. The interesting thing is that whilst we can decompose it into four terms there are only two states for each
observer. Looking at myself, for instance, we can rewrite this in
terms of states relative to *my* records/memories.
psi>_2
=
(
me[r],right> ( down,you[d]> (i1) 
up,you[u]> (i+1) )
+
me[l],left> ( up,you[u]> (1i) + down,you[d]>
(1+i) )
)
/2*sqrt(2)
And we see that
there are only two
copies of *me*. Equally we can rewrite
the expression in terms
of states relative to *your* records/memory.
psi>_2
=
(
( me[l],left> (1i)  me[r],right> (i+1) )
up,you[u]>
+
( me[r],right> (i1) + me[l],left>
(1+i) ) down,you[d]>
)
/2*sqrt(2)
And see that
there are only two
copies of *you*. We have each been
split into two copies, each perceiving a different
outcome for our electron's spin, but we have not been split by the measurement of the remote
electron.
*After* you and I communicate our readings to each other,
> four years later, we get:
psi>_3
=
(
+
me[r,d],right,down,you[d,r]> (i1)

me[r,u],right,up,you[u,r]> (i+1)
+
me[l,u],left,up,you[u,l]> (1I)
+
me[l,d],left,down,you[d,l]> (1+i)
)
/2*sqrt(2)
The decomposition into four worlds is only forced
and unique after
communication between the
remote systems. Until the two observers
communicated their results to each other they
were each unsplit by each others' remote measurements, although their own local measurements had split themselves. The splitting is a local process that is causally transmitted from
system to system at light or sublight speeds.
(This is a point that
Everett stressed about Einstein's remark about the observations of a mouse, in
the Copenhagen interpretation, collapsing the wavefunction of the universe. Everett observed that it is the mouse that's split by its observation of
the rest of the universe. The rest of
the universe is unaffected and unsplit.)
When all communication is complete the worlds have finally
decomposed or decohered
from each other. Each world contains
a consistent set of observers, records and electrons, in perfect agreement with
the predictions of standard
QM. Further observations of the
electrons will agree with the earlier ones and so each observer, in each world, can
henceforth regard the
electron's wavefunction
as having collapsed to match the historically recorded, locally observed
values. This justifies our operational adoption of the collapse of the wavefunction upon measurement, without having to strain our
credibility by believing
that it actually
happens.
To recap. Manyworlds
is local and deterministic. Local measurements split local systems (including observers) in a
subjectively random fashion; distant systems are only split when the causally
transmitted effects of the local
interactions reach them. We have not assumed
any nonlocal FTL effects, yet we have
reproduced the standard
predictions of QM.
So
where did Bell and Eberhard
go wrong? They
thought that all theories that reproduced the standard predictions must be
nonlocal. It has been pointed out by
both Albert [A] and Cramer [C] (who both support
different
interpretations of QM) that
Bell and Eberhard had
implicity assumed that every possible
measurement  even if
not performed  would have yielded
a *single* definite result. This
assumption is called contrafactual definiteness or CFD [S]. What Bell and Eberhard really proved was that every quantum theory must
either violate locality *or* CFD.
Manyworlds with
its multiplicity of results in different
worlds violates CFD, of course, and thus can be local.
Thus manyworlds is the only local quantum theory in accord with the standard predictions of QM and, so far, with experiment.
[A] David Z Albert, “Bohm's
Alternative to Quantum
Mechanics” Scientific American (May
1994) [As] Alain Aspect, J Dalibard, G Roger, “Experimental test of Bell's inequalities using timevarying analyzers”,
Physical Review Letters Vol 49 #25
1804 (1982). [C] John G Cramer, “The
transactional interpretation of quantum mechanics”, Reviews of Modern Physics
Vol 58 #3 647687 (1986)
[B] John S Bell: “On the Einstein Podolsky Rosen paradox”, Physics 1 #3 195200 (1964).
[E] Albert Einstein,
Boris Podolsky, Nathan
Rosen: “Can quantummechanical
description of physical reality
be considered complete?” Physical
Review Vol 41, 777780 (15 May 1935).
[S] Henry P Stapp, “Smatrix
interpretation of quantumtheory”, Physical
Review D Vol 3 #6 1303 (1971)
Q31 References and further reading
[1] Hugh Everett III,
The Theory of the Universal Wavefunction, Princeton thesis
(1956?) The original and
most comprehensive paper
on manyworlds. 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 454462, (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
463465 (July 1957) Wheeler was
Everett's PhD supervisor.
[4a] Bryce S DeWitt,
“Quantum Mechanics and Reality”, Physics
Today, Vol 23 #9 3040 (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 ManyUniverses 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 manyworlds Interpretation of Quantum
Mechanics, Contains
[1],[2],[3],[4a],[4b] plus
other material. Princeton Series in Physics, Princeton
University Press (1973) ISBN 0691 081263 (hard cover), 069188131X (paper back) The definitive guide to manyworlds, if you can get hold of a copy, but now (1994) only available xeroxed from microfilm
(ISBN 0783719426) from Books On Demand,
300 N Zeeb Road, Ann Arbor, MI 481061346, USA.
Tel: +01313 761 4700 or 800 521 0600.
[6] John A Wheeler,
Wojciech H Zurek eds Quantum Theory and
Measurement
Princeton Series in Physics, Princeton University Press (1983) ISBN
0691083169. Contains
49 classic articles, including [2], covering the history
and development of interpretations of quantum theory.
[7] Wojciech H Zurek “Decoherence
and the Transition from the Quantum to the Classical”, Physics Today, 3644 (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.
[8] Max Jammer The Philosophy of Quantum Mechanics Wiley, New York
(1974) Almost every interpretation of quantum mechanics is
covered and contrasted. Section 11.6 contains
a lucid review of manyworlds theories.
[9] Marian O Scully,
BetholdGeorg Englert, Herbert Walther “Quantum optical tests of
complementarity” Nature, Vol 351,
111116 (9 May 1991). Demonstrates that
quantum interference effects are destroyed
by irreversible objectapparatus correlations, not by the measurement process itself.
[10] Murray GellMann, James B Hartle “Quantum Mechanics in the Light of Quantum
Cosmology” Proceedings of the 3rd
International Symposium on the Foundations of Quantum Mechanics (1989)
321343. They accept the Everett's decoherence analysis, and
have extended it further, but reject manyworlds' metaphysical
stance. Tests of the Everett metatheory:
[11] David Deutsch “Quantum theory as a universal physical
theory” International Journal of
Theoretical Physics, Vol 24 #1 (1985).
Describes an experiment which tests for the existence of superpositions
of *consciousness (in an AI). [16] David Deutsch “Three connections between Everett's interpretation and
experiment” Quantum Concepts of Space and
Time, eds Roger Penrose and Chris Isham, Oxford University Press
(1986). Discusses
a testable split observer experiment and quantum computing. On quantum
computers:
[12] David Deutsch “Quantum theory, the ChurchTuring principle and the universal quantum
computer” Proceedings of the Royal Society of London, Vol. A400,
96117 (1985).
[13] David Deutsch “Quantum computational networks”
Proceedings of the Royal Society of London, Vol. A425,
7390 (1989).
[14] David Deutsch and R. Jozsa “Rapid solution of problems by quantum
computation” Proceedings of the Royal Society of London, Vol. A439,
553558 (1992).
[15] Frank
J Tipler “The manyworlds interpretation of quantum mechanics in quantum
cosmology” in Quantum Concepts of Space
and Time eds Roger Penrose and Chris Isham, Oxford University Press
(1986). Has a discussion of Ockham's razor. On
quantum theory, measurement
and decoherence generally:
Mike Price
price@price.demon.co.uk