# Everett's Relative-State Formulation of Quantum Mechanics

*First published Wed Jun 3, 1998; substantive revision Thu Feb 20, 2003*

Everett's relative-state formulation of quantum mechanics is an attempt to solve the measurement problem by dropping the collapse dynamics from the standard von Neumann-Dirac theory of quantum mechanics. The main problem with Everett's theory is that it is not at all clear how it is supposed to work. In particular, while it is clear that he wanted to explain why we get determinate measurement results in the context of his theory, it is unclear how he intended to do this. There have been many attempts to reconstruct Everett's no-collapse theory in order to account for the apparent determinateness of measurement outcomes. These attempts have led to such formulations of quantum mechanics as the many-worlds, many-minds, many-histories, and relative-fact theories. Each of these captures part of what Everett claimed for his theory, but each also encounters problems.

- 1. Introduction
- 2. The Measurement Problem
- 3. Everett's Proposal
- 4. The Bare Theory
- 5. Many Worlds
- 6. Many Minds
- 7. Many Histories
- 8. Relative Facts, Correlations without Correlata, and Relational Quantum Mechanics
- 9. Summary
- Bibliography
- Other Internet Resources
- Related Entries

## 1. Introduction

Everett formulated his relative-state interpretation of quantum mechanics while he was a graduate student in physics at Princeton University. His doctoral dissertation (1957a) was recommended for publication in March 1957 and a paper reporting the results of his dissertation (1957b) was published in July of the same year. He also later published an extended discussion of his relative-state interpretation in the DeWitt and Graham anthology (1973). After graduating from Princeton, Everett worked as a defense analyst. He died in 1982.

Everett's no-collapse formulation of quantum mechanics was a reaction to problems that arise in the standard von Neumann-Dirac collapse formulation. Everett's proposal was to drop the collapse postulate from the standard formulation of quantum mechanics then deduce the empirical predictions of the standard theory as the subjective experiences of observers who are themselves treated as physical systems described by his theory. It is, however, unclear precisely how Everett intended for this to work. Consequently, there have been many, mutually incompatible, attempts at trying to explain what he in fact had in mind. Indeed, it is probably fair to say that most no-collapse interpretations of quantum mechanics have at one time or another been attributed to Everett.

In what follows, I will describe Everett's worry about the standard collapse formulation of quantum mechanics and his proposal for solving the problem as it is presented in his 1957 paper. I will then very briefly describe a few approaches to interpreting Everett's theory.

## 2. The Measurement Problem

Everett presented his relative-state formulation of quantum mechanics
as a way of avoiding the problems encountered by the standard von
Neumann-Dirac collapse formulation. The main problem, according to
Everett, was that the standard collapse formulation of quantum
mechanics required observers always to be treated as *external*
to the system described by the theory. One consequence of this was
that the standard collapse formulation could not be used to describe
the universe as a whole since the universe contains observers.

In order to understand what Everett was worried about, one must first understand how the standard formulation of quantum mechanics works. The standard von Neumann-Dirac theory is based on the following principles (von Neumann, 1955):

**Representation of States**: The possible physical states of a system*S*are represented by the unit-length vectors in a Hilbert space (which for present purposes one may regard as a vector space with an inner product). The physical state at a time is then represented by a single vector in the Hilbert space.**Representation of Properties**: For each physical property*P*that one might observe of a system*S*there is a linear (so-called projection) operator(on the vectors that represent the possible states of*P**S*) that represents the property.**Eigenvalue-Eigenstate Link**: A system*S*determinately has physical property*P*if and only ifoperating on**P**(the vector representing*S**S*'s state) yields. We say then that**S***S*is in an eigenstate ofwith eigenvalue 1.**P***S*determinately does not have property*P*if and only ifoperating on**P**yields 0.**S****Dynamics**:**(a)**If no measurement is made, then a system*S*evolves continuously according to the linear, deterministic dynamics, which depends only on the energy properties of the system.**(b)**If a measurement is made, then the system*S*instantaneously and randomly jumps to a state where it either determinately has or determinately does not have the property being measured. The probability of each possible post-measurement state is determined by the system's initial state. More specifically, the probability of ending up in a particular final state is equal to the norm squared of the projection of the initial state on the final state.

According to the eigenvalue-eigenstate link (Rule 3) a system would typically neither determinately have nor determinately not have a particular given property. In order to determinately have a particular property the vector representing the state of a system must be in the ray (or subspace) in state space representing the property, and in order to determinately not have the property the state of a system must be in the plane (or subspace) orthogonal to it, and most state vectors will be neither parallel nor orthogonal to a given ray (or subspace). Further, the deterministic dynamics (Rule 4a) typically does nothing to guarantee that a system will either determinately have or determinately not have a particular property when one observes the system to see whether the system has that property. This is why the collapse dynamics (Rule 4b) is needed in the standard formulation of quantum mechanics. It is the collapse dynamics that guarantees that a system will either determinately have or determinately not have a particular property whenever one observes the system to see whether or not it has the property. But the linear dynamics (Rule 4a) is also needed to account for quantum mechanical interference effects. So the standard formulation of quantum mechanics has two dynamical laws: the deterministic, continuous, linear Rule 4a describes how a system evolves when it is not being measured, and the random, discontinuous, nonlinear Rule 4b describes how a system evolves when it is measured.

But what does it take for an interaction to count as a measurement? Unless we know this, the standard formulation of quantum mechanics is at best incomplete since we do not know when each dynamical law obtains. Moreover, and this is what worried Everett, if we suppose that observers and their measuring devices are constructed from simpler systems that each obey the deterministic dynamics, then the composite systems, the observers and their measuring devices, must evolve in a continuous deterministic way, and nothing like the random, discontinuous evolution described by Rule 4b can ever occur. That is, if observers and their measuring devices are understood as being constructed of simpler systems each behaving as quantum mechanics requires, each obeying Rule 4a, then the standard formulation of quantum mechanics is logically inconsistent since it says that the two systems together must obey Rule 4b. This is the quantum measurement problem in the context of the standard collapse formulation of quantum mechanics. See the entry on measurement in quantum theory.

In order to preserve the consistency of quantum mechanics, Everett
concluded that the standard collapse formulation could not be used to
describe systems that contain observers; that is, it could only be
used to describe a system where all observers are *external* to
the described system. And, for Everett, this restriction on the
applicability of quantum mechanics was unacceptable. Everett wanted a
formulation of quantum mechanics that could be applied to any physical
system whatsoever, one that described observers and their measuring
devices the same way that it described every other physical
system.

## 3. Everett's Proposal

In order to solve the measurement problem Everett proposed dropping the collapse dynamics (Rule 4b) from the standard collapse theory and proposed taking the resulting physical theory as providing a complete and accurate description of all physical systems whatsoever. Everett then intended to deduce the standard statistical predictions of quantum mechanics (the predictions that depend on Rule 4b in the standard collapse formulation of quantum mechanics) as the subjective experiences of observers who are themselves treated as ordinary physical systems within the new theory.

Everett says:

We shall be able to introduce into [the relative-state theory] systems which represent observers. Such systems can be conceived as automatically functioning machines (servomechanisms) possessing recording devices (memory) and which are capable of responding to their environment. The behavior of these observers shall always be treated within the framework of wave mechanics. Furthermore, we shall deduce the probabilistic assertions of Process 1 [rule 4b] assubjectiveappearances to such observers, thus placing the theory in correspondence with experience. We are then led to the novel situation in which the formal theory is objectively continuous and causal, while subjectively discontinuous and probabilistic. While this point of view thus shall ultimately justify our use of the statistical assertions of the orthodox view, it enables us to do so in a logically consistent manner, allowing for the existence of other observers (1973, p. 9).

Everett's goal then was to show that the memory records of an observer as described by quantum mechanics without the collapse dynamics would somehow agree with those predicted by the standard formulation with the collapse dynamics. The main problem in understanding what Everett had in mind is in figuring out how this correspondence between the predictions of the two theories was supposed to work.

In order to see what happens, let us try Everett's
no-collapse proposal for a simple measurement interaction. One can
measure the *x-*spin of a physical system. More
specifically, a spin-1/2 system will be found to be either
"*x*-spin up" or "*x*-spin down" when
its *x-*spin is measured. So suppose that *J* is a good
observer who measures the *x*-spin of a spin-1/2 system
*S**.* For Everett, being a good *x*-spin
observer means that *J* has the following two dispositions (the
arrows below represent the time-evolution described by the
deterministic dynamics of Rule 4a):

If *J* measures a system that is determinately *x*-spin
up, then *J* will determinately record "*x-*spin
up"; and if *J* measures a system that is determinately
*x*-spin down, then *J* will determinately record
"*x-*spin down" (and we assume, for simplicity, that
the spin of the object system *S* is undisturbed by the
interaction).

Now consider what happens when *J* observes the
*x*-spin of a system that begins in a *superposition* of
*x*-spin eigenstates:

The initial state of the composite system then is:

Here *J* is determinately ready to make an *x-*spin
measurement, but the object system* S*, according to Rule 3, has
no determinate *x-*spin. Given *J*'s two dispositions and
the fact that the deterministic dynamics is linear, the state of the
composite system after *J*'s *x*-spin measurement will
be:

On the standard collapse formulation of quantum mechanics, somehow
during the measurement interaction the state would collapse to either
the first term of this expression (with probability equal to *a*
squared) or to the second term of this expression (with probability
equal to *b* squared). In the former case, *J* ends up
with the determinate measurement record "spin up", and in
the later case *J* ends up with the determinate measurement
record "spin down". But on Everett's proposal no
collapse occurs. Rather, the post-measurement state is simply
this entangled superposition of *J* recording the result
"spin up" and *S* being *x-*spin up *and*
*J* recording "spin down" and *S* being
*x-*spin down. Call this state ** E** for
Everett. On the standard eigenvalue-eigenstate link (Rule 3)

*is not a state where*

**E***J*determinately records "spin up", neither is it a state where

*J*determinately records "spin down". So the puzzle for an interpretation of Everett is to explain the sense in which

*J*'s entangled superposition of mutually incompatible records is supposed to agree with the empirical prediction made by the standard collapse formulation of quantum mechanics. The standard collapse theory, again, predicts that

*J*either ends up with the fully determinate measurement record "spin up" or the fully determinate record "spin down", with probabilities equal to

*a-*squared and

*b-*squared respectively.

Everett confesses that a post-measurement state like ** E** is
puzzling:

As a result of the interaction the state of the measuring apparatus is no longer capable of independent definition. It can be defined onlyrelativeto the state of the object system. In other words, there exists only a correlation between the states of the two systems. It seems as if nothing can ever be settled by such a measurement (1957b, p. 318).

And he describes the problem he consequently faces:

This indefinite behavior seems to be quite at variance with our observations, since physical objects always appear to us to have definite positions. Can we reconcile this feature of wave mechanical theory built purely on [Rule 4a] with experience, or must the theory be abandoned as untenable? In order to answer this question we consider the problem of observation itself within the framework of the theory (1957b, p. 318).

Then he describes his solution to this determinate-record (determinate-experience) problem:

Let one regard an observer as a subsystem of the composite system: observer + object-system. It is then an inescapable consequence that after the interaction has taken place there will not, generally, exist a single observer state. There will, however, be a superposition of the composite system states, each element of which contains a definite observer state and a definite relative object-system state. Furthermore, as we shall see,eachof these relative object system states will be, approximately, the eigenstates of the observation corresponding to the value obtained by the observer which is described by the same element of the superposition. Thus, each element of the resulting superposition describes an observer who perceived a definite and generally different result, and to whom it appears that the object-system state has been transformed into the corresponding eigenstate. In this sense the usual assertions of [the collapse dynamics (Rule 4b)] appear to hold on a subjective level to each observer described by an element of the superposition. We shall also see that correlation plays an important role in preserving consistency when several observers are present and allowed to interact with one another (to ‘consult’ one another) as well as with other object-systems (1973, p. 10).

To this end Everett presents a principle that he calls the
fundamental relativity of quantum mechanical states. On this
principle, one can say that in state ** E**,

*J*recorded "

*x*-spin up"

*relative to*

*S*being in the

*x*-spin up state and that

*J*recorded "

*x*-spin down"

*relative to*

*S*being in the

*x*-spin down state. But this principle cannot by itself provide Everett with the determinate measurement records (or the determinate measurement experiences) predicted by the standard collapse formulation of quantum mechanics. The standard formulation predicts that on measurement the quantum-mechanical state of the composite system will collapse to precisely one of the following two states:

and that there is thus a single, simple matter of fact about which
measurement result *J* recorded. On Everett's account it is
unclear whether *J* ends up recording one result or the other
or perhaps somehow both.

The problem is that there is a gap in Everett's exposition between
what he sets out to explain and what he ultimately ends up
saying. He set out to explain why observers get precisely the
same measurement records (experiences) as predicted by the standard
collapse formulation of quantum mechanics in quantum mechanics without
the collapse dynamics, but he ends up with an account where it is unclear
what if any determinate records an observer has after a typical
measurement interaction. Since it is unclear exactly how Everett
intends to explain an observer's determinate measurement records
(experiences), it is also unclear how he intends to explain why one
should expect one's determinate measurement records to exhibit the
standard quantum statistics. This gap in Everett's exposition has led
to many mutually incompatible reconstructions of his account of
quantum mechanics. Each of these reconstructions can be taken as
presenting a different way of explaining how one's records can be
determinate (or* appear* to be determinate to an observer, or
why it should not matter whether or not they are determinate) in a
post-measurement state like * E*.

## 4. The Bare Theory

Albert and Loewer's bare theory (Albert and Loewer, 1988, and Albert, 1992) is arguably the wildest interpretation of Everett's theory around. On this reading, one supposes that Everett intended to drop the collapse dynamics but to keep the standard eigenvalue-eigenstate link.

So how does the bare theory account for *J*'s determinate
experience? The short answer is that it doesn't. Rather, on the bare
theory, one tries to explain why *J* would *falsely*
believe that he has an ordinary determinate measurement record. The
trick is to ask the observer not what result he got, but rather
whether he got *some* specific determinate result. If the
post-measurement state was:

then *J* would report "I got a determinate result, either spin
up or spin down". And he would make precisely the same report if he
ended up in the post-measurement state:

So, by the linearity of the dynamics, *J* would
*falsely* report "I got a determinate result, either spin up or
spin down" when in the state * E*:

Thus, one might argue, it would *seem* to *J* that he
got a perfectly determinate ordinary measurement result even when he
did not (that is, he did not determinately get "spin up" and did not
determinately get "spin down").

The idea is to try to account for all of *J*'s beliefs about
his determinate experiences by appealing to such
*illusions*. Rather than predicting the experiences that we
believe that we have, a proponent of the bare theory tells us that we
do not have many determinate beliefs at all and then tries to explain
why we nonetheless determinately believe that we do.

While one can tell several suggestive stories about the sort of illusions that an observer would experience, there are at least two serious problems with the bare theory. One problem is that the bare theory is not empirically coherent: If the bare theory were true, it would be impossible to ever have empirical evidence for accepting it as true. Another is that if the bare theory were true, one would most likely fail to have any determinate beliefs at all (since on the deterministic dynamics one would almost never expect that the global state was an eigenstate of any particular observer being sentient), which is presumably not the sort of prediction one looks for in a successful physical theory (for more details on how experience is supposed to work in the bare theory and some the problems it encounters see Bub, Clifton, and Monton, 1998, and Barrett, 1994, 1996 and 1999).

## 5. Many Worlds

DeWitt's (1971) many-worlds interpretation (also called the splitting-worlds
theory) is easily the most popular reading of Everett. On this theory
there is one world corresponding to each term in the expansion of
* E* when written in the preferred basis (there are
always many ways one might write the quantum-mechanical state of a
system as the sum of vectors in the Hilbert space; in choosing a
preferred basis, one chooses a single set of vectors that can be used
to represent a state and thus one chooses a single

*preferred*way of representing a state as the sum of vectors in the Hilbert space). The theory's preferred basis is chosen so that each term in the expansion of

**describes a world where there is a determinate measurement record. Given the preferred basis (surreptitiously) chosen above,**

*E***describes two worlds: one where**

*E**J*(or perhaps better

*J1*) determinately records the measurement result "spin up" and another where

*J*(or

*J2*) determinately records "spin down".

DeWitt and Graham describe their reading of Everett as follows:

[Everett's interpretation of quantum mechanics] denies the existence of a separate classical realm and asserts that it makes sense to talk about a state vector for the whole universe. This state vector never collapses and hence reality as a whole is rigorously deterministic. This reality, which is describedjointlyby the dynamical variables and the state vector, is not the reality we customarily think of, but is a reality composed of many worlds. By virtue of the temporal development of the dynamical variables the state vector decomposes naturally into orthogonal vectors, reflecting a continual splitting of the universe into a multitude of mutually unobservable but equally real worlds, in each of which every good measurement has yielded a definite result and in most of which the familiar statistical quantum laws hold (1973, p. v).

DeWitt admits that this constant splitting of worlds whenever the states of systems become correlated is counterintuitive:

I still recall vividly the shock I experienced on first encountering this multiworld concept. The idea of 10^{100}slightly imperfect copies of oneself all constantly spitting into further copies, which ultimately become unrecognizable, is not easy to reconcile with common sense. Here is schizophrenia with a vengeance (1973, p. 161).

But while the theory is counterintuitive, it does (unlike the bare
theory) explain why observers end up recording determinate measurement
results. In the state described by * E* there are two
observers, each occupying a different world and each with a perfectly
determinate measurement record. There are, however, other problems
with the many-worlds theory.

A standard complaint is that the theory is ontologically
extravagant. One would presumably only ever need one physical world,
*our* world, to account for *our* experiences. The idea
behind postulating the actual existence of a different physical world
corresponding to each term in the quantum-mechanical state is that is
allows one to explain our determinate experiences while taking the
deterministically-evolving quantum-mechanical state to be in some
sense a complete and accurate description of the physical facts. But
again one might wonder whether the sort of completeness one gets
warrants the vast ontology of worlds.

Perhaps more seriously, in order to explain our determinate measurement records, the theory requires one to choose a preferred basis so that observers have determinate records (or determinate experiences) in each term of the quantum-mechanical state as expressed in this basis. The problem is that not just any basis will do this. Making the total angular momentum of all the sheep in Austria determinate by choosing such a preferred basis to tell us when worlds split, would presumably do little to account for the determinate memory I have concerning what I just typed. But this is the problem, we do not really know what basis would make our most immediately accessible physical records, those records that determine our experiences and beliefs, determinate in every world. The problem of choosing which observable to make determinate is known as the preferred-basis problem.

One might hope that the selection of a preferred basis would work the
other way around: that the biological evolution of observers would
select for observers who record their measurement results in whatever
physical observable is in fact determinate. The idea is that
observers would either start recording their measurement results in
whatever physical observable is in fact determinate or face some sort
of failure in action for not having determinate measurement
records. The full explanation for why this does not work in a
straightforward way is subtle, but the basic idea is simple: in a
no-collapse theory, there is no decreased fitness for a good observer
who fails to have determinate measurement records. Suppose that only
the position of particles is in fact determinate, as in Bohm's
theory, but that an observer nonetheless tries to record his
measurements in terms of the *x*-spin of particles in his
brain. Such an observer would typically not have any determinate
measurement records, but it would be difficult for anyone to
tell. The observer would himself not know because, for bare
theory reasons, he would falsely believe that he had determinate
measurement records. But neither would other observers typically know
that he failed to have determinate records, for as soon as the
observer's brain state becomes quantum-mechanically correlated
with the position of anything, the observer would have an
*effectively determinate* measurement record by dint of this
correlation in the physically preferred quantity. The evolutionary
upshot of this is that, as soon as there is the possibility of a
determinate failure in action, a good observer would have precisely
those determinate dispositions that would lead to successful action
*regardless of whether he started with a determinate measurement
record*. While such an observer eventually has something that
serves the dispositional role of a measurement record, his belief that
he had a determinate measurement record before he correlated his brain
state with the state of the determinate preferred observable was
simply false. (See Albert's 1992 discussion of measurement records
in GRW for more details on the formation of effectively determinate
records from an observer's dispositions to act.)

Given the constraints on property ascription posed by the Kochen-Specker theorem, one might argue that we do need to select a preferred basis in order to have any significant set of physical properties determinate. (See the article The Kochen-Specker Theorem.) Among the facts that one would want to have determinate are the values of our measurement records. But saying exactly what a preferred basis must do in order to make our most immediately accessible measurement records determinate is difficult since this is something that ultimately depends on the relationship between mental and physical states and on exactly how we expect our best physical theories to account for our experience. The preferred basis problem involves quantum mechanics, ontological questions concerning the philosophy of mind, and epistemological questions concerning the nature of our best physical theories. It is, consequently, a problem that requires special care.

Another problem with a splitting-worlds theory concerns the
statistical predictions of the theory. The standard collapse theory
predicts that *J* will get the result "spin up" with
probability *a-*squared and "spin down" with probability
*b-*squared in the above experiment. Insofar as there will be
two copies of *J* in the future, *J* is guaranteed to
get each of the two possible measurement results; so, in this sense,
the probability of *J* getting the result "spin up", say, is
one. But that is the wrong answer. A principle of indifference might
lead one to assign probability ½ to each of the two possible
measurement outcomes. But such a principle would be difficult to
justify, and probability ½ is the wrong answer anyway. The
moral is that it is impossible to get the right answer for
probabilities without adding something to the theory.

In order to get a better idea concerning what one would have to add
to get the right probabilities here, one might note that the question
"What is the probability that *J* will record the result
‘spin up’?" is strictly speaking nonsense if one cannot
identify which of the future observers is *J*. That is, if one
does not have transtemporal identities for the observers in a theory,
then one cannot assign probabilities to their future experiences. So
in order to get probabilities out of the many-worlds theory, the first
step is to provide an account of the transtemporal identity of
observers. Since there is no rule telling us which worlds are which at
different times, the splitting-worlds theory cannot, as it stands,
make any statistical predictions whatsoever concerning an observer's
future experiences. And not being able to account for the standard
quantum probabilities is a serious problem since it was the successful
statistical predictions of quantum mechanics that made quantum
mechanics worth taking seriously in the first place. See the entry on
the
many-worlds interpretation of quantum mechanics
for more details concerning splitting-worlds and the many-worlds
theory. For more on the metaphysics of many worlds see Geroch (1984),
Stein (1994), Healey (1984), Bell (1987), Butterfield (1995), Albert
and Barrett (1995), Clifton (1996), Saunders (1997, 1998), Barrett
(1999) and Wallace (2002).

## 6. Many Minds

Everett said that on his formulation of quantum mechanics "the formal theory is objectively continuous and causal, while subjectively discontinuous and probabilistic" (1973, p. 9). Albert and Loewer (1988) have captured this feature in their many-minds theory by distinguishing between the time evolution of an observer's physical state, which is continuous and causal, and the evolution of an observer's mental state, which is discontinuous and probabilistic.

Perhaps the oddest thing about this theory is that in order to get
the observer's mental state in some way to supervene on his physical
state, Albert and Loewer associate with each observer a continuous
infinity of minds. The physical state always evolves in the usual
deterministic way, but each mind evolves randomly (with probabilities
determined by the particular mind's current mental state and the
evolution of the global quantum-mechanical state). On the mental
dynamics that they describe, one should expect *a-*squared of
*J*'s minds to end up associated with the result "spin up" (the
first term of ** E**) and

*b-*squared of

*J*'s minds to end up associated with the result "spin down" (the second term of

**). The mental dynamics is also stipulated to be memory-preserving.**

*E*
An advantage of this theory over the many-worlds theory is that there
is no *physically* preferred basis. To be sure, one must choose
a preferred basis in order to specify the mental dynamics completely
(something that Albert and Loewer never completely specify), but as
Albert and Loewer point out, this choice has absolutely nothing to do
with any physical facts; rather, it can be thought of as part of the
description of the relationship between physical and mental
states. Another advantage of the many-minds theory is that, unlike the
many-worlds theory, it really does make the usual probabilistic
predictions for the future experiences of a particular mind (this, of
course, requires that one take the minds to have transtemporal
identities, which Albert and Loewer do as part of their unabashed
commitment to a strong mind-body dualism). And finally, it is one of
the few formulations of quantum mechanics that is manifestly
compatible with special relativity. (For a discussion of why it is
difficult to solve the quantum measurement problem under the
constraints of relativity see Barrett 2000 and 2002, for discussions
of locality in the many minds theory, see Hemmo and Pitowski, 2001,
and Bacciagaluppi, 2002, and for the relationship between relativity
and the many worlds theory see Bacciagaluppi 2002.)

The main problems with the many-minds theory concern its commitment
to a strong mind-body dualism and the question of whether the sort of
mental supervenience one gets is worth the trouble of postulating a
continuous infinity of minds associated with each observer. Concerning
the latter, one might well conclude that a *single*-mind
theory, where each observer has one mind that evolves randomly given
the evolution of the standard quantum mechanical state, would be
preferable. (See Albert, 1992, Donald, 1997 (in Other Internet
Resources section), and Barrett, 1995 and 1999, for more details and
criticism; for a broader discussion see Lockwood, 1989 and 1996.)

Both the single-mind and many-minds theories can be thought of as hidden-variable theories like Bohmian mechanics. (See the entry on Bohmian mechanics.) But instead of position being made determinate, as it is in Bohm's theory, and then hoping that the determinate positions of particles will provide observers with determinate measurement records, it is the mental states of the observers that are directly made determinate here, and while this is a non-physical parameter, it is guaranteed to provide observers with determinate measurement records.

## 7. Many Histories

Gell-Mann and Hartle (1990) understand Everett's theory as one that describes many, mutually decohering histories. The main difference between this approach and the many-worlds interpretation is that, instead of stipulating a preferred basis, here one relies on the physical interactions between a physical system and its environment (the way in which the quantum-mechanical states become correlated) to effectively choose what physical quantity is determinate at each time for each system.

One problem concerns whether and in what sense environmental
interactions can select *a physically preferred basis for the
entire universe*, which is what we presumably need in order to
make sense of Everett's formulation. After all, in order to be
involved in environmental interactions a system must have an
environment, and the universe, by definition, has no environment. And
if one considers subsystems of the universe, the environment of each
subsystem would presumably select a different preferred physical
observable (at least slightly different for each decohering
system). Another problem is that it is unclear that the
environment-selected determinate quantity at a time is a quantity that
would explain *our* determinate measurement records and
experience. Proponents who argue for this approach often appeal to
biological or evolutionary arguments to justify the assumption that
sentient beings must record their beliefs in terms of the
environment-selected (or decohering) physical properties. (See
Gell-Mann and Hartle, 1990, and Zurek, 1991, for this sort of
argument.) The short story is that it is not yet clear how the account
of our determinate experience is suppose to work when one relies on
decoherence to select a preferred basis. (See Dowker and Kent, 1996, for
an extended discussion of some of the problems one encounters in such
an approach.)

It is worth noting that if one allows oneself the luxury of
stipulating a preferred basis (more specifically a basis where every
observer's measurement records are in fact determinate, whatever that
is), one can construct a many-histories theory from Albert and
Loewer's many-minds theory even without the requirement that the
histories mutually decohere. Take the trajectory of each of a specific
observer's minds to describe the history of a possible physical
world. One might then stipulate a measure over the set of all possible
histories (trajectories) that would represent the *prior*
probability of each history actually describing our world. These prior
probabilities might then be Bayesian updated as one learns more about
the actual history of our world. This is a version of something called
the many-threads theory in Barrett (1999). Since such worlds (and
everything in them) would have transtemporal identities, unlike the
many-worlds theory, there would be no special problem here in talking
about probabilities concerning one's future experience — the
quantum probabilities in such a theory might naturally be interpreted
as *epistemic* probabilities.

It is instructive to consider the relationship between a no-collapse
hidden-variable theory like Bohmian mechanics and a many-worlds theory
like the many-threads theory. In Bohmian mechanics the wave function
always evolves in the usual deterministic way, but particles are taken
to always have fully determinate positions. For an *N*-particle
system, the particle configuration can be thought of as being pushed
around in 3*N*-dimensional configuration space by the flow of the
norm squared of the wave function just as a massless particle would be
pushed around by a compressible fluid (the compressible fluid here is
the probability distribution in configuration space given by the
standard wave function). Here both the evolution of the wave function
and the evolution of the particle configuration are fully
deterministic. Quantum probabilities are the result of the
distribution postulate. The distribution postulate sets the initial
prior probability distribution equal to the norm squared of the wave
function for an initial time. One learns what the new
*effective* wave function is from one's measurement results,
but one never knows more than what is allowed by the standard quantum
statistics. Indeed, Bohm's theory always predicts the standard
quantum probabilities for particle configurations, but it predicts
these as *epistemic* probabilities. Bohm's theory is supposed
to give determinate measurement results in terms of determinate
particle configurations (say the position of the pointer on a
measuring device). See Barrett (1999) and the entry on
Bohmian mechanics
for more details about Bohmian mechanics.

If one chooses position as the preferred physical observable and
adopts the particle dynamics of Bohm's theory, then one can construct
a version of the many-threads theory by fixing a single Hamiltonian
and by considering every possible initial configuration of particles
to correspond to a different thread (world). Here the prior
probabilities are given by the distribution postulate in Bohm's
theory, and these probabilities are Bayesian updated on the results of
measurements. The updated epistemic probabilities yield the
*effective* Bohmian wave function. So the only difference
between Bohm's theory and the associated many-threads theory is that
the many-threads theory treats all possible Bohmian worlds as
simultaneously existing worlds, only one of which is ours. A
many-threads theory can be constructed for virtually any determinate
physical quantity just as one would construct a hidden-variable or a
modal theory. (See the entry on
modal interpretations of quantum theory.)

If something like the many-minds theory or the many-thread theory is what it takes to get determinate measurement records and the standard quantum probabilities in a formulation of Everett, then fixing Everett amounts to adding a hidden-variable to quantum mechanics, mental states in the former theory and the preferred observable in the latter. It is the determinate value of this so-called hidden variable that determines our determinate measurement records, and it is the dynamics of this variable together with the prior probabilities that yields the standard quantum statistics. But Everett himself presumably did not intend a hidden-variable theory.

## 8. Relative Facts, Correlations without Correlata, and Relational Quantum Mechanics

Perhaps the approach closest in spirit to Everett's relative-state
formulation would be simply to deny that there are typically any
absolute matters of fact about the properties of physical systems or
the records, experiences, and beliefs of observers. (See Saunders, 1995,
and Mermin, 1998, for examples of how this might work.)
In the experiment above, quantum mechanics would not describe
*J* as believing that his result was "spin up", and it would
not describe *J* as believing that his result was "spin down";
rather, on this sort of theory all quantum-mechanical facts would be
relative and all quantum probabilities would describe basic
correlations, not the correlata on which one might have thought the
correlations would supervene. Here quantum mechanical facts are not
relative to a particular world, mind, or history, but relative to each
other: Here *J* believes that his result was "spin up"
*relative to* *S* being *x*-spin up and
*J* believes that his result was "spin down" *relative
to* *S* being *x*-spin down. But, one might ask,
what is the state of* S* then? Well, *S* is
*x*-spin up *relative to J* believing that his result
was "spin up", etc. Again, on this sort of theory there are typically
no absolute matters of fact about the properties of individual
physical systems. (For a related approach, which however does not
imply a multiplicity of properties, see Rovelli, 1996, and the entry
on
relational quantum mechanics.)

Here, rather than account for determinate measurement records, one simply denies that there is any matter of fact concerning what an observer's measurement record is. Which means that insofar as one believes that there really is a simple matter of fact about what one got in a particular measurement, a relative-fact formulation of quantum mechanics provides no account of one's experience. Similarly, one cannot make sense of the usual statistical predictions of quantum mechanics insofar as one takes these to be predictions concerning the probability that a particular measurement outcome will in fact occur. Again, there are typically no such simple facts in such a theory. This is why, on this view, all quantum probabilities concern correlations, not correlata. But it is difficult to interpret probabilistic claims about correlations in the context of a theory that denies that there are determinate correlata to be correlated. That is, one might have thought that any coherent talk about the probabilistic correlations between events presupposes that there are determinate matters of fact concerning what events occur.

One reply to such objections would be to claim that accounting for our determinate measurement records is simply outside the proper domain of quantum mechanics. Since our measurement results are presumably recorded in the states of physical systems, this would be to take quantum mechanics to not apply to all physical systems. But to take this view would be to fall prey to Everett's initial complaint about the external collapse formulation of quantum mechanics not being applicable to systems containing measuring devices. Or one might reply that there really are no determinate measurement records. But this would require an explanation for why we seem to have fully determinate measurement records. Also, we presumably want a physical theory that is empirically coherent: As we saw with the bare theory, if one does not have reliable access to determinate measurement records, then it is unclear how empirical science is possible.

## 9. Summary

Such are some of the ways of understanding Everett's relative-state formulation of quantum mechanics. It will probably never be entirely clear precisely what Everett himself had in mind, but his goal of trying to make sense of quantum mechanics without the collapse postulate was heroic. And even in light of the problems one faces, puzzling over how one might reconstruct Everett's theory continues to hold promise.

## Bibliography

- Albert, D. Z.: 1992,
*Quantum Mechanics and Experience*, Harvard University Press, Cambridge, MA. - Albert, D. Z., and J. A. Barrett: 1995 "On What It Takes To Be
a World",
*Topoi*14: 35-37. - Albert, D. Z., and B. Loewer: 1988, "Interpreting the Many Worlds
Interpretation",
*Synthese*77: 195-213. - Bacciagaluppi, G.: 2002, "Remarks on Space-time and Locality in
Everett's Interpretation", in T. Placek and J. Butterfield (eds),
*Non-Locality and Modality*(Kluwer Academic, Dordrecht, 2002), pp. 105-122. [Preprint available online]. - Barrett, J.: 1994, "The Suggestive Properties of Quantum Mechanics
Without the Collapse Postulate",
*Erkenntnis*41: 233-252. - Barrett, J.: 1995, "The Single-Mind and Many-Minds Formulations of
Quantum Mechanics",
*Erkenntnis*42: 89-105. - Barrett, J.: 1996, "Empirical Adequacy and the Availability of Reliable
Records in Quantum Mechanics",
*Philosophy of Science*63: 49-64. - Barrett, J.: 1999,
*The Quantum Mechanics of Minds and Worlds*(Oxford University Press, Oxford). - Barrett, J.: 2000, "The Nature of Measurement Records in Relativistic
Quantum Field Theory," in M. Kuhlman, H. Lyre, and A. Wayne (eds.),
*Ontological Aspects of Quantum Field Theory*, Singapore: World Scientific. [Preprint available online]. - Barrett, J.: 2002, "Are Our Best Physical Theories (Probably
and/or Approximately) True?",
*Philosophy of Science*, forthcoming. [Preprint available online]. - Bell, J. S.: 1987,
*Speakable and Unspeakable in Quantum Theory*(Cambridge University Press, Cambridge). - Bub, J., R. Clifton and B. Monton: 1998, "The Bare Theory Has No
Clothes", in R. Healey and G. Hellman (eds),
*Quantum Measurement: Beyond Paradox*Minnesota Studies in the Philosophy of Science 17. - Butterfield, J.: 1995, "Worlds, Minds, and Quanta",
*Aristotelian Society Supplementary Volume*LXIX: 113-158. - Clifton, R.: 1996, "On What Being a World Takes Away",
*Philosophy of Science*63: S151-S158. - DeWitt, B. S.: 1971, "The Many-Universes Interpretation of
Quantum Mechanics", in
*Foundations of Quantum Mechanics*(Academic Press, New York). Reprinted in DeWitt and Graham (1973), pp. 167-218. - DeWitt, B. S., and N. Graham (eds): 1973,
*The Many-Worlds Interpretation of Quantum Mechanics*(Princeton University Press, Princeton). - Dowker, F., and A. Kent: 1996, "On the Consistent Histories
Approach to Quantum Mechanics",
*Journal of Statistical Physics*83(5-6): 1575-1646. - Everett, H.: 1957a,
*On the Foundations of Quantum Mechanics*, thesis submitted to Princeton University, March 1, 1957, in partial fulfillment of the requirements for the Ph.D. degree. - Everett, H.: 1957b, "‘Relative State’ Formulation of
Quantum Mechanics",
*Reviews of Modern Physics*29: 454-462. Reprinted in Wheeler and Zurek (1983), pp. 315-323. - Everett, H.: 1973, "The Theory of the Universal Wave Function", in DeWitt and Graham (1973).
- Gell-Mann, M., and J. B. Hartle: 1990, "Quantum Mechanics in the
Light of Quantum Cosmology", in W. H. Zurek (ed.),
*Complexity, Entropy, and the Physics of Information*, Proceedings of the Santa Fe Institute Studies in the Sciences of Complexity, vol. VIII (Addison-Wesley, Redwood City, CA), pp. 425-458. - Geroch, R.: 1984, "The Everett Interpretation",
*Nous*18: 617-633. - Healey, R.: 1984, "How Many Worlds?",
*Nous*18: 591-616. - Hemmo, M., and I. Pitowsky: 2001, "Probability and Nonlocality in
Many Minds Interpretations of Quantum Mechanics",
*British Journal for the Philosophy of Science*, forthcoming [Preprint available online]. - Lockwood, M.: 1989,
*Mind, Brain, and the Quantum*, Blackwell, Oxford. - Lockwood, M.: 1996, "Many Minds Interpretations of Quantum
Mechanics",
*British Journal for the Philosophy of Science*47(2): 159-188. - Mermin, D.: (1998) "What is quantum mechanics trying to tell
us?",
*American Journal of Physics*66: 753-767. [Preprint available online]. - Rovelli, C.: 1996, "Relational Quantum Mechanics",
*International Journal of Theoretical Physics*35: 1637. [Preprint available online]. - Saunders, S.: 1995, "Time, Quantum Mechanics, and Decoherence",
*Synthese*102(2): 235-266. - Saunders, S.: 1997, "Naturalizing Metaphysics (Philosophy, Quantum
Mechanics, The Problem of Measurement)",
*Monist*80(1): 44-69. - Saunders, S.: 1998, "Time, Quantum Mechanics, And
Probability",
*Synthese*114(3): 373-404. - Stein, H.: 1984, "The Everett Interpretation of Quantum
Mechanics: Many Worlds or None?",
*Nous*18: 635-52. - von Neumann, J.: 1955,
*Mathematical Foundations of Quantum Mechanics*(Princeton University Press, Princeton). Translated by R. Beyer from*Mathematische Grundlagen der Quantenmechanik*(Springer, Berlin, 1932). - Wallace, D.: 2002, "Worlds in the Everett Interpretation",
*Studies in History & Philosophy of Modern Physics*, 33B(4) (Dec): 637-661. [Preprint available online]. - Wheeler, J. A., and W. H. Zurek (eds): 1983,
*Quantum Theory and Measurement*(Princeton University Press, Princeton). - Zurek, W. H.: 1991, "Decoherence and the Transition from
Quantum to Classical",
*Physics Today*44(October): 36-44.

## Other Internet Resources

- Donald, M. J.: 1997,
"On Many-Minds Interpretations of Quantum Theory", in
*Pittsburgh PhiSci Archive*. - The New Scientist: "Dead or Alive"