FOUNDATIONS OF QUANTUM MECHANICS

VIII. 4. THE MEASUREMENT PROBLEM IN THE NARROW SENSE 175
This relative state yields the usual conditional probability distribution for the possible outcomes of
measurement of a quantity in case the object system is found in the state |ϕ i ⟩. This is substantiated by
Everett by showing that, if we set the right conditions for the state |ϕ i ⟩, all predictions for quantities
which only refer to the object system S can be determined using the relative state. Therefore, we can
act as if a projection to that state has taken place. In reality, however, the superposition (VIII. 15)
remains.
Now the question is, of course, how this superposition must be interpreted. Especially DeWitt
has propagated a radical view; all terms in this superposition represent real, existing worlds. The
transition during the measurement process is a division of the world in uncountably many copies,
where a different result is registered in each of them. All these worlds exist and develop further next
to one another, without being able to have mutual contact. The problem how to choose one really
realized term from the superposition, as we do using the projection postulate, is avoided because all
terms are realized.
Postulating the existence of such an multiplicity of worlds, with which, moreover, we absolutely
cannot make contact, is acceptable only for a small number of people. But probably worse is the
idea that any decay process in a star in a remote part of the universe can split up our local world into
millions of copies of itself.
Moreover, a difficult point in this theory is how the ‘splitting’ must be understood exactly. It
seems that DeWitt intends a special kind of physical process which emerges at registration. This
would look like adopting a second type of process besides the Schrödinger evolution, in contrast to
the objective of the interpretation; the measurement problem in the broad sense would not be solved.
There is also the problem which process we have to suggest for the reversed evolution; a ‘melting’ of
worlds? In Everett’s original work the idea of a physical splitting of the universe does not occur. He
only regards this as a ‘bookkeeping’ transition to a relative state.
Finally there is the supposition that to a set of states |r j ⟩ of the measuring apparatus the interpretation
can be given that herewith an outcome of measurement is permanently registered. This
supposition cannot without problems be brought into conformity with quantum mechanics because it
still concerns superpositions.
VIII. 4. 5
SUPERSELECTION RULES
Again another option is to introduce superselection rules. Certain superpositions of microscopic
states do not seem to occur in nature, for example, superpositions of states with unequal charge, e.g.
electric, baryonic, or superpositions of states with integer and half integer spin. Therefore, it could be
assumed that superpositions of macroscopically different states do not occur also, and the dynamics
of quantum mechanics must then be adapted to account for this.
In such a setup of quantum mechanics, e.g., in which the superposition principle is not valid
in general, it is possible to have W ′ , (VIII. 16), as the final state of the measurement process, see
Beltrametti and Cassinelli (1981, p. 57). More precisely, in the presence of superselection rules the
mixture (VIII. 16) and the pure state (VIII. 15) become equivalent; the superselection rules provide
the same expectation values for all physical quantities allowed by the superselection operators.
An example of this approach is the suggestion of R. Penrose (1996) that in a future unified theory
for quantum gravitation a superselection rule would apply to the space - time metric. Because