Objective-collapse theories, also known as
quantum-mechanical spontaneous-localization
models (QMSL), are an approach to the interpretational
problems of quantum mechanics.
They are realistic and indeterministic and
reject hidden variables.
The approach is similar to the Copenhagen
interpretation, but more firmly objective.
The most well-known examples of such theories
are:
Ghirardi–Rimini–Weber theory
Penrose interpretation
== 
Compared to other approaches ==
Collapse theories stand in opposition to many-worlds
interpretation theories, in that they hold
that a process of wavefunction collapse curtails
the branching of the wavefunction and removes
unobserved behaviour.
Objective-collapse theories differ from the
Copenhagen interpretation in regarding both
the wavefunction and the process of collapse
as ontologically objective.
The Copenhagen interpretation includes collapse,
but it is non-committal about the objective
reality of the wave function, and because
of that it is possible to regard Copenhagen-style
collapse as a subjective or informational
phenomenon.
The ontology of objective theories regards
the wave as real; the wave corresponds to
the mathematical wave function, and collapse
occurs randomly ("spontaneous localization"),
or when some physical threshold is reached,
with observers having no special role, as
an indifferent wave in an ocean.
== Variations ==
Objective-collapse theories regard the present
formalism of quantum mechanics as incomplete,
in some sense.
(For that reason it is more correct to call
them theories than interpretations.)
They divide into two subtypes, depending on
how the hypothesised mechanism of collapse
stands in relation to the unitary evolution
of the wavefunction.
Collapse is found "within" the evolution of
the wavefunction, often by modifying the equations
to introduce small amounts of non-linearity.
A well-known example is the Ghirardi–Rimini–Weber
theory (GRW).
The evolution of the wavefunction remains
unchanged, and an additional collapse process
("objective reduction") is added, or at least
hypothesised.
A well-known example is the Penrose interpretation,
which links collapse to gravitational stress
in general-relativistic spacetime, with the
threshold value being one graviton.
Another example is the deterministic variant
of an objective-collapse theory
== 
Problems and drawbacks of GRW ==
GRW collapse theories have unique problems.
In order to keep these theories from violating
the principle of the conservation of energy,
the mathematics requires that any collapse
be incomplete.
Almost all of the wave function is contained
at the one measurable (and measured) value,
but there are one or more small tails where
the function should intuitively equal zero
but mathematically does not.
Critics of collapse theories argue that it
is not clear how to interpret these tails.
Under the premise that the absolute square
of the wave function is to be interpreted
as a probability density for the positions
of point particles, as is the case in standard
quantum mechanics, the tails would mean that
a small bit of matter has collapsed elsewhere
than the measurement indicates, or that with
very low probability an object might jump
from one collapsed state to another.
These options are counterintuitive and physically
unlikely.
Supporters of collapse theories mostly dismiss
this criticism as a misunderstanding of the
theory, as in the context of dynamical collapse
theories, the absolute square of the wave
function is often interpreted not as a probability
density of positions, but as an actual matter
density.
In this case, the tails merely represent an
immeasurably small amount of smeared-out matter,
while from a macroscopic perspective, all
particles appear to be point-like for all
practical purposes.The original QMSL models
had the drawback that they did not allow dealing
with systems with several identical particles,
as they did not respect the symmetries or
antisymmetries involved.
This problem was addressed by a revision of
the original GRW proposal known as CSL (continuous
spontaneous localization) developed by Ghirardi,
Pearle, and Rimini in 1990.The straightforward
generalization of continuous collapse theories,
such as CSL, to the relativistic case, leads
to problematic divergencies of the particle
density.
The formulation of a proper Lorentz-covariant
theory of continuous objective collapse is
still a matter of research, although suggestions
have been published e.g. by Philip Pearle.
== Notes ==
Giancarlo Ghirardi, Collapse Theories, Stanford
Encyclopedia of Philosophy (First published
Thu Mar 7, 2002; substantive revision Tue
Nov 8, 2011)
== See also ==
