Paradoxes and Primitive Ontology in Collapse Theories of Quantum Mechanics

Paradoxes and Primitive Ontology in Collapse Theories of Quantum Mechanics Collapse theories are versions of quantum mechanics according to which the
collapse of the wave function is a real physical process. They propose precise
mathematical laws to govern this process and to replace the vague conventional
prescription that a collapse occurs whenever an “observer” makes a “measurement.”
The “primitive ontology” of a theory (more or less what Bell called the
“local beables”) are the variables in the theory that represent matter in spacetime.
There is no consensus about whether collapse theories need to introduce a
primitive ontology as part of their definition. I make some remarks on this question
and point out that certain paradoxes about collapse theories are absent if a
primitive ontology is introduced. Although collapse theories (Ghirardi, 2007) have been invented to overcome the paradoxes
of orthodox quantum mechanics, several authors have set up similar paradoxes in
collapse theories. I argue here, following Monton (2004), that these paradoxes evaporate
as soon as a clear choice of the primitive ontology is introduced, such as the flash
ontology or the matter density ontology. In addition, I give a broader discussion of the
concept of primitive ontology, what it means and what it is good for.
According to collapse theories of quantum mechanics, such as the Ghirardi–Rimini–
Weber (GRW) theory (Ghirardi et al., 1986; Bell, 1987a) or similar ones (Pearle, 1989;
Di´osi, 1989; Bassi and Ghirardi, 2003), the time evolution of the wave function ψ in our
world is not unitary but instead stochastic and non-linear; and the Schrödinger equation is merely an approximation, valid for systems of few particles but not for macroscopic
systems, i.e., systems with (say) 1023 or more particles. The time evolution law for ψ
provided by the GRW theory is formulated mathematically as a stochastic process, see,
e.g., (Bell, 1987a; Bassi and Ghirardi, 2003; Allori et al., 2008), and can be summarized
by saying that the wave function ψ of all the N particles in the universe evolves as
if somebody outside the universe made, at random times with rate Nλ, an unsharp
quantum measurement of the position observable of a randomly chosen particle. “Rate
Nλ” means that the probability of an event in time dt is equal to Nλ dt; λ is a constant
of order 10−15 sec−1
. It turns out that the empirical predictions of the GRW theory
agree with the rules of standard quantum mechanics up to deviations that are so small
that they cannot be detected with current technology (Bassi and Ghirardi, 2003; Adler,
2007; Feldmann and Tumulka, 2012; Bassi and Ulbricht, 2014; Carlesso et al., 2016).
The merit of collapse theories, also known as dynamical state reduction theories, is
that they are “quantum theories without observers” (Goldstein, 1998), as they can be
formulated in a precise way without reference to “observers” or “measurements,” although
any such theory had been declared impossible by Bohr, Heisenberg, and others.
Collapse theories are not afflicted with the vagueness, imprecision, and lack of clarity of
ordinary, orthodox quantum mechanics (OQM). Apart from the seminal contributions by
Ghirardi et al. (1986); Bell (1987a); Pearle (1989); Di´osi (1989, 1990), and a precursor by
Gisin (1984), collapse theories have also been considered by Gisin and Percival (1993);
Leggett (2002); Penrose (2000); Adler (2007); Weinberg (2012), among others. A feature
that makes collapse models particularly interesting is that they possess extensions to
relativistic space-time that (unlike Bohmian mechanics) do not require a preferred foliation
of space-time into spacelike hypersurfaces (Tumulka, 2006a,b; Bedingham et al.,
2014); see Maudlin (2011) for a discussion of this aspect.
Collapse theories have been understood in two very different ways: some authors
[e.g., Bell (1987a); Ghirardi et al. (1995); Goldstein (1998); Maudlin (2007); Allori et al.
(2008); Esfeld (2014)] think that a complete specification of a collapse theory requires,
besides the evolution law for ψ, a specification of variables describing the distribution of
matter in space and time (called the primitive ontology or PO), while other authors [e.g.,
Albert and Loewer (1990); Shimony (1990); Lewis (1995); Penrose (2000); Adler (2007);
Pearle (2009); Albert (2015)] think that a further postulate about the PO is unnecessary
for collapse theories. The goals of this paper are to discuss some aspects of these two
views, to illustrate the concept of PO, and to convey something about its meaning and
relevance. I begin by explaining some more what is meant by ontology (Section 2) and
primitive ontology (Section 3). Then (Section 4), I discuss three paradoxes about GRW
from the point of view of PO. In Section 5, I turn to a broader discussion of PO. Finally
in Section 6, I describe specifically its relation to the mind-body problem.