Understanding Quantum Physics: An Advanced Guide for the Perplexed

would be
beyond experimental constraints (Pearle and Squires 1996). In conclusion, it
seems that the noise field introduced in the CSL model cannot have a
gravitational origin required by the model, and this may raise strong doubts
about the reality of the field.
    58 Note that Ghirardi, Grassi and Benatti
(1995) and Ghirardi (1997) already explicitly proposed the so-called mass
density ontology in the context of dynamical collapse theories. According to
Ghirardi (2008), "what the theory is about, what is real ‘out there’ at a
given space point x, is just a field, i.e. a variable m(x, t) given by the
expectation value of the mass density operator M(x) at x obtained by
multiplying the mass of any kind of particle times the number density operator
for the considered type of particle and summing over all possible types of
particles.
    On the other hand,
even though the approach of semiclassical gravity is viable and the noise field
in the CSL model can be the gravitational field, one still need to answer why
the gravitational field has the very ability to collapse the wave functions of
all quantum systems as required by the model. It is worth noting that the
randomly fluctuating field in the model, w 0 (x, t), is not the
gravitational field of the studied quantum system but the background
gravitational field. Thus Penrose’s gravity-induced wavefunction collapse
argument, even if valid, does not apply to the CSL model, which is essentially
an interaction induced model of wavefunction collapse. The fluctuations of the
background gravitational field can readily lead to the decoherence of the wave
function of a quantum system, but it seems that they have no ability to cause
the collapse of the wave function.
    Lastly, let’s
briefly discuss another two problems of the CSL model. The first one is the
well-known problem of energy non-conservation. The collapse in the model
narrows the wave function in position space, thereby producing an increase of
energy [100] . A possible solution is that the conservation laws
may be satisfied when the contributions of the noise field w(x, t) to the
conserved quantities are taken into account. It has been shown that the total
mean energy can be conserved (Pearle 2004), and the energy increase can also be
made finite when further revising the coupling between the noise field and the
studied quantum system (Bassi, Ippoliti and Vacchini 2005). But a complete
solution has not been found yet, and it is still unknown whether such a solution
indeed exists. The second problem is to make a relativistic quantum field
theory which describes collapse (Pearle 2009). Notwithstanding a good deal of
effort, a satisfactory theory has not been obtained at present (see Bedingham
2011 for a recent attempt). The main difficulty is that the hypothetical
interaction responsible for collapse will produce too many particles out of the
vacuum, amounting to infinite energy per sec per volume, in the relativistic
extension of these interaction-induced collapse models. Note that the
spontaneous collapse models without collapse interaction (e.g. the
energy-conserved collapse model) don’t face this difficulty. We will discuss
the problem of compatibility between wavefunction collapse and the principle of
relativity in the next Chapter.

 
    Chapter 5
    On the Unification of Quantum Mechanics and Special Relativity
    We have an apparent incompatibility, at
the deepest level, between the two fundamental pillars of contemporary theory
... It may be that a real synthesis of quantum and relativity theories requires
not just technical developments but radical conceptual renewal.
    —John
Bell
    In this chapter,
we will briefly analyze random discontinuous motion of particles and its
collapse evolution in the relativistic domain [101] . It is first shown that the Lorentz
transformation seriously distorts the picture of random discontinuous motion of
particles, and the distortion results from the relativity of simultaneity. We
then argue that absolute simultaneity is not only possible in the relativistic
domain, but also necessitated by the existence of random discontinuous motion
of particles and its collapse evolution. This leads to the existence of a
preferred Lorentz frame when combined with the requirement of the constancy of
speed of light. It is further shown that the collapse dynamics may provide a
way to detect the frame according to the energy-conserved collapse model. If
quantum mechanics indeed describes random