Understanding Quantum Physics: An Advanced Guide for the Perplexed

noise field) is still in its infancy.
    [100] Note that with appropriate choice for the parameters in the CSL model,
such a violation of energy conservation is very tiny and hardly detectable by
present day technology.
    [101] Our analysis is in the low-energy regime and does not consider the
high-energy processes described by relativistic quantum field theory, e.g. the
creation and annihilation of particles.
    [102] There is no consensus among contemporary philosophers and physicists
concerning the solution to this incompatibility problem. For a comprehensive
discussion of this issue see Maudlin (2002) and references therein.
    [103] Certainly, in these frames there are still correlation and synchronicity
between the jumpings of the two particles at different instants. As noted
above, however, these instants are discontinuous and random, and thus the
correlation and synchronicity can hardly be identified.
    [104] For more discussions about this issue see Janis (2010) and references
therein.
    [105] Why does each instantaneous jump of a particle in one inertial frame
last much long time in another inertial frame? The lapse of time cannot be
explained in physics, and it can only result from the inappropriate synchrony
of clocks at different locations in the later frame.
    [106] Note that there exists no causal influence between these two events, and
they both result from the measurement of the local measuring device, which is
the common cause.
    [107] Similarly, if the invariance of the one-way speed of light or standard
synchrony is assumed as by the Lorentz transformation, then the collapse
evolution of random discontinuous motion will also single out a preferred
Lorentz frame, in which the collapse of the wave function happens
simultaneously at different locations in space, no matter whether the frame can
be actually determined. In the final analysis, the emergence of a preferred
Lorentz frame is the inevitable result of the combination of the constancy of
two-way speed of light and the existence of random discontinuous motion and its
collapse evolution. Thus, no matter which assumption is adopted, the preferred
Lorentz frame can always be defined as the inertial frame in which the one-way
speed of light is isotropic and the collapse of the wave function happens
simultaneously in the whole space.
    [108] It has been argued that quantum nonlocality and special relativity are
incompatible, and a consistent description of wavefunction collapse demands the
existence of a preferred Lorentz frame (see, e.g. Bell 1986a; Percival 1998b).
But it is widely thought that the preferred Lorentz frame cannot be measured
even within the framework of dynamical collapse theories.
    [109] This assumption seems reasonable, as the collapse time formula in our
model already contains the speed of light c via the Planck time t p .
By contrast, the dynamical collapse theories in which the collapse time formula
does not contain c are not directly applicable in the relativistic domain.
    [110] Here we still use the standard synchrony for the convenience of
practical realization.
    [111] This seems to be an inevitable consequence of the requirement of energy
conservation for wavefunction collapse.
    [112] In general, we can measure the collapse time of a wave function through
measuring the change of the interference between the corresponding collapse
branches for an ensemble of identical systems. The main difficulty of this
approach is to exclude the influence of environmental decoherence (cf. Marshall
et al 2003).
    [113] A further analysis is needed to determine whether this is true in
theory.