Understanding Quantum Physics: An Advanced Guide for the Perplexed

these two events should be regarded as
simultaneous. Note that this conclusion is irrelevant to whether the two events
and their causal connection are observable. Furthermore, simultaneity cannot be
relative but be absolute, otherwise these two distinct events will be not
simultaneous in all but one inertial frame [105] .
    Let’s further
consider the collapse evolution of random discontinuous motion during a
measurement. It can be seen that the measurement on one branch of the
superposition has a causal influence on the other branch (as well as on the
measured branch) via the collapse process, and this nonlocal influence is
irrelevant to the distance between the two branches. Accordingly, the time
order of the measurement and the collapse of the superposition happening in the
two separated regions cannot be conventional but must be unique. Since the
collapse time can be arbitrarily short, the measurement and the collapse of the
superposition can be regarded as simultaneous. Moreover, the collapses of the
superposition in the two regions, which are spacelike separated events, are
also simultaneous [106] . The simultaneity is irrelevant to the selection of
inertial frames, which again means that simultaneity is absolute.
    Certainly, the
collapse of an individual superposition cannot be measured within the framework
of the existing quantum mechanics. However, on the one hand, the above
conclusion is irrelevant to whether the collapse events can be measured or not,
and on the other hand, the collapse of an individual superposition may be
observable when the quantum dynamics is deterministic nonlinear (Gisin 1990),
e.g. when the measuring device is replaced with a conscious observer (Squires
1992; Gao 2004).
    5.3 Collapse dynamics and preferred Lorentz
frame
    The random
discontinuous motion of particles and its collapse evolution requires that
simultaneity is absolute. If the collapse of the wave function happens
simultaneously at different locations in space in every inertial frame, then
the one-way speed of light will be not isotropic in all but one inertial frame.
In other words, if the absolute simultaneity is restored, then the
non-invariance of the one-way speed of light will single out a preferred
Lorentz frame, in which the one-way speed of light is isotropic [107] . The detectability of this frame seems to
depend on the measurability of individual collapse. Once the collapse of an
individual wave function can be measured, the clocks at different locations in
space can be synchronized with the help of the instantaneous wavefunction
collapse in every inertial frame, and the preferred Lorentz frame can then be
determined by measuring the one-way speed of light, which is isotropic in the
frame.
    However, even if
the collapse of an individual wave function cannot be measured, the preferred
Lorentz frame may also be determined by measuring the (average) collapse time
of the wave functions of identical systems in an ensemble according to our
energy-conserved collapse model [108] . The reason is that the law of collapse
dynamics in our model, like the time order of the collapses in different
positions, is not relativistically invariant either. Let’s give a more detailed
analysis below.
    According to the
energy-conserved collapse model, the (average) collapse time formula for an
energy superposition state, denoted by Eq. (4.13), can be rewritten as

    where t P is the Planck time, ∆E is the energy uncertainty of the state. It can be seen
that this collapse time formula is not relativistically invariant, and thus
there exists a preferred Lorentz frame according to the collapse model. We
assume the formula is valid in the preferred Lorentz frame, denoted by S 0 ,
in the relativistic domain [109] . Then in another inertial frame the collapse time
will depend on the velocity of the frame relative to S 0 . According
to the Lorentz transformation [110] , in an inertial frame S with velocity v
relative to the frame S 0 we have:

    Here we only
consider the situation where the particle has very high energy, namely E ≈ pc,
and thus Eq. (5.21) holds. Besides, we assume the Planck time t P is
the minimum time in the preferred Lorentz frame, and in another frame the
minimum time (i.e. the duration of a discrete instant) is connected with the
Planck time t P by the time dilation formula required by special
relativity. Then by inputting these equations into Eq. (5.22), we can obtain
the relativistic collapse time formula for an