Understanding Quantum Physics: An Advanced Guide for the Perplexed

motion of particles is distorted by the
Lorentz transformation due to the nonlocality and randomness of motion. In the
following, we will further show that the nonlocal and random collapse evolution
of the state of motion (defined during an infinitesimal time interval) will be
influenced by the Lorentz transformation more seriously.

    ψ u ϕ u + ψ d ϕ d , can only obtain correlated results in every
inertial frame. If a measurement on particle 1 obtains the result u or d,
indicating the state of the particle collapses to the state ψ u or ψ d after the measurement, then a second measurement on particle 2 can only obtain
the result u or d, indicating the state of particle 2 collapses to the state ϕ u or ϕ d after the measurement. Accordingly, although the instantaneous
correlation and synchronicity between the motion of two entangled particles is
destroyed in all but one inertial frame, the distorted picture of quantum
entanglement cannot be measured.
    5.2 On the absoluteness of simultaneity
    The above analysis
clearly demonstrates the apparent conflict between the random discontinuous
motion of particles and the Lorentz transformation in special relativity. The
crux of the matter lies in the relativity of simultaneity. If simultaneity is
relative as required by the Lorentz transformation, then the picture of random
discontinuous motion of particles will be seriously distorted except in one
preferred frame, though the distortion is unobservable in principle. Only when
simultaneity is absolute, can the picture of random discontinuous motion of
particles be kept perfect in every inertial frame. In the following, we will
show that absolute simultaneity is not only possible, but also necessitated by
the existence of random discontinuous motion of particles and its collapse
evolution.
    Although the
relativity of simultaneity has been often regarded as one of the essential
concepts of special relativity, it is not necessitated by experimental facts
but a result of the choice of standard synchrony (see, e.g. Reichenbach 1958;
Gr¨unbaum 1973) [104] . As Einstein (1905) already pointed out in his first
paper on special relativity, whether or not two spatially separated events are
simultaneous depends on the adoption of a convention in the framework of
special relativity. In particular, the choice of standard synchrony, which is
based on the constancy of one-way speed of light and results in the relativity
of simultaneity, is only a convenient convention. Strictly speaking, the speed
constant c in special relativity is two-way speed, not one-way speed, and as a
result, the general spacetime transformation required by the constancy of
two-way speed of light is not the Lorentz transformation but the Edwards-Winnie
transformation (Edwards 1963; Winnie 1970):

    The above analysis
demonstrates the possibility of keeping simultaneity absolute within the
framework of special relativity. One can adopts the standard synchrony that
leads to the relativity of simultaneity, and one can also adopts the
nonstandard synchrony that restores the absoluteness of simultaneity. This is
permitted because there is no causal connection between two spacelike separated
events in special relativity. However, if there is a causal influence
connecting two distinct events, then the claim that they are not simultaneous
will have a nonconventional basis (Reichenbach 1958, 123-135; Gr¨basis
(Reichenbach 1958, 123-135; Gr¨ 368). In particular, if there is an arbitrarily
fast causal influence connecting two spacelike separated events, then these two
events will be simultaneous. In the following, we will show that random
discontinuous motion and its collapse evolution just provide a nonconventional
basis for the absoluteness of simultaneity.
    Consider a
particle being in a superposition of two well separated spatial branches.
According to the picture of random discontinuous motion, the particle jumps
between these two branches in a random and discontinuous way. At an instant the
particle is in one branch, and at the next instant it may be in the other
spatially-separated branch. The disappearance of the particle in the first
branch can be regarded as one event, and the appearance of the particle in the
second branch can be regarded as another event. Obviously there is an
instantaneous causal connection between these two spacelike separated events;
if the particle did not disappear in the first branch, it could not appear in
the second branch. Therefore,