Understanding Quantum Physics: An Advanced Guide for the Perplexed

process. These "electron
avalanches" create electric pulses which then can be amplified
electronically and counted by a meter to calculate the number of initial
ionization events. In this way, a Geiger counter can detect low-energy
radiation because even one ionized particle produces a full pulse on the
central wire. It can be estimated that the introduced energy difference during
a detection is ∆E ≈ 10 9 eV , and the corresponding collapse time is τ c ≈
10 −5 s according to our collapse model.
    [85] In a similar way, a spherically symmetric wave function will be detected
as one linear track in a cloud chamber (cf. Mott 1929).
    [86] The uncertainty of the total energy of the whole system is still very
small even if the influences of environment are counted. Thus no observable
collapse happens for the above situation according to the energy-driven
collapse models (Pearle 2004).
    [87] It is interesting to note that the state of a macroscopic object can
also be localized by the linear Schrödinger evolution via interactions with
environment, e.g. by absorbing an environmental particle with certain energy
uncertainty. For example, if a macroscopic object absorbs a photon (emitted
from an atom) with momentum uncertainty of ∆p ≈ 10 −6 eV/c, the
center-of-mass state of the object, even if being a momentum eigenstate initially,
will have the same momentum uncertainty by the linear Schrödinger evolution,
and thus it will become a localized wavepacket with width about 0.1m. Note that
there is no vicious circle here. The energy spreading state of a microscopic
particle can be generated by an external potential (e.g. an electromagnetic
potential in general) via the linear Schrödinger evolution, and especially they
don’t necessarily depend on the localization of macroscopic objects such as
measuring devices. Thus we can use the existence of these states to explain the
localization of macroscopic objects.
    [88] When assuming the energy uncertainty of an object is in the same order
of its thermal energy fluctuation, we can estimate the rough size of its
wavepacket. For instance, for a dust particle of mass m = 10 −7 g, its
root mean square energy fluctuation is about 10 3 eV at room
temperature T = 300K (Adler 2002), and thus the width of its wavepacket is
about 10 −10 m.
    [89] The GRW model was originally referred to as QMSL (Quantum Mechanics with
Spontaneous Localizations). In this model, it is assumed that each elementary
constituent of any physical system is subjected, at random times, to random and
spontaneous localization processes (or hittings) around appropriate positions.
The random hittings happen much less frequently for a microscopic system, e.g.
an electron undergoes a hitting, on average, every hundred million years. If
these hittings are assumed to be brought about by an external system, then the
GRW model should be regarded not as a spontaneous collapse model but as an
interaction-induced collapse model.
    [90] If the involved noise field in the CSL model is not taken as real, then
the model should be regarded as a spontaneous collapse model.
    [91] It is interesting to note that Feynman considered this conjecture even earlier
at the 1957 Chapel Hill conference (see DeWitt and Rickles 2011, ch.22).
    [92] Note that if the problem of ill-definedness cannot be solved in
principle for the superpositions of very different space-time geometries, then
the wavefunction collapse may be relevant here. Concretely speaking, if the
superpositions of very different space-time geometries cannot be consistently
defined in nature, then it is very likely that these superpositions cannot
exist, which means that they must have collapsed into one of the definite
space-time geometries before formed from the superpositions of minutely
different space-time geometries. In this case, the large difference of the
space-time geometries in the superposition will set a upper limit for
wavefunction collapse. Though the limit may be loose, it does imply the
existence of wavefunction collapse. However, this possibility might be very
small, as it seems that there is always some kind of approximate sense in which
two different spacetimes can be pointwise identified.
    [93] However, the concomitance of mass and charge in space for a charged
particle does not necessarily require that they must satisfy the same law of
interaction. For example, the fact that electromagnetic fields are quantized in
nature does not necessarily imply