7.1 Introductory Notes
169
The second model consists in the composition of two systems: of the previous
(QD) one and of a point particle scattered on it; the QD-spin chain occurs initially
in its specific stationary state. The scalar particle (moving in the configuration space
R
3 ) perturbs locally the infinite system (by scattering on its ‘first two’ spins) and
the chain develops then (after t → ∞) with some probability to a macroscopically
different state. This process can be interpreted as modeling detection of the particle
by a macroscopic detector. The model is interesting by that it does not correspond
to an “ideal measurement” the results of which are described usually by a projector
valued measure (PVM) realizing, e.g., the spectral decomposition of some selfadjoint operator—the ‘measured observable’. In our case, however, we obtain a positive
operator valued measure (POVM) describing the probabilities of responses to incoming states of the particle; this expresses the technical characteristics of the detector
with less than 100% efficiency. This model is presented here in detail, since it is
presented here for the first time—it is a more complex and more complete version
of an older model. The original version of this model was published in [38].
The third presented model is based on an ‘X-Y modification’ of the Heisenberg
spin-chain models, cf. e.g. [267]. This “model of quantum measurement” consists
of the 1/2-spin chain with a nearest neighbourhood interaction, which is interrupted
in one link, and in the point of the interruption an additional 1/2-spin modeling a
simplest possible “measured microsystem” is included (together with its interaction
with the rest of the chain).
The fourth model consists of a finite portion of QD of the length N 1 coupled to
Fermi field and working so that in the initial state “all the N spins are pointing down”,
but after reversing the first spin the chain moves until all the spins are “pointing up”
and, after reversing the last N -th spin, the chain emits a Fermi particle. With the
time t → ∞ the particle moves freely to infinity and the chain remains in a new
stationary state with “all spins pointing up”. The finite length of the chain needs a
different interpretation as a “measuring device” in comparison with the preceding
three infinite models.
7.2 On ‘Philosophy’ of “Models”
The term “model” is used repeatedly in this Chapter, as well as in science in general.
This word is generally used in various connections and meanings. It is usually considered as denoting human constructs (material or mental) approximating in some
way an aspect of a considered ‘part of reality’. But, can we determine where there
is a borderline between ‘only approximation’ and ‘full picture of truth’? What is the
‘reality’? What is the meaning of ‘the truth’ (as it was asked also by Pontius Pilate
very appropriately in Bible—New Testament: John 18:38)?
Let us consider (not only here) any human symbolic formulation of any knowledge as a “model”. Hence, also our laws of nature including the whole physics are
models—they are provisional and waiting for further completions and/or reformulations.
169
The second model consists in the composition of two systems: of the previous
(QD) one and of a point particle scattered on it; the QD-spin chain occurs initially
in its specific stationary state. The scalar particle (moving in the configuration space
R
3 ) perturbs locally the infinite system (by scattering on its ‘first two’ spins) and
the chain develops then (after t → ∞) with some probability to a macroscopically
different state. This process can be interpreted as modeling detection of the particle
by a macroscopic detector. The model is interesting by that it does not correspond
to an “ideal measurement” the results of which are described usually by a projector
valued measure (PVM) realizing, e.g., the spectral decomposition of some selfadjoint operator—the ‘measured observable’. In our case, however, we obtain a positive
operator valued measure (POVM) describing the probabilities of responses to incoming states of the particle; this expresses the technical characteristics of the detector
with less than 100% efficiency. This model is presented here in detail, since it is
presented here for the first time—it is a more complex and more complete version
of an older model. The original version of this model was published in [38].
The third presented model is based on an ‘X-Y modification’ of the Heisenberg
spin-chain models, cf. e.g. [267]. This “model of quantum measurement” consists
of the 1/2-spin chain with a nearest neighbourhood interaction, which is interrupted
in one link, and in the point of the interruption an additional 1/2-spin modeling a
simplest possible “measured microsystem” is included (together with its interaction
with the rest of the chain).
The fourth model consists of a finite portion of QD of the length N 1 coupled to
Fermi field and working so that in the initial state “all the N spins are pointing down”,
but after reversing the first spin the chain moves until all the spins are “pointing up”
and, after reversing the last N -th spin, the chain emits a Fermi particle. With the
time t → ∞ the particle moves freely to infinity and the chain remains in a new
stationary state with “all spins pointing up”. The finite length of the chain needs a
different interpretation as a “measuring device” in comparison with the preceding
three infinite models.
7.2 On ‘Philosophy’ of “Models”
The term “model” is used repeatedly in this Chapter, as well as in science in general.
This word is generally used in various connections and meanings. It is usually considered as denoting human constructs (material or mental) approximating in some
way an aspect of a considered ‘part of reality’. But, can we determine where there
is a borderline between ‘only approximation’ and ‘full picture of truth’? What is the
‘reality’? What is the meaning of ‘the truth’ (as it was asked also by Pontius Pilate
very appropriately in Bible—New Testament: John 18:38)?
Let us consider (not only here) any human symbolic formulation of any knowledge as a “model”. Hence, also our laws of nature including the whole physics are
models—they are provisional and waiting for further completions and/or reformulations.