**1. Introduction**

32 Measurement Systems

370 Advanced Topics in Measurements

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#### **1.1 Wave and particle duality in quantum measurements**

Right from the introduction of Plank's modern quantum concept, measurement effects have played a central role in both theoretical and experimental considerations [Jammer (1974)]. Einstein (1916) photon effects favor a particle based explanation. de Broglie (1923) proposed wave and particle duality. Heisenberg proposed a matrix approach to handling complex operations based on spectra measurements. Schrödinger established a wave equation for quantum construction extending de Broglie's schemes. von Neumann (1932,1996)'s contribution placed quantum mechanics in Hilbert space to establish a solid mathematical foundation for modern quantum mechanics. Despite developments in the quantum approach spanning more than a century, fundamental measurement problems remain unsolved [Penrose (2004)]. All their lives, Bohr and Einstein engaged in many debates, discussions and arguments trying to reach a common understanding on wave and particle issues [Jammer (1974)]. The EPR (Einstein, Podolsky, Rosen) Paradox [Einstein et al. (1935)] is said to have given Bohr many sleepless nights [Bohr (1935; 1949)].

#### **1.2 Criteria conditions and modern experiments**

Quantum measurement puzzles have been explored by [Feynman (1965); Feynman et al. (1965,1989)]. From the 1940s, Feynman emphasized that: "The entire mystery of quantum mechanics is in the double-slit experiment." This experiment establishes an interactive model that can directly illustrate both classical and quantum interactive results. Under single and double slit conditions, dual visual distributions are shown in particle and wave statistical distributions. Both particle probability and wave interactive interference patterns are observed [Barnett (2009); Hawking & Mlodinow (2010); Healey et al. (1998)].

(a) (b)

<sup>373</sup> From Local Interactive Measurements to Global Matrix Representations on Variant

Construction – A Particle Model of Quantum Interactions for Double Path Experiments

Fig. 1. (a-b) Double Path Model (a) Mach-Zehnder Double Path Model (b) Description Model

A given logic function *f* , can be represented as two meta logic functions *f*<sup>+</sup> and *f*<sup>−</sup> to simulate single and double path conditions. *N* bits of input vectors are exhausted by 2*<sup>N</sup>* states for measured data, recursive data are organized into eight histograms. Results are determined by

a set of histograms. Eight sets of histograms are represented as eight matrices in a selected C code configuration. Under this construction, it is possible to visualize different combinations

From these results, both additive probability properties in particle condition and wave interference properties with non-addition behaviors are observed. Both types of result are obtained consistently from this model under synchronous/asynchronous conditions. From a simulation viewpoint, this system satisfies all of Feynman's criteria conditions for double slit

The Mach-Zehnder interferometer is the most popular device used to support a Young double

In Fig 1(a) a double path interferometer is shown. An input signal *X* under control function *f* causes Laser *LS* to emit the output signal *ρ* under *BP* (Bi-polarized filter) operation. The output is in the form of a pair of signals: *ρ*<sup>+</sup> and *ρ*−. Both signals are processed by *SW* output

A Stern-Gerlach spin measurement device provides equivalent information for double path experiment [Jacques et al. (2008); Jammer (1974)]. This device divides composed signals into vertical ⊥ and horizontal � components, in *BP* part *ρ* → {*ρ*⊥, *ρ*�}, through controls and *IM*

*<sup>L</sup>* , *ρ*<sup>−</sup>

functions are applied to generate

*<sup>R</sup>* ) . In Fig 1(b), a representation

symmetry/anti-symmetry properties in histograms. All 22*<sup>n</sup>*

**2. Double path model and measurements of quantum interaction**

*<sup>R</sup>* , and then *IM* to generate output signals *IM*(*ρ*<sup>+</sup>

model has been described with the same signals being used.

from symmetry and anti-symmetry categories.

**2.1 Mach-Zehnder interferometer model**

experiments.

slit experiment.

**2.1.1 Other devices**

output *IM*(*ρ*⊥

*<sup>L</sup>* , *ρ* � *R*).

*ρ*+ *<sup>L</sup>* and *ρ*<sup>−</sup>
