We discuss on feasibility of experiments to test if the wave function collapses at the level of microscopic events. The original idea is Bussey's 'thought' experiment introduced in 1984. Bussey's proposal is to collide two particles and then two pairs of scattered and unscattered waves of each particle are examined by a pair of Mach-Zehnder type interferometers (MZI). Different coincidence rates between different sets of combinations of MZI outputs are expected depending on the collapse/non collapse assumption. In our proposition to realize this idea, a pair of low-energy electron beams is collided nearly head-on in a nanometer-size region. Then each combination of two waves scattered at small angles is thrown into the MZI. Each MZI is composed of Moellenstedt biprisms as two arms and mirrors, and then brought together at single crystal films which act as half reflecting mirrors (beam splitters). Coincidence counting is done among four outputs of the beam splitters. Another method to measure the position correlation after the biprisms is also proposed.
We discuss on feasibility of experiments to test if the wave function collapses at the level of microscopic events. The original idea is Bussey's 'thought' experiment introduced in 1984. Bussey's proposal is to collide two particles and then two pairs of scattered and unscattered waves of each particle are examined by a pair of Mach-Zehnder type interferometers (MZI). Different coincidence rates between different sets of combinations of MZI outputs are expected depending on the collapse/non collapse assumption. In our proposition to realize this idea, a pair of low-energy electron beams is collided nearly head-on in a nanometer-size region. Then each combination of two waves scattered at small angles is thrown into the MZI. Each MZI is composed of Moellenstedt biprisms as two arms and mirrors, and then brought together at single crystal films which act as half reflecting mirrors (beam splitters). Coincidence counting is done among four outputs of the beam splitters. Another method to measure the position correlation after the biprisms is also proposed.
In this paper, a realistic interpretation (REIN) of the wave function in quantum mechanics is briefly presented. We demonstrate that in the REIN, the wave function of a microscopic object is its real existence rather than a mere mathematical description. Specifically, the quantum object can exist in disjointed regions of space just as the wave function is distributed, travels at a finite speed, and collapses instantly upon a measurement. Furthermore, we analyze the single-photon interference in a Mach-Zehnder interferometer (MZI) using the REIN. Based on this, we propose and experimentally implement a generalized delayed-choice experiment, called the encounter-delayed-choice experiment, where the second beam splitter is decided whether or not to insert at the encounter of two sub-waves along the arms of the MZI. In such an experiment, the parts of the sub-waves, which do not travel through the beam splitter, show a particle nature, whereas the remaining parts interfere and thus show a wave nature. The predicted phenomenon is clearly demonstrated in the experiment, thus supporting the REIN idea.
\n\nThe Mach-Zehnder interferometer (MZI) is a regular yet simple instrument to test wave-particle duality. One key device in a standard MZI is the beam splitter 2 (BS2). Here we make a simple quantum mechanics analysis about the wave function evolution and find that the strong and exclusive interaction of BS2 with the incident microscopic particle beam (photons, electrons, etc.) is the fundamental reason why standard MZIs could not allow for the simultaneous observation of wave and particle properties of these particles. A weak-measurement (WM) MZI setup is then proposed, where BS2 is replaced with a deliberately designed highly transparent interference screen operating via either weak absorption or weak-scattering effect. Quantum-mechanical analysis on this WM-MZI shows that the overall power to make simultaneous observation of interference fringe (wave nature) and which-path information (particle nature) of microscopic particles can be significantly enhanced compared with the standard MZIs.\n
Electron biprism technique, if extended to any charged particles, will make comparison possible among two-beam interference fringes of electrons and other particles under the same(including wave length)geometrical condition. Combination of the technique with sharply focusing mass spectroscopy will realize such experiments. Due to the tradition since Young-Fresnel, it is believed that two-beam visibilities of particles of various masses under the same geometrical setup are constant and independent of each total sum of macroscopically separated path-lengths, which is not to be confused with ordinary path-difference.(See Fig. 2.)But the assumption of such constant visibility has never been verified experimentally and seems to become gradually unnatural as the masses increase. Experimental reexamination of the assumption is proposed with method of observing an expected mass effect on interdependence between visibility and pathlengths. The smaller visibilities are expected for the heavier masses and the longer path-lengths, contrary to conventional constant visibility; e.g., ≅0.4 for protons of wave length 0.02Å and beam width0.2μ in a realizable experimental setup. Technical problems for the experiment and effects to the observation theory are discussed.
I propose to resolve the controversy over the speed of collapse of quantum-mechanical wavefunctions by means of an experimental test with a modified symmetric Mach-Zehnder atom interferometer, with non-intersecting, parallel, widely separated final beams. According to the conventional collapse scenario, the coherent twin-peak atomic wavefunction in the beams of the interferometer suffers an instantaneous collapse, at infinite speed, when the atom is captured by one of the two detectors at the ends of the beams, but it remains coherent until that instant. In contrast, according to the Hellwig-Kraus relativistic collapse scenario, the wavefunction collapses at the speed of light, backward in time along the past light cone of each detector. This leads to a premature collapse, or pre-collapse, which for a beam-to-beam separation of 3 m extends over a time span of 10 ns before arrival at the detectors. Within this time span the paired wavepackets in the two beams will be incoherent. The difference between the coherent wavepackets of the conventional scenario and the incoherent wavepackets of the relativistic scenario can be tested by probing the atomic beams with a transverse laser beam crossing them near the detectors. If the paired atomic wavepackets in the two beams are coherent, the light scattered by the two beams will also be coherent and generate a standing light wave in the space between the beams, with detectable interference fringes. If the paired wavepackets are incoherent, no such interference fringes will be generated, and the distribution of the scattered light will be that of two independent dipoles. The design parameters for this test seem to lie within reach of the techniques of atom interferometry.
The many-Hilbert-space approach to the measurement problem in quantum mechanics is applied to a typical ``yes-no'' experiment relative to two branch routes corresponding to mutually exclusive propositions. First, we reformulate the notion of wave-function collapse by measurement as a dephasing process between the two branch waves of an interfering particle (from our own point of view as opposed to the conventional Copenhagen interpretation). In this way, the concept of ``wave-function collapse'' is replaced by that of a statistically defined dephasing process. One of the most important points of this paper is the introduction of an order parameter \ensuremath{\epsilon} that quantitatively describes the degree of decoherence. Its value ranges from \ensuremath{\epsilon}=0 (which describes the case in which the two waves are perfectly coherent) to \ensuremath{\epsilon}=1 (which describes the case in which coherence is totally lost); for this reason \ensuremath{\epsilon} is named the ``decoherence parameter.'' In terms of this parameter we formulate a definite criterion to judge whether an instrument works well or not as a measuring apparatus. Then, we study the interaction between a microscopic particle and a macroscopic system (a detector), by modeling the macrosystem with a linear array of complex \ensuremath{\delta} potentials, which undergo several kinds of statistical fluctuations. This leads us, under particular conditions, to the so-called wave-function collapse, which is attained in the limit \ensuremath{\epsilon}=1. We also examine in some detail which kind of elastic and/or inelastic collisions can give the wave-function collapse. Some connections with recent experimental results in neutron interferometry and quantum optics are also stressed.