Double Slit to Cross Double Slit to Comprehensive Double Slit Experiments

Young’s double slit experiments, which represent the mystery of quantum mechanics, have been interpreted by quantum probability waves and de Broglie-Bohm’s trajectory/pilot waves. To study in detail, the double slit experiments are extended to the cross double slit experiments. We argue that an interpretation must be able to explain all of the double slit and cross double slit experiments consistently. To test the interpretations, the comprehensive double slit experiments have been performed, which challenge both the wave interpretation and the trajectory interpretation. The cross double slit experiments and comprehensive double slit experiments provide a new tool for studying the mystery of double slit, wave-particle duality, complementarity principle, wave theory and trajectory theory. In this article, we review the cross double slit experiments and comprehensive double slit experiments, and report new experiments.


Introduction
The Young's double-slit experiment was performed in the year 1801 [1] [2], which, 100 years later, led to wave-particle duality. Feynman called it "a phenomenon […] has in it the heart of quantum mechanics. In reality, it contains the only mystery [of quantum mechanics]" [3]. Moreover, the nature of photons really puzzled Einstein. He wrote to M. Besso: "All these 50 years of conscious brooding have brought me no nearer to the answer to the question: What are light quanta?" [4].
To explore the nature of photons further, Young's double-slit experiment was modified to whichway-double-slit experiment by observing which slit a photon would pass through. Once which slit a photon passing through is determined, the wave-like interference pattern disappears. The operational definition of "wave/particle" stands for "ability/inability to create interference" [5] [6] [7]. A variety of which way double slit experiments have been proposed and performed, such as double-double-slit experiment [8].
In 1978 and 1984, Wheeler proposed a series of thought experiments, delayed-choice experiments, which was designed to resolve the fundamental issues in quantum physics [9]. The standard interpretation of the MZI-delayed choice experiment states that photons made "retroactive decision", which challenges the causality. A variety of delayed choice experiments have been proposed and performed, such as quantum eraser delayed choice experiment [10] [11].
Recently, for studying the mystery of double slit experiments and testing the wave interpretation and trajectory interpretation, the cross-double-slit experiments [12] [13] and comprehensive double slit experiments [14] [15] [16] have been proposed/performed. In this article, we review the cross double slit and comprehensive double slit experiments, and report new experiments.

Cross Double Slit Experiments
For studying the double slit experiments and wave-particle duality, the cross-double-slit       Combination of Figures 2.9, 2.10 and 2.11 suggests that double-slit and cross-double-slit have the rotation-invariance around its normal vector. If we increase the number of double-slits that are intersected at the same spot, the shape of the intersection will approach to a circular disc. To rotate either a double-slit or cross-double-slit around its normal vector, each slit is tangent to the intersection and forms disc-3 that is surrounded by ring-2. The final pattern can be obtained by either rotating the double-slit apparatus during experiment or by applying an apparatus of disc-3 with a diameter that is equal to the spacing between two slits, and ring-2 of the width that is equal to the width of a single-slit.
We argue that Figure 2.12 indicates that double-slit and cross-double-slit have the rotationinvariance around its normal vector.  Conclusion: it is a challenge to consistently interpret the experiments in Section 2.1.

Double-Slit Crossing Triple-Slit Experiments
A typical triple slit and its pattern show below.       [20]. When the photon is detected, the interference pattern disappears.
We argue that, if we shift the focus from detecting photons to observe the patterns, then to cover a slit of a double slit apparatus is equivalent to use a single slit apparatus, namely, *) Observing photons at a slit is equivalent to block photons passing through the slit; *) To block photons passing through a slit is equivalent to cover that slit; *) To cover a slit is equivalent to using a single slit instead using double slit and covering one   The significant difference is that for the standard which way experiment, they must go through slit "B", while for which way cross double slit experiment, if photons do not go through slit "A", photons can go through either slit "B" or "C" or "D".        Conclusion: it is challenge to interpret the experiments in Section 2.3 consistently.

Delayed Choice Cross Double Slit Experiments
The standard MZI version of the delayed choice experiment is shown below. The standard interpretation is the following: Figure 2.41 (a) shows an open-MZI, photons are detected by D1 and D2, and behave the same, as particles, from the time of its emission to the time of its detection.    Conclusion: Rule-1 is proved. Photons detected on both D1 and D2 have the same particle nature.
Namely the particle nature is not changed by either reflected by BS or passing through BS.  Conclusions: Rule-2 is proved. Removing the slide, experiment-2.37 becomes experiment-2.36, which implies that it is the slide that affects photons' behavior. Combination of Rule-1 and Rule-2 shows that BS does not affect the behavior of a single input beam of photons, which leads to Postulate-1.
We perform two experiments to test Postulate-1 (Experiment-2.38 and Experiment-2.39).  Conclusion: D1 shows the particle nature of photons. Based on Rule-1, photons passing through BS1 towards slide behave as particle as well, namely before arriving at slide, photons behave as particle. Postulate-1 is proved. On the other hand, D1 and D3 show interference patterns. Particle nature and wave distribution coexist in "the same experiment". For studying wave-particle duality and complementarity principle, let's define the term, "the same experiment", as: when there is "only one source" emitting light/photon, regardless configurations of experimental apparatus, the experiment is defined as the same experiment.  (1) Based on Rule-1, photons passing through B1 and B3 behave as particle, thus, before arriving slide-2 and slide-4, photons behave as particle respectively.

Modified Delayed Choice Double Slit Experiments
(2) Slide-2 and slide-4 convert photons' particle behavior (before arriving) to wave distribution (after passing through) respectively. The slide determines the behavior of photons only when photons passing through it, but not behavior before passing it. Thus, slide-2 and slide-4 can be removed any time during experiment, which makes the delayed choice experiments easier to be performed.
(3) Particle nature and wave distribution coexist in the same experiment.
(4) There is no retroactive decision phenomenon. The standard interpretation of the delayed choice experiments is challenged at the macroscopic level.
It would be interesting to perform the experiment by emitting photons one at a time.

Modified-MZI Version of Delayed Choice Experiments
In the interpretations of delayed-choice experiments, photon is described as a "person" to "decide" its own behavior. To explore the interpretations further by MZI configurations, we combine the MZI and     Postulate-2 predicts that in zone-3, each fringe is formed independently and can be formed partially.
Indeed, the experimental results of testing the prediction strongly support postulate-2.
Postulate-1 have been confirmed experimentally in Section 2.4.
There are multi-experiments testing postulate-2 from different perspectives. An analogy is a breakwater that break water waves.

Experiments
The experiment is performed in two setups. The experiment is carried out in three setups. Note that the picture was shot from the "Entrance" to the detector so that the interference pattern and apparatus show on the same picture and thus, Entrance looks wider.    Postulate-2 is experimentally confirmed.
Some of photons form fringes on blockers, meanwhile, some of photons are distributed like partial of a wave interference pattern on the detector.

Experiments Testing Trajectory Theory by Blocking Half of Interference Patterns
The purpose of the experiments below is to test the behaviors of light/photons in Z-3 near the detector. In the following experiments, the blocker is 128 inches away from the diaphragm of double slit. To avoid losing generality, we perform experiments with a cross-double slit [16]. First, let us show the interference pattern of a cross-double slit experiment (Figure 3.13) without a blocker.       Note that all experiments in Section 3.3 are observed by the naked-eye, and there are no noticeable changes in the brightness of fringes. We cannot determine whether the trajectories cross.
We have shown that the 2D interference patterns are created independently and partially; and that, in Zone-3, photons move along trajectories and behave as particles. according to the practical definition of wave/particle. Bohm's theory has the same statement [22].
The observation of the regular which way double slit experiment is shown in Figure 3.21, where an "observer" is set behind slit A (denoted by dashed slit A).            Although each photon travels along its own trajectory, it is challenge for the trajectory theory to interpret the which way 2D cross double slit experiments described in Section 3.5.

Experiments Testing Postulate-2 with Shields and Blocker.
We have shown that, on the one hand, longitudinal shield(s) do not disturb the interference pattern        (2) Observation (Figure 3.38): Photons pass through two triangle-shaped cuts and form exactly the same triangle-shaped patterns on the detector, which shows the particle nature of photons, namely photons move along straight lines. Note that photons are not directly from the source; they are just pass through a double slit and were supposed to behave as waves. The conclusion is that photons behave as particles.
Meanwhile, some of photons are distributed like a partial wave interference pattern on the detector.

Testing Postulate-2 with 2D-cross-double slit
Without losing generality, we perform comprehensive double slit experiments with two crossdouble slit that consist of five and six double slits crossing at the same spot. Each of double slit creates an interreference pattern independently.   Conclusion: 2D patterns are created independently and partially. Only particle can behave in such way. Postulate-2 is confirmed experimentally: in zone-3, photons move along predetermined trajectories to form fringes and thus, behave as particles.

Experiment
It is a challenge to consistently interpret the experiments in Section 3. Shield-2

Experimental Test of Trajectory
Right Pattern particle (Figure 4.1a, extracted from reference [26]) [27] [28] and for photons (Figure 4.1b, extracted from reference [29]) cannot cross. We notice an implicit prediction that there is a triangle-shaped area behind the double slit, in which there is no trajectory (Figure 4.1a and 4.1b), namely, no particle/photons pass through this area (hereafter referred both as "predictions"). To our knowledge, no experiment has either been performed or proposed to test these two predictions.
In this Section, we perform more comprehensive double slit experiments that test above mentioned two predictions of computer simulations of de Broglie-Bohm trajectory theory in Z-2.

Experiments Testing Trajectory Theory: Shield Contacting Diaphragm of Double Slit
We observed that the height of the triangle is longer than the spacing between two slits. Thus, we test whether there are photons in the triangular area using shield (Figure 4.2). Experimental Setup: making a shield (gray colored) and gluing it to an object (Figure 4.3b). The shield is 2.8 mm long, 9.5 mm wide, and 0.12 mm thick. Note that the drawing is not to scale. Place the shield along the virtual centerline and contacting the double slit at the position between two slits, where the spacing "d" between two slits is 1 mm (Figure 4.3a). Figure 4.3c is the picture taken from the right side of the shield, and Figure 4.3d is the picture taken from the left side.
Note that the "contact" is macroscopic "contact", namely there are actually "gaps" between the shield and the double slit. More precise apparatus is designed in Appendix.
Then turning on the laser.
Observation: the light from the right-side slit shins on the right side of the shield (    It is reasonable to assume that, without the shield (Figure 4.8b), the behavior of light/photons in and near the triangular area would be the same as that with the shield (Figure 4.8a).  (1) For experiment-4.3, the wavelength is 650 nm, the distance from the double slit to one end of the shield is one inch, the spacing between two slits is 0.25mm, and the cross-section, thickness, of the shield is 0.3 mm. Substituting into Eq. (1), we obtain , namely up to the 4 th bright fringes are all blocked by the cross section of the shield.

Experiment-4.4:
In previous comprehensive double slit experiments, we placed the blocker(s) to block individual fringes. According to Bohm's theory, photons' trajectories from different slits cannot cross, namely, blocking one side of fringes should not affect the fringes formed by photons passing through other slit.
We place the blocker to block more, even half, of the fringes simultaneously. The purpose is to test, when we place the blocker to block the portion of the interference pattern, what will happen to the remaining portion of the interference pattern.
Experimental Setup (Figure 4.10): using the regular double slit apparatus. The blocker is placed one inch from the slide. The spacing between two slits is 0.25mm.  On the other hand, each remaining fringe becomes dimmer.
According to the Bohm theory, the blocked photons from the left slit would make no contribution to the right-side fringes. The experimental observations show the opposite; and thus, the trajectory theory is challenged. Note that there is a "tail" on the left side of the zeroth-order-fringe, which is due to the diffraction of the edge of the blocker [30].
Conclusion: it is a challenge to consistently interpret the experiments in Section 4.

Appendix: Novel Diaphragm for Double Slit Experiments
In preliminary Experiment-4.1 and Experiment-4.2 of Section 4.2, the shields contact the diaphragms of the double slit ( Figure 4.3 and 4.6). However, the "contact" is a macroscopic-type contact, i.e., actually, there are "gaps" between the shield and the diaphragm of the double slit.
For further double slit experiments, we design new apparatuses to eliminate the gap between the shield and the double slit, they are one piece now ( Figure A1) [16].