Novel Mystery of Double Slit/Cross-double Slit Experiments--- Curved Interference Pattern andInterference Pattern Depending on Orientation of Diaphragm

Young’s double slit experiments express the mystery of quantum mechanics. To explore the mystery, varieties of the double slit and cross-double slit experiments were performed. In this article, we show novel mystery phenomena: (1) the characteristics of the interference patterns of the double slit and cross-double slit experiments depend on the orientation of the diaphragm used in the experiment, specifically on which axis the diaphragm rotates around, the rotating angle and how to rotate, clockwise or counterclockwise; and (2) in the cross-double slit experiments, the characteristics of the interference patterns also depend on which slit photons pass through; (3) unlike the regular double slit and regular cross-double slit experiments, in which the interference patterns are along the straight line, the interference patterns of the double slit/cross-double slit experiments can be along curve, and the curvatures depend on the orientations of the diaphragms of the double slit/cross-double slit. Those experiments show more mysteries of the double slit and cross-double slit experiments and provide comprehensive data for developing/testing a theoretical model. the light perpendicular to the of the diaphragm of the double the We study the orientation-dependence of the interference pattern of a


Introduction
Young's double slit experiment was first performed in 1801 [1] [2], which, 100 years later, led to wave-particle duality. Feynman called it "a phenomenon which is impossible […] to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery [of quantum mechanics]." [3]. Moreover, the nature of photons truly 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].
In the double slit experiments, the characteristics of the interference pattern is determined by three factors, wave length, the spacing between two slits and distance between the double slit and screen, as Note that (1) there is only one factor related to the parameter of the diaphragm of the double slit, the spacing d; (2) the fringes of the interference pattern distribute along a straight line.
We raise a question that whether there are other factors related with the diaphragm affect the characteristics of the interference pattern? To answer this question, we emphasize that in the standard double slit experiments, the light beam is perpendicular to the plane of the diaphragm of the double slit.
We are interested in how the interference patterns vary with different orientations of the diaphragm of double slit/cross-double slit. We study the orientation-dependence of the interference pattern of a standard double-slit/cross-double slit rotating around the x-axis, y-axis, and z-axis, respectively.
Recently, to further explore the mystery, it has been shown that the photons' behaviors/interference pattern depend on the orientations of the diaphragms of the double slit and cross-double slit [5] [6].
We show in detail the dependance of the interference patterns on the orientations of diaphragms.

Apparatus
The experiments utilize a laser source, the diaphragms of the double slit ( Figure 1a) and cross-double slit (Figure 1b), a protractor ( Figure 1c) and a screen/detector.

Figure 1 Apparatus
We study the orientation-dependence of the interference pattern of the double slit and cross-double slit rotating, either clockwise or counterclockwise, different angles around the X, Y and Z-axis.

Rotating Diaphragm of Double Slit Around Y-Axis
The schematic of the experimental setup for the double slit experiments is shown in Figure 2.

Figure 2 Schematic drawing of apparatus
The double-slit-AB is in the y-z plane, slit A and slit B are along the z-axis, its normal vector is along the x-axis and points to source, the spacing between slits A and B is "d", and photons travel along the negative x direction. Its interference pattern is shown in Figure 3a.

Rotating Diaphragm of Double Slit Around Y-Axis Continuously (Appendix-1 Video)
Let us place the double slit at the position that the double slit rotates 75 0 from the original orientation counterclockwise. Turning on the laser source, we observed the curved interference patten.
Then rotating the double slit clockwise continuously and the curved pattern continuously change, the curvature of the interference pattern becomes larger and larger. We reach a position that the laser light is perpendicular to the plane of the double slit, which we referred as the original position, and at that position, the curved interference pattern becomes the regular straight interference pattern. Then continuously rotating the double slit clockwise. The interference pattern starts to curve again but to the opposite direction. See the attached Appendix-1 Video.

Rotating Diaphragm of Cross-Double Slit Around Y-axis (A) Three Double Slits Crossing
Experiment-3 ( Figure 5, 6,7,8): the left of Figure 5 shows the diaphragm rotating 0 0 around Y-axis, referred as the original orientation. Its interference pattern is the right of Figure 5.  Photons' behavior depend on which slit they passing through.

Discussion:
We show that the interference patterns of the double slit and cross-double slit depend on the orientation of the diaphragms. It is a challenge to interpret the experiments consistently.

(B) Two Double Slits Crossing
Experiment-4 ( Figure 9, 10, 11): the left of Figure 9 shows the diaphragm rotating 0 0 around Y-axis, referred as the original orientation. Its interference pattern is the right of Figure 9.

Figure 9 Schematic drawing of cross-double slit and its regular interference pattern
Note that the spacing between slit-A and slit-B is different with that between slit-C and slit-D. The schematic drawing in Figure 9 is not to scale.
Rotating the cross-double slit-ABCD clockwise around Y-axis with different discrete angles.  It is a challenge to interpret the phenomena/experiments consistently.

Rotating Diaphragm of Triple Slit Around Y-axis
The rotations of the diaphragm of the triple slit create the curved interference patterns. Figure 12 Interference patterns of rotating triple slit Figure 12b shows the pattern curved towards right attributed to the counterclockwise rotating of the diaphragm. Figure 12c shows the pattern curved towards left attributed to the clockwise rotating of the diaphragm.

Rotating Diaphragm of Single Slit Around Y-axis
Rotating 75 0 of the single slit, there is no noticeable curve of the pattern ( Figure 13).

Figure 13
Patter of single slit rotating 75 0

Rotating Diaphragm Around Z-axis: Orientation-dependence of Interference Pattern
Let us derive the Orientation-dependence Formular first. Then we use the formular to describe the experiment and show that the experiments support the derived formular.

Derivation of Orientation-dependence Formular of Interference Pattern of Double Slit
The schematic drawing is the following. The path difference between two waves passing through two slits respectively is ( ( + ) ). The requirement of the interference of two waves is that the path difference satisfies the following relation, where, ) ≈ , where, ( ) ) = * ! ! + ! ! , "y" is the position of a bright/dark fringe from the zeroth-order fringe.

Rotating Diaphragm of Double Slit Around Z-axis
The experiments show the orientation-dependence of the interference patterns visually.

Experiment-5:
(A) The diaphragm at the original orientation and its interference pattern (Figure 15).    (E) The diaphragm rotates 75 0 from the original orientation ( Figure 19).

Original orientation
The experimental results support the derived formular (6) describing the orientation-dependence of the interference patterns. Figure 13 to figure 19 show the evolution of the interference pattern varying with angles of the double slit rotating around the z-axis.

Rotating Diaphragm of Cross-Double Slits Around Z-axis
The cross-double-slit apparatus consists of source, cross-double-slit, protractor and screen.       Observation: the interference patterns perpendicular to the double slits created them, respectively. The angles between the slits are the same as that between the interference pattens.

Experimental
Step-1 (Figure 31): the diaphragm rotates 60 0 around Z-axis. Observation (Figure 31): the angles between two interference patterns are smaller than that shown in Figure 30. The distances between two fringes of the same patten are larger than that in Figure 30. Observation (Figure 32): the angles between two interference patterns are smaller than that shown in Figure 31. The distances between two fringes are larger than that shown in Figure 31.

Conclusion:
The interference patterns created by two tilt double slits tend to get closer to Y-axis. The triple slit rotating around Z-axis causes the same phenomena that the distances between fringes are extended.

Rotating Diaphragm of Double Slit Around X-axis
We consider two situations: discrete and continuous rotations.
First situation: discrete rotation.
Experiment-9: (Figure 35). Rotating the double-slit clockwise a discrete angle, for example, 15 degrees. Figure 35 Double-slit rotates around x-axis at angle and its pattern Observation: the pattern rotates the same angle clockwise and without change.
The interference pattern is perpendicular to the double slit.

Second situation: continuous rotation
The combination of the interference patterns of the cross-double slit experiments with different number of double slits crossing to each other suggests that the double slit and cross-double slit have rotation-invariance around their normal vectors. If we increase the number of double slits that intersect at the same spot, the shape of the intersection will approach a circular disc, each slit is tangent to the intersection and forms disc-3, which is surrounded by ring-2 ( Figure 36a). The zero-order fringe rotates at the same spot, and forms a bright fringe 0, while the rotation of its first-, second-and third-order fringes form bright rings 1, the dark fringes form dark rings 2, and so on (Figure 36b).
.(a) (b) Figure 36 Predicted pattern of continuously rotating double slit/cross-double slit around x-axis The above prediction has been tested by the experiment.
Experiment-10 ( Figure 37): The apparatus consisting of obstacle 1 with a hole, disc 3 placed at the center of hole-2 and leaving ring-shape gap 2 between disc 3 and obstacle 1 (Figure 37).

Summary
We show the novel mystery phenomena of the double slit/cross-double slit/triple slit experiments: (1) the characteristics of the interference patterns of the double slit/cross-double slit/triple slit experiments depend on the orientation of the diaphragm used in the experiment, i.e., the rotation around which axis, the rotation angle, the rotation direction (clockwise or counterclockwise); and (2)  In the regular double slit experiment, photons only need to know one factor that is whether there is a double slit. Now photons also need to know more factors: the orientation of the double slit. In the cross-double slit experiments, photons also need to know which slit they passed through.

A-2 Novel Multi-Slits for Exploring Mystery of Cross-Double Slit
To explore the mystery of the double slit/cross-double slit, we designed novel multi-slits in which a cross-double slit is divided into different parts/sections to test the function of each part/section of the cross-double slit. The widths of every slit are the same, and spacing between all of vertical double slits and between all of horizontal double slits are the same.
The normal Cross-double-slit-ABCD, the double slit-AB perpendicular to the double slit-CD, is shown in Figure A1 for the purpose of comparation.
The novel multi-slits are shown below.
Novel Multi-Slits-1: Figure A2 shows the intersection of the cross-double slit-ABCD. The purpose: testing whether the intersection of the cross double slit creates the whole interference pattern.  Novel Multi-Slits-4 ( Figure A5).