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# Incompleteness of Wave Theories of Light

Hui Peng

► To cite this version:

Hui Peng. Incompleteness of Wave Theories of Light: — Non-Interference Patterns and Interference Patterns Emerging Simultaneously on Screen in Same Experiment. 2023. [https://hal.science/hal-03974531](https://hal.science/hal-03974531)

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Preprint submitted on 6 Feb 2023

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# Incompleteness of Wave Theories of Light
---
# Non-Interference Patterns and Interference Patterns Emerging Simultaneously on Screen in Same Experiment

Hui Peng, davidpeng1749@gmail.com

## Abstract

Young's double slit experiments revived the wave theory of light. The standard interpretation is that the light behaves as waves *before and after* passing through the double slit. Feynman called the double slit experiment the only mystery in quantum mechanics. By placing a convex lens at different positions, we have shown: (1) Near the diaphragm, light behaves as photons and produces a non-interference pattern; near the screen, the photons produce an interference pattern; (2) The non-interference pattern evolves to the orthogonal interference pattern gradually in the same experiment; (3) The convex lens stops the further evolution. It is heuristic for study the nature of light by showing all of three different kinds of patterns on the screen simultaneously. For this purpose, in this article, we setup three paths. The light is divided into three portions, each portion propagates along one path. Then inserting three lenses to different Zones of different paths. Experiments show that two non-interference patterns and interference pattern simultaneously emerge on the same screen.

<figure><img src="image_3.png" /></figure>

The experiments: (1) challenge the wave theories of light; (2) violate Bohr's complementarity principle; (3) provide profound phenomena for further development of optics and for study of the nature of light; (4) suggest that a complete theory should be able to simultaneously interpret the non-interference pattern, the interference pattern, and the evolution from the non-interference to the interference pattern in the same experiment.
**Keywords:** wave optics, double slit, interference pattern, diffraction pattern, non-interference pattern, evolution of patterns, cross double slit, grating, wave nature of light, particle nature of light, Bohr's complementarity principle, incomplete theory

# 1. Introduction

Historically, the study of the nature of light reached basically two concepts: wave and particle.

In 1690, Christiaan Huygens established the wave theory of light [1].

In 1704, Newton established particle theory [2], which states that light is made up of small discrete particles that travel in a straight line with a finite velocity.

In 1801, Young's double slit experiment [3] and the Arago-spot experiment [4] revived Huygens' wave theory.

In 1905, Einstein's photon theory [5] revived, in some sense, particle theory.

In 1927, Bohr proposed the complementarity principle [6] that stating that either (1) the wave and particle phenomena cannot be observed simultaneously in the same experiment or (2) if these two phenomena can be observed simultaneously in the same experiment, then the interpretations of the phenomena given by the wave theories are not complete. The wave-particle duality emerged.

In 1950s, wave-particle duality still puzzled physicists. Einstein (1951) [7] 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?". Feynman (1956) [8] called the interference pattern of the double slit experiment "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]."

In 2003, Afshar [9,10] conducted the double ping-hole experiment with a convex lens and a wire grid (Figure 1). Afshar claims that, the light exhibits wave-like behavior when going past the wire grid. But the image of two pinholes exhibits particle-like behavior after going through the lens. This behavior violates the complementarity principle. However, Afshar did not show (1) when place the lens near screen, the interference pattern emerges; (2) the phenomena of the non-interference pattern evolving to the interference pattern in the same experiment; and (3) the lens stops the evolution.

<figure><img src="image_4.png" /><figcaption>Figure 1. Afshar experiment</figcaption></figure>

There are also arguments (e.g., [11,12]) on Afshar's conclusion.

In the textbook (e.g., [14,15]), the lens is used in the model of the multi-slit experiments for establishing the math formulars to descript the pattern (Figure 2(a) and 2(b)). In the model of Figure 2(a) and 2(b), the convex lens is used to bring parallel light rays to a focal point *P* on the screen. But the textbook did not show experimental data to support the assumed role of the lens in this model.

Moreover, the textbooks state that according to Huygens's principle, light waves incident on two slits will spread out and exhibit an interference pattern in the region beyond (Figure 2(c)). The pattern is called an interference pattern. On the other hand, if no bending occurs and the light wave continue to
travel in straight lines, then no interference pattern would be observed (Figure 2(d)).

<figure><img src="image_5.png" /><figcaption>Figure 2. Textbook: (a) and (b) establishing formular of multi-slits;</figcaption></figure>

(c) Spreading of light leading to interference pattern.

(d) Absence of diffraction pattern if the paths of the light wave are straight lines

We show in this article that this model is impropriate, the real role of the lens is more complex.

Table 1 compares the roles/finding of the lens in Afshar's experiment and Textbook

<table><caption>Table 1: Comparing Afshar experiment and Textbooks</caption><thead><tr><th></th><th>Afshar [9,10]</th><th>Textbook [14,15]</th></tr></thead><tbody><tr><td>Experiment</td><td>yes</td><td>no</td></tr><tr><td>Component</td><td>lens + wire grid</td><td>lens,</td></tr><tr><td>Findings/role<br>(claimed)</td><td>(1).wire grid shows wave nature;<br>(2).image of pinholes shows particle nature</td><td>Establishing the math formulars to<br>calculate the pattern</td></tr></tbody></table>

In 2021, the double slit experiments with shields and blockers showed for the first time that, light behaves as a particle propagating along straight line, and distribute as wave (Figure below) [16-18].

<figure><img src="image_6.png" /><figcaption>Figure 3. Double slit experiments with shields and blockers showing particle nature of light</figcaption></figure>

In 2022, the photon chamber was proposed and applied to the standard experiments for the first time, such as double slit, 1D grating and 2D grating experiments.

<figure><img src="image_7.png" /><figcaption>Figure 4. Photon chamber showing patterns near diaphragm (a) and near screen (b)</figcaption></figure>

The photon chamber has been used to study the photon behavior near the detecting screen. Both the particle nature and the wave-like distribution of light are observed simultaneously in the same
experiment. The photons propagate along the straight-line trajectories and the trajectories are distributed as waves (Figure 4(b)) [19-22].

Then, utilizing three methods to study the photon behavior near the double slit/cross double slit has been proposed [23-25]. Experiments (Figure 4a) show that within a certain macroscopic distance from the double slit/cross double slit, the diaphragm-shape patterns of the double slit experiments having two equal maximum intensities near the double slit, i.e., the pattern is non-interference. Namely, by the definition, the photons behave as particles near the double slit. Furthermore, we show that when the distance increases, the non-interference gradually evolves to the orthogonal interference pattern for the first time [26]. The non-interference and the orthogonal interference patterns coexist in the same “wave” experiment.

Recently, we show the universal phenomena in the single slit, double slit, cross double slit, disc ring, 1D grating and 2D grating experiments [27]: (1) in Zone-1, the diaphragm-shape patterns are non-interference; in Zone-2, the transition patterns are non-interference; and in Zone-3, the patterns are interference; (2) the non-interference patterns in Zone-1 evolve to the orthogonal interference patterns in Zone-3 in the same experiment; (3) The convex lens stops the evolution of the patterns at where it is placed; (4) The wave theories of light are incomplete, and it is a challenge to interpret the phenomena; (5) Bohr's complementarity principle is experimentally violated. Figure 5 shows examples of evolution: patterns in Zone-1, Zone-2 and Zone-3 respectively.

<figure><img src="image_8.png" /><figcaption>Figure 5. Evolution of non-interference pattern to interference pattern</figcaption></figure>

In the previous experiments, the non-interference patterns and interference patterns created by a lens in three Zones did not show simultaneously on the screen.

It is heuristic for study of the nature of light by showing all of three different patterns on the screen simultaneously. For this purpose, in this article, we setup three paths for the light to propagate. The light coming out from the diaphragms is divided into three portions, each portion propagates along one path. Two non-interference patterns and one interference pattern created by three lenses placed in three
Zones simultaneously show on the screen in the same experiment. It is a challenge to interpret the phenomenon.

## 2. Non-interference pattern and interference pattern simultaneously emerging on screen: 3 lenses

### 2.1. Double slit experiment

**Experiment-1** (Figure 6 and Figure 7): for comparison, we perform Experiment-1 in two steps.

**(A) First step** (Figure 6):

Without lens, three standard interference patterns simultaneously emerging on the screen

**Experimental setup-1-A:** the laser light propagates along three paths and produces three interference patterns at three locations, D-1, D-2 and D3, on the screen. Beam Splitter = BS.

* Path-1: laser/diaphragm/BS-2/BS-1/D-1;

* Path-2: laser/diaphragm/BS-2/mirroe-2/D-2;

* Path-3: laser/diaphragm/BS-2/BS-1/mirror-3/D-3.

<figure><img src="image_9.png" /><figcaption>Figure 6. Experiment-1: first step</figcaption></figure>
**Observation** (Figure 6): three standard interference patterns of the same double slit are shown at D-1, D-2 and D-3 respectively. Each pattern is formed independently.

**Discussion:** the first step of Experiment-1 shows that BS-1, BS-2, Mirror-2 and Mirror-3 have no effect on the interference patterns. Experiment-1 can be described by wave optics.

## (B) Second step (Figure 7):

**Experimental setup-1-B:** with three lenses, three paths are:

Path-1: laser/diaphragm/BS-2/BS-1/lens-1/D-1;

Path-2: laser/diaphragm/BS-2/mirroe-2/lens-2/D-2;

Path-3: laser/diaphragm/BS-2/BS-1/mirror-3/lens-3/D-3;

Note that each Path is divided to Zone-1, Zone-2 and Zone-3 independently (Appendix B2):

Path-1 is divided into Zone-1/Path-1, Zone-2/Path-1 and Zone-3/Path-1;

Path-2 is divided into Zone-1/Path-2, Zone-2/Path-2 and Zone-3/Path-2;

Path-3 is divided into Zone-1/Path-3, Zone-2/Path-3 and Zone-3/Path-3.

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Figure 7. Experiment-1: second step</figcaption></figure>
When lens-1 is placed in Zone-1/Path-1, Zone-2/Path-1 and Zone-3/Path-1 respectively, it will create the diaphragm-shape non-interference pattern, the transition non-interference pattern, and the interference pattern respectively. The same for lens-2 and lens-3. The laser light respectively propagates along three paths and produces three patterns emerging at three locations, D-1, D-2 and D3, on the screen.

For convenience and without losing generality, we place lens-1 in Zone-1/Path-1, lens-2 in Zone-2/Path-2, and lens-3 in Zone-3/Path-3.

**Observation** (Figure 7): lens-1 create the diaphragm-shape non-interference pattern showing on D-1, the lens-2 creates the transition non-interference pattern showing on D-2, while the lens-3 creates the interference pattern showing on D-3.

**Discussion:** the two non-interference patterns show the particle nature of light, while the interference pattern shows the wave distribution. Namely, the particle nature and wave distribution of the light simultaneously show on screen. It is mystery that:

(1) the light needs to tell which path they are propagating along with;

(2) the light needs to tell, in which Zone, lens-1, lens-2 and lens-3 are respectively placed in.

(3) each pattern is formed independently.

The phenomenon of the second step of Experiment-1 cannot be described by wave theory of the light, and violates complementarity principle.

**Experiment-2** (Figure 8 and Figure 9): For comparison, we perform Experiment-2 in two steps.

**(A) First step** (Figure 8):

Without lens, three interference patterns and image of laser simultaneously show on the screen.

**Experimental setup-2-A:** adding BS-0 between the laser and the diaphragm and mirror-0. The light lands at D-0 on screen. The Path-0 is: Path-0: laser/BS-0/mirror-0/D-0.

**Observation** (Figure 8): the light passes through path-0, path-1, path-2 and path-3 respectively, and produces the image of the laser at D-0, three interference patterns at D-1, D-2 and D-3 respectively.

**Discussion:** the first step of Experiment-2 shows that the light behaves as particles before passing through the diaphragm, but not as waves.

It is mystery that: the light needs to tell whether it passes the diaphragm to determine how to behave.

<figure><img src="image_12.png" /></figure>
<figure><img src="image_13.png" /><figcaption>Figure 8. Experiment-2: first step</figcaption></figure>

(B) Second step (Figure 9):

**Experimental setup-2-B:** Placing lens-1 in Zone-1/path-1, lens-2 in Zone-2/path-2, lens-3 in Zone-3/path-3.

**Observation** (Figure 9): the light respectively passes through path-0, path-1, path-2 and path-3, and produce the image of the laser on D-0, two non-interference patterns on D-1 and D-2, and one interference pattern on D-3 respectively.

**Discussion:** the second step of Experiment-2 shows that the light behaves as particles before passing through the diaphragm, but not as waves. The two non-interference patterns show the particle nature of light, while the interference pattern shows the wave distribution.

It is mystery: to determine its behavior,

(1) the light needs to tell whether it will pass the diaphragm;

(2) the light needs to tell which path it is propagating along;

(3) the light needs to tell, in which Zone, lens-1, lens-2 and lens-3 are respectively placed in.

(4) each pattern is formed independently;

The second step of Experiment-2 cannot be described by wave theories of the light, and violate complementarity principle.

<figure><img src="image_14.png" /></figure>
<figure><img src="image_15.png" /><figcaption>Figure 9. Experiment-2: second step</figcaption></figure>

## 2.2. 1D grating experiment

The wave optics contains the interference of the double slit and the diffraction of the grating. Now let us study the grating. For simple, we referred both the interference and diffraction as “interference”.

**Experiment-3** (Figure 10 and Figure 11): for comparison, we perform Experiment-3 in two steps.

**(A) First step (Figure 10):**

**Experimental setup-3-A:** the experimental setup-3-1 is the same as Experimental setup-1-A, except that the diaphragm is 1D grating.

<figure><img src="image_16.png" /></figure>
<figure><img src="image_17.png" /><figcaption>Figure 10. Experiment-3: first step</figcaption></figure>

**Observation:** D-1, D-2 and D-3 show three standard interference patterns of 1D grating.

**Discussion:** The First step of Experiment-3: (1) shows that BS-1, BS-2, Mirror-2 and Mirror-3 have no effect on the produced interference patterns of 1D grating; (2) can be described by wave optics.

**(B) Second step (Figure 11):**

**Experimental setup-3-B:** the experimental setup-3-B is the same as Experimental setup-1-B, except that the diaphragm is 1D grating. Placing lens-1, lens-2 and lens-3 in Zone-1/Path-1, Zone-3/Path-2 and Zone-2/Path-3, respectively.

**Observation:** lens-1 creates the diaphragm-shape non-interference pattern shown at D-1, the lens-2 creates the interference pattern showing at D-2, while the lens-3 creates the transition non-interference pattern shown at D-3.

<figure><img src="image_18.png" /></figure>
<figure><img src="image_19.png" /><figcaption>Figure 11. Experiment-6</figcaption></figure>

**Discussion:** the two non-interference patterns show the particle nature of light, while the interference pattern shows the wave distribution. It is mystery that: to determine how to behave

(1) the light needs to tell which path it is propagating along with;

(2) the light needs to tell, in which Zone, lens-1, lens-2 and lens-3 are respectively placed in.

(3) each pattern is formed independently

The second step of Experiment-3 cannot be described by wave theories of the light, and violate Bohr's complementarity principle.

**Experiment-4** (Figure 12):

(A) **First step** (Figure 12):

**Experimental setup-4-A:** Experimental setup-4-A is the same as Experimental setup-2-A, except the diaphragm is 1D grating.

<figure><img src="image_20.png" /></figure>
<figure><img src="image_21.png" /><figcaption>Figure 12. Experiment-4: first step</figcaption></figure>

**Observation:** the light passes through path-0, path-1, path-2 and path-3 respectively, and produces the image of the laser on D-0, three interference patterns on D-1, D-2 and D-3 respectively.

**Discussion:** the first step of Experiment-4 shows that the light behaves as particles before passing through the diaphragm, but not as waves.

It is mystery that: the light needs to tell whether it passes the 1D grating to determine how to behave.

## (B) Second step (Figure 13)

**Experimental setup-4-B:** the experimental setup-4-B is the same as Experimental setup-2-B, except that the diaphragm is 1D grating. Placing lens-1, lens-2 and lens-3 in Zone-1/Path-1, Zone-3/Path-2 and Zone-2/Path-3, respectively.

<figure><img src="image_22.png" /></figure>
<figure><img src="image_23.png" /><figcaption>Figure 13. Experiment-4: second step</figcaption></figure>

**Observation:** lens-1 create the diaphragm-shape non-interference pattern shown at D-1, the lens-2 creates the interference pattern showing at D-2, while the lens-3 creates the transition non-interference pattern shown at D-3. The light propagating along Path-0 creates the image of the laser, which shown on D-0.

**Discussion:** the image of the laser at D-0 shows the particle nature of light, the two non-interference patterns show the particle nature of light, while the interference pattern shows the wave distribution.

It is mystery that: to determine how to behave,

(1) the light needs to tell whether it passes the diaphragm;

(2) the light needs to tell, after passing the diaphragm, which path it is propagating along with;

(3) the light needs to tell, in which Zone, lens-1, lens-2 and lens-3 are respectively placed in.

(4) each pattern is formed independently

Experiment-4 cannot be described by wave theories of the light, and violate complementarity principle.

## 2.3. Cross double slit experiment

### Experiment-5:

#### Experimental setup-5 (Figure 14):

<figure><img src="image_24.png" /><figcaption>Figure 14. Experiment-5</figcaption></figure>
Lens-1, lens-2 and lens-3 are placed in Zone-1/path-1, Zone-2/path-2 and Zone3/path-3 respectively.

**Observation:** lens-1 create the diaphragm-shape non-interference pattern shown at D-1, the lens-2 creates the transition non-interference pattern showing at D-2, while the lens-3 creates the interference pattern shown at D-3.

**Discussion:** the two non-interference patterns show the particle nature of light, while the interference pattern shows the wave distribution. It is mystery that: to determine how to behave:

(1) the light needs to tell which path it is propagating along with;

(2) the light needs to tell, in which Zone, lens-1, lens-2 and lens-3 are respectively placed in.

(3) each pattern is formed independently

Experiment-5 cannot be described by wave theories of the light, and violate complementarity principle.

### 3. Non-interference pattern and interference pattern simultaneously emerging on screen: 2 lenses

**Experiment-6:** tilt cross double slit experiment: three paths and two lens (for detail of cross double slit, see [28]).

**Experimental setup-6** (Figure 15):

<figure><img src="image_25.png" /><figcaption>Figure 15 Experimental setup</figcaption></figure>

Three paths are:

* Path-0: laser/BS-0/mirror-0/D-0;

* Path-1: laser/BS-0/diaphragm/BS-1/lens-1/D-1;

* Path-2: laser/BS-0/diaphragm/BS-1/mirror-2/lens-2/D-2.

Experiment-6 is performed in two situations:

* First situation: placed lens-2 in Zone-2/path-2, and lens-1 in Zone-1/path-1.

* Second situation: placed lens-2 in Zone-3/path-2, and lens-1 in Zone-1/path-1.

<figure><img src="image_26.png" /><figcaption>Figure 16: (a) Lens-1 in Zone-1/Path-1, lens-2 in Zone-2/Path-2; (b) Lens-1 in Zone-1/Path-1, lens-2 in Zone-3/Path-2.</figcaption></figure>

**Observation** (Figure 16): the diaphragm-shape non-interference patterns show at D-1 for First situation and Second situation.

Figure 16(a) shows the transition pattern emerges at D-2 for First situation.

Figure 16(b) shows the interference pattern emerges at D-2 for Second situation.
**Experiment-7** (Figure 17-20): 1D grating experiment: three paths and two lens.

**Experimental setup-7** (Figure 17): Three paths are:

Path-1: laser/diaphragm/BS-2/BS-1/lens-1/mirror-1/D-1;

Path-2: laser/diaphragm/BS-2/lens-2/mirror-2/D-2;

Path-3: laser/diaphragm/BS-2/BS-1/D-3.

<figure><img src="image_27.png" /><figcaption>Figure 17. Experimental setup</figcaption></figure>

Experiment-7 is performed in three situations:

**Experiment-7-1** (Figure 18): placed lens-2 in Zone-1/path-2, and lens-1 in Zone-2/path-1.

<figure><img src="image_28.png" /><figcaption>Figure 18. Co-existence of particle pattern, transition pattern and interference pattern</figcaption></figure>

**Observations:** D-1 shows the transition pattern; D-2 shows the particle pattern; and D-3 shows the regular interference pattern.

**Experiment-7-2** (Figure 19): placed lens-2 in Zone-1/path-2, and lens-1 in Zone-3/path-1.

<figure><img src="image_29.png" /><figcaption>Figure 19. Co-existence of particle pattern and two interference patterns</figcaption></figure>

**Observation:**
D-1 shows the interference pattern; D-2 shows the particle pattern; and D-3 shows the regular interference pattern.

<figure><img src="image_30.png" /><figcaption>Figure 20. Co-existence of two particle patterns and interference pattern</figcaption></figure>

**Observation:** D-1 shows the particle pattern; D-2 shows the particle pattern; and D-3 shows the regular interference pattern.

## 4. Summary

We have shown that the space between the diaphragm and the screen can be divided into three Zones. When placing a lens in Zone-1, the diaphragm-shape non-interference pattern shown on the faraway screen, while placing a lens in Zone-2, the transition non-interference pattern shown on the screen, and while placing a lens in Zone-3, the interference pattern shown on the screen. Namely the complete evolution of pattern from one Zone to next is shown respectively.

It is heuristic for study the nature of light by showing all of three different patterns on the screen simultaneously. For this purpose, in this article, we setup three paths for the light to propagate after it passing the diaphragm. The light coming out from the diaphragms is divided into three portions, each portion propagates along one path. We show that before inserting the convex lenses, three interference patterns are observed on D-1, D-2 and D-3 respectively on the same screen, which can be described by the wave theories of the light.

Then inserting three lenses to different Zones of different paths. Then we simultaneously observe the diaphragm-shape non-interference pattern, the transition non-interference pattern and the interference pattern on the screen. This phenomenon violates the wave theories of light.

We suggest that the particle nature and wave distribution simultaneously shown in the same experiment indicates the incompleteness of the wave theories of light, and violates Bohr's complementarity principle.

Now let us compare Afshar's experiment, Textbooks and Author's experiments

<table><caption>Table 2: Comparison of Afshar, Textbooks and Author's experiments</caption><thead><tr><th></th><th>Afshar [9,10]</th><th>Textbook [14,15]</th><th>Author</th></tr></thead><tbody><tr><td>Experiment</td><td>yes</td><td>none</td><td>yes</td></tr><tr><td>Observation/finding</td><td>(1). Wire grid indicates wave nature of light;<br>(2). Image of pinhole shows the particle nature</td><td>none</td><td>(1). Non-interference patterns and interference pattern emerge simultaneously on the screen; (2). the wave theories of light are incomplete; (3) Bohr's complementary principle is violated.</td></tr><tr><td>Pattern</td><td>One type of non-interference pattern</td><td>regular interference pattern</td><td>Two different types of non-interference patterns, and regular interference pattern</td></tr><tr><td>Type of experiment</td><td>Two pinholes</td><td>Single slit, double slit, multi-slits</td><td>Single slit, double slit, multi-slits, cross double slit, disc ring, 1D grating, 2D grating</td></tr></tbody></table>
# Appendix

## A. Postulates: precise rules of convex lens [26,27]

Hereafter, we use the term “diaphragm” to represent the single slit, double slit, cross double slit, ring, 1D grating and 2D grating. In the experiments, the light coming out of the slits has the certain pattern. However, we will show that the pattern changes when the lens is placed at the different distance from the diaphragm. The convex lens moves and thus, the patterns arriving at the input surface of the convex lens change. Namely, the light patterns arriving at the input surface of the convex lens are different. Let us define two terms, input and output surfaces, for the convex lens (Figure A1).

<figure><img src="image_31.png" /><figcaption>Figure A1. Convex lens enlarges the image arriving at its “input surface”</figcaption></figure>

We suggest the following Postulates.

**First Postulate:** the convex lens enlarges the input image that arrives at the input surface (Figure A1).

**Second Postulate:** The convex lens does not change the nature and characteristics of the input pattern.

**Third Postulate:** The convex lens breaks/stops the evolution of the patterns.

**Example-1 of First Postulate:** For a regular object, the shape of the image of the object does not change. Thus, the input image that arrives at the input surface of the convex lens is the same image of the object. Namely the image of an object is not the distance dependent.

**Example-2 of First Postulate:** For the wave experiments, the input image that arrives at the input surface of the convex lens is distance dependent and thus, the shapes of the input images are different, even in the same experiment.

**Experiment of Second Postulate:** After passing through a convex lens, the pattern keeps the same nature: e.g.,

(a) if an input pattern is a particle pattern, the output pattern is still the particle pattern;

(b) if an input pattern is a transition pattern, the output pattern is still the transition pattern;

(c) if an input pattern is an interference pattern, the output pattern is still the interference pattern.

**Example of Third Postulate:** as a consequence of Second Postulate, the input image and the output image of the convex lens are the same, and the output image keep the same nature and characteristics of the pattern as that of the input image; namely the evolution is stopped.

Experiments in reference [23-26] are based on three Postulates and experimentally confirm them.

Note that the boundaries between Zone-1 and Zone-2, and between Zone-2 and Zone-3 are not clear cut. Patterns in one zone gradually transform to the patterns in another zone.

## B. Photon chamber, zones, particle pattern, transition pattern and interference pattern

### B1. Photon chamber (Figure B1)

The photon chamber is a transparent container filled with a mixture of water and fine powder.
<figure><img src="image_32.png" /><figcaption>Figure B1. Schematics of the Double Slit Experiment with a Photon Chamber
The photon chamber has been placed near the screen [19-22], and near the diaphragms [23-26]</figcaption></figure>

## B2. Zone [26,27]

For convenience in the following discussion, let us divide the space between the source and screen into four zones (or areas) (Figure B2):

(1) **Zone-0**: between the source and the double slit, in which the pattern is non-wave, which has been experimentally confirmed [16];

(2) **Zone-1**: near the double slit, in which the pattern is the image of the diaphragm and is *non-interference*, referred to as the **particle pattern**;

(3) **Zone-2**: transition Zone, between zone-1 and zone-3, in which the particle pattern evolves to the orthogonal interference pattern, referred to as the *transition patterns* that are also the non-interference pattern.

<figure><img src="image_33.png" /><figcaption>Figure B2. Four Zones</figcaption></figure>

(4) **Zone-3**: near the screen, in which the patterns are orthogonal *interference patterns*;

## B3. Particle pattern, transition pattern and orthogonal interference pattern [16-20]

(1). **particle pattern** (Figure B3): classical particles going through a double slit will form the pattern that has the same shape as the double slit. Thus, we define the pattern of two photon tracks as “particle patterns” (or “diaphragm-shape non-interference pattern”) that indicates that the light behaves as particles in Zone-1.
<figure><img src="image_34.png" /><figcaption>Figure B3. Photon Tracks --- particle patterns in Zone-1</figcaption></figure>

Figure B3(a) and B3(b) are top view and cross-section view of the particle pattern respectively.

(2). **Transition pattern** (Figure B4):

<figure><img src="image_35.png" /><figcaption>Figure B4. Transition pattern in Zone-2</figcaption></figure>

When the particle pattern gradually transits to the orthogonal interference pattern, they are neither particle pattern nor wave pattern and thus, the light behaves not as a wave in Zone-2, called “transition patterns”.

(3). **Interference pattern** (Figure B5): Figure B5 shows the orthogonal interference pattern.

<figure><img src="image_36.png" /><figcaption>Figure B5. Interference pattern in Zone-3</figcaption></figure>

Note that the boundaries between zone-1 and zone-2, and between zone-2 and zone-3 are not clear cut.
Patterns in one zone gradually transform to the patterns in another zone.

**B4. Non-interference pattern: photon chamber placed near double slit (Zone-1)** [23-25]

Figure B6(a)) shows two photon tracks in the photon chamber, which indicates that the light propagates as photons along the straight-line photon tracks (trajectories). The pattern is non-interference. Thus, the standard double slit experiments violate the standard wave interpretations.
<figure><img src="image_37.png" /><figcaption>Figure B6. Non-interference pattern and interference pattern in same experiment</figcaption></figure>

## B5. Orthogonal interference pattern: photon chamber placed near screen (Zone-3)

Figure B7 shows the top view of the interference pattern in photon chamber-1 placed in Zone-3. Light propagates along photon tracks/trajectories, and photon tracks are distributed as waves [16-20].

<figure><img src="image_38.png" /><figcaption>Figure B7. Photon tracks showing light propagating as particles in Zone-3</figcaption></figure>

## B6. Non-interference pattern in Zone-1 evolving to interference pattern in Zone-3 [26,27]

It is difficult to utilize the top views shown by a photon chamber to study the evolution of the patterns, thus we introduce convex lens.

The diaphragms in Figure B8 show: the diaphragms of the single slit, double slit, triple slit, cross double slit, disc ring, 1D grating and 2D grating respectively.

<figure><img src="image_39.png" /><figcaption>Figure B8. Diaphragms</figcaption></figure>
It is challenging to describe the evolutions shown in experiments below. The experiments in Section B6 have the same setups as shown in Figure B9.

<figure><img src="image_40.png" /><figcaption>Figure B9. Experimental setup</figcaption></figure>

**B6.1. Single slit (Figure B11): horizontal slit of width 0.04 mm**

Figure B10 shows the standard diaphragm and pattern of a single slit.

<figure><img src="image_41.png" /><figcaption>Figure B10. Standard single slit experiment</figcaption></figure>

Placing the convex lens at different distance L from the single slit shows the evolution of the patterns.

<figure><img src="image_42.png" /><figcaption>Figure B11. Evolution of pattern of single slit experiment</figcaption></figure>

**B6.2. Double slit (Figure B13):** Figure B12 shows the standard diaphragm and pattern of a double slit.
<figure><img src="image_43.png" /><figcaption>Figure B12 Standard double slit experiment</figcaption></figure>

Placing the convex lens at different distance L from the double slit shows the evolution of the patterns.

<figure><img src="image_44.png" /><figcaption>Figure B13. Evolution of patterns of double slit experiment</figcaption></figure>

### B6.3. Tilt cross double slit (Figure B15):

Figure B14 shows the standard interference pattern of the tilt cross double slit.

<figure><img src="image_45.png" /><figcaption>Figure B14. Tilt cross double slits and its cross pattern (1)</figcaption></figure>

Placing the convex lens at different distance L from the diaphragm shows the evolution of the patterns.

<figure><img src="image_46.png" /></figure>
<figure><img src="image_47.png" /><figcaption>Figure B15. Evolution of patterns of tilt cross double slit experiment (1)</figcaption></figure>

### B6.4. Cross double slit (Figure B17):

Figure B16 shows the standard interference pattern of the cross double slit.

<figure><img src="image_48.png" /><figcaption>Figure B16. Cross double slits and its cross pattern (2)</figcaption></figure>

Placing the convex lens at different distance L from the diaphragm shows the evolution of the patterns.

<figure><img src="image_49.png" /></figure>
<figure><img src="image_50.png" /><figcaption>Figure B17. Evolution of patterns of cross double slit experiment (2)</figcaption></figure>

### B6.5. Disc ring (Figure B19) [27]

<figure><img src="image_51.png" /><figcaption>Figure B18. Disc ring and its pattern</figcaption></figure>

Figure B18 shows the standard interference pattern of the disc ring.

Placing the convex lens at different distance L from the diaphragm of the disc ring. We observe the following evolution of the patterns (Figure B19).

<figure><img src="image_52.png" /></figure>
<figure><img src="image_53.png" /><figcaption>Figure B19. Evolution of patterns of disc ring experiment</figcaption></figure>

**B6.6. 1D grating** (Figure B21): Figure B20 shows the 1D grating and its standard pattern.

<figure><img src="image_54.png" /><figcaption>Figure B20. 1D grating and its pattern</figcaption></figure>

Placing the convex lens at different distance L from the diaphragm of the 1D grating.

<figure><img src="image_55.png" /><figcaption>Figure B21. Evolution of patterns of 1D grating experiment</figcaption></figure>

**B6.7. 2D grating** (Figure B23): Figure B22 shows the 2D grating and its standard pattern.

<figure><img src="image_56.png" /><figcaption>Figure B22. Standard pattern of 2D grating experiment</figcaption></figure>

Placing the convex lens at different distance L from the diaphragm of the 2D grating.
<figure><img src="image_57.png" /><figcaption>Figure B23. Evolution of patterns of 2D grating experiment</figcaption></figure>

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[27] Hui Peng. Universal phenomena of single slit, double slit, cross double slit, triple slit, disc ring, 1D grating and 2D grating wave experiments —Non-interference patterns evolving to orthogonal interference patterns. 2023. hal-03932202

[28] Hui Peng, "Observations of Cross-Double-Slit Experiments." International Journal of Physics, vol. 8, no. 2 (2020): 39-41. doi: 10.12691/ijp-8-2-1, April, 2020.