Huyue Li

Tianyu Lang
email: tlang@ualberta.ca

A Survey: Factors to be Considered in Moving Camera's Background Subtraction

Keywords: Background Subtraction, Image processing, Computer Vision, Optical flow, Camera Calibration, Data Augmentation, Motion Detection

Given a video sequence, moving objects usually contain important information. So, detecting moving objects becomes the most significant part of various applications. In computer vision, the detection of moving objects from a video sequence based on moving objects is crucial in many visionbased applications such as action recognition, traffic controlling, industrial inspection, and human behavior identification. There is much research that has been done for detecting moving objects by the stationary camera. But a moving camera brings new challenges to moving object detection. Recently several methods for background subtraction from moving cameras were proposed. The background is often obtained by dominant single or multiple planes with a complex BG/FG probabilistic model. Some of them use bottom-up cues to segment video frames into foreground and background regions.They may fail to detect an object when the clues are ambiguous in the video. It is often due to this lack of explicit models. This article will discuss possible solutions to resolve the ambiguity in the moving camera's background subtraction problem and introduce factors that influence the BS's efficiency.

I. INTRODUCTION

In computer vision, Background subtraction is a problem that separates the moving parts from motionless parts. For instance, Given a video sequence of a bear walking in the wild, the background subtraction algorithm can separate the bear from the surrounding scene. Research within this area has a vast application field, Includes but not limited to video conferencing, video monitoring, optical motion capture, and multimedia applications. In previous research, background subtraction mainly aims at classifying each pixel into two classes, foreground class background class which represents the background scene [START_REF] Zhao | Background subtraction based on integration of alternative cues in freely moving camera[END_REF]. Traditionally, it assumes that the video sequences are from a stationary camera. Under this assumption, the moving object more likely stands out. In previous approaches, Gaussian Mixture Model [START_REF] Stauffer | Adaptive background mixture models for real-time tracking[END_REF], as a static model, can be used in the background and foreground estimation problem. This model resolves background modeling in the complex scene but it failed to model fast-changing background situations. Yan [START_REF] Yan | Variational bayesian learning for background subtraction based on local fusion feature[END_REF] et al. purposed variational bayesian learning for background subtraction based on local fusion feature, LFVBGM. Although it considered the spatial factor of the pixel, the background's low update rate limits this algorithm's performance. Recent research shows that given a video sequence captured by a freely moving camera, where the background pixels are no longer maintain their respective positions, the static model does not acquire a promising result. Because of the camera's motion, the once static scene can not be regarded as still. The background becomes another source of motion. It poses a new challenge to the background subtraction problem. Moreover, the moving background problem in static camera's background subtraction gets more challenging for moving camera. Moving background is the problem that some background objects e.g. waving trees, will move. These objects are more easily be falsely detected. To find the clues that might help to model background and foreground in the moving camera's background subtraction problem. this article will introduce factors such as camera, image segmentation, image filtering, motion detection, and image processing.

II. BACKGROUND SUBTRACTION IN MOVING CAMERA

A. Existing Work

To detect the objects, a general method via different pictures first proposed by Jain and Nagel [START_REF] Jain | On the analysis of accumulative difference pictures from image sequences of real world scenes[END_REF]. Another group of methods is background (BG) subtraction using different models, e.g., the pixel-wise Gaussian model proposed by Wren et al. [START_REF] Wren | Pfinder: real-time tracking of the human body[END_REF], the Gaussian mixture model presented by Stauffer and Grims. However, the assumption of a stationary camera limits the application of computer vision algorithms. With the growth of free-moving camera videos, the issue of detecting moving objects is a concern in recent years. Traditionally, background subtraction methods [START_REF] Elgammal | Background and foreground modeling using nonparametric kernel density estimation for visual surveillance[END_REF] attempt to achieve foreground segmentation by assuming that any motion in the video data is due to moving objects. These algorithms have led to their use in surveillance systems. The assumption of a static camera limits their use in videos by a moving camera. These methods use a homography 2D affine transform to compensate for the motion. This allows them to handle scenes that can be approximated by a plane or when the camera rotates but does not translate. Recently, several methods proposed for background subtraction from moving cameras. [START_REF] Sheikh | Background subtraction for freely moving cameras[END_REF] uses orthographic motion segmentation over a sliding window, following by sparse per frame appearance modeling to segment images.

B. Challenges in BSMC

A moving camera brings challenges to the moving object detection issue. First, object motion is mixed together in the view, where BG is moving due to the moving camera and foreground is moving due to camera motion and object motion. Second, the projection principle of the pinhole camera model is not only induced by camera translation but also affected by 3D scenes. The differences in the 2D motion of areas within the 3D scene at different depths are called 3D parallax motion. Third, many complex scenarios such as fast-moving cameras and multiple moving objects with various sizes and speeds are more complex comparing scenes from a stationary camera.

C. Exterior Factors

1) Feature detection: Feature Detection is an important factor in Background subtraction, and Panoramic feature detection shows its advantages in FD. In most cases, normal camera's field of view is 180°. Research shows that Panoramic images with 360°field-of-view have more advantages when dealing with object tracking problems. [START_REF] Fiala | Hough transform for feature detection in panoramic images[END_REF] Fiala et al. used the Hough transformation for feature detection in Panoramic images.They presents a template for object detection in Panoramic images. Meanwhile, It is designed to solve the feature detection problem in the panoramic image. while other detection methods often fails when detecting straight lines. In this paper, A new method is proposed to locate horizontal line features. the existence and location of horizontal lines are found by mapping edge pixels to a new 2D parameter space for each mirror lobe. Panoramic Hough transform is derived from the Hough transform which identifies lines or curves by creating a separate parameter space and finding groupings in this parameter space. This new method transfers the Hough transform of the plane space to the panoramic picture. The main idea of this paper is transforming the Hough transform into a certain field, in this case, the panoramic images.

2) Compression: Image compression perform a important role in Background subtraction model because it affects the calculation's efficiency. Knowing the series of image compression method is one of our major topics. Basu et al. provided a novel image compress method called variable resolution [START_REF] Basu | Variable resolution teleconferencing[END_REF]. This transform's idea comes from the animals' vision system in the dynamic world. This vision system focuses more on areas of greater interest. In this area(fovea), more detail is preserved while the outside area(periphery) requires less detail. Two advantages are shown in this method. The first one is the compression ratios are obtained by controlling the sampling. The other is that VR transforms process images using a lookup table, which will accelerate the compression procedure. Traditional VR transform has a defect that the compressed image is not rectangular. This problem is solved by using multiple scaling factors to make sure the transformed image can be mapped to a rectangle with full space utilization. Moreover, real images with multiple foveas are compressed using a weighted transformation, which avoids foveas misplacement. At last, the compression performances are evaluated based on three criteria: the compression ratio, compression time, and resulting image quality. The VR transform has promising performances in these criteria, especially in the compression time, where the method save 50 percent compression time in certain situation. In this paper, The authors proposed a fast encoding and decoding technique for lossy compression of motion capture data. Experimental results show the algorithm is much faster than other comparable methods. It can be planted in real-time online 3D games that have a large amount of data flow. They achieved perceptually guided compression of motion data by considering the human visual system when compressing 3d motions. Their method is derived from the Wavelet-Based Approach, applying a one-dimensional wavelet transform on each channel of motion data. Then they preserve a certain percentage of the wavelet coefficients while zero out the rest. After that, the quantization process follows to produce the compressed output stream. Considering the need for fast compression and availability for human perceptual factors of animation, the authors upgraded the traditional wavelet-based approach by selecting different numbers of coefficients for different channels of data based on the importance of each channel on the perceived quality of motion.

Taha, Bilal et al. managed to extract compressed 2d data from 3d models in order to decrease model training time [START_REF] Taha | Fused Geometry Augmented Images for Analyzing Textured Mesh[END_REF].3D data requires more storage compared to the 2D images. It is crucial to extract the 3D data's features while avoiding to be lossy. Automatically learned feature representations in terms of activations of a trained deep neural network have shown their superiority on many tasks using 2D RGB images, the authors purposed a novel method to deal with 3D data similarly. They proposed an approach to extend the application of deep learning solutions to 3D data given in the form of triangular meshes by exploiting the idea of establishing a map between the 3D mesh domain and the 2D image domain.Firstly, they perform a down-sampling on the facial surface derived from the full 3D face model. Then, To align the new 3D model and 2d texture, they designed an algorithm to map the texture image on the compressed mesh. In the end, they extract a group of local shape descriptors that contain most information from the original 3D model. A novel scheme is proposed to map the extracted geometric descriptors onto 2D textured images. These images are called GAIs. Each image corresponds to a 3D model and its texture. Then GAIs are fused into three-channel images called FGAIs. At last, An CNN network is implemented to extract the features of FGAIs. Eventually, the output is the compressed 3D data. These data can be used in various of CNNs in a diverse area.

Mahalingaiah, Kushal and Sharma et al. found an novel way for Image compression [START_REF] Mahalingaiah | Semantic Learning for Image Compression[END_REF]. In this paper, the author proposes a lossy compression approach developed using a CNN based model. It is a combination of existing image classification CNN network-ResNet and a classical image compression paradigm Joint Photographic Experts Group(JPEG).

Fig. 2: Image compression approach

3) Tracking: Given a video sequence, if the first frame is successfully segmented, the following mask can be obtained by tracking.Lijun Yin, Anup Basu. purposed an face tracking method with model based coding [START_REF] Yin | Integrating active face tracking with model based coding[END_REF]Bernogger, S et al. purposed an eye tracking method used in video to capture eyes' motion inspires us about the idea of POI tracking [START_REF] Bernogger | Eye tracking and animation for mpeg-4 coding[END_REF]. CG technology often extracts animation from real action from individuals. For now, we can extract the body's action easily. Automatic facial feature detection and tracking along with facial expression analysis and synthesis still poses a big challenge. Eyes,faces, as the most active organ in the human body, must be precisely detected in such work. The authors purposed an algorithm for accurate localization and tracking of eye features. This algorithm is derived using the heuristic approach, from facial feature detection and tracking algorithms in other parts of the body. They present an approach to synthesizing the eye movement by using the extracted eye features to compute the deformation of the eyes of the 3D model by mapping the model to the first frame of the face sequence then applying the extracted parameters to the 3d model. For the eye's feature extraction part, firstly, the Hough transform is implemented to detect the iris. Secondly, the deformable templates for eyelids are initialized. After getting the features' parameters, these parameters are mapped to the 3D model. Instead of using all the parameters. they use the most significant part of the eyes' feature to map the model. Finally, The eyes' movement is showed in the 3d model from the start frame sequence to the end. The experimental results show that by implementing the Hough transform. This feature extraction method is very robust against noise as well as edges that are not produced by the contour of the iris.

4) Color and Quality: Color and image Quality are intuitively a factor that separate foreground from background. Shen, Rui et al. [START_REF] Shen | Qoe-based multi-exposure fusion in hierarchical multivariate gaussian crf[END_REF] propose a novel MEF method based on perceptual quality measures that exploit both contrast and Fig. 3: Eyes key points mapping color information [START_REF] Bernogger | Eye tracking and animation for mpeg-4 coding[END_REF]. It generates images with better quality than existing ones for a variety of scenes. And here is another novelty about this method, human perceptual parameters are taken into consideration to evaluate pixel contributions more accurately. The perceived contrasts(luminance and color) are used in the MAP-HMGCRF model for pixel-level contribution evaluation. HMGCRF is a hierarchical architecture of MGCRF. It is used to efficiently estimate the pixel contributions/fusion weights(MAP) configuration on a lattice graph. The purposed method QBF beats other fusion methods in many criteria, like QAB/F and DRIVDP. The research team even invites people to evaluate the outputs of the methods. In both views, The purposed image fusion method has a good performance. Their focus on the performance is not merely in the accuracy level, but also in time level. So that they derived HMGCRF from the slower MGCRF.

5) Camera Calibration: Basu, Anup. purposed an automatic camera calibration methods to estimates the parameters of a lens and image sensor of an image [START_REF] Basu | Active calibration of cameras: theory and implementation[END_REF]. There were two main method groups:linear methods that are easier to implement but incapable of lens distortion problem and non-linear methods that have good performances in complex situations but expensive to calculate. The author purposed a new dynamic solution for camera calibration that is derived from human vision. The initial observation is human's eyes can automatically calibrate when fixed on an object. And we get the sense because our eyes rotate when looking at something. By using the small pad and tilt movements, an active camera can estimate its center. The author provided two strategies. first is to use three distinct image contours, or three different positions of the camera to estimate the error in the estimated lens center.Then these estimates can be used to estimate Focal length in pixels. Second is Using a single image contour, estimate focal length in pixels first and use the length to estimate the error in the estimated lens center. By comparison, No.2 is more robust than No.1 even though No.1 is theoretically more precise.

III. IMAGE SEGMENTATION

Image segmentation is a key step in image processing. From a mathematical point of view, image segmentation is dividing a digital image into disjoint areas. Image segmentation is also a marking process, that is, the pixels belonging to the same area have the same number.

A. Bayesian segmentation

The Bayesian classification algorithm is a classification method of statistics, it is a class of algorithms that use probability and statistics knowledge for classification. Rossol, Nathaniel et al. provided a framework for Virtual reality rehabilitation [START_REF] Rossol | A framework for adaptive training and games in virtual reality rehabilitation environments[END_REF]. A framework based on Bayesian networks for self-adjusting adaptive training in virtual rehabilitation environments is purposed. This method is proven effective according to the user's feedback.The framework can measure patients' ability changes over time with Bayesian networks to better arrange the training process. Firstly, this system is a software that can run on computers of systems. Its control system has an amazing moldability. Secondly, it uses Bayesian networks to attempt to determine patient skill levels to create immersive and custom experience for individuals. This network scientifically evaluates an individual's performance on a certain task and feedback future's training intensity. From the result evaluation, Participants commonly have a better performance in real-world obstacle courses after training on the purposed wheelchair. The mean time advantage is 81.5 seconds in the trained group compared to 104.5 seconds in the untrained group. the method to use. Sometimes, CT images do not provide a conclusive picture of surgical outcomes.To solve this problem, the authors purposed a model for kidney segmentation in CT scans. model is trained using nnU-Net which is derived from U-Net. U-Net is widely used in the field of medical image analysis such as MRI and CT scans. As the figure shows, The blue line indicates training loss and the red line indicates validation loss. The green line represents the evaluation metric, its scale is on the right axis. We can see that the overall accuracy is above 0.8 and in some cases, it can exceed 0.9. Although the model produced excellent results for kidney segmentation, the model was unable to interpret the CT scan and produced no segmentation in some cases.

IV. OPTICAL FLOW CALCULATION

A. Determining optical flow [START_REF] Berthold | Determining optical flow[END_REF] Optical flow can give important information about the spatial arrangement of the objects viewed and the rate of change of this arrangement. [START_REF] Berthold | Determining optical flow[END_REF] Discontinuities in the optical flow can help in segmenting images into regions that correspond to different objects. However, The optical flow cannot be computed at a point in the image independently of neighboring points without introducing additional constraints, because the velocity field at each image point has two components while the change in image brightness at a point in the image plane due to motion yields only one constraint. For the constrain of optical flow, the motion of the brightness patterns in the image is directly determined by the motions of corresponding points on the surface of the object. Computing the velocities of points on the object is a matter of simple geometry once the optical flow is known so the brightness should be constant.

B. Evolution of Optical Flow Estimation with Deep Networks

The FlowNet by Dosovitskiy et al. [START_REF] Fischer | Flownet: Learning optical flow with convolutional networks[END_REF] represented a paradigm shift in optical flow estimation. The FlowNet demonstrated that optical flow estimation can be cast as a learning problem. The idea of using a simple convolutional CNN architecture to directly learn the concept of optical flow from data was completely disjoint from all the established approaches. However, first implementations of new ideas often have a hard time competing with highly fine-tuned existing method. Eddy et al [START_REF] Ilg | Flownet 2.0: Evolution of optical flow estimation with deep networks[END_REF] proposed FlowNet2.0, they advance the concept of end-to-end learning of optical flow and make it work really well. The large improvements in quality and speed are caused by three major contributions. First, they focus on the training data and show that the schedule of presenting data during training is very important. Second, they develop a stacked architecture that includes warping of the second image with intermediate optical flow. Third, they elaborate on small displacements by introducing a sub-network specializing on small motions. FlowNet 2.0 is only marginally slower than the original FlowNet but decreases the estimation error by more than fifty percent.

C. Enhancement of optical flow

The conventional calculation of optical flow is the pattern of apparent motion of image objects between two consecutive frames. Sandeep and Susanta proposed an enhanced optical flow method [START_REF] Singh | Detection of moving objects based on enhancement of optical flow[END_REF]: (i) extracting frames from video and converting it into gray image. (ii) Using Gaussian filter on each frame for denoising. (iii) The novel part is that they computed the optical flow not just between the (a) current frame and previous frame OF 1 but also computed the (b) current frame and the next frame OF 2 separately.The overall optical flow of each video frame is then computed by algebraically combining the optical flow components OF 1 and OF 2 . . Finally, the segmented video output is obtained by employing morphological operation on equalized and thresholded optical flow. More details about computation of optical flow are shown below.

1) Computation of optical flow: Before computing optical flow, they applied Gaussian filter on individual frame using one-dimensional Gaussian masks. This filter can be employed to each video frame (F i ) as given below.

F smooth i = 1 σ √ 2π [ F i (x, y)e -(x 2 +y 2 )/2σ 2 dx)]dy (1)
The select three consecutive frames and put these images into above Gaussian filter. Then they get (1)currentF i (x, y), =

F smooth i (x, y) (2)previous F i-1 (x, y), = F smooth i-1
(x, y) and (3) next F i+1 (x, y), = F smooth i+1 (x, y). Then they estimate the optical flow across the frames F i-1 (x, y) and F i (x, y) as well as the optical flow across the frames F i (x, y) and F i+1 (x, y) separately. Next, they combine the optical flow in both horizontal and vertical direction respectively.

D. Object detection

After acquiring image mask by optical flow, the next step is to extract objects. In this section lists several methods for image detection and segmentation.

1) Object detection by clustered features: For extracting the objects in a image, Marcin and Dawid use blur and emboss filters [START_REF] Woźniak | Object detection and recognition via clustered features[END_REF] to extract the most important object shapes. They distinguish between three kinds of clustered shapes: below average (which means that the object is small, and it can be from the background or not important for further processing), normal size ( is important and can be further processed), and above average (which means this object is big so it can represent something not important).

2) Bilayer Segmentation: Object color, gradient, and displacement are integrated to infer the foreground layer in real time. The approaches presented in [START_REF] Criminisi | Bilayer segmentation of live video[END_REF] estimate the foreground layer from a Web camera video using different spatial and temporal priors. But they only use the color/contrast information or require special camera configuration. Frequent user interaction is generally needed for challenging video examples. In the bilayer segmentation step, depth and motion are used to handle layer occlusion and resolve color similarity. Unlike traditional solutions that weight different terms in an objective function, Guofeng et al [START_REF] Zhang | Robust bilayer segmentation and motion/depth estimation with a handheld camera[END_REF] employ a simple voting-like strategy to effectively balance the set of terms and automatically reject occasional outliers. The bilayer segmentation result is used to refine the optical flow field on the dynamic foreground, avoiding the errors caused by connecting a foreground pixel with a background one.

V. CONCLUSION

The interest in the Moving camera's background subtraction for a variety of applications. Research within this area has a vast application field, Includes but not limited to video conferencing, video monitoring, optical motion capture, and multimedia applications. In this article, Possible solutions to resolve the ambiguity in the moving camera's background subtraction problem are discussed. Factors that influence the BS's efficiency are discussed such as camera, image segmentation, image filtering, motion detection, and image processing are analyzed. . In this survey, we have discussed the factors that need consideration when solving background subtraction problems. E.g, when preprocessing video sequences, the features within each frame should preserve to provide a basis for the tracking algorithms. In terms of specific applications, Some applications such as online video conferencing require real-time background subtraction. Compression methods in multimedia implemented in video preprocessing are introduced, inspiring to increase algorithms efficiency while preserving video quality in terms of color, resolution, etc. The concept of Camera calibration estimates intrinsic and extrinsic parameters, helping to understand the parameters related to the camera's moving. On the other hand, Image segmentation, including traditional and network approaches, showed its advantages in producing binary masks for the BS problem. Besides, more and more BS algorithms using optical flow as binary mask's calculation basis. For it contains contour of moving objects and filters out the redundant texture detail.

Fig. 1 :

 1 Fig. 1: Variable Resolution transform

  Figure below showed their overall process. As for the network part. The reason they chose the Resnet model as the fundamental is that the model can be transferred as a Region of Interest extraction model with only a few configurations. Their modifications are developed on top of the Class Activation Mapping. By deleting the average pooling, flattening, and the final connected layers in the network, and replacing them with a 2D convolutional layer, 2-D depthwise convolution, and finally another convolutional layer, they can identify the regions of interests in the image. Eventually, they got a heatmap for each image showing the region of interest. After knowing the region of interest, they transferred the information to JPEG which consists of two parts -an encoder and a decoder. The encoder divides the image into blocks and applies DCT to obtain coefficients. The decoder performs the inverse operations when the image is displayed. They split the compression regions into three different areas, each of them has a different compress percentage.

Fig. 4 :

 4 Fig. 4: Bayesian network

Fig. 5 :

 5 Fig. 5: KIDNEY segmentation result


Oded Shor

Felix Benninger

Khrennikov

Andrei

Representation of the universe as a dendrogramic hologram endowed with relational interpretation

A proposal for a fundamental theory is described in which classical and quantum physics as a representation of the universe as a gigantic dendrogram are unified. The latter is the explicate order structure corresponding to the purely number-theoretical implicate order structure given by p-adic numbers. This number field was zero-dimensional, totally disconnected, and disordered. Physical systems (such as electrons, photons) are sub-dendrograms of the universal dendrogram. Measurement process is described as interactions among dendrograms; in particular, quantum measurement problems can be resolved using this process. The theory is realistic, but realism is expressed via the the Leibnitz principle of the Identity of Indiscernible. The classical-quantum interplay is based on the degree of indistinguishability between dendrograms (in which the ergodicity assumption is removed). Depending on this degree, some physical quantities behave more or less in a quantum manner (versus classic manner). Ideologically, our theory is very close to Smolin's dynamics of difference and Rovelli's relational quantum mechanics. The presence of classical behavior in nature implies a finiteness of the Universe-dendrogram. (Infinite Universe is considered to be purely quantum.) Reconstruction of events in a four-dimensional space type is based on the holographic principle. Our model reproduces Bell-type correlations in the dendrogramic framework. By adjusting dendrogram complexity, violation of the Bell inequality can be made larger or smaller.

Introduction

The last several years have been characterized by new attempts to analyze quantum mechanics from a realistic perspective [START_REF] Cohen | Realism and Causality II : Retrocausality in Energetic Causal Sets[END_REF][START_REF] Cohen | Realism and causality I : Pilot wave and retrocausal models as possible facilitators[END_REF][START_REF] Fuchs | [END_REF][START_REF] Smolin | Einstein's Unfinished Revolution: The Search for What Lies Beyond the Quantum[END_REF]. Our theory, the Dendrographic Hologram Representation of Physical Processes (DH theory), originates from the very natural foundational principle, namely, Leibnitz's principle of the identity of the indiscernible [START_REF] Leibniz | [END_REF][START_REF] Smolin | The Dynamics of Difference[END_REF].

Corresponding author: Andrei Khrennikov, Faculty of Technology, Department of Mathematics Linnaeus University, Växjö, Sweden; Andrei.khrennikov@lnu.se Email of all authors Oded Shor shor.oded@gmail.com Felix Benninger benninger@tauex.tau.ac.il

The consequences of endorsing this principle (or rather declining the Leibnitz principle of the assumption of identity in the micro/quantum world) are the rejection of ergodicity which is central in all of the current physical formulation [START_REF] Gallavotti | ensembles, irreversibility in Boltzmann and beyond[END_REF]. In turn, this process will lead to the formulation of implicate and explicate orders and the holographic principle [START_REF] Bohm | The Undivided Universe: An Ontological Interpretation of Quantum Theory[END_REF],which comes about very naturally. Moreover, we then come to the conclusion and understanding of the measurement problem as a simple apparent dynamic in which classicality suggests a bound universe. We note that Barbour's and Smolin's maximal variety paradigm [START_REF] Barbour | Extremal variety as the foundation of a cosmological quantum theory[END_REF] is a consequence of our results on the measurement process/apparent dynamics.

The DH-theory is closely related to Bohm's paradigm [START_REF] Bohm | The Undivided Universe: An Ontological Interpretation of Quantum Theory[END_REF] of implicate versus explicate orders and the holographic principle, which plays the main role in string theory and quantum gravity [START_REF] Bousso | The holographic principle[END_REF][START_REF] Susskind | The world as a hologram[END_REF]. These approaches can be coupled to number theory, to p-adic numbers. In Bohm's terminology, we start with pre-space given by the p-adic manifold. This space is considered zero dimensional (as a topological space), and it is a totally disconnected and disordered space (so, its structure matches with Bohm's heuristic image of implicated order [START_REF] Bohm | Wholeness and the Implicate Order[END_REF]). It was noted that p-adic numbers have already been widely used in physics, but as a batch of concrete models in string theory, gravity, cosmology, quantum physics, and complex disordered systems [START_REF] Parisi | P-adic numbers and replica symmetry breaking[END_REF][START_REF] Vladimirov | P-adic Analysis and Mathematical Physics[END_REF][START_REF] Volovich | p-adic string[END_REF][START_REF] Aref'eva | The wave function of the Universe andp-adic gravity[END_REF][START_REF] Freund | Adelic string amplitudes[END_REF]. Our theory aimed for the reconstruction of the whole body of physics in the very general and consistent framework. The main distinguishing feature of our theory is solid coupling with experimental data. From the data, the implicate order behind such data could be reconstructed. The latter resolves the basic mysteries of modern physics by explaining the origin of nonlocal quantum correlations and collapse of the wave function in a natural way and provided a solution for the measurement problem. At the same time, when keeping to the realistic description of nature, the points of p-adic pre-space can be treated as a kind of hidden variable. However, the transition from the zero-dimensional space of hidden variables to experimental data is not straightforward, and it includes a few steps (with growing dimension of structures at each step). Thus, starting in the number-theoretical framework [START_REF] Volovich | Number theory as the ultimate physical theory. P-Adic Numbers[END_REF], we proceed to experimental data. As indicated, the pathway from the implicate to explicate order is not straightforward. P-adic numbers have a tree-like formation (homogeneous tree with p edges leaving each vertex and one incoming edge). The first step toward explicate order is an association with each point of the p-adic space with respect to its expansion into the p-adic series. This process generates a one-dimensional string of digits such that aj=0,1,…,p-1 (for p = 2, binary strings), and geometrically, this string is a branch of the p-adic tree. The p-adic tree is the source of huge variety of dendrograms termed finite subtrees. These subtrees belong to the domain of explicate order. These subtrees are elementary structures of our theory (explicate order layer), and they play the role of elementary particles in quantum physics. It can be noted that these are two-dimensional structures. To describe interactions between dendrograms, a four-dimensional space is needed. Thus, our theory immediately determines the four-dimensional structure of physical processes. This way of representation of physical processes can be considered a special realization of the holographic principle in the very special form in which the zero-dimensional p-adic horizon encodes dynamics in three-dimensional space through their dendrogram representation, a dendrogramic hologram.

Dendrograms can have different degree of complexity, and simpler dendrograms have higher degrees of correlation. Correlations are generated not as expressions of causality, but because of repeatability of dendrograms of low complexity. At this stage, calculation of correlations, dendrograms partially lose their individuality and are treated as partly indistinguishable structures. In our approach, indistinguishability is quantified, and it is not just a simple yes/no but up to some degree (which corresponds to all possible combinations of dendrogram structures that can be constructed from N edges). Higher degrees of indistinguishability (or more accurately smaller size of phase space of all possible dendrograms constructed from N edges produces higher indistinguishability) can generate stronger correlations. Bell correlations are modeled in this way as correlation of indistinguishable dendrograms.

Planck's constant can be coupled to this degree of indistinguishability. From this viewpoint, Planck's constant can be introduced not only in quantum physics but in any sufficiently complex system as characteristics of indistinguishability between its subsystems (not only in physics, but also biology, economics, and social science).

We finally comment on coupling to Bohm-Hiley's [START_REF] Bohm | The Undivided Universe: An Ontological Interpretation of Quantum Theory[END_REF] unification of mental and physical processes based on implicate-explicate orders. The neural networks of the brain have a treelike organization. In the simplest ideal model, the brain can be represented by p-adic numbers. Conscious information processing (explicate order) is described by the quantum potential on pre-space [19]. This theoretical construction led to applications to medicine through dendrogram [START_REF] Shor | [END_REF] representation of brain electroencephalographic (EEG)-signals and reconstruction of the Bohmian quantum potential.

Reality is obscured by the assumption of ergodicity

We now introduce the foundational principle of our theory, the Leibnitz principle (hereafter called the Principle):

The identity of indiscernibles is usually formulated in a specific manner such that if, for every property F, object x has F if and only if object y has F, then x is identical to y, or in the notation of symbolic logic: ∀F(Fx ↔ Fy) → x = y, namely: if x and y are distinct, at least one property that x has and y does not or vice versa can be found.

Ergodicity is an assumption that was introduced by statistical mechanics in order to understand the "Universe" macro-state from "undistinguished" or partially "undistinguished" collections of micro-states. This assumption of "indistinguishability" of micro-states is clearly wrong and was originally formed for the construction of an adequate model to describe the "Universe" with minimal under-standing of the micro-states [START_REF] Patrascioiu | The Ergodic-Hypothesis, A Complicated Problem in Mathematics and Physics[END_REF] (see also Martineau et al. for a general discussion on coupling of ergodicity and indistinguishability [START_REF] June | Ergodicity and indistinguishability in percolation theory[END_REF]).

As we see, ergodicity is just a simplification of reality (or rather the consequence of intentionally using Leibnitz principle to make properties of the micro-states indistinguishable) in which it is known that each micro-state in the universe has at least one attribute different from the other at a given time (space and time coordinates, momentum, angular momentum, energy, spin, among others). Thus, we have to reject this simplification/as-

Two sets of raw data (black dots) are clustered into two dendrograms each containing 30 edges (B). The same data were clustered into two sets of six dendrograms each with five edges (A). Colored spheres represent the 2-adic values of an edge route in the dendrogram. When examining the correlation between the two sets of 2-adic values on the right, it can be seen that the correlations did not violate the Clauser-Horne-Shimony-Holt (CHSH) inequality. The same raw data, divided into groups of five datapoints and then clustered into a five-edge dendrogram produced pairs of 2-adic values that violate CHSH inequality.

sumption. Otherwise, a very ambiguous way is used to describe nature, for example, at our convenience an apple on a tree will be identical to an apple on the ground based on features that ignore space and time (or a tennis ball will be identical to a planet based only on the scale-free geometrical features), but in another feature choice, they will be non-identical or if we simplify and "turn our head" from distinguishable features of two micro-states we face the non-realist consequence of Leibnitz principle that an "apple" on a tree is the same "apple" on the ground and is indistinguishable (or we can make any X indistinguishable from Y even if X is a planet and Y is a tennis ball).In this sense, Bell's experiment is flawed by the simplification assumption that we consider all photons indistinguishable in all properties but its spin and all same spin photons are completely indistinguishable. Moreover, the application of ergodicity in science is flawed twice, not just in the simplification process. Basically, the process in science proceeds in the following manner:

The three-step process (TSP): 1. Detachment from contextuality all micro-states (in a more rigorous manner, a microstate from all or significant portion of its relations to the "universe" is isolated). 2. Using the above process is assumed that the microstates are indistinguishable.

It is attempted to insert these indistinguishable mi-

cro-states back into the "Universe" in which they were before step 1 became clearly distinguishable.

So, in fact a different "Universe" exists in which a "universe" of distinguishable micro-states existed before the three steps. After the three steps, a "universe" of indistinguishable micro-states exists. These three steps are applied to quantum/statistical physics, economical models (indistinguishability of buyers/sellers), social science, and biological and medical sciences.

Regarding a very complex system (the "Universe"), if these three steps are followed, correlations are immediately introduced between the sub-systems. These correlations are "side effects" of our assumption of indistinguishability and its immediate consequence of ergodicity.

Correlation emergence: methods and results

As an example, we reproduced the Bell violations of correlations from a very classical double slit diffraction experiment was reproduced [START_REF] Aspden | Video recording true singlephoton double-slit interference Video recording true single-photon double-slit interference[END_REF]. We first treated an instance frame as a random binary string of length 512, which was called string S at time t. From each S, 𝑙𝑜𝑔10(∏ 𝑓𝑖𝑛𝑑(𝑆 == 1)) was used. Thus, each frame was encoded with only one unique number 𝐴 𝑓 in which f ∈ frame 1,2...n. From each number of consecutive frames, N, the pairwise distances between each of the N 𝐴 𝑓 was calculated and a dendrogram using ward linkage was constructed. Each dendrogram was then represented in a matrix in which each row (r) represented the 2-adic expansion of the edge route in the dendrogram tree. Each 2-adic expansion was converted to a rational number using the equation:

q= -find (r=1) 2 ∑ q∈[0,1] .
Following, for each edge 𝑖, 𝑖∈1,2..𝑁, in which 𝑁 is the number of edges in dendrogram, 𝑞 𝑖 (this corresponds to step 1 and 2 in the three steps process described in section 1 as each where the unit dendrogram with N edges is our very simple electron, photon, among others) was calculated and then repeated for all consecutive events (fig. 1). We next proceeded to step three in the TSP described in section 1 by inserting these unit dendrograms back into the "Universe" in a chronological manner. The first half of these 𝑞 2-adic values were then correlated after which they were correlated with the second half. The mean and standard deviation (std) of the ratio of correlation coefficient to 2-times the standard error (SE) of the confidence bound for N edges unit dendrogram (N = 3, 4.. 980) were 2.4884±0.5775 (fig. 2C). The mean and std of the correlation coefficient for N edges unit dendrogram (N = 3, 4.. 980) were 0.1243±0.0299 (fig. 2D; first temporal half of the diffraction frames correlated to the second temporal half of the diffraction frames).

Moreover, the p-adic quantum potential field of each such dendrogram was calculated and for each edge, its quantum potential value was calculated in the following manner: In order to extract the 2-adic quantum potential double slit diffraction experiment, the estimated probability distribution function (pdf) ρ(q) of 𝑞 𝑖 with a kernel function of bandwidth was constructed: (max(𝑞 𝑖 ) -min (𝑞 𝑖 ))/𝑁

The quantum potential field (QP) was calculated according to Holland [START_REF] Holland | Computing the wavefunction from trajectories : particle and wave pictures in quantum mechanics and their relation[END_REF] as shown below:

Qp= 1 4ρ ( 1 2ρ ∂ρ ∂q ∂ρ ∂q - ∂ 2 ρ ∂q ∂q )
The quantum potential in this formulation is very trivial information measure of the dendrogram topology. Each edge was attributed with its Qp value. Qp values of the first half of the diffraction experiment to the second half figures were correlated. The mean and std of the correlation coefficient ratio to std of the cross correlation sample and of the of the correlation coefficient for N edges unit dendrogram (N = 3 .. 980) were 1.8079 ± 0.7727 and 0.0923 ± 0.0420, respectively (fig. 2A andB; first temporal half of the diffraction frames correlated to the second temporal half of the diffraction frames). Both analyses described above resulted in very good correlation when compared to the correlations with the detectors of a real bell experiment (fig. 2E).

In order to test the Bell violations present in the dendrogramic representation,the Clauser-Horne-Shimony-Holt (CHSH) inequality violations for each pair of the unique p-adic values (or rather p-adic features) that were produced from the two halves of the diffraction experiment upon the above-described transformation to dendrogramic units.

When reviewing at all data representations with unit dendrograms of increasing number of edges (N=5,6,….86) combined, we found that although most (~80% of the unique p-adic pairs) showed classical correlations, ~20% of the unique p-adic pairs showed violation of bell inequality (fig. 2F). With increasing N of dendrogram edges, the fraction of frames in the diffraction experiment (represented as p-adic numbers) that violated the CHSH inequality decreased. Thus, upon dividing the data to very simple unit dendrograms (small number of edges) very well mixed quantum and classical correlation was produced. Progressively, when the data are divided into more complex unit dendrograms (high numbers of edges), a reduction of quantum correlations and the increase of classical correlations can be observed. Thus our model implies a mechanism for the transition from the quantum to the classical domain (fig. 2G).

We note that the transition to the classical domain was a clear indication of the finite "universal" dendrogram, and upon reaching it, no quantum correlations were present as each edge was uniquely determined and different from others. Thus, this analysis supports a finite explicate universe within a bounded implicate universe. This paradigm was partially advocated by Bohm [START_REF] Bohm | Wholeness and the Implicate Order[END_REF], Smolin [START_REF] Unger | The Singular Universe and the Reality of Time : a Proposal in Natural Philosophy[END_REF], and Barbour [START_REF] Barbour | The End of Time[END_REF].

Our physical theory is supported by extended mathematical modelling of the process of percolation [START_REF] Lyons | Probability on Trees and Networks[END_REF]. Percolation is concerned with the study of random subgraphs of a given graph (G) and more specially, its infinite connected components, which are called clusters. The fundamental theorem of Lyons and Schramm [28] states that under some constraints, if several infinite clusters are produced, they all "look alike". the rigorous formulation of this theorem is presented in this study without going into a deeper explanation of mathematical notions related to it:

Theorem (Cluster indistinguishability): Let G be a graph with a transitive unimodular closed automorphism group g, a subgroup of Aut(G). Every g-invariant, insertion-tolerant, bond percolation process on G has indistinguishable infinite clusters.

In conclusion, by reproducing the Bell correlations from a "classical system", showed emergent nonlocality as a side effect of the assumption of indistinguishability/ partial indistinguishability was demonstrated. It was also shown that the transition from the "quantum domain" of very small phase space of simple dendrograms to the "classical domain" of more complex and larger phase space of complex dendrogram occurred.

Planck's constant meaning

We claim that Planck's constant is actually a measure of the indistinguishability of sub-systems (from photons  electrons  atoms heat baths), so Planck's constant will emerge for any system that is divided into indistinguishable/partly indistinguishable sub-systems.

Reflections on Relation to holographic principle and horizon

Let the whole "Universe" be represented as a giant dendrogram in which all of the information in that universe is present at the circumference with no dynamics, and inside the circle, the dynamics of information emerges (fig. 3). Now, it was suggested that Planck's constant represents a fixed amount of information bits [START_REF] Dicke | Gravitation without a principle of equivalence[END_REF][START_REF] Lloyd | Computational Capacity of the Universe[END_REF][START_REF] Lloyd | Ultimate physical limits to computation[END_REF]. This complex dendrogram with all information is contained in the edge's routes at which the edges are on the horizon (of the dendrogram). When coarse grain edges of the dendrogram are started or rather used in only a disconnected fashion, detached sub-dendrograms of the complex "Universal" dendrogram dynamics emerge.

Results. The universal dendrogram was coarsely grained by joining fixed number (fig. 4A)/random number of edges (fig. 4B). The ratios between "p-adic order of edges"/"sum of p-adic-expansion" was -4.0831±0.6331 and -4.1677±0.5071 for fixed number of edges and random number of edges, respectively, which was approximately the ratio of 2 log (h)

2 log (c) ≈ -𝟑.𝟗𝟏 .
Please note that at relatively small N (N=5,6..15) compared to the number of edges in the "Universal" dendrogram, the mean result was in agreement up to 0.6% of the 𝒍𝒐𝒈𝟐(𝒉)/𝒍𝒐𝒈𝟐(𝒄) ratio (fig. 4A).

Implicate order present in the explicit order:

Upon correlating the unit simple dendrogram (or its p-adic numbers representative of its edges) in terms of

3: Abstract description of the implicate and extrinsic order along side the emergence of Planck' s constant as a measure of indistinguishability. The "Universal" dendrogram is shown at the center of the circle with its color spheres edges describing each edge 2-adic expansion values of edge route. The outer spheres circles describe the 2-adic values of each edge in the "unit" temporal dendrogram with decreasing edge numbers N = 20, 10, 5. Each unit dendrogram 2-adic values were best-matched to its corresponding edges in the smaller (higher edge number) circle compared to its non-corresponding edges (see for example 5 spheres with rings in each circle). Planck' s constant is the measure of indistinguishability, which is a consequence of the ignorance of each dendrogram edge from the infinite sub dendrograms that continue from it (outer dotted circles).

Fig. 4: Ratio of log2(p-adic order of edge) to log2 (sum of edge p-adicexpansion) corresponded to the ratio by dividing the data to fixed number of edges dendrograms (A) and by dividing the data to a dendrograms with random number of edges (B).

Definition: C=Mean of log2(padic order)/log2(∑padic expansion)

A B -2.5 cross-correlation coefficient, it was found to be best matched to all of its corresponding components in the "Universal" dendrogram or to its corresponding components in the more complex and larger dendrograms (0.1425±0.1515) than if it was compared to the dendrogram's non-corresponding edges in the universal dendrogram or non-corresponding edges in the more complex dendrogram (0.0108±0.0098). Hence, the holographic principle in terms of implicate and explicate orders by Bohm [START_REF] Bohm | Wholeness and the Implicate Order[END_REF] was satisfied (fig. 5).

Wave function out of classical subsystems

Suppose a very large "Universe" of heat bath exists. Sufficiently equal sized large units of sub-heat baths are detached. Each heat bath state can be represented by a finite dendrogram. It can be claimed that if the sub-heat baths have the same N of particles, a finite set of dendrograms that can represent all of them and all of their possible states should exist. This finite set may be considered a "wave function" and upon measuring one particular unit of sub-heat bath, the structure of its dendrogram can be realized, and thus the collapse of the "wave function"will occur.

Notice, as already shown in section 6, that each subheat bath dendrogram was very well correlated to its corresponding edges in the dendrogram of the "universal" heat bath.

Measurement process as dynamical process in

our (based on Lee Smolin's and Julian Barbour's) maximal variety dynamics.

Consider an ensemble of dendrograms. As was shown (section 6), each unique dendrogram in the ensemble correlated best to its corresponding edges in the "universal" dendrogram or in the more complex dendrograms containing these edges.

Thus, when one unique dendrogram in the ensemble interacts with the ensemble, it will measure a maximal different unique dendrogram (such as in the maximal variety principle); in doing so, this unique dendrogram will provide much more information on the structure of the whole "universal" dendrogram .

The dynamical change in our "Unit" dendrograms was quantified by cross-correlating their p-adic representation first (fig. 7A, blue trace) to the "chronological" consecutive and next with median of the cross-correlation coefficients (0.1016). It was then cross-correlated (fig. 7A, orange trace) between all non-chronological unit

6: An abstract example of measurement of the wave function which is the ensemble of possible combinations of possible 2-adic values, which is illustrated as a collection of colored spheres between two dendrograms. The maximal variety principle suggest both dendrogram on each side of the "wave function" should be maximally different.

dendrograms, with median of the cross-correlation coefficients 0.2300, thirdly (fig. 7A, yellow trace) two pairs of random sets of N p-adic values (N as the number of edges in the unit dendrogram and each p-adic value is one value out of all possible of 2 (maximal branch length of actual unit dendrogram) combinations) were correlated to each other, with median of the cross-correlation coefficients 0.4025. For all different sizes of unit dendrograms the results are shown (fig. 7A).

The chronological unit dendrograms "chose" to interact with much different other, much different unit dendrograms (fig. 7A; blue), while the non-chronological cross-correlation between "unit" dendrogram was much more similar (orange). Moreover, random dendrograms with same edge numbers were even more similar (yellow). This finding is in accordance to the maximal variety principle [START_REF] Barbour | Extremal variety as the foundation of a cosmological quantum theory[END_REF][START_REF] Barbour | Shape Dynamics. An Introduction[END_REF] alongside the proposition made in section 7 on wave function of heat bath ensembles and the collapse of such wave function upon measurement.

When the universal dendrogram for each N frames in the "Universal" as one edge in a new dendrogram was coarse grained, it can be seen again that a clear distinction between differences in p-adic representation between consecutive chronological dendrograms compared to the p-adic representation of non-chronological dendrograms edges were found (figure 7B). Moreover, the coarse-grained chronological p-adic representation differences resembled randomized data with median values for non-chronological of 8.4681, chronological of 9.2804, randomized data 9.5731, and random binary data of 9.7620 (fig. 3B).

In conclusion, we demonstrated that the measurement process between two dendrograms occurs between two maximally different topologies in order for both topologies to experience different locations of the universal dendrogram; this process is in accordance with section 6 in which the connection of the implicate order to the explicit order was shown. In more detail, a sub-system in the explicit order was best-fitted to itself in the implicate order (more complex dendrogram). Thus, as our results in this section show, only two very different sub-systems would interact/measure with each other, which in turn reflected interactions between two very different areas of the implicate order. We emphasize that the measurement process is in fact dynamic (more accurately, apparently dynamic). These statements are well supported with our analysis in this section and section 6 above and in accordance with Roveli's (and Smolin's) relational quantum mechanics interpretation [START_REF] Rovelli | Relational quantum mechanics[END_REF].Thus we modeled the measurement process as a linkage/relational property of two sub-systems in which, in fact, the apparent dynamics unfolds/reveals different areas of the "universal" dendrogram and the implicate order. Moreover, by using em- pirical data, the validity of the maximal variety principle suggested in past studies was confirmed [START_REF] Barbour | Shape Dynamics. An Introduction[END_REF][START_REF] Smolin | Quantum Mechanics and the Principle of Maximal Variety[END_REF].

.980 (A, blue trace). CDF of correlation coefficients in the diffraction experiment between non-temporally ordered 2-adic representation of edges of dendrograms of different sizes N=5...980 (A, orange trace). CDF of correlation coefficients between randomly constructed, 2-adic representation of edges of dendrograms of different sizes N=5...980 (A, yellow trace). Coarse graining the universal dendrogram for each N=5...980 frames show differences in p-adic representation between consecutive chronological dendrograms coarse grained edges (B, blue trace) non chronological dendrograms coarse grained edges (B, orange trace) randomization of chronological sequence of dendrogram edges before coarse graining (B, yellow trace), random binary data (B, purple trace).

9.

Reconstruction of space time using the maximal variety least action principle.

In accordance with recent studies [START_REF] Smolin | The Dynamics of Difference[END_REF][START_REF] Cortês | The universe as a process of unique events[END_REF], the least action principle, which is based on the maximal variety principle [START_REF] Barbour | Extremal variety as the foundation of a cosmological quantum theory[END_REF], is a very natural consequence of our analysis. Thus, how well the chronological "Universal" dendrogram (edge by edge according to real chronological sequence) fits with the chronological time and position of detectors in the diffraction experiment that detected photons in each frame was examined.

The measure of distinguishability between all edges was encoded in the dendrogram and defined: 𝑉𝑖=2-𝑎𝑑𝑖𝑐 𝑝𝑜𝑖𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑑𝑔𝑒 𝑖𝑛 𝑑𝑒𝑛𝑑𝑟𝑜𝑔𝑟𝑎𝑚 is the measure of distinguishability of edge 𝑖 from all edges 𝑗≠𝑖

The potential energy was taken to be proportional to the negative of the measure of distinguishability or variety in Lee Smolin's and Julian Barbour's terminology [START_REF] Smolin | The Dynamics of Difference[END_REF][START_REF] Smolin | Quantum Mechanics and the Principle of Maximal Variety[END_REF][START_REF] Cortês | The universe as a process of unique events[END_REF]:

2

= kinetic E As we showed in section 8, 𝑞 𝑖𝑗 should be maximal through the chronological measurement/dynamic process. Thus: i P = ij qjk q tend to be 0 in order that ij q i=1, j=i+1 n ∑ will be maximal, and our version of the action is slightly different than in the above mentioned study [START_REF] Smolin | The Dynamics of Difference[END_REF]:

ECS S + RE S = ! N ij 2 q 2 i=1, j=i+1 n ∑ + i ! z i=1 n ∑ i P +gV
The variation by 𝑞 𝑖𝑗 yielded:

0= ! N ij q + i ! z +g ∂ i V ∂ ij q
As shown previously [START_REF] Smolin | The Dynamics of Difference[END_REF], the spacetime intervals were represented by the Lagrange multiplier 𝑧ĩ after substituting 𝑞 𝑖𝑗 and V 𝑖 into the equation above. We calculated 𝑧ĩ and correlated the result with real space and time in the diffraction experiment data [START_REF] Aspden | Video recording true singlephoton double-slit interference Video recording true single-photon double-slit interference[END_REF] (Fig. 8). We evaluated the values of the correlation coefficients divided by 2 times the standard error of the confidence bound, which yielded the value of the real chronological spacetime intervals. These values were correlated to the reconstructed intervals is in the upper 0.9922 and 0.9998 percentile of the values for randomized walk on dendrogram edges sequence correlated to the real chronological spacetime and to the real, but non-chronological, spacetime, respectively.

Differences between our and Smolin's theories

In our model, kinetic energy and momentum are consequences of measurement (that produce an apparent dynamic) between unit and unit dendrograms or edge and edge in the universal dendrogram (𝑞 𝑖𝑗 ).

Potential energy (V) is defined as a measure of distinguishability, which is encoded in the Universal dendrogram or in the coarse-grained dendrogram.

The quantum potential encodes the information contained in the topology of the dendrogram. It is possible to In contrast to Smolin [START_REF] Cohen | Realism and Causality II : Retrocausality in Energetic Causal Sets[END_REF][START_REF] Cohen | Realism and causality I : Pilot wave and retrocausal models as possible facilitators[END_REF][START_REF] Smolin | The Dynamics of Difference[END_REF][START_REF] Smolin | Quantum Mechanics and the Principle of Maximal Variety[END_REF], we emphasize that all p-adic points are always present (this emphasis is more in accordance to Barbour's [START_REF] Aspden | Video recording true singlephoton double-slit interference Video recording true single-photon double-slit interference[END_REF][START_REF] Barbour | Shape Dynamics. An Introduction[END_REF] "always present events'') and do not need to appear by a dynamic process. In contrast to Barbour, we did not require probabilities in phase space to produce the apparent dynamics.

We note that we do not need to postulate the fundamentality of time momentum and energy as in Smolin's study [START_REF] Smolin | The Dynamics of Difference[END_REF][START_REF] Smolin | Quantum Mechanics and the Principle of Maximal Variety[END_REF][START_REF] Cortês | The universe as a process of unique events[END_REF].

We note again that at the implicate order level, all dimensional points of the Universe already exist and are not dependent on referenced measurement (as the holographic principle clearly states for the horizon). Only upon the process of expansion into p-adic expansion strings does the p-adic points acquire a relational nature among themselves. So, in fact we grew from nonrelational dimensionless p-adic numbers (points) to relational information between p-adic expansions (encoded as one-dimensional information string) to dendrograms (as two-dimensional information structure) and then to dynamics (relationships) between points/dendrograms (coarse grained) that produce spacetime. It should be noted that the dimensionality of spacetime is produced by the sequence 2 -∞  2 0  2 1  2 2 . Thus, although our theory is relational, and at its core, it is a collection of non-referenced determined numbers and thus a purely number theory

Concluding remarks

The presented DH-theory is an attempt to re-establish realism in physics (including quantum mechanics) by combining it with so popular nowadays information approach to physics starting with Wheeler's [36] "it from bit" to modern quantum information reconstructions of quantum theory, such as found in a study by D' Ariano [START_REF] Dariano | Quantum Theory from First Principles[END_REF]. We formalized the Bohmian implicate versus explicate order structuring of physics via p-adic number theoretic versus dendrogram representations. The latter is of the purely information nature. All observable physical processes are realized as interactions between "universal'' dendrograms representing physical systems in which the "Universe" is modeled as a huge dendrogram; four-dimensional spacetime physics is reconstructed based on the holographic principle. Classical-quantum interplay was quantified through the degree of indistinguishability between dendrograms. Dendrograms can be considered special mathematical structures in Smolin's views on events. His least action principle was used to connect dendrogramic model with processes in physical space-time.

We restricted matching of our theory with the real experiment to the data from diffraction experiment but in fact it can be applied to any classical or quantum. In the future, we plan to perform extended analysis of the experimental data both from quantum physics and statistical mechanics to validate further data matching with our theory.

Finally, we remark that creation of the DH-theory can be considered as the important step in coupling the mathematical models developed within p-adic theoretical physics [START_REF] Vladimirov | P-adic Analysis and Mathematical Physics[END_REF][START_REF] Volovich | p-adic string[END_REF][START_REF] Aref'eva | The wave function of the Universe andp-adic gravity[END_REF][START_REF] Freund | Adelic string amplitudes[END_REF][START_REF] Volovich | Number theory as the ultimate physical theory. P-Adic Numbers[END_REF] with real experimental data and correlations produced in classical and quantum physics. We remark that p-adic theoretical physics was born within string theory. Heuristically theory of interacting dendrograms has some similarity with theory of interacting strings. We also point to the monograph [19] in that the basic model with p-adic pre-space was presented in very detail although without any coupling to real experimental data (or even the method for such coupling).

Acknowledgements

Varda and Boaz Dotan; Michal Shor; Kalman Shor

figure 1 :BFig. 1 :

 11 figure 1: three steps produce quantum correlation

Fig. 2 :

 2 Fig. 2: Emergence of quantum correlations and transition to classicality is a consequence of the TSP: A significance of correlation between two sets of quantum potential values versus number of edges in unit dendrogram. Values were calculated for each unit dendrogram with fixed number of edges (N = 3,4,5….980) after which two temporal halves of quantum potential values were then cross-correlated . B correlation coefficients of the two sets of quantum potential values versus number of edges in unit dendrogram. C significance of correlation between two sets of p-adic values versus number of edges in unit dendrogram. Values were calculated for each edge route in unit dendrogram (as described in section 3). D correlation coefficients of the two sets of p-adic values versus number of edges in a unit dendrogram. , fraction of CHSH values versus CHSH values. CHSH values were calculated for each possible pair of p-adic values obtained from two halves of the diffraction data divided by unit dendrograms of size N = 5 .. 86. The proportion of CHSH values violating CHSH inequality versus number of edges in a unit dendrogram.

Figure 3 :

 3 Figure 3: explicite to implicite order and the emergance of planck constant

  figure 4: emergence of planck constant and speed of light

Figure 5 :Fig. 5 :

 55 Figure 5: implicate order encoded in explicate order

Figure 6 :

 6 Figure 6: measurement of the wave function according to maximal variety principal

Fig.

  Fig. 6: An abstract example of measurement of the wave function which is the ensemble of possible combinations of possible 2-adic values, which is illustrated as a collection of colored spheres between two dendrograms. The maximal variety principle suggest both dendrogram on each side of the "wave function" should be maximally different.

Figure 7 :

 7 Figure 7: CDF of correlation coefficients in the diffraction experiment between temporally ordered 2-adic representation of edges of dendrograms of different sizes N=5...980 (A, blue trace). CDF of correlation coefficients in the diffraction experiment between non-temporally ordered 2-adic representation of edges of dendrograms of different sizes N=5...980 (A, orange trace). CDF of correlation coefficients between randomly constructed, 2-adic representation of edges of dendrograms of different sizes N=5...980 (A, yellow trace). Coarse graining the universal dendrogram for each N=5...980 frames show differences in p-adic representation between consecutive chronological dendrograms coarse grained edges (B, blue trace) non chronological dendrograms coarse grained edges (B, orange trace) randomization of chronological sequence of dendrogram edges before coarse graining (B, yellow trace), random binary data (B, purple trace).

figure 7 :

 7 figure 7: wave function measurement and emergent dynamics from maximal veraity

  RE S =gV 𝑞 𝑖𝑗 = 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑓𝑟𝑜𝑚 𝑉 𝑖 𝑡𝑜 𝑉 𝑗 𝑖,𝑗∈1…𝑛=𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑑𝑔𝑒𝑠 𝑖𝑛 𝑑𝑒𝑛𝑑𝑟𝑜𝑔𝑟𝑎𝑚 ,𝑖≠𝑗 is a measure of distinguishability between edges 𝑖 and 𝑗 The energy momentum relationships are shown below: ij 2 q

Figure 8 :Fig. 8 :

 88 Figure 8: reconstruction of space-time intervals