T Mavroeidakos

V Chaldeakis
email: vchaldeak@cosmote.gr

Threat Landscape of Next Generation IoT-enabled Smart Grids

Keywords: Smart Grid, IoT, Cloud Computing, Threat Landscape

The Smart Grids (SGs) consist of an emerging paradigm that pave the way for the power grids modernization and seek novel techniques for improving the transmittion and distribution of power to consumers, as well as achieving end-to-end real-time governance. Thus, the prospect of SGs are to behave intelligently, through the deployment of advanced technologies, applications and standards. A subset of such technologies and applications consists of Software Defined Netowrks (SDNs), Cloud Computing (CC), Machine-to-Machine (M2M) communications, Big Data applications, Internet-of-Things (IoT), 5G and wireless standards such as IEEE 802.15.4g and IEEE 802.16.1. The SGs, the CC and the IoT paradigms convergence lie on satisfying the clients needs, improving efficiency and in the same time maintaining overall control. However, the coupling of diverse technologies under a unified architecture raise multiple interdependencies which pose new challenges, ranging from the reliability of the whole power system to novel cyber-security risks. This paper sheds new light in the overall definition of the threat landscape that emerges by the convergence of CC and IoT in a SG.

Introduction

Electricity is the most valuable resource of social structure supporting the operation of health care, banking, means of transportation and the provision of public utilities such as natural gas and water. Electricity is generated on large power plants consisting of steam, hydro and combustion turbines which require energy sources such as water, oil, coal, gas and thereupon the produced energy is routed into an interconnected high voltage transmission network. Following its generation, it is transferred through a series of distribution transformers to the consumers. The power transmission network has progressively developed for over a century, from the original design of local low-voltage DC networks, to AC three-phase high voltage networks deployed over Supervisory Control and Acquisition (SCADA) System and eventually to modern massive interconnected networks with various voltage levels and complex electrical components such as substation transformers and Phasor Measurement Units (PMUs). Throughout the power grids evolution, several industrial challenges have been dealt in view of provisioning power to the customer premises fast and uninterruptedly. In light of the SGs technological innovations and novel communication links amongst its architectural components, the security risk is increased due to the expansion of the points of interests from the attackers perspective.

Nowadays, the complexity of power grid is multifaceted and depends on the interconnection of heterogeneous electrical and electronic components, the integration of Renewable Energy Resources (RES), the Energy Management System (EMS), the Distribution Management System (DMS), the Intelligent Electronic Devices (IEDs) and systems operations. Furthermore, in view of encountering periods of peak demand, the Transmission System Operator (TSO) balances supply and demand across the transmission network by deploying automation systems. The automation and control capabilities of transmission and distribution networks, add a new layer of complexity that burdens the power grid with new challenges concerning reliability and performance.

By exploiting the emergence of telemetry technologies, the already deployed conventional static networks controlled so far by SCADA systems, evolve into modern and dynamic smart grids. The SGs' telemetry technologies, lead to the deployment and control of energy sources such as wind, solar, geothermal, which pave the way for disburdening the strained power grid suffering from serious problems such as power outages, voltage drops and overloads, leading to greatly reduce power quality. To this end, SGs are comprised of many moving parts leading to the challenge that the exposure of a component may result to cascading failures across the power grid.

The correlation of SDNs, CC, M2M, IoT, 5G and Big Data on SGs, as well as the insufficiencies residing on previous conventional cyber-security models that are utilized on power grids compel the industry and the relevant national authorities to advise upon safeguards and best practices to encounter vulnerabilities and security risks. On the grounds that the power grid's role is very important for the social structure, the SGs' security safeguards and measures, should be treated with caution and be placed high in the priority hierarchy set by the organizational operations. To this end, security challenges, threats and requirements should be classified side by side with performance and functionality issues prior the SG's deployment.

Background

In recent years there has been growing interest in threat analysis and security model propositions in support of SG infrastructure. The current threat landscape of SGs is largely addressed by standards and solutions both by the academia and the industry, as described below. However, the next generation SGs are characterized by the addition of new technologies that introduce novel threats.

A systematic study on cyber security guidelines for smart grid was conducted by the National Institute of Standards and Technology (NIST) aiming to close the gaps, scrutinizes security requirements, a framework for assessing risks, an evaluation of privacy issues, and additional information about strategies to protect the modern power grids from their attack surface. This study was later reviewed due to the emergence of novel technologies and standards [START_REF] Lee | Guidelines for smart grid cyber security[END_REF]. Following the initial approach of NIST, the European Network and Information Security Agency (ENISA) puts forward 10 recommendations, in order to resolve concerns about cyber-security in modernized power grids consisting of a SGs [START_REF] Mattioli | Communication network interdependencies in smart grids[END_REF]. These recommendations provided practical advice aimed at improving current initiatives, raising awareness, developing new countermeasures and good practices with scope to reduce barriers, which are encountered amidst the sharing of information intelligence. More work on securing SGs has been carried out by ENISA in [START_REF]Smart grid security certification in europe challenges and recommendations[END_REF][START_REF] Ruland | Smart grid security-an overview of standards and guidelines[END_REF], where the cyber security certification process of the SG is analysed and several aspects of it are scrutinized such as, architectural guidelines, recommendations and good practices.

In a cutting edge survey, Mahmud et al. [START_REF] Mahmud | A survey on smart grid metering infrastructures: Threats and solutions[END_REF], presented a classification of attacks on the communication networks of SGs and henceforth proposed a security framework for the SG's metering infrastructure which consists of a variety of requirements that ensure effective preservation of the Confidentiality, Integrity and Availability (CIA) triad. A more recent survey, Tong et al. [START_REF] Tong | A survey on intrusion detection system for advanced metering infrastructure[END_REF], highlights the role of Intrusion Detection Systems on Advanced Metering Infrastructure (AMI) by analysing the attack surface, penetration techniques and consequences in AMI components. Then, security recommendations and guidelines are proposed on the basis of designing an IDS architecture suitable for AMI.

According to [START_REF] Humayed | Cyber-physical systems securitya survey[END_REF], a cyber-physical security framework that incorporates Cyber-Physical System (CPS) aspects into the security aspects is proposed for the protection of SGs. The framework captures the methodology behind attacking scenarios and their consequences on the physical domain of a CPS and accordingly effective controls and solutions can be deployed to eliminate cyber-physical attacks. With regards to [START_REF] Chin | Energy big data security threats in iot-based smart grid communications[END_REF], a breakdown of security and energy big data analytics issues is carried out with scope to determine critical attacks based on malware targeting metering data and big data from the distributed databases. Over and above this, Pour et al., argue in [START_REF] Pour | A review on cyber security issues and mitigation methods in smart grid systems[END_REF] about the vulnerabilities of SG infrastructure (i.e. the lack of standards and regulations), different kinds of attacks in the system (i.e. false data injection attack) and countermeasures (i.e. IP fast hopping mechanism) to increase the security level of the future power grid.

Next Generation Smart Grid Apparatus

Smart Grid Infrastructure

The SG apparatus upon which the core idea of this paper is illustrated, has developed on the basis of the Smart Grid Architecture Model (SG-AM) framework which is the reference architecture of SG use cases. The SG-AM framework consists of five interoperability layers namely, Business, Functions, Information, Communications and Components. Each one of these layers address different aspects of SG and encompass services, operations, assets and devices in support of the power grid's functionality.

Across the SG, the main architectural element is the communication infrastructure which interconnects the interoperability layers of the SG-AM framework architecture and comprises of four networking sectors as indicated in Figure 1 the core or backbone network, the middle-mile or backhaul network, the last-mile or access network and the Premises Area Network (PAN). The four interconnected sectors are supported by various technologies and substantially aggregate the communication infrastructure of SG.

-The core network supports the link between the numerous substations and the seats of public utilities.

-The backhaul network bridges data concentrators to the AMI with distribution automation systems and control centers related to the operation of public utilities. This sector provides broadband following a cost-efficient economy concerning its deployment and operation. In addition, the communication paths through which operational and sensorial data traverse, must be flexible and uninterrupted. To that end, this network may be owned and managed by operators and may utilize wired or wireless technologies such as Wi-Fi, WiMAX and mobile networks such as LTE and 5G.

Cloud Computing Infrastructure

By virtue of the distributed nature of SG's communication infrastructure and the multiple data generation sources, it is required a highly scalable and elastic computing infrastructure in order to support the deployment of industrial applications. The CC infrastructure is the best computing structure in the case of SG due to the fact that provides scalable storage, appropriate processing capabilities for data analysis and cost-efficient services throughout the SG's operation. Moreover, this paradigm can handle the data generation rhythm of sensors, actuators and IoT devices in general.

The most useful applications in the context of SG, are big data analytics and remote control of components such as PMUs. The CC paradigm offers ideal conditions for the deployment of big data applications. The integration of CC applications in the operations of SGs, is comprised by development of big data Application Programming Interfaces (APIs), implementation of interoperability standards that will link the already deployed computing infrastructure with the CC applications, as well as configuration of the SG's components.

IoT Infrastructure

Cellular technology has been continually evolving with the aim of unlocking new possibilities to the industry. The advent of the Low-Power Wide-Area Network (LPWAN) technologies serve the IoT paradigm; therefore this paradigm's integration in a SG architecture is supported by LPWAN equipment and protocols.

The IoT infrastructure resides at the edge of the SGs and consists of four layers [START_REF] Ali | Internet of things security, device authentication and access control: a review[END_REF], namely the perception, the network, the processing and the application. The network layer is the SG's PAN, which facilitates governance over IoT devices deployed in houses. Across the SG, the intermediate link between the IoT devices and the SC controller, is the smart meter. Beyond the time-based consumption data, billing interval data and data related to the clients' usage history resulted by the smart meters operation, the IoT devices generate huge streams of data daily. Thus, many measurements and logs may be concentrated in Data Lakes residing in the backend CC environment.

Threat Landscape

Smart Grid Attacks

The attack vectors and threats that emerge in the Next Generation SG apparatus can be classified in the following categories as illustrated also in Figure 2: [START_REF] Mattioli | Communication network interdependencies in smart grids[END_REF][START_REF] Wang | Cyber security in the smart grid: Survey and challenges[END_REF][START_REF] Sanjab | Smart grid security: Threats, challenges, and solutions[END_REF][START_REF]European Union Agency for Network and Information Security (ENISA): Adhoc & sensor networking for m2m communications -threat landscape and good practice guide[END_REF][START_REF] Nazir | Assessing and augmenting scada cyber security: A survey of techniques[END_REF][START_REF] Pidikiti | Scada communication protocols: vulnerabilities, attacks and possible mitigations[END_REF]:

-Physical Layer Attacks: The interference channel is one of the most effective ways to initiate a physical-layer DoS attack, especially for wireless communications. The intruders only need to connect to communication channels where it is easy to unleash DoS attacks on the physical layer. In SGs, where wireless technologies are used, the main objective is to achieve wireless interference.

-Side Channel Attacks: M2Ms are located in accessible locations that attackers can easily access and perform attack on the channel side. These attacks could be based on any power consumption, timing information, error or electromagnetic leakage and allow the recovery of secret keys. -Software Modification and Malwares: Software modifications can be performed by an attacker, or even a malicious user, affecting the expected operation of M2M devices. Malicious users can do so in order to reduce the amount of fees they have to pay. But the impact of these threats is even worse when it comes to e-health or automotive applications. -Destruction or Theft of the M2M Device or the Universal Integrated Circuit Card (UICC): M2M or UICC devices can be easily stolen because they are placed in accessible locations. However, this is somewhat solved by welding the integrated UICC known as eUICC to the M2M. -Logical Attacks: Targeting the correct operation of the system without changes to the device software when dealing with M2M communications, an intruder may forge the identity of a back-end server, an M2M device or a gateway, and so on. These attacks can lead to significant economic and human losses. For example, an attacker who manages to forge a smart gauge identity can make his owner pay for the charges himself without his permission. In the case of electronic health, such attacks can pose a threat to human life. -Relay Attacks: An attacker can carry out an attack and disguise an entity to make others believe it is in the sender or receiver area. This attack can target the device, gateway or network domain. -Jamming Attacks: This attack is channel-based in which the legitimate signal is overwhelmed by noise [START_REF] Tazi | Review on cyber-physical security of the smart grid: Attacks and defense mechanisms[END_REF]. -Data Link Layer Attacks: In this layer, the attackers target the exchange of intra-operational information.

-Privacy Attacks: Because of the deployment models followed on M2M architecture concerning the utilized equipment in its device domain, malicious users can invade M2M devices and thus infer user habits, but also tamper with Personally Identifiable Information (PII). -Data Modification and False Information Injection: The data may be violated during transport, as well as in a resting state of an application's device or server. Taking into account the case of e-Health or e-Call, modyfying the measured values of information tracking can endanger the lives of people. On the other hand, in some applications, the introduction of false data can cause financial losses. -Bad Data Injection Attacks: This attack aims at making inferences of the power network topology from the correlations in line measurements using independent component analysis. The inference results can then be utilized to design stealth attacks [START_REF] Huang | Bad data injection in smart grid: attack and defense mechanisms[END_REF]. -Selective Forwarding / Interception: An attacker can track and delay or intercept the received packets. The impact of such a threat depends on the content of rejected packages. Such attacks are launched from the network infrastructure, but they could also be carried out by the M2M gateway. -Application Layer Attacks: These attacks focus primarily on damaging the bandwidth of communication channels. However, over and above their primary goal, they also intend to exhaust computing resources, such as CPU or Input/Output (I/O) bandwidth. Moreover, attacks against integrity and confidentiality generally occur in the application layer and enable the manipulation of information. Attacks to data integrity can be considered less violent than DoS. These attacks attempt to disclose data in order to disturb the exchange of information across the SG.

-Social Network Misinformation: This attack focuses on diffusing misinformation in social networks in order to damage the SG's operations as illustrated in [START_REF] Pan | Threat from being social: Vulnerability analysis of social network coupled smart grid[END_REF] by leveraging the Misinformation Attack Problem in Social-smart grid (MAPSS).

Cloud Attacks

The most daunting CC threats are associated to data loss, interception and tampering with the network traffic, insecure Application Programming Interfaces (APIs), malicious insiders, hijacking of virtualization technologies and threats against the end-services confidentiality, integrity and availability. Due to the existence of multiple abstraction layers on any given CC infrastructure, the cloud consumers acquire access in-depth for the purpose of the end-services utilization. In the context of this paper, the cloud consumers are the personnel of the SG provider but also the IoT devices. To this end, the attackers leverage a huge number of attacks, aiming to target different points of the CC infrastructure. Despite the large number of attacks against CC, the impact and the risk of successful penetrations in SG assisted by CC and IoT, is greater.

Overall, following the initial stages of any attack (e.g. passive and active information gathering), the attackers are in position to coordinate their penetration methodology by exploiting vulnerabilities across the whole infrastructure. To this end, new attack vectors emerge due to the conjunction of these technologies and as a result the threats' impact on the end-service, is hazardous.

A taxonomy of threats [START_REF] Islam | A classification and characterization of security threats in cloud computing[END_REF][START_REF] Khan | Cloud security threats and techniques to strengthen cloud computing adoption framework[END_REF] targeting the industrial environment of SGs where CC solutions are utilized is the following :

-SQL Injection: In this attack, malicious queries target the production database aiming to gain unauthorized access. -Malware Injection: In this attack, malicious code is implanted in legitimate software or systems aiming to give remote Control & Command to the attacker in order to control services and extract data. -XML Signature Wrapping: The SOAP protocol facilitates communication amongst different systems. The communication is secured by XML signatures where vulnerabilities can be exploited. -Deep Packet Inspection: In this attack, analysis of internal and external network traffic is performed with scope to acquire sensitive network information about the data circulating the network architecture. -Denial of Service: In this attack, the policies of CC services concerning scalability and elasticity are leveraged maliciously in order to misuse the CC resources and exhaust them. -Eavesdropping: In this attack, network information is captured and malicious actions such as interruption of network packets propagation to reach their destination.

IoT Attacks

The security issues and concerns surrounding the IoT, occur as a consequence of threats emerging due to unaccounted vulnerabilities and 0-day exploits extended both on hardware and software, sensitive data circulating the IoT architecturte (i.e. clinical health data, spatial data) and weak communication paths facilitating interconnection of sensors and devices through a diversity of protocols and standards.

The majority of IoT attacks are based on the weaponization of Proof of Concepts (PoC) exploits with malicious payloads against known vulnerabilities. Many vulnerabilities are left unpatched due to performance, cost related issues, or because of the fact that the implementation of proper security controls on IoT devices is a costly process requiring part of the limited energy resources.

The most dangerous IoT attacks, focusing on vulnerabilities laying on the paradigm itself, are classified in the following categories:

-Malware: is malicious software that hijacks the sensors' functions and spreads in the IoT infrastructure in order to gather operational intelligence, which can be leveraged to exploit critical components linked to the IoT devices such as smart meters. Having integrated IoT devices in the SG, several malwares capable to damage both the clients and the SG provider. For example, the IoT reaper was a malware botnet that gathers and assesses information in order to use ideal exploits with regard to the discovered vulnerabilities. Already infected two million devices and growing at rate of 10,000 new devices per day. -Botnet: is a network of infected devices spread across the world and controlled remotely from a master following the client-server architecture. For example, the Mirai was a self-replicating and self-propagating botnet worm based on telnet scanning, which launches Distributed Denial-of-Service (DDoS) attacks and targets Linux-based embedded systems such as IP cameras, home routers and home automations simiral to those, which are met in an industrial environment such as SGs, where the same principles are applied. Since its source code publication, many blackhat groups utilize it in the midst of malware development. The Botnets can be utilized by the master not only for DDoS, but also to achieve cascading failures in the SG, leading even to physical damages (i.e. stuxnet). -Ransomware: targets data storage both in the IoT and CC paradigm and blocks access to the collected data by encrypting them. A good example of ransomware is CryptoWall that generates and stores a key on the backend IoT infrastructure and then sends the key to Command-and-Control (C&C) server which is behind a proxy chain and controlled by the attacker. Moreover, the Curve-Tor-bitcoin Locker (CTB-Locker) uses AES encryption by compression step using ZLib and communicates with the C&C server through proxy websites (Tor2web).

Having overviewed these attacks, there are several threats that emerge by the adoption of Narrowband 5G and the mesh topology of IoT devices. A synopsis of threats and attacks is presented.

-Physical Layer Attacks on 5G: In this layer several threats exist [START_REF] Lichtman | 5g nr jamming, spoofing, and sniffing: threat assessment and mitigation[END_REF], which exploit vulnerabilities of the physical channel over which the communication paths between devices are established.

-Selectively Jamming PSS/SSS: Similar to the Long-Term Evolution (LTE) standard, the 5G also consists of the Primary Synchronization Signal (PSS) and the Secondary Synchronization Signal (SSS) which can be interrupted by a jammer transmitting fake signals with greater power immitating those. -Sniffing and Spoofing Vulnerability of the PBCH: The Physical Broadcast Channel (PBCH) is utilized by the System Information Block (SIB) messages, which overlay information about the power thresholds responsible for the handover process of a device from a cell to another. The information that the SIB messages carry, is transmitted unencrypted, leaving it vulnerable to malicious acivities. --Network Attacks [START_REF] Deogirikar | Security attacks in iot: A survey[END_REF] :

-Traffic Analysis: In this attack, network information is captured and analysed in order to acquire useful information about the operation of the IoT architecture. -Sleep Deprivation: This type of attack targets to the power reserves of wireless nodes by keeping them busy with useless request which are broadcasted recursively by the perpetrator. -Sybil: This attack lies on exploiting the identity verification process of Wireless Sensor Networks (WSNs) where the malicious node disguises its identity with multiple others.

-Resource Consumption: In this attack, the main aim is to degrade the network's latency and capacity by broadcasting Route Request (RREQ) packets.

-Key Reinstallation Attacks (KRACKs): In this series of attacks, the propagated network packets are captured and then are decrypted [START_REF] Vanhoef | Key reinstallation attacks: Forcing nonce reuse in wpa2[END_REF].

Most of WiFi devices are vulnerable of installing zero encryption key, this is feasible due to a fault in the WPA2 protocol. Upon this fault, the KRACKs are enabled during 4-way handshakes of IoT devices with the network Access Point (AP). -Man in the Middle: In this attack, interception of data flowing from a source to a destination is implemented by the attacker in order to read them and extrack useful knowledge. In several occasions, the attacker focuses on modifying the data in-transit from the source to the destination. -Kr00k: This attack leverages a bug in order to decrypt the WiFi network traffic [START_REF] Eset | A serious vulnerability deep inside wi-fi encryption[END_REF]. Many IoT devices are equiped with Broadcom and Cypress wifi chips, which are affected by this bug. According to this bug, a short wifi disconnection, called disassociation, is enforced by the attackers leading the devices to reset the session key which can be all-zero.

Conclusion and Future Work

This work scrutinizes the threat landscape that exist in next generation SGs. The main point to focus is that there is a huge number of attack vectors against a next generation SG due to its architectural components and its distributed functionality. By summarizing the majority of threats, proper security guidelines would be possible to be set up in order to protect modern applications on top of SGs. Future reaserch should focus on analysing the majority of these attacks in depth for the purpose of formulating ideal security measures that will mitigate this landscape.

-

  The last-mile network is supported by Neighborhood Area Network (NAN) and the Field Area Network (FAN), as well as the AMI. This network facilitates the collection of data from smart energy meters and their propagation to the concentrators back to the control center of AMI. -The PAN is implemented by Home Area Networks (HANs), which are based on IEEE 802.15.4, IEEE 802.11 and PLC standards. The HAN regulate several components such as thermostats, HVAC (heating, ventilation and air conditioning), smart devices, lighting control, home automation and PHEV / EV (Plug-in Hybrid Electric Vehicle / Electric Vehicle).

Fig. 1 .

 1 Fig. 1. Smart Grid Infrastructure

Fig. 2 .

 2 Fig. 2. Smart Grid Attacks


Developments of Research on Grating Experiments A1. Recent Developments of 1D-Grating Experiments A2. Recent Developments of 2D-Grating Experiments

Screen-2

Introduction

The interference patterns of the 1D-double slit and 2D-cross-double slit experiments have been studied experimentally [START_REF] Peng | Double Slit Experiment Still Has Much to Offer (1) -2D-Cross-Double Slit Experiments[END_REF][START_REF] Peng | Double Slit Experiment Still Has Much to Offer (2): Extended-Which-Way Experiments-Violating Complementarity Principle[END_REF][START_REF] Peng | Double Slit Experiment Still Has Much to Offer (4): New Double Slit Experiments Violating Wave Description[END_REF][START_REF] Peng | Double Slit Experiment Still Has Much to Offer (5): -New Double Slit Experiment Violating Bohm's Trajectory Theory[END_REF][START_REF] Peng | Double Slit Experiment Still Has Much to Offer (6): Curved, Expanded and Inclined Interference Patterns -Dynamic Double Slit/Cross-Double Slit Experiments[END_REF][START_REF] Peng | Double Slit Experiment Still Has Much to Offer (8): -Photons Behaving as Particles Create Curved Interference Pattern[END_REF]. The universal phenomena of the curved, expanded and inclined interference patterns were observed. Recently, the orientation-dependence of the diffraction patterns of the 1D-grating and 2D-grating experiments have been studied [START_REF] Peng | Double Slit Experiment Still Has Much to Offer (7): Particle Nature of Photons, Normal Diffraction Pattern and Curved Diffraction Pattern Emerging in Same Grating Experiment[END_REF][START_REF] Peng | Double Slit Experient Still Has Much to Offer (9): -Continuously Curved Diffraction Patterns of 2D-Cross-Grating Experiments[END_REF][START_REF] Peng | Non-Uniform, Curved, Expanded and Inclined Diffraction Pattern of 1D-Grating Experiments -Rotating Grating Around Three Axes[END_REF][START_REF] Peng | Non-Uniform Diffraction Pattern of 2D-Cross-Grating -Rotating Grating Around Three Axes[END_REF]. The simultaneously non-uniform spacing, curved, expanded and inclined diffraction patterns emerged in the same grating experiment.

Indeed, the characteristics of the transmission diffraction patterns depend on the orientations of the grating.

The common gratings contain transmission gratings and reflective gratings.

We show novel phenomena: (1) a transmission grating produces simultaneously the reflective diffraction patterns and transmission diffraction patterns respectively, namely it plays simultaneously dual-roles of a transmission grating and a reflective grating; [START_REF] Peng | Double Slit Experiment Still Has Much to Offer (2): Extended-Which-Way Experiments-Violating Complementarity Principle[END_REF] the so produced reflective diffraction patterns are orientation-dependent, as well as the so produced transmission diffraction patterns; (3) the reflective diffraction patterns and the transmission diffraction patterns have the same characteristics.

Indeed, in the experiments, the dual-grating reflects the partial of the incident light, i.e., playing the role of a reflective grating, we refer the so produced diffraction pattern as "reflective pattern"; while the partial of the incident light passing through the grating, i.e., the dual-grating playing the role of a transmission grating, we refer the so produced diffraction pattern as "transmission pattern". To increase the efficiency, one may coat reflective layers on the reflective surfaces and anti-reflective layers on the transmission surfaces.

In this article, we defined "Dual-Grating": a transmission grating that plays roles as both a transmission grating and a reflective grating simultaneously in the same experiment.

"Dual-Pattern": both a transmission pattern and a reflective pattern produced by a dual-grating simultaneously in the same experiment.

Two Speculates

Next let us consider a normal transmission grating (Figure 1). Now we raise questions:

(1) whether the orange surfaces between slits play any role in the experiment; if so,

(2) whether the orange surfaces reflect the incident light beams; if so,

(3) whether the reflected light beams produce a diffraction pattern; if so, (4) whether the so produced reflective diffraction pattern has the same characteristics as that of the transmission diffraction pattern produced by the same transmission grating.

To answer the above questions, we propose two speculates:

First speculate: a dual-grating functions as both a transmission grating and a reflective grating simultaneously in the same experiment; the transmission function produces the transformation pattern, while the reflective function produces the reflective pattern.

Second speculate: the so produced two patterns have the same characteristics. Namely the equations describing two patterns (dual-pattern) have the same form.

In this paper, First speculate and Second speculate are confirmed experimentally. Namely the dualgrating does play a dual-role of a reflective grating (shown by orange surfaces) and a transmission grating (shown by green surfaces) (Figure 2).

! ! ! " d ! ! ! " d transmission grating ! ! ! " ! ! ! "# d transmission grating ! ! ! "$ . (a) (b) (a) (b) (a) (b) ! ! ! " d ! ! ! " d transmission grating ! ! ! " ! ! ! "# d transmission grating ! ! ! "$ Grating normal A B C Tilt Grating ! ! ! " O D ! # O' d
Figure 2a shows a dual-grating, while Figure 2b shows a rotated (tilt) dual-grating. In both Figure 2a and 2b, the orange surfaces and orange arrows represent the reflection phenomena, while the green surfaces and green arrows represent the transmission phenomena.

Experimental Setup

We set the slits of a transmission grating (dual-grating) in three orientations (Figure 3). Figure 4b shows that the dual-grating CW rotates at an angle, for example, 45 0 , for simplicity.

Although the screens show the phenomena more visualizable, the setups utilizing CCD/telescopes, instead of screen, provide more accurate data.

Experiments: dual grating of spacing of 100 lines/mm

In First steps of Experiments of Section 4 and Section 5, we use the setup of Figure 4a, i.e., the light normally incidents on the dual-grating, the reflective patten show on screen-3. In Second steps (CW rotates the dual-grating) of Experiments, we use the setup of Figure 4b, the light obliquely Screen-3

incidents on the dual-grating, the reflective patterns show on screen-2. In both steps, the transmission patterns are always on screen-1.

Experiment-1 (Figure 5 to 8): dual-grating of spacing of 100 lines/mm with vertical slits

First step:

Experimental setup (Figure 5): Utilizing the experimental setup (Figure 4a) and the dual-grating with vertical slits (Figure 3a). The dual-grating produces both transmission pattern and reflective pattern simultaneously.

Not that in the First steps of Experiment-1, -2 and -3, we adjust slightly the position of the dualgrating, so that all of the reflective orders shown on screen-3.

Second step:

Experimental setup (Figure 7): Utilizing the experimental setup (Figure 4b) and the dual-grating of spacing 100 lines/mm with vertical slits (Figure 3a).

Conclusion:

the dual-grating does produce both the transmission pattern and the reflective pattern respectively. Namely the dual-grating does function as both the transmission grating and the reflective grating simultaneously in the same experiment. The transmission pattern and the reflective pattern have same characteristics. Namely, attributing to the rotation of the dual-grating with vertical slits around the Z-axis, both patterns are expanded.

The expanded transmission pattern produced by a rotated transmission grating have been observed before [START_REF] Peng | Double Slit Experiment Still Has Much to Offer (7): Particle Nature of Photons, Normal Diffraction Pattern and Curved Diffraction Pattern Emerging in Same Grating Experiment[END_REF][START_REF] Peng | Double Slit Experient Still Has Much to Offer (9): -Continuously Curved Diffraction Patterns of 2D-Cross-Grating Experiments[END_REF]. The Novel phenomenon is that the reflective patterns produced by the dualgrating are expanded also. The First speculate and the Second speculate are confirmed experimentally for the dual-grating with vertical slits.

Experiment-2 (Figure 9 to 12): a dual-grating of spacing of 100 lines/mm with horizontal slits

First step:

Experimental setup (Figure 9): Utilizing the experimental setup (Figure 4a) and the dual-grating of spacing 100 lines/mm with horizontal slits (Figure 3b). The dual-grating produces transmission pattern and reflective pattern simultaneously.

Second step:

Experimental setup (Figure 11): Utilizing the experimental setup (Figure 4b) and the dual-grating of spacing 100 lines/mm with horizontal slits (Figure 3b). The curved transmission patterns produced by a rotated transmission grating have been observed before [START_REF] Peng | Double Slit Experiment Still Has Much to Offer (7): Particle Nature of Photons, Normal Diffraction Pattern and Curved Diffraction Pattern Emerging in Same Grating Experiment[END_REF][START_REF] Peng | Double Slit Experient Still Has Much to Offer (9): -Continuously Curved Diffraction Patterns of 2D-Cross-Grating Experiments[END_REF]. The novel phenomenon is that the reflective patterns produced by the dual-grating are curved also. The First speculate and the Second speculate are confirmed experimentally for the dual-grating with horizontal slits.

Experiment-3 (Figure 13 to 16): dual-grating of spacing of 100 lines/mm with tilt slits

First step:

Experimental setup (Figure 13): Utilizing the experimental setup (Figure 4a) and the dual-grating of spacing 100 lines/mm with tilt slits (Figure 3c). The dual-grating produces transmission pattern and reflective pattern simultaneously.

Second step:

Experimental setup (Figure 15): Utilizing the experimental setup (Figure 4b) and the dual-grating of spacing 100 lines/mm (Figure 3c). The transmission pattern and the reflective pattern have same characteristics. Namely, attributing to the rotation of the dual-grating, both patterns are curved, expanded and inclined.

The curved, expanded and inclined transmission patterns produced by rotating a transmission grating have been observed before [START_REF] Peng | Double Slit Experient Still Has Much to Offer (9): -Continuously Curved Diffraction Patterns of 2D-Cross-Grating Experiments[END_REF][START_REF] Peng | Non-Uniform, Curved, Expanded and Inclined Diffraction Pattern of 1D-Grating Experiments -Rotating Grating Around Three Axes[END_REF]. The novel phenomenon is that the reflective patterns produced by the rotating dual-grating are curved, expanded and inclined also. The First speculate and the Second speculate are confirmed experimentally for the dual-grating with tilt slits.

Experiments: dual-grating of spacing of 500 lines/mm

To show the universality of the dual-grating plays two roles simultaneously, we use a dual-grating with 500 lines/mm to perform the same experiments as that in Section 4.

The experiments in this section are performed with the experimental setup in Figure 4 and5.

Experiment-4 (Figure 17 to 21): dual-grating of spacing of 500 lines/mm with vertical slits

First step:

Experimental setup (Figure 17): Utilizing the experimental setup (Figure 4a) and the dual-grating of spacing 500 lines/mm with vertical slits (Figure 3a). Experimental setup (Figure 19): Utilizing the experimental setup (Figure 4b) and the dual-grating of spacing 500 lines/mm with vertical slits (Figure 3a). Attributing to the rotation of the dual-grating around the Z-axis, both patterns are expanded. Note that, in order to position both diffraction patterns on the screen-1 and screen-2 simultaneously, we move the dual-grating closer to screen-1 and screen-2, thus the expansion of the patterns is not obvious.

Otherwise, we would need big screen-1 and screen-2.

Conclusion:

the dual-grating does produce both the transmission pattern and the reflective pattern simultaneously in the same experiment. The transmission pattern and the reflective pattern have same characteristics, i.e., due to the rotation of the dual-grating, both patterns are expanded.

The First speculate and the Second speculate are confirmed experimentally.

Experiment-5 (Figure 21 to 24): dual-grating of spacing of 500 lines/mm with horizontal slits

First step:

Experimental setup (Figure 21): Utilizing the experimental setup (Figure 4a) and the dual-grating of spacing 500 lines/mm with horizontal slits (Figure 3b). Second step (Figure 23): Utilizing the experimental setup (Figure 4b) and the dual-grating of spacing 500 lines/mm with horizontal slits (Figure 3b). Rotating the dual-grating CW around the Y axis. The First speculate and the Second speculate are confirmed experimentally.

Experiment-6 (Figure 25 to 28): dual-grating of spacing of 500 lines/mm with tilt slits

First step:

Experimental setup (Figure 25): Utilizing the experimental setup (Figure 4a) and the dual-grating of spacing 500 lines/mm with tilt slits (Figure 3c).

Model and Explanation

The schematics of a reflective blazed grating and a binary grating (rectangular profile) are shown in Figure 29a and 29b respectively. respectively.

In Figure 30a, the green surfaces and green beams represent the transmission surfaces and transmission light beams respectively.

Figure 30. Schematic of transmission grating

The text book states that a regular transmission grating produces the transmission pattern only (Figure 30a). The transmission equation is

𝑑(𝑠𝑖𝑛𝜃 ! -𝑠𝑖𝑛𝜃 " ) = 𝑚𝜆 (1)
Where 𝜃 ! and 𝜃 " are the incident angle and transmission diffraction angle respectively.

Figure 30b shows the conclusion of the experiments of this article that a regular commercial transmission grating (we have referred and used it as Dual-grating) functions as both a reflective grating and a transmission grating.

Grating normal ! ! ! " A B C d O Blazed Grating ! ! ! ! ! " ! ! ! " d ! ! ! " d Binary grating . (a) (b) . (a) (b) ! ! ! " d ! ! ! " d transmission grating ! ! ! " ! ! ! "# d transmission grating ! ! ! "$
We suggest that the reflective grating equation of the dual-grating (Figure 30b) is

𝑑(𝑠𝑖𝑛𝜃 ! -𝑠𝑖𝑛𝜃 "# ) = 𝑚𝜆 (2)
Where 𝜃 "# is the reflective angle. The transmission grating equation of the dual-grating is

𝑑(𝑠𝑖𝑛𝜃 ! -𝑠𝑖𝑛𝜃 "$ ) = 𝑚𝜆 (3)
Where 𝜃 ! and 𝜃 "$ are the incident angle and diffraction angle respectively.

Equation (1) has been modified when the transmission grating rotating (or incident) at an arbitrary angle or when a transmission grating rotating around three axes. We suggest that Equation 2 and 3 should be modified accordingly, which is beyond the scope of this article.

To understand the reflective behavior of a tilt dual-grating, let us compare the reflective function of a dual-grating (Figure 31a) rotating at an angle with a reflective blazed grating (Figure 31b). Figure 31 shows that, principally, the mechanism and characteristics of the reflective pattern of a dual-grating is same as that of a blazed grating.

Discussion

The preliminary experiments of this article show, the first time: (2) the so produced reflective pattern and transmission pattern have the same characteristics.

(3) the phenomena of a dual-grating playing both roles exist commonly.

The phenomena suggest to study both the standard theory of the 1D-grating for the normal incident light beam and the theories of 1D-grating for the oblique incident light beam [START_REF] Harvey | Description of Diffraction Cross-grating Behavior in Direction Cosine Space[END_REF][START_REF] Braig | An EUV beam-splitter based on conical grazing incidence diffraction[END_REF][START_REF] Ninad | Novel cases of diffraction of light from a cross-grating: Theory and experiment[END_REF][START_REF] Heuberger | Light diffraction from a phase cross-grating at oblique incidence in the intermediate diffraction regime[END_REF] further.

"The rather ancient grating experiment continues to surprise" (Ian Miller).

Appendix: Recent Developments of Research on Grating Experiments

A1. Recent Developments of 1D-Grating Experiments

A1.1. non-uniform spacing between adjacent diffraction orders of patterns of 1D-grating

The non-uniform spacings increasing from one end to another end. Curved, expanded and inclined patterns of the 1D-grating are shown, the first time.

A1.2. Particle Nature of Photons, Normal Diffraction Pattern and Curved Diffraction Pattern

Emerging in Same Grating Experiment

In the same experiment with only one grating, D1 shows the particle nature, D3 shows the straight pattern, and D2 shows the curved, expanded and inclined pattern.

Figure 1 .

 1 Figure 1. Schematic of transmission grating Figure 1 shows a normal commercial transmission grating. In the text book, a normal transmission grating acts as transmission grating only. The green surfaces represent slits, and green arrows represent the transmission light beams. The orange surfaces represent the surfaces between slits.

Figure 2 .

 2 Figure 2. Schematic of transmission grating acting as transmission grating and reflective grating

Figure 3 .

 3 Figure 3. Orientations of transmission grating Figure 3a, 3b and 3c show the vertical slits, horizontal slits and tilt slits (for example, CW rotating 45 0 ) respectively. Note that the tilt slits can be formed by CCW rotating the grating. The experimental setups are shown in Figure 4 respectively.

Figure

  Figure4ashows that the light beam is normally incident on the dual-grating. Screen-1 and screen-3 are on the opposite sides of the dual-grating. Screen-2 is perpendicular to the screen-1/screen-3.

Figure 4 .

 4 Figure 4. Schematic of experimental setup with non-rotating dual-grating

Figure 5 .Figure 6 .

 56 Figure 5. Schematic of dual-grating experiments with vertical slits

Figure 7 .Figure 8 .

 78 Figure 7. Schematic of rotating dual-grating experiments with vertical slits

Figure 9 .Figure 10 .

 910 Figure 9. Schematic of dual-grating experiments with horizontal slits

Figure 11 .Figure 12 .

 1112 Figure 11. Schematic of rotating dual-grating experiments around Y axis with horizontal slits

Figure 13 .Figure 14 .

 1314 Figure 13. Schematic of dual-grating experiments with tilt slits

Figure 15 .

 15 Figure 15. Schematic of rotating dual-grating experiments with tilt slits

Figure 17 .

 17 Figure 17. Schematic of dual-grating experiments with vertical slits

Figure 19 .

 19 Figure 19. Schematic of rotating dual-grating experiments with vertical slits

Figure 21 .

 21 Figure 21. Schematic of dual-grating experiments with horizontal slits

Figure 23 .Figure 24 .

 2324 Figure 23. Schematic of dual-grating experiments with horizontal slits

Figure 25 .Figure 26 .

 2526 Figure 25. Schematic of dual-grating experiments with tilt slits

Figure 27 .

 27 Figure 27. Schematic of dual-grating experiments with tilt slits

Figure 29 .

 29 Figure 29. Schematic of reflective gratingFigure29aand 29b show schematics of a blazed grating and binary grating (rectangular profile)[START_REF] Braig | An EUV beam-splitter based on conical grazing incidence diffraction[END_REF]

Figure 31 .

 31 Figure 31. Schematics of reflective function of dual-grating (a) and of a reflective blaze grating (b) Figure 31c show the dual roles of a dual-grating. The "orange surfaces" indicate the reflective surfaces. The "green surfaces" in indicate the transmission surfaces.

  a dual-grating produces both a transmission diffraction pattern and a reflective diffraction pattern simultaneously in the same experiments.

yA2. 2 .A2. 3 .A2. 5 .

 235 experiment with only one grating, D1 shows the particle nature, D3 shows the straight pattern, and D2 shows the curved, expanded and inclined pattern. A1.3. Orientation-Dependence of Diffraction Patterns of 1D-Grating *) Expanded diffraction patterns of the same 1D-grating *) Curved patterns of the same 1D-grating , expanded and inclined patterns of the same tilted 1D-grating Curved, expanded and inclined patterns of 1D grating rotating around 3 axes Rotation angle "a" (in degree) Positions (Y) of orders vs rotation angles (Eq. 2) Inclinasion angle vs rotation angle The patterns of 2D grating are non-uniform, curved, expanded and inclined due to the CW and CCW rotations of the 2D-grating around 3 axes. Mirror-symmetric patterns of the same tilted 2D-cross-grating: Curved, expanded and inclined patterns of the same tilted 2D-cross-grating A2.4. Curved and expanded patterns of the same 2D-cross-grating: Light beam behaving as particles before striking on screen: Grating experiments Schematic of Setup and Pattern of Cross-Cross-grating without Blocker

  Blockers block partially the pattern without disturbing the remaining diffraction pattern of wave theory .


Brian Craig
email: ybcraig1@gmail.com

The formation of 3-dimensional Euclidean space and the fine structure constant

Keywords: fine structure constant, Kaluza-Klein, magnetic charge

This paper explores the formation of 3-Dimensional Euclidean space. A periodic lattice of sites, with each site being the centre of a ball possessing charge, angular momentum and tachyon-like mass, is shown to provide a good model for a short-lived 3-dimensional Euclidean space that possesses 3-dimensional aether-like characteristics. This virtual state is proposed to decay to a Lorentz symmetric state characteristic for the observable universe. Of particular interest is the derivation of the value for the fine structure constant , finds each ball to be a hollow 7-sphere and with the charge of a dyon. The value for  is reproduced to the accuracy of the lattice Madelung constant which is ten significant figures.

Introduction

This work is a study of the formation of a stable three-dimensional space from an apparent void, where the latter possesses no extended spatial dimensions and has zero energy. The key questions are by what means could the stable three-dimensional space, as observed in our universe, arrive from such a void? and what is the evidence that could support further investigations? In this paper the derivation of the value for the fine-structure constant provides the evidence.

The approach is a twist of the tachyon field method, where the sombrero is turned upside down by reversing the sign of the coefficients as well as including the sixth order, to give 𝑉(𝜑) = - +  𝜑 - 𝜑 +  𝜑 where o , 1 , 2 , 3 are all positive. The global minimum is = 0 where for small  , V(0±)= -o+r 2 , and r is a real mass. The system has Lorentz symmetry at = 0, and the Lorentz invariant system is stable. However Lorentz symmetry may be broken at ≠0 at a local maxima, occurs at =T, where V(T ± )= -i 2 , noting the sign of i indicates a tachyon mass (mi).

All local maxima and minima are obtained by ∂V()/∂ =0, giving the following equation 0 = 𝜑( -2 𝜑 +3 𝜑 ) with solution

𝜑 = 0,  3 1 ± 1 -3   
where = 0 is a minimum. The local maximum is given by

𝜑 =  3 1 -1 -3    Which gives V(T)=0 if  =  3 𝛬  -  3 𝛬 1 - 1 3 𝛬
where

𝛬 = 1 -1 -3   
Indicating a virtual state possessing zero energy, and a finite life-time t , ≈ h/(mic 2 ). A second minimum occurs

at= 𝜑 =   (2 + 𝛬).
The proposed key process is that such a virtual tachyon (=T) state (not possessing Lorentz symmetry) may occur for a short time. It will be shown below that the tachyon state is a periodic lattice of dyons, with each dyon containing a coulomb charge either e/2 or -e/2 plus magnetic charge, either 26g or -26g such that the value for  is reproduced to ten significant figures. The second stage of the proposed process is the this decay of the tachyon to a combination of a stable =0 Lorentz symmetric state for free coulomb charge, and the (=L) lattice of purely magnetic charge, with a release of free energy. The free energy is directly observed in a Lorentz invariant universe as excitations within the associated fields. The remaining (L) relic state containing the lattice, strongly bound by magnetic charge and not possessing Lorentz symmetry, may be detected through gravitational effects.

First of all, some simple underlying assumptions are made for the virtual tachyon (=T) state. The fundamental object of space is assumed to be the N-sphere, a spatial object of radius r and possessing N angles. This object has N+1 spatial dimensions and a hypersurface of N spatial dimensions. An extended object is assumed to be a network of touching spheres. A simple model for an extended object is a periodic lattice of touching spheres. The charge of the sphere is assumed to be at the centre of the sphere, and the quantum rigid rotor model is used for the angular momentum of the sphere, where mass is located on the hypersurface.

The virtual T lattice has aether-like qualities rather than Lorentz symmetry. Of particular interest is the value for the fine structure constant  Each ball is a N-sphere (S N ) possessing angular quantum number L [START_REF] Frye | Spherical Harmonics in p Dimensions[END_REF], radius r, and dyonic charge q=(e/n, jng) where -e is the electron charge and g is the Dirac magnetic charge, with integers n and j. The fine structure (=0.00729735256) is given by the relationship

ħ𝑐 = 𝜇 4𝜋 𝑒 𝛼 where 𝛼 𝑛 + (𝑗𝑛) 4𝛼 = (-𝑀) 4 𝐿(𝐿 + 𝑁 -1)
where the integers n=2, N=7, the angular momentum quantum number L=10115 and M is the Madelung constant of the lattice structure (position vectors ri), given by

𝑀 = 𝑒 𝑒 𝑒 𝑟 𝒓 -𝒓 exp - 𝒓 -𝒓 𝑟 𝑜
where the term (ro -1 =mic/h) is an attenuation factor, h is the Planck constant, c the velocity of light, mr and mi describe the respective real and imaginary parts of the mass of the N-sphere. The distance rac=2r is that between nearest neighbours (possessing charge (ei and gi) with the same magnitude but opposite sign), and for ro >> rac, the value of M is very close to the solid state value calculated for an infinite crystal. In fact no significant attenuation is found for the proposed state for T as the solid state value gave complete agreement. An analogy of this 3-dimensional Euclidean space is a salt crystal where rac is the distance between a cation and an adjacent anion. The additional five spatial dimensions for the 7-sphere are compactified, which is a key quality for the Kaluza-Klein equation [START_REF] Th | Zum Unitätsproblem in der Physik Sitzungbar[END_REF][START_REF] Klein | Quantentheorie und fünfdimensionale Relativitätstheorie[END_REF] describing the unified field of gravitation and electromagnetism.

Fine structure Constant

The value for  is given by the following equation

𝛼 = 1 4𝜋𝜀
𝑒 ħ𝑐 which is the Coulomb expression for  for electronic charge q=e. On the other hand assuming the charge unit q is instead the Dirac magnetic monopole, possessing charge g, defined as

𝑔 = 𝑗 2𝛼 𝑒𝑐
where the Dirac normalisation condition require j to an integer, then for j=1,

(4𝛼) = ħ𝑐 𝜇 4𝜋 𝑔
which is the magnetic charge expression for . The aim of this work is to derive an expression for ħc in terms of Kq 2 , where q is the charge unit and K is a constant, and thereby gain an expression for .

The third type of particle is the dyon, possessing both electronic charge and magnetic charge. The interaction between two dyons with respective charge (e1,g1) and (e2,g2) sees the Potential energy is of the form [START_REF] Chuu | Path integral quantization of the relativistic dyonium system[END_REF]

𝑉(𝑟) = 𝑒 𝑒 4𝜋𝜀 𝑟 + 𝜇 4𝜋
𝑔 𝑔 𝑟 and magnetic potential vector A(r) for r =(x1,x2,x3) is

𝑨(𝒓) = ħ𝑄 𝑥 𝒙 𝟐 -𝑥 𝒙 𝟏 |𝒓|𝑥 𝑥
where x⊥=(x1,x2,0) and Q=e1g2-e2g1. The parameter Q = 0 when e1 = -e2 = e/n, and g1 = -g2 = jng for n, which satisfies the Dirac condition for magnetic charge. A value of n=1 indicates the electron charge, while n>1 considers the coulomb charge unit to be a fraction of the electron charge, such as n=2 considers weak isospin while n=3 considers the down quark. The value for the lattice energy ELE is given by the expression

𝐸 = ½ 𝑀 𝑟 𝑒 4𝜋𝜀 + 𝜇 4𝜋 𝑔 = ½ 𝑀 𝑟 1 𝑛 + 4𝜋𝜀 𝜇 4𝜋 (𝑗𝑛𝑐) 4𝛼 𝑒 4𝜋𝜀 = ½ 𝑀 𝑟 1 𝑛 + 𝑗 𝑛 4𝛼 ħ𝑐𝛼 giving ħ𝑐 𝑒 = 𝛼 𝑛 + 𝑗 𝑛 4𝛼 1 4𝜋𝜀

The Model

Space is assumed to be quantised with half the spatial quanta (sites) possessing positive charges q+ and the other half negatively charged q-. Each element of three-dimensional array has the same value of tachyon-like mass-energy (m = mr + imi). A tachyon possesses a non-zero imaginary part of the mass-energy and such quantum states may have a virtual or transient existance [START_REF] Garmon | Bound states, scattering states and resonant states in PT-symmetric quantum systems[END_REF]. The lattice energy due to lattice interaction between these charges, the mass-energy, the rotational energy and gravitational interaction are the same for each site and the summation of all these energy components is assumed to be zero. The interactions within the tachyon state are limited to an extended although finite range, as dictated by mi. The total energy per site is given by Dirac expression 𝐸 = ((𝑝𝑐) + (𝑚 𝑐 ) ) / + 𝑉 where the potential energy is the sum V=ELE+EG of the lattice energy ELE and the Gravitational energy EG. The interaction is modified by the transient lifetime and range (ro= h/cmi), with c being the velocity of light, while h and ħ are Planck's constant and the reduced Planck's constant (h=2ħ) respectively. At this stage no assumption is made on the nature of q or K, giving

𝐸 = ½ 𝐾 𝑟 𝑞 𝑀
where M is always negative. The Madelung constants calculated for salt crystals [START_REF] Tavernier | Clifford boundary conditions: a simple direct-sum evaluation of Madelung constants[END_REF][START_REF] Zucker | Madelung constants and lattice sums for hexagonal crystals[END_REF] provide good estimates when 𝑟 ≫ 𝑟 . Otherwise an effective Madelung constant could be calculated as a convergent finite summation, arising from significant exponential attenuation when ro and rac are of comparable magnitude. For a dyon then q=e and K=(n -2 +(jn/2) -2 )/4o.

The gravitational energy for the transient state having a mass-energy of m is

𝐸 (𝑚) = - 1 2 𝜌 exp (- 𝑥 𝑟 )𝑢(𝑥)4𝜋𝑥 𝑑𝑥
where  is the mass-energy density. Newtonian gravity is initially assumed as the rigid lattice is uniform and all positions are fixed, such that 𝑢(𝑥) = 𝐺 , giving

𝐸 (𝑚) = -2𝜋 𝑚 𝐺𝐷𝑟 𝑟 = -𝑉 𝑟 𝑚 𝑚 + 𝑖
where

𝑉 = 2𝐺𝜋𝐷 2𝜋ħ 𝑐 = 2𝐺𝑚 𝜋𝐷 2𝜋ħ 𝑚 𝑐 = 2𝐺𝑚 𝜋𝐷(𝑟 )
noting that the functional form for u(x) is not critical for the derivation of the expression for, as it participates only in the expression for a extremely small residual term , as shown below.

The spatial quanta are assumed to be an N-sphere of radius r = rac/2, which implies this model Euclidean space to be a system of touching spheres. The momentum squared p 2 , where there is only angular momentum within an N-sphere, which is given by the expression [START_REF] Frye | Spherical Harmonics in p Dimensions[END_REF]

〈𝑝 〉 = 1 𝑟 〈𝐿 〉 = ħ 𝑟 𝑊(𝐿, 𝑁)
where 𝑊(𝐿, 𝑁) = 𝐿(𝐿 + 𝑁 -1) for a rigid rotor of the radius r and angular quantum number L. The mass-energy density  is derived from the particle mass energy m, is given by the expression 𝜌 = 𝐷𝑚𝑟 where D is proportional to the packing density of the touching spheres within the lattice, which for example, the zinc blende and wurzite structures is D=  , while D=   for the CsCl structure and D=/6 for the NaCl structure.

The total energy E is assumed to be zero, describing a transient state which does not require either an input or a release of energy, giving (𝑝𝑐) + (𝑚𝑐 ) = (𝐸 + 𝐸 (𝑚)) Which, on substitution becomes The transient state is assumed to have a value for mi that cannot too large as the model requires ro>>r. The value for mi cannot be zero as we need an imaginary contribution to the above equation, as will be shown below. However mi can have an extremely small but positive value and in such a case the transient state may become very long lived.

The expression for the fine structure constant

Multiplying both sides of the previous expression by r 6 which, on using the results of the imaginary terms, is simplified to

𝑐 𝑟 = - 𝐾𝑞 𝑟 𝑀𝑉 2𝑚 + 2 𝑉 𝑚 (𝑚 -𝑚 )
leading to a quadratic in terms of VG/(mi 2 c 2 )

𝑟 = - 𝐾𝑞 𝑟 𝑀𝑉 2(𝑚 𝑐 ) + 2 𝑉 𝑚 𝑐 𝑚 𝑚 -1
from which the solution is divided by r 3 to give

[𝑉 ] ± 𝑚 𝑐 𝑟 = 𝐾𝑞 𝑀 2𝑚 𝑐 r ± 𝐾𝑞 𝑀 2𝑚 𝑐 r 1 + 16(𝑚 -𝑚 )𝑐 𝑟 (𝐾𝑞 𝑀) 4 𝑚 𝑚 -1
which is the expression for the assumed small term. For the case of mc 2 >Kq 2 /r the right hand side becomes approximately ½ implying the Gravity term is also larger than Kq 2 /r and therefore this is not a valid case. Therefore we assume mc 2 <<Kq 2 /r. The additive case (+) is rejected as this implies the Gravity term is similar magnitude the Kq 2 term and therefore too high.

For mc 2 <<Kq 2 /r the square root term is of the form (1+) 1/2 where 0<<<1. Using the expansion (1+) 1/2 ≈1+½for small , we have for the subtractive (-) case of the ± solution, where the term on the right hand side is 10 -35 for mr=0, mi = Higgs tachyon field mass (similar magnitude to the W particle). If mi is the order of the Higgs tachyon mass then  is still extremely small. Therefore we have

ħ𝑐 𝐾𝑞 = 𝛼 𝑛 2 + 𝑗 2 𝑛 2 4𝛼 -1 = (-𝑀) 4 𝑊(𝐿, 𝑁)
The possible values for L and N are deduced by testing integer pairs (L and N) in the expression for the magnetic charge expression (subtractive case) to the known value of  and searching for a close match for any of the four binary lattice types (zincblende, wurtzite, CsCl and NaCl). The combination of n=2, j=13, L=10115 and N=7, the NaCl lattice Madelung value of 1.7475645946 reproduces the accepted value of to the accuracy of M, which is at least ten significant figures.

While the value of L=10115 is surprisingly high, the set of eight spatial dimensions for the 7-sphere is consistent with work beyond the Standard Model. The model for the ball is a hollow 7-sphere leading to the matter localised in the 7-dimensional hypersurface. The value of n=2 is consistent with the electron isospin component of e/2. The value for j=13 is another surprise, resulting in a large magnetic charge of 26g. However such magnitude of magnetic charge provides a basis for very strong forces.

The decay of the virtual aether state may see either a return to the void or a transition to another state possessing spatial dimensions. Of particular interest is the latter case where a potential separation of the Coulomb charge and magnetic charge to form a state of two weakly interacting components. One is a relic and stable ionic lattice of magnetic charge, without Lorentz symmetry, and the other is a boson gas containing the Coulomb charge and possessing Lorentz symmetry. While a relationship between this state and Dark matter and Dark energy may be speculated, no strong connection has been derived.

Concluding remarks

This paper presents an interesting model for the initial formation of Euclidean three dimensional space. The dyon charge plays a central role in binding space as an entity, qualitatively similar to ionic-Coulomb charge binds a binary salt lattice (crystal). The finding of compacted extra dimensions is in accord with the Kaluza-Klein theory. Overall the concepts explored within this current paper has the potential to be very important to a broad range of frontier efforts beyond the Standard Model.

The author does not have sufficient understanding in pure mathematics and advanced particle physics to provide a complete explanation of the results, such as the values of L and j. Work will continue but at an age of sixty six, the author struggles with the very advanced level of mathematics and quantum mechanics. Incomplete explanations have been removed from this paper and the author hope that other researchers may be able to make good use of this work.

  /m 2 gives

	(ħ𝑐) 𝑟 𝑊(𝐿, 𝑁)	(𝑚 -𝑚 ) -2𝑖𝑚 𝑚 (𝑚 + 𝑚 )		+ 𝑐 𝑟
		=	(𝐾𝑀𝑞 ) 16	(𝑚 -𝑚 ) -2𝑖𝑚 𝑚 (𝑚 + 𝑚 )	𝑟 -	𝐾𝑞 𝑟 𝑀𝑉 2𝑚	+	𝑉 𝑚	(𝑚 -𝑚 ) + 2𝑖𝑚 𝑚
	Grouping imaginary terms gives
			-(ħ𝑐) 𝑊(𝐿, 𝑁) +	(𝐾𝑀𝑞 ) 16	= 4(𝐺𝑚 𝜋𝐷)	𝑟 𝑟	𝑚 𝑚	+ 1
	which can be rewritten as
			(ħ𝑐) 𝑊(𝐿, 𝑁) =	(𝐾𝑀𝑞 ) 16	+	𝑉 𝑟	𝑚 𝑚	+ 1
	noting that if the second term on the right hand side is much smaller than the first term, then
				ħ𝑐 ≈	4 𝑊(𝐿, 𝑁) (-𝑀)	(𝐾𝑞 )
	as M is negative. Grouping the real terms gives
	(ħ𝑐) 𝑟 𝑊(𝐿, 𝑁)	(𝑚 -𝑚 ) (𝑚 + 𝑚 )	+ 𝑐 𝑟 =	(𝐾𝑀𝑞 ) 16	(𝑚 -𝑚 ) (𝑚 + 𝑚 )	𝑟 -	𝐾𝑞 𝑟 𝑀𝑉 2𝑚	+	𝑉 𝑚	(𝑚 -𝑚 )