# 4A: Existing Laws

### 3.   Existing Laws

The list of some of the well known laws of conservation is (a) Law of conservation of mass, (b) Law of conservation of energy, (c) Law of conservation of linear momentum (d) Kirchhoff’s current law (e) Kirchhoff’s voltage law etc. We briefly describe them in the next section with the goal of highlighting an unifying concept behind them.

#### Conservation of mass law

This is one of the most fundamental laws of nature. It says [Beiser, p.104] that the total mass in a closed system remains constant. It can only be transformed from one form to another. This is widely used in chemistry in the analysis of chemical reactions.

The closed system is an assumption. It is not necessary. The mass will never be destroyed, and therefore the law will remain valid even in open system. For the purpose of analysis and verification a closed system will be necessary.

#### Conservation of energy law

This is another version of the sigma law. It says that we can neither create nor destroy energy [Serway, p.199], energy is always conserved. The total energy remains constant in a closed system. This is also known as the first law of thermodynamics. The book [Crowell, p.146] says – “The law of conservation of energy is also known as the first law of thermodynamics”. Usually the laws of thermodynamics are stated in a different way. You may have to interpret it carefully to see that it is indeed the sigma law.

#### Kirchhoff’s Current law

This law says that the sum of the currents entering any junction in an electric circuit must equal the sum of the currents leaving that junction [Serway, p.869]. This is same as the sigma of all currents at any junction is zero. This law is valid for all kinds of through or flow variables for all types of networks.

# 4B: Thermodynamics

 5. Thermodynamics While discussing the action-reaction law, we briefly mentioned two important concepts. For every action there will be many reactions. And that these reactions will spread everywhere creating a global space time (GST) effect. Actually these two concepts are interrelated. We want to elaborate them to show that the second law of thermodynamics is really a sigma law. The Assumptions Everything in this nature is interconnected, in global space, and over global time. This means that any action we take now will affect our entire environment. The reactions will spread to many places and will continue to spread over time to affect more and more elements in the environment. The environmental pollution is clearly an example of such an effect. Earth quake, Tsunami, Financial Crisis, etc. are all very well known examples of GST. Thus the GST concept says that for every action there are always multiple reactions. This is a fact of nature; there is no isolated system or environment. However, the sum of all these reactions must be equal to the original action as in (4.4). By considering isolated systems we may make things simpler, but we hide the real nature of things, and possibly create confusions about the reality. Another view point of the multiple reactions theory is to recognize that you cannot produce a single reaction from a single action as in (4.3). This is impossible, also because we are all interconnected by GST, which prevents single reaction. You cannot create an isolated system; it goes against the laws of nature. The idea of isolation takes us away from the GST perspective. This is also known as simultaneity law that we have investigated in chapter one. The GST concept also says that the same action cannot produce the same result, because the first action has already impacted the environment. Second time the environment is different. Therefore the second action is not exactly the first action; the second action cannot produce similar chain of reactions, because it is working on a different environment and at different time. Both time and space has changed after the first action, the GST is different now for the second action. This essentially means that no process is reversible. The environment has changed. It was square before, and now it is a circle. The reverse action is not meaningful anymore inside this circle. Thus two of the most important assumptions of thermodynamics – isolated system and reversible process – are against the GST concept. They are against the concept that everything is working simultaneously, interactively, and at same time. And we all agree that if the assumptions are invalid then the theory will not work in engineering. In many cases, we may not need to analyze all the reactions. We may need to study only one of the reactions, or some of the reactions, but not all of the reactions. But we must remember that all the reactions exist, we cannot ignore them. With this background in mind let us see the statement of the second law of thermodynamics. The Second Law of Theromodynamics The laws of thermodynamics are usually defined using heat and work [Serway, p.670] and in the context of an engine. The second law says It is impossible to construct a heat engine that produces no effect other than the input of energy by heat from a reservoir and the performance of an equal amount of work. That is, all the heat taken cannot be converted into work. Heat Input = Work Desired     (impossible) Some heat will be always lost. The heat input is the action, which produces two reactions, some work and some heat loss. If you analyze the two reactions carefully you will find that they both include many reactions. The work produced has, loss of work due to friction in the gear boxes, loss of work in all mechanical joints etc. Similarly the loss of heat also has many reactions, some heat was lost straight into the environment, some heat was lost in the engine body, some was lost in heat transmission pipes etc. Thus the original action, taking heat, has produced many reactions of many work types and many heat loss types and can be written as in (4.13).

 Heat Input = Heat Loss + Work Loss + Work Desired          (4.13) There are other reactions also like producing some sound or noise. If we sum all the reactions we will always find that it will be equal to input heat amount. Thus the second law is really the sigma law. Now the second law says we cannot prevent the losses in heat. We say that we cannot prevent the losses in the work also. That is we cannot channel all the input heat directly into usable work output. We call that as trying to isolate a system from its global space time (GST) environment. That is not possible; it is against the reality of GST. Thus taking heat and then producing some work and some heat loss, is equivalent to saying that heat input has produced two reactions. That is, the sum of the two reactions must be equal to the heat input, which is the sigma law. If you consider one of the outputs say the work, and the input, it is clear you cannot get 100% efficiency, because it will violate the sigma law. You cannot produce only one reaction or in other words you cannot have an isolated system. The two requirements – isolated system and 100% efficiency – are equivalent, and violate the concept of GST. The Disorder Associated with the second law of thermodynamics is the concept of entropy. The entropy theory says [Serway, p.683], Isolated systems tend toward disorder and that entropy is a measure of this disorder. Again, in the above statement the assumption of isolated system is not feasible. The GST theory says we are all globally connected and constantly interacting with each other. We have mentioned before, if the assumptions are wrong, then the results will be wrong also. The concept of disorder has not been defined in thermodynamics. Random motion of molecules or atoms in an isolated environment is given as an example of disorder. This motion surely can be modeled using differential equations and then we will find it as a very well defined motion. The fact that we cannot write such a set of differential equations, because of its complexity; and the fact that we have taken a statistical approach because of its simplicity; do not mean that the atomic motion is an example of disorder. If we expand the microscopic space and if we expand the nanosecond time scale then we will find perfect order in the motion. We illustrate with one example. We have observed from our backyard looking up at the sky that airplanes often fly along a perfect straight line at very high altitude. We see that there is a perfect order in this motion. However, the pilot sees the cockpit meters almost steady with little vibration in the needle tips; which we may interpret as a little disorder. This needle display comes from a space time filter of the navigation computer data. The computer is running at nanosecond time scale, but the data is taken for display maybe every tenth of a second, thus it uses a time scale filter. Similarly the data also is a 32-bit number inside the computer, but the computer averages it over space scale, thus filtering data according to the space range of the cockpit meter. These space time filters thus remove almost all appearances of internal disorder inside the computer. There are many registers inside this navigation microprocessor of the digital electronic circuit board. If you plot the values of any one of these registers, over time, you will find that the graph will look like a random process, and may appear like a completely disordered system. Many such graphs have been published in literature [Nylund]. This happens because the register is changing at nanosecond time scale. But we know that the microprocessor is doing a meaningful work, because we have programmed it, that is, there is an order inside. Thus the appearance of order and disorder are related to space and time scales. In reality there is no disorder in nature. Note that the microprocessor is part of nature too; it is created using the elements of the periodic table of chemistry. It is difficult to believe in the concept of disorder under the frame work of GST. We are inside a global system, as discussed later in this chapter, defined by millions of simultaneous differential equations in millions of variables. According to this theory the universe is precisely defined and precisely predictable. That is to say, predictability cannot indicate disorder. We do not have any example in the universe that shows that the nature is creating disorder. Death for example, is not a disorder; it is a law of nature and precisely predictable. Everything in nature goes through a birth process, maturity process, and death process. Recognize that, they all have different space time scales, which may create an illusion of disorder. Thus the second law of thermodynamics is nothing but the sigma law. The heat loss, work loss, and work done are just three reactions.

# 4C: Derivatives sum must satisfy the limiting values defined by (4.17). We should recognize that the changes happen only because of actions and not because of passage of time. Thus a careful evaluation will always show that the derivative is an action reaction law and therefore is a sigma law. In modern days we analyze our systems using differential equations. Since the derivative obeys the laws of conservation, the differential equations will also obey them. Thus our system models can be designed using the sigma law (4.17). It appears also that there is only one law in nature, and that is the sigma law. It is very unlikely then, that our modeling effort will violate any unknown law of nature. The ideal model will automatically satisfy the sigma law, and therefore will represent the true nature of all systems. The algorithm to create such a model is based on the concept of system theory, which is briefly outlined in the following section. Our objective is to show the existence of a systematic algorithm for such a model and our emphasis is on the development of a thought process based on the laws of conservation. The existence of such a model will prove that all systems obey the sigma law.

# 4D: Systems Concepts

 7. Systems Concepts Many things in our nature, and probably everything, can be considered as systems and they can be analyzed using certain generalized principles. We show how the sigma law is used in these principles, and thereby show how the systems naturally obey the sigma law. What is a System? Every system has some components. In economic system for example, we may consider agricultural sector, commercial sector, financial sector, consumers, government, and banks as components. In our human brain we may consider, vision part of the brain, hearing part of the brain, body motion control part of the brain as the components. If you think analytically, you will find components in every system, however big or small. We will also find that all these components are interconnected by some interfaces. The components are not isolated. In economic systems the components are connected by some financial transaction mechanism. Similarly, the human brain components are connected by some neurons and glial cells. Finally, you may recognize that all systems have some purposes; they are created to perform some functions. For example, in the economic system, the purpose may be to sustain full population employment. In the brain system, the purpose may be to control harmoniously all physical organs inside the body. That is, all systems have some coherency or consistency in them to make this purpose happen. Thus every system is composed of three things (a) components, (b) interfaces, and (c) objectives. Through & Across Variables All components have terminals. The terminals of two components are connected together to create the interfaces between components. As a result of these interfaces, the components form a network in the system. All systems can be modeled using across and through variables. Across variable is measured across the terminals of the components. Similarly, the through variable is the quantity that flows through the terminals or through the interfaces into and out of the components. As an example for the economic system, the across variable may be the price and the trough variable may be the flow of goods. Similarly in a hydraulic system the across variable may be the pressure and the through variable may be the fluid flow rate, etc.    Predictability We are not suggesting writing down these equations of our systems. It is not practical to do that. What we are trying to show is that there is a possibility of creating a very large set of equations that will describe the totality of all systems. And we are also showing a constructive approach in producing that set (4.22). In addition we are using the sigma law as the foundation of this approach. The feasibility of such an approach, and the existences of such a set of millions of equations in millions of variables that will describe the entire society and nature, should be understandable now. If we do that then there will be no unknowns anywhere, there will be no fuzziness in our knowledge. However, if we use a small set we will get only an approximate view; and there is a possibility that it may give a completely wrong view. This is because a local view cannot capture the global view, and the real truth may lie outside this local view. Thus the global space time (GST) view is absolutely necessary to find the real truth of nature. Note that this idea of covering all objects of the entire universe is an attempt to combine the views of all local objects in a simultaneous, interactive, and dynamic way. This will prevent the possibility of remaining in the dark like the blind men and the elephant story. But can this modeling concept reveal the existence of soul and reincarnation? Definitely yes, if we cover all objects, all details, of all activities, over all time. It will show that a person dying in one place is coming back after some days, months, or years in another place, with the characteristics he had before. This model will represent the true knowledge or the existence of such knowledge. The idea should highlight the complexity of this model. Solutions of DE Once we have the equations, like in (4.22), then we can imagine their solutions. The mathematical theory of differential equations ensures the existence of a solution under fairly realistic conditions [Farlow]. It has also been shown that the solution is unique under a given set of initial conditions. The theory also says that the solution can be extended in both directions of the initial time t0, that is, from minus infinity to plus infinity on time scale. Thus the solutions can in theory, predict the past and the future. The solution is continuous. If a break happens, then it will start again at some other time, exactly from that break point in a continuous way. Better the model is better will be this prediction. Thus the solution of the DE represents the memory of the system. This is because it shows how the system behaves in the past, at present, and in the future. This global time is also a key feature of the system theory based model of (4.22). This solution helps us to study the nature using the laws of nature. The literature on the theory of relativity also talks about the predictability of future. It has been written in [Eddington, p. 46] “Events do not happen; they are just there, and we come across them”. Our view point, that the solution exists in the future, supports the above statement. It seems the theory of relativity has not made any conclusive determination about the predictability of future. Some authors [Hogarth] say it is completely predictable and some say it is not possible [Manchak]. However our approach is different. We are considering a very large dimensional space as opposed to only four dimensions in the relativity theory; we are also considering very large set of simultaneous equations and relativity considers only a very limited number of field equations. The philosophy of our approach is also fundamentally different along with our definitions. Our focus is on the laws of conservation. Although our view point is different, but there are many literature available on the internet on the subject presented in this section. Some concepts of general system theory have been discussed in the paper [Bertalaffy] and laws of nature in economic theory in [Halls]. It should be realized now that everything is a system. Our solar system is a very big system. Similarly, the model of our atoms is also a system, but a very small microscopic system. Since the derivative is a law of conservation, the differential equations represent the laws of conservation also. We have just shown that all systems can be represented by differential equations; therefore all systems follow the laws of conservation. Note that it is not that the models follow the sigma law; it is the real systems in nature that follow the sigma law. We can see that the collection of all systems, which is the GST, naturally follows the sigma law or the memory law. Memory We will discuss human memory in another chapter and in more details. We will give a generalized definition of memory there. But in this chapter we can also see some meaningful definitions of memory. The state variable x(t) at any time t represents the status of the universe at time t. Everything that you want to know about nature is included in the state. But when you find x(t) at some other time than present time t, say at time t1 , then the state x(t1) becomes the memory. The theory of differential equations says that x(t) can be determined by the solution for all time t, both past and present. The solution can be used to find memory of the universe. Since these state equations are based on the conservation laws, this memory can never be lost. That is why we call it eternal memory. It is obvious that DE theory does not allow us to actually find past or future memory. However, the theory confirms that the memory exists and its feasibility of finding them is also meaningful. All we need is a technology to get them. In the chapter on yogic power we will see that yogis can find such memories.