# Theory of everything

Theory of everything is the ultimate theory of physics , that should describe all physical aspects and occurrences in a consistent manner. Such theory , if it is found, needs to unify all fundamental forces of nature. String theory is the best candidate for theory of everything. It is a theoretical framework that have merged quantum mechanics with theory of relativity. According to string theory universe has nine space dimensions and one time dimension. All the dimensions other than three are curled up and tiny so that we can not directly perceive them. Besides this crucial feature, the principles of string theory say that what appears to be elementary particles are tiny vibrating pieces of strings. Somehow if we can work out resonant or vibrational pattern of the piece of string we will be able to explain the observed properties of the elementary particles. The conclusion is that the universe is a cosmic symphony of strings resonating through ten dimensional hyperspace. What are we ? We are nothing but the melodies. We are nothing but cosmic music played on the same cosmic strings or membranes.

+ = Everything

Readers from all over the world , have you a feeling that you are bad at mathematics? Do not fear mathematics. Once I was also a victim. You can now conquer mathematics easily. The secret is behind logic. Logical ideas alone can define mathematics. I will state russell's paradox first. If you understand this you can safely assume that you have a good mathematical sense .
Suppose R is a set of all sets that are not members of themselves. Now is this set R is a member of itself or not? If it is a member of itself then it is one of the sets which are not members of themseves. So it is not member of itself. And if this set R is not member of itself then by definition it is a member of itself. So in either way we come to a contradiction!

### Mathematics

Mathematics is the language of nature. It is hard to define mathematics . In general it is the study of change, numbers and shapes. Mathematics consists of various branches like arithmetic, geometry, topology, calculus and many more. Science can not progress without mathematics. This is so obvious fact that needs not be mentioned. Mathematics , in a certain sense , an exact science. We all accept the mathematical theorems and truth because we can prove those. we all accept 2+2 = 4. Mathematics is always flawless. That is what mathematicians thought every time. But Kurt Godel gave a death blow to mathematics by claiming that no mathematical system is complete. Axiomatic systems are necessary incomplete. That means there will always be some statement within the system , whose truth can not be proven using the system. This was very frustrating idea for the mathematical society and no one has yet been able to refute Godel's claim. This is known as the Godel's first incompleteness theorem. This theorem is kind of related to the "liar paradox" of usual language. Suppose there is a sentence " he is lying". Now if the sentence is true then when he says that he is lying , he is indeed lying. That means he is telling the truth. The sentence's truth can not be determined as we come to a contradictory situation. There are other similar paradoxes explained here.
"Mathematics has a better sense than the common sense"
There is hardly any branch of engineering and science where mathematics does not apply. Mathematics is a sense you never have. So nobody is gifted with mathematical ability. You can not be good at it without practising it. But it seems surprising that our mind which is so well organized can not adapt with mathematics everytime. Or may be it is a wrong idea.
"pure mathematics is a poetry of logical ideas"
Without speaking about numbers the importance of mathematics can not be described. To describe numbers or define numbers we need to know how to count. To count , in turn, will need three steps : 1) the idea of many-ness 2) one-to-one mapping and 3) sequentially speak or say the number words
First we need to have the idea of many-ness. We need to answer the question of how many? How many objects do we a collection have? Then we map each objects to other objects with one-to-one relation.
Mapping: mapping is assigning each element of a set to exactly one element of another set.
When we assign an element , say our finger to each element of a collection , we speak one for one finger , two for two fingers and so on to last one which will be the cardinal number of our collection or set. Then we give a symbol for the number if we like. This symbol will represent that particular number.
The invention of calculus has changed the world. Calculus was invented by Leibniz and Newton at the same time although there is priority dispute about who invented it first. Application of calculus is everywhere. Where there is change there is calculus. Where there is curvature there is calculus. Both the theory of relativity and quantum mechanics were developed using calculus. Everybody knows that the idea of calculus is rooted in the notion of limit. When we speak about something approaching another one or some point approaching another point , the notion of limit appears. There is precise definition of limit. You can think of it as a scheme to manipulate infinite number of small quantities. We know we can sum infinite number of terms in a geometric series, which converges. Same thing happens in case of limit. One quantity converges to another and in the end they become equal. This is the core idea of limit and calculus.

Real numbers are all the numbers that can be traced on number line. It includes both rational and irrational numbers. Real number line contains no gap or it is continuous. Irrational number was defined in order to make the real number line complete. It is the set R. It is extended from - (infinity) to +(infinity) including zero. Real numbers are also called measurable numbers. It includes the set of integers too. Calculus is certainly established using the concepts of real numbers. Cantor first proved that the set of real numbers is non denumerable. It can not not put in one-to-one correspondence with natural numbers(1,2, 3, 4, 5,6 ......). Real numbers has cardinality 2^(ℵ0) , which is called cantorian continuum. Cantor also proposed that there is no set which cardinality lies strictly between that and ℵ(0). This is called continuum hypotheses. These two infinite numbers of continuum hypotheses play exactly the same role as integers 0 and 1. There is no integer in between 0 and 1. Cantor knew that this was the case but he never came up with a proof. Later Kurt Godel showed that this hypotheses is consistent with axiomatic set theory.
Pythagoras law has made a great impact on science and mathematics. This law holds for any right angle triangle in Euclidean geometry. The law says square of the hypotenuse is equal to sum of squares of other two sides. This law not only bears the fact of geometry but also laid the foundation of many scientific theories like theory of relativity and electromagnetism. Pythagoras law also states that there is a 3-tuple of integers which satisfy it. In another words there are infinite number of solutions of Pythagoras law. More specifically , there are infinite solutions for x, y and z in integers which represent the three sides of any right angle triangle. This brings us to Fermet's last theorem. The theorem states that there are no solution for x, y and z in integers for power greater or equal to 3. Proof of Farmet's last theorem took much time to be discovered. This proof involves number theory.
Gauss was perhaps one of the greatest mathematicians of all time. He was first to study the curved surfaces. What we call plane is particular cases of 2-dimensional surfaces or manifolds. In physics he contributed also. We all know Gauss's law of electromagnetism. Gauss was very talented in his early childhood. One day his teachers asked everybody in his class to add all the numbers from 1 to 100. Gauss calculated it more quickly than others within seconds. He just did it by adding two numbers and multiplying it by 50. How ? 50 pairs of numbers have the same summation like 1+99 =100 , 2+ 98 = 100, and so on.. So the total sum is 50*100 = 5000. Gauss also developed many theorems which are still very usefull.
"Mathematics gives you wings"
Roger Penrose is the world's leading mathematical physicist. He collaborated with Hawking and proved that time had a beginning. The proof concerns the postulates of the theory of relativity. He is a mathematician too. He is specialized in recreational mathematics. He makes many complicated mathematical problems seem easy by graphical representation. Mathematics, according to him, has certain platonic existence. There are three kinds of worlds :one is physical world, second is mental world and the third is platonic world. Mathematical objects and forms exist in platonic world. Mathematical objects or forms are numbers, triangles, circles, sets and many more. There is no perfect circle in real world. We can not see perfect flat space anywhere in the universe. This kind of pure mathematical or geometric objects exist only in the platonic realm.
Our mental world consists of all our thoughts and abstract percepts. It has no connection to physical reality. Our mental world contains particular or percepts. Universals are certain concepts which can exist without our mind. Mental world does not necessarily make logic and mathematics dependent on it.
Physical world is the materialistic world that we inhabit. It is the whole universe or multiverse-as we may call it.

So what is the most complicated topic in mathematics? Is it topology or geometry or calculus? or is it linear algebra or statistics? It is none. Mathematics builds upon itself. If you want to understand calculus you need to understand limit and functions. If you need to understand topology you need to understand set theory. It is like a chain. If one link is missing the whole system is broken. We do not understand mathematics because of these missing links. Lot of things is dependent on definitions. We can define something when there are notions which have a certain relation to some term , which is itself one of the said notions. Why is physics hard to understand? Physics has lots of notation and symbols which scares us away. You can talk about general relativity. In relativity all boils down to 21 numbers that Riemann curvature tensor assigns at each event in spacetime. In classical electromagnetism at each event in spacetime there are 16 numbers that electromagnetic field tensor assigns. How does these numbers creep in? I guess you have to have some ideas about those theories. Take another example of quantum field theory. This theory treats particles as excitation of the fields. Everything in QFT can be thought as perturbation in an infinite number of sets of infinite number of tiny springs. Particles come from energy that the fields represent. In quantum electrodynamics there are three functions which give three different numbers describing all interaction between matter and radiation. I guesss I have to say that Pythagoras was right all along when he said that numbers rule the universe. If you know only calculus well and have some basic ideas of linear algebra you can understand a lot of advanced theoretical physics theories.
"If the multiverse theory is correct then there is someone exactly like you (doppleganger) which is reading this sentence in another universe!!"

### Chaos Theory

Some systems are very sensitive to initial conditions. A small change in the initial conditions can create a huge disturbances in the system. Such system is known as chaotic system. For example, a flapping of the butterfly wings in New York can cause a hurricane in London. This is known as butterfly effect. Mathematics of such system is very complicated. To analyze chaotic system chaos theory has been developed. The dynamics governing such chaotic system is also very complex. We can not predict the behaviour of such system as exact initial condition is always unknown.

Miscellaneous pages
Algebra   |  coordinate geometry   |  Topology for dummies   |  Symmetry   |   Bertrand Russell philosophy   |  Sir issac newton   |   Statistical mechanics   |  Albert Einstein  |   Artificial intelligence   |  Leonhard Euler   |  Carl Friedrich Gauss   |  Number theory   |   what is science   |  complex analysis   |  perihelion of mercury  |   string theory explained  |  Calculus and differential equation   |  Medical Science definition   |  Mathematical universe   |  Calculus for dummies   |  Weyl's theory  |   electron and proton
Complex analysis
quantum mechanics and elementary physics |  Mathematics (Advanced)

# Quantum Field Theory

Feynman's sum over histories   |   S-matrix   !   quantum field theory

# Theory of relativity

Relativity made simple   |   Special theory of relativity   |   General theory of relativity   |   Tensor calculus  |   Hamiltonian mechanics   |   Field equation  |   Perihelion of mercury|   Geodesic distance

# Quantum mechanics

Schrodinger equation   |   Matrix mechanics   |  Dirac equation

## P VS NP

P VS NP problem is one the hardest problems in mathematics. If you can solve this problem you will win a million dollar prize from clay institute of mathematics. P here means those problems which can be solved in polynomial time. It is deterministic set of problems. P also means that a problem is solvable by Turing type algorithm. Whereas the NP means indeterministic problem. Given a problem there are altenative choices. And from that alternative there are more alternatives to choose from. A particular set of steps from those will determine the problem's solution. But a prior one would not know which steps to follow to solve a particular problem. Hence it is NP (non-deterministic). Real number is the basis of mathematics and theoretical physics. What is real number? A real number is nothing but a class of rational numberss. The class of rational numbers less than 1/2 is a real number. This was the consequence of the theory of real number. The irrationals were found to be some series of rational numbers, which has no rational limit nor infinite limit. And real numbers are the totality of rationals and irrationals. This was the idea behind defining real number as the class of rational numbers. The whole theory deserves another page , which will be made very soon.

Love formula

## P VS NP

P VS NP problem is one the toughest problems in mathematics. If one can solve it he will get a million dollar prize from clay mathematics institues. P means that a class of problems is sovable by Turing type algorithm in polynomial time. On the other hand non-deterministic

The world could be a computer simulation. In the movie “matrix” this truth is depicted. The laws of physics and the effectiveness of physics in describing the universe reflect this fact too.

## the Matrix

Have you ever seen the movie matrix? if you like science you must watch this. This movie tells us that our world is in a computer simulation or inside a matrix. what if our world is a complex computer program. We are nothing but the strings of binary digits 1 and 0. It is hard to believe but many scientists believe it to be so. According to the simulation theory even our consciousness is simulated by computer program. I do not know whether this theory is right or wrong but such theory has many advantages.
yes we are inside the matrix. We are living in a dream world. About 14.4 billion years ago an accidental explosion happened. Everything including spacetime was created through that explosion we call big bang. What exists now is a consequence of that. We are here because our universe had no boundary at that special event. The universe started expanding rapidly ever since big bang happened.
Everything follows simple rules which are universal and eternal. The grand design of the universe reflects this fact. Both small things and the large structure have to obey these laws which are scientific. Small world of atom is governed by chance and God plays dice all the time. Our universe can appear from nothing due to chance taking quantum leap from eternity. Our reality is a model which can be described by fundamental particles and forces. Without these forces you can not see this sentence and our earth would not stay on its orbit around the sun. The matrix is everywhere even when you look into the very room. It is the chair you are sitting on, it is the air you breath and electricity that is powering you and your computer.
It is possible that our universe is not the only universe. There is a multiverse of universes each of which has fundamental laws and constants. This universe is a gigantic simulation.

What is real? If you want to talk about what you can taste, see, touch or feel, then the “real” is just the electrical signals interpreted by your brain.

New theory of the universe:

Where does the law come from? Physics has a lot universal laws that describe our reality. But the provenance of these laws is unknown. The laws are supposed to exist all the time. So my contention is that laws exist as a logical necessity. The laws exist all by themselves. Mathematics is the only language that describes these laws precisely. Every physical law is a mathematical law. Mathematics can be built from purely logical grounds. Logic can be very abstract and removed from empirical world. So it can be assumed that physical laws exist all by themselves like logic and mathematics. The question of how the laws came from is solved apparently. Geometry is a priori ( that does not depend on experiment) from of human intuition. All possible worlds must confront to mathematics , not only this accidental world that we live in. Otherwise the idealism states that reality is our thoughts and imagination. Better still, it is the figment of our imagination. This is also consistent with this interpretation of the existence of physical laws.

The edge and boundary of the universe :

The universe that we live in may be finite without any boundary. It can be like the surface of the earth. The surface of the earth has no boundary but it is finite. There is no report of someone falling off . So we might be trapped inside a three-dimensional surface. A surface of an n-dimensional space is a n-1 dimensional subspace. So our universe can itself a surface of four dimensional space, which we can not perceive. You can not also ask what happened before the big bang. There was no notion of time prior to big bang. Space and time were created at the instant of big bang. It is like asking what is there at the south of south pole. There is nothing south of south pole of the earth. This issue can be tackled in another way:

Theory of relativity has improved our understanding of space and time. In theory of relativity space-time has dynamical characteristics. Time as well as space are relative. What we can observe is space and time. Footrule and a chronometer give the description of all the events in our universe. Now question may arise what is outside our visible universe. There is nothing actually. It is the same as the question of what happened before the big bang. We only know the universe through space and time. When there is no existence of space and time , there is no issue regarding what is outside our universe. We tend to think that we can reach the boundary or horizon of our universe. But this is not only theoretically impossible but also implausible. Space and time must cease to exist as soon as you reach the edge or boundary. We should not think ourselves outside the framework of relativity or Newtonian absolute space and time.

Weirdness of the world:

Life may not have a purpose but when you try to observe deeply everything seems mysterious and interesting. Take for example our very mind and its nature. What is the ground for believing that other people are thinking like you are? We can not perceive other people’s mind like we perceive our own minds. It is only the analogy by using which we can infer that other people are thinking like me. We can not directly experience their thoughts and emotions. We can not be acknowledged of anything happening inside their heads. This is very consistent with the concept of solipsism. Solipsism states that only you are sure to exist and everything else is just your imagination. What is happening to us is very occult and arcane. We are being played by the laws of physics. Physics only reveals the causal structure of the world. That is to say, it can only say that something is the cause of any other thing. It only can say that something is going to happen after some other thing has happened. This is the nature of the world; cause-effect, action and reaction . We are forever slave to it as the Merovingian’s quotes go. What goes on inside the mind might also have causal relationships with one another. This will need a comprehensive and through analysis of the causal theory of perception.

Anomaly or glitch in the system:

This world or the universe is a gigantic machine. It is better to call it a physical system. The universe can be explained as a physical system or it can be explained as a gigantic computer program. In the movie “matrix reloaded” the universe is depicted as a computer generated dream world. A physical system can be a computer simulated world but it is not always the case. But a computer generated system must be a physical system as was shown in the matrix. It is very reasonable to ask whether our universe has a glitch in it so that we can find it to utilize for our purpose. Universe contains singularity like the center of a black hole and the big bang. But this is not the kind of glitch I am talking about. A glitch , I suppose, should be a disruption in the simultaneous rendering of the reality and our perception of it. Our reality is the model created to suit our five senses and mind. There is close connection between the reality, mind and our senses. At this point it is irrelevant whether the world is materialistic and idealistic. I have taken for granted that it is a model . If we have created this model we can change it , if not, not. It may be asked whether the same model of reality is applied to other animals and insects. So far no glitch has been found and we can not escape from this reality. But there are anomalies in the system. You are not the anomaly but someone is. Now I will elaborate on the anomalies in the system.

This is the story of the one who does not like the rules of our society. He does not want to cling to the norms and tenets of his society, that people advocates. He is a man of science and his beliefs are tentative and not dogmatic. He questioned everything about the world. So he tries to make sense of the religion and God. All the people of the society believe in God and religion. He become very shocked by seeing people blindly follow religious rules and also by seeing them performing rituals. This does not make any sense to him. How could educated and elite class believe in such a deity as God ? The universe is rational and logical . There is hardly any place for God in it. Laws of physics are sufficient to describe the universe. So after being surprised he tries to convert them and dissuade them of their belief. Otherwise there are several flaws in God’s hypothesis. God is thought to be all powerful. So let us ask a question :

God is requested to build a heavy stone that he can not lift above by himself.

So even if he is able to build such a stone he would not be able to lift it or elevate it. Hence he is not all powerful.

So there is anomaly in the system. There is always someone who is against the system. He is enemy of all those who want to protect the system by supporting the orthodox and traditional ideas. Do you think you are the anomaly? The anomaly does not listen to the creator of the system. He is against the system or his creator (if there is one).

Cyclic nature or periodicity in the universe:

Everything in the universe is cyclic. The earth revolves around the sun. The sun revolves around the galaxy taking all the planets of her with herself. The galaxy also rotates relative to a bigger part of the universe. And , in turns, the universe itself is rotating. Yes, the universe has a spin or angular momentum. Without cyclic motion universe and life would be impossible. Everything come back to itself sooner or later. The most important ingredient in quantum mechanics is wave which is usually a sine or cosine function. These waves represent particle in quantum mechanics. But wave is a phenomena that repeat its behavior over and over again. Like wave everything in the universe come back to itself inexorably. This is the nature of the world. We see same person again and again, we do same thing again and again. May be we will go back to the place where we were born first time. We cannot escape this inevitable cyclic occurrences.

Nikola Tesla famously quoted that if you want to find the secret of the universe think in terms of energy , frequency and vibration. In everything there is vibration and energy. Electron is a wave vibrating through three dimensional space. Light is also a periodic process.

Human as scientific construction:

Human beings are scientific construction in every aspects. If you talk about how our body function internally you have to resort to biological study. The anatomy explains the structure of the human body. Biological science is very efficient in describing the processes that occur in our body. Take , for example , our heart. It is a pump that circulates bloods into our body. The energy of the pumping comes from the heat of the body. Human body is a big source of heat energy which is measured in BTU(british thermal unit). The body cells converts heat into electrical signals and when the signals reach the heart the muscles of the heart contract . Doctor detects this kind of electrical activity using the ECG(electrocardiogram). Without electricity we could not think and see. The brain interprets all the electrical signals coming from different parts of our body. As regard the mechanical function of the body it is hard to make a perfect model of our movement. It involves a lot of non linear equations and parameters. Leonardo Da Vinci first developed a mechanical model of our body parts to explain the movements of these parts like the arms and hands. On the other hand, our brain is the most complicated object in the entire universe. Although neuroscience is very advanced science we are still lacking necessary skill to explain brain function properly. It has certain relationship with quantum mechanics. Consciousness is mysterious and so is quantum mechanics. May be they are the same. Creation of the first biological cell was a process involving certain compounds and electricity. That cell had DNA and RNA molecule which are supposed to contain all genetic information of life. These molecules give the instructions to carry out all the functionalities needed to develop living organisms. DNA is also known as the double helix due to its spiral like structure. Unraveling the structure of human genom was a great leap towards the understanding the human body and its functions. All these evidence shows that humans are only scientific construction.

The rule of law:

Laws are governing our lives. They are in effect when we go to church, and pay our taxes and even when we go out shopping. We have to follow rules in every sphere of our lives. It is for the laws that we are safe from criminals and terrorists. You do not understand why you are forced to stand at the end of a line of people waiting to take money from bank’s cashier if you are late than others. You do not understand why you can not speak loudly in a public place. Everywhere there are laws of some sort or the other. We have created these laws for our protection. But is it really our own creation? These laws are derivative and manifestation of more universal and natural laws. These universal laws are the laws of physics. Laws of gravity is probably most important in the universe. Gravity permeates everywhere. We can not escape gravity even in the outer space. Einstein radically changed our understanding about gravity and spacetime. He taught us that gravity was not a force but curvature of spacetime. You are able to sit on the chair in your room because spacetime is pushing you from above. The earth is in its orbit because it moves in a geodesic in spacetime. Quantum laws are even more bizzare. These laws are probabilistic laws. By “probabilistic” it is to mean that you can not predict with hundred percent certainty everything. We have laws determining radioactive decays of some elements. But we can not tell when the decay will happen. Even if we can we do not know their cause. Probability is more fundamental than you can think. May be space and time are not continuous and smooth as we think but quantized like the space around the nucleus of an atom. What we call elementary particles are just vibrations in the corresponding quantum fields in space and time. There are electron fields , gluon fields and other matter fields which are endless and pervasive throughout the universe. When a field , for example electron field, is excited at a particular position in space and at a particular instant in time the matter-like electron appears. These fields contain energy even in the vacuum state. The rule of Maxwell’s equations is even more apparent in daily lives. It is seen when we turn on our television, when we speak on our cell-phones and particularly when we see other objects with our bare eyes. The universe is a grand design and the architect was perhaps a great mathematician. When we are on the fourth floor of a building we will age slowly relative to ground floor. Time flows at different rate at different places in the universe. The earth’s center may be few years older than its surface.

Universe as a gigantic time machine:

The universe is a gigantic time machine. We are not likely to travel to another galaxy or another solar system any time soon. Our neighboring galaxy Andromeda is millions of light-year away. One light year is the distance that light travel in one year. Such a huge distance can not traversed in short time. We will be old and die on the way by the time we reach there. Even if we reach there by the time we come to the earth , nothing will be here. It is only possible if we can build time machines. Warp drive could take us to another galaxy in a very short time. To do so we must be able to bend space to create a worm-hole like shortcut through spacetime. Thus we can travel between two distant points in short time. Suppose one day we create such a worm hole to reach Andromeda galaxy. By reaching there we can see our past events such as the extinction of dinosaurs on the earth. The light from the event is still rushing towards the Andomeda and by reaching there fast we can catch those lights. Otherwise there is a possibility for closed time-like curves (CTC) to exist in spacetime. Following this curve we can travel back to our past. For example we can start our journey at the morning of one day and can come back to previous day at night. Otherwise there arise many paradoxes and logical contradictions in time travelling to the past. This makes it improbable the fact that we can travel back to our past. It is still a good science fiction. But time dilation is a true fact. It has been proven countless numbers of times. We have a lot of evidences for that. On the other hand , black hole can also be used as a gateway or portal to go to another universe. The center of a black hole is a singularity of spacetime. It is one of the biggest mystery that gravity or general theory of relativity can not explain.

“Have you ever had a dream that you are not sure if you are asleep or awake. What if you could never wake up from that dream! Could you tell the difference between the real world and the dream world”

Multiverse theory:

The idea of multiverse is probably the most daring concept in science. At one time this universe meant everything that are in the cosmos ; the stars , the galaxies and us. But multiverse theory predicts these are not the totality of things. There are infinite multiverse of universes. Each universe may contain a copy of you reading this sentence right now. The idea of multiverse came from the “many world” interpretation of quantum mechanics. When we do do observe a quantum system the system possess an infinite number of possibilities. There are an infinite number of outcomes that exist simultaneously. Many suggest that each outcome is as real as the other and exists at an individual world. The whole collection of such individual worlds is called the multiverse. String theory says that big bang is not the beginning of our universe. General theory of relativity says that we are like the insects on the surface of a gigantic soap bubble. This soap bubble expands outward. But string theory says there are other bubbles and there are actually an infinite number of them. Big bang occurs when two such bubbles collide or a bubble spits into two baby bubbles. That is modern string theoretical interpretation of big bang. According to string theory physics is the harmony that the strings create. Chemistry is the melody played on the same strings. And our universe is cosmic symphony resonating through ten dimensional hyperspace. Among the cosmological models of our universe the no boundary proposal developed by Stephen hawking is the most notable. This proposal says that our universe had no boundary at the event of big bang. Usual model states that space and time themselves were created at big bang. Time had a beginning. This might sound ridiculous but theory of relativity had taught us time is relative. Consequently it was the big bang when time started its journey. Hawking later suggested that at the big bang space and time were the same and spacetime was like a smooth surface without any boundary. It was like the south pole of the earth. The boundary condition of the universe is that there is no boundary.

### Free will

Another matter that is of great debate is the problem of free will. According to principles of classical mechanics everything is predictable. Our actions are not governed by us. Every will and volition have previous causes and that cause in turns has another cause. Thus we certainly do not have any free will. But in quantum mechanical world nothing is predictable with absolute certainly and we might possess free will after all. We have freedom to make our own decision. According to classical physics we have only one of two alternatives (yes or no) in our mind. Our choice is predetermined with yes or no option. But according to quantum principles we have both yes and no options, which exist simultaneously in our mind. Thus Quantum mechanics has rescued free will from drowning.

The phenomena of having both yes and no states in our mind is called

the principle of quantum superposition. Scientists have been able to find the exact location of the brain where this quantum superposition seems to take place. This part of the brain is called micro-tubules. There is a close connection between our consciousness and quantum mechanics. Both are mysterious and thus both may be the same.

### One electron universe

One electron universe is a concept or idea which tells that there are only one electron in the universe. What we observe to be different particles is really one electron going back and forth through time. The world lines traced by a single electron make a twisted structure like a knot in spacetime. Any slice through time represent the single electron at different locations. Positron can be viewed as electron going from future to past in space.

Richard Feynman quoted something which represents this fact of electron going back and forth in time :

” I know why all the electrons have identical mass and charge because they are all the same electron. “
Electron is a point mass which have negative charge. Electrons are the singularities in electromagnetic field. That is to say,
they have infinite divergence. What it means need a careful study of maxwell equation.

### Physics of the impossible

Michio kaku have tried to explain all the paranormal activities in the context of science. These are telekinesis , telepathy, mind reading , psychokinesis and many others. We see all these in sci-fi Hollywood movies every now and then. But are these phenomena real or scientific? There is no direct relationship between these and science. Science like to explain stuff in terms of causal relationships. As far as causality is concerned there are no hope for these kinds of phenomena to be true. In science we have explanation and evidences. Paranormal activities have no explanation otherwise these were not called paranormal in the first place.

That does not mean we give up. May be, some future science will explain or make these phenomena possible.

Quantum teleportation:

Have you seen the movie “star trek”. Here the crews of the spaceship become teleported from one place to another instantaneously. By teleportation it is possible to move physically from one to another instantaneously without being in the intermediate place. That also amounts to say that something disappears from one place and reappears at other place instantaneously. In the context of quantum mechanics teleportation means the transfer of information from one place to another instantaneously. This idea of quantum teleportation came from the idea of quantum entanglement of quantum mechanics. According to the principles of quantum entanglement information can travel faster than light. By properly utilizing these quantum information same copy of a particle or a group of particles can be reconstructed out of nothing. The principle is that using only the quantum information it is to create a particle in another place. The quantum teleported particle should have the same properties as the origin one so after the original particle is destroyed the identical one would be created. At the moment only one particle has been teleported successfully by scientists. But as the energy and time needed to encode the information of a large number of particles are huge it not very practical to teleport a massive body. But it is still a possibility.

A universe from nothing:

The energy content of our universe is zero. This might sound absurd but our universe can emerge from nothing which is zero energy. The quantum fluctuation in the vacuum can give rise to particle and anti-particle for a brief moment of time. These particle then annihilate again to keep the total energy zero. The inflationary cosmology states that our universe can be spontaneously created from pure vacuum fluctuation. The other explanation is that gravity is negative energy. If you separate two objects far away then the system possesses negative energy. Due to gravity our universe has a macroscopic stable structure. And the energy of all the planets , stars and galaxies would have negative energy. This negative energy can be balanced by the energy equivalence of matter content in the whole universe. This equivalence energy can be found from Einstein’s famous equation E = mc^2 . Thus it is very logical that the energy of the whole universe is zero(0). May be we are inside an electric battery which has exhausted all of its energy. Reality is very illusive but a persistent one. The first thing that is illusive is the atom.

The reality of atom:

Atom is the greatest mystery although everything is made up with it. Einstein first proved the reality of atom by observer a kind of random motion called Brownian motion. We can not see atom with bare eyes but it is the fundamental constituents of all the matter in the universe. Inside the atoms there are electrons in the quantum orbits. Protons and neutron stay inside the nucleus. These particles are so minuscule that we can never see them with the naked eye. But that is not the end of the story. Inside protons , if we zoom in we will be able to see quarks. By the exchange of gluons, quarks are held together inside the proton. The force induced from this exchange is called strong nuclear force. Quarks are not the end of the story too. String theory now posits that there are further fundamental entities inside these quarks. But these entities are not matter-like. These are string like filaments of energy. Like the strings of the violin these can vibrate but in multi-dimensional space. All these phenomena are part of the atomic world. The cosmos is the music of these vibrating strings. Various vibrational patterns create various particles. Graviton which is supposed to carry gravitational force is one such pattern. There is another force that works inside the nucleus of the atom. This force is called weak nuclear force. It is very weak and short range. Due to this weak force radioactive decay of elements occurs. All the phenomena happening inside the nucleus are very mysterious and only quantum mechanics can explains this weird stuffs accurately.

Arrow of time:

This was one of the chapters in the famous book “brief history of time” written by Stephen W . Hawking . He compared three kinds of time: the one is psychological time, the second is thermodynamic time and the third is physical time. Are they the same? The concept of psychological time is hard to explain. But the other two can be given much easily. Time always flows from past to future. This is the arrow of time. It can not run backwards. This apparent done direction flow of time can be accounted from the fact that entropy of a closed system always increases. The entropy of our universe is increases. We are destined to face heat death of the universe, when temperature will be uniform throughout the universe. No process will run anymore. This is the consequence of entropy change. Entropy is the measure of disorder of the universe. Things only get more and more disorder over time. If you put a hot cup of coffee on the table the coffee will be cold. That means entropy will increase. Boltzmann found that atoms plays a fundamental role in the universe. He based the concept of entropy purely on the statistics of the arrangement of atoms and molecules. He was able to define entropy in terms of probability. Microscopic properties of the system gives it macroscopic behavior. Time may be the result of some such microscopic properties of the universe. Time is a one-way street and it has its direction fixed by the thermodynamical property of entropy.

Histories of our universe:

Einstein did something quite remarkable. He united history with geography though his theory of relativity. Newton thought that our universe was only run by one master clock. We all share one absolute time. But Einstein radically changed our understanding. Our physical universe evolves through time. Only mathematical language can perfectly explain this accurately. The upshot is that our universe not only has different spatial properties at different location but also it has a history. The geometry of the universe changes with time too. It was very astonishing idea which helped scientist to unlock the secret of the creating and evolution of the universe. We now know that big bang happened some 14 billion years ago. Two scientists were awarded noble prize for sharing their discovery with the world. The relic or leftover from the big bang was experimentally found. This relic is the cosmic background radiation(CMB). The temperature of this CMB matches the prediction of the theory. You can actually see some of this radiation leftover when you tune in the TV in your home. The noise in some blank channel is that radiation coming from the big bang. But this is not the end of the story. The next revolution came from quantum mechanics.

Feynman discovered his famous “sum over histories”. According to the principles of classical physics an object goes from one place to another place in one definite trajectory , which can be determined by Newton’s law of motion. The object has one definite history. But in quantum physics a particle can go through all the paths that are possible. It includes the most bizarre path across the entire universe. It also includes the paths where particles travels backward in time and forward again. The particle has not a single history but an infinite number of histories. Quantum mechanics forbids a single history. So in the context of quantum mechanics it is called “sum over histories”. Similarly when applied to our universe as a whole , it contains a infinite number of histories. Our universe is only one among infinite number of other possible universe. This now brings us to quantum cosmology.

Quantum cosmology:

Michio Kaku argued that big bang must be explained in the context of quantum mechanics. Big was a tiny event and universe was like a particle. So we can apply Schrodinger equation at the time of big bang. Our universe must have a wave function. Heisenberg’s uncertainty forbids a single big band accidentally. We can neither locate precisely where it happened nor can know how it happened. This is all quantum mechanical principles which destroys accuracy of measurement. Certain amount of energy can be borrowed from empty space and matter can be created out of nothing to initiate the big bang. Quantum fluctuation can initiate big bang , which was inevitable to happen due to chance. There are a flat infinite stage , where big bang is happening all the time due to this quantum fluctuation. Each big bang is creating a pocket universe all the time , even when you are reading this sentence. This process is called bubble nucleation. The proper theory of this quantum bubble-bath of universes can only be properly described by inflationary cosmology proposed by Alan Guth. The upshot is that the universe can emerge from nothing taking a quantum leap from eternity.

Consciousness and its relation to physics:

Consciousness is hard to explain. Why do we feel conscious? Why are we self-aware. It is remarkable that we are the only living organisms who are self-aware. Consciousness arises solely due to our memory system and sensory data that we receive from our five senses. Memory creates the perception of time. If we could not remember the past we could not perceive time. Memory process or functions are associated with certain part of the brain called hippocampus. So memory directly relates to the physical structure of the brain and neurons. Consciousness directly relates to a model that is in our mind. Our mind is continually updating the model based on the sensory data to give us the true perception of reality. We can not know a table by first looking at it. It must match the model in our brain or mind to be properly recognized. I must recall Stephen Hawking’s quote that every reality is model dependent. Through our conscious mind we perceive our reality directly.

The other theory of consciousness is that we are not conscious but the universe as a whole is conscious itself. There are information encoded in the electromagnetic field of spacetime. We are like an antenna leaving information as our memory in the field. Everything is there is the field which is the universal consciousness. We are just experiencing it like everybody else. The difference with the concept of the usual definition of consciousness is the reverse of the flow of information. Now lets return to the connection of consciousness with physics.

Our current understanding of physics is unable to explain consciousness. Everything in physics is computational problem. We can find the solution of a problem in finite number of steps within finite time. We can also compute the numerical solution. All the physics can be called computational physics in this sense. Roger Penrose has argued that our consciousness is something that lies beyond our current understanding of physics. Consciousness can not be computed using the laws of physics existing at present.

Artificial intelligence:

Artificial intelligence is the ability which machine can acquire to act and think consciously. Alan Turing first proposed the idea of AI . His hypothetical abstract machine called “Turing machine” was the precursor to modern computer. Although modern computer is constrained by finite memory, ideal Turing Machine has infinite memory storage. So if the computational power increases beyond certain range , all computers can become self aware and intelligence. This higher level of computational power will be called A. I . There are two version of A.I : one is the strong a.i and the other is weak a.i. Strong A.I is the ability for a machine to think like human beings and also gives insight of how the thinking process works. But weak A.I does not give insight about the process of how the mind work. Deep Blue Sea, a computer program , which defeated Kasporav is an example of weak A.I. The rise of machines will be the rise of artificial intelligence. Machines will one day be able to think consciously. The will become conscious and thus will dominate us. Although this is purely a science fiction, some regard it as a serious issue. One of the most notable examples are movies where A.I is portrayed is “Matrix”. In this movie machines have suddenly taken control over human by making them a source of energy.

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