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.
General theory of relativity theory of quanta

General theory of relativity + theory of quanta = Everything

General advice

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!
This was Russell famous paradox. All mathematics are basically logical deductions. You can follow my website for more logical analysis of mathematics.

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.
integration
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.

carton
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!!"
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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 for dummies   |  Medical Science definition   |  Mathematical universe   |  Weyl's theory
Complex analysis
quantum mechanics and elementary physics |  Mathematics (Advanced)

"The best thing about science is that you can apply it to your life"

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

heisenberg's equation of motion
Proof
In quantum mechanics operators are replacements for classical quantities like position and momentum. They are some kind of functions too. There are seven ideas that shook the universe. These are
1. Newtonian mechanics
2. Energy and entropy
3. relativity
3. quantum theory
4. conservation principles
5. copernican astronomy
6. symmetries
7. Theory of everything

Real numbers


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.

Physics of everything


equations of everything physics


equations of physics


equations of physics


equations of physics

Love formula
equations of physics


equations of physics

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.

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 space. 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 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 is mysterious and interesting. Take for example our very mind and its nature. What is the ground 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 acknowledge of anything happening inside their head. 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 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 detail 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.

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