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"Science is the source of all other knowledge"
"Mathematics is about numbers and physics is all about mathematical functions"


crazy Quantum mechanics + beautiful relativity = Universe (including us?)

"All that we know from common sense are necessary mistaken or erroneous.. "

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 piece 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.
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 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.

"Universe is not what it seems to be"

Introduction

The main purpose of this website is to give some basic ideas of classical physics, quantum mechanics, relativity and quantum field theory for those who wants to become a science major or philosopher in science. Theories are at the heart of physical sciences and mathematics. Here most of the major and interesting theories of physics have been discussed. Those who want to understand popular science books will get help from this website. Some electrical and electronics engineering concepts have also been given for undergraduates of electrical engineering. This website is not supposed to include everything. Those who are very curious to understand scientific theories and spacetime physics in somewhat non technical way, will find this website very usefull. So far a little subject matters have been included. In the future more and more topics will be added. Many topics of Mathematics and its applications are also demonstrated in a simple manner. I have already said, all physics is interpreted by mathematical functions. The principle aim will be to justify this claim.

Theories are basically mathematical descriptions of natural phenomena. A theory is like a boat. How well the boat floats gives the soundness of the theory. The better the boat floats, the better the theory is. As long as a theory is able to describe particular phenomena , it is accepted as valid. But it can never be taken as irrefutable and absolute. For a better theory can replace the old one. Such is the case with Newton's universal law of gravitation


Theoretical physics,

Quantum Field Theory

Feynman's sum over histories   |   S-matrix

Theory of relativity

Relativity made simple   |   Special theory of relativity   |   General theory of relativity   |   Tensor calculus  |   Hamiltonian mechanics   |   Field equation

If you give you only get in returns...

Quantum mechanics

Schrodinger equation   |   Matrix mechanics   |  Dirac equation

string theor theory
In quantum mechanics operators are replacements for classical quantities like position and momentum. They are some kind of functions too.
all the physics in one equation (excluding string theory)
all physics equation

This is the equation which is derived in analogy with Feynman's path integral equation.
paradox of physics

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

"we are all here to do what we are all here to do"

Newtonian mechanics made it possible to develop the first mathematical model of the universe. It was a great revolution in science. Everything in science is founded upon principles of newtonian mechanics. It is hard to imagine anything which does not correspond to Newton's law. Quantum mechanics and relativity are developed to account for the phenomena which classical newtonian mechanics fails to explain. But in the limit both theories reduce to newtonian framework. Application of Newton's law is almost everywhere from rocket science to automobile engineering. We have developed an innate sense of the principles of newtonian mechanics in us. We move and throw objects as if we know the position in advance.
On the other hand we can not predict the outcome of quantum mechanics experiment precisely. Principles of quantum mechanics violate our common sense. It is developed using logic and mathematics which defy our intuition. Suppose you throw a electron in the wall and on the wall there are several objects placed. Then there is always some chance that the electron will hit those objects at the same time. This is the kind of weirdness that our commonsense can not grasp. There are other bizzare consequences of quantum mechanics like entanglement and quantum tunnelling. According to Quantum mechanics spooky action at a distance is possible. This faster than light communication had disturbed Einstein too much. According to theory of relativity nothing can travel faster than light and causality is not violated. Quantum mechanics have certainly made many phenomena non-causal. The state of affairs in quantum world can be described with the following example:
You are now seeing an advertisement below served by google. See how it is displayed on your device's screen. Electrons manuevre the liquid crystals to block or pass the light from small light bulbs. The light that comes from the display are making this ad look so beautiful. Each pixel on the ad is excited electronically. What you are seeing is only light. Now when you will touch the ad , a set of instructions encoded inside the memory system of your device will be triggered. How will this happen? Well computer has all the informations that are displayed on your device's screen. When you touch the ad , the display will help develop a resistance or capacitance on the specific part of the screen you touch. This will tell the system to take necessary action. Believe it? Now touch the advertisement ..
if we adopt the theory of radiation, the atom seems to live a "self contained life" - " the world forgotten by the world forgot". But the atom sometimes involves in parcel-post activity. That is to say, it can give a parcel of energy to a postman or it can receive one from him. The postman(who is not a teetotaller) who receives the parcel sways from side to side. The bigger the parcel is, the faster he sways. He runs at the same speed every time whether the parcel is big or small. The postman is the only link between the world of atom and the outside world.

Giving to others is a great virtue....

"I know everything is in the mind but mind is a very powerful thing"

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 microtubules. There is a close connection between our consciousness and quantum mechanics. Both are mysterious and thus both may be the same.

Quantum tunnelling

Another bizzare consequences of quantum mechanics is quatum tunnelling. A classical object can not pass through a rigid barrier but an electron has always some chance to be found on the other side of the a potential barrier.


quantum tunnelling
"time is the most precious commodity in the whole universe"

quantum entanglement

Quantum entanglement is a physical phenomena which occurs when pairs or groups of particles are produced or interact or share spatial proximity in a way such that the measurement of states of each particle can not determined independently of the state of others. In such a situation the particles are said to be entangled. quantum pure states are rays or elements of Hilbert space (H). Hilbert space is a generalized Euclidean space where inner product between two elements are well defined. A point in Hilbert space can be seen as a state of vibrating string , which can be projected on to coordinate axes representing different overtones or harmonics. In general Hilbert space is the infinite dimensional analog of Euclidean space. Pure states or rays are usually represented by ket vector. Particles in these pure state can be separable. But there are states where such separation is not possible. These states are entangled states which can be modelled mathematically.
Quantum entanglement should better be classified as an example of non-locality. Classical physics is always concerned with local measurement or it only enables us to compare local quantities. Non-locality violates causality . This is weird but non-locality seems to be inherent in quantum mechanics.
quantum entanglement
This quantum entanglement permits faster than light communication which is also known as spooky action at a distance. Suppose two electrons are entangled so that when we measure one electron's spin then the spin of other is determined with certainty. Spin states can be either up or down. So when we fix one of this , the other is also fixed. This will happen no matter how far apart the two electrons are. This is quite mysterious yet experimentally verified.


"Simplicity is beauty.." equations of physics

Some of the revolutionary equations of physics in one package

equations of physics

Theory of relativity

Space-time is a four-dimensional haussdroff differentiable manifold on which a metric tensor is imposed and the metric tensor gives rise to geodesics so that particles experiencing no forces except gravity travel along such geodesics.
This the core idea of General theory of relativity. Unification of space and time was the most significant result of the theory of relativity. We need four coordinates to specify an event in space-time. Events are the four dimensional analog of points and are the fundamental entity in relativity. Distance between two events is space-time interval. Theory of relativity has modified physics to a great extent. It has a lot of philosophical consequences as well. Question now arises whether there is any distinction between past, present and future. Time is relative according to this new theory. All the events that are simultaneous to one observer may not be simultaneous to other observer moving relative to the first observer. Abosolute distinction between past and the future is no longer valid. Topological features which are only spatial description for one observer can be a mixture of both spatial and temporal features for another observer.
The most radical idea was that our space-time is curved. Not only our space is curved but also time becomes distorted near massive objects. How is our space curved? The simple explanation is that light bends when passing near the sun. Clocks and rulers does not remain rigid but vary from point to point in space. We know clocks and rulers remain rigid in Euclidean geometry but in curved spaces this hypothesis is no longer valid. There are lots of other facts which confirm that space time is indeed curved. Although some complicated mathematics are needed to explain the curvature of space, the idea is quite simple. This was Einstein's famous equivalence principle. This principle simply states that acceleration and gravity are equivalent to each other.
Suppose you are in a lift and you can not see the outside world. If the lift start accelerating , can you tell whether your weight is caused by acceleration or by the gravitational pull of the earth? This reasoning alone motivated Einstein to develop his theory of general relativity.
The mathematical laws of Newtonian mechanics differ from those of relativity in a fundamental way. The laws of Newtonian mechanics is the differential equations with respect to time while those in relativity are the differential equations of second order with respect to space-time interval.
One of the greatest applications of General theory of relativity is the GPS(global positioning system). The time difference that arises due to different gravity at the orbit of artificial satellite needs to be corrected in order to perfectly design the GPS. Otherwise the error in GPS reading would be few second in 24 hours. There are a lots of applications of General relativity in cosmology as well.


"A knowledgeable friend is better than keeping one thousand books and giving to others is a great virtue.."

quantum gravity

Quantum gravity is the first attempt to merge quantum mechanics with General theory of relativity. But there were many loopholes and inconsistencies in such theory of quantum gravity. First why do we need a theory of quantum gravity? The space-time which General theory describes is assumed to be smooth and continuous. But if we look into smaller and smaller parts of space , the space becomes bumpy and irregular. That is , at quantum scale , which is the planck's length , there arise bubbles and quantum weirdness. So general relativity breaks down at this scale of length. For example , At the instant of big bang universe was very small and dense. And at the singularity of a black hole the laws of relativity no longer works. We need quantum mechanics to describe such singularity. On the other hand quantum mechanics do not apply to macroscopic scale. For these reasons we need a theory like quantum gravity.


"what is mind never matters and what is matter never mind.."

Abstractness of physics

There are abstracted in physics, which modern physics have proven repeatedly. What is matter? We can explain it using theory of relativity or Quantum mechanics. This will lead us to conclude that matter is an attribution an of certain abstract properties. If we continue to divide matter we will see that what remains is formless and immaterial substance. Electron is made up of quarks , quarks are also made up with other sub atomic particles which can be devided further. According to string theory quarks are made up with strings or vibrating filament. This certainly obliges us to accept that matter ultimately consists of things which should not be regarded as matter.
Quantum field theory states there are fields which are everywhere and endless. This fields are the description of sub atomic particles. There are electron field, quarks field, neutrino field and other particle fields. The oscillation of quantum field creates this kind of particles. There is higgs field which permeates everywhere. Higgs field provides mass to particles by interaction. Field is nothing but some property of spacetime.
Mathematics that describes the particles in standard model is very abstract. There is group theory which characterizes the symmetry of the law governing particle physics. Sub atomic particles can be grouped together with certain properties like isospin and hypercharge. This group describes certain transformation laws. This is called symmetry group. This symmetry implies certain kind of conservation of physical properties. For example a phase shift in the quantum wave function correspond to the conservation of charge. In short , symmetry is the properties of physical system which leaves the system unchanged under certain kinds of transformations. Thus the standard model can be modeled with SU(3)xSU(2)xSU(1) , which leave the symmetry invariant. This unified model is the combination of three symmetry groups SU(3) , SU(2) and SU(1) which describe strong interaction, weak interaction and electromagnetic forces respectively. The symmetry shown by strong interaction can be explained as follows:
The strong force is carried by three quarks of different colors (red, yellow and green). The interaction between two identical quarks (red to red or yellow to yellow) are the same. On the other hand the interaction between two different colors are also the same. In addition if we shift the three different quark (from red, yellow, green to orange, violet, blue), even if the shift involves a change in space and a change in time , everything remains the same. Thus strong interaction shows some kind of symmetry. Physicists call it the "gauge symmetry" of particle physics. The word "gauge" came from the concept "gauge transformations" coined by Hermann Weyl. You can follow here for more explanation about well theory.
SU(n) is special unitary group whose elements are matrices. Each of these matrices is a representation of certain other group elements. This special unitary group elements represent certain transformation laws. The determinant of this SU(n) is one. That is why its name is special unitary. More explanation needs analysis of group theory and representation theory.
A particle can be an element of a vector space, upon which an element of the above group acts. Through this action another element of the same vector space can be found, which can describe another particle. This is the core idea behind developing standard model.
Physics can be categorized in three different branches: one - corpuscular physics, touch physics and sight physics. Touch physics is what we regard as those events happening to the billiard balls. From the common sense notion it could be noticed that the billiard balls touch each other when they collide or come into contact. But from the standpoint of physics those billiard balls never touch each other. The repulsive force between the electrons prevent them from touching. According to new quantum theory this force, however , is interpreted as exchange of other sub atomic particles.

"We are the children of atoms, so understand the atom if you try to understand the universe"

Teaching is the most respectable profession. We should do and work as the teachers say

Quantum theory of atom

An atom is composed of electrons and protons, the latter being inside the nucleus, the former partly in the nucleus (except in hydrogen) , partly planetary. The number of the protons in nucleus gives the atomic number. When the atom is unelectrified the number of planetary electron is the same as the atomic number. If the quantum theory is correct , an atom has ceratin number of characters, each measured by integers called quantum numbers, which are allways small. It has also a property called energy, which is a function of the quantum numbers; and in connection with each of the quantum numbers there is periodic process which is subject to quantum rules. Each quantum number is capable of changing suddenly from one integer to another integer. When the atom is left to itself, the change will be such as to diminish energy. But when it recieves energy from outside the change may increase the energy. All this , however, is more or less hypothetical. What we really know is the interchange of energy between the atom and the surrounding medium; here there are simple laws as to form the radiant energy will take (classical laws). There are at present no definite laws determining when quantum change will take place in the atom.
The theory of atom had made it possible to develop periodic table where all the elements are arranged in specific order. The position of the elements depends on the number of electron they contain. These elements take part in chemical reactions and form various kinds of other compounds and mixtures. The chemical properties of the atoms can be deduced using quantum mechanical principles. A relatively new branch called "molecular quantum mechanics" has been developed. All the elements and compounds are basically replica of simple structure like hydrogen or helium. Combining multiple numbers of hydrogens and heliums we can create other atoms. The only difference lie in the number of protons, neutrons and electrons. What are these electron, proton and neutrons made of? These , in turns, are composed of quarks , gluons and other tiny particles which particle physics deal with.
How did atom come into existence in the first place? How did nature make a well-organized, symmetric and miniscule structure like atom? This is the question which should probably be addressed in TOE(theory of everything). All the three forces are in effect in the atom. If we analyze quantum characteristics inside the atom we find these fundamental forces there. In nucleus strong and weak nuclear forces exist and between proton and planetary electron electromagnetic force works. But in principle gravitational force also exist inside the atom. Proton, electron and neutron have certain mass. All the forces exist inside the atom. Atom is a tiny universe so to speak.

Let us eradicate ignorance and illiteracy of the science from the world.. Thank you

"Knowledge is power"

Electrical and electronics Engineering

Power Engineering   |   Telecommunication   |   Control System Engineering   |   Electronics  |   Fundamentals of EEE  |   Digital signal processing  |   Digital Filters |   Maxwell equations  |   Differential equation and calculus

"God is a great mathematician"

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 arthmetic, 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 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.

"If the multiverse theory is correct then there is someone exactly like you (doppleganger) which is reading this sentence in another universe!!"
"When you got nothing , you got nothing to loose.."

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.

"Things you own end up owning you"

Fractals

Fractals are geometric objects. Fractal is self -similar object which pattern is never ending - a appearing again and again. For example a snowflake is a fractal like object which contains similar parts within it. If one looks closer and closer at this kind of fractal like object he will see the same structure over and over again. Fractals are a great subject matter for mathematicians. We can see fractals almost everywhere. These are in the leaves of trees, in the painting of an artist and in many other things. These kinds of structure certainly can reveal many secret about our universe. Fractal can be defined using scales. Fractals are scale invariant. That is these are the same whether you look into smaller parts or bigger parts.
Mandelbrot set is an example of fractal like structure. The equation of Mandelbrot set is the iteration map :

mandelbrot set
"Mathematics may not teach us how to add love or subtract hate but it ensures every problem has a solution..."

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 qouted 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's equations.

"If an idea does not seem absurd at the first time, then there is no hope for it.."

Causality

Causality is the the deep connection between physical objects and phenomena. Causality means links. There is cause for every effect or every effect has a cause. Remember what the villain in the movie "matrix" , Merovingian said : we are forever slave to causality, cause-effects, action -reaction .. he drank too much so he must took a piss." , this kind of stuff we are talking here. Causality has a close connection to physics. Physics is always concerned with the causal structure of the world however complex it may be. Classical physics reveals to us that world is composed of continuous structure. Space and time are smooth and continuous. All the changes are causually connected by next to next relation. We must be able to infer which thing happens before another thing.
Again there comes quantum mechanics into the picture. Quantum mechanics made some weird predictions about nature and experiment verified it repeatedly. Quantum mechanics is not a single law but a combination of laws. It permits many non causal phenomena like spooky action at a distance, quantum tunneling, quantum jumping inside atom. In Schrodinger's word - " if these damn electron jumping were to stay , I would rather not be involved in quantum mechanics" . Electron can jump from one orbit to another without being in the intervening space between the two orbits. We have no other option than to suppose that space is quantized in microscopic scale. Causality is destroyed in one stroke. Neither we know when an electron jumps from one orbit to another. But we can determine the macroscopic behavior from statistical average of many quantum phenomena. For more explanation follow here.

"The universe is the ultimate free launch.."

Nature of reality

There is a concept in philosophy called "the brain in a vat". It could be that an intelligent being has kept our brain inside a vat and he is constinuously feeding electrical signals and sensations into our brain using a computer. This is constinuously creating the very reality that we percieve. One can ask what our own brain inside the skull is doing? We can not distiguish the brain in the vat from the brain inside the skull because the brain in vat gives and recieves the same impulses that the brain in the skull would do. So from the perspective of that brain we can not tell wheter it is in the vat or in our skull. Something similar is depicted in the movie "The Matrix".
I start with the qoute of Morphes of the movie "matrix" : "what you can see, taste or hear are just the electrical signals interpreted by your brain....". Reality is in our mind? We create our own reality. This is what quantum mechanics also suggests. Nature is not what it seems to be but it responds to our method of reasoning.
Every reality is model dependent. The reality we perceive is also model dependent. There is no reason to suppose that our physical reality is the only reality that exists. It is like the tv channels that we tune for our own purposes. There are many tv channels which exist other than the one we see. Our reality is the suitable channel that we have evolved with.
Physics has made matter less matterial like psychology has made mind less mental. What we find from analyzing physics are only mathematical relationships which can be further broken down into numbers. You can talk about mass. Mass , according to conventional physics, is the certain absolute quantity which does not change. It is the physical quantity which is a proportionality constant in equation F = ma. Without measuring force and acceleration can we define mass of a material body? Force and acceleration are certainly some concepts derived using geometry and algebra. That was the conventional or orthodox definition of mass. If we consider theory of relativity matter becomes more abstract. Mass and energy are spacetime curvature. In scientist wheeler words : "matter tells space how to curve and space tells matter how to move".
The structure of our world is more abstract than we think. That is if we look depper and deeper, the reality loses it meaning. Physical world is just the structure revealed by mathematics and logic. Matter is a phenomena in certain sense. Nothing inside matter or atoms is stationary. What we call inert objects is not really passive. Distinction between living organisms and inert matter is not justified in deeper sense. Biology and chemistry fall under the scope of physics. They are part of physics. We can not separate those branches from physics.
Consider the phenomena of electricity. It certainly involves current, charges and force. We do not see charge or electron which is a tiny particle with our bare eyes. But electricity works like magic. Reality is more abstract in quantum level. Only mathematics can reveal to us what is happening. Nature certainly obeys mathematical rules to hide its true character from us. Nature is very skillful in camouflaging .
What about our thoughts and psychological affairs? As far as theory of relativity is concerned our thoughts can be given same properties as the events in spacetime. What we call mind is certain group of events connected together. These are space-like events which any material objects cannot travel through. Mind falls under the scope of physics too in this sense. So we might be able to predict what we will think or decide as well as what we can write and where we will go. This will introduce a new branch of physics called the dynamics of mind. Actually a German philosopher tried to develop a theory for the dynamics of mind. He gave a metaphysical theory to describe our mind's action , decision and thoughts. The theory is probably dying. But we should not care less about such a intriguing matter and we should revive those as soon as possible.
Reality has been shaped by the laws of nature. Our universe is a grand design. The solar system, milky way and the universe are formed in a way that reflects a great work of an painter or craftman. There are order and beauty in the universe. These are the manifestation of great laws of physics. Stephen Hawking has beautifully summarized the behavior of quantum world and space-time in his book "the grand design". The universe may happen to come by an accident but all the things and phenomena obey physical laws. The big bang was an accidental event and a singularity. Anything can happen from a singularity. In this case our universe was created or happened.
In the book "brief history of time" Stephen Hawking tried to answer some really big questions : how did the universe begin?, What is time? , Can time run backwards? and last of all where do the laws of physics come from? These are the most profound questions in science. Science might not be able to answer all these questions but it gives us explanation for almost everything which is irrefutable.

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"If you want to reveal the secret of the universe , think in terms of energy, frequency and vibration.."

Duffing equation for harmonic oscillators

The equation below contains some interesting terms. First one is the inertia which is the force of Newtonian mechanics. The seconds term is the damping force which is proportional to the velocity. The third term is spring force which is proportional to position of spring . The forth is the non-linear term in x^3 . The right hand side contains a variable force.
Duffing equation
What does an equation mean ? Any equation is plausibility of any natural phenomena. According to Ramanujan " An equation has no meaning unless it expresses the mind of God"

Uncommon Wisdom

What is consciousness? It is the awareness of our mind to take right decision. Human mind is place of vast electrical activity. When we take decision lot of neuron fire simultaneously. Electrical signals pass from one neuron to another with the speed of light. Brain is a complicated electrical circuit. The complete scientific model of human mind is still unknown. We can only explain it partially. Human mind has two sides : one is left hemisphere and other is right hemisphere. These two parts are responsible for certain voluntary and involuntary actions. For example our logical and analytic skills are processed in left hemisphere. How consciousness arises is really a difficult problem. It is mysterious and simillar to quantum mechanics. May be quantum mechanics will explain consciousness completely one day.
Carl Sagan has tried to explain consciousness in his famous book "cosmos". He argues that fourteen billions of years of universe's evolution has turned matter into counsciousness. The laws of physics have played the vital role in this evolution.
But is there anything special about consciousness? Uncommon wisdom says a piece of rock is as conscious as us. The whole universe is conscious according to some basic interpretation. We are part of the universe and nature. Gia hypotheses regards the whole earth as an organism. Life form is nothing but some combination of specific compounds named organic compound. Life emerged on earth four billions years ago according to scientific evidences. First a biological cell which is the basic component of life was formed by some natural event. This cell transformed and various other living organisms were created afterwards. That is what modern life sciences have claimed to be the fact. If a planet has been left for millions of years, some kind of life form will emerge.


Black Hole

The space-time diagram of black hole describes the event horizon and singularity. At the event horizon the light-cones tip over and falls into singularity. The diagram actually describes the sapcetime collapsing of a star when it forms a black hole. When the star shrinks the matter inside the star shrinks too and the density starts to increase.


black hole dynamics

At some point the density becomes very extreme and event horizon forms. Light wave can no longer escape the horizon. This phenomena is depicted in the diagram above. Our earth can be turned into a black hole of it can be squeezed into a sufficient small size object. Time comes to a halt at the event horizon of the black hole. To an outside observer this time dilation fact will be apparent. Space time diagram above also suggests space and time come to a star.


Miscellaneous pages
Algebra   |  coordinate geometry   |  Topology for dummies   |  Symmetry   |   Bertrand Russell philosophy   |  Sir issac newton   |  Topology for dummies   |  Albert Einstein  |   Artificial intelligence   |  Leonhard Euler   |  Carl Friedrich Gauss   |  Number theory   |   what is science

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this website is about theoretical physics and mathematics, theory of relativity general, theories of phyiscs

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psycho analysis

Sigmund Freud was perhaps one of the best experimentalists or clinical psychologists. He used to study and experiment with his patients. He coined the term psychoanalysis. Psycho analysis is the study of mind or it is the theory of how activities and interaction of our mental life is described . Phyche means mind. Psychoanalysis , in general, is concerned with how human behaves. Psycho analysis is based on three apparatus :one is ego, the second is Id, and the third is superego. Id is the uncoordinated instinctual trends, superhero is the critical and moralistic act. Ego plays the role of mediating between id and superego. Freud based the model of psyche with these three apparatus. In terms of these concepts he interpreted the process of dreaming. He also claimed that all sexuality is psycho-sexuality. His theories have impacted modern psychology to a great degree. He concluded some strange consequences from his theories. For example we certainly enjoy pleasure of anal sex from defecation. A child develops sexuality when it sucks its mother's nipple and so on. Full explanation of psychoanalysis needs much space but the basic ideas are those explained above.

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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.



All equations
"Without electricity we would not think, your heart would not beat..."

Academic courses concerning electrical and electronics engineering

Science of telecommunication and electronic engineering is very impressive branch of education now a days. Power electronics and semiconductor devices are some of the sub fields of electrical and electronics engineering. The courses and subjects of it are huge in numbers and vary from universities to universities. Some of the courses of computer science are Boolean algebra, data structures, microprocessor design, automata theory, complexity theory and many types of computer programming languages. The courses of electrical and electronics engineering are divided into two main fields : one is telecommunication and other is power engineering. Each field has number of courses to be studied by students of electrical and electronics engineering. Some of the courses have prerequisite courses to be passed in order to take the former courses. All courses are distributed among a number of semesters during certain interval of time. This gives student sufficient time to study and understand the concepts of the subjects. It is imperative that students of EEE understand the basics of dc and ac circuit. Transient analysis plays an important role in circuit analysis. Transient state is the interval during which system changes its behavior from one state to another state. During transient state system output may be very oscillatory and thus it can be unstable. It is the time a system takes to reach steady state. The time taken is called transient time. The relationship between voltage and current that system gives during transient state are called the transient response. More details will be studied when we analyze dc and ac R-L-C circuit and control system engineering. Elementary circuit theory utilize Thevenin's theorem and Norton theorem. These two theorems or laws play an important role in simplifying linear circuits.

"You have created this goddamn universe.."

Supersymmetry and superpartners

The guage symmetry describes whole of particle physics and it is the crucial property of standard model. Standard model is considered the most ugliest theory in physics although it has underlying symmetry principles. Physicist now seek for more abstract and hihger order symmetry properties that can desrcibe relationships of all the fundamental elementary particles and messanger particles altogether. Messenger particles are force carrying particles like photons, gluons, w bosons and others. This symmetry will be called supersymmetry. More specifically, this supersymerry involves more subtle spin angular momentum of sub-atomic particles. All particles will have superpartners. The unification of electromagnetic force, strong nuclear force and weak nuclear force needs supersymmetry to be incorporated. The experimental result confirms that the straight of the three forces do not meet at a point as the distance scale increases. That is something missing in the usual theories, which can be overcome by supersymmetry.


I like to finish with anthropic principle which states that universe is the way it is because we are here to observe it. It is a cosmological principle. The universe is constrained by the necessity to allow human existence. Have you ever have a feeling why all the things are specifically happening to you? The answer is the anthropic principle.


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Reference materials:


Law of thermodynamics
A briefer history of time by S. Hawking
A brief history of time by S. Hawking
Quantum mechanics
Grand Design by Stephen Hawking
Higher Engineering Mathematics ( PDFDrive.com ).pdf
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