Non-existence of magnetic mono poles from classical mechanics

As a start in the New year, I made a basic outline of my theory regarding Magnetic mono poles. Now, I am getting into the mathematical structure of it. But this theory gave me a little satisfaction over on it. And the abstract starts in a hypothetical manner,

Abstract (Hypothesis):
Over a period of time, if a physical vector rotates with respect to some fixed axis in a plane then the physical vectors associated with that vector will also rotate with respect to some fixed axis in any physical process.

Mechanical Example:
The definitions of any physical vector in rotational mechanics serves as the perfect example.
If we consider the definition of linear velocity in a rotating object,
linear velocity = radius from the rotating axis * the angular velocity
v = r * w

where,
linear velocity, radius and angular  velocity are interconnected and all this vectors rotate with respect to some fixed axis in any plane.

Similar examples could be seen in Rotational mechanics.

Analogous example in Electrodynamics:
The Lorentz force acting on a charged particle is given by,

F = q ( v cross B)
where,
F - force acting on the charge
q- magnitude of electric charge
v- velocity of the particle
B- magnetic field acting on the particle

Here,  the vectors namely force acting on the body,  velocity of the particle and the magnetic field acting on the particle are related to each other obeying Lorentz force law.

From the experimental evidence, we know that, the force acting on the particle and the velocity of the particle in a magnetic field rotates about some fixed axis in a plane.

From the abstract (Hypothesis) given above, it needs to be the third vector i.e. The Magnetic field acting on the charge should be rotating with respect to some fixed axis in a plane.

Hence, the magnetic field acting on a charged particle should be rotating about some fixed axis through time and provides that the curl of the magnetic field should be non-zero.
Divergence of curl is always zero.

Thus, the divergence of magnetic field should always be zero, which in turn, avoids the existence of magnetic mono poles.

Divergence of a magnetic field should always be zero.

Need for a new formalism of Mechanics

 After Newton made his mathematical explanation of the entire natural phenomenon with his fundamental three laws, all the scientists started to work out many physical problems using that.

The three laws of Newton were conceived to be an essential thing for every motion and all the problems were tried to solve based on these.

But, solving of the problems headed into a great many difficulties.

There is no any single doubt about the applicability or pertinence of these three laws.

Newton’s three laws are always applicable but it is not always a useful one.

The reason may be,

Newton’s definitions starts with the definition of a concept called particles. It says that, the motion of each particle follows from the net external force acting on that particle.

 But all the entities in nature are not a single particle. They all are some system of particles with definite shape, size, etc. Besides, all the forces will not act at a single particle, but rather at a certain position of the system of particles.  

So, we need a new way or mechanism to deal with these kinds of problems. The reason is because, if you try to apply Newton’s laws for each of these molecules, then note that, there are some order of 10^23 molecules in a mole of substance.

Though Newton’s laws are applicable here,

though it is certain that it will give a correct answer,

it cannot be used here since we know for sure that it will never be achieved writing equations of motion for all these particles.

It may look, this need somewhat satisfied by the introduction of center of mass concept but not completely.

Centre of mass concept is just a simplified version of Newton’s law, where the third law is utilized completely, where all the internal forces are taken as action, reaction pairs and canceled out from the equations of motion.

But this doesn’t alter anything about the nature of the force. The force is again somewhat regarded as acting on a single particle, which is too much different from the real situation.

All these problems need a general way to solve the system of particles without considering the internal properties of the system.

Let us say the system is just a shadow. We don’t know whether there are particles inside it and we know just the forces acting on that system.

Thus, there is a great need for the sake of simple explanation of mechanical system.

Looking for a new idea with this condition, it is found that the idea is there already in our Physics, i.e. Thermodynamics.

In Thermodynamics, though Volume, Pressure and Temperature are the manifestation of microscopic phenomena, we characterize the thermodynamic system just only with the macroscopic variables.

It is just the final external effect i.e. Effective motion in mechanics is significant.

There is no any concern about “the way how the final external effect is achieved”.

As a result, one thing is to be sure that, the new mechanism should involve a more geometrical approach rather than the physical approach. And so, Mathematics plays a more fundamental role in this mechanism. 

Explaining the system with this new approach started by introducing a new concept namely, Constraints.

Correspondingly, the concept of constraints led to some new other essential concepts such as, degrees of freedom; generalized coordinates; configuration space, etc.  All these things exhibit the greatness of classical mechanics in other fields of Physics. 

Thermodynamic system – first variable “Volume”

When we do any experiment, we focus our attention to a specific part or a system with boundaries.

Now in our purpose of learning thermodynamics, we mostly take the system of some air or water with certain boundaries.

For our convenience we made a word for that specific system with its boundaries and that is so called Thermodynamic System.

The first independent variable in a Thermodynamic system to notice by a common man is Volume.

Volume is the measure of amount of space occupied by the boundary of the system, and for gases and liquids the volume of the container is considered to be the volume of the system.

Besides, its measurement is very simple and done using our everyday measurements such as length, breadth and width. This is the reason why most of our thermodynamics study involves none other than other shapes but cylinder, being one of the simplest shapes.  

Since length, breadth and height are measured in unit lengths, the volume will be measured in cube of the power to that unit length. 

Unit length is yours to choose. In general for most of the purpose, meter is used as the unit length.

All the information about the volume of the system is thus possible to obtain just using our standard measurement scales. As a result, now it is quantitatively analyzed.  

Note that,

We never cared about the internal structure of the particles or the forces between them or how this volume was created by this particles or etc. in this thermodynamic system.

We don’t even know whether it is atoms are inside this volume.

You may ask the question,

We don’t know anything about the internal properties but we just define the external properties to understand the thermodynamic system. Doesn’t it meaningless?

It is like explaining an object by just seeing its outside shadow and not caring about its internal structure.

It is true and the doubt is quite meaningful.

Moreover, “Everything depends on the purpose”. If we start to try and analyze the internal structure, we may not get a correct solution or we may get complicated and even we don’t know how to analyze it. There is no information about internal structures at those times.

But for the survival, there is a conditional purpose for the people and scientist to understand a thermodynamic system.

Hence, we forget to care about its internal structure and just put our concern on trying to explain it from the external behaviours.

That is why the thermodynamic relations doesn’t hold good at all situations. But it is a good estimated outline for basic understanding.

And studying the outline to understand its behaviour is not a wrong approach.

Whatever may be the internal structure, the outer structure should be the same for a same state.

It is like from the shadow, for example from a human shadow,

If you predict his behavior, color and etc. it would go wrong.

But the properties of the shadow will not change. From all these things, it is certain that it is a human shadow.

The internal properties may vary accordingly to the same external property.

When the information about the system is more accurately known, the internal behaviours are also predictable based upon those data. And it needn’t to be worried.

Therefore, the external properties are perfectly logical to define a thermodynamic system. But the relations between them needn’t to be an absolutely correct one.

Introduction to Thermodynamics

Blind definitions are the first place where misconception starts to grow. And it would be nice to discuss without any of those blind things.

An easy tip to avoid blind definitions is, by imaging yourself at the old time when the discovery was made. Then, believe yourself as the scientist and do the research.

Our first discussion in our society started with Thermodynamics. 

Let us begin our research on that.

What is thermodynamics? What is the purpose of studying it?

To get the feeling of its original creation,

Let us say we are in some 18^th century or before. At that time what would be the need for this study of thermodynamics?

In 18^th century, there are proof for the usage of many machines and pumps using the suction of air and water. 

Moreover even the manual water pumps in our houses are made by the study of air in a column of cylinder.

And also it would have known or easily predicted that the weather is related with the flow of air and determined by the temperature and pressure of the atmosphere, which plays a fundamental importance in agriculture.

Thus, there are many grateful needs for this study.

So, the things to be sure are that this study should have started with the properties of air and water and their behaviour.

So, the major concern of the physicists is now to explain the behavior of these systems (especially fluids, gases).

But now the question may arise,

How can you straightly put these new words called Pressure, temperature, etc.

From analyzing our daily processes each concept is created separately, as follows,

In a heating process the conception of heat and temperature comes into play,

In the construction of a dam, the term pressure comes into play,

and also the term volume comes into play.

Thus the terms like pressure, volume, temperature describing the system should be dealt separately before learning about this weather.

Using mathematics,

The words can be replaced as,

The behavior of any fluid or gas system is the function of Pressure,
Temperature and Volume, Where,

Pressure (especially atmospheric pressure),

Temperature

and volume are independent variables.  

To understand our functional behavior, it is necessary to find a way to measure all its independent variables.  

Hence, We (The scientist) should start to build instruments to measure and analyze these independent variables.  

New Decision – Philosophical Science Society

Practicing for swimming in the ocean is much better than practicing it in a swimming pool. And also the ocean will be more thrilling.

Finding people like you with desired characters is a very occasional thing. But it happens sometimes, also for me. I got exceptional friends with exact similar characters as mine. Everyone loves to be with their friends and so do I.  

I was just discussing with my friends about “what to do after our studies”?

          
         The discussion started as usual but ended with a good decision. We thought about all kind of possibilities. But most of the possibilities implied we can’t be together within the future years.

         
          Getting into the same institute is not possible for all of us. There needs some other way.

So, we tried to figure out a way to be together and also with physics.

          We realized that the only thing we know is a little Physics. Let it be so ...

My friend suggested a beautiful way,

       “What about making a tuition center or an institute for teaching physics, different from others such as schools and other institutions?

All the things were decided in a sudden.

We love teaching physics. And this suggestion compiles all our expectations and moreover it is the most enjoyable one.

          Hence the decision was finalized.

The most inspired words for this decision are from none other than Adolf Hitler.

         

          “If you don’t like something, don’t get rid away from that. Instead get into that thing, and change it completely.”

          It perfectly suited for us, since from our childhood we don’t like the way Physics taught to students. All the people are trained to do something in Physics, but they really don’t understand physics.

We like to change the teaching style and that is the reason we want to become teachers. 

         

          Instead of thinking, we decided to jump.

We thought a lot for the name and finally fixed on the origin name of the Physics itself that is Philosophical Science.

          We named our organization as “Philosophical Science Society”.

         

We started to practice with each other on how to teach. We are sure about only one thing that is we are not going to do the usual stuff as teachers but rather a different stuff as their friends.

 We don’t want to make the place as the tuition center but a place to gather and discuss physics with their friends. Not anything more.

And moreover my friend came up with a temporary symbol for our society,

And thus our Philosophical Science Society was started. 

Symmetry in our body

Symmetry has something to do with our body.  I got this from my own experience.

One day in the classroom, everyone was taking notes from the teacher. It was a very boring class. So, I couldn’t stop my eyes from wandering around the class room. I came to see that my friend was trying to write the notes using his left hands. I think he also was bored.  

         

          So, naturally I also tried my left hand because it is better than sleeping in the class. It is a good decision.   

I started my try.

          I know it needs more practice to use left hand for writing.  

Mostly I don’t used to try my left hands.

The handwriting was terrible and I couldn’t do it perfectly.

Moreover I am not in a mood for practicing a new way of handwriting. I was very lazy at that time.

However I noticed a specific thing in the writing.     

We should focus on the words carefully,

          It is not that we cannot write using left hands but writing the words as you know as English in right side order is difficult. That is writing the words as same as right hand side is difficult.

It means the left hand already has its own way of writing the English. But it is not as same as the right hands. That is the only problem.

So I just swing my left hands like a music conductor to write English alphabets.  I tried for the letter “a”.

Yeah I could write it but in the reversal way.

Ultimately I write everything in backside order.

There is specialty about this. For these many years I just gave practice only to my right hand. I am right handed.

Now, without any training, my left hand symmetrically and exactly writes in a same manner as my right hand. The handwriting itself is same as the right hand. They are just in reverse order since it is symmetrical from the center.

These are mirror imaged letters – a symmetrical one.

Besides I can easily write mirror imaged letters. I tried for a photo.

This shows that "Leonardo da Vinci" never struggled to write mirror image letters. He just found the Natural ability hidden in humans.  

Way to write mirrored letters

The reason for mirror image letters is that,

            

           The own way of writing of the left hands is the symmetrical one with the right hands.

Practicing using left hand does not mean that you are really learning to write using left hands. 

          

          You are just learning to “Practicing to change the way of your left hand writing as the right hand writing”.  

When your brain commands your hands to write the letter “a”,

Your both hands will get the signal as symmetrical images.

Though you gave practice only for your right hands, your both hands will know how to write. No matter which hand you are using, your brain is what just matters. It is a symmetrical machine.  

Unless and until you tamper with your brain, anyone can write in this manner. You just shouldn’t think that you are writing. Just go with your instincts. 
            
        Just think you are writing using right hand but use your left hand instead of the right. I think it is the best way just as Davinci's. 

Conclusion:

Easiest way to write mirror image letters is "Don't tamper with your mind". 

Experiment with broken Specs

 When I was cleaning my specs, I accidently put my grip on the center and tilted the other side. Eventually I broke my specs into two parts. It took 5 days for a new one.

For five days my time died suffering severe headaches.

I tried to fix it in many ways. But it gave no use. Cello tapes gave me an irritating feeling.

So, what I repeatedly done is fixing and breaking. I will fix with cello tapes and again will break it due to irritation.

Finally I got a best thing with rubber bands. That is an "Easily flexible spectacle". 

But the problem is not finished. One lens was tilted slightly upwards than the other.

The problem is that the focusing points for the two lenses are tilted and it gave strain to my eyes.

Consequently our eyes need to focus in different way to focus on single point. And this again led to the same headaches.

But I really don’t get the exact point how the tilting of the spectacles is the reason for headaches. I am not satisfied with my explanation.

The doubt follows as,

If you place two transparent glasses left and right before your respective eyes, then you can focus on a single point. And that will not give so much strain.

May be in curved glasses there will be strain due to curvature and aberration. 

But my question is how small tilt also makes the strain i.e. that is big effect in my head. How my brain easily knows even small effects in our body?

Why our eyes needs symmetrical things. Not only our eyes but the whole body needs symmetry. It is the essential one. How does this happen in nature?

  

Why Nature loves symmetry?

I will give a great example of symmetry in our body in the next post.

But anyhow I learned great conclusions after doing experiments with my broken spectacles. I will never forget that. 

The conclusion is,

Don’t or Never do any experiments with your eyes ‼!  

Don’t Say “You are Wrong”

Don't or Never say "You are Wrong" to anyone because you might be killing a great idea. 

Don't forget to remember that
"A theory is correct until and unless it is proven to be wrong".

When someone explains a theory in a wrong way, Don’t say “You are Wrong”.

There are a lot of advantages in saying like that. I will try to point some of those. This is especially for teachers because they are the one used to say this to their students. So, I will take the case of the students.

When someone comes and discuss you about some theory. Let’s say some Physics concept for example force.

If someone explains the force as the follows where he don’t know anything about Physics (e.g. students),

"The force is amount of thrust that is given to an object to move from its motionless state. Depending on the amount of thrust the object will travel to some distance. The movement is proportional to the thrust applied on the object."    

         

       We Physicists know the explanation is wrong. The force is not the amount of thrust.

But that doesn’t mean he is completely wrong because his explanation is good. Moreover this is how the great Aristotle himself thought for the first time. This point of view was agreed for more than many centuries.

         

          But you can ask me “yeah.. it is Aristotle’s explanation. But it is proven to be wrong. Then, How will I say he is correct?

           You needn’t say he is correct. But either don’t say it wrong. Instead of saying "you are wrong" just give him the situation of a real life problem where Aristotle’s explanation of force would go wrong.

          

         If he is arrogant in his theory, then it is very good. He will try his best to prove that his theory is correct. Every time when he comes up with some better explanation to explain the situation, you will have to give new situations. 

Depending on the capability of the student’s new explanation, you will need to give him a tough problem than the previous.

The profit is for both of us. In the case of teacher and the student,

When student comes up with good explanation, the teacher needs to think hard than the previous to give him a more difficult problem. And to solve that difficult problem, the student will have to take more effort every time.

         

        At the end, both will be very clear on that topic. They will know the history, they will know the different type of problems faced in real life, they will know the various ways of thinking about the same concept, and how scientists overcome those problems in any concept, etc.

And also at each time he will understand his mistakes. Maybe he will come up with a better solution than Newton, Hamilton, Lagrange and others. Maybe it is possible to create a new scientist.  

From this method both will learn new way of thinking.

Various students will have various kind of thinking skills. If you can manage all those students, you will be the one of the finest person in the world to clearly understand the concept.

Note: And moreover one should try to think in other's point of view when they need to give the correct situation and problems. Only then they will get new ideas.  

To think in other's point of view, you just need to forget who you are and what you have learned And completely go with your student’s concept. Then you will understand him.

         

        And "student" doesn’t mean only students but everyone who comes to discuss with you. 

One of the ways to Understand Mathematics

         I have seen many people doing mathematics without thinking at all. They will do mathematics somehow like a computer which doesn’t know why it is doing.

      I don’t like to do pure Mathematics. What I mean by pure is somewhat not thinking about the Physical meaning. The concepts will look as a vague one.

There is difference between saying 

         one apple + two apples = three apples

from simply saying 1 + 2 = 3

      Human brain always used to understand anything by visualization.

      When you say “y is a function of x” there is no so much Understanding. But when you say “Velocity is the function displacement and time” there is a real understanding because it is understandable from everyday experience. 

          The reason is because the mathematics itself is created to explain physical things.

      When we do any mathematics, we should try to understand each and every line. It is nice to read mathematics in an elaborated manner and it will help you a lot to think. For example instead of studying “dy/dt” you can read it as

Rate of change of y with respect to x

   

   Instead of just saying, ∫ y dx (Integral y dx) you can read it as, summation of function y with respect to the independent variable x.     

   So each time you will remember the meaning of differentiation. And you will have a great clarity in the topic.

     

We should avoid using the formulas blindly.

    

     In any problem, we shouldn’t straightly use formulas but we should always try for the derivation.

     

     First it will take more time to completely derive all the things in a problem. But when you derive it for more than 5 or 10 times, then it will start to come fluently. 

     But after you got practiced, no matter what size the derivation is, it will come in a great flow and you can just do it in your mind. 

Depending on the size of the derivation, you need to practice it more times.

      So, we can learn everything in a perfect way.

Nothing needs to be remembered at all as a mug up thing. But everything can be remembered from the fundamental derivations.

    

    And it will also help you in thinking skills. Each time when you derive the formulas, you may not use the same method. But you will have the chance to derive the formula in a different ways. And you will get a different kind of thinking about the single concept.

   

     Maybe it will lead to great innovations!!    

When you try to analyze a mathematical thing to explain in words, you will get deeper understanding than just looking at the equation.

      Max Born got Nobel Prize only for his famous explanation on Quantum Mechanics.

      Explaining in words is a very good thing.

What My opinion is ,

       Studying mathematics using words is the one of the best way to understand any concept.

      So, you will always understand the physics behind that and may understand the real meaning of the concept.   

      That is why I used to discuss any concept in physics with mostly consisted of words other than just mathematical equations.