Science is simpler than psychology

It is so common to hear from students and parents that "i am not good in science. so am choosing arts, commerce, visual communication etc., as a career option"

Too good to be true. not really. lets argue.

The argument goes like this.



Scene 1: That is our friend Hachi from the famous Hachiko movie.



- Can we predict which way will our friend go? To the left, to the right or just turn around and walk back. There may be one too many reasons for our friend to choose an option. It gets almost unpredictable.




Scene 2: The financial market. Can we predict which way would it go?

Scene 3: Global economy. How is the currency value decided?









Scene 4: How about an art something like this. This one of Escher's.

All these scenes above require very high level of skills. Skills like group theory, statistics, probability and more importantly creativity. Add to this the regime of chaos, fractals and self-organizing systems. Mind boggling.


Compare this with science.



Science deals with predictions of motion of inanimate objects. They don't think on their own. All we requires is the concept of acceleration and and a few mathematical tools like arithmetic, geometry and calculus.

With the advent of simulation software's, things have got much simpler.



So, can we say science is simpler than psychology?

A pit stop and road map

How far have we traveled? and Where are we going?

"Journey is more important that the Destination"

                                               Experience parabolic motion in 24 seconds

We began with acceleration, added few words to our physics vocabulary like displacement, velocity, power, rest and also took a peek at the concept of Field and Flux. We also transgressed into the topics on electricity and a bit on Planck;s constant, dealing with Energy.

A word on our overall approach.

Classical mechanics seems to be the foundation for comprehending subjects like electricity, magnetism, heat, sound etc. Why? All of these are a study of motion of a particle, rigid body, molecule/atom (heat and temperature), electron (electricity) or electron spin (magnetism). 

A strong understanding of motion (translation, rotation, wave and quantum) are built on top of the concepts of displacement, velocity, force, field, energy and power.  In the due course, i came to understand that "acceleration" is the key.  once we comprehend acceleration, all other concepts seem to become simple. May be reason why apple-newton story became such a legend.

Though we have identified acceleration as the core concept and study of motion will enable us to comprehend other subjects, there is one more challenge. The challenge is that each individual approaches a subject from a different perspective and also every concept would require a different approach.

Keeping this in mind, our articles will have one or more of the following approaches.

• Start with an application and introduce the underlying physics vocabulary.
• Provide precise explanations. for ex. distance is used in geometry which considers only the length.Whereas displacement should take time interval into account. displacement as a shortest distance is not sufficient.
• Use evolution based approach for topics that are considered to be complex

If you have come this far and find the journey to be interesting, let us move forward. we shall have a discussion on mass, weight and force. These are quite confusing for most of us. let us make an attempt.

In a few more articles we will be discussing on collisions, moment, work and energy. To these we will be linking the concept of power. We are still dealing with one dimensional motion. Just to keep things simple.

With this lets us reflect upon the contents we learned and summarize on the concepts of equilibrium and conservation. These are 2 important tools of science.
Equilibrium: Force, Moment
Conservation: Mass, Momentum, Energy

Till this stage, we were dealing with a simple object like ball. We call it simple because, it is geometrically symmetric and considered to be made of the same material. We considered all of the mass of ball to be concentrated at a single point. Hence, we did not have to bother about shape and size of the object. We just needed to know what is the mass of the object?. Since we have assumed something, we shall give it a word particle and add it to our vocabulary.

But real world objects are need not be symmetric. so we need to get to the concept of center of mass, center of gravity and moment of inertia. We are entering into the regime of rigid bodies. For rigid bodies we will have to consider the shape and hence the mass distribution into account.

Subsequently, we shall get into the regime of 2 dimensional motions. The parabolic and circular motions.

Beyond this the road gets a bit rough but interesting and adventurous. We will be getting into the lands of potential energy, electricity, magnetism etc . The adventure requires a few tools. so, we will be taking a little detour into vectors, complex numbers and calculus.

During the adventures journey, we may have a few short breaks and get to know astronomy, sound, optics and heat.

If we have crossed this far, we will be in a position to enjoy the panorama of space-time curvatures and quantum mechanics.

The Field of Gravitation

Article status:                              Draft
Time Estimate for Reading:        30 min
Learning Objectives:                  Concept of "Field"
Effort Required:                          Medium
Pedagogy Model:                       Evolution, Formula Analysis, Inter-disciplinary
Prior Physics Concepts:             displacement, velocity, acceleration, mass, power, force
Prior Math Tools:                       Secondary school level Arithmetic, geometry and algebra


This article helps in understanding the concept of "field" as used in physics.

Who said only mathematics can have constants like pi and e? Physics can also have constants. The one dimensional gravitational constant G, the first of the physical constants (1640 AD). What seems continuous to our senses seems to have a discrete value. This paves the way for further exploration and leads to Avogadro's constant (a fixed number of atoms or molecules matter can contain), Boltzmann constant (relating energy of particle and temperature), velocity of light (maximum limit for electromagnetic radiation) and the all important Planck's constant (the minimum quantity of energy). There are more...

Being the first physical constant, it gets close to heart. So, let us explore it a little.

In the process of understanding how Newton would have arrived at this formula involving gravitational constant 'G' a couple of questions comes to the mind.
1. Why product of the masses. it could have been an addition as well?
2. Why square of distance in the denominator?
3. How did newton eliminate other parameters like magnetism, electricity, atmospheric pressure, friction and air drag from appearing in this formula?


Newton must be right. so, we take this for granted as it is a law and move on to static electricity. A similar formula pops up.
                           

Force due to gravity and force due to electric charges. just replacing mass with charge and G with 1/Eo.  But there is a 4*Pi downstairs.

'Eo', (the number of field lines or permittivity) of electric charges depends on the medium.

Compare this with G. G is a constant through out the universe. It seems, gravity can to travel through everything. Whether we hide inside a metal cage (faraday's cage), enter into a vacuum chamber, heat it, change the color. Gravity is all prevailing. Initially it was thought that light is made of photons, photons do not have mass and cannot be attracted. But with Einsteins prediction of space-time curvature, light bends around massive objects like sun. Philosophically speaking we may even say guilt and grudge pulls us down and may be gravity is the reason.

Having discussed about Eo, we need to understand the 4*pi*r^2 downstairs. For that we need to introduce and understand the concept called field. Let us start with equation for the electric field,

Getting to understand the concept of 'Field' was not so easy. Isaac Asimov, the famous fiction author, came to my help. I learned to see through the formulas from his books on science.

Seeing through the formula, these are the observations. A 'q' has been removed from the right hand side of the equation. 'F' has been replaced by 'E'. So, mathematically 'q' should have gone under 'F'. Scientists and physicists naturally are tempted to give a name for concepts involving more than one variable. so. F/Q is given a name "Field". it is similar to naming 'mv' as momentum and 'ma' as force.

Why should we remove the Q in the first instance? It becomes simple from the mathematical perspective. Instead of 2 variables, we just have 1 variable and is easy to solve. More importantly, it becomes very easy when we consider the effects of multiple objects (more of this later).

It is ok for mathematics. But, how do we intuitively understand the concept of 'Field'. The clue is in 4*Pi*r^2 downstairs. This incidentally is the surface area of a sphere. let us imagine that, we place a charge in the center of a sphere. what happens when a charge is divided by surface area. we shall take help of an analogy.

Sphere is three dimensional. but let us begin with 2 dimensions and later extend it to three dimensions. Consider a pizza placed in the center of table of radius 'r'. let us imagine people of unit dimensions (1) occupying the circumference of the table. The single pizza will be divided equally among all the persons. Keeping the pizza size same, if we increasing the radius of the table, the same pizza will be shared by more people (circumference 2*pi*r increases with r). Lets us extend this to a spherical table and assume that people (imagine house flies for a better scale) can sit around such a spherical table. Each one will get a very little share. This is the idea of a field.

So, a force field can be imagined to get shared or rather get diluted as we move away from the center. it can be calculated by dividing the force (considered to be concentrated at the center) by surface area of the sphere enclosed.

Now we know where Gauss's Law comes from.  The flux is the integral product of 'field and surface area'. Interesting.

We have added field and flux to our vocabulary. we just have an intuitive understanding. A mathematical treatment of the same should await a treatment with calculus.

Having understood, the reason for 4*Pi*r^2 being in the downstairs of the formula for electrostatic force, we may apply the same concept to the formula for gravitational force. We need to multiply and divide the equation by 4Pi

                                     

The gravitational constant now will have a value of 8.385E-10 instead of 6.674E-11. With all these, we have converted the 1 dimensional gravitational constant into a three dimensional Gravitational constant.

Why do we need a three dimensional gravitational constant?

It makes understanding simple. Let us consider 2 examples.

1. Gauss law of gravity

                                          

    With 3 dimensional G, we can do away with the 4*pi here. 

2. Intuitive understanding of Planck's constant and Heisenberg's uncertainty principle.

     Planck's Constant,

     E = hf    ;   E is the packet of energy, h the Planck's Constant and f the frequency of radiation.

     Heisenberg's uncertainty principle

             

      Notice a strike over the h on the right hand side of the equation. it is called h-bar

    If you have followed our discussion on the 3-D 'G' and 1-D 'G', we can intuitively       understand the need for h, h-bar and h-bar/2.

h is a three dimensional constant used in wave equations (3-dimensional;). Dividing h-bar by 2 will be h/4*pi. this incidentally can be visualized as a 1-D Planck's constant. Since sigma x, the standard deviation of position (1-D) and sigma p, the standard deviation of momentum (1-D), h/4*pi can be considered to be a 1-D Planck's constant. The r^2 term disappears as we consider unit radius.

      

On a similar note, dividing h by 2*Pi makes h a 2-D Planck's constant and is used in angular momentum calculations.

Would there be any implications on Eintein's General Theory of Relativity?

                                                

If 'G' in that equation is multiplied by 4*Pi, the 8*pi in the numerator of the equation gets replaced by '2'. Does it lead to some other interpretations? 

There seems to be order in Chaos too. The Feigenbaum constant for bifurcation rate in chaos (and also to fractals). What seems to be chaos at first, may lead to order in the long run and result into self organizing systems. 

                                               
You may refer to this article for more information on self-organizing systems. Science gets amazing.

This article might seem to be more like a random walk, transgressing various fields and seemingly unrelated areas. At the end of it, it is nice to know that, Newton was dealing with one dimensional motion or one dimensional forces (though circular and elliptic orbits are 2 dimensional, the force that makes it happen is one dimensional) and he should have been happy with one dimensional constant.

Note to readers:
If you come across any formulas that involves 'G' please do send me a note.

References:
http://mathworld.wolfram.com/FeigenbaumConstant.html
https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation
https://en.wikipedia.org/wiki/Gauss%27s_law_for_gravity
https://en.wikipedia.org/wiki/Planck_constant
https://en.wikipedia.org/wiki/Self-organization