Einstein's Greatest Equation

Deriving Einstein’s Greatest Equation

E = mc^2

Stationary box A is floating in Space.

A Photon is then emitted from the left and moves towards the right.

E=Energy of the photon

Momentum(p) of a Photon=E/c

The box experiences a recoil force and moves towards the left with a velocity v.

p of box=Mv

Where M = mass of the box

By Conservation of momentum,

M∆x/∆t=E/c - 1

Where ∆x is the distance the box moves in time ∆t when the photon makes it to the other side.

∆t=L/c

Where L = the length of the box

Substituting this in 1,

M∆x=EL/c^2

Assuming the photon has mass m, if the box has a position x1 and the photon has a position x2, the centre of mass for the whole system is,

=(Mx1+mx2)/(M+m)

Since no external force was applied, the centre of mass of the whole system should not change.

Therefore,

(Mx1+mx2)/(M+m)=(M(x1-∆x)+mL)/(M+m)

The photon starts at the left of the box.

Thus x2 + 0

Hence,

mL=M∆x

mL=EL/(c^2)

m=E/c^2

Or,

E=mc^2

Quarks: The building blocks of atoms

We all know that atoms are made up of negatively charged electrons revolving around a positively charged nucleus made up of neutrons and protons. But are these protons, neutrons and electrons too made up of something? Or are they the fundamental and smallest units of the atom? Now before you try to answer that question, lets ponder on another equally relevant point...... How do you discover what the protons and neutrons are made up of if they are indeed not the smallest and fundamental units? How?............ Confused?......... Well try asking yourself this...... Suppose you wanted to find out what was inside you remote controlled car, or you wanted to find out how the land phone in your house worked....... What would you have done then? The answer is fairly obvious I assume......... You would most definitely open it.

Just like that scientists literally tore apart the neutrons and protons. The only difference was that the scientists didn't use screw drivers or spanners to take care of the job, instead they used high energy collisions. That is, they bombarded protons with highly accelerated charged particles to tear them apart and studied them (somewhat similar to what we do when some screw in the machine won't budge and we have to "bombard" the phone or camera with hammers and other household tools accelerated to highly critical rates..............). And when they did that, they observed the presence of tiny charged particles in the protons and neutrons. These constituent particles of protons and neutrons are named as Quarks.

Now, let me tell you some very interesting facts about quarks:

• One can never find a quark by itself (i.e. they are always found in certain combinations). This behaviour of theirs' is explained by Quantum Chromodynamics, about which we shall learn later.

• They are found to possess a charge of either +2/3 or -1/3 (Anti-quarks, about which we shall learn later, possess a charge of either -2/3 or +1/3).

• They always arrange themselves to form particles of integer charge. e.g. 0, 1, 2, 3, etc.

Quarks are of six types (in pairs):

1. Up - Down

2. Top- Bottom

3. Charmed - Strange

(These are all types of quarks, i.e. there are up quarks and down quarks which form the protons and neutrons)

The charges of the diff. types of quarks are as given below:

up +2/3

down -1/3

top +2/3

bottom -1/3

charmed +2/3

strange -1/3

The composite particles formed by the combination of quarks are called Hadrons. e.g. protons, neutrons etc.

Two up quarks and 1 down quark combine to form a proton.

i.e. 2/3 +2/3 - 1/3

or, 4/3 - 1/3

or, 3/3 = 1

Hence the +1 charge of the proton.

For the neutron, it is the opposite. Two down quarks and one up quark combine to form a particle of zero charge.

We shall discuss more about the other types of quarks and the other possible type of Hadron (a Meson) later.

Our Sincere thanks to Rooplata Mam, the Person who Made it all Possible (Thank You Mam)....

Thank You,

Thinkers

Science: The Beginning..... The Atomic Nucleus

The word science originates from the Latin word scientia meaning "knowledge", and knowledge is precisely what we seek in this quest of ours.

I am assuming the reader is already aware of the basics of science such as the existence of atoms and the presence of protons, neutrons and electrons in them, Newton's laws, Gravity etc . Assuming this, I shall now move on to the intricacies and details of atoms, the laws of physics, gravity, etc., all of which is not discussed in our text books in a manner which shall be comprehensible by all......

First, let us take a look at our atom again. Now, we all know that an atom is made up of a positively charged nucleus (comprising of neutrons, which has no charge, and protons, which has a positive charge). But let us look at the nucleus again..... Picture the minuscule yet fundamental creation of nature in your mind again..... Concentrate on the tiny core of the atom.......... The nucleus. Now, there are enormous amounts of positive (as well as neutral) particles crammed inside it..... But hey! Didn't our teacher tell us that like charges repel? And since all protons are positively charged (or like charged)........ aren't they supposed to repel each other? In that case, the atom ought to go BOOM (some what like Kieron Pollard blasting a daring enough bowler, daring to bowl to him that is, out of the stadium as if he were batting against a bunch of schol girls....... just that it wud have been more chaotic and numerous)?............ Or is some mysterious force (of which our dear teachers refused to tellus about) holding them together? Or is the science learnt at school about like charges repelling wrong?............ Now, don't go running off to school to organize a protest against your school all of a sudden........ coz its not option C. It is actually a mysterious force (mysterious to us not the scientists who already know of its' existence) that holds the protons in the nucleus together without going BOOM and following in Kieron Pollard's footsteps.

So, what is this mysterious force that holds the protons together? What is this glue that keeps it from going apart? The answer is a force called the Strong Nuclear Force. This force acts between the protons, the neutrons, and between the protons and neutrons (as we shall see later, this force actually acts between the quarks, the composite particles of protons and neutrons. We shall also investigate more deeply the force carrying particles of the S.N. Force or the Gluons). This force holds all the protons and neutrons together. At very short distances, the strong force is superior in strength to the Electrostatic force (the force that acts between charged particles). Hence it is able to easily over power the repulsion of the like charged protons.

Thus, our first problem in science is solved............... Mission Accomplished.............. For now.....

Hope you enjoyed it.

Thank You,

Thinkers