Visiting the Uncertain Utopia

Ever wondered how it looks to live in a world where there is no future and no past – you were born and died at the same time but yet you are alive to read this article. Welcome to the "Quantum Realm".

Life

When you toss a coin, you can either get heads or tails, but in this world of Uncertainty, you are bound to get both or none at the same time! When you are walking, you are located everywhere – India, US, UK, Australia, etc. When Virat Kohli is hitting a ball in the World Cup, it is both a wicket and a six. Imaginable? Yes, it is possible in my world – "Uncertain Utopia".

To be precise, you don't have a life but what occurs is "God plays dice", which is assertive of Einstein's "God doesn't play dice".

Probability is the Government

Coming to Science, it is the pure probabilistic approach to understand the system. Mathematically, if there is an event which can give two outcomes, then either of them will occur with a 50:50 chance. Putting it in layman terms, you can either have a tail or a head when a coin is flipped in the air but can never be both at the same time. But the issue which one will face is the thinking.

Probability (getting heads) = ½; Probability (getting tails) = ½, totaling to the probability of 1. But what will occur in the Quantum world is that the Total Probability of getting both heads and tails is 1.

Everything is a Wave

"The Wave-Particle Duality" introduced mainly by the de Broglie equation shows that in the microscopic scale the subatomic particles like electrons are not like "imagined ball of negative charge" but is a wave and thus looks almost like the tilde sign (~). Not only are subatomic particles and light are waves but also you, the coin you tossed, the ball which Kohli did hit and the cricketer himself are all waves! How can it be?

It is just the energy and waves' "size" that makes all look as it is in real life. Many things can be explained in Science considering either wave or particle nature of matter. For example, light can be considered as an Electromagnetic Wave and also a collection of Photons.

1. The Beginning of the Quantum World

   Making a list of things that paved the way for Quantum Mechanics are:
   ·         Black Body Radiation
   ·         Photoelectric Effect
   ·         Hydrogen Atomic Spectrum
   ·         Young's Double Slit Experiment
   ·         Wave-Particle Duality
   ·         Louis de Broglie's Hypothesis
   ·         Planck's Quantum Hypothesis
   ·         Uncertainty Principle
   ·         Schrödinger's Equation
   ·         Wave functions
   
   

   The Fight with Classical Physics

   The Black Body Radiation and the Photoelectric Effect could not be explained by Classical Physics, which was the main governing body of the then Science – even many Atomic Structures devised then was unable to be followed by Classical Physics.

   Black Body Radiation

   Imagine you are in a laboratory having a furnace which can provide temperatures of around 10,000 degrees centigrade and you are given an iron rod which won't melt at any temperature. When you start heating the rod, it first becomes red. Then if you continue heating it gets white and ultimately becomes blue or violet. This observation was plotted and the search for its equation began.

   Here comes the issue with the then Physics. It cannot be explained then. Many of them tried their best by manipulating the Mathematics but were only approximately close to the graph of the emission spectrum but was not exactly. The Mathematics also showed that there could be an Ultraviolet Catastrophe where the electromagnetic radiation from the rod would be in the UV Region of the Electromagnetic Spectrum.

   Photoelectric Effect

   This was the research area in which Einstein received his Nobel Prize in Physics in the year 1921.
   It was found that when light or rather any Electromagnetic Radiation falls on a substance then it emits an electron. Initially, radiation is considered as a wave, the effect was explained such that the waves oscillate the electrons at the metal surface and hence the ejection is seen. But the actual point is that the intensity or amplitude of the wave – greater the intensity, greater is the emission with higher Kinetic Energy.
   In reality, the above isn't the case. Kinetic Energy is independent of the intensity. Here came Einstein's ground-breaking research where he assumed from Quantum Hypothesis that radiation existed as small packets of energy and hence the observation. Using simple mathematics, he came up with Packets of Energy as Photons and gave his equation,
   K.E. = ½ mv2 = hv – φ; where φ is the work function of metal

   Young's Double Slit Experiment

        This was one of the most groundbreaking experiments which changed our idea regarding electrons. Why so? Until then we knew that electrons are particles which are hard spheres, but the experiment showed that electrons are waves.
         Though Young used light as a tool for his experiment, later on, the same experiment was performed with electrons and gave the same results.
         A source of light was taken and then was passed through two very small slits separated by some distance and the pattern was studied keeping a screen behind. It showed that there is a very bright spot right at the centre of the screen which was actually between the two slits and there were an alternate light and dark spots with decreasing brightness of the bright spots. Same was the conclusion for electrons instead of light.
   This pattern was due to interference, which is a property of waves. So, electrons are waves!?
   For this reason, Light is said to show Wave-Particle Duality and so does Electrons.
   
   

   What is at the Atomic Level?

   Here comes the real mathematics, but before this, let us get the idea about the arguments.
   

   Atomic Structure

   Atoms are so small that it is invisible to the human eye. Earlier its structure was thought of as a hard-sphere, then the plum-pudding model and then like the solar system – each having its significance. But the wave-particle duality changed our idea.
   Electron having thought of as both particle and wave came from the Uncertainty Principle established by Heisenberg – momentum and position of an electron can never be calculated with high precision, simultaneously. Thus, it is assumed that there is a probability density in which we can find the electron – these densities being called as orbitals.

   Atomic Spectrum

   Initially, it was seen that the spectrum (both absorption and emission ones) would be simple lines separated by some distance. Later on, by the vigorous study of the atomic spectrum by calculating and experimenting wavelengths of light released and absorbed by an atom it came to our surprise that these simple lines are lines of lines – called hyper fine structures, giving us the idea that there are many states within orbitals, each having different energies.

   Schrödinger's Equation and Wave function

   Here came the bombastic approach of a great mind with the equation, the most fundamental one, that can be applied to each object – from electrons to spring and celestial bodies,
   
   
   Here, i is the complex number (square root of -1), h (with a cut mark) is the Planck's constant divided by 2*pi, V is the Potential Energy and Ψ is the wave function which is considered as the characteristic of the wave considered.
   This is how the evolution of the quantum realm occurred, whose understanding is very fundamental in the sense that the more you play in this world the more you can feel your presence as a quantum being.

Signing Off.