Quantum Physics and Its Beauty

Once a little boy asked his father, “Dad, how big is the sky?” The father replied, “It is of infinite dimensions”. At the first instant the boy found his father’s answer to be totally a ridiculous one. He thought to himself, “How can something be of infinite length, with no beginning and no end?!” But what the father actually tried to mean was to show a simple comparison of how minuscule was he when compared to the vastness of the sky. Now that there are things which physically dominate us, question might arise, how small are we? Or do things smaller than us exist in this universe? One might easily come up with the answer- atom. Others might argue that there are even smaller things in an atom. But how further can we go into the quest of finding the smallest existence in the universe - Quantum physics holds the answer.
It was probably the Greek philosopher Democritus who came up with the idea that matter was made up of the tiny indivisible particles we call atom today. The idea was further modified by the British chemist John Dalton. He seemed to be very much satisfied with the idea that matter is made up of spherical structures called atom. Dalton considered the atom to be more or less like a uni-dimensional point which could not be further divided. But Michael Faraday, in his experiments of electrolysis, showed that atoms gave up or accepted quantized amount of electrical charge. This eventually led to a completely new version of the atomic picture which was known as ‘The Plum Pudding Model’ where the atoms were no more considered to be point structures but spherical volumes of uniform positive charge in which smaller particles called electrons were embedded like the plums in a pudding. The distribution of the electrons was such that, mutual repulsion was in exact balance by the mutual attraction. Thomson’s plum pudding model could explain some basic properties of the atom but failed to explain complex phenomena of multi-electron atoms and the discreteness of the frequencies observed in atomic spectra.

Then in 1911, Ernest Rutherford’s gold foil experiment, more commonly known as the alpha scattering experiment, showed some observations that were in direct contradiction with what J.J Thomson had theorized. According to the experiment, Rutherford put incident alpha particles from a radioactive source on a very thin gold foil and observed that very few of the alpha particles rebounded by angles of 900 or more when incident and most the particles simply passed through with some small deviations in angle whereas J.J Thompson’s theory predicted that all of the positive charged alpha particles should pass through the atom with minor deviations if any. This demanded the evolution of a completely new atomic picture which was later done by Ernest Rutherford in his famous planetary model of the atom where he considered the atom to be mostly a vast empty space in which a very small portion was occupied by electrons and at the center there was tiny nucleus containing the entire positive charge and almost all the mass of the atom.

Rutherford’s model could satisfactorily explain quite complex behaviors of the atom, but had a serious flaw in its basics. It was in contradiction with Maxwell’s electromagnetic theory. Rutherford’s atom model said that electrons revolve around the nucleus like the planets do around the sun in the solar system, which according to Maxwell’s equations should have radiated out electromagnetic energy continuously due to centripetal acceleration. In course of time, the electrons should have exhausted all their energy and eventually would have spiraled down towards the nucleus leading to the ultimate catastrophe of the atom which of course does not happen in the nature (Luckily!). So it turned out that no one could come up with a convincing model of the atom and this gave a hard blow to the scientific community of that time. It was not until the mid 18th century that a young Danish physicist name Niels Bohr came up with a satisfactory representation of the atomic model. He came up with two revolutionary ideas that shook the world of physics.
A simplified version of the postulates set forward by Niels Bohr is:-
1.Electrons in atoms move around the nucleus in certain allowed orbits (which Niels Bohr called energy levels) where the electrons do not loose energy due to centripetal acceleration.
2.Energy of the electrons in the energy levels is quantized i.e. it can be an integer multiple of a basic energy level and there can be no fractional multiple of the basic energy level. In other words, the radius of the path of electron around the nucleus is discrete and cannot be continuous. Energy is given out or taken when an electron moves from a higher energy level to a lower energy level and vice versa respectively.
These two simple yet revolutionary ideas held key to the appropriate understanding of atomic phenomena at the microscopic levels. Little bit Niels Bohr knew that his version of the atomic model would be able to explain many other phenomena in physics that could not be explained by existing theories of that time.
One such unexplained phenomenon of that time was related with the blackbody radiation. The blackbody is one which absorbs radiations of all frequencies that falls upon it, and reflects and transmits none and as a good absorber is also a good radiator, a black body is supposed to be a perfect radiator as well. The intensity of different wave lengths of radiation emitted from a black body appears somewhat likes this:

The Rayleigh-Jeans Law based on classical physics, predicted that the intensity-frequency relationship should be:

I = 8πf2kT/c3

This suggested that at higher frequencies the intensities of radiation will also be high and at a frequency tending to infinity, the intensity will also tend to infinity as well. This is obviously nonsensical and did not agree with the experimental observation. At that time Rayleigh-Jeans Law was the only applicable law for low frequency radiation and could not explain the appearance of this spectrum for greater ranges. This is when quantum physics came to the rescue.
In order to explain the frequency distribution of radiation from a hot cavity (blackbody radiation) Planck proposed the ad hoc assumption that the radiant energy could exist only in discrete quanta which were proportional to the frequency. This would imply that higher modes would be less populated and avoid the ultraviolet catastrophe of the Rayleigh-Jeans Law.

The quantum idea was soon used to explain the photoelectric effect, became part of the Bohr’s Theory of discrete atomic spectra, and quickly became part of the foundation of modern quantum theory.
Photoelectric effect is perhaps the most important phenomenon that could be explained by quantum physics. For a very long time, light and other electromagnetic radiation were thought to be waves. Maxwell and Lorentz had firmly established the wave nature of electromagnetic radiation in electromagnetic theory. Numerous experiments on interference, diffraction, and scattering of light had confirmed it. Then in 1905, Einstein argued that under certain circumstances light behaves not as continuous waves but as discontinuous, individual particles. These particles, or “light quanta,” each carried a “quantum,” or fixed amount, of energy, much as automobiles produced by an assembly plant arrive only as individual, identical cars—never as fractions of a car. The total energy of the light beam (or the total output of an assembly plant) is the sum total of the individual energies of these discrete “light quanta” (or automobiles), what are called today “photons.” Although Einstein was not the first to break the energy of light into packets, he was the first to take this seriously and to realize the full implications of doing so.
Now the question is, what is photoelectric effect? Basically it refers to the emission, or ejection, of electrons from the surface of, generally, a metal in response to incident light. Electrons given off in this way are photo-electrons. Why or more precisely how quantum physics played an important role into explaining this phenomenon? Here is the answer…
According to the classical mechanics, light travels as a wave which means the wave with higher amplitude carries more energy. Bigger amplitude of the light means the light is brighter, so a brighter light will give off more photo-electrons. Is this right? Well actually… No!

Look at these diagrams, which show what happens when light shines on a clean surface of the metal lithium:

● A dim blue light will make the lithium give off a few electrons, so there will be a small, measurement current.

● A brighter blue light will give a bigger photoelectric current, because there are more photo-electrons.

This seems exactly what you would expect… but a light just as bright as the bright blue light, gives off no electrons at all, and the current is zero!

This is impossible to explain – if light is a wave.
Now if we consider that light is made of tiny particles known as photons which were mentioned before, then we can explain the 3 results above:

►The photons of blue light contain enough energy to eject electrons from lithium. A dim blue light has few photons, so few electrons are liberated. This gives a small photo-electric current.
►A bright light has more of these high-energy photons; so more electrons are liberated, giving a larger photo-electric current.
►But red light has more consists of photons that do not have enough energy to emit electrons from lithium.
Even though a bright red light has very many of these photons, not one of them has enough energy to eject an electron.
























Analysis of data from such experiments showed that the energy of the ejected electrons was proportional to the frequency of the illuminating light. This showed that whatever was knocking the electrons out had an energy proportional to light frequency. The remarkable fact that the ejection energy was independent on the total energy of illumination showed that the interaction must be like that of a particle which gave all of its energy to the electron! This fit in well with Planck’s hypothesis that light in the blackbody radiation experiment could exist only in discrete bundles with energy

E = hν

So, does light consist of particles or waves? When one focuses upon the different types of phenomena observed with light, a strong case can be built for a wave picture:














Interference














Diffraction














Polarization

By the turn of the 20th century, most physicists were convinced by phenomena like the above that light could be fully described by a wave, with no necessity for invoking a particle nature. But the story was not over.

Phenomenon	Can be explained in terms of waves.	Can be explained in terms of particles.
Reflection
Refraction
Interference
Diffraction
Polarization
Photoelectric effect

Most commonly observed phenomena with light can be explained by waves. But the photoelectric effect suggested a particle nature for light. Then electrons too were found to exhibit dual natures.

Most commonly observed phenomena with light can be explained by waves. But the photoelectric effect suggested a particle nature for light. Then electrons too were found to exhibit dual natures.
Quantum physics could also explain the presence of emission spectrum of an atom. Classical physics could not explain the presence of discrete wave lengths in emission spectrum. Because classical physics predicted the presence of spectrum for continues range of wavelengths, but quantum physics said, since electrons in atom can only move from one definite energy level to another, the corresponding frequency of radiation from the atom due to the transition of the atom should also have definite frequency value, which was an exact accordance of emission spectrum obtained for wide range of atoms.
Now how far has quantum mechanics gone? We have seen how quantum mechanics has described black body radiation, photoelectric emission and emission spectrum which were mysteries to the physicist for many years.
So does it explain everything? Even unification!
Unification would be the formation of a law that describes perhaps everything in the universe. It is the quest for one single idea; one master equation. Physicists think that there might be a master equation that can explain all the physical phenomena because through the course of last two hundred years or so, our understanding of the universe has given variety of explanations that are all pointing towards one nugget of an idea that physicists are still trying to find out.

Long before Einstein, the quest of unification began with the most famous accident in the history of science. As the story goes, one day in 1665, a young man was sitting under a tree when all of a sudden he saw an apple fall from above. And with the fall of that apple, Isaac Newton revolutionized the picture of the universe. In an audacious proposal for his time, Newton proclaimed that the force pulling the apple to the ground and the force keeping the moon in an orbit around the earth were actually one and the same. In a moment, Newton unified the heavens and the earth in a single theory, he called gravity. It was a fantastic unification of our picture of nature.

Gravity was the first force to be understood scientifically, though three more would have eventually followed. Although Newton discovered his law of gravity more than three hundred years ago, his equations describing this force made such accurate predictions that we still make use of them today.
Yet there was a problem. While his laws described the strength of gravity with great accuracy, Newton was harboring an embarrassing secret. He had no idea how actually gravity works.

Then in the early 1900’s, an unknown clerk, working in the Swiss patent office would change all that. While reviewing patent applications, Albert Einstein was also pondering upon the behavior of light and little did Einstein know that his musings on light would lead him to solve Newton’s mystery of what gravity is.
At the age of twenty six, Einstein made a startling discovery that the velocity of light is a kind of cosmic speed limit; speed that nothing in the universe can exceed, but no sooner Einstein published this idea, then he found him self squaring off with the father of gravity.
To understand this conflict we have to run a few experiments. Let’s create a cosmic catastrophe. Imagine that all of a sudden, without any warning, the sun vaporizes and completely disappears.
Now what would have happen to the planets according to Newton? Newton’s theories predict that, with the destruction of the sun, the planets would immediately fly out of their orbits. In other words, Newton thought that the gravity was a force that acts instantaneously across any distance and we would immediately feel the effect of the sun’s destruction, but Einstein saw a big problem with Newton’s theory. Einstein knew light does not travel instantaneously. In fact it takes about eight minutes for the sun rays to travel the ninety three million miles to the earth. And since he had shown that nothing, not even gravity can travel faster than light, then how the earth could be released from the orbit before the darkness resulting from the sun’s disappearance reached our eyes. To the young upstart from a Swiss patent, anything outrunning light was impossible and that meant 250 years old Newtonian picture of gravity was wrong.

In his late 20’s, Einstein had to come up with the picture of the universe in which gravity does not exceed the cosmic speed limit. Then after nearly ten years of racking his brain, he found the answer in a new kind of unification.
Einstein came to think of the three dimension of space and single dimension of time. Einstein thought of these dimensions to be somewhat woven together into a fabric of space-time like the surface of a trampoline. This unified fabric is warped and stretched by heavy objects like planets and creates what we feel as gravity. A planet like the earth is kept in an orbit not because the sun reaches out instantaneously and grabs hold of it as par Newton’s theory, but simply because it follows curves in this fabric caused by the sun’s presence.

So with this new understanding of gravity, let’s review the cosmic catastrophe. Now what would happen because of the sun’s disappearance?
The gravitational disturbance that results will form a wave that travels across the fabric in much the same way that a pebble dropped into a pond makes ripples across the surface of the water. So we would not feel a change in our orbit around the sun until this wave reached the earth.

Einstein’s dream was to unify the gravitational force with the other fundamental forces of nature in The Standard Model. But the basics of quantum physics prevented him from doing so. Quantum physics is physics of the micro-world. Quantum physics gives impressive conclusions at atomic levels where the strength of the electromagnetic, strong nuclear and weak nuclear forces is significant. But gravitational force is only significant for large masses and this obviously is not possible within atomic scopes.
Another thing that is quite intriguing in the realm of quantum physics is the “uncertainty” factor involved with it. Quantum physics adds the presence of odds, or probability to everyday outcomes. Things that appear to happen so obviously are actually outcomes with highest probability of occurrence and quantum physics instructs us to appreciate the fact that there are infinite numbers of ways an outcome may appear. A billiard ball is expected to bounce off the walls of the billiard table while traversing a particular path. What quantum physics adds to this scenario is that, the ball has also some chance of going straight through the wall instead of bouncing back, but the probability of this happening is so small that it can be neglected reasonably.

Unifying gravity with the quantum world is proving to be difficult than ever. Einstein disliked the idea of a universe full of uncertainties and chances. Probably it is for this reason he once said, “God does not play dice!” Moreover, the inconsistencies in the strength of the forces in quantum physics and general relativity are delaying any chances of unification even further. This has led to the evolution of new, extremely radical theories like string theory, M-theory and so on but they are still at their infancy and they predict manifestations that cannot be tested by any experiment. We just can hope that one day, mankind will come up with a theory of everything and accomplish The Grand Unification!
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By Mohammad Atif Bin Shafi
East West University, Dhaka, Bangladesh
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The Aftermath Publications, Issue 1
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