Awesome and Mysterious Quantum Mechanics

While Ernest Rutherford, Hans Geiger and Ernest Marsden were bombarding Gold foils with Alpha particles in 1909 leading to the discovery of atomic nucleus, Chemists were finishing analysis of gas emission spectrum. When light obtained from heating up gases in a glass tube was passed through a prism, it formed distinct lines of light of different colors for example in case of Hydrogen, Red, Blue/Cyan and Violet colored lines were obtained. Niels Bohr, by putting together Einstein’s theory of light and J.J. Balmer's empirical formula came up with an explanation in 1913. He figured that Electrons absorb energy when gas is heated up and leap to higher energy orbits around the nucleus, but they only leap to certain orbits after absorbing specific amount of energy. When cooled down the Electrons emit energy in specific amounts termed as Quanta and leap in to lower energy orbits. We obtain distinct lines of different colored light because electrons absorb and emit energy in certain amounts. Electrons can only have certain amounts of energy, not just any value. This explanation also rescued Rutherford’s atomic model because now it was understood why Electrons did not get pulled into the nucleus given their opposite charges.

Balmer's formula

Here R_H is Rydberg constant for Hydrogen, n₁=2 and n₂ greater than n₁

Louis-Victor De Broglie after intensely studying wave particle duality of light pioneered by Max Planck and Albert Einstein, presented his famous hypothesis in 1924 stating not only light has both wave and particle properties but particles such as Electrons too should have both wave and particle like characteristics. De Broglie called the wave associated to a particle, matter wave. He showed that wave, characteristic to a particular particle should have a wavelength of

λ=h/p

Where h=Planck’s constant having a value of 6.626068*10^-34m²kg/s and p=momentum of the particle.

Werner Heisenberg et al presented matrix mechanics to describe wave nature of particles in 1925. In 1926 Erwin Schrodinger created wave mechanics in an attempt to describe matter waves. Latter Schrodinger showed that matrix mechanics and wave mechanics are equivalent. Max born showed a statistical version of wave function and pointed that solution to Schrodinger’s wave equation for particles gives probability of finding a subatomic particle like an Electron at a particular location, it doesn't describes a smeared out Electron as Schrodinger himself had thought. By 1927 George Paget Thomson in UK and Clinton Davisson and Lester Germer in US had experimental evidence of wave like properties of Electrons. They were conducting their experiments with Electron beams although with different purposes but found similar diffraction patterns indicating wave like nature of Electrons. These were very first experimental support for De Broglie’s matter waves, 3 years after they were presented. Latter while calculating probability of finding an Electron at different locations using Schrodinger’s wave equation, scientists found a definite probability of finding the Electron on other side of the detector screen. Further they found a certain probability of finding an Electron on other side of a thick wall and even a mountain. This surprising probability is described as Quantum Tunneling and it is real. It is thought that Electron borrows energy required to get through solid wall from future and returns that energy once it is on the other side. As bizarre as it may sound but most probably, that’s how it is. Scientists are harnessing this property of Electrons in creating faster and smaller transistors and Quantum Computers. Transistors utilizing Quantum Tunneling will be much smaller and much faster than the smallest transistors we have today like those 11nm CMOS transistors.

After the equivalence of Matrix and wave mechanics was established, Jordan in Gottingen University and Paul Dirac in Cambridge university merged these two different ways of representing a matter wave mathematically and came up with what became known as transformation theory. Heisenberg while pondering over the papers of Jordan and Dirac figured that more precisely the position of a subatomic particle is known, less precisely its momentum can be known. In 1927, He came up with a mathematical expression to quantize this uncertainty.

ΔxΔp ≥ h/4Π

Where Δx= Standard deviation of position, Δp= Standard deviation of momentum, h= Planck’s constant

Same uncertainty holds for certain other pair of variables too such as energy and time for which the particle can have that energy. In order to explain this result Heisenberg thought up an experiment using Gamma ray microscope. Gamma rays have higher frequency than Electrons and therefore when used to determine position of Electron it will significantly change the direction of motion of Electron upon impact. Even visible light when shone to find the location of Electron will alter its velocity by some amount as energy of photon is comparable to energy of an Electron, leading Heisenberg to conclude that uncertainty is inbuilt into nature itself. As a matter of fact, with Uncertainty principle the predictions of Quantum Mechanics became consistent. Of ‘course the principle has been verified in many experiments since 1927, most common of them being the slit experiment. 

In 1801 Thomas Young took up the task of measuring light’s wavelength. He used a paper card to split a single pinhole beam of sunlight into two to carry out his experiment. Latter the practice of using two narrowly separated slits caught on. Italian physicists Pier Giorgio Merli, Gian Franco Missiroli and Giulio Pozzi did the double slit experiment with a single Electron in 1974. They found an interference pattern on the detector screen, kind of pattern which is created by waves, proving the predictions of Quantum Mechanics. Latter on Scientists discovered that when they look at the Electron fired from Electron gun, it formed a particle like pattern on detector screen and when they did not look, it formed a wave interference pattern. But, how a single Electron can form wave interference pattern? Although the predictions of Quantum Mechanics were verified, nobody had any idea, how. This mystery is still without a good explanation. In more recent versions of this experiment, Scientists observed the Electron after it crossed the slits. To their surprise they found that when they look, the Electron formed a particle like pattern and when they didn’t, it again formed a wave like pattern. How is that possible? Nobody knows the answer even today, but we do know now that Bohr was right. That, act of observation does really changes behavior of a particle. In addition, these observations also gave support to Heisenberg’s Uncertainty Principle. These experiments supported probability wave nature of Electron as predicted by Schrodinger’s wave equation and supported De Broglie’s matter waves or wave particle duality. We know now that the Electron can be in many positions at the same time or wave like if we are not looking at it, a Quantum Mechanical phenomena known as Quantum Superposition, and takes a particular position or behaves particle like if we do look at it.

Time-dependent Schrödinger equation- General

Ψ is wave function of Quantum system, Ĥ is Hamiltonian operator, ћ is reduced Planck’s constant, i=sqrt(-1), r is 3d position vector

Albert Einstein had other ideas about Quantum Mechanics. He and two of his colleagues Boris Podolsky and Nathan Rosen came up with a prediction of Quantum Mechanics in 1935, which he thought cannot be true, leading to his declaration that Quantum Mechanics is not wrong but it is incomplete. That prediction was Quantum Entanglement. Einstein together with his colleagues said that according to Schrodinger’s wave equation and other principles of Quantum Mechanics if two fundamental particles share their source of origin then their properties will have to be linked in such a way that sum of measurements of their Quantum properties give the Quantum property of source particle no matter how far apart these two particles are. This can be possible only if an act of measurement on one of these entangled particles simultaneously affects the Quantum state of other particle thus keeping the sum total same as it would be for the Quantum state of the source particle. This indicates some form of communication between the two particles happening at speeds greater than speed of light, leading Einstein to conclude that the theory is incomplete and requires modifications. Bohr and his colleagues remained unmoved. In his 1964 paper, Irish Physicist John Stewart Bell came with an inequality to settle this dispute. According to the inequality if Einstein was right then Quantum Mechanics would not be just incomplete but it would be wrong. When experiment was done in 1972 by John Clauser and Stuart Freedman, Einstein was found wrong. Results of this experiment supported immediate communication between entangled particles. Latter in 1981-82 a more precise experiment was conducted by Alain Aspect which corroborated faster than light communication between entangled particles when an act of measurement is performed. Bell’s inequality indicated that if Quantum Entanglement was real then entangled particles will have higher correlation than classical physics would allow. Results obtained from experiments based on Bell’s inequality unequivocally indicated a higher correlation between entangled particles. Now scientists around world are harnessing this phenomenon for creating Quantum Computers and to achieve Teleportation.

Because of the uncertain nature of reality, first indicated by Heisenberg, we can’t say with certainty that empty space is without any energy-mass density. According to Quantum Mechanics there is a finite probability that empty space may have certain amount of energy as long as nobody observes it. More specifically, particles and antiparticles may originate from empty space in pairs and exist for a certain while before annihilating each other. Amount of time they exist for depends on their energy, as Quantum Mechanics predicts. More the energy, shorter the duration they exist for and vice versa. This prediction came to be known as quantum vacuum fluctuations of electromagnetic field and is inherent to space.

Hendrik Casimir while investigating the discrepancies in measurements done on colloids, using the theory of Fritz London concerning Van Der Walls forces, the forces that govern colloids, thought up an interesting event. In his 1948 paper he indicated that if two neutral conducting plates are placed about a micron apart in vacuum, then vacuum between plates could only create virtual photon pairs with very small wavelengths compared to vacuum around as kind of wavelengths that can exist between plates becomes limited because of the very short gap. This will cause a higher pressure due to impact of colliding virtual photons from vacuum around compared to pressure caused by virtual photons contained in between, causing plates to get pushed together. This became known as Casimir effect. Until recently, scientists were not able to create experimental conditions required to measure the force predicted by Casimir’s equation.

F=(Πhc/480L⁴)A

F= Force experienced by the plates, h= Planck’s constant, c= Speed of light, L= Gap between plates, A= Area of plates

In 1996, Steven Lamoreaux finally succeeded in creating lab conditions required for the experiment and found the experimental results to be within 5% of the value predicted by Casimir. By 2011, more accurate experimental confirmations have been achieved. Particles other than Photons also affect the plates but in magnitudes too small to be measurable by current technology. Effect of Bosons is attractive on the other hand effect of Fermions is repulsive. Existence of Casimir effect reveals a lot about nature of reality. For one it entails a broken Super symmetry, because it indicates absence of Fermionic photinos. Super symmetry has not been detected yet. It has other implications such as quantum gravity and about nature of space-time itself. Dynamic Casimir effect is a direct derivation and predicts that if the two plates move to and fro at speeds close to speed of light then virtual particles of vacuum may become real by converting energy of motion of plates.

References:

1) https://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-lecture.pdf

2) http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/quantum_theory_ origins/
3) http://math.ucr.edu/home/baez/physics/Quantum/bells_inequality.html
4) http://www.casimir-network.org/IMG/pdf/Casimir_20effect.pdf

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