Light and An Ideal Gas

In 1905, Einstein’s comparison between dim (or dilute) light, and an ideal (dilute) gas led him to conclude that under certain conditions, light will behave as a particle.

Einstein on Planck’s Derivation

“[Planck’s] derivation was of unparalleled boldness, but found brilliant confirmation. … However, it remained unsatisfactory that the [classical mechanical] analysis, which led to [Planck’s Radiation Law], is incompatible with quantum theory, and it is not surprising that Planck himself and all theoreticians who work on this topic incessantly tried to modify the theory such as to base it on noncontradictory foundations.” –Einstein

The Ramifications of Quantum Mechanics

The Problem with Schrödinger’s Wave Equation

The biggest question still plaguing Schrödinger’s wave equation was the role of the wavefunction. Sure, mathematically it’s clear: it’s the solution to Schrödinger’s wave equation and the “all-powerful function” as a result. However, physically it was still a big mystery to everyone, including Schrödinger himself.

Continue …

Bose’s Derivation of Planck’s Radiation Law

With his work in 1916-7, Einstein was able to arrive at a “much more” quantum derivation of Planck’s Radiation Law. However, in the end he fell short, having to rely on assumptions. In 1924, Satyendra Nath Bose provided the first “fully” quantum derivation of Planck’s radiation law, which revealed the deeper nature of light that had eluded everyone else, including Einstein.  With this work, he created the new area of physics known as quantum statistics.

Light and Einstein

Einstein Revisits His Theory of Light

By 1911, Einstein had already hypothesized that light consists of particles he called light quanta (later called photons). Moreover, he had shown that light has an inherent quality, whereby it exhibits both wave and particle properties. Although, he had seen further than anyone into the mysterious nature of light, it continued to perplex him:

“I do not ask anymore whether these [light] quanta really exist. Nor do I attempt any longer to construct them, since I now know my brain is incapable of advancing in that direction.”

Continue …

Einstein’s Nobel Prize

In 1921, Einstein won the Nobel Prize. The citation reads:
“To Albert Einstein for his services to theoretical physics and especially for his discovery of the law of the photoelectric effect.”

To be sure, Einstein is being acknowledge for the “the law of the photoelectric effect”, in other words for his photoelectric equation, but not for the photon concept. This attitude would persist until 1923, when new experimental results would convert pretty much everyone to the existence of photons.

Bohr and The Atom

Niels Bohr’s Early Career

In March of 1912 Niels Bohr (1885–1962) arrived in Manchester to begin working with Rutherford. Previously, he had worked with Thomson in Cambridge. Unfortunately, their relationship had been strained from the start, and never really flourished as Bohr had hoped. Writing to his brother Harald, Bohr said:

“… Thomson has so far not been as easy to deal with as I thought the first day. …”

Perhaps, Bohr’s initial encounter with Thomson was to blame, where upon entering Thomson’s office, Bohr proclaimed:

“This is wrong.”

Continue …

Max Planck’s Rough Road to Quantum Theory

Max Planck’s Early Life

Max Planck (1858–1947) was born in Kiel, (in modern day Germany), the sixth child to the distinguished jurist and professor of law at the University of Kiel, Johann Julius Wilhelm Planck and his second wife, Emma Patzig. His family culture would bestow in Planck’s life and work a sense of excellence in scholarship, incorruptibility, idealism, reliability, and generosity.

In 1867, when Planck was nine, his father received an appointment at the University of Munich. The family moved and Planck enrolled in the city’s Maximilian Gymnasium where his interest in physics and mathematics was piqued. However, Planck excelled in his other studies as well, in particular music. Thus at the time of graduation, now 16, Planck had the difficult decision of choosing a future in either music or physics; he chose physics.
Continue …

Zero Point Energy

The zero point energy of a system is a direct consequence of the Heisenberg uncertainty principle.

The Intensity of Light

In terms of quantum theory, increasing the intensity of light means increasing the number of photons.

Compton Scattering

In 1923, Arthur Compton’s (1892-1962) light scattering experiments provided further support for Einstein’s hypothesis for the particle nature of light.

Solid Helium

Although possible, helium does not easily solidify due to quantum effects related to its small atomic size.

The Resistance to Einstein’s Light Quanta

Einstein’s light quanta hypothesis met with tremendous resistance, taking almost twenty years after its introduction in 1905 to be fully accepted. Despite such opposition, Einstein continued to use the concept in his work with significant success.

Wave-Particle Duality

In 1905, Einstein established wave-particle duality for light. In 1923, de Broglie extended it to all quantum particles. In an interview in 1963 de Broglie reflected on his epiphany:

“As in my conversations with my brother we always arrived at the conclusion that in the case of X-rays one had both waves and [particles], thus suddenly – … it was certain in the course of summer 1923 – I got the idea that one had to extend this duality to material particles, especially to electrons.”

Bose-Einstein Condensation and Quantum Entanglement

In 1925, Einstein predicted a very unusual phase transition that occurs for the quantum ideal gas. Einstein describes the phenomenon in a letter to Paul Ehrenfest (1880–1933):

“From a certain temperature on, the molecules ‘condense’ without attractive forces, that is, they accumulate at zero velocity.”

In other words, as the temperature is lowered, the atoms in the gas begin to “pile up” or condense into the lowest (single particle) energy state, which is the one with zero kinetic energy; there’s a critical temperature whereby a phase transition (now called (Bose-Einstein condensation) occurs. This effect becomes most pronounced as the temperature is lowered to absolute zero, at which point, all the gas atoms condense into this lowest energy state. This phenomenon is an example of quantum entanglement.

Einstein and The Quantum Ideal Gas

In 1925, Einstein made his last contribution to quantum theory (consider by many to be his last significant scientific contribution as well) with his work on the quantum ideal gas.

Einstein’s Light Quanta Hypothesis Explains Physical Phenomenon

In his1905 paper, On a Heuristic Point of View Concerning the Production and Transformation of Light, Einstein showed how his newly introduced light quanta hypothesis could be used to interpret several well-known experimental observations, the most notable of these phenomena being the photoelectric effect.

Einstein’s Photon

The major theme of Einstein’s 1905 paper, On a Heuristic Point of View Concerning the Production and Transformation of Light, was that light (under certain circumstances) behaves as if it’s comprised of individual particles rather than waves. These particles, or “chunks” of light were originally called light quanta, and then later came to be called photons.

Einstein’s Light Quanta Hypothesis and The Nobel Prize

It was the first of Einstein’s 1905 papers, On a Heuristic Point of View Concerning the Production and Transformation of Light, which he referred to as “very revolutionary” – the only time he would ever say this about any of his work, in fact – and which, in part would win him the Nobel Prize in 1921.

Atomic Energy States are Discrete

The energy states available to atoms and molecules occur at specific intervals. In other words, they are discrete rather than continuous.