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

Einstein’s Miracle Year 1905

In 1905, at the age of 26, Einstein published four major papers and finished his PhD thesis. Each of these papers was groundbreaking and would change physics forever.

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.

Einstein’s Paper on Brownian Motion

In 1905, a young Albert Einstein wrote a paper (while working as a patent clerk) on a well-known physical phenomenon of the time, Brownian motion, which had first been noted in 1827. Einstein’s theory correctly described Brownian motion, and at the heart of his theory was the existence of atoms that were in constant motion.



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.

Carnot the Outsider

During his formal education Sadi Carnot (1796-1832) was literally surrounded by renowned physicist, chemists and mathematicians on the faculty. However, Carnot was never a member of this distinguished group, and did his most important work (as a founder of modern day thermodynamics) as an outsider.

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.

Why is The Sky Blue?

Shorter wavelength blue light is scattered more by air molecules than red light. It’s this “Rayleigh scattering” that results in the blue color of the sky.

The Superheated Liquid

When a liquid has been heated to a temperature above its boiling but still doesn’t boil, it’s superheated.

The Supercooled Liquid

If a liquid is cool rapidly enough it can miss the freezing point and end up as a supercooled liquid.

An Amorphous Solid Versus A Glass

While all glasses are amorphous solids, not all amorphous solids are glasses; glasses exhibit an actual glass transition. Even though we say solid, a glass is actually a very viscous liquid that moves very slowly over time.

Glass is Really a Liquid

The glass in a window (for example) is really a very viscous liquid that moves very slowly over time.

When a Light Bulb Burns Out

A light bulb is more likely to burn out when first turned on since this is when the electrical resistance is the lowest. As the current flows it heats up the wire and the atoms begin to “jiggle”, which increases the electrical resistance.

The Weight of Heat

The chemist Lavoisier actually tried to weigh heat; he found it was weightless.

Speed of Sound and Material Phase

The speed of sound depends on the phase of the material (solid, liquid, or gas). In general, sound travels fastest in solids, then liquids, then gases.

Feynman on Why We Need Math

“If you want to learn about nature, to appreciate nature, it is necessary to understand the language [of mathematics] that she speaks in. She offers her information only in one form; we are not so unhumble as to demand that she change before we pay any attention.” -Feynman on Why We Need Math

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.


A laser is possible because photons are Bosons and not Fermions.

Matter in transition

Democritus saw material objects (matter) as existing in a temporary state, being created or destroyed as atoms respectively come together or fall apart under the influence of natural forces; all that remains then are the atoms comprising those material objects.

Atomos and Atoms

Democritus considers everything in the universe – including the human mind and soul, and even the gods – to be comprised of atomos, which is Greek for indivisible and from which we get “atom”.

Dalton and Atomic Weights

With a firm belief in atoms, impressive physical insight and armed with a few simple rules, Dalton was able to construct a table of relative weights, which he first presented in 1803 at a talk to the Literary and Philosophical Society of Manchester. In 1805, this effort first appeared in print, with a systematic explanation of the method appearing in 1808 when Dalton published the first volume of his book A New System of Chemical Philosophy. Here, with hydrogen as his reference, he gave the following relative weights: hydrogen (H) 1; nitrogen (N) 5; carbon (C) 5.4; oxygen (O) 7; phosphorus (P) 9; sulfur (S) 13 and so on, including several elements and compounds.

Newton on Light Diffraction

Newton felt there were some properties a wave theory of light simply could not explain, such as diffraction. For example, diffraction is the property of waves that allow them to bend around objects and spread through openings. In the case of sound waves, it’s why a sound in one room can often be heard in another room farther away by someone not directly in the path of the oncoming sound; the sound wave travels from the one room, spreading out through the doorway into the other room where it’s then heard. Light doesn’t appear to behave this way, after all, you can’t see around corners – can you? The diffraction of light is usually unnoticeable because light waves have such short wavelengths – much smaller compared to the wavelengths of sound waves. Nonetheless, light will diffract if the opening is small enough.

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.”

The speed of light

The speed of light was measured as early as 1862 by Leon Foucault giving good agreement with the modern value of 299,792.458 Km/s.

The Drinking Bird as a Heat Engine

The drinking bird is a nice example of a heat engine. The evaporation of water at the bird’s beak results in a cooler temperature there than at its base (around the tail feather). In turn, this temperature difference causes a pressure difference (high to low from base to beak) that causes the (very volatile) liquid to rise up, eventually toppling the bird forward causing it to “drink”.

The Drinking Bird

Cooling Soup

Cooling soup by blowing on a spoonful prior to placing it in your mouth works because the hotter atoms are literally blown away.  This is because the soup is made up of atoms comprised of a range of speeds. The atoms with the higher speeds – the hotter ones – are on top, hovering above the atoms with the lower speeds – the cooler ones. So, the end result of blowing on the spoonful of soup is that the hotter atoms are blown away, while the cooler ones are left behind.

Maxwell, the Rings of Saturn and Kinetic Theory

In 1855, Maxwell devised a theory that correctly predicted the composition of the rings of Saturn. While at Aberdeen, Maxwell devoted much of his time to the problem and in a letter to Thomson describes the rings as:

“… a great stratum of rubbish jostling and jumbling round Saturn without hope of rest or agreement in itself …”

Maxwell constructed a theory that showed Saturn’s rings couldn’t be solid, liquid or gas, but rather were made of many small, solid, colliding particles orbiting the planet, which were dynamically stable and provided a solid-like appearance; the solution won him the prize. Today, we do know that Saturn’s rings are comprised of tiny rocks that collide with each other as they orbit the planet. In is interesting to note that what led Maxwell to kinetic theory was, oddly enough, Saturn’s rings.

Galileo and The Telescope

By mid-1609, Galileo was working on his treatise about the science of motion, when upon hearing of the invention of the spyglass (the precursor to the telescope) he dropped everything to make his own version. By the end of August, Galileo had a 9X telescope. Around December 1, 1609, Galileo had in his possession a 20X telescope, allowing him to observe the moon’s rough mountainous surface, four (of the currently sixty-seven known) moons of Jupiter, and several new stars.

Galileo, Professor at Pisa

In 1589, Galileo became professor at the University of Pisa making half of his predecessor’s final salary.

Atomic Weight

The atomic weight of a mid-sized atom is around 0.00000000000000000000001 grams; a 1/400th of an inch grain of sand weighs about 0.001 grams.

Earth’s Atmosphere

Earth’s atmosphere is 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.039% carbon dioxide, and small amounts of other gases.

The Mechanical Philosophy

The notion that the universe runs like a mechanical clock arose in the 17th century leading to the mechanical philosophy.

Newton’s Intervening God

While Newton saw the world as following definite laws, he also imagined an intervening God to keep things running smoothly.

Galileo’s Distraction

In mid-1609 Galileo turned his focus away from the laws of motion and pointed his telescope towards the sky.

Pendulum and Small Swings

A pendulum goes to and fro in the same amount of time regardless of how big the swings are – only when the swings are small.

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.

Energy vs Momentum Conservation

Hints of energy being conserved, much like momentum, were showing up by the 1840s. But unlike momentum conservation, which by comparison was quickly accepted and understood (pretty much by 1687 with Newton’s Principia), energy conservation remained a mystery until 1850.

Heat is “Motion”

In 1798, while boring holes into cannon barrels (as part of the manufacturing process), Count Rumford concluded that heat was the result of some sort of motion within objects.

Descartes’ Conservation of Motion

In 1644, in his Principles of Philosophy, René Descartes (1596-1650) proposed that the total motion of the universe is conserved. While this conservation of motion concept bears a certain similarity with Newton’s conservation of momentum, it’s still wrong.

Galileo’s New Title

Unhappy with his arrangement at University of Padua, Galileo managed to strike a new deal in 1610 whereby he became “Chief Mathematician of the University of Pisa and Philosopher and Mathematician to the Grand Duke of Tuscany”. The appointment was for life and he wasn’t obligated to teach at the university. He also wasn’t required to reside in Pisa, which allowed him to finally return to his beloved Florence.

Galileo’s Private University

In 1599, Galileo acquired a large house with a garden and vineyard. Here he housed students who stayed with him for extended periods (along with their servants), and maintained a workshop (complete with a coppersmith) for the manufacture of instruments. The private lessons he gave along with his university courses kept Galileo very busy.

Feynman on Energy

“It is important to realize in physics today, that we have no knowledge of what energy is … It is an abstract thing in that it does not tell us the mechanism or the reasons …”

Photon Momentum

In 1905, Einstein said light is a particle (photon) with energy proportional to its frequency. Although photon momentum was known much earlier to Einstein, he waited until 1916 to finally declare it.

The Imponderable Fluids

By the end of the eighteenth century, heat along with its cohorts light, magnetism and electricity were regarded as an imponderable fluid capable of flowing between the spaces assumed to be present in matter.