History of Science -- Part Twelve: Louis de Broglie

Louis de Broglie was Prince Louis de Broglie. His aristocratic family intended a career in the French diplomatic service for him, and young Prince Louis studied history at the Sorbonne. But after receiving an arts degree, he moved to theoretical physics. Before he could do much physics, World War One broke out, and de Broglie served in the French army at a telegraph station in the Eiffel Tower.

With the war over, de Broglie started work on his physics Ph.D., attracted he says, “by the strange concept of the quantum.” Three years into his studies, he read the recent work of the American physicist Arthur Compton. An idea clicked in his head. It led to a short doctoral thesis and eventually to a Nobel Prize.

Compton had, in 1923, almost two decades after Einstein proposed the photon, discovered, to his surprise, that when light bounced off electrons its frequency changed. This is not wave behavior. When a wave reflects from an object, each incident crest produces one other wave crest. The frequency of the wave therefore does not change in reflection from a stationary object. On the other hand, if Compton assumed that light was a stream of particles, each with the energy of an Einstein photon, he got a perfect fit to his data.

The “Compton effect” did it. Physicists now accepted photons. Sure, in certain experiments light displayed its spread-out wave properties and in others its compact particle properties. As long as one knew under what conditions each property would be seen, the photon idea seemed less troublesome than finding another explanation for the Compton effect. Einstein, however, still “a man apart,” insisted a mystery remained, once saying “Every Tom, Dick, and Harry thinks they know what the photon is, but they’re wrong.”

Graduate student de Broglie shared Einstein’s feeling that there was a deep meaning to light’s duality, being either extended wave or compact particle. He wondered whether there might be symmetry in Nature. If light was either wave or particle, perhaps matter was also either particle or wave. He wrote a simple expression for the wavelength of a particle of matter This formula for the “de Broglie wavelength” of a particle is something every beginning quantum mechanics student quickly learns.

The first test of that formula came from a puzzle that stimulated de Broglie’s wave idea. If an electron in a hydrogen atom were a compact particle, how could it possibly “know” the size of an orbit in order to follow only those orbits allowed by Bohr’s by-now-famous formula?

The length of violin string required to produce a given pitch are determined by the whole number of half-wavelengths of vibrations that fit along the length of the string. Similarly, if the electron was a wave, the allowed orbits might be determined by a whole number of electron wavelengths that fit around the orbit’s circumference. Applying this idea, de Broglie was able to derive Bohr’s ad hoc quantum rule.

(In the violin, it’s the material of the string that vibrates. What vibrates in the case of an electron “wave” was a mystery. It’s become an even deeper one.)

It’s not clear how seriously de Broglie took his conjecture. He certainly did not recognize it as advancing a revolutionary view of the world. In his own later words:

[H]e who puts forward the fundamental ideas of a new doctrine often fails to realize at the outset all the consequences; guided by his personal intuitions, constrained by the internal force of mathematical analogies, he is carried away, almost in spite of himself, into a path of whose final destination he himself is ignorant.

De Broglie took his speculation to his thesis adviser, Paul Langevin, famous for his work on magnetism. Langevin was not impressed. He noted that in deriving Bohr’s formula de Broglie merely replaced one ad hoc assumption with another. And de Broglie’s assumption, that electrons could be waves, seemed ridiculous.

Were de Broglie an ordinary graduate student, Langevin might have summarily dismissed his idea. But he was Prince Louis de Broglie. Aristocracy was meaningful, even in the French republic. So no doubt to cover himself, Langevin asked for a comment on de Broglie’s idea from the world’s most eminent physicist. Einstein replied that this young man has “lifted a corner of the veil that shrouds the Old One.”

Meanwhile, there was a minor accident in the laboratories of the telephone company in New York. Clinton Davisson was experimenting with the scattering of electrons from metal surfaces. While Davisson’s interests were largely scientific, the phone company was developing vacuum tube amplifiers for telephone transmissions, and for that the behavior of electrons striking metal was important.

Electrons usually bounced off a rough metal surface in all directions. But after the accident, in which a leak allowed air into his vacuum system and oxidized a nickel surface, Davisson heated the metal to drive off the oxygen. The nickel crystallized, essentially forming an array of slits. Electrons now bounced off in only a few well-defined directions. The discovery confirmed de Broglie’s speculations that material objects could also be waves.

I began these recent “Histories” with the first hint of quantum in 1900. It was a hint largely ignored. We now reach the state of physics in 1923 where scientists finally are forced to accept a wave-particle duality and the concept of quantum. A photon, an electron, an atom, a molecule — in principle any object — can be either compact or widely spread-out. You can choose which of these two contradictory features to demonstrate. The physical reality of an object depends on how you choose to look at it.

So we go from the strange concept of quantum energy in physics to the even weirder view that energy waves can be particles and solid objects can be waves. This duality of Nature is not the strangest thing in Quantum Mechanics. It’s strange and weird, that’s for sure, but there’s more to come — even stranger and weirder.

Afterthought:

Since I really consider this series in my blog a “rough draft” of some ideas that need polish and editing, I still have time to go back and correct an oversight in Chapter One. The ancient Greeks recognized that the music from their stringed instruments was most pleasing when the various notes in a melody came from whole number fractions of the basic (or tonic) string. Out of that came modern music with octaves (when the string length is one-half), thirds, fourths, fifths, etc. This was reflected in their mathematics and what we call “rational numbers.”

The Greeks thought that all numbers were made up of fractions of whole numbers just like the pleasing music of the whole number fractions on stringed instruments.

A story is told that when the first mathematician realized that the square root of two was not a number made from a fraction, that he was thrown overboard (literally) as some kind of heretic.

It has always been my hypothesis that it was this recognition of the connection between simple fractional string lengths and the pleasing esthetics of the musical result that demonstrated to the Greeks that concepts of Nature could be represented as simple formulas. That idea was the beginning of scientific thought.

So isn’t it interesting that the concept of string lengths and half-wavelength explanation that impressed the Greeks appears again a couple of thousand of years later in the most sophisticated science we know of.

That fact has always been a significant point to me. I probably won’t win the Nobel Prize for describing it. But it is something to think about — isn’t it? Who knew that science would be so advanced by “music.”

The History of Science -- Part Thirteen

History of Science -- Part Eleven: The Atom

Niels Bohr grew up in a comfortable and respected family that nurtured independent thought. His father, a professor of psychology at Copenhagen University, was interested in philosophy and science and encouraged those interests in his two sons. Niel’s brother, Harald, eventually became an outstanding mathematician. Niels Bohr’s early years were supportive. Unlike Einstein, he was never the rebel.

In college in Denmark, Bohr won a medal for some clever experiments with fluids. But I’ll skip ahead to 1912 when, with his new Ph.D., Bohr went to England as a “postdoc,” a postdoctoral student.

By this time the atomic nature of matter was generally accepted, but the atom’s internal structure was unknown — actually, it was in dispute. Electrons, negatively charged particles thousands of time lighter than the atom, had been discovered a decade earlier by J.J. Thompson. An atom, being electrically neutral, must somewhere have a positive charge equal to that of its negative electrons, and that positive charge presumably had most of the mass of the atom. How are the atom’s electrons and its positive charge distributed?

Thompson had made the simplest assumption, that the massive positive charge uniformly filled the atomic volume and the electrons — one in hydrogen and almost 100 in the heaviest known atoms — were distributed throughout the positive background like raisins in a rice pudding. (I personally call that the chocolate chip cookie theory, since I prefer cookies to pudding.) Theorists tried to calculate how various distributions of electrons might give each element its characteristic properties.

There was a competing model for the atom. Ernest Rutherford at the University of Manchester in England explored the atom by shooting alpha particles (helium atoms stripped of their electrons) through a gold foil. He saw something inconsistent with Thompson’s uniformly distributed positive mass. About one alpha in 10,000 would bounce off at a large angle, sometimes backwards. The rest of the particles seemed to pass through the thin gold without any deflection. The experiment was likened to shooting prunes through rice pudding — collisions with raisins could not knock a fast prune much off track. Rutherford concluded that his alpha particles were colliding with an atom’s positive charge, and that almost all the atom’s mass was concentrated in a small lump, a “nucleus.”

Why, then, didn’t the negative electrons, attracted by the positive nucleus, not just fall into it? For the same reason that the planets don’t crash down into the son. They orbit the sun. Rutherford decided that electrons orbited a small, massive, positive nucleus.

There was a problem with Rutherford’s planetary model: instability. Since an electron is charged, it should radiate as it races around its orbit. Maxwell’s equations had shown that a charge in motion would radiate electromagnetic waves. Calculations showed that an electron should give off its energy as light and spiral down to crash into the nucleus in less than a millionth of a second.

Most of the physics community considered the instability of the planetary model a more serious problem than the rice pudding model’s inability to explain the rare large-angle deflections of Rutherford’s alpha particles. But Rutherford, a supremely confident fellow, knew his planetary model was basically right. Experiments trump philosophy!

When the young postdoc Bohr arrived in Manchester, Rutherford assigned him the job of explaining how the planetary atom might be stable. Bohr’s tenure in Manchester lasted only six months, supposedly because his support money ran out. But eagerness to get back to Denmark to marry the beautiful Margrethe likely shortened his stay. (After all, scientists are human just like the rest of us.) While teaching at the University of Copenhagen in 1913, Bohr continued to work on the stability problem.

How he got his successful idea is not clear. But while other physicists were trying to understand how the quantum of energy and Planck’s constant, ℎ, arose from the classical laws of physics, Bohr took an “ℎ is okay!” attitude. He just accepted quantization as fundamental. After all, it worked for Planck, and it worked for Einstein.

Bohr wrote a very simple formula that stated that “angular momentum,” the rotational motion of an object, could exist only in quantum units. If so, only certain electron orbits were allowed. And, most important, he wrote his formula so that there was a smallest possible orbit. By fiat, Bohr’s formula “forbids” an electron to crash into the nucleus. If his ad hoc formula was correct, the planetary atom was stable.

Without more evidence, Bohr’s quantum idea would be rejected out of hand. But from his formula, Bohr could readily calculate all the energies allowed for a single electron orbiting a nucleus, that is, for the hydrogen atom. From those energies he could then calculate the particular frequencies of light that could be emitted from hydrogen atoms electrically excited in a “discharge,” something like a neon sign only with hydrogen instead of neon.

Those frequencies had been carefully studied for years, though Bohr was initially unaware of that work. Why only certain frequencies were emitted was a complete mystery. The spectrum of frequencies, unique to each element, presented a pretty set of colors. But were they any more significant than the particular patterns of a butterfly’s wings? Now, however, Bohr’s quantum rule predicted the frequencies for hydrogen with stunning accuracy — precise to parts in 10,000. But at this time, while Bohr had light quanta emitted by atoms, he, along with essentially all other physicists, still rejected Einstein’s compact photon.

Some physicists nevertheless dismissed Bohr’s theory as “number juggling.” Einstein, however, called it “one of the greatest discoveries.” And others soon came to agree. No one understood why it worked. But work it did. And for Bohr that was the important thing. Bohr’s pragmatic “ℎ is okay!” attitude toward the quantum brought him quick success.

(Bohr's equations contained the value of ℎ divided by 2π. That is because of the relationship of angular momentum and a circle. There are 2π radians in the circumference of a circle and the electrons orbited in circles. This relationship of ℎ / 2π appears so much in modern formulas, that a special symbol for the value of ℎ / 2π was created called h-bar: "ℏ."
ℏ = ℎ / 2π)

Contrast Bohr’s early triumph with his quantum ideas with Einstein’s long remaining “a man apart” in his belief in the almost universally rejected photon. I often wonder how the early experiences of these two men are reflected in their lifelong friendly debate about quantum mechanics.

(That story, however, is several chapters into the future History of Science. For the next episode we will learn of a possible explanation of Bohr’s formula and restrictions on electron orbits.)

Please forgive a little anti-climatic addition to an essay that is really complete, but I must say more about Niels Bohr:

Much later he conceived the principle of complementarity: that items could be separately analyzed as having contradictory properties, like behaving as a wave or a stream of particles. The notion of complementarity dominated his thinking on both science and philosophy. This principle attempts to explain the duality that everyone found so difficult to accept with Einstein’s proposal that light could act like particles.^*

This is a history, so I should also add that, during the 1930s, Bohr gave refugees from Nazism temporary jobs at the Institute of Theoretical Physics at the University of Copenhagen, now known as the Niels Bohr Institute, which he founded. He provided them with financial support, arranged for them to be awarded fellowships from the Rockefeller Foundation, and ultimately found them places at various institutions around the world. After Denmark was occupied by the Germans, he had a dramatic meeting in Copenhagen with Heisenberg, who had become the head of the German nuclear energy project.

In 1943, fearing arrest, Bohr fled to Sweden, where he persuaded King Gustav V of Sweden to make public Sweden's willingness to provide asylum. He was then flown to Britain, where he joined the British Tube Alloys nuclear weapons project, and was part of the British team of physicists who worked on the Manhattan Project.

After the war, Bohr called for international cooperation on nuclear energy. He was involved with the establishment of CERN, and became the first chairman of the Nordic Institute for Theoretical Physics in 1957. He was also involved with the founding of the Risø DTU National Laboratory for Sustainable Energy.

He died in 1962 at 77 years of age.

^*In physics, complementarity is a fundamental principle of quantum mechanics, closely associated with the Copenhagen interpretation which will be discussed in following chapters. It holds that objects governed by quantum mechanics, when measured, give results that depend inherently upon the type of measuring device used, and must necessarily be described in classical mechanical terms. Further, a full description of a particular type of phenomenon can only be achieved through measurements made in each of the various possible bases — which are thus complementary.

The History of Science -- Part Twelve

What I Think

I spend a lot of time on Facebook. I suppose some people watch television when they want to take a break. I just don’t find much on TV these days that interest me – OK, I do like NCIS, but I get plenty of that in reruns on some station on the dial. I also watch the Cooking Channel a lot. I like both Chopped and Restaurant Impossible. But that’s only two nights a week. During the day and most nights I’m either cuddled up with a good book (or Kindle) or I’m walking the dog or taking a walk or just walking. I love the out-of-doors, especially the beauty that is Colorado.

But when I have a few minutes to sit down and drink some coffee or just relax, I always turn to FB. Mostly I view it on my phone except when I want to write something.

I’ve been busy for over a week now on a nice little tale of the history of science. At least, it is nice for me. I just love explaining science and sharing just how we got to today, complete with Facebook, servers, laptops, tablets, and smart phones. The journey is really interesting … at least to me.

I’ve spent a lot of time in a classroom. I’ve been a student for many, many hours of lecture and lab and homework. I’ve also stood in the front and tried to share the knowledge as best I could. These days I don’t lecture, except to a keyboard. I’m also back in class, although that is primarily via video and more text books, but the homework is just as hard (if not harder).

So why is FB attractive to me? What do I get out of it? Well, I like sharing my life with my friends, both past and present. I like to see the pictures and share the adventures and just have a feeling that I know a little better what my loved ones are up to.

I read all the comments with great interest. Some just share their lives with food and kids. A lot focus on music or current events or take the platform to present their personal political view or to denounce the views of those they don’t agree with. Some share the activities of their lives or their interests in travel or birds or scenery of whatnot. All that is very interesting to me.

Many of my friends and acquaintances, not to mention many of my family, are deep in faith and they freely share that too. That’s good. I understand clearly the people that have made God the center of their lives and their desire to share the Gospel message with others. They’re actually obeying one of God’s commandments when they do so. Many also share how they are living their lives for God’s glory in the works they do and the activities they support. I like to read about those charities and works too. They build me up to see the love in other people’s actions. God knows we need to be exposed to more love in other’s actions with all the hate that is floating around in the current events.

After all, the Gospel is free, it makes you free, and it is free for all. A theme I picked up in church today. I was thinking about how people’s lives are shaped by what happens in their life. That is, their future is often a reflection of their past.

Many people have had to deal with great tragedy in their life. For some, that tragedy strengthened their will like fire strengthens iron. For others the tragedy has become a theme that they carry like a heavy burden, making them all bent to the ground.

The Gospel is good news because it says you can lay that burden down. Faith is not a burden, but rather it lifts the burden.

Me, I’ve had no tragedy. I thought about what word is the opposite of “tragedy,” its antonym. I think, at least in my case, it is “luck.” I often consider myself the luckiest guy in the world.

I was born to fine and loving parents and grew up in a home full of love and laughter and music in a wonderful town in a wonderful state in a wonderful country. Throughout my life I’ve been lifted up by good events and happenings and my marriage has been a blissful union with the most loving and precious of wives and great family and children. I’ve had the freedom to explore the things that interest me most, while my professional life always provided support for my family and my interests and left over plenty for savings. Now I find myself retired with an excellent pension, good government support, and savings that let me continue to live a life of interest and loving relationships. I know that many, if not most people in the world are not so lucky … or blessed.

Oh, I’m lucky all right. However, not everything has been perfect, and I’ve had losses. But the positive always seems to exceed any kind of negativity in my life. I don’t even feel a need to document my losses, even though some have been great, for I have memories that compensate for those that are no longer in my life or those that the Lord has called home. No, those tragedies are not what have shaped my life.

Anyone who has read more than two of my postings on Facebook know that my great delights are in science and music. Lots of other interests too, but those are the main ones.

I am a man of Faith and my beliefs are the rock that my life rests upon. I was just thinking this morning how lucky I was to get to baptize my son and also my wife. Me, myself, I was baptized by a friend with an audience of other friends. My Christian beliefs are part of what makes me who I am. They are integral to my family and our interactions. They are the strength of our lives that can survive even the greatest adversity, although there has been no need … at least so far.

I recently did some musical work for another friend who writes and directs plays and dances and other enjoyable works of art. It is such a pleasure to be involved in her artistic efforts. This time it is a dance recital with the theme of Jack and the Beanstalk as the Prodigal Son … an interesting and logical combination. I’ve completed the basic sound tracks and voice-overs, and we’re currently refining the music production and getting it all down on disk for the performance.

The story of the Prodigal Son is a very special story for me. Jesus tells it, so it is literally straight from the Lord’s mouth. It is a simple story, yet one that a person must read carefully. There are three characters. The father, the prodigal son, and the “good” son. There are so many lessons in the actions of all three, but the greatest lesson is the lesson of grace and of love.

These are lessons the world is much in need of, especially at this time of tragedy … while we await news of the next tragedy. How these events affect us and how they make us feel and, even more important, how they make us act is a test, a measure, an experiment to gauge our faith and our grace and our love. I just hope we don’t all fail the test … schoolteacher speaking here.

So, this is my dilemma. I have so many friends and family that it is very obvious from their Facebook comments, live lives that are focused on their faith. So why aren’t my comments always about my faith? Is my love of science and music greater than my faith in Jesus Christ? That’s a good question.

I suppose that I could be like the Apostle Paul, not after his conversion, but before. Remember, he was the greatest of the Pharisees. He lived the law to the best of his ability. But, after the conversion, after the blessing of grace, he lived a law of freedom: Freedom to live a life under grace. He knew that his behavior toward God did not affect God’s behavior toward him. That is the freedom of the Gospel. God’s grace transforms us. It is not something we earn, but something given as a gift. We don’t deserve it, but it is freely given anyway.

So, I choose to exercise my freedom in God’s love by pursuing the things that I love. I worship God in the creation and in music. That’s why I do what I do and that’s why I write what I write.

I may be the prodigal son … wandering in the wilderness, but I know I have a loving Father that will take me in with open arms. I don’t think he will hold a little attempt to understand the wonder of His creation against me. I could spend all day studying his word, as I know many do. That is a wonderful way to spend your time. Moreover, I consider my studies of the wonders of the universe to also be studying His word, just in a different medium.

God forgive me if I error. And I know He will. Thank God.

History of Science -- Part Ten: Particles vs. Waves

Recall that Newton had a troubling time classifying light during his research. He thought it had some wave properties, but he finally decided light was a particle that he called a “corpuscule.” He postulated that, since light followed his laws of motion in both reflection and refraction, it had to be a stream of particles. Others thought it was a wave, but Newton's reputation won out his view, at least in England. Finally Thomas Young proved conclusively that light was a wave with his double slit experiment. And then Maxwell showed that light was a complex electromagnetic wave that was a combination of an electric field and a magnetic field. That was the state of the science at the turn of the twentieth century.

But God is more subtle than even all these great minds had concluded. It took another scientist to finally discover the surprising truth. Another troubling result that is part of Quantum Mechanics. Planck had already calculated that these tiny, atom-sized particles that made up all matter followed rules unlike any we had experienced in our “macro” world. Now more mystery and confusion will be added to QM.

His parents worried about mental retardation when this young boy was slow in starting to talk. Later, though he became an avid and independent student of things that interested him, his distaste for the rote instruction of the Gymnasium (High School) led to his not doing well. Asked to suggest a profession that he might follow, the headmaster confidently predicted, “I doesn’t matter, he’ll never make a success of anything.”

His parents left Germany for Italy after the family electrochemical business failed. The new business in Italy fared little better and soon the young man was on his own. He took the entrance exam to the Zurich Polytechnical Institute but did not pass. He was finally admitted the next year. On graduation, he was unsuccessful in trying for a position as Privatdozent. He had the same luck in applying for a teaching job at the Gymnasium. For a while he supported himself as a tutor for students having tough with high school. Eventually, through a friend’s influence, he got a job in the Swiss patent office.

His duties as Technical Expert, Third Class, were to write summaries of patent applications for his superiors to use in deciding whether an idea warranted a patent. He enjoyed the work, which did not take his full time. Keeping an eye on the door in case a supervisor came in, he worked on his own projects.

Initially, he continued on the subject of his doctoral thesis, the statistics of atoms bouncing around in a liquid. This work soon became the best evidence for the atomic nature of matter, something still debated at that time. He concluded that the apparent random movement of tiny dust motes suspended in water was caused by the microscopic jostling of individual atoms. This is called Brownian Motion. He was the first to understand the cause.

Then he was struck by a mathematical similarity between the equation for the motion of atoms and Planck’s radiation law. He wondered: Might light be not only mathematically like atoms, but also physically like atoms?

If so, might light, like matter, come in compact lumps? Perhaps the pulses of light energy emitted in one of Planck’s quantum jumps did not expand in all directions as Planck assumed. Could the energy instead be confined to a small region? Might there be atoms of light as well as atoms of matter?

He speculated that light is a stream of compact lumps, “photons” (a term that came later). Each photon would have an energy equal to Planck’s quantum (Planck’s constant times its frequency). Photons would be created when electrons emit light. Photons would disappear when light is absorbed.

Seeking evidence that his speculation might be right, he looked for something that would display a granular aspect to light. It was not hard to find. The “photoelectric effect” had been known for almost twenty years. Light shining on a metal could cause electrons to pop out.

The situation was messy. Unlike thermal radiation, where a universal rule held for all materials, the photoelectric effect for each substance was different. Moreover, the data was inaccurate and not particularly reproducible.

But never mind the poor data. Spread out light waves shouldn’t kick electrons out of a metal at all. Electrons are too tightly bound. While electrons are free to move about within a metal, they can’t readily escape it. We can “boil” electrons out of a metal, but it takes a very high temperature. We can pull electrons out of a metal, but it takes a very large electric field. Nevertheless, dim light, corresponding to an extremely weak electric field, still ejects electrons. The dimmer the light, the fewer the electrons. But no matter how dim the light, some electrons are always ejected.

The photoelectric effect was just what the twenty-five year old scientist needed. Planck’s radiation law implied that light came in packets, quanta, whose energy was larger for higher frequency light. If the quanta were actually compact lumps, all the energy of each photon could be concentrated on a single electron. A single electron absorbing a whole photon would gain a whole quantum of energy.

Light, especially high-frequency light with its high-energy photons, could then give electrons enough energy to jump out of the metal. The higher the energy of the photon, the higher the energy of the ejected electron. For light below a certain frequency, its photons would have insufficient energy to remove an electron from the metal, and no electrons would be ejected.

In 1905, the young scientist wrote, “According to the presently proposed assumption the energy in a beam of light emanating from a point source is not distributed continuously over larger and larger volumes of space, but consists of a finite number of energy quanta, localized at points of space which move without subdividing and which are absorbed and emitted only as units.”

This scientist believed what Max Planck did not. He believed in the quantum theory which all the others had ignored.

Assuming that light comes as a stream of photons and that a single electron absorbs all the energy of a photon, he used the conservation of energy of the ejected electrons. If you plot the energy-frequency of ejected electrons it shows that photons with energy less than the binding energy of the metal does not kick any electrons out. That explains the photoelectric effect being different for different metals. He hypothesized it was tied to the electron binding energy.

A striking aspect of his photon hypothesis is that the slope of the straight line in his graph is exactly Planck’s constant, "ℎ." Until this time, Planck’s constant was just a number needed to fit Planck’s formula to the observed thermal radiation. It appeared nowhere else in physics. Before this young scientist’s photon hypothesis, there was no reason to think the ejection of electrons by light had anything at all to do with the radiation emitted by hot bodies. This slope of the graph was the first indication that the quantum was universal.

Ten years after this work on the photoelectric effect, the American physicist Robert Millikan found that his formula in every case predicted “exactly the observed results.” Through careful experiment the quality of the photoelectric effect data was finally improved. Nevertheless, Millikan called the photon hypothesis leading to that formula “wholly untenable” and called the young scientist's suggestion that light came as compact particles “reckless.”

Millikan was not alone. The physics community received the photon postulate “with disbelief and skepticism bordering on derision.” Nevertheless, eight years after proposing the photon, the young scientist had gained a considerable reputation as a theoretical physicist for many other achievements and was nominated for membership in the Prussian Academy of Science. Planck, in his letter supporting that nomination, felt he had to defend the young scientist. “[T]hat he may sometimes have missed the target in his speculations, as, for example, in his hypothesis of light quanta, cannot really be held too much against him …” Remember, even Planck didn’t believe in quanta, although he had first thought of it.

Ultimately, in 1922, this scientist was awarded the Nobel Prize for his analysis of the photoelectric effect, yet the citation avoided explicit mention of the then seventeen-year-old idea, but still unaccepted photon. A biographer later wrote, “From 1905 to 1923, he was a man apart in being the only one, or almost the only one, to take the light-quantum theory seriously.”

Though the reaction of the physics community to photons was, in a word, rejection, they were not just being pig-headed. Light was proven to be a spread-out wave. Light displayed interference. A stream of discrete particles could not do that.

Recall my description in a previous chapter of the History of Science of Young’s experiment with the double slit. Light coming through a single narrow slit illuminates a screen more or less uniformly, displaying the spreading nature of waves. Once a second slit is added a pattern of dark bands appears whose spacing depends on the spacing of the two slits. At those dark places, wave crests from one slit arrive together with wave troughs from the second slit. Waves from one slit thus cancel waves from the other. Interference demonstrates that light is a wave. There was no other possible conclusion.

Nevertheless, the now Nobel Prize winning physicist held that the photoelectric effect showed light to be a stream of photons — tiny compact bullets. But how could tiny bullets produce the interference patterns seen with light?

One might suppose that the tiny bullets might bounce off each other and stack up non-uniformly making the bands that were assumed to be an interference pattern, but that loophole was quickly closed by careful experiments that sent one photon at a time through the slits. This had to be repeated hundreds of times, but the ultimate effect was the build up of an interference pattern.

A great mystery: Choosing to demonstrate interference, something explicable only in terms of waves, you could prove light to be a widely spread-out wave. However, by choosing a photoelectric demonstration, where a single electron absorbed a whole light quantum, you could prove light to be a stream of tiny compact objects. There seems to be an inconsistency. It appeared that light was playing with the experimenters and would act like a wave if tested as a wave and act like particles if tested as particles. But it has to be one or the other. Right?

Though the paradoxical nature of light disturbed the young scientist, he clung to his photon hypothesis. He declared that a mystery existed in Nature and that we must confront it. He did not pretend to resolve the problem.

And we do not pretend to resolve it now. The mystery is still with us a hundred years later. The implications of our being able to choose to prove either of two contradictory things extend beyond physics. It’s the quantum enigma. We now accept this dual nature of light, even though we still don’t understand it. Remember, we use experimental results to demonstrate the truth of theories. In this case, the various experiments seem to contradict each other, and we’re left with no choice but to accept the dual nature. Light manifests itself both as a wave and as a particle. This dual nature of light is disturbing, but — as the magician said — you ain't seen nothin' yet.

In 1906, the young scientist I’ve been talking about had discovered photons, firmly established the atomic nature of matter in his work on Brownian Motion, and formulated the theory of Relativity. Yes, the young man’s name was Albert Einstein. In that year he was promoted by the Swiss patent office to Technical Expert, Second Class.

The History of Science -- Part Eleven

History of Science -- Part Nine: Max Planck

As the nineteenth century ended, the search for Nature’s basic laws seemed close to its goal. There was a sense of a task accomplished. Physics presented an orderly scene that fit the proper Victorian mood of the day.

Objects both on Earth and in the Heavens behaved in accord with Newton’s laws. So, presumably, did atoms. The nature of atoms was unclear. But to most scientists the rest of the job of describing the universe seemed a filling in of the details of the giant machine as the British scientist James Jeans pointed out.

What we now call Classical Physics explains the world quite well; it’s just the details it can’t handle. Ironically, Quantum Physics handles the details perfectly; it’s just the world it can’t explain. (More later on that point.)

Quantum physics does not replace classical physics the way the sun-centered solar system replaced the earlier view with the Earth as the cosmic center. Rather, quantum physics encompasses classical physics as a special case. Classical physics is usually an extremely good approximation for behavior of objects that are larger than atoms. But, you dig deeply enough into any natural phenomenon — physical, chemical, biological, or cosmological — you hit quantum mechanics.

Quantum theory has been subject to challenging tests for almost 100 years. No prediction by the theory has ever been shown to be wrong. It is the most battle-tested theory in all of science. Nevertheless, if you take the implications of the theory seriously, it is downright mind boggling. Niels Bohr, a founder of quantum theory, claimed that unless you’re shocked by quantum mechanics, you have not understood it.

On Friday, April 27, 1900, the British physicist Lord Kelvin gave a speech entitled "Nineteenth-Century Clouds over the Dynamical Theory of Heat and Light," which began:

The beauty and clearness of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds.

Kelvin went on to explain that the "clouds" were two unexplained phenomena, which he portrayed as the final couple of holes that needed to be filled in before having a complete understanding of the thermodynamic and energy properties of the universe, explained in classical terms of the motion of particles.

Note that, even though Lord Kelvin identified these two issues of physics, he strongly believed the main role of physics in that day was to just measure known quantities to a great degree of precision, out to many decimal places of accuracy. He must have assumed the two holes would easily be filled in using the basic physics known at that time.

The "clouds" to which Kelvin was referring were:

1. The inability to detect the luminous ether, specifically the failure of the Michelson-Morley experiment.
2. The black body radiation effect known as the ultraviolet catastrophe.

The last chapter of this history described how Einstein’s theory of Relativity addressed the first cloud in a most unexpected way.

The second “cloud,” the so-called “ultraviolet catastrophe” started a chain of discoveries and propositions that revolutionized physics in a way at least equal to Einstein’s theories. In the final week of the nineteenth century, Max Plank suggested something outrageous — that the most fundamental laws of physics were violated. This was the first hint of the quantum revolution, that the worldview we now call “classical” had to be abandoned.

Max Planck, son of a distinguished professor of law, was careful, proper, and reserved. His clothes were dark and his shirts stiffly starched. Raised in the strict Prussian tradition, Planck respected authority, both in society and in science. Not only should people rigorously obey the laws, so should physical matter. Not your typical revolutionary.

In 1875, when young Max Planck announced his interest in physics, the chairman of his physics department suggested he study something more exciting. Physics, he said, was just about complete: “All the important discovers have already been made.” (Notice that this opinion of the completion of science was very prevalent in the late 1800s.)

Undeterred, Planck completed his studies in physics and plugged away for years as a Privatdozent, an apprentice professor, receiving only the small fees paid by students attending his lectures.

Planck chose to work in the most properly lawful area of physics, thermodynamics, the study of heat and its interaction with other forms of energy. His solid but unspectacular work eventually won him a professorship. His father’s influence is said to have helped.

A nagging unexplained phenomenon in thermodynamics was thermal radiation: the spectrum, the colors, of the light given off by hot bodies. (Problem #2 of Kelvin’s two “clouds.”) Planck set about to solve it.

What’s the problem? That a hot poker should glow seems obvious. Although at the turn of the century the nature of atoms, even the existence of atoms, was unclear, electrons had just been discovered. Presumably these little charged particles jiggled in a hot body and therefore emitted electromagnetic radiation. This light seemed important to understand a fundamental aspect of Nature because it was the same no matter what material it came from.

The radiation one observed seemed reasonable. As a piece of iron gets hotter, its electrons should shake harder and, presumably, at a higher rate, meaning at a higher frequency. Therefore, the hotter the metal, the brighter and higher the frequency of the glow. As it gets hotter, its color goes from the invisible infrared, to a visible red, to orange, and eventually the metal becomes white hot as the emitted light covers the entire visible frequency range.

Since our eyes can’t see frequencies above the violet, superhot objects, which emit mostly in the ultraviolet, appear bluish. Materials on Earth vaporized before they get hot enough to glow blue, but we can look at hot blue stars. Even cool objects “glow,” though weakly and at low frequencies. Bring you palm close to your cheek and feel the warmth from the infrared light your hand emits. The sky shines down on us with invisible microwave radiation left over from the flash of the Big Bang.

In this figure that I’ve sketched the actual intensity of radiation from the Earth’s Sun and its 6,000° C surface at different frequencies, which are labeled as colors. (Colors are different frequencies of light.) An object hotter than our Sun emits more light at all frequencies, and its maximum intensity is at a higher frequency. But the intensity always drops at very high frequencies.

The dashed line is the problem — it is the intensity calculated with the laws of physics accepted in 1900. It worked well in the infrared. But at higher frequencies, classical physics not only gave a wrong answer, it gave a ridiculous answer. It predicted a forever increasing light intensity at frequencies beyond the ultraviolet.

Were this true, every object would instantaneously lose its heat by radiating a burst of energy at frequencies beyond ultraviolet. This embarrassing deduction was derided as the “ultraviolet catastrophe.” But no one could say where the seemingly sound reasoning of Classical Physics went wrong.

Max Planck struggled for years to derive a theory that fit the experimental data. In frustration, he decided to work the problem backward. He would first try to guess a formula that agreed with the data and then, with that as a hint, try to develop the proper theory. In a single evening, studying the data others had given him, he found a fairly simple formula that worked perfectly.

(What a wonderful example of one way we do science.)

If Planck put in the temperature of the body, his formula gave the correct radiation intensity at every frequency. His formula needed a “fudge factor” to make it fit the data, a number he called “ℎ.” We now call it “Planck’s constant” and recognize it as a fundamental constant of Nature, like the speed of light.

With his formula as a hint, Planck sought to explain thermal radiation in terms of the fundamental principles of physics. In the most straightforward models, an electron, though bound to its parent atom, would start vibrating if it were bumped by a jiggling neighboring atom in a hot metal. This little charged particle would then gradually lose its energy by emitting light. The following sketch is a plot of such an energy loss. In a similar fashion, a pendulum bob on a string, or a child on a swing, given a shove, would continuously lose energy to air resistance and friction.

However, every description of the electron radiating energy according to the physics of the day shown in this graph led to the same crazy prediction, the ultraviolet catastrophe. After a long struggle, Planck ventured an assumption that absolutely violated the universally accepted principles of classical physics. At first, he didn’t take it seriously, He later called it an “act of desperation.”

Max Planck assumed an electron could radiate energy only in chunks, in “quanta” (the plural of quantum). Moreover, each quantum would have an energy equal to the number ℎ in his formula times the frequency of vibration of the electron.

Behaving this way, an electron would vibrate for a while at constant energy. That is, this electric charge would vibrate without losing energy to radiation. Then, randomly, and without cause, without an impressed force, it would suddenly lose a quantum of energy, radiating it as a pulse of light. (Electrons would also gain their energy from the hot atoms by such “quantum jumps.”)

In the following sketch I plot an example of such energy loss in sudden steps. The dashed line repeats the classically predicted, gradual energy loss.

Planck was allowing the electrons to violate both the laws of electromagnetism and Newton’s universal equation of motion. Only by this wild assumption could he get the formula he had guessed, the formula that correctly describe thermal radiation.

If this quantum-jumping behavior is indeed a law of Nature, it should apply to everything. Why, then, do we see the things around us behaving smoothly? Why don’t we see children on swings suddenly change their swinging motion in quantum jumps? It’s a question of numbers, and ℎ is an extremely small number.

Not only is ℎ small (ℎ = 6.626 times 10^-34 joule-seconds), but since the frequency of a child moving back and forth on a swing is much lower than the frequency at which an electron vibrates, the quantum steps of energy (ℎ times frequency) are vastly smaller for the child. And, of course, the total energy of a swinging child is vastly larger than that of an electron. Therefore, the number of quanta involved in the child’s motion is vastly, vastly greater than the number involved in the motion of the electron. A quantum jump, the change in energy by a single quantum, is thus far too small to be seen for the child on a swing.

But back in Planck’s day the reaction to the solution he proposed for the thermal radiation problem was not very good, even though his formula fit the experimental data well. But his explanation seemed more confounding than the problem it presumed to solve. Planck’s theory seemed silly. No one laughed, at least no in public — Herr Professor Planck was too important a man for that. His quantum-jumping suggestion was simply ignored.

Physicist were not about to challenge the fundamental laws of mechanics and electromagnetism. Even if the classical laws gave a ridiculous prediction for the light emitted by glowing bodies, these basic principles seemed to work everyplace else. And they made sense. Planck’s colleagues felt a reasonable solution would eventually be found. Planck himself agreed and promised to seek one. The quantum revolution arrived with an apology, and almost unnoticed.

In later years, Planck even came to fear the negative social consequences of quantum mechanics. Freeing the fundamental constituents of matter from the rules of proper behavior might seem to free people from responsibility and duty. The reluctant revolutionary would have liked to cancel the revolution he sparked.

But Nature is not to be ignored and experimental results are the deciding factor, not social comfort. Now enters a familiar character from a previous episode. Tune in next time to learn the rest of the story.

The History of Science -- Part Ten

History of Science -- Part Eight: Relativity

I introduced Lord Kelvin in the last chapter of this series so that I could use a quotation attributed to him. There probably was no scientists since Newton who was held is such regard, had such a scientific reputation, or was held in such high esteem by the general public and the government than Lord Kelvin at the end of the nineteenth century.

At that point it seemed that science had completely wrapped up the issue of describing Nature and discovering all her secrets. With a complete set of the rules of motion based on Newton’s discoveries and improved and expanded upon, with a complete understanding of heat and energy, and with Maxwell’s equations describing the electromagnetic wave and the application via telegraph and wireless radio, the dawn of the twentieth century was to be a bright dawn indeed.

Although there is some conflict among historians on whether Lord Kelvin said this or not, this quotation is often used in popular books on science to make the point of just how wrong he could be. Put this quote along side Bill Gate’s, “No one will need more than 640 K of memory” that he stated at the advent of the IBM PC in 1982.

To be historically accurate, it appears it was the Albert Michelson, the Nobel Prize winning physicists of the Michelson-Morley experiments described below who is the source of the quotation. He quoted Lord Kelvin, perhaps inaccurately. But this statement certainly indicates the mood of the Victorian era in the late 1800's.

Michelson said that, in physics, there were no more fundamental discoveries to be made. Quoting Lord Kelvin, he continued, “An eminent physicist remarked that the future truths of physical science are to be looked for in the sixth place of decimals.” In other words, all the major discoveries had been done, and now it was just the work of science to add a few more decimal points to what was already known.

Some scientists expressed sadness for the next generation of physists because they thought all the fundamental work had been done and there were no more great discoveries to be made.

Yes, that is a statement worth posting in the “could not be more wrong — ever!” Hall of Shame. Odd that one of the scientists so intimately involved with the very experiment that would be a trigger to the thoughts of another young scientist just starting his career would make such a claim. But then it did fit well with the Victorian era of science with all its formality of class and thought. But there were several warning signs in the body of knowledge at the start of the next century that should have cautioned these learned men to not be so cocksure of what was coming.

When light became accepted as being a wave, it was assumed that something had to be waving. Electric and magnetic fields would be distortions in this waving medium. Since material bodies moved through it without resistance, it was ethereal and was called the “luminiferous aether” or just “ether.” It presumably pervaded the universe since we receive light from the starts. Motion with respect to this ether would define an absolute velocity, something not meaningful without ether as a stationary “reference point” for the universe.

In the 1890’s Albert Michelson and Edward Morley set out to determine how fast our planet was moving through the universal ether. A boat moving in the same directions as the waves sees the waves pass more slowly than when the boat moves in the direction opposite the waves. From the difference in these two wave speeds, one can determine how fast the boat is moving in the water. This is essentially the experiment Michelson and Morley did with light waves.

They measured the speed of light, very accurately, from a distant star at two times of the year six months apart. Therefore one measurement was at a point where the Earth in its orbit was speeding toward the star at a rate of nearly 30 km per second or about 19 miles per second or 68,000 mph, and the second measurement was when the Earth was speeding away at the same velocity.

To their surprise, the Earth seemed not to be moving at all. They measured the speed of light to be the same in all directions. Ingenious attempts to untangle this result with electromagnetic theory failed.

Enter Albert Einstein. He postulated the observed fact that the speed of light is the same no matter how fast the observer moves. He took it as a new law of Nature. Two observers, though moving at different speeds, would each measure the same light beam to be passing them at the same speed. The speed of light in a vacuum is therefore a universal constant and it is called “c.”

In that case, an absolute velocity could not be measured. Any observers, whatever their constant velocity, could consider themselves at rest. There is no absolute velocity; only relative velocities are meaningful. This became the theory of “Relativity.”

His initial theory is now called the “Special Theory of Relativity,” because ten years later Einstein expanded this theory into the “General Theory of Relativity,” which included gravity and space.

Relativity is a theory of the structure of space-time. It was introduced in Einstein's 1905 paper "On the Electrodynamics of Moving Bodies." Special relativity is based on two postulates that are contradictory in Classical Physics:

1. The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity).
2. The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light.

The resultant theory copes with experiment better than classical mechanics, e.g. in the Michelson–Morley experiment that supports postulate 2, but also has many surprising consequences. Some of these are:

• Relativity of simultaneity: Two events, simultaneous for one observer, may not be simultaneous for another observer if the observers are in relative motion.
• Time dilation: Moving clocks are measured to tick more slowly than an observer's "stationary" clock.
• Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer.
• Mass–energy equivalence: E = mc², energy and mass are equivalent and transmutable.
• Maximum speed is finite: No physical object, message or field line can travel faster than the speed of light in a vacuum.

The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. Basically, Einstein proved that Newton’s equations were wrong. Or, at least, they required a correction. We now recognize Newton’s laws as approximations. They work well under normal circumstances, but must be adjusted for situations that involve high velocity or high mass. (The latter a result of the General Theory of Relativity.)

In physics, the Lorentz transformation (or transformations) is named after the Dutch physicist Hendrik Lorentz. It was the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism. The Lorentz transformation is part of special relativity, but was derived well before the theory was published by Einstein.

The Lorentz transformation is given mathematically by this formula:

Where v is the velocity of the object and c is the speed of light. As long as v is very small relative to c, this reduces to very nearly one and can be ignored. But, at high velocities, it must be taken into account.

It was already known that Mercury didn’t exactly match in its orbit the mechanics of Newton. It was close, but precise measurement showed disagreement with theory. Some supposed it was due to another planet closer to the Sun than Mercury. That supposed planet even got a name: Vulcan. It was searched for, but in vain. Upon applying Einstein’s corrections to Newton’s laws, scientists found a match. As the innermost planet, Mercury traveled the fastest in its orbit, and, therefore, needed the correction more than the other planets. We now adjust all our measurements of planets and stars using the special and general theories of Relativity.

With just simple algebra, Einstein deduced further testable predictions from his postulate. The prediction most important is that no signal, no information, can travel faster than the speed of light. Another prediction is that mass is a form of energy and can be converted into other forms of energy. It’s summarized as E = mc². Both of these predictions have been confirmed, sometimes very dramatically.

The prediction that is hardest to believe is that the passage of time is relative: Time passes more slowly for a fast-moving object than it does for something at rest. This too has been proven multiple times with experiments involving the life of particles created when cosmic rays strike the upper atmosphere to very accurate clocks flown around the world. This isn’t fiction. It is fact.

Although the seeds of the special theory were widely planted and growing in many gardens, Einstein's follow up, the General Theory of Relativity, was a complete surprise to everyone. This greater, in-depth theory by a man who was likely the greatest thinker of the twentieth century caught all of physics off guard.

The special theory only worked with constant velocity. Einstein began to ponder acceleration, a changing velocity, Newton's second law, and the cause of gravity, Newton's other famous discovery.

He developed what is called "General Relativity." General relativity is a geometric theory of gravitation published by Albert Einstein in 1916 and the current description of gravitation in modern physics. General Relativity generalizes Special Relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or space-time. In particular, the curvature of space-time is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.

Some predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational redshift of light, and the gravitational time delay. This theory solves an age old question about the difference between the acceleration of gravity and the force of acceleration on a body. The issue was how one could tell the difference between being accelerated in an elevator in free space, causing "weight" vs. a stable box on the surface of the Earth where the notion of "weight" comes from gravity. Einstein's simple answer is that there is no measurable difference. Again a result he developed from his Gedankenexperiment or "though experiment." However, Einstein's conclusions have been proven over and over again by experiment.

The predictions of general relativity have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data. However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity. This attempt, sometimes called "GUT" or Great Unified Theory was a focus of Einstein's for the rest of his life, but he did not accomplish it. It is still a search going on in modern physics and the solution has yet to be discovered.

Unlike Lord Kelvin at the dawn of the twentieth century, scientists today have many challenging problems to work on. We know we're not done yet.

The general theory is the most important tool used today in Cosmology, the study of the origin and eventual fate of the universe. Out of this theory comes predictions of black holes and other astrological objects which have since been discovered and studied.

Yet this wonderful, and powerful, and thought provoking, and somewhat unbelievable new discovery and way of looking at physics was proven by every experiment devised to test its authenticity. Einstein's contemporaries did not all accept his new theories at once. However, the theory of relativity is now considered as a cornerstone of modern physics.

Although it was brilliant thinking by Einstein that established these principles, the special theory of relativity had many other contributors and discoverers. The history of special relativity consists of many theoretical results and empirical findings obtained by Albert Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Einstein, and subsequent work of Max Planck, Hermann Minkowski and others. Minkowski, particularly, improved on the simple math of Einstein and put the space-time continuum on solid mathematical and geometrical grounds. Einstein later adopted the principles of Minkowski in his work on the general theory.

Einstein arrived at his conclusions through logical reasoning and “thought experiments” that would have made Aristotle proud. However, it was the experimental evidence that eventually convinced the scientific community of the theories relevance. In 1905 Einstein had no reputation with which to make an appeal as an authority. His brilliant work was accepted because, as contrary to most views of the universe, his view matched the experimental data and every prediction of his theory proved true.

But relativity wasn’t the only unimaginable idea of science to find root at the turn of the Twentieth Century. Basically unrelated was another new concept now called Quantum Physics. Einstein had a big hand in that too, but it is really separate from Relativity and much of Quantum Mechanics was also an approximation in need of correction for Relativity. That is our next chapter.

The History of Science -- Part Nine

History of Science -- Part Seven: Energy

Energy is a concept pervading physics, chemistry, biology, and geology, as well as technology and economics. Wars have been fought over the chemical energy stored in oil. The crucial aspect of energy is that, though its form may change, the total amount of energy stays constant. That fact, the “conservation of energy,” is the first law of thermodynamics. But what is energy? I’ll define it by pointing to energy in several of its different forms.

I struggled a bit with whose picture I should attach to this article. I finally decided on Lord Kelvin. There were many scientists during the nineteenth century that contributed to the concepts of energy and the conservation of energy, but Lord Kelvin is both the most distinguished and I want to prepare for the use of a quotation of his to introduce the next chapter in the story. That’s the chapter after this one. But first, I’ll introduce Lord Kelvin more thoroughly, and then get back to this chapter on Energy.

William Thomson, 1st Baron of Kelvin, holder of the Order of Merit, Royal Victorian Order (knight GCVO), Her Majesty's Most Honorable Privy Council, President of the Royal Society, and member of the Royal Society of Edinburgh, was born in 1824 and died in 1907. He was a Belfast-born, British mathematical physicist and engineer.

At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging discipline of physics in its modern form. He worked closely with mathematics professor Hugh Blackburn in his work. He also had a career as an electric telegraph engineer and inventor, which propelled him into the public eye and ensured his wealth, fame, and honor.

For his work on the transatlantic telegraph project he was knighted by Queen Victoria, becoming Sir William Thomson or Lord Kelvin. He had extensive maritime interests and was most noted for his work on the mariner's compass, which had previously been limited in reliability.

Lord Kelvin is widely known for determining the correct value of absolute zero as approximately −273.15 Celsius. A lower limit to temperature was known prior to Lord Kelvin, as shown in "Reflections on the Motive Power of Heat", Sadi Carnot, written before Lord Kelvin's birth in 1824. "Reflections" used −267 as the absolute zero temperature. Absolute temperatures are stated in units of kelvin in his honor. (Note that the “K” is shown without the term or symbol for degree in modern usage.)

Getting back to energy, first of all, there is energy in motion. The larger the mass and the speed of a moving object, the greater its “kinetic energy.” Energy due to the motion of objects is kinetic energy. The adjective "kinetic" has its roots in the Greek word κίνηση (kinesis) meaning "motion" — the same root as in the word cinema (referring to motion pictures). In Classical Physics the term “Momentum” refers to straight line motion precisely termed linear momentum or translational momentum.

Recall that Newton’s second equation was F = ma, where both force and acceleration are vector quantities. Since momentum, symbol “p,” is the right side of the equation, this can be written as F = p, both vectors. That is actually the way Newton wrote the second law in Prinicipia.

Considering gravity, the farther a rock falls, the faster it goes and the greater its kinetic energy. A rock held at a certain height has the potential of gaining a certain speed. It has a gravitational “potential energy,” which is larger for a larger mass or a greater height. The sum of a rock’s kinetic and potential energy, its total energy, remains constant as the rock falls. This is an example of the conservation of energy.

Of course, after the rock hits the ground, it has zero kinetic energy and zero potential energy. As it contacts the ground, the energy of the rock itself was not conserved. But the total energy is conserved. On impact, the rock’s energy is given to random motion of the atoms of the ground and those of the rock. These atoms now jiggle about with greater agitation. The haphazard motion of these atoms is the microscopic description of thermal energy or “heat.” Where the rock hit the ground, the ground is warmer. The energy imparted to the jiggling atoms is just equal to the energy the rock lost on impact. To be more precise, some of the energy may be converted to sound which is vibration of atoms in the air and ground and we can hear that.

When giant space rocks hit the ground … we call those “meteors” … the energy conversion can melt the ground where it hits and create shockwaves, which are giant sound waves, that can knock over trees. But the total energy remains constant.

Although the total energy is conserved when the rock stops, the energy available for use decreases. The kinetic energy of falling rocks, or falling water, could, for example, be used to turn a wheel. But once the energy goes over to the random motion of atoms, it is unavailable to us except as thermal energy. Moreovoer, the second law of thermodynamics tells us that in any action some energy becomes unavailable. When we’re enjoined for environmental reasons to “conserve energy,” we’re being asked to conserve available energy.

The entire science of “Thermodynamics,” of which I’ve quoted two laws, is about getting useful work from energy and how some energy is always lost. That is why there can not be any “perpetual motion machines,” systems that run forever without the input of additional energy.

Quoting from Wikipedia:

The history of thermodynamics as a scientific discipline generally begins with Otto von Guericke who, in 1650, built and designed the world's first vacuum pump and demonstrated a vacuum using his Magdeburg hemispheres. Guericke was driven to make a vacuum in order to disprove Aristotle's long-held supposition that 'nature abhors a vacuum'. Shortly after Guericke, the physicist and chemist Robert Boyle had learned of Guericke's designs and, in 1656, in coordination with scientist Robert Hooke, built an air pump. Using this pump, Boyle and Hooke noticed a correlation between pressure, temperature, and volume. In time, Boyle's Law was formulated, stating that for a gas at constant temperature, its pressure and volume are inversely proportional. In 1679, based on these concepts, an associate of Boyle's named Denis Papin built a steam digester, which was a closed vessel with a tightly fitting lid that confined steam until a high pressure was generated.

Later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a piston and a cylinder engine. He did not, however, follow through with his design. Nevertheless, in 1697, based on Papin's designs, engineer Thomas Savery built the first engine, followed by Thomas Newcomen in 1712. Although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time.

The concepts of heat capacity and latent heat, which were necessary for development of thermodynamics, were developed by professor Joseph Black at the University of Glasgow, where James Watt worked as an instrument maker. Watt consulted with Black on tests of his steam engine, but it was Watt who conceived the idea of the external condenser, greatly raising the steam engine's efficiency. Drawing on all the previous work led Sadi Carnot, the "father of thermodynamics", to publish Reflections on the Motive Power of Fire (1824), a discourse on heat, power, energy and engine efficiency. The paper outlined the basic energetic relations between the Carnot engine, the Carnot cycle, and motive power. It marked the start of thermodynamics as a modern science.

The first thermodynamic textbook was written in 1859 by William Rankine, originally trained as a physicist and a civil and mechanical engineering professor at the University of Glasgow. The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily out of the works of William Rankine, Rudolf Clausius, and William Thomson (Lord Kelvin).

The foundations of statistical thermodynamics were set out by physicists such as James Clerk Maxwell, Ludwig Boltzmann, Max Planck, Rudolf Clausius and J. Willard Gibbs.

From 1873 to '76, the American mathematical physicist Josiah Willard Gibbs published a series of three papers, the most famous being "On the equilibrium of heterogeneous substances.” Gibbs showed how thermodynamic processes, including chemical reactions, could be graphically analyzed. By studying the energy, entropy, volume, chemical potential, temperature and pressure of the thermodynamic system, one can determine if a process would occur spontaneously. Chemical thermodynamics was further developed by Pierre Duhem, Gilbert N. Lewis, Merle Randall, and E. A. Guggenheim, who applied the mathematical methods of Gibbs.

Getting back to our falling rock, there is only one kind of kinetic energy, but there are many kinds of potential energy. The energy of that rock held at some height is gravitational potential energy. A compressed spring or stretched rubber band has elastic potential energy. The elastic energy of the spring can be converted to kinetic energy in projecting a rock upward.

When a positive and a negative electrical charge are held apart from each other, those charges have electrical potential energy (measured in volts). If released, they would fly toward each other with increasing speed and kinetic energy. In an atom, the electrons orbiting the nucleus have both kinetic and potential energy.

The chemical energy of a bottle of hydrogen and oxygen molecules is greater than the energy those molecules would have if they were bound together as water at the same temperature. Should a spark ignite that hydrogen-oxygen mixture, the greater energy would appear as kinetic energy of the resulting water molecules. The water vapor would therefore, be hot. The chemical energy stored in the hydrogen-oxygen mixture would have become thermal energy.

That is what gives us the heat and light of a campfire. The wood and other combustibles, mostly carbon, combine with the oxygen in the air and give off energy as heat and light. The resulting ash and carbon dioxide have a lower chemical potential energy than the original substances, and the loss of chemical energy is matched by the increase in thermal energy and light energy. But the total is conserved.

Nuclear energy is analogous to chemical energy, except that the forces involved between the protons and neutrons that make up the nucleus include the nuclear (strong and weak) forces as well as electrical forces. A uranium nucleus has a great total energy than do the fission products it breaks into. That greater energy becomes the kinetic energy of the fission products. That kinetic energy is thermal energy and can be used in a nuclear reactor to make steam to turn turbines that turn generators to produce electrical power. It can also be a bomb.

When light is emitted from a glowing hot body, energy goes to the electromagnetic radiation field, and the glowing body cools, unless it is supplied with additional energy. When a single atom emits light, it goes to a state of lower energy.

The law of conservation of energy, first formulated in the nineteenth century, is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time. For an isolated system, this law means that energy is localized and can change its location within the system, and that it can change form within the system, for instance chemical energy can become kinetic energy, but that it can be neither created nor destroyed.

The formula, then is a simple E = K + V, where E is the total energy of the system and K is the kinetic energy and V is the potential energy. We don’t use “P” for potential energy since P stands for “momentum.” (I know, why not use “M” for momentum … well m = mass.) I’m not sure where the “V” came from, but I suspect it comes from “Volt,” which is the measure of electric potential or “voltage.”

The conservation of energy is a common feature in many physical theories. From a mathematical point of view it is understood as a consequence of Noether's theorem, which states every continuous symmetry of a physical theory has an associated conserved quantity; if the theory's symmetry is time invariance then the conserved quantity is called "energy". The energy conservation law is a consequence of the shift symmetry of time; energy conservation is implied by the empirical fact that the laws of physics do not change with time itself. Philosophically this can be stated as "nothing depends on time per se." In other words, if the physical system is invariant under the continuous symmetry of time translation (that is fancy talk for “passing time”) then its energy is conserved.

Conversely, systems which are not invariant under shifts in time (an example, systems with time dependent potential energy) do not exhibit conservation of energy — unless we consider them to exchange energy with another, external system so that the theory of the enlarged system becomes time invariant again. Since any time-varying system can be embedded within a larger time-invariant system, conservation can always be recovered by a suitable re-definition of what energy is.

For example, we might assume that the rock lost its potential and kinetic energy when it hits the ground and energy is not conserved. But if we add the ground and the air around the rock to our system, we see the energy was translated as heat and the total energy was conserved.

The concept of time invariance implies that the rules of physics are the same now as they were yesterday, last week, and last year. We know that the rules of science have not changed with time because we observe the light from stars so distant that they left their home billions of years ago and that light demonstrates the laws of physics on the suns that were the source are the same as our sun today. So we don’t just take it on faith that the laws of physics don’t change with time. We know from experiment and observation.

Therefore these rules are symmetrical in time and therefore, by Noether's theorem, energy is conserved.

How many forms of energy are there? That depends on how you count. Chemical energy, for example, is ultimately electrical energy, though it is usually convenient to classify it separately. There may be forms of energy we don’t yet know about. Just a few years ago it was discovered that the expansion of the universe is not slowing down, as was generally believed — it’s accelerating. The vast amount of energy causing this acceleration has a name, “dark energy,” but there is still more mystery about it than understanding.

Thermodynamics and a true understanding of the properties of heat was a major accomplishment of the nineteenth century. These conservation of energy laws led to alternative methods for solving problems in the motion of object, something now called “Classical Mechanics.” These new methods provided alternatives to using Newton’s laws of motion and not only gave better methods for calculation in some circumstances, but also increased the understanding of just how these mechanical processes worked … a better understanding of Nature. All this work was based on the foundation in mathematics from the eighteenth century. It was during the one hundred years after Newton and Leibniz started the revolution that many minds and many hands added to the structure and power of this mathematical method for dealing with change.

Many of the formulas and theorems from that century, along with the names of the discoverers were transformed into a better understanding of physics via application of the conservation of energy principle. This all leads to a culmination at the very end of the nineteenth century with hints of the changes about to come in such work as Maxwell’s. So the stage has been set and the players are in the wings, ready to triumphantly enter and start this new revolution that we are still expanding today.

There are actually two, twin ideas that are about to hatch from the egg produced by the two hundred years of work post Newton. These ideas are separate yet intertwined, both in the result and the discoverers. But they are separate ideas and some times one idea is only an approximation until the other idea can be applied. We’re about to enter the modern world of physics … a world much changed by those discoveries … the world of today … a world of technology … a world that we translate from the world of “steam” to the world of “STEM” (or, as I prefer, STEAMD).

The History of Science -- Part Eight