Don’t Go Breaking Her Heart: Breach of Promise Suits

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TTtCH tour bannerI am happy to welcome Maria Grace back to Outtakes as she introduces her latest release, The Trouble to Check Her, where Lydia Bennet must face the consequences of running off with Mr. Wickham. Here, Grace tells us how a jilted bride could make her former fiancé pay, literally.—Kim

By Maria Grace

Maria Grace 2014Even after the decline of arranged marriage after 1780, marriage still remained largely a business transaction. Even the promise to marry was considered an enforceable contract, with a breach of promise suit a possible consequence of a broken engagement.

History

As early as the 15th century, English ecclesiastical courts equated a promise to marry with a legal marriage. By the 1600s, this became part of common law; a contract claim one party could make upon another in civil court suits. (And you thought this was just the stuff of modern daytime television!)

To succeed in such a suit, the plaintiff, usually a woman, had to prove a promise to marry (or in some cases, the clear intention to offer such a promise), that the defendant breached the promise (or the implied promise to promise), and that the plaintiff suffered injury due to the broken promise (or failure to make the implied promise). Don’t think about it too hard, it’ll make your head hurt.

Breach of Promise Claims

A breach of promise suit required a valid betrothal. Promises to marry when both parties were below the age of consent were not valid. Similarly, promises to marry made when one was already married (as in I’ll marry you if/when my current spouse dies—how romantic) or between those who could not legally marry were not enforceable.

If significant and material facts were discovered that could have influenced the agreement, then betrothal could be dissolved without penalty. So issues like misrepresentation of one’s financial state, character, or mental or physical capacity presented valid reasons to end an engagement.

If a betrothal was valid, a breach of promise claim could be presented in court.

Painting of jilted bride

Eduard Swoboda’s 19th century painting of a bride jilted at the altar

Reasoning

Why were such claims filed when it seems like it would be far easier, less painful, and less embarrassing for a couple to simply go their separate ways? When a promise to marry was broken, the rejected party, usually female, suffered both social and economic losses.

Socially, an engaged couple was expected to act like an engaged couple. Though it seems unfair in modern eyes, the acceptable behaviors she may have shared with her betrothed, would leave her reputation damaged if he left her. Moreover, though premarital sex was officially frowned upon, it was known that a woman was much more likely to give up her virginity under a promise to marry. But if that promise was not kept, her future search for a husband would be significantly hampered for having broken the code of maidenly modesty.

The loss of reputation translated to serious economic losses, since middle and upper class women did not work outside the home and required a household supported by a husband’s wealth. A woman with a tarnished reputation was unlikely to marry well.

Illustration of breach of contract suit

An 1823 illustration of a jilted bride seeking redress from her former fiancé

Damage Awards

Perhaps as a result, a woman was far more likely to win a breach of promise claim than lose one. Middle-class ladies were generally able to obtained larger damage awards than working women, though cases varied greatly. About half of women winning damages obtained £50-£200. (For reference, middle class family of four could live comfortably on £250 a year.)

While these awards could indeed offer assistance to wronged plaintiffs, the system was also ripe for abuse. Jurors were often unduly sympathetic toward jilted women, especially when they were attractive or portrayed as particularly virtuous. Damage awards could easily be swayed by such sympathies, making false claims very tempting. All this sounds so much like modern reality television, doesn’t it?

The more things change, the more they stay the same!

Images in the public domain, via Wikimedia Commons.

About The Trouble to Check Her

Lydia Bennet faces the music…

Running off with Mr. Wickham was a great joke—until everything turned arsey-varsey.  That spoilsport Mr. Darcy caught them and packed Lydia off to a hideous boarding school for girls who had lost their virtue.

It would improve her character, he said.

Ridiculous, she said.

Mrs. Drummond, the school’s headmistress, has shocking expectations for the girls. They must share rooms, do chores, attend lessons, and engage in charitable work, no matter how well born they might be. She even forces them to wear mobcaps! Refusal could lead to finding themselves at the receiving end of Mrs. Drummond’s cane—if they were lucky. The unlucky ones could be dismissed and found a position … as a menial servant.

Everything and everyone at the school is uniformly horrid. Lydia hates them all, except possibly the music master, Mr. Amberson, who seems to have the oddest ideas about her. He might just understand her better than she understands herself.

Can she find a way to live up to his strange expectations, or will she spend the rest of her life as a scullery maid?

The Trouble to Check Her is available on Amazon, Barnes and Noble, and Kobo.

About Maria Grace

Though Maria Grace has been writing fiction since she was 10 years old, those early efforts happily reside in a file drawer and are unlikely to see the light of day again, for which many are grateful. After penning five file-drawer novels in high school, she took a break from writing to pursue college and earn her doctorate in educational psychology. After 16 years of university teaching, she returned to her first love, fiction writing.

She has one husband, two graduate degrees and two black belts, three sons, four undergraduate majors, five nieces, six new novels in the works, attended seven period balls, sewn eight Regency era costumes, shared her life with nine cats through the years, and published her 10th book last year.

She can be contacted at author.MariaGrace@gmail.com. You can also connect with her at:

I Use Real Research to Create Believable Lies

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When I first started writing the post for Unusual Historicals’ theme “My Characters Lived in…” I got nervous. Who am I to write a short blog post about Carolingian Francia, a time period that has been the subject of entire books?

Heck, I have some of those books in my home office. I can write my novels because someone else translated the medieval Latin, or studied the archaeology, or read between the lines of royal annals for clues of the truth the anonymous authors didn’t want revealed.

I just picked and chose the information most useful in crafting my fiction, which by its nature is not entirely accurate. Scholars must admit when facts are unknown. We novelists don’t have that luxury if our characters would know that information, and we must resort to making something up.

But I try to get the culture right, and although I would never want to live in eighth and ninth century Europe, its melding of the personal and political, religion and magic, provides too much fodder for an author to resist.

So as I sat down to write the post, I realized I couldn’t include everything about Carolingian Francia. I am still learning about it as I write in this period and must give deeper thought to historical events I read in passing. But I could include a few elements about this society that fascinate me from afar.

For a flavor of the era my characters lived in, see Unusual Historicals.

Image from Frankish Psalter

From a ninth century Psalter (public domain, via Wikimedia Commons)

Why I Use the Term ‘Dark Ages’

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What should we call that period between roughly 500 and 1000, which includes the setting of my novels?

In my scholarly-like moments, I say early medieval times, but often, I’ll type Dark Ages.

That term riles some readers, and I can understand why. Dark Ages conjures a stereotype of a dim, smoky hall with a bunch of drunken, grunting guys who’d start knife fights at the slightest offense. While early medieval times were hardly ideal by my 21st century standards, I don’t like this oversimplified version of history, and I get irritated with questions like, “But how could those barbarians have art?”

True, most of the population couldn’t read, many children died of disease before age 5, teenage girls were married to older men, and wars were common. But we could say that about a lot of societies and eras. This time period did have its share of intellectuals, trade, art, poetry, and complicated politics, and its women were far from weak willed—they were protectors of their sons’ rights, supporters of political alliances, diplomats, and missionaries.

So why do I use Dark Ages while railing against the connotations? Readers recognize the term easily, especially in the limited space of a title or a social media post, and Dark Ages is more likely to get attention.

9th century illustration

From the ninth century Folchard Psalter (public domain, via Wikimedia Commons)

Two Labs across the Atlantic Prove That Electrons Behave Like Waves

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In this installment on the history of atom theory, physics professor (and my dad) Dean Zollman discusses how two separate teams an ocean apart proved Louis de Broglie right about matter sometimes behaving as waves rather than particles.—Kim

By Dean Zollman

Dean ZollmanIn the last post, I discussed Louis de Broglie’s radical hypothesis that matter sometimes behaved as waves. De Broglie did not have any direct evidence for his theory. However, he was able to show how his ideas could be connected to Niels Bohr’s model of the atom. Once de Broglie introduced these ideas, both theoretical and experimental progress occurred rather quickly. In this post, I will discuss the experiments that were able to conclude that de Broglie was right. Next time, we will look at the major theoretical advance in the 1920s. (This approach is not quite chronological, but many things happened and influenced each other over a short time.)

As I have discussed previously, the fundamental property that distinguishes waves from particles is interference. When two particles meet, they bounce off each other. Two waves can reinforce each other (constructive interference), cancel each other (destructive interference), or have some result between these two extremes.

To observe interference experimentally, we need to arrange for waves to move along two different paths and then meet. The distance that each wave travels determines the type of interference. In one method, the wave goes through two openings simultaneously and then combines. In another, the waves reflect off two surfaces that are very close to each other.

This second method is more common in everyday life. When you look at a soap bubble or at a puddle with a thin layer of oil on it, you frequently can see colors, with each color at a different location. The colors are created by some light reflecting from the top of the oil and interfering with light that travels through the oil and reflects from the water. The colors appear because each color has a different wavelength and thus constructive interference occurs at different places. Light passing through opening is less common in everyday life. Although, you may have seen an interference effect by looking at light through a fine lace curtain.

Interference on a soap bubble

Interference on a soap bubble (by Cosmic73, Creative Commons BY-SA 4.0, via Wikimedia Commons)

Red light interferes constructively

Paths of light for a thickness of a bubble where red light interferes constructively (Theresa Knot, GNU Free Documentation License via Wikimedia Commons)

Blue light interferes destructively

Paths of light for a thickness of a bubble where blue light interferes destructively (Theresa Knot, GNU Free Documentation License via Wikimedia Commons)

Animation showing light passing through two openings

Animation showing light passing through two openings and interfering as the light from the two openings meet. (By Lookang, with many thanks to Fu-Kwun Hwang and authors of Easy Java Simulation: Francisco Esquembre, CC BY-SA 3.0, via Wikimedia Commons)

To show that particles have wave properties, physicists needed to observe some type of interference with particles. Then, they would need to compare the results of the interference with de Broglie’s predictions. The most logical particle to start with was the smallest one known at that time—the electron.

The biggest difference when we consider electrons instead of light is the size of the objects and wavelengths. To cause interference, the sizes need to be approximately the same as the wavelength of the object doing the interfering. The wavelength of light is quite small but within the general range of the thickness of a soap bubble or an oil slick. One can also make openings for light to pass through by using a razor blade carefully. But using de Broglie’s result, we find that the wavelength of an electron is much smaller than that of visible light. It is similar to the wavelength of X-rays.

The solution to this problem is to use crystals. In a crystal, such as table salt, the atoms line up in nice, neat patterns. The layers of atoms create surface from which waves can reflect while the spaces between atoms can be used for opening through which waves can pass. The distances between atoms in the crystal are the sizes we need to observe interference.

Two research efforts—one in the U.S., the other in the U.K.—independently worked on this experiment. In his Nobel Prize lecture one of the experimenters, Clinton Davisson, described the two locations as “… in a large industrial laboratory in the midst of a great city, and in a small university laboratory overlooking a cold and desolate sea.” The experiment in the large industrial laboratory used the reflection method while the one near the cold and desolate sea used transmission through small openings. Both involved crystals.

The effort in the United States took place at Bell Labs. This laboratory was established in 1925 by the old version of AT&T. Its general mission was to conduct research to improve communications. However, a large amount fundamental research also took place. Over many years, many important scientific discoveries were made at Bell Labs, and some significant devices which are now part of our everyday life (and not just telephones) were invented there. The Wikipedia article on Bell Labs lists these achievements and the Nobel Laureates who worked there.

Clinton Davisson (1881–1958) began working for Western Electric, a division of AT&T, during World War I. After the war, he remained with the company and joined Bell Labs when it was founded. Lester Germer (1896–1971) worked for Western Electric for just a couple of months before entering military service in World War I. During the war, he was one of the first airplane pilots to see action on the front. After the war and a short rest, he was rehired by Western Electric and assigned to work with Davisson. They were assigned projects to look at some aspects of metals that were used in parts of the telephone company’s amplifiers. One aspect of this work involved shooting electrons at the metals. They were looking at how the electrons bounced off metals to better understand the metals’ properties. (Physicists use the phrase elastic scattering of electrons rather than bouncing off.) Wave behavior of electrons were not part of the research agenda. And for a while, they did not see any such behavior.

Clinton Davisson and Lester Germer

Clinton Davisson (left) and Lester Germer in 1927 hold the apparatus that they used to detect electron interference (public domain via Wikipedia Commons).

Schematic drawing of the Davisson-Germer experiment

Here’s a schematic drawing of the Davisson-Germer experiment. The electrons’ speeds are set by the apparatus in the lower left. The movable detector looks at the number of electrons coming off at different angles (by Roshan, CC BY-SA 3.0, via Wikimedia Commons).

Davisson described how they became interested in looking at the details of the electron scattering. “Out of this grew an investigation of the distribution-in-angle of these elastically scattered electrons. And then chance again intervened; it was discovered, purely by accident, that the intensity of elastic scattering varies with the [angle].” This change in intensity with angle was much like the different colors of light appearing at different angles when it reflects from the surfaces on a bubble. The phenomenon implies an interference pattern.

As Davisson and Germer investigated the scattering of electrons from crystals, they completed 21 different experiments. For each experiment, they could accelerate the electrons to a speed that they knew. So they also knew the electron’s momentum. In turn, they could calculate the wavelength of the electron and determine at which angle the constructive interference should occur. They compared their results for angle of the maximum number of electrons with the angle predicted by using de Broglie’s wavelength. For 19 of the experiments, their results matched extremely well with the wavelength predicted by de Broglie.

George Paget Thomson

George Paget Thomson (by Nobel Foundation, public domain, via Wikimedia Commons)

At about the same time George P. Thomson (1892–1975), son of the J.J. Thomson, who discovered the electron, was conducting a similar investigation in Aberdeen, Scotland. His experiment involved transmitting electrons through a crystal. In his Nobel lecture, Thomson said, “A narrow beam of [electrons] was transmitted through a thin film of matter. In the earliest experiment of the late Mr. Reid, this film was of celluloid, in my own experiment of metal. In both, the thickness was of the order of 0.000001 cm. The scattered beam was received on a photographic plate … and when developed showed a pattern of rings … An interference phenomenon is at once suggested.”

The picture below shows the result of a modern version of Thomson’s experiment, one that is done by many college physics majors. The light and dark circle are locations where constructive and destructive interference of electrons (respectively) occur.

Modern version of Thomson’s experiment

A modern version of Thomson’s experiment shows rings similar to the ones that he saw in his photographs (by And1mu, CC BY-SA 4.0, via Wikimedia Commons).

The results indicated that electrons had wave-like behaviors. As with the Davisson-Germer experiment, Thomson accelerated the electrons to a speed that he knew very well. So he could use de Broglie’s hypothesis to determine the wavelength. Using that wavelength, he predicted where the bright rings should occur in the photographs. The agreement between predictions and measurements were “within 1 percent.” G.P. Thomson had shown that indeed electrons behaved as waves.

These two experiments definitively established the wave behavior of matter. This behavior is at the foundation of most of contemporary physics and is critical to the development of many devices that today we take for granted. However, measuring the wave behavior was just one important step. Next time, we will look at the major theoretical advance that was underway at about the same time as these experiments.

Dean Zollman is university distinguished professor of physics at Kansas State University where he has been a faculty member for more than 40 years. During his career he has received four major awards — the American Association of Physics Teachers’ Oersted Medal (2014), the National Science Foundation Director’s Award for Distinguished Teacher Scholars (2004), the Carnegie Foundation for the Advancement of Teaching Doctoral University Professor of the Year (1996), and AAPT’s Robert A. Millikan Medal (1995). His present research concentrates on the teaching and learning of physics and on science teacher preparation.

Previously

What Are Things Made of? Depends on When You Ask.

Ancient Greeks Were the First to Hypothesize Atoms

The Poetry of Atoms

Atom Theory in Ancient India

Religion, Science Clashed over Atoms

Medieval Arabic Scholarship Might Have Preserved Scientific Knowledge

Rediscovering a Roman Poet – and Atom Theory – Centuries Later

Reconciling Atom Theory with Religion

Did Atom Theory Play a Role in Galileo’s Trouble with the Inquisition?

Did Gifted Scientist’s Belief in Atoms Led to His Obscurity?

Does Atom Theory Apply to the Earthly and the Divine?

A Duchess Inspired by Atoms

Separating Atoms from Atheism

Isaac Newton: 300 Years Ahead of His Time

Issac Newton and the Philosopher’s Stone

When Chemistry and Physics Split

Redefining Elements

Mme Lavoisier: Partner in Science, Partner in Life

With Atoms, Proportionality and Simplicity Rule

Despite Evidence of Atoms, 19th Century Skeptics Didn’t Budge

Mission of the First International Scientific Conference: Clear up Confusion

Rivalry over the First Periodic Table

The Puzzle of Dark Lines amid Rainbow Colors

The Colorful Signature of Each Element

Light Waves by the Numbers

Even Scientific Dead Ends Can Contribute to Knowledge

Discovery of the Electron Took Decades and Multiple Scientists

‘Wonders of the X-ray’

The Accidental Discovery of Radioactivity

Marie Curie: A Determined Scientist

Pierre and Marie Curie Extract Radium – and Pay a High Price

Scientists Delve into Radioactivity and Make Their Own Discoveries

The First Attempts to Visualize Atoms

Did Busy Work Lead to Models for Atoms?

Why Does Ice Melt? The Answer Lies in Physics.

Einstein Explains How a Dim Light Can Release More Energy Than a Bright One

How Bohr’s Famous Model of the Atom Was Created

Bohr’s Model of the Atom Answers Fundamental Questions – but Raises More

Bohr’s Model of the Atom Draws Critics

‘A First Feeble Ray of Light’ to Explain Electrons’ Orbits

Did the Queen Help Create Charlemagne’s Intellectual Circle?

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When Charlemagne decide to travel to Rome for important business in 780, he took his wife, Hildegard, with him, and she likely did more than provide companionship.

She was an Agilolfing, a member of the powerful, established family that ruled Bavaria. And if she was like most medieval women, she wanted the inheritance to go her sons, not the offspring from Charles’s first marriage.

At that time, Charles had reigned 12 years and was 32, no longer a young man by medieval standards. It might have been time to think about their children’s future. When Charles and Hildegard reached Rome in 781, their two youngest boys, ages 3 and 4, were anointed subkings, and their 6-year-old daughter was betrothed to the child emperor of Byzantium.

Another indication that the royal couple was thinking long term: when they returned to Francia, they brought scholars with them. If they wanted their subjects, and their enemies, to associate their realm with ancient Rome, they needed intellectuals. For more about learned men in Charles’s court, see my post in Unusual Historicals.

Hildegard and Charlemagne

A 1499 illustration of Hildegard and Charlemagne (public domain via Wikimedia Commons)

Sympathy for the Monster’s Mom

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Whoever wrote Beowulf probably didn’t intend for the audience to feel sorry for a killer.

Yet I must admit I sympathize with Gendel’s mother, called a “monstrous hell-bride” and “troll-dam” among other names. Her murderous son is the worst possible enemy for the residents of Heorot Hall—a joyless being who cannot be appeased. So, the only way to stop him is to slay him. When Beowulf fatally wounds Grendel, we understand why Heorot Hall celebrates.

Yet we can also understand why a mother who is “grief-racked and ravenous, desperate for revenge” would make Heorot Hall pay a bloody price.

Grendel and his mother are ingenious literary creations, blending pagan and Christian beliefs. For more, see my post at English Historical Fiction Authors.

Source

Beowulf, translated by Seamus Heaney

Beowulf

From Jean Lang’s A Book of Myths, 1915 (public domain, via Wikimedia Commons)

An Ex-First Lady Who Founded Something Bigger

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When I was thinking of a real-life character to feature for Unusual Historicals’ “First Ladies” theme, Saint Cuthburga came to mind.

First lady is defined as the wife of a political leader or the first woman recognized for a particular accomplishment. In this case, Cuthburga is the ex-wife of a seventh-century Northumbrian king.

Usually, a divorce in the Dark Ages was an insult to the woman and her family, so it was not done lightly. When Charlemagne parted from his second wife in the eighth century, he ended up going to war with his former father-in-law. As for Himiltrude, the first ex-wife, the consequences of that separation are the subject of my work in progress, Queen of the Darkest Hour. (Whether Himiltrude was a concubine or a wife is a topic that deserves its own post.)

No one questions whether Cuthburga was a queen, although for how long is up for debate. Also the sister of a king, she founded Wimborne Minster at Dorset after she left her husband, and that decision would have an impact beyond her lifetime. Read my post about Cuthburga on Unusual Historicals.

Anglo-Saxon woman of rank

A ninth century Anglo-Saxon woman of rank, from Kretschmer and Rohrbach’s Costumes of All Nations (public domain)

Dreams of a Garden as Spring Draws Near

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As I wrote a post about early spring gardens in the Dark Ages for English Historical Fiction Authors, one thought came to mind: I want one. Well the garden, not the Dark Ages.

The backyard in our prior house was too shady for many vegetables, so we grew summer tomatoes, peppers, and a few herbs in pots. I slipped some Swiss chard along a walk one year and have planted herbs and garlic in the front, but it’s not the same. I miss the lettuces and greens, kale, and peas. I long for asparagus and strawberry patches.

When we moved, we chose a property with a good sized backyard and a lot of sunshine. But the yard is grass rather than garden beds, so we will need to dig first. That means waiting for warmer weather and drier soil. Maybe next year, we’ll sow crops that can tolerate a few frosts, and I’ll see seedlings of those vegetables I described earlier.

Of course the stakes for me and my husband are a heck of lot lower than the imaginary friends I write about. For us, this is waiting a little longer to pursue a hobby. For them, it was life or death.

March in the 16th Century

A 16th century illustration of what happens in March (public domain via Wikimedia Commons).

‘A First Feeble Ray of Light’ to Explain Electrons’ Orbits

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In this installment on the history of atom theory, physics professor (and my dad) Dean Zollman discusses the work of Louis de Broglie, who sought to explain why electrons adhere to certain orbits. As a grad student, de Broglie looked to the properties of waves. And even Albert Einstein weighed in. – Kim

By Dean Zollman

Dean ZollmanTo create a model that worked, Niels Bohr needed to assume that the electron could orbit the nucleus at only certain radii and that all other radii were forbidden. In the two previous posts, I mentioned that this assumption was a major concern. Bohr could not justify the assumption but used it in order to make the model match the data had been collected for more than half a century.

A justification was forthcoming in the 1920s. In this post, I will discuss this research. However, the underlying reason for the discrete orbits very quickly became much more than just a justification for Bohr’s model. It was the beginning of a revolution in the understanding of atoms and other small objects. And it basically put the Bohr model “out of business” as a serious contender for the model of atoms. More about that revolution will come next few posts. First we need to learn about the critical step to get the revolution started.

From his name alone, you know that Louis-Victor-Pierre-Raymond, seventh duke of Broglie (1892–1987) came from an aristocratic French family. In the 1920s, he was not yet the seventh duke and used the somewhat less pretentious name Louis de Broglie. As a student, he began graduate studies in history but decided that theoretical physics was more interesting. He was motivated in part by his elder brother, the sixth duke of Broglie, an experimental physicist.

Louis de Broglie

Louis de Broglie in 1929 (by Nobel Foundation, public domain, via Wikimedia Commons)

“I was attracted to theoretical physics by the mystery enshrouding the structure of matter and the structure of radiations, a mystery which deepened as the strange quantum concept introduced by Planck in 1900 in his research on black-body radiation continued to encroach on the whole domain of physics,” he said during his Nobel lecture.

For his PhD dissertation, de Broglie was greatly influenced by the work of Planck and Einstein. A few months ago, I discussed how Einstein had explained the photoelectric effect by assuming that light sometimes acted as if it came in small packets (photons) of energy rather than in waves. One of Einstein’s conclusions was that the energy of the photon was equal to Planck’s constant times its frequency. In symbols:

Einstein's equation

The relation between the energy and frequency of a photon. (From The Fascination of Physics by Jacqueline Spears and Dean Zollman, used with permission.)

By applying Planck’s hypothesis, Einstein concluded that light which is normally considered a wave sometimes acted like a particle with its energy given by the equation above.

De Broglie thought that if light could sometimes act as particles, then maybe particles could sometimes act as waves. If objects like electrons behaved like waves, they needed to have a wavelength. Using Einstein’s equation and his special theory of relativity, de Broglie derived an equation for the wave length of any object that has a mass. It says the wavelength is inversely proportional to the mass times the velocity (the momentum). In symbols:

The relation among the wavelength, mass and velocity of an object with mass. (From The Fascination of Physics by Jacqueline Spears and Dean Zollman, used with permission.)

The relation among the wavelength, mass and velocity of an object with mass. (From The Fascination of Physics by Jacqueline Spears and Dean Zollman, used with permission.)

In those days, it was not uncommon for a graduate student to work on his or her own and deliver a completed dissertation to the examining committee. Basically, de Broglie worked in this way. However, his hypothesis was not received well by the committee. Certainly part of the problem that the committee saw was that de Broglie could not refer to a single experiment that supported his work.

A member of the committee was Paul Langevin (1872–1946), a prominent physicist in the 1920s. De Broglie later said that Langevin was “probably a bit stunned by the novelty of my ideas.” Even though he may have been stunned, Langevin sent a copy of the dissertation to Einstein for his review. Einstein rather quickly responded, “I believe it is a first feeble ray of light on this worst of our physics enigmas.” De Broglie wrote in the German translation of his dissertation, “Einstein from the beginning has supported my thesis.” (De Broglie’s dissertation is also available in a modern translation into English at the Fondation Louis de Broglie site. However, it has some heavy duty mathematics.) With Einstein’s endorsement, de Broglie received his PhD.

To explain why the electron in an atom could have only certain orbits, de Broglie relied on the interference property of waves. As shown in the figure below when two waves meet, the result is a bigger wave or a smaller one. On the left side of the figure is the result when the troughs and the crests of the two waves match up. The result shown at the top is a bigger wave. This effect is called constructive interference. On the right, the crests of one wave matches with the troughs of the second. As shown at the top of this one, the two waves cancel each other. This one is destructive interference.

Interference of two waves

Interference of two waves (by Haade, GFDL or CC-BY-SA-3.0, via Wikimedia Commons

For the electrons in atoms, the wave needs to exist as they move in a circle. The drawing below show different situations for these circular waves. For the waves in (a) each of the waves can fit on a circle and close on themselves. When they come back around they act like the waves on the left in the figure above. Toughs meet troughs and crests meet crests, and we have constructive interference. So they add nicely. Because the wave of the electron is not zero, we can conclude that the electron can exist in these two orbits.

However, when the wave in (b) comes back around the troughs will eventually meet crests. They act like the waves on the right of the figure above. Thus, the wave is canceled (destructive interference), so the electron cannot exist in the orbit because its wave is zero. The net result is that only certain radii can meet the condition that an electron’s wave just fits nicely on the circumference of the circle. Only when the electron’s wave can exist, can the electron be in that orbit. Thus, de Broglie’s electron waves give a reason for Bohr’s orbits.

de Broglie's waves in circles

De Broglie waves on a circle. Part (a) shows two waves which can fit on a circle and close on themselves. Part (b) shows one that does not. In (b) when the wave comes back around the troughs and crests meet. The result will be no wave of this wavelength can exist in a circle with that radius. (From The Fascination of Physics by Jacqueline Spears and Dean Zollman, used with permission)

A result of a detailed analysis of the electron orbits and several other phenomena provided evidence that de Broglie was on to something. However, the explanations of the Bohr orbits and other phenomena were indirect evidence of the wave behavior of matter. Constructive and destructive interference can only occur with waves; particles cannot do it. If electrons really have wave properties, physicists should be able to devise an experiment in which they can directly observe the constructive and destructive interference of electrons. Within a few years of publication of de Broglie’s dissertation such experiments were completed on both sides of the Atlantic. There are some interesting stories connected to the experiments, so I will save them for next time.

Dean Zollman is university distinguished professor of physics at Kansas State University where he has been a faculty member for more than 40 years. During his career he has received four major awards — the American Association of Physics Teachers’ Oersted Medal (2014), the National Science Foundation Director’s Award for Distinguished Teacher Scholars (2004), the Carnegie Foundation for the Advancement of Teaching Doctoral University Professor of the Year (1996), and AAPT’s Robert A. Millikan Medal (1995). His present research concentrates on the teaching and learning of physics and on science teacher preparation.

Previously

What Are Things Made of? Depends on When You Ask.

Ancient Greeks Were the First to Hypothesize Atoms

The Poetry of Atoms

Atom Theory in Ancient India

Religion, Science Clashed over Atoms

Medieval Arabic Scholarship Might Have Preserved Scientific Knowledge

Rediscovering a Roman Poet – and Atom Theory – Centuries Later

Reconciling Atom Theory with Religion

Did Atom Theory Play a Role in Galileo’s Trouble with the Inquisition?

Did Gifted Scientist’s Belief in Atoms Led to His Obscurity?

Does Atom Theory Apply to the Earthly and the Divine?

A Duchess Inspired by Atoms

Separating Atoms from Atheism

Isaac Newton: 300 Years Ahead of His Time

Issac Newton and the Philosopher’s Stone

When Chemistry and Physics Split

Redefining Elements

Mme Lavoisier: Partner in Science, Partner in Life

With Atoms, Proportionality and Simplicity Rule

Despite Evidence of Atoms, 19th Century Skeptics Didn’t Budge

Mission of the First International Scientific Conference: Clear up Confusion

Rivalry over the First Periodic Table

The Puzzle of Dark Lines amid Rainbow Colors

The Colorful Signature of Each Element

Light Waves by the Numbers

Even Scientific Dead Ends Can Contribute to Knowledge

Discovery of the Electron Took Decades and Multiple Scientists

‘Wonders of the X-ray’

The Accidental Discovery of Radioactivity

Marie Curie: A Determined Scientist

Pierre and Marie Curie Extract Radium – and Pay a High Price

Scientists Delve into Radioactivity and Make Their Own Discoveries

The First Attempts to Visualize Atoms

Did Busy Work Lead to Models for Atoms?

Why Does Ice Melt? The Answer Lies in Physics.

Einstein Explains How a Dim Light Can Release More Energy Than a Bright One

How Bohr’s Famous Model of the Atom Was Created

Bohr’s Model of the Atom Answers Fundamental Questions – but Raises More

Bohr’s Model of the Atom Draws Critics

Did King Pepin and Queen Bertrada Love Each Other?

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We don’t know how Bertrada of Laon felt about marrying Pepin, mayor of the palace. Was she overjoyed to join a Frankish family more powerful than the royal Merovingians? Or did she see herself fulfilling her duty to her kin as a partner in building an alliance? What did she think of Pepin as a man?

Whatever her sentiments during the nuptials in 744, she was not about to give up on her relationship with her husband when he sought to end the childless union two years later. At least, I think that’s what Pepin tried when he asked the pope about illicit marriages – he and Bertrada shared a set of great-grandparents.

Had Bertrada been willing to go quietly, she could have taken the veil, perhaps even held out for her own abbey to rule. But she didn’t. And the pope told Pepin canon law prohibited remarriage after a divorce.

So Pepin and Bertrada stayed together, and the story has a surprisingly happy ending, the reason I’ve chosen to write about them as an unlikely romance at Unusual Historicals.

Bertrada's and Pepin's tombs

Bertrada’s and Pepin’s tombs at Saint-Denis, France (photo by Roi Boshi (CC BY-SA 3.0 or GFDL, via Wikimedia Commons)

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