Murder by Physics

Judging by murder mystery novels, physics is a safer science than chemistry and biology (or even psychology!). Sure, you could say that any murder involving gunshots involve ballistics, but the details of the physics are hardly ever relevant. Maybe an angle in the bullet’s trajectory is important, or perhaps the force required to perform a particular act is significant to the plot (especially in the novels of Agatha Christie). Nevertheless, chemistry and biology—with their focus on poisons and rigor mortis and so forth—are the key sciences in murder. Physics murder attempts are reserved for madmen in movies (“No, Mister Bond, I expect you to die!”), and hardly ever does a plot turn on the theoretical concepts at the heart of physics. (“No, Captain Hastings! We must not open the door of the locked room, lest we collapse Lady Herringbone’s wavefunction!”)

However, when the notorious Doctor Rubidium asked me to contribute a post to the “Murderers Carnival”, a collection of blog posts linking science and crime, I had to say yes. I had several criteria: the book had to be one I knew already (i.e., I wasn’t going to comb the library stacks for a book with the perfect scenario), it had to be one in which physics played an important role in either the crime or the solution, and it had to be a book that one of my fellow bloggers hadn’t already picked. One book stood out immediately: Busman’s Honeymoon by Dorothy L. Sayers. If you haven’t read the book, some spoilers will follow; while I won’t reveal the name of the murderer, I do have to discuss the method used in the murder, so be warned.

Lord Peter Wimsey: the Man and His Times

Busman’s Honeymoon (published in 1937) is the final novel featuring my favorite literary detective: Lord Peter Wimsey, the aristocratic English sleuth who investigated crimes in a series of books and short stories in the 1920s and ’30s. Unlike the prickly Sherlock Holmes, the difficult Hercule Poirot, or the reclusive Nero Wolfe, Wimsey was a dapper man-about-town, with a love for literature, history, and fine wine. He had no regular sidekick, though he was always aided in his investigations by various allies: his manservant Mervyn Bunter (an excellent investigator in his own right), his good friend Inspector Charles Parker of Scotland Yard, and ultimately the love of his life, detective novelist Harriet Vane. (My cat Harriet is named for Harriet Vane.) Busman’s Honeymoon, as the name suggests, takes place mostly during Peter’s and Harriet’s honeymoon—which turns out to be more dramatic than they intended when the former owner of their house is found murdered in the cellar.

The Wimsey mysteries are not usually complex puzzles; for that, read Agatha Christie. Instead, the stories often hinge on personality, sorting through the complicated motivations, cultural landmines, and the detective’s own uncertainty about his right to investigate—knowing that the consequence will likely involve the murderer being hanged. The central mystery in Busman’s Honeymoon is less satisfying than some of the other novels, but the human drama and comedy are heightened. After all, Peter and Harriet have just been married, with all the powerful emotions that entails. As Sayers writes in the epistolary “Foreword”, “It has been said, by myself and others, that a love-interest is only an intrusion upon a detective story. But to the characters involved, the detective-interest might well seem an irritating intrusion upon their love-story.” As a result, there are several love scenes in the book interspersed with interviewing witnesses and suspects, and the final chapter of the novel is incredibly powerful.

Busman’s Honeymoon began as a play (by Sayers and her college friend Muriel St. Clare), and while I haven’t read the script, it seems many of the scenes in the novel draw directly on the earlier version. (I have seen the movie, called Haunted Honeymoon in the American release, which is frankly pretty bad. The most notable thing for me is the presence of Robert Newton as Frank Crutchley, whose portrayal of Long John Silver in Treasure Island is directly responsible for every pirate stereotype ever since.) The book is definitely a product of its time and culture. Several characters are reminded of their place in the rigid class system of the day (how to properly address a lord if one is a common auto mechanic, who eats in the kitchen vs. who dines with the homeowners), and the single Jewish character is a cringe-inducing lisping stereotype. Generally speaking, Sayers seems minimally racist for her era, but by today’s standards her scenes with Jewish or non-white characters read very uncomfortably, at least for me. Certainly she breaks the class stratification by connecting commoners (Harriet, Charles Parker) with nobility (Lord Peter, Lady Mary Wimsey), and even explicitly argues that the offspring will be better off for it, especially in contrast with Peter’s brother the Duke of Denver, who married his own first cousin.

It’s the Power Behind It

“Must have facts,” said Lord Peter, “facts. When I was a small boy I always hated facts. Thought of ’em as nasty, hard things, all knobs. Uncompromisin’.”
(from Clouds of Witness, the second Lord Peter Wimsey novel)

However, I’m off subject, which is Murder by Physics. William Noakes, the murdered man, was very tall, yet he was killed by a blow on the head from above and behind. That means Noakes was either killed by an equally tall person (meaning Sayers provides two tall suspects, one with an excellent motive, in the fine tradition of mystery novels), sitting down when he was struck, or he was murdered by some mechanical means. (There’s a lot more medical stuff, which I’ll leave another blogger to write about, if they want.) As you can probably guess from my build-up, the answer is the last one.

Over the course of the novel, Sayers gradually reveals that a large cactus in a hanging pot has been removed, placed on a longer chain, and the outer pot filled with a quantity of lead shot. The entire assembly was raised up to ceiling level, then allowed to swing down. The trap was rigged to the lid of a wireless set (a large radio cabinet, something pretty much lost to history now). When Noakes—an elderly, short-sighted man with regular and penny-pinching habits—came into the dim room to listen to the radio as he always did, he opened the lid, releasing the cactus pot, which swung down. In this way, the murderer didn’t need to be in the room, didn’t have to be tall, and didn’t even have to be particularly strong—as long as they knew enough about physics to get the job done.

The physics of the murder involve three related principles, taught in introductory-level classes: the pendulum principle, the conservation of energy, and the conservation of momentum. The pendulum principle is very simple: a pendulum always passes directly beneath its point of suspension, so the murderer moved the cabinet slightly to center it below the place where the cactus pot was hung. That ensured the victim’s head would be exactly in the right position when the pot swung down.

Conservation laws are some of the deepest principles in physics. At their most straightforward (as with our murder weapon), they simply tell how mechanical systems work, but at their most profound, they lead to results such as the Higgs mechanism, by which particles acquire mass. We don’t need to understand particle physics for Busman’s Honeymoon (“Bunter, I suspect a new particle is carrying momentum away from this collision!”): introductory physics is enough.

The murder weapon in Busman’s Honeymoon. Using a weighted cactus pot as a pendulum, the murderer set a booby trap. The speed the pot has at the bottom of its swing is the same as the speed it would have if it were dropped vertically from the same height.

Conservation of energy tells us that the murderer can use gravity to give the cactus pot a high speed—but they have to give it a long chain. As it turns out, the key quantity is the vertical distance the pot moves: if it falls through a larger height, it will have greater speed at the bottom. The horizontal distance is actually irrelevant in this case! If you rigged a booby trap with a mass that falls directly downward through the same height, it would have the same speed as the cactus pot when it reached the victim’s head. (I use the term speed deliberately. Velocity, which is a related important concept, involves both speed and direction, but energy doesn’t depend on velocity—only how fast the object is moving.) Interestingly, the mass of the pot doesn’t affect how fast it moves at the bottom of the swing, as long as we can neglect air resistance—which we can in this case, since the pot is heavy enough and is moving through a relatively small distance.

A shorter chain means less speed at the bottom of the swing.

Mass does make a difference, however, when the pot actually collides with the victim’s head. (Please suppress vivid imaginations for a moment.) The key quantity in a collision is momentum, which is the mass of the moving object multiplied by its velocity. If the murderer didn’t add extra mass to the pot in the form of lead shot, it would move just as fast at the bottom of the swing, but it wouldn’t hit as hard. To see this, go back to a vertical drop: take a baseball and a bowling ball, and drop them from the same height. They will take the same amount of time to fall (again if we can neglect air resistance), and have the same speed upon landing, but there’s no question which one hurts more if you dropped them on your foot. Energy tells us how fast they move, but momentum tells us how much they hurt. By loading the cactus pot with lead shot, the murderer guaranteed it would have enough momentum to kill the victim.

All of this is revealed dramatically in the novel, of course, and in less physics-oriented language. The purpose isn’t to be a textbook example of physics in action, after all, but a revelation of the character of the murderer, who had to plan his actions carefully to make it work properly. The sequence where Wimsey solves the mystery and those following are full of symbolism, with themes of justice, mercy, and responsibility intertwined. Murder mysteries aren’t really about the method or mechanism, but about morality, something that lies beyond the purview of science. However, science and its tools are central to the genre—rational inquiry, skepticism about the “obvious” answers, and the need to accept evidence, no matter how uncomfortable it is to do so.

One response to “Murder by Physics”

  1. Dorothy Sayers is one of my favorite authors, and this explanation of the physics of the murder method is great. Thanks!

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