The Amazing Story of Quantum Mechanics (6 page)

 

 

Readers of the February 1930
issue of
Science Wonder Stories
were treated to thrilling tales of the “Streamers of Death” and “A Rescue from Jupiter”; they traveled to “The Land of the Bipos” and visited “The World of a Hundred Men.” The cover features a scene from the “Bipos” yarn. Two robbers who have broken into the home laboratory of a Dr. Sanborn, who was experimenting on methods to send living beings to another world (whether in this universe or an alternate one is never made clear), have been trapped in a large glass device. This cylinder, large enough to hold two grown men, is described in the story as a “cathode ray tube”—though its appearance is quite different from the cathode-ray tubes one finds in older-model television sets. Sanborn is shown moments before throwing a switch that will convert the two thieves into electricity. They will then travel at the speed of light to the land of the Bipos, where they will be reassembled into their human form. Bipos, apparently, are a race of intelligent three-foot-tall penguins. The means of transportation appears to be an early ancestor of
Star Trek
’s famed transporter. That Sanborn was able to construct such a fantastic scientific marvel, with no outside assistance and using his own financial resources, is perhaps not so surprising once we discover that in his day job Dr. Sanborn is . . . a druggist!

Science Wonder Stories
was not devoted solely to fantastic scienctifiction but also featured descriptions and discussions of real-world current scientific advances. This particular issue contained a “Symposium,” in which an essay on the question “Can Man Free Himself from Gravity?” was followed by letters from knowledgeable experts. The short essay by Th. Wolff of Berlin was translated for the pulp from the original German. Wolff tantalized readers with a report of an American physicist, Charles Brush, who claimed to have discovered a material made up of silicates (the exact composition known only to Brush) that exhibited an acceleration due to gravity of only 9.2 meters per second per second, rather than the larger value of 9.8 meters per second per second that all normal matter experiences. “If true, this would be a fine achievement,” allowed Wolff, for “by increasing the valuable property of these mysterious substances one might perhaps attain approximate or even complete freedom from gravity. Let us wait for it!”

Figure 5:
Dr. Sanborn about to test his homemade transporter device (that looks like an overgrown vacuum tube), which will send two intruders to the Land of the Bipos in 1930’s
Science Wonder Stories.

But Wolff did not think we should hold our breaths while waiting, for he went on to correctly point out that such a material would represent an “irreconcilable contradiction” to the Newtonian law of gravity, which indicates that the acceleration of a falling object is the same for all matter, regardless of composition. Brush’s report, Wolff informed readers, “must with absolute assurance be relegated to the realm of fiction. If there were exceptions and deviations from the general law of gravity, these would certainly have appeared before now in manifold and various ways, and it would not need the discovery of mysterious substances to bring them to our knowledge.” So much for flying cars—even back in 1930! But then Wolff goes too far—and dismisses space travel when he incorrectly calculates that the chemical fuels of the time would limit any rocket ship to heights no greater than 400 kilometers above the Earth’s surface, a mere fraction of the 384,000 kilometers from the Earth to the moon.

This last point was challenged in letters from members of the
Science Wonder Stories
Board of Associate Editors, notably Robert H. Goddard of Clark University in Worcester, Massachusetts. Goddard pointed out that in 1919 he had authored a scientific publication in the Miscellaneous Collections of the Institute (namely, the Smithsonian Institute, which was funding his rocket research), stating that a multistage rocket, essentially of the design employed by NASA fifty years later, would indeed be able to exceed this 400-kilometer limit. Thus, while hopes of flying cars and perpetual motion
¹⁰
were dashed, the promise of rocket trips to the moon and beyond were affirmed in the science fiction pulps.

Goddard was an early example of a prominent scientist whose research would inspire many science fiction tales and whose choice of field and research subject was, in turn, inspired by science fiction. In a fan letter sent to H. G. Wells, the sixteen-year-old Goddard extolled the influence that reading
The War of the Worlds
had on him, such that no more than a year later, he “decided that what might conservatively be called ‘high altitude research’ was the most fascinating problem in existence.” Goddard was not the first scientist, of course, to find a muse in science fiction. Hermann Oberth, the Transylvanian-born scientist who is considered the “father of modern rocketry,” had an encounter at age eleven with Jules Verne’s
From the Earth to the Moon
that set the trajectory of his scientific career. Both Oberth and his pupil Wernher von Braun would serve as technical advisers for
Woman in the Moon,
a 1929 Fritz Lang science fiction motion picture that featured the first countdown to launch a rocket, in film or in the real world.

Real science, as opposed to fiction, was also imparted in
Science Wonder Stories
’ regular features “What Is Your Science Knowledge?,” “Science Questions and Answers,” and “Science News of the Month.” Here, in this latter section, a brief item entitled “Electron Found to Have Dual Character” read, in its entirety:

If the magazine had contained a detailed description of the chemical composition of an actual antigravity shield, it would not have presented a more profound or revolutionary report than this brief blurb regarding the electron’s “dual character.”

The second quantum principle listed at the top of this chapter states that, just as there is a particle aspect to light, there is a corresponding wavelike nature to matter. Unlike the case of the photoelectric effect in the last chapter, this strange symmetrical hypothesis about the nature of matter was not proposed in order to resolve a mysterious experimental observation that contradicted expectations of classical physical theory—but was suggested precisely because it was a strange symmetrical hypothesis.

In 1923, Prince Louis de Broglie (yes, he actually was a French prince as well as a physicist), struck by the counterintuitive suggestion that light was comprised of corpuscular particles, proposed that there was a wave—originally termed a “pilot wave”—associated with the motion of real particles, such as electrons, protons, and atoms. De Broglie had an answer for why this “pilot wave” had not been previously observed—its wavelength varied inversely with the momentum of the moving object, so the larger the object (which is easier to observe), the smaller the wavelength of its pilot wave.

How to test the proposal that there is a wave associated with the motion of matter? As mentioned in the last chapter, interference effects, such as when white light creates a spectrum of reflected colors from an oil slick suspended on a wet surface, are an excellent test of the existence of waves. To recap, when the thickness of the slick is exactly equal to specific fractions of a given color’s wavelength, the waves corresponding to this color reflected from the top and those that have traveled through the slick, bounced off the bottom, and passed again through the slick and exited from the top surface add together coherently. When this happens, the color is brighter to us due to this constructive interference. Other waves corresponding to other colors at this location add up incoherently, out of phase, and the net effect is that from the white light shining on the oil, one color is primarily reflected from the slick from a given point on the slick. As the thickness of the slick can vary from point to point, we observe different colors across its surface.

The thickness of an oil slick can be several thousand nanometers (one nanometer is approximately the length of three carbon atoms, stacked one atop the other), while the wavelength of visible light ranges from 650 nanometers for red light to 400 nanometers for violet light. Thus, only very thin oil slicks, whose thickness is no more than a few times the wavelength of light, exhibit the interference pattern described above (if the slick is too thick, then the light traveling through the oil has too great a chance to be absorbed and won’t make it back through the top surface). If we want to use a similar interference effect to verify the wavelike nature of the motion of matter as proposed by de Broglie, we first need to know how large or small the “matter wavelength” will be. De Broglie proposed that the connection between the wavelength of the “pilot wave” for any moving object and its momentum is given by the following expression:

This equation indicates that the larger the momentum, the smaller the wavelength. The product of the two quantities is a constant, and de Broglie suggested that it should be Planck’s constant. Again, this equation is mathematically no different from the relationship described in the last chapter connecting distance traveled and time driving, that is, distance = (speed) × (time). In order to determine how long a car trip to Chicago from Madison, Wisconsin, may take, we note that the distance is a constant, approximately 120 miles, and not open to alteration. If our average speed is 60 miles per hour, then this equation indicates that the trip will last 2 hours. A slower speed will lead to a longer trip, and to shorten the trip to 1 hour, we must look to a speed of 120 miles per hour.
¹¹
In principle, the trip may last as short or as long as we like, as long as we vary our average velocity so that, when multiplied by the travel time, it yields a distance of 120 miles.

The momentum of an object is defined as the product of its mass and its velocity. The bigger an object, the more momentum it has at a given speed, and the harder it would be to stop. Which would you rather have collide with you: a linebacker or a ballerina, both running at the same speed? If we use the mass and speed of a major league fastball in de Broglie’s equation above, we find that its de Broglie wavelength is smaller than a millionth trillionth of the diameter of an atomic nucleus. There is no structure that can be conceived of that would exhibit interference effects of a baseball.

One way to increase the size of the de Broglie wavelength is to decrease the momentum of the object, as their product is a constant, and the simplest way to do that is to consider smaller objects. That is, the smaller the object, the lower its momentum (just as the ballerina has a smaller momentum than the football player), and consequently the larger its de Broglie wavelength. An electron obviously has a much smaller mass than a baseball, and a correspondingly smaller momentum. Even for an electron traveling at a speed of nearly 1 percent of the speed of light, its momentum is a trillion trillion times smaller than the baseball’s, and its corresponding de Broglie wavelength is a trillion trillion times larger. For just such an electron the de Broglie wavelength turns out to be about one-fourth of a nanometer, or roughly the diameter of an atom. In order to observe interference effects that would reflect the wavelike nature of matter, we would thus need to send a beam of electrons at an “oil slick” that is only a few atoms thick. That’s still pretty small, but fortunately nature provides us with just such “slicks”—we call them crystals.