The Amazing Story of Quantum Mechanics by James Kakalios Read Free Book Online Page B

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:
    Momentum × Wavelength = h
    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