Читать книгу Quantum Physics is NOT Weird - Paul J. van Leeuwen - Страница 17

Thomas Young (1773-1829) let sunlight light shine through a double slit, mounted in one of the sides of a closed box. A piece of frosted glass was mounted at the opposite side of the double slit. The double-slit was manufactured by making two narrow parallel scratches on a soot-coated piece of glass. With this device he was able to observe the pattern that was projected by the light passing through the double slit. A pattern of colored light and dark bands appeared on the frosted glass at the back of the box. This was a phenomenon that could not be explained by Newton's light corpuscles. It could only be explained by assuming that light behaves like waves.

Figure 3.1: Youngs drawing of interference of monochrome light waves.

In 1803 Young presented his explanation of the results of his double-slit experiment to the Royal Society in London. He produced the above sketch to explain these dark and light bands, called fringes. The cause of these fringes is called interference. Light waves, coming from the left – not shown here – do arrive at the narrow slits A and B. In these slits two synchronously vibrating elementary wave sources are created, in the way Huygens had supposed. The two synchronous wave sources will generate circular wave fronts expanding from both slits. These synchronous circular expanding waves are necessarily moving exactly in phase and will have the same wavelength. Young's sketch represents the circularly expanding wave-fronts – the crests – of the supposed waves. Where these wave crests, expanding from slits A and B, intersect, they reinforce each other and create higher wave crests, maxima. Where the wave troughs – the minimum heights – extending from A meet the wave crests from B, or troughs extending from B meet crest from A, they will annihilate each other. In Young's sketch you can see that the intensity maxima will be found along lines fanning out from between the slits. These lines are formed by the intersections of the wave crests. Where those lines of maximum wave crests reach the screen (C-D-E-F), the light will show maximal intensity. Halfway in between these lines of maximum wave crests the light waves will annihilate each other so you will observe dark bands where these annihilation lines reach the screen. This reinforcing and annihilating phenomenon is called interference.

Wikipedia: In physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive interference result from the interaction of waves that are correlated or coherent ^[1] with each other, either because they come from the same source or because they have the same or nearly the same frequency ^[2]. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves ^[3]. The resulting images or graphs are called interferograms.

The moiré effect ^[4] – see figure 3.2 – is also an interference phenomenon. When you slide two sets of concentric circles, drawn on transparent sheets, over each other the visual result is strikingly like Young's drawing in figure 3.1. Watch the effect in the moiré animation film by Amanita ^[5]. Where the circles overlap the interference is constructive. Observe in the animation how the lines of constructive interference move, depending on the varying distance of the two central circles. These can be equated to the two wave sources in the slits.

Figure 3.2: Moiré effect of two overlapping sets of concentric circles. Compare this with Young’s sketch of wave interference.

Source: Wikimedia Commons.

Frequency – usually denoted by the Latin letter f or the Greek letter ν (pronounced ‘nu’) – tells us the number of complete vibrations per second. The international standard unit for frequency is the Hertz (Hz), which is the number of oscillations per second. The most elementary wave type applied in physics theory is the sine wave. The phase of a sine wave is expressed in degrees of a circle and represents the state of the wave within the timespan of a full oscillation period. So:

 0o is the moment when the wave height is zero and rising,

 90o is the moment when the wave height is maximal (a crest),

 180o is the moment when the wave height is zero and falling,

 270o is the situation when the wave height is minimal (a trough).

When two waves are in opposite phase, their phase difference is 180^o.The deflection from the middle when the maximal height is reached (phase 90^o) is called: the peak amplitude ^[6].

Figure 3.3: Constructive and destructive interference.

Source: Wikimedia Commons.

The bold wave (upper left) or line (upper right) in figure 3.3 depicts the oscillation of a single point in time. Imagine a fishing float going up and down with waves coming from two different sources. The horizontal axis is the timeline of the up and down movement of the float. Both bold graphs are the summation of the two thinner drawn waves below. These are the waves meeting each other at the fishing float. The two thinly drawn waves on the lower left arrive in-phase at the float. Adding these two waves together will produce constructive interference, resulting in a greater peak amplitude of the float at their meeting point. The two waves on the right meet each other at the float with opposite phases. They extinguish each other completely, which is called destructive interference. The float will be at rest.

This summing of waves is called superposition. Interference and superposition are concepts that will become utterly important in understanding the double-slit experiments we will encounter frequently in this book.

Figure 3.4: Interference as a result from differences in traveled distance . P is the location of the first maximum. The wavelength will then be equal to δ.

Figure 3.4, with a monochromatic light source on the left, two slits and a screen, depicts the geometric approach taken for explaining the interference effect by path length differences.

Please note: the distance O-Q of the double-slit to the screen, in relation to the distance between the slits S1-S2, is depicted here considerably smaller than it is in a real experimental configuration.

Circular wave fronts originating from the source on the left arrive simultaneously in the slits S1 and S2. As a result, synchronous oscillating elementary wave sources originate in S1 and S2. Synchronous elementary Huygens waves will depart then from S1 and S2. When O-Q is considerably longer than the mutual slit distance S1-S2, the path-length difference between S1-P and S2-P can be determined, in very good approximation, by drawing a line from S1 perpendicular to S2-P. This creates two similar triangles S2-R-S1 and Q-O-P. From this similarity the following geometrical relationship can be derived:

δ : S1-S2 = O-P : P-Q.

When δ is exactly equal to an integer number of wavelengths, the arriving waves will constructively reinforce each other, and a maximum of light intensity will be observed at P. But when δ is exactly equal to an odd number of half-wave lengths, the waves will arrive at the screen with opposite phases. This causes destructive interference and therefore a minimum, which will be observed as a dark band. When P is the first observed maximum, counted from the central maximum in O in figure 3.4, δ must be equal to the wavelength: λ. This relationship can be used to measure and define λ very accurately.

From this moment in history, interference is among physicists the undisputed signature of a wave phenomenon. However, less than a century later, a major and paradoxical problem arose with this wave concept of light.

Did you note perhaps the logical error that is made here? The logical reasoning here is "If light is a wave, then we will see interference, so if we see interference, light is a wave." Which is the same logic as "If B follows from A, then A follows from B". I hope you agree with me that this is not strictly correct conform the rules of logic. As you will understand later, this rather loose logic will become the origin of the wave-particle paradox of light that emerges in the start of the 20^th century.

Please note: Thomas Young’s (1805) double-slit interference test has become a very basic experiment in the research and understanding of quantum phenomena in the twentieth century. In the following chapters you will encounter sophisticated adaptations of the double-slit experiment. It is therefore very important that you understand that interference is a wave phenomenon and how it comes about, which is the reason I have extensively covered this topic here.

A really good way to ensure your understanding of Young's experiment is by trying to explain the double-slit pattern and its conclusion to someone, if necessary, an imaginary person! Doing so is an excellent way to find out if you have really got the idea of double-slit interference right.

A DIY double-slit experiment with sound waves.

Ingredients:

A computer (Windows, Apple)

Two loudspeaker boxes

A tone generator program - free online: https://onlinetonegenerator.com/ ^[7]

Place the boxes approx. 3 feet apart and start the tone generator program. Choose a frequency between 1 and 5 kHz (Kilohertz). Start the tone generator. Stand about 4 feet away from the boxes and move to the left and then to the right, change the height of the tone if necessary. You will clearly discern the maxima and minima.

With this DIY experiment you will have demonstrated the wave character of sound by evoking maxima and minima of sound at certain locations. The maxima and minima of light in the double-slit experiment demonstrate the wave character of light in the same way.