Quantum Physics is not Weird. On the Contrary.. Paul J. van Leeuwen
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 shows the oscillation of a single point in time. Think of a fishing float going up and down with waves coming from two different sources. The horizontal axis is the time line of 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 that 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 important in understanding the double-slit experiments we will encounter repeatedly 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, shows the geometric approach taken for explaining the interference effect by considering path length differences.
Please note: the distance O-Q of the double-slit to the screen, as compared with the distance between the slits S1-S2, is depicted here considerably smaller than it is in a real experimental set-up.
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 follows the geometrical relationship:
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 appear 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, counting from the central maximum in O in figure 3.4, δ has to be equal to the wavelength: λ. This can be used to measure 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.
Do you see 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 source of the wave particle paradox of light emerging in the start of the 20th century.
Please note here: 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 really important for you to 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 exactly the same way.
Fields, electromagnetic waves
Nowadays everybody agrees that light is an electromagnetic wave phenomenon. How did we discover this? From ancient times we were already familiar with electrical and magnetic phenomena. De term 'electricity' is said to be derived from electrum, the Latin name for amber. Rubbing amber with a woolen piece of cloth evokes small sparks. We discovered two types of electrical charges. Similarly charged objects repelled each other and dissimilar ones attracted each other. Magnetic compasses were used in navigation.
It turned out in the 18th century that applying the same mathematical methods as with Newton's gravity mechanics, one was able to calculate the dynamic behavior of objects with attracting or repelling electric charges or with magnetic properties. The mathematical tools that Newton had laid down for gravity could be applied in the same way to the electrical attraction between two charged objects. The electrical or magnetic force is, just like gravity, inversely proportional to the square of the mutual distance and directly proportional to the product of the two electrical or magnetic charges. However, when one wanted to calculate with these methods the simultaneous behavior of more than two charged objects, mathematical problems arose. Exact mathematical tools are simply not available for multiple body interactions. In those early days one had to make do with approximative methods and calculations with pen and paper. Nowadays we use computers for more accurate approximations.
To simplify the multiple body calculation problem, the field concept was developed. A good approximation of the behavior of more than two attracting or repelling bodies was found by assigning to every location in the empty space around an electric or magnetic charge a field vector property. A vector is a mathematical object representing a both magnitude and direction. An electric field vector [8] represents the direction and the magnitude of the force that an electric unit charge would experience in that location of space. The same principle applies for a magnetic field vector [9]. Assigning these mathematical vectors to every location in space around a charge, defines thus the electric or magnetic field of that charge. Ask yourself now if you think that such a field is an objective tangible thing.
Figure 3.5: Electric field lines.