past and the future of the universe would be fully determined if classical physics would be right. It is at this moment in history that physics encounters a phenomenon that unquestionably shows that there had to be a false premise, hidden somewhere in her basic assumptions about nature. A paradox emerged, unwilling to leave. The idea of a quantized wave, of discrete packets of EM energy, could in no way be reconciled with Maxwell's EM-wave model. In such a position we have two options:
we either give up and decide that human imagination simply falls short and that we just have to accept the paradox,
or we decide to investigate our basic assumptions about reality to establish what could be wrong there.
In the end, Planck proved to be a courageous out-of-the-box thinker. In 1931 he demonstrated this by stating:
"I consider consciousness to be fundamental. I consider matter as derived from consciousness."
We will see later why this is a well-argued position. In my view Max Planck is the icon of the courageous scientist.
First, he followed his interest in physics going against the common stream.
Secondly, he was not satisfied with a mathematical expression that accurately predicted the observations but did not reveal its fundaments. He wanted to understand and therefore searched until he had found a way to derive his expression from basic principles. That he had to make uncomfortable assumptions did not stop him. He was willing to put aside his "how-it-is" idea. He ignored his cognitive dissonance.
Thirdly, because of his courage to come out with a result that would be received in the scientific world with disapproval and rejection. A risky action that seriously could have damaged his career. Just think how long it took for him to be awarded a Nobel prize for physics, 18 years.
Such scientists exist, but they seem to be in a minority.
By the way, Planck only supposed discrete energy transfer between the walls of the Black Body emitter. He did not theorize about speeding light particles (photons) as Einstein would do later in his publication of the photoelectric effect. As you will see later in this book, Einstein's light particles actually lead a very dubious existence.
4: The collapse of classical physics
"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality"
Albert Einstein, physicist 1879-1955
In this chapter we start with a more extensive treatment of the character and behavior of different types of waves - standing waves in particular- in different mediums, in order to understand that they all have very common characteristics. Before the end of the nineteenth century physicists were already very proficient in mathematics describing the behavior of every known type of wave. Applying their wave mathematics to the quantum world seemed an obvious choice and proved itself to become so highly apt for creating a quantum theory, that quantum physics would become the most successful and accurate physics theory in the 20th century.
But before quantum theory was firmly established many questions concerning the atom and its behavior had to be solved. And every inspired solution seemed to generate more questions than it had solved. Newtonian physics seemed poised to slide away into unpredictable depths.
Einstein used Planck's idea of discrete energy packets to solve the riddle as to why only light above certain frequencies could free electrons from metal and was awarded a Nobel prize. His solution was however in paradoxical contradiction with Maxwell's EM-waves. Louis De Broglie, a French prince, suggested standing electron waves around the atom nucleus, which was later confirmed, serendipitously, by electron interference. But how is it possible for an electron be a particle and a wave at the same time? Is it possible to reconcile these disparate views?
Waves
From the introduction of Maxwell's equations for electromagnetic waves, three major different types of waves [1] were distinguished in classical physics. For understanding the quantum physical wave phenomena that will be discussed in the coming chapters it is a good idea to delve a little bit deeper into the subject of waves at this point as wave behavior plays an extremely important role in quantum physics.
Surface waves propagate in liquids. The movement of the particles in waves traveling along the liquid surface is more or less perpendicular to the surface. The particles move only slightly back and forth in the propagation direction of the wave. The wave transports no liquid in the direction of propagation. This type of wave is easy to recognize visually. It is also easy to generate them, throwing a pebble in a pond is sufficient. In figure 4.1 the movement of the liquid particles is indicated by ellipses. The deeper under the surface, the smaller the ellipses, the less the liquid moves. A diver will notice this when swimming a little below the troubled surface. Every fluid particle - including the ones at the top - moves actually not far from its equilibrium position. Surface waves that intersect with each other exhibit superposition and interference, they reinforce or weaken each other for a moment and then simply roll on again.
Figure 4.1: The movement of particles in a liquid transporting a surface wave.
Source: Mpasternak on Wikimedia Commons.
Sound waves are propagations [2] of pressure fluctuations occurring in gases, liquids and solids. Their constituent particles - atoms or molecules - oscillate in the same direction as the propagation of the wave. The superposition principle also applies to sound waves, so they will also show interference. Interference of sound waves with slightly differing frequencies, will be experienced as overtones. Sound waves are not experienced as oscillations but as tones. Healthy, young ears can experience sound frequencies between 20 Hz and 20,000 Hz (Hertz: the number of complete oscillations per second).
Figure 4.2: A sound wave. Propagating compression variations.
Source: Pluke on Wikimedia Commons
Electromagnetic waves consist of varying electric and magnetic fields aligned perpendicular to the wave direction and also perpendicular to each other. See figure 3.7. We experience electromagnetic waves between 400 THz and 790 THz (Terahertz: 1 THz = 1,000,000,000,000 Hz) as light. We do not experience the wave behavior of light as oscillations but as colors. EM-waves also exhibit interference and superposition.
Modern physics has also identified other types of waves, e.g. gravity waves and quantum waves; we will deal extensively with those quantum waves in the following chapters. For gravitational waves I have to refer you to other literature.
All these types of waves exhibit refraction, which occurs when a wave propagates into another, slower, medium at an oblique angle with the boundary. Note that the level of abstraction increases in the above-mentioned order - liquid, sound and EM-waves. It is easy for us to see the everyday occurrence of waves on water. We hear sound waves, but we do not see them
