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      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 neither do we experience the pressure variations as oscillations. But we are still able to visualize the propagating pressure variations in our imagination. However, trying to visualize oscillating magnetic and electric fields becomes rather difficult because those waves do not need matter for their propagation. We will see that EM-waves are more like clouds of unimaginable small particles of pure energy traveling through empty space with light speed.

      Note: The quantum wave is something that we never observe as a material wave. This will become important in the unmasking of the often-quoted particle-wave duality.

      Einstein's photons

      In 1905, in his Annus Mirabilis, Albert Einstein (1879-1955) published four extremely important physics articles, presenting explanatory theories concerning:

      In 1921 Einstein received the Nobel Prize for his explanation of the photoelectric effect. He based his theory on the photoelectric effect by applying a version of the Planck Black Body radiation law. He realized that he could treat the radiation within the hollow space of a Black Body emitter as if it was a gas of light particles ^[7]. His adaptation was based on the statistical derivation of the gas laws, formulated by Ludwig Boltzmann (1844-1906) in 1884. Boltzmann's statistical approach could be applied to Einstein's gas of light particles model with some slight adjustments.

      Boltzmann's classic statistical gas laws assumed enormous numbers of very small and fast-moving and colliding particles. Initially Boltzmann's statistical approach was not received favorably by many of his colleagues because, according to them, there was no place for chance and probabilities in Newtonian mechanics. Tragically, he did not experience the enormous success of his statistical approach. Boltzmann was manic-depressive. In 1906 he fell into a deep depression leading to suicide.

      Now for the problem that Einstein solved. The photoelectric effect is the phenomenon that, under the condition that the light frequencies are above certain limits, when light shines on a metal surface it will release electrons from the metal. This was in obvious contradiction with Maxwell's continuous EM-waves. The frequency of the light was the decisive prerequisite for the occurrence of the effect, not the total amount of its energy. So, for example red light - low frequency - did not release electrons, no matter how high the intensity of the red light was. Like when you cannot fill a glass from a tap with a wide opening, from which the water flows broadly with little force, but is filled easily from a narrow spout from which the water spouts with great force.

      Figure 4.3: Photoelectric effect. Red light photons have too little energy, 1.77 eV, to release an electron from the metal. Green light has just enough energy, 2.25 eV. Violet light has more than enough so that the electron shoots away with a kinetic energy of 3.1-2.25 eV = 0.85 eV. Source: Wikipedia.org

      The photoelectric effect begged for an explanation, but classical Newton physics - more specifically Maxwell's equations - could not provide an explanation. That is because any EM wave of any frequency could in principle provide enough energy if you applied it long enough.

      Einstein's solution ^[8] was that light had to be quantized in particles, later called photons , according to Planck's formula: E = h.f. The energy for each light particle had to be above a certain minimum value in order to be able to release an electron from the metal. Einstein's paper was therefore a wonderful confirmation of Planck's quantum hypothesis. A single photon with the right frequency - and therefore sufficient energy - could release one electron, a whole bunch of photons of a low frequency achieved nothing, although their combined energy would be more than sufficient. You could actually regard this as a certain rehabilitation for Newton's corpuscles theory, where each particle carries its own color - which is now its frequency. Photons are therefore to be considered as discrete energy packages.

      The physical significance of the frequency and wavelength of a photon was not clear, and this has not become clear until today. We cannot imagine a particle that is also a wave of a single frequency properly. It has been tried. Just try to visualize water waves on a lake that are concentrated in little blobs, each with its own frequency and energy. An impossible task for our imagination.

      How a spherical expanding electromagnetic Maxwell wave, whereby the energy also spreads out over the same spherical shape, becomes the very localized and precise energy transfer of the electromagnetic quantum, could not be explained by any means. The surface of the expanding sphere will increase with the square of the distance to the source. The energy per square inch of the wave will therefore decrease in an inverse square ratio to the distance from the source. To test this, just walk towards a bright light with a camera with the exposure setting in the A-mode (fixed aperture ^[9]) and observe the inverse quadratic relationship between distance and shutter speed.

      According to the very local discrete energy transfer, that is the photon, when it releases an electron in the photoelectric effect, this spherical distributed EM-wave would have to alter suddenly into a single discrete photon. This energy transfer per photon only depends on its frequency and not at all on

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