Some Fundamental Experiments
Some selected experiments are described in this chapter, both from the early days of quantum physics and from recent time, the interpretation of which is not possible on the basis of classical physics. The interpretation of these experiments requires novel unconventional ways of thinking because of the observed particle-wave duality. Special emphasis is laid on the photoelectric effect, the Compton effect, the diffraction of particle waves and the disappearance of interference patterns by gaining additional “Which Way” information about the particle path.
KeywordsInterference Pattern Pixel Detector Photoelectric Effect Compton Effect Double Slit Experiment
It is interesting to follow the development of today’s quantum physics by considering difficulties in the interpretation of important experimental results. In particular, around the end of the 19th and the beginning of the 20th century empirical facts accumulated which demonstrated the limits of interpretations on the basis of classical physics, Newton’s mechanics and Maxwell’s theory of electromagnetic fields. Such a historic approach is not intended in the present book. Instead, I want to select some few fundamental experiments, which indicate directly the peculiarities of atomic systems. The experiments are chosen such that they intuitively motivate the basic assumptions of quantum mechanics.
2.1 Photoelectric Effect
An explanation of these phenomena is obviously not possible on the basis of classical Maxwell’s electrodynamic theory, it became possible by means of Einstein’s light quantum hypothesis  (1905, Nobel prize 1921). In Einstein’s revolutionary new assumption light consists of small particles, the photons, which carry the energy ħω=hν. Energy can be transferred from the light beam to the metal only in portions of these quanta. Each electron which leaves the metal with an energy E el (2.1a) has taken over the energy of a photon. The intensity of a light beam with frequency ω is proportional to the number of photons with energy ħω in the beam. Thus, the emission current is also proportional to the number of photons. These assumptions consistently explain the photoelectric effect (Fig. 2.1).
2.2 Compton Effect
2.3 Diffraction of Massive Particles
While photoelectric and Compton effect can only be interpreted on the basis of the particle character of electromagnetic radiation, there are meanwhile numerous diffraction experiments (typical for waves) with all kinds of massive particle beams as electrons, neutrons, atoms, molecules etc. which doubtlessly demonstrate the wave-like propagation of these particles.
Diffraction intensity is thus expected on a cone with opening angle (π/2−ϑ) around the atom row along A and B. Since the arrangement of scattering atoms is 2-dimensional a second condition for constructive interference, analogously to (2.19), must be fulfilled in a direction normal to AB in the surface. The two conditions together limit the spatial range for constructive interference to only one direction, that is, the direction of a particular LEED reflex (bright spot in Fig. 2.5). The different diffraction spots in Fig. 2.5 belong to higher diffraction orders, that is, to different numbers n in (2.19) and the corresponding second equation. For the interpretation of a LEED pattern as in Fig. 2.5, one calculates the electron wavelength from the kinetic energy of the primary electrons, or respectively from the acceleration voltage according to (2.18a), (2.18b). By means of (2.19), the observation angle for a particular LEED reflex yields information about the interatomic distance, more accurately the periodicity interval, within the sample surface. LEED is meanwhile a standard analysis technique in surface science. Each LEED experiment, many times performed around the globe, demonstrates the wave character of propagating electrons.
All these experiments with particle beams demonstrate clearly and doubtlessly, that the propagation of massive particles as electrons, neutrons, molecules etc. must be described in terms of wave expansion. Otherwise, we could not understand the occurrence of diffraction and interference phenomena observed with these particles and which are used meanwhile worldwide in standard characterization and analysis techniques in solid state and surface physics. Present cutting edge research in this field aims at the physical limits for the observation of particle interference with bigger and bigger particles.
Interference patterns have already been observed even with Huge Bucky ball molecules cinsisting of 60 carbon atoms (C60). Experiments with viruses are on the way. The interesting question is, at what particle size is the quantum character lost and the particle starts to behave classically.
2.4 Particle Interference at the Double Slit
2.4.1 Double Slit Experiments with Electrons
Already in 1956, G. Möllenstedt and H. Düker performed a double slit experiment with electrons by means of a bi-prism . The bi-prism for electrons in this experiment consisted of a positively charged metallic filament arranged between two planar electrodes on ground potential (Fig. 2.8b). This set-up is incorporated into an electron microscope column, where an electron beam is focused in a focal point F (Fig. 2.8b). The double prism arrangement splits the electron beam into two partial beams, similarly as in the optical analogon, and deflects the two beams to the center again. The electric field of the positive filament is proportional to r −1 (r distance from filament). An electron passing the wire in close vicinity is strongly deflected horizontally, but only for a short time. An electron passing further away experiences a smaller force, but this for a longer time. The total deflection angle of the electrons in the field of the wire surprisingly depends only on the electron energy and not on the distance from the wire. Thus the two partial electron beams are focused and superimposed on a photosensitive screen behind. An interference pattern with bright and dark fringes is observed (Fig. 2.8c). Electrons with a fixed energy thus behave as light waves passing Fresnel’s bi-prism or Young’s double slit, a further demonstration of the wave character of electrons.
Electrons expand in space according to the laws of waves, they produce interference patterns, just as light does. But the interference fringes become visible only after the observation of a sufficiently large number of electrons. The observation of only 10 electrons which have passed the bi-prism (Fig. 2.9a) yields a random flash of one pixel somewhere on the screen. An interference pattern can not be recognized. Collecting 100, 3000, or 70,000 events of electrons which have passed the bi-prism builds up step by step the double slit interference pattern (Fig. 2.9d). Only for an ensemble with huge numbers of electrons the laws of wave propagation are valid. One single electron behaves randomly; totally unexpected and statistically the response of a pixel on the screen is caused by an impinging electron which transfers its kinetic energy to the point-like pixel detector.
It must be emphasized at this point that an electron–electron interaction can be excluded while the electrons pass the double prism arrangement to form the interference fringes. Two subsequent electrons do not “see” each other in space and time. The intensity of the electron beam current is so low that only after the detection of one electron in a pixel detector the next electron leaves the cathode of the microscope column.
Single electrons have the choice to take one or the other path—through this or the other slit—they are detected as point-like particles in a pixel detector, but randomly distributed over the screen. We do not know their individual history, but as an ensemble they build up the interference pattern without having information about each other. This particle-wave duality, which is absolutely counter-intuitive, weird in our imagination, is at the heart of quantum mechanics. Feynman  describes this behavior being apparent in the double slit experiment as “impossible, absolutely impossible to explain in any classical way, and has in it the heart of quantum mechanics”. We have to get familiar with the idea, that nature behaves completely different from our everyday experience on an atomic scale or below. For human beings, the natural length scale is that of centimeters and meters corresponding to the perception horizon in our macroscopic surrounding. It would be astonishing, on the other hand, if our sense organs and our brain, which have adapted during more than 100 million years of biological evolution to a macroscopic environment, could perceive the reality of the whole cosmos, the smallest and largest on subatomic and cosmological length scales. In these periods of adaptation it was much more important for human survival to correctly estimate the width of a creek or the distance between two branches of an arbor than the path of an electron. We should, therefore, not be surprised that the atomic and sub-atomic world as it appears in quantum physics is not accessible to our limited senses and imagination. We should, however, be surprised that mathematics opens the way to create an abstract picture of the atomic behavior which allows even quantitative predictions of experimental results. The most straightforward explanation is certainly that a structured reality does exist beyond human perception and imagination which obeys the laws of logic. Mathematics and logic obviously go beyond the reality accessible to our senses and enable the invention of theoretical systems as quantum theory which can correctly describe wide fields of reality extending much further than our meter and centimeter environment.
2.4.2 Particle Interference and “Which-Way” Information
The behavior of atomic and sub-atomic particles becomes even more strange when we ask the question through which particular slit has the particle moved in the double slit experiment (Sect. 2.4.1). Is this question for the detailed way of the particle compatible with the observation of the double slit interference pattern? Already in the early days of quantum mechanics, around 1920, this question was discussed extensively in gedanken (thought) experiments by Heisenberg, Einstein and others and later by Feynman . The essential conclusion of all these discussions always was that the interference pattern can only be observed without additional experiments to elucidate the detailed path (“which-way” information) of the particles. Every measurement of the detailed way, e.g. by scattering of a photon (see Compton effect, Sect. 2.2) in front of one of the two slits transfers so much momentum p=ħk to the electron that interference of the electron waves is not possible anymore, the fringe pattern is washed out due to phase shifts. According to the arguments of Heisenberg and Feynman the photon energy of the probing light can be decreased to such an extent that its effect on the electron is negligible. But simultaneously one has to increase the wavelength of the light, because of p=ħk=h/λ, to an amount which does not resolve the spatial distance between the two slits anymore. Microscopic imaging of a structural dimension d, namely, requires λ<d. In the gedanken experiment, the measurement of the detailed particle path requires a light wavelength λ<slit distance, which simultaneously is accompanied by a momentum transfer to the electron high enough to destroy the interference pattern.
A special property of this experiment is due to the fact that the diffracted Rb atoms are characterized, beside their spatial information, that is, the probability of being somewhere, also by internal degrees of freedom as spin excitations etc. We will be able to understand details of the described experiment only much later in this book (Sect. 8.2.4) after we have learnt a lot more about quantum theory. Nevertheless, it should be anticipated at this point, that irradiation of microwave radiation with a frequency of 3 GHz excites the Rb atoms into an excited state before entering the first diffraction grating (1st standing wave). A second microwave pulse irradiated after the splitting into the two partial beams B and C allows the distinction between the two possibilities if the interference pattern (beams D and E respectively, F and G) originates from an atom of the partial beam B or C.
In this experiment, the two beams of the double slit experiment are realized by the partial beams B and C. By means of microwave pulses before and after passing the first diffraction grating (1st standing light wave) one can distinguish between the ways B and C which could have been taken by the atom. It is easily estimated (Sect. 8.2.4) that a photon of 3 GHz microwave radiation can not transfer enough momentum to the relatively heavy Rb atom such that the interference pattern is washed out. Nevertheless switching on the microwave radiation as the measurement probe destroys the interference (Fig. 2.10c). Only a monotonous intensity background corresponding to the average Rb atom density in the beams D and E respectively, F and G is detected. This experimental result is found independently on the observation by a human experimentalist; only the read-out of the which-way information by the corresponding hard-ware probe is essential for the appearance or disappearance of the interference pattern.
What do we learn from this experiment? First, we see that not the human observer has an effect on the outcome of the interference experiment, only the switched on measurement probe for the which-way information is responsible for the destruction of the interference pattern.
Real world does not worry if it is observed by a human being (Realism instead of Idealism!). Furthermore, there must exist a correlation between the observed particle and the measurement probe, which can not be reduced to energy or momentum transfer between particle and measurement set-up. This phenomenon which is inherently of quantum mechanical character is typical for atomic and sub-atomic systems and beyond our macroscopic perception. It is called “entanglement” (Verschränkung in German, as Schrödinger called it), we will better understand what it means after having learnt more about quantum physics (Chap. 7).
- 4.L. de Broglie, C. R. Acad. Sci. Paris 177, 507 (1923) Google Scholar
- 8.G. Möllenstedt, H. Dücker, Z. Phys. 145, 366 (1956) Google Scholar
- 11.R.P. Feymann, R.B. Leighton, M. Sands, The Feymann Lectures on Physics—Quantum Mechanics (Addison-Wesley, Reading, 1965) Google Scholar