Wave-particle dualism

The wave-particle dualism is a finding in quantum physics , according to which the properties of classical waves as well as those of classical particles must be ascribed to the objects of quantum physics . Classic waves spread out in space. They weaken or strengthen each other through overlapping and can be present in different places at the same time and have different effects. A classical particle can only be present in one specific place at a time. Both properties seem to be mutually exclusive. Nevertheless, several key experiments for various quantum objects have shown that both properties are present, so that a matter wave is ascribed to each body .

The question of whether electrons or light quanta are particles or waves cannot be answered. Rather , they are quantum objects that show different properties depending on the type of measurement that is carried out on them. This problem was initially solved in quantum mechanics in the Copenhagen Interpretation (1927) with the principle of complementarity formulated there in such a way that the definition of the property observed in each case should not only be assigned to the quantum object, but rather represent a phenomenon of the entire arrangement of quantum object and measuring apparatus. A number of other interpretations of quantum mechanics with alternative explanatory approaches emerged later .

The wave-particle dualism does not appear in the everyday world, because the wavelength of the matter wave in macroscopic bodies is much too small to cause phenomena that can only be explained clearly with wave-like behavior. At very small wavelengths, the wave image and the particle image agree in their observable consequences despite the different approaches, as was known earlier from the relationship between ray optics and wave optics . On the other hand, the wave-particle dualism is by no means restricted to the smallest quantum objects. It has already been demonstrated in experiments for large molecules made up of over 800 atoms.

The quantum field theory understands both particles and interactions as a discrete input from fields. There is thus no difference between these two categories on the formal level. However, the problem remains that the two opposing images apply here.

history

The prehistory of the discovery of the wave-particle dualism in electromagnetic radiation goes back to the 17th century, when the laws of geometric optics for the reflection and refraction of light rays were explored in more detail. This resulted in two competing theories:

Christiaan Huygens (1629–1695) was able to interpret the laws of optics with the help of the wave concept and is therefore considered the founder of wave optics . The Huygens principle developed by him is still used unchanged today.

Isaac Newton (1643–1727) interpreted the same laws using the corpuscle concept , according to which light represents a stream of fast, light particles.

Both theories agreed equally well with the observations of the time, although their starting points appeared incompatible. In the absence of experimental possibilities of differentiation, the corpuscle theory initially prevailed, mainly thanks to Newton's greater authority. But in 1802 Thomas Young demonstrated the wave character of light. With the double slit experiment , Young demonstrated that light can be extinguished by interference , which is unthinkable for particle beams. The wave nature of light was not generally recognized until late in the 19th century, after further discoveries had been made that did not fit the corpuscle theory: polarization ( François Arago et al.), Diffraction (theoretical prediction by Augustin Jean Fresnel , inter alia experimental proof of the Poisson spot by Arago 1821), lower speed of propagation in optically denser media ( Léon Foucault 1853), the connection between the speed of light and electrodynamics ( James C. Maxwell 1867) and electromagnetic waves ( Heinrich Hertz 1886).

In 1900 Max Planck discovered during the analysis of the thermodynamic equilibrium between the electromagnetic waves of thermal radiation and the surrounding walls that the energy transfer between radiation and matter was only in quanta of size

{\ displaystyle E = hf}

can take place ( Planck's quantum of action , frequency of the wave). Planck first assumed a quantization of energy values of the harmonic oscillator (see quantum hypothesis ). This was initially done purely for mathematical reasons. ${\ displaystyle h}$ ${\ displaystyle f}$

In 1905 Albert Einstein proved that even with the photoelectric effect, the energy transfer to the electrons cannot be explained by light waves, but by light quanta with the energy specified by Planck.

{\ displaystyle E = h \, f = h \, {\ frac {c} {\ lambda}}}

where are the speed of light and the wavelength of the photon. This relationship also applies to mechanical waves, such as lattice vibrations in a solid . The quanta in this case are called phonons . ${\ displaystyle c}$ ${\ displaystyle \ lambda}$

Finally, Einstein showed in 1909 that the thermal radiation must show statistical fluctuations, the size of which can only be interpreted by the fact that the radiation itself consists of waves and quanta. He called for the development of a theory in which radiation has both particle and wave character, and is therefore considered to be the originator of the principle of wave-particle dualism. However, he mistakenly suspected the solution in the direction that the constantly changing electromagnetic wave would arise from the superposition of the fields of many closely spaced “singular points”. Other well-known physicists, including Max Planck and Niels Bohr , also doubted that all properties of a particle should be ascribed to the photon. This knowledge only became generally accepted with the discovery of the Compton effect and its interpretation as an elastic collision between a quantum of electromagnetic radiation and an electron by Arthur Compton in 1922.

Louis de Broglie postulated in 1924 that particles with mass also have a wave character. He gave a wavelength of for a particle with momentum ${\ displaystyle p}$ ${\ displaystyle \ lambda}$

{\ displaystyle \ lambda = {\ frac {h} {p}}}

on. With the help of de Broglie formula a diffraction behavior could be predicted by particle which experimentally by diffraction of an electron beam over a nickel crystal by 1927 Davisson and Germer , and finally by the electron double-slit experiment of Claus Jönsson was confirmed in 1961st The wave character of matter has now been proven by interference experiments for much larger particles, for example complex molecules such as fullerenes .

The double slit experiment

Experimental setup of the double slit experiment (schematic)

Results of the double slit test

Fig. 1: Diffraction pattern of a classic wave at a double slit (computer simulation)

Fig. 2: Distribution of classical particles (computer simulation)

$Electron diffraction double slit rendered.png$

Fig. 3: Computer simulation: diffraction patterns of quantum objects (e.g. electrons)

Fig. 4: Experimental results with different numbers of electrons

The behavior of quantum objects in the so-called double slit experiment is particularly impressive. With this experiment, Thomas Young was able to demonstrate the wave nature of light for the first time. The corpuscle theory , which goes back to Newton, initially seemed to be refuted.

Experimental setup

“Rays” emanate from a source - these can be electromagnetic waves or particles of matter - and hit a diaphragm with two very fine, closely spaced slits. This diaphragm is called a " double slit ". There is a screen behind the panel. The rays that pass through the double slit hit the screen and are registered there in a suitable manner.

Classic waves

If the rays are classic waves, they show a typical diffraction pattern , as can be seen in Figure 1 on the right: Depending on the wavelength of the radiation and the geometry of the double slit, areas on the screen appear light or dark in stripes. The brightest spots are where the two elementary waves emanating from the double slit show a path difference that is an integral multiple of the wavelength, because then the two waves are "in phase" and interfere constructively. In the middle between two such places, the two waves are out of phase and cancel each other out through destructive interference.

Apart from its strip-like structure, the diffraction pattern appears continuous. The brightness in a place can assume any value between complete darkness and maximum lighting.

Classic particles

Classical particles (i.e. individual mass points ) show no interference (see Figure 2). You get through either the left or the right slit and then hit the screen within a clearly defined area. As a result, exactly two light stripes appear on the screen (one for each of the two columns). On closer inspection, the grainy structure of the two stripes is noticeable. Each particle hits exactly one point and leaves a bright spot there. There is no continuous brightness curve. A location is marked either lightly or darkly, because either it was hit by a particle or not.

Quantum objects

The objects of quantum physics, on the other hand, behave as shown in the third and fourth figures: As with classical waves, the intensity distribution on the screen shows a typical diffraction pattern. So there must be interference. On the other hand, the intensity curve is not continuous. Bright points appear, but with different densities. Each quantum object can therefore (at least retrospectively) be assigned a specific location where it hit the screen. It is therefore clearly a countable, point-shaped object.

discussion

The quantum objects obviously show properties of both classical models: They interfere with each other, which is typical for waves. On the other hand, they are countable and point-like, which completely contradicts the wave nature and rather points to a particle nature. It is not possible to modify one of the two models without contradiction in such a way that it could explain all aspects of the test result. For example, a particle can only pass through one of the two slits, but not through both at the same time. If you alternately cover one of the two slits, you get the distribution of particles that have passed through either the right or the left slit. This corresponds approximately to the distribution from Figure 2 if one ignores the diffraction phenomena at the edges that always occur with quantum objects. If you open both columns again, the diffraction pattern from Figure 3 or 4 appears. It follows that the distribution pattern of the quantum objects on the screen cannot be explained if one assumes that the individual quantum object either goes through one of them or through takes the other gap. Nevertheless, they must be individual, indivisible, point-like particles, because as such they are registered spatially and temporally separated from each other on the screen, as can be seen particularly clearly in Fig. 4 (b). The idea of a spatially extended wave that can pass through both gaps at the same time and then interfere with itself is therefore just as wrong.

Quantum objects show a behavior that cannot be satisfactorily explained with either the classical wave picture or the classical particle picture.

Key experiments

Initially, the wave-particle dualism was based on studies on the spectrum of thermal radiation ( Planck ), the photoelectric effect and statistical fluctuations in thermal radiation ( Einstein ) and theoretical considerations on the possibility of the matter wave ( de Broglie ). So it was discovered indirectly, but played a central role in wave mechanics ( Schrödinger ). Therefore, the aim of further experiments was to test the wave-particle dualism in a much more direct way.

Compton effect

Arthur Compton was able to prove in 1923 that electromagnetic waves, when scattered by electrons, behave in exactly the same way as a stream of individual particles that have the energy and momentum of a photon and perform an elastic collision with an electron. With this, Compton convincingly demonstrated the particle character of the quanta of the X-rays in the experiment, using, of all things, their wave character. This was used to determine the wavelength of each scattered photon before and after the collision in the same apparatus by means of an interference phenomenon, namely Bragg diffraction on a crystal. In 1925 Compton was also able to show that the pushed electron flies away at the same time as a scattered photon, which has the appropriate energy for the deflection angle. Other explanations were thus refuted.

Electron diffraction on the crystal lattice

In 1927, Clinton Davisson and Lester Germer were able to show that a beam of electrons is partially reflected back from a crystal surface without any loss of energy and then shows interference phenomena such as X-rays in Bragg diffraction. Physically, this can only be described with the propagation of each electron in the form of a wave. That the electrons are also particles, on the other hand, becomes clear in the same experiment in the fact that another part of the incident electrons had each elastically collided with an electron in the crystal and thereby lost energy. The electrons scattered in this way do not form an interference pattern. They are now incoherent due to the accidental release of energy .

Interference from larger molecules

In order to clarify whether the wave-particle dualism only applies to elementary particles such as photons and electrons or also to composite systems, atoms and molecules were examined. Corresponding interference patterns were first detected in 1930 by Immanuel Estermann and Otto Stern with H ₂ molecules after reflection on a crystal surface of LiF. They corresponded exactly to the matter waves predicted for the molecules. On the way to particles with ever greater mass, it was possible in 1999 in Vienna to generate interference patterns on C ₆₀ . These molecules, also known as "buckyballs", consist of 60 carbon atoms, which are put together in the shape of a soccer ball and contain a total of 360 protons, 360 neutrons and 360 electrons. They are around 1 nm in size and can easily be seen under the scanning tunneling microscope as small “lumps of matter”. Its de Broglie wavelength was around 3 pm and was thus four to five orders of magnitude smaller than the lattice constant of 100 nm - the smallest technically feasible at present. The interference maxima on the screen at a distance of about 1 m were therefore only 0.03 mm apart. In the diffraction experiment, the particle character of the buckyballs was also made clear by the fact that they were counted individually after passing through the diffraction grating. The largest molecule with which such diffraction patterns could be generated up to 2016 is meso-tetra (pentafluorophenyl) porphyrin (TPPF20, C ₂₈₄ H ₁₉₀ F ₃₂₀ N ₄ S ₁₂ ) with a molecular mass of 10123 amu.

Recent experiments

In 2005, Parisian physicists working with Yves Couder developed a macroscopic system for testing de Broglie's approach using an oil droplet experiment. Oil droplets surfing on the waves of an oil bath could show quantum-like behaviors. “For example, they only followed certain“ quantized ”paths that ran around the center of the liquid baths. And sometimes the droplets jumped randomly back and forth between the orbits, much like electrons do in atoms. ”However, new experiments from 2015 indicate that Couder's demonstration of quantum-like phenomena does not withstand the strict conditions of the double-slit experiment. At the same time, these experiments also bring down de Broglie's pilot wave theory. If one inserts a partition wall perpendicular to the gaps, which separates the pilot wave or the particles that will pass one or the other gap, well before it passes through, the particles “lose contact with the pilot wave on the other side of the barrier placed perpendicular to the screen. Without contact with the particle or oil droplet, however, the wavefront quickly runs out of breath; it comes to a standstill long before it reaches the gap. ”As a result, an interference pattern can no longer form behind the double gap.

Dissolution of the wave-particle dualism in quantum mechanics

In quantum mechanics, every particle is described by a wave function . The wave function of a particle is complex and therefore not a measurable quantity . Only its square of the magnitude can be interpreted as the probability of the particle's location (more precisely: as the volume density of the probability of location) and determined in the experiment. The temporal development of the wave function of the particle and thus the change in its probability of being located is described by the Schrödinger equation.

Quantum mechanics and statistical physics

On the microscopic level, the wave-particle dualism serves as a heuristic explanation for some physical phenomena. According to de Broglie, the wavelength of a particle depends on its speed and thus also on its temperature. At low temperatures, the De Broglie wavelengths of atoms can become larger than the atomic diameter and overlap, which partly explains the effects of the superfluidity of helium- 3 and helium-4. For a complete and quantitative treatment of these topics, however, quantum mechanics must be used.

Macroscopic observation

The wave character of the particles is not evident in macroscopic objects, which has two principal causes:

Even when moving slowly, macroscopic objects have, due to their large mass, a wavelength that is considerably smaller than the dimensions of the object. In this case one can no longer treat the entire object as a quantum mechanical object, but rather has to describe its components separately.
In macroscopic objects there are permanent thermodynamically irreversible processes and photons (thermal radiation) are exchanged with the environment. Both of these lead to the decoherence of the system, which means that a state that may initially be capable of interference changes very quickly into a non-interfering state, which then behaves like a classic particle, i.e. not like a wave.

Application example X-ray spectroscopy

In X-ray spectroscopy , the properties of the characteristic X-ray radiation are used. The X-ray spectrum of a substance provides information about the internal structure of its atoms and can therefore be used for analysis. The measurement can either be wavelength or energy dispersive . In the energy-dispersive method, the energies of the individual photons are determined directly (in the classical language a “particle property”), from which the atomic energy levels can be calculated. For the same purpose, however, one can also measure the wavelength of the X-rays (a “wave property”). Both - energy and wavelength - are characteristic properties of X-ray quanta, which consequently can neither be classical waves nor classical particles.

literature

Wilhelm Westphal, Dictionary of Physics , Berlin - Göttingen - Heidelberg, 1952
Karl Mütze (Ed.): ABC of Optics , Leipzig 1961
Richard Feynman QED - The Strange Theory of Light and Matter (Original: QED - The Strange Theory of Light And Matter , Princeton 1985) - A popular science introduction to quantum electrodynamics

Individual evidence

↑ Albert Einstein: On the development of our views on the nature and constitution of radiation , in: 81st Assembly of German Natural Scientists and Doctors in Salzburg, 1909
↑ Jörn Bleck-Neuhaus: Elementary Particles. From the atoms to the standard model to the Higgs boson . 2nd Edition. Springer, Heidelberg 2013, ISBN 978-3-642-32578-6 , doi : 10.1007 / 978-3-642-32579-3 . Cape. 6.4.3
↑ Arthur H. Compton: A Quantum Theory of the Scattering of X-rays by Light Elements . In: Phys. Rev . tape 21 , 1923, pp. 483-502 .
↑ Davisson, C. and Germer, LH: Diffraction of Electrons by a Crystal of Nickel . In: Phys. Rev . tape 30 , 1927, pp. 705-740 .
↑ Markus Arndt, Olaf Nairz, Julian Vos-Andreae, Claudia Keller, Gerbrand van der Zouw and Anton Zeilinger: Wave-particle duality of C60 molecules . In: Nature . tape 401 , no. 6754 , October 14, 1999, ISSN 0028-0836 , p. 680–682 , doi : 10.1038 / 44348 ( nature.com [accessed October 4, 2016]).
↑ Thomas Juffmann, Stefan Truppe, Philipp Geyer, András G. Major, Sarayut Deachapunya, Hendrik Ulbricht, and Markus Arndt: Wave and Particle in Molecular Interference Lithography . In: Physical Review Letters . tape 103 , no. 26 , December 29, 2009, pp. 263601 , doi : 10.1103 / PhysRevLett.103.263601 .
↑ Immanuel Estermann, Otto Stern: Diffraction of molecular beams . In: Journal of Physics . tape 61 , 1930, p. 95-125 .
↑ Olaf Nairz, Markus Arndt, Anton Zeilinger: Quantum interference experiments with large molecules . In: American Journal of Physics . tape 71 , 2003, p. 319 , doi : 10.1119 / 1.1531580 .
↑ Christian Brand, Sandra Eibenberger, Ugur Sezer, Markus Arndt: Matter-wave physics with nanoparticles and biomolecules . In: Les Houches Summer School, Session CVII – Current Trends in Atomic Physics . 2016, p. 13 ( online [PDF; accessed March 13, 2019]).
↑ Natalie Wolchover: Oil droplet experiment: Out for analog quantum theory . In: Spektrum.de . February 21, 2019 ( Spektrum.de [accessed February 27, 2019]).

[Einstein1909-1] Albert Einstein: On the development of our views on the nature and constitution of radiation , in: 81st Assembly of German Natural Scientists and Doctors in Salzburg, 1909

[2] Jörn Bleck-Neuhaus: Elementary Particles. From the atoms to the standard model to the Higgs boson . 2nd Edition. Springer, Heidelberg 2013, ISBN 978-3-642-32578-6 , doi : 10.1007 / 978-3-642-32579-3 . Cape. 6.4.3

[3] Arthur H. Compton: A Quantum Theory of the Scattering of X-rays by Light Elements . In: Phys. Rev . tape 21 , 1923, pp. 483-502 .

[4] Davisson, C. and Germer, LH: Diffraction of Electrons by a Crystal of Nickel . In: Phys. Rev . tape 30 , 1927, pp. 705-740 .

[5] Markus Arndt, Olaf Nairz, Julian Vos-Andreae, Claudia Keller, Gerbrand van der Zouw and Anton Zeilinger: Wave-particle duality of C60 molecules . In: Nature . tape 401 , no. 6754 , October 14, 1999, ISSN 0028-0836 , p. 680–682 , doi : 10.1038 / 44348 ( nature.com [accessed October 4, 2016]).

[6] Thomas Juffmann, Stefan Truppe, Philipp Geyer, András G. Major, Sarayut Deachapunya, Hendrik Ulbricht, and Markus Arndt: Wave and Particle in Molecular Interference Lithography . In: Physical Review Letters . tape 103 , no. 26 , December 29, 2009, pp. 263601 , doi : 10.1103 / PhysRevLett.103.263601 .

[7] Immanuel Estermann, Otto Stern: Diffraction of molecular beams . In: Journal of Physics . tape 61 , 1930, p. 95-125 .

[8] Olaf Nairz, Markus Arndt, Anton Zeilinger: Quantum interference experiments with large molecules . In: American Journal of Physics . tape 71 , 2003, p. 319 , doi : 10.1119 / 1.1531580 .

[9] Christian Brand, Sandra Eibenberger, Ugur Sezer, Markus Arndt: Matter-wave physics with nanoparticles and biomolecules . In: Les Houches Summer School, Session CVII – Current Trends in Atomic Physics . 2016, p. 13 ( online [PDF; accessed March 13, 2019]).

[10] Natalie Wolchover: Oil droplet experiment: Out for analog quantum theory . In: Spektrum.de . February 21, 2019 ( Spektrum.de [accessed February 27, 2019]).