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In this chapter we review the main experimental results showing the dual behaviour of light. In the last section the concept of probability amplitude playing a keyrole in quantummechanics is introduced
Elements of classical mechanics, interference of light. Elements of calculus and probability theory. The concept of probability distribution.
The nature of light, whether it consists of corpuscles or is it a wave of an unidentified medium, called ether, intrigued scientists for a long time before the beginning of the 20th century, and there was a long standing dispute between the two views. A seemingly final solution came along with the numerous interference experiments in the beginning of the 19th century performed by Thomas Young, Augustine Fresnel and others, which had shown the wave nature of light. Here we present the double slit experiment of Young. It is interesting that about a 100 years later in 1909 Geoffrey Taylor repeated the experiment with a very weak beam that resulted in the same fringes after a sufficiently long time.
It turned out however, that nature is more complicated than simple man’s imagination. The first step towards a deeper understanding of what light is was done by Max Planck in 1900. In order to explain correctly the spectral distribution of radiation emitted from a hot body like the sun, or a heated piece of iron, he had to assume that light waves emerging from the body took up energy from it in quanta . The smallest amount of quantum is determined by the frequency \( \nu \) of the emitted light and a universal constant h so that a single quantum has
energy, where the requirement to be in agreement with the experimental observations determined the value of
called the Planck constant. This is an extremely small value therefore even for visible light the energy of a single quantum is only of the order of 10 − 19 J, that is why we do not observe this granular property of light.
The next fundamental step was when A. Einstein extended Planck’s ideas to the explanation of the photoelectric effect discovered by Hallwachs and Stoletov and studied in detail by P. Lenard and Herz. If light falls on the surface of a metal, it becomes positively charged. The reason for this is that electrons i.e. negatively charged particles called photoelectrons are emitted from the surface of the metal. On the details of this phenomenon we refer here to courses of experimental physics. The observations were explained by Einstein, by the assumption that the electrons in the metal absorb the energy of the light field in quanta. Following the idea of Planck, Einstein assumed that the energy of a single light quantum is
where \( \nu \) is the frequency of the light, h is Planck’s constant. A frequently used notation is
and with the angular frequency \( \omega=2 \pi \nu \) we can write Einstein’s relation as
which is used more often is theoretical physics. The energy quantum of light obtained the name photon . The kinetic energy of the emitted electrons is given by the following equation:
where W a – called “work function” – is the energy needed to extract the electron from the metal, which is characteristic for the metal. If \( h \nu \) is smaller than W a , there is no electron emission. For alkaline metals Na, Cs even visible light shows the effect, while for most metals the threshold frequency determined by \( h \nu_{t}=W_{a} \) falls into the ultraviolet region.
The assumptions of Einstein were proven exactly later by experiments of Millikan in the photoelectric effect. The value of E kin can be determined by the countervoltage U 0 given to the electrode registering the electrons. The value of q 0 U 0 – where q 0 is the electron’s charge – that stops the electrons gives W a . Eq. (1.6) is Einstein’s photoelectric equation, which can be proven plotting U 0 versus the light frequency \( \nu \).
The photoelectric effect can be investigated with this simulation. A virtual experiment can be performed to determine the Planck-constant and the “work function” W a .
According to Einstein the photons must posses not only energy but momentum, as well: A light quantum with frequency \( \nu \), whose wavelength in vacuum is \( \lambda=c / \nu \), has momentum
\( \mathbf{p}=\frac{h \nu}{c} \hat{\mathbf{k}}=\frac{h}{\lambda} \hat{\mathbf{k}}=\hbar \mathbf{k} \) (1.7)
where k̂ is a unit vector pointing in the direction of the propagation of light field which is assumed to be a monochromatic plane wave, \( \mathbf{k}=k \hat{\mathbf{k}} \) is the vector called wave-number with absolute value \( k=2 \pi / \lambda \). This value of p is in accordance with the fundamental relation of relativity, valid for any particle of rest mass m 0 :
assuming that the photon’s rest mass is m 0 =0.
Among the several evidences of the photon hypothesis a very important one is the Compton effect, which is seen in figure 1.4. In this experiment, performed by Arthur Compton, an X ray of wavelength \(\lambda_{0}\) falls on a sample and ejects electrons from it. There appear also a secondary X ray, whose wavelength \(\lambda_{s}\) and direction, given by the angle φ is different from the original one. These can be measured by the experiment shown in the figure 1.4.
We can consider the effect as the scattering of the photon on the electron where both of them are classical point-like objects. The conservation of energy and momentum requires:
\(\begin{aligned} h \nu_{0}+E_{0} &=h \nu_{s}+E_{e} \\ \frac{h \nu_{0}}{c} &=\frac{h \nu_{s}}{c} \cos \varphi+p_{e} \cos \vartheta \\ 0 &=\frac{h \nu_{s}}{c} \sin \varphi-p_{e} \sin \vartheta \end{aligned}\) (1.9)
Here \(E_{0}=m_{e} c^{2}\) is the rest energy of the electron, \(E_{e}\) and \(p_{e}\) are the energy and momentum of the electron after the collision
\(E_{e}=\frac{m_{e} c^{2}}{\sqrt{1-v^{2} / c^{2}}}, \quad p_{e}=\frac{m_{e} v}{\sqrt{1-v^{2} / c^{2}}}\) (1.10)
according to the relativistic formulas.
Both of them are treated as classical point-like objects From the three equations above, and using \( \nu=c / \lambda \) we get with some algebra the result
(Strictly speaking the result is valid for free electrons in rest. In the experiments the electrons are set free from atoms, where they have some negative binding energy, but this can be neglected compared to other energies occurring here.) The expression above connects the change of the wavelength of the X ray photon during the scattering and the scattering angle φ. Compton’s experiments approved the theoretical result. The length
is called the Compton wavelength of the electron. Note that sometimes the value \(\tilde{\lambda}_{C}=\frac{\hbar}{m_{e} c}=\frac{\lambda_{C}}{2 \pi}\) is called the Compton wavelength.
Study the Compton effect with the animation on the page and answer the questions appearing there.
According to these experiments the electromagnetic field can manifest itself of being of discrete nature, and for a given frequency and direction of propagation, it interacts as a particle with atomic matter with the corresponding energy and momentum.
After the photon hypothesis had proven to be true, many physicists tried to reconcile the two views, how it is possible that light behaves as a kind of a wave, whereas it consists of quanta or particles that have energy and momentum. While these attempts were not successful, another view emerged. L. de Broglie a French physicist set up the hypothesis that perhaps the behaviour of the electrons in atoms can be explained, if one assumes that electrons – that were known to be massive particles and possessing well defined negative charge – might also behave like waves. Later on, this assumption was proven experimentally by G. P. Thomson, and independently by Davisson. The property that an electron just like photons can behave either as a particle or as a wave is called duality. This very unexpected property was resolved by Max Born in 1926 by purely theoretical arguments. But before explaining Born’s idea, let us turn to an experiment revealing explicitly the duality property. This is the famous double slit experiment – one of the most interesting experiments in physics – first performed with electrons by Clauss Jönsson in 1961 and popularized later by Akira Tonomura.
The experiment seen in Fig. 1.6 was first performed by Clauss Jönsson in 1961. A famous variant of the experiment was done by Akira Tonomura, he made the result visibly available, the video of which is shown here.
Looking at the experiment in more detail, it turns out that the picture is formed by individual pointlike impacts of particles, as it is seen in the sequence of figure 1.6. A result definitely different from the case of water waves.
This extraordinarily surprising phenomenon can be explained with the fundamental concept of quantum mechanics: called the probability amplitude . We shall consider only one of the coordinates, the x coordinate which is perpendicular to the fringes seen on the screen where the particles are detected. We do not know exactly what was the state of the particle before arriving at the screen. This state will be denoted by \(\psi\). But we know that after falling on the screen we realize that it is at a place say x 1 . This event will be characterized by a complex number to be denoted by \(\left\langle x_{1} \mid \psi\right\rangle\). So to each x we attribute a complex number \(\left\langle x \mid \psi\right\rangle\). Considering all the possible x values we get a function of x , which is a complex valued function of the real variable – the position of the particle – x :
This function will be used to characterize the state of the particle, and this function is called the coordinate wave function . The important law of quantum mechanics is that the probability of finding the particle around x in a small interval dx is \(|\psi(x)|^{2} d x\). In the language of probability theory, \(|\psi(x)|^{2}\) is the probability density function of the coordinate of the particle which is a random variable. So we have
\(|\langle x \mid \psi\rangle|^{2}=|\psi(x)|^{2}=\psi^{*}(x) \psi(x)=: \rho(x) \geq 0\) (1.14)
In quantum mechanics we use the notation \(\rho(x)\) for the probability distribution. The probability of finding it at a point x in the interval \(x_{1}<x<x_{2}\) is given by:
\(P\left(x_{1}<x<x_{2}\right)=\int_{x_{1}}^{x_{2}}|\psi(x)|^{2} d x=\int_{x_{1}}^{x_{2}} \rho(x) d x\) (1.15)
which is valid for arbitrary \(x_{1}<x_{2}\). The probability of finding the particle somewhere on the real axis must be 1, therefore:
\(\int_{-\infty}^{\infty} \rho(x) d x=\int_{-\infty}^{\infty}|\psi(x)|^{2} d x=1\) (1.16)
Accordingly the wave function describing a particle must be such that the integral of its absolute value square between −∞ and ∞ should give 1.
The interference pattern seen in Fig 1.6 can be explained by the rules of quantum mechanics, as we shall do it in the following. The particle which was assumed to be in a state ψψ can arrive to the first slit on the screen, and this state, i.e. particle in the first slit will be denoted by \(\psi_{1}\). The corresponding amplitude is then \(\left\langle\varphi_{1} \mid \psi\right\rangle\). Continuing its path it arrives somewhere to the second screen, where it is registered at the point x . The amplitude corresponding to this second part of its way is \(\left\langle x \mid \varphi_{1}\right\rangle\). The total amplitude belonging to the process that the particle arrives at xx through slit 1 is the product of the two amplitudes \(\left\langle x \mid \varphi_{1}\right\rangle\left\langle\varphi_{1} \mid \psi\right\rangle\). Similarly, the amplitude of the other possible path of the particle, that it went through slit 2 before arriving at x is \(\left\langle x \mid \varphi_{2}\right\rangle\left\langle\varphi_{2} \mid \psi\right\rangle\), where \(\psi_{2}\) is the state of the particle, when it is at the second slit. The total amplitude is the sum of the amplitudes of the two possible paths.
\( \begin{aligned} \langle x \mid \psi\rangle &=\left\langle x \mid \varphi_{1}\right\rangle\left\langle\varphi_{1} \mid \psi\right\rangle+\left\langle x \mid \varphi_{2}\right\rangle\left\langle\varphi_{2} \mid \psi\right\rangle, \text { or equivalently } \\ \psi(x) &=\varphi_{1}(x)\left\langle\varphi_{1} \mid \psi\right\rangle+\varphi_{2}(x)\left\langle\varphi_{2} \mid \psi\right\rangle=c_{1} \varphi_{1}(x)+c_{2} \varphi_{2}(x) \end{aligned}\) (1.17)
where \(c_{1}=\left\langle\varphi_{1} \mid \psi\right\rangle\), \(c_{2}=\left\langle\varphi_{2} \mid \psi\right\rangle\). These latter amplitudes have been set to be two (complex) numbers instead of functions, because we have assumed here that the slits are small, and we need not distinguish between the different positions within the slits. What small means, will become more definite a little later. The sum of the amplitudes above is the superposition of the two possibilities. The probability of finding the particle at position xx is the absolute value square of the sum of the two possible amplitudes:
\(\begin{aligned} |\psi(x)|^{2} &=\left|c_{1} \varphi_{1}(x)\right|^{2}+\left|c_{2} \varphi_{2}(x)\right|^{2}+c_{1}^{*} c_{2} \varphi_{1}^{*}(x) \varphi_{2}(x)+c_{1} c_{2}^{*} \varphi_{1}(x) \varphi_{2}^{*}(x) \\ &=\left|c_{1}\right|^{2}\left|\varphi_{1}(x)\right|^{2}+\left|c_{2}\right|^{2}\left|\varphi_{2}(x)\right|^{2}+2 \operatorname{Re}\left(c_{1}^{*} c_{2} \varphi_{1}^{*}(x) \varphi_{2}(x)\right) \end{aligned}\) (1.18)
The interference appears because of the last term. There will be places where the particles arrive with a small probability, these will be the dark fringes, whereas there will be places where the detection probabilities are large. Quantum mechanics gives the explicit form of the two functions \(\varphi_{1}(x)\) and \(\varphi_{2}(x)\), but we will not deal with this here.
We cannot tell which of the slits the particle went through, the interference pattern is the witness that it went simultaneously through both. It can be shown, that if we try to detect somehow which path the particle has taken, then a successful detection will destroy the interference pattern, so we cannot see simultaneously the interference pattern and distinguish between the two ways the particle went along. The same experiment has been performed with particles larger than electrons, like neutrons, atoms, small molecules. More recently the effect was demonstrated with the molecular object called fullerene , consisting of 60 Carbon atoms.
We did not emphasize so far, but it is important that the amplitude, i.e. the wave function depends also on time. If we wish to make use of time dependent wave functions we will denote it by a capital Greek letter: \(\Psi(x, t)\). How does such a function look in any concrete case? This depends on the physical situation in question, and one of the important problems of quantum mechanics is to find the form of this function. In general we have to prescribe the property of square integrability with respect to x , because for any fixed value of the time variable t \(|\Psi(x, t)|^{2}\) is the probability density of the coordinate of the particle. This interpretation of the wave function was first given by Max Born. Accordingly:
at any time instant. We say then that \(\Psi(x, t)\) is normalized to unity. This requirement will be (i) refined later and (ii) will necessitate certain prescriptions on how the wave function should depend on the time variable.
If we wish to give the position of the particle in three dimensional space, instead of the line, then the wave function shall depend on all three coordinates of the points in space: \(\Psi(x, y, z, t)=\Psi(\mathbf{r}, t)\). Here the random variable will be the position vector of the particle. The probability density is then the function \(|\Psi(\mathbf{r}, t)|^{2}\), for which the normalization is prescribed in three dimensions.
Coming back to one dimension, a frequently used wave function (real in this specific case) for a particle localized more or less around the origin is \(\psi(x)=\mathcal{N} e^{-x^{2} / 4 \sigma_{0}^{2}}\) at a given instant, where σ 0 is a constant independent of x, while \(\mathcal{N}\) is a normalization factor. The corresponding probability density is \(|\psi(x)|^{2}=: \rho(x)=\mathcal{N}^{2} e^{-x^{2} / 2 \sigma_{0}^{2}}\). Its integral along the real axis must give 1, this is the condition that determines the factor \(\mathcal{N}\). As it is known from probability theory, this is the probability density of the so called standard normal, or Gaussian distribution function, if \(\mathcal{N}=\left(2 \pi \sigma^{2}\right)^{-1 / 4}\).
Show that the normalization factor in \(|\psi(x)|^{2}=: \rho(x)=\mathcal{N}^{2} e^{-x^{2} / 2 \sigma_{0}^{2}} \text { is } \mathcal{N}=\left(2 \pi \sigma^{2}\right)^{-1 / 4}\).
According to what we said before, the function can depend on time as well, so that instead of σ 0 we can have a time dependent σ ( t ) in it, and then of course (\mathcal{N}\) will be also time dependent. Besides the Gaussian wave function above there are many other possibilities depending on the physical problem in question.
Later on, we shall consider in detail the problem of the dynamics of the state, which means we shall consider how the state, i.e. the wave function changes with time given a force or a potential acting on the particle.
Investigating the photoeffect with a photocell where the cathode is covered by Cesium the electrons are stopped if the voltage is larger than 0.33V for a light wave of wavelength 546nm, while the corresponding value for 365nm is 1.46V. Derive the value of Planck’s constant from these results. What is the work function of Cesium? How much is the stopping voltage using light of 436nm? What is the threshold wavelength producing electron emission?
Estimate the cost of one green photon in the case of a traditional 100W light bulb working with 5% efficiency, and switched on for 1 second.
for Compton scattering using the equations expressing conservation of energy and momentum:
\(\begin{aligned} h \nu_{0}+E_{0} &=h \nu_{s}+E_{e} \\ \frac{h \nu_{0}}{c} &=\frac{h \nu_{s}}{c} \cos \varphi+p_{e} \cos \vartheta \\ 0 &=\frac{h \nu_{s}}{c} \sin \varphi-p_{e} \sin \vartheta \end{aligned}\) (1.21)
Prof. dr. sir george paget thomson > research profile.
Nobel Prize in Physics 1937 together with Clinton Davisson "for their experimental discovery of the diffraction of electrons by crystals".
George Paget Thomson was awarded the Nobel Prize for Physics in 1937 for his work in Aberdeen in discovering the wave-like properties of the electron. Whereas his father, J. J. Thomson, had been able to demonstrate the existence of the electron, the son, G. P. Thomson, demonstrated that it could be diffracted like a wave, a discovery proving the principle of wave-particle duality, which had first been posited by Louis-Victor de Broglie in the early 1920s. The Prize was shared with Clinton Joseph Davisson who had made the same discovery in the US, independently and following a quite different research path.
While Thomson maintained his interest in electron diffraction, in the early 1930s, after the discovery of the neutron and the positron and the related discovery of artificial radioactivity, he became deeply involved in the area of nuclear physics. In 1939, with the incredible expansion of the field following the announcement of the existence of the fission process, Thomson became instrumental in the establishment of the British wartime atomic energy project aiming at obtaining a controlled chain reaction. The dramatic events leading to the outbreak of World War II prompted Thomson to form the crucial MAUD committee of the Ministry of Aircraft Production in 1940--1941, which concluded that an atomic bomb was feasible. At the end of the war, Thomson became interested in the peaceful application of thermonuclear fusion and was instrumental in promoting the establishment of the British fusion programme as the first in the world.
Following his father's steps George Paget Thomson was born in 1892 from a family of physicists, and bred in the privileged environment of the Cambridge elite. His father was Sir J. J. Thomson, Cavendish Professor of Experimental Physics from 1884 to 1919, director of Cavendish Laboratory, and subsequently master of Trinity College. His mother was Rose Paget, daughter of Cambridge Regius Professor of Medicine Sir George Paget, and herself a physics student of J. J.’s at the Cavendish Laboratory. On his mother's side he had a strong medical tradition, but both from his mother and father he derived a passion for mathematics and physics. In 1906, when G. P. was 14 years old, his father J. J. was awarded the Nobel Prize for Physics “in recognition of the great merits of his theoretical and experimental investigations on the conduction of electricity by gases.” His work showed that atoms are not the most fundamental units of matter, as had long been believed, opening the door to a new era in the physical sciences.
During his whole life, G. P. Thomson had a passion for model ship-building, that helped him develop his manual skill and apply his ingenuity. After attending King's College Choir School and Perse School, he won a scholarship to Trinity College, where he entered in October 1910. At Trinity he gained a double first in mathematics and physics and in 1911 he became a Major Scholar. After graduation, he started research in the Cavendish Laboratory under his father's supervision. At that time, J. J. was studying the characteristics of the so called “canal rays”, produced as positive rays in discharge tubes, separating the different kinds of atoms and atomic groupings present in them. During these experiments J. J. demonstrated that certain atomic groups, such as CH, CH2 and CH3, could be produced, even though they have no stable existence under ordinary conditions. He also found that samples of the inert gas neon contained atoms with two different atomic weights, an achievement in which he was greatly helped by his collaborator Francis Aston, who was working at the Cavendish Laboratory since 1910 on the invitation of J. J. Aston resumed this kind of experiments after the war constructing the first mass-spectrograph, a device that eventually provided the most satisfactory proof of the existence of isotopes among the elements in general. At the time, these studies added evidence to the existence of isotopes and proved important in the understanding of the heavy radioactive elements, such as uranium and radium. J. J. Thomson's brilliant experimental researches and his excellent teaching attracted a host of the world's most talented young physicists to Cambridge University. Many of those who worked at the Cavendish under him eventually became Nobel laureates. His son G. P. was greatly influenced by this background to his early studies and experimental training. He also acknowledged the advantages he had at that time from interacting with Charles Wilson, who was in charge of the advanced teaching of practical physics at the Cavendish Laboratory until 1918. At that time, Wilson was perfecting his first cloud-chamber, which would become a fundamental tool for nuclear and particle physics in the years to come. Early in 1911, he was the first person to see and photograph the tracks of individual alpha- and beta-particles and electrons. But it was not until 1923 that the cloud chamber was brought to perfection and led to his two, beautifully illustrated, classic papers on the tracks of electrons. Rutherford's remark that the cloud chamber was "the most original and wonderful instrument in scientific history" has in fact been fully justified. Many important achievements were related to the use of the Wilson chamber. “For his method of making the paths of electrically charged particles visible by condensation of vapour,” Wilson was awarded the Nobel Prize in Physics in 1927. His technique was promptly adapted with startling success in all parts of the world, eventually leading in 1952 to the development by Donald A. Glaser of the bubble chamber, an achievement for which he was awarded the 1960 Nobel Prize in Physics.
In 1914, G. P. Thomson was elected Fellow and Mathematical Lecturer at Corpus Christi College, Cambridge, positions that he held until 1922 though he was absent from Cambridge on war service from 1914 to 1919. First, he served for a short time in France with the Queen's Regiment and then he was attached to the Royal Flying Corps for duty at the Royal Aircraft Factory at Farnborough and learned to fly at the Central Flying School. From the latter experience he derived an interest in aerodynamics that he applied to practical problems of stability and performance of aircraft, combining his skills as a mathematician, engineer and pilot, a combination of abilities that he used a lot in his later scientific life. After the war, he wrote Applied Aerodynamics , a comprehensive textbook on the subject outlining the basic physical theory and experimental methods applied to the aerodynamic performance of each part of an airplane's structure and to the airplane as a whole. His work on this field was of considerable practical value, giving to the subject a new degree of coherence and completeness. When he returned to Cambridge in 1919, he resumed research on the behaviour of electrical discharges in gases, the work he had begun as a student under his father's direction. In the process he discovered, simultaneously with Francis Aston, that the element lithium occurs as two isotopes of masses 6 and 7. At that time, Aston had completed building his first mass spectrograph. Subsequent improvements of this instrument, employing electromagnetic focusing, allowed him to identify more than two hundred naturally occurring isotopes, with a much improved mass resolving power and mass accuracy. His work on isotopes also led to his formulation of the whole number rule which states that “the mass of the oxygen isotope being defined [as 16], all the other isotopes have masses that are very nearly whole numbers.” For his fundamental work, Aston was awarded the Nobel Prize in Chemistry in 1922.
Matter waves In 1922, Thomson was appointed Professor of Natural Philosophy (Physics) in the University of Aberdeen, Scotland, a position he held until 1930 when he moved as professor of physics to Imperial College in London. It was at Aberdeen that Thomson made his most noteworthy contributions to theoretical physics. At first, he resumed his experimental work on a range of gas discharge phenomena, in particular those involving positive rays and he studied the field of forces existing within the hydrogen molecule between the protons and electrons. In 1925 he read with enthusiasm the recently published theory of matter waves of Louis de Broglie, bringing together the concepts of particle and wave in atomic physics.
In 1922, the young Louis, who worked in the spectroscopic laboratory of his brother Maurice in Paris, had suggested associating a small mass with a light quantum at rest, in order to treat it statistically like a material particle. He formulated the main ideas in three notes presented in September and October 1923 to the Paris Academy of Sciences. In Summer 1924 he completed the presentation of these concepts in a further note where one can also find the famous equation relating the wavelength lambda to the velocity of a non-relativistic particle (i.e., a matter particle and not the light quantum) of mass m , through Planck's constant h: lambda = h/mv . This was quite a revolutionary concept, since there was no evidence at the time that matter behaved like waves. In the early months of 1926, Erwin Schrödinger's remarkable series of papers on wave mechanics appeared, formalising de Broglie's ideas. Thomson's interest in quantum theory and in de Broglie's ideas led him to work out a theory of the Bohr atom in which the constituent particles were described by a combination of this theory and his father's ideas on light-quanta as structures in the ether. He also reflected on problems related to the scattering of slow positive rays and slow electrons when, most probably towards 1925, he heard about studies on the interaction of electrons with metal surfaces performed by Clinton Davisson and his collaborators Lester Germer and Charles Kunsman, at Bell Laboratories in the US.
Beginning in 1920, Davisson and Germer had investigated the question: What is the nature of the secondary electron emission from grids and plates subjected to electron bombardment? For this project, Davisson was given a new assistant, Charles Kunsman, a new PhD from California. Soon after beginning their secondary electron emission studies, they observed an unexpected phenomenon: a small percentage (about 1%) of the incident electron beam was being scattered back toward the electron gun with virtually no loss of energy: the electrons were being scattered elastically. As he pictured it, the mechanism of scattering was similar to that of alpha ray scattering by a gold foil investigated in Geiger and Marsden experiments, following which Ernest Rutherford had announced his nuclear model of the atom in 1911. Davisson thus hoped to use these elastically scattered electrons to probe the extra-nuclear structure of the atom, just as alpha particles had been a probe for the nuclear core. He was so enthusiastic that he succeeded in obtaining permission to devote a large fraction of their time to this new project and had a specific apparatus built for this investigation. The basic piece was a vacuum tube with an electron gun, a nickel target inclined at an angle of 45° to the incident electron beam and a Faraday cup acting as collector, which could move through the entire 135° range of possible scattered electron paths. The Faraday cup was set at a voltage to accept electrons that were within 10% of the incident electron energy. After a couple of months they submitted a paper to Science, presenting their scattering program, the obtained curves and a shell model of the atom accounting for the observed angular distribution of electrons scattered by platinum and magnesium. But the data, the model, and the prediction were not definite, quite far from the Rutherford-Geiger-Marsden connection between experimental results and theoretical explanation. Notwithstanding the disappointment, Davisson and Kunsman continued these investigations for a couple of years, also building new tubes and trying other metals as targets, developing rather sophisticated experimental techniques at high vacuum. On the whole their scattering enterprise had a limited success, and, when Kunsman left Bell in the end of 1923, Davisson abandoned the project.
Investigations on the scattering of electrons by metals were resumed only in October 1924, when Lester Germer returned to work after a long period of illness. New experiments on a specially polished nickel target bombarded with electrons initially gave results very similar to those obtained during the previous years. Then suddenly, they obtained new unprecedented and puzzling results that appeared to have been caused by a change in the polycrystalline structure of the nickel target. The extreme heating had formed about ten crystal facets in the area from which the incident electron beam was scattered, and Davisson and Germer concluded that the new intensity pattern of the scattering electrons must have its origin in the new arrangement of the atoms in the crystals, not in the structure of the atoms. Neither Davisson nor Germer knew much about crystals, so they spent several months examining the damaged target and other nickel surfaces until they became thoroughly familiar with the X-ray diffraction patterns obtained from nickel crystals in various states of preparation and orientation. At the time of Davisson and Germer's experiments, the study of crystals by X-ray diffraction was in full development, and its incredible impact on the chemical, biochemical, physical, material and mineralogical sciences was just beginning. The technique of X-ray diffraction had originated in 1912, when Max von Laue expressed the idea that the spacings of a crystal lattice would be of the right size to cause the diffraction of X-rays, supposing them to be very short electromagnetic waves. An experimental proof had immediately confirmed von Laue's hypothesis, and the technique had later been fully developed by Henry Bragg, and especially by his son Lawrence Bragg. They had both reduced X-rays analysis of simple materials to a standard procedure by 1914. Their findings created the new science of X-ray crystallography, a discipline later informing almost every branch of science, also leading to further developments in spectroscopy and solid-state physics and providing a means to understand the structure of highly complex molecules and materials, eventually giving rise to the field of molecular biology. Von Laue was awarded the 1914 Nobel Prize for Physics for his breakthrough discovery, while the Braggs, father and son, were jointly awarded the 1915 Prize for Physics “for their services in the analysis of crystal structure by means of X-rays.” After spending several months in their investigation on crystals and on the examination of their damaged nickel target, Davisson and Germer decided that a large single crystal oriented in a known direction would make a more suitable target and by April 1926 they had obtained a suitable crystal and mounted it in a new set-up. However, after an entire year spent in preparation, they obtained quite uninteresting experimental results and Davisson was again highly disappointed. During the summer of 1926 he planned a vacation trip to visit England, which he had envisioned as a "second honeymoon" with his wife, but which would give him a completely new perspective of the whole matter.
Only a couple of years before Davisson and Germer's experiments, Arthur Compton had announced the outcome of five years of work, both experimental and theoretical, related to experiments on the scattering of monochromatic X-rays from electrons in a carbon target. According to what Compton had found, scattered X-rays had a longer wavelength than those incident upon the target, the shift increasing with the scattering angle. In 1923, he published a paper in the Physical Review where he explained his data by assuming that X-rays as electromagnetic quanta have a particulate nature and applied conservation of energy and momentum to the collision between the quantum of radiation and the electron. During the early 1920s, the particle nature of light suggested by Einstein in 1905 was still debated. Now Compton's experiments actually provided clear and independent evidence for the particle-like behaviour. Compton was awarded the 1927 Nobel Prize in Physics for the "discovery of the effect named after him." At the time of Davisson and Germer's experiments, the dual wave-particle nature of light had thus just been proven. But at the same time, while defending his thesis on 25 November 1924, de Broglie had explicitly suggested a diffraction experiment on electrons by crystals in order to investigate his idea about the wave-particle duality of matter. In the meantime, several European physicists had attempted such experiments abandoning them because of the difficulties of producing the required high vacuum and detecting the low-intensity electron beams. In particular, in early 1925 Max Born's student in Gottingen, Walter Elsasser, became interested in the problem and suggested that some earlier experiments on slow electron scattering performed by Carl Ramsauer (the anomalous behaviour of the electron cross section for small velocities in noble gases), as well as the Davisson and Kunsman results, might be interpreted as evidence for the wave nature of electrons, the scattering patterns corresponding to those to be expected from wave diffraction. According to de Broglie's proposal, electrons have wavelengths that are inversely proportional to their momentum. Consequently, high-speed electrons have short wavelengths, comparable to the spacings between atomic layers in crystals. A beam of such high-speed electrons should undergo diffraction, a characteristic wave effect, when directed through thin sheets of material or when reflected from the faces of crystals. Elsasser checked the approximate magnitudes and found the electron wavelengths to be of the right order. He published a short note in Die Naturwissenschaften and also tried to perform an experiment to confirm his guess quantitatively, but did not succeed and eventually gave up. De Broglie's papers, along with the new matrix mechanics of Werner Heisenberg, Max Born and Pascual Jordan, were the subjects of lively discussions at the Oxford meeting of the British Association for the Advancement of Sciences held in summer 1926. Davisson, who was largely unaware of these recent developments in quantum mechanics, attended the meeting. He was quite surprised in hearing a lecture by Born in which his and Kunsman's curves of 1923 were cited as confirmatory evidence for de Broglie's electron waves. Their feeble peaks actually appeared to be exciting evidence to physicists already convinced of the correctness of the wave mechanical interpretation of quantum theory. After the meeting, Davisson discussed with Born, James Franck and Patrick Blackett, showing them some of the recent results that he and Germer had obtained with the single crystal. They convinced him that Elsasser's guess was correct and that his results were due to the effects of de Broglie waves.
Electron diffraction After learning about matter waves and wave mechanics, Davisson spent the whole return transatlantic voyage trying to understand Schrodinger's papers, thinking that an explanation might reside in them. He had become convinced that, in view of the extremely fundamental nature of de Broglie's theory, it was highly desirable that it should rest on more direct evidence, and, in particular, that it should be shown capable of predicting as well as of merely explaining. After his return, they examined the new curves that Germer had obtained during Davisson's absence and found a relevant discrepancy between the observed electron intensity peaks and the angles they expected from the de Broglie-Schrodinger theory. They carefully inspected the whole set-up and decided that most of the discrepancy could be accounted for by an accidental displacement of the collector-box opening. After a period of careful preparation, they started a new series of experiments to look for diffracted electron beams. Tests were specifically designed to see if any effect could be discerned for a changed electron wave-length, according to the de Broglie relationship. A search for “quantum peaks” (voltage-dependent scattered electron beams) was launched by late December, together with a new assistant, Chester Calbick, a recently graduated electrical engineer. In January 1927, they found conclusive evidence of an interference phenomenon resulting from electron diffraction by a single crystal of nickel. They had actually succeeded where outstanding experimenters like Elsasser, Blackett, Chadwick and Ellis, had failed, even if they had in mind the idea of electron diffraction considerably ahead of Davisson and Germer. Recalling his conversations at Oxford, and the comments that had been made, Davisson felt urged to publish, feeling that others might be pursuing similar investigations.
Actually, unknown to Davisson, G. P. Thomson at that time was indeed making progress at revealing the phenomena of electron diffraction with high-voltage electrons and thin metal foils. He had learned of Davisson's studies in September 1926, while they were both attending the British Association Oxford meeting. Already deeply interested in de Broglie's work, Thomson immediately saw how his work with positive rays might be adapted to test the idea. In his case, the path from theory to experiment was linear, in contrast to Davisson and Germer, who arrived at their discovery in the course of a long lasting investigation that can be fully understood only within the research and development activities at Bell Laboratories. G. P. Thomson worked in a small university, whereas Davisson and Germer worked in a large industrial laboratory in the midst of a great city. The technical virtuosity of the low-energy experiments of Davisson and Germer, conducted as part of a more general investigation, is in strong contrast to the more directly targeted high-energy transmission experiments of Thomson and Reid. According to the theory, a wave must be associated with the motion of any material corpuscle; a direct test could be obtained by producing a diffraction phenomenon when a beam of electrons went through a crystal lattice, the same test that Max von Laue and his associates had used in Munich to prove the wave nature of X-rays in 1911. Reasoning that the effect should be easier to analyse with a solid than with a gaseous target, Thomson asked one of his students, Alexander Reid, to modify an existing apparatus and investigate the scattering of a beam of electrons with energy in the keV range though thin celluloid films at normal incidence. Many of the energetic electrons that passed through the film were deflected to form diffuse rings on a photographic plate behind the target, quite similar to the Debye-Scherrer rings, well known from the corresponding experiment with X-rays. An interference phenomenon was at once suggested. This would occur if each atom of the film scattered in phase a wavelet from the incoming wave associated with the electrons forming the cathode rays. Since the atoms in each small crystal of the metal are regularly spaced, the phases of the wavelets scattered in any fixed direction would have a definite relationship to one another. In some directions they would agree in phase and build up a strong scattered wave, in others they would destroy one another by interference. The strong waves are analogous to the beams of light diffracted by an optical grating. At the time, the arrangement of the atoms in celluloid was not known with certainty and only general conclusions could be drawn, but for metals the structure had been determined previously by the use of X-rays. So Thomson and Reid changed to metal targets (aluminium, gold, platinum) with a known crystal lattice. In each instance, the deflected beam formed well-defined rings of a size that was in excellent agreement (to within 5 percent) with predictions from de Broglie's wave theory of matter. Thomson and Reid made a remarkable modification of the experiment that is worth mentioning. The beam, after passing through the film, was subjected to a uniform magnetic field. It was found that the beam whose impact on the plate formed the ring pattern was deflected in the same manner as the beam that had passed through holes in the film. This distinguished the effect from anything produced by X-rays and showed that it must be a true property of electrons. The experiments beautifully confirmed the de Broglie-Schrödinger wave theory.
These results were published in brief in December 1927 in Nature . Two months later, Thomson wrote two more detailed articles in the Proceedings of the Royal Society . The conclusion was: "The detailed agreement shown in these experiments with the de Broglie theory must, I think, be regarded as strong evidence in its favour. These means accepting the view that ordinary Newtonian mechanics (including the relativity modifications) are only a first approximation to the truth, bearing the same relation to the complete theory that geometrical optics does to the wave theory. However difficult it may seem to accept such a sweeping generalisation, it seems impossible to explain the results obtained except by the assumption of some kind of diffraction, and the numerical agreement with the wave-length given by the theory is striking." Meanwhile, Davisson had published in April 1927 his own results on the scattering of slow electrons by single crystals in terms of de Broglie's theory. Both results established the wave nature of the electron, and, in principle, of all matter. The simultaneous discovery of electron diffraction is characterised by great differences in the two experimental techniques, in the institutional contexts, and in the scientific paths that eventually led to the final achievement. In his Nobel Lecture, Thomson himself testified to the magnitude of Davisson and Germer's technical achievement as a triumph of experimental skill, mainly because the relatively slow electrons they used were most difficult to handle and the vacuum had to be quite outstanding, in order to get results of any value: "If one compares the two sets of experiments it is clear that those of Davisson and Germer were great triumphs of experimentation, among the greatest ever made. Those at Aberdeen were singularly simple and easy, the only serious difficulty being to prepare good specimens. It is not hard to see the reason for this difference. Davisson had discovered an effect that he thought might be important in a particular way. He had to study this effect more or less as he had found it."
During the fifth Solvay Conference held in Brussels in October 1927, Bohr, de Broglie, Born, Heisenberg and Schrödinger all hailed the experiments of Davisson and Germer as confirming the general provisions and even the formulas of wave mechanics. The probabilistic interpretation of the wave-function, proposed by the physicists of the so-called Göttingen-Copenhagen school, provided the general conceptual framework in which the wave-corpuscle dualism found a theoretical coherence, and two years later the 1929 Nobel Prize in Physics was awarded to Louis de Broglie "for his discovery of the wave nature of electrons". Davisson and Thomson were awarded the Nobel Prize in 1937, “for their experimental discovery of the diffraction of electrons by crystals.” Illness prevented Thomson from attending the award ceremony, but he travelled to Stockholm the following year to deliver his Nobel lecture. After some initial thanks and comments, he opened his talk with the following sentence: "The goddess of learning is fabled to have sprung full-grown from the brain of Zeus, but it is seldom that a scientific conception is born in its final form, or owns a single parent. More often it is the product of a series of minds, each in turn modifying the ideas of those that came before, and providing material for those that come after. The electron is no exception." In outlining the history of the electron, he recalled how during the last years of the XIXth century, the electron, as "atom of electricity", had "acquired not only mass but universality, it was not only electricity but an essential part of all matter." Among the many names associated with this advance, Thomson could not avoid mentioning his father J. J. who had been able to demonstrate the existence of the electron, whereas he, the son, had demonstrated that it could be diffracted like a wave. The path was now open to study crystal structures by electron diffraction. X-ray diffraction by crystals is a powerful tool to probe the depths of metals and other crystals. Electrons, however, interact more strongly with matter than do X-rays and hence can be used for more sensitive studies of small samples, such as gas molecules, thin films, or surfaces. X-rays are useless for such surface and thin film studies. They are so piercing that they go right through the sample without disclosing the desired information. Electrons - far less piercing - are stopped, scattered and reflected by crystal surfaces and thin films and thus are vitally useful for this type of research. A long period elapsed before improvements in electron optics and in vacuum technology enabled the unique properties of electrons to be widely used as a sensitive probe of the local microstructure and composition of matter. Electron diffraction, as well as neutron diffraction, discovered by von Halban and Preiswerk in 1936, became an extremely important tool, providing information on the structure of matter - crystalline and non-crystalline - at the atomic and molecular levels. Electron microscopy and diffraction-contrast methods developed and supplanted X-ray diffraction as the dominant microstructural tool in many laboratories, in materials science, chemistry, mineralogy, and biology. An indication of the importance and diversity of applications of diffraction by crystals is given by the large number of Nobel Prizes awarded for studies involving X-ray, neutron, or electron diffraction.
Bibliography Gehrenbeck R. K. (1978) Electron diffraction: fifty years ago. Physics Today 31: 34--41 Heilbron J. L. (2008) Thomson, Joseph John. in Complete Dictionary of Scientific Biography. Vol. 13. Detroit: Charles Scribner's Sons, pp. 362-372. Gale Virtual Reference Library, http://go.galegroup.com/ps/i.do?id=GALE%7CCX2830904305&v=2.1&u=mpi_vb&it=r&p=GVRL&sw=w&asid=a4b35784121009d2caa74c2d733d8e6 7 Heilbron J. L. (1963) Interview with Sir George Paget Thomson June 20; http://www.aip.org/history/ohilist/4913.html Moon P. B. (1977) George Paget Thomson. 3 May 1892 -- 10 September 1975. Biographical Memoirs of Fellows of the Royal Society 23: 529-556 Thomson G. P. (1938) Electronic Waves. Nobel Lecture (June 7); http://www.nobelprize.org/nobel_prizes/physics/laureates/1937/thomson-lecture.html Wasson, T. (ed.) (1987) Thomson, G. P. In Nobel Prize Winners, H. W. Wilson Company, New York, pp. 1053--1054
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- J.J.. Thomson - Nobel Lecture: Electronic Waves
George Paget Thomson
Nobel lecture.
Nobel Lecture, June 7, 1938
Electronic Waves
Ever since last November, I have been wanting to express in person my gratitude to the generosity of Alfred Nobel, to whom I owe it that I am privileged to be here today, especially since illness prevented me from doing so at the proper time. The idealism which permeated his character led him to make his magnificent foundation for the benefit of a class of men with whose aims and viewpoint his own scientific instincts and ability had made him naturally sympathetic, but he was certainly at least as much concerned with helping science as a whole, as individual scientists. That his foundation has been as successful in the first as in the second, is due to the manner in which his wishes have been carried out. The Swedish people, under the leadership of the Royal Family, and through the medium of the Royal Academy of Sciences, have made the Nobel Prizes one of the chief causes of the growth of the prestige of science in the eyes of the world, which is a feature of our time. As a recipient of Nobel’s generosity I owe sincerest thanks to them as well as to him.
The goddess of learning is fabled to have sprung full-grown from the brain of Zeus, but it is seldom that a scientific conception is born in its final form, or owns a single parent. More often it is the product of a series of minds, each in turn modifying the ideas of those that came before, and providing material for those that come after. The electron is no exception.
Although Faraday does not seem to have realized it, his work on electrolysis, by showing the unitary character of the charges on atoms in solution, was the first step. Clerk Maxwell in 1873 used the phrase a “molecule of electricity” and von Helmholtz in 1881 speaking of Faraday’s work said “If we accept the hypothesis that elementary substances are composed of atoms, we cannot well avoid concluding that electricity also is divided into elementary portions which behave like atoms of electricity.” The hypothetical atom received a name in the same year when Johnstone Stoney of Dublin christened it “electron”, but so far the only property implied was an electron charge.
The last year of the nineteenth century saw the electron take a leading place amongst the conceptions of physics. It acquired not only mass but universality, it was not only electricity but an essential part of all matter. If among the many names associated with this advance I mention that of J.J. Thomson I hope you will forgive a natural pride. It is to the great work of Bohr that we owe the demonstration of the connection between electrons and Planck’s quantum which gave the electron a dynamics of its own. A few years later, Goudsmit and Uhlenbeck, following on an earlier suggestion by A.H. Compton showed that it was necessary to suppose that the electron had spin. Yet even with the properties of charge, mass, spin and a special mechanics to help it, the electron was unable to carry the burden of explaining the large and detailed mass of experimental data which had accumulated. L. de Broglie , working originally on a theory of radiation, produced as a kind of by-product the conception that any particle and in particular an electron, was associated with a system of waves. It is with these waves, formulated more precisely by Schrödinger, and modified by Dirac to cover the idea of spin, that the rest of my lecture will deal.
The first published experiments to confirm de Broglie’s theory were those of Davisson and Germer, but perhaps you will allow me to describe instead those to which my pupils and I were led by de Broglie’s epoch-making conception.
A narrow beam of cathode rays was transmitted through a thin film of matter. In the earliest experiment of the late Mr. Reid this film was of celluloid, in my own experiment of metal. In both, the thickness was of the order of 10 -6 cm. The scattered beam was received on a photographic plate normal to the beam, and when developed showed a pattern of rings, recalling optical halos and the Debye -Scherrer rings well known in the corresponding experiment with X-rays. An interference phenomenon is at once suggested. This would occur if each atom of the film scattered in phase a wavelet from an advancing wave associated with the electrons forming the cathode rays. Since the atoms in each small crystal of the metal are regularly spaced, the phases of the wavelets scattered in any fixed direction will have a definite relationship to one another. In some directions they will agree in phase and build up a strong scattered wave, in others they will destroy one another by interference. The strong waves are analogous to the beams of light diffracted by an optical grating. At the time, the arrangement of the atoms in celluloid was not known with certainty and only general conclusions could be drawn, but for the metals it had been determined previously by the use of X-rays. According to de Broglie’s theory the wavelength associated with an electron is h/mv which for the electrons used (cathode rays of 20 to 60,000 volts energy) comes out from 8 X 10 -9 to 5 X 10 -9 cm. I do not wish to trouble you with detailed figures and it will be enough to say that the patterns on the photographic plates agreed quantitatively, in all cases, with the distribution of strong scattered waves calculated by the method I have indicated. The agreement is good to the accuracy of the experiments which was about 1%. There is no adjustable constant, and the patterns reproduce not merely the general features of the X-ray patterns but details due to special arrangements of the crystals in the films which were known to occur from previous investigation by X-rays. Later work has amply confirmed this conclusion, and many thousands of photographs have been taken in my own and other laboratories without any disagreement with the theory being found. The accuracy has increased with the improvement of the apparatus, perhaps the most accurate work being that of v. Friesen of Uppsala who has used the method in a precision determination of e in which he reaches an accuracy of I in 1,000.
Before discussing the theoretical implications of these results there are two modifications of the experiments which should be mentioned. In the one, the electrons after passing through the film are subject to a uniform magnetic field which deflects them. It is found that the electrons whose impact on the plate forms the ring pattern are deflected equally with those which have passed through holes in the film. Thus the pattern is due to electrons which have preserved unchanged the property of being deflected by a magnet. This distinguishes the effect from anything produced by X-rays and shows that it is a true property of electrons. The other point is a practical one, to avoid the need for preparing the very thin films which are needed to transmit the electrons, an apparatus has been devised to work by reflection, the electrons striking the diffracting surface at a small glancing angle. It appears that in many cases the patterns so obtained are really due to electrons transmitted through small projections on the surface. In other cases, for example when the cleavage surface of a crystal is used, true reflection occurs from the Bragg planes.
The theory of de Broglie in the form given to it by Schrödinger is now known as wave mechanics and is the basis of atomic physics. It has been applied to a great variety of phenomena with success, but owing largely to mathematical difficulties there are not many cases in which an accurate comparison is possible between theory and experiment. The diffraction of fast electrons by crystals is by far the severest numerical test which has been made and it is therefore important to see just what conclusions the excellent agreement between theory and these experiments permits us to draw.
The calculations so far are identical with those in the corresponding case of the diffraction of X-rays. The only assumption made in determining the directions of the diffracted beams is that we have to deal with a train of wave of considerable depth and with a plane wave-front extending over a considerable number of atoms. The minimum extension of the wave system sideways and frontways can be found from the sharpness of the lines. Taking v. Friesen’s figures, it is at least 225 waves from back to front over a front of more than 200 Å each way.
But the real trouble comes when we consider the physical meaning of the waves. In fact, as we have seen, the electrons blacken the photographic plate at those places where the waves would be strong. Following Bohr, Born, and Schrödinger, we can express this by saying that the intensity of the waves at any place measures the probability of an electron manifesting itself there. This view is strengthened by measurements of the relative intensities of the rings, which agree well with calculations by Mott based on Schrödinger’s equation. Such a view, however successful as a formal statement is at variance with all ordinary ideas. Why should a particle appear only in certain places associated with a set of waves? Why should waves produce effects only through the medium of particles? For it must be emphasized that in these experiments each electron only sensitizes the photographic plate in one minute region, but in that region it has the same powers of penetration and photographic action as if it had never been diffracted. We cannot suppose that the energy is distributed throughout the waves as in a sound or water wave, the wave is only effective in the one place where the electron appears. The rest of it is a kind of phantom. Once the particle has appeared the wave disappears like a dream when the sleeper wakes. Yet the motion of the electron, unlike that of a Newtonian particle, is influenced by what happens over the whole front of the wave, as is shown by the effect of the size of the crystals on the sharpness of the patterns. The difference in point of view is fundamental, and we have to face a break with ordinary mechanical ideas. Particles have not a unique track, the energy in these waves is not continuously distributed, probability not determinism governs nature.
But while emphasizing this fundamental change in outlook, which I believe to represent an advance in physical conceptions, I should like to point out several ways in which the new phenomena fit the old framework better than is often realized. Take the case of the influence of the size of the crystals on the sharpness of the diffracted beams, which we have just mentioned. On the wave theory it is simply an example of the fact that a diffraction grating with only a few lines has a poor resolving power. Double the number of the lines and the sharpness of the diffracted beams is doubled also. However if there are already many lines, the angular change is small. But imagine a particle acted on by the material which forms the slits of the grating, and suppose the forces such as to deflect it into one of the diffracted beams. The forces due to the material round the slits near the one through which it passes will be the most important, an increase in the number of slits will affect the motion but the angular deflection due to adding successive slits will diminish as the numbers increase. The law is of a similar character, though no simple law of force would reproduce the wave effect quantitatively.
Similarly for the length of the wave train. If this were limited by a shutter moving so quickly as to let only a short wave train pass through, the wave theory would require that the velocity of the particle would be uncertain over a range increasing with the shortness of the wave train, and corresponding to the range of wavelengths shown by a Fourier analysis of the train. But the motion of the shutter might well be expected to alter the velocity of a particle passing through, just before it closed.
Again, on the new view it is purely a matter of chance in which of the diffracted beams of different orders an electron appears. If the phenomenon were expressed as the classical motion of a particle, this would have to depend on the initial motion of the particle, and there is no possibility of determining this initial motion without disturbing it hopelessly. There seems no reason why those who prefer it should not regard the diffraction of electrons as the motion of particles governed by laws which simulate the character of waves, but besides the rather artificial character of the law of motion, one has to ascribe importance to the detailed initial conditions of the motion which, as far as our present knowledge goes, are necessarily incapable of being determined. I am predisposed by nature in favour of the most mechanical explanations possible, but I feel that this view is rather clumsy and that it might be best, as it is certainly safer, to keep strictly to the facts and regard the wave equation as merely a way of predicting the result of experiments. Nevertheless, the view I have sketched is often a help in thinking of these problems. We are curiously near the position which Newton took over his theory of optics, long despised but now seen to be far nearer the truth than that of his rivals and successors.
“Those that are averse from assenting to any new Discoveries, but such as they can explain by an Hypothesis, may for the present suppose, that as Stones by falling upon water put the Water into an undulating Motion, and all Bodies by percussion excite vibrations in the Air: so the Rays of Light, by impinging on any refracting or reflecting Surface, excite vibrations in the refracting or reflecting Medium or Substance, much after the manner that vibrations are propagated in the Air for causing Sound, and move faster than the Rays so as to overtake them; and that when any Ray is in that part of the vibration which conspires with its Motion, it easily breaks through a refracting Surface, but when it is in the contrary part of the vibration which impedes its Motion, it is easily reflected; and, by consequence, that every Ray is successively disposed to be easily reflected, or easily transmitted, by every vibration which overtakes it. But whether this Hypothesis be true or false I do not here consider.”
Although the experiments in diffraction confirm so beautifully the de Broglie-Schrödinger wave theory, the position is less satisfactory as regards the extended theory due to Dirac. On this theory the electron possesses magnetic properties and the wave requires four quantities instead of one for its specification. This satisfies those needs of spectroscopy which led to the invention of the spinning electron. It suggests however that electronic waves could be polarized and that the polarized waves might interact with matter in an anisotropic manner. In fact detailed calculations by Mott indicate that if Dirac electrons of 140 kV energy are scattered twice through 90° by the nuclei of gold atoms the intensity of the scattered beam will differ by 16% according to whether the two scatterings are in the same or in opposite directions. Experiments by Dymond and by myself have established independently that no effect of this order of magnitude exists, when the scattering is done by gold foils. While there is a slight possibility that the circumnuclear electrons, or the organization of the atoms into crystals might effect the result, it seems very unlikely. Some of the theorists have arrived at results conflicting with Mott, but I understand that their work has been found to contain errors. At present there seems no explanation of this discrepancy which throws doubt on the validity of the Dirac equations in spite of their success in predicting the positive electron.
I should be sorry to leave you with the impression that electron diffraction was of interest only to those concerned with the fundamentals of physics. It has important practical applications to the study of surface effects. You know how X-ray diffraction has made it possible to determine the arrangement of the atoms in a great variety of solids and even liquids. X-rays are very penetrating, and any structure peculiar to the surface of a body will be likely to be overlooked, for its effect is swamped in that of the much greater mass of underlying material. Electrons only affect layers of a few atoms, or at most tens of atoms, in thickness, and so are eminently suited for the purpose. The position of the beams diffracted from a surface enables us, at least in many cases, to determine the arrangement of the atoms in the surface. Among the many cases which have already been studied I have only time to refer to one, the state of the surface of polished metals. Many years ago Sir George Beilby suggested that this resembled a supercooled liquid which had flowed under the stress of polishing. A series of experiments by electron diffraction carried out at the Imperial College in London has confirmed this conclusion. The most recent work due to Dr. Cochrane has shown that though this amorphous layer is stable at ordinary temperature as long as it remains fixed to the mass of the metal, it is unstable when removed, and recrystalizes after a few hours. Work by Professor Finch on these lines has led to valuable conclusions as to the wear on the surfaces of cylinders and pistons in petrol engines.
It is in keeping with the universal character of physical science that this single small branch of it should touch on the one hand on the fundamentals of scientific philosophy and on the other, questions of everyday life.
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1.6: de Broglie Waves can be Experimentally Observed
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Learning Objectives
- To present the experimental evidence behind the wave-particle duality of matter
The validity of de Broglie’s proposal was confirmed by electron diffraction experiments of G.P. Thomson in 1926 and of C. Davisson and L. H. Germer in 1927. In these experiments it was found that electrons were scattered from atoms in a crystal and that these scattered electrons produced an interference pattern. The interference pattern was just like that produced when water waves pass through two holes in a barrier to generate separate wave fronts that combine and interfere with each other. These diffraction patterns are characteristic of wave-like behavior and are exhibited by both matter (e.g., electrons and neutrons) and electromagnetic radiation. Diffraction patterns are obtained if the wavelength is comparable to the spacing between scattering centers.
Diffraction occurs when waves encounter obstacles whose size is comparable with its wavelength.
Continuing with our analysis of experiments that lead to the new quantum theory, we now look at the phenomenon of electron diffraction.
Diffraction of Light (Light as a Wave)
It is well-known that light has the ability to diffract around objects in its path, leading to an interference pattern that is particular to the object. This is, in fact, how holography works (the interference pattern is created by allowing the diffracted light to interfere with the original beam so that the hologram can be viewed by shining the original beam on the image). A simple illustration of light diffraction is the Young double slit experiment (Figure 1.7.1 ). Here, light as waves (pictured as waves in a plane parallel to the double slit apparatus) impinge on the two slits. Each slit then becomes a point source for spherical waves that subsequently interfere with each other, giving rise to the light and dark fringes on the screen at the right .
The double-slit experiments are direct demonstration of wave phenomena via observed interference. These types of experiment were first performed by Thomas Young in 1801, as a demonstration of the wave behavior of light. In the basic version of this experiment, light is illuminated only a plate pierced by two parallel slits, and the light passing through the two slits is observed on a screen behind the plate (Figures 1.7.1 and 1.7.2 ).
The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles (Figure \(\PageIndex{0c}\)). However, the light is always found to be absorbed at the screen at discrete points, as individual particles (not waves); the interference pattern appears via the varying density of these particle hits on the screen. Furthermore, versions of the experiment that include detectors at the slits find that each detected photon passes through one slit (as would a classical particle), and not through both slits (as would a wave).
Interference is a wave phenomenon in which two (or more) waves superimpose to form a resultant wave of greater or lower amplitude. It is the primary property used to identify wave behavior.
Diffraction of Electrons (Electrons as Waves)
According to classical physics, electrons should behave like particles - they travel in straight lines and do not curve in flight unless acted on by an external agent, like a magnetic field. In this model, if we fire a beam of electrons through a double slit onto a detector, we should get two bands of "hits", much as you would get if you fired a machine gun at the side of a house with two windows - you would get two areas of bullet-marked wall inside, and the rest would be intact (Figure 1.7.3 (left) and Figure 1.7.2 ).
However, if the slits are made small enough and close enough together, we actually observe the electrons are diffracting through the slits and interfering with each other just like waves (Figure 1.7.3 (right) and Figure 1.7.2 a,b). This means that the electrons have wave-particle duality , just like photons, in agreement with de Broglie's hypothesis discussed previously. In this case, they must have properties like wavelength and frequency. We can deduce the properties from the behavior of the electrons as they pass through our diffraction grating.
This was a pivotal result in the development of quantum mechanics. Just as the photoelectric effect demonstrated the particle nature of light, the Davisson–Germer experiment showed the wave-nature of matter, and completed the theory of wave-particle duality. For physicists this idea was important because it meant that not only could any particle exhibit wave characteristics, but that one could use wave equations to describe phenomena in matter if one used the de Broglie wavelength.
An electron microscope use a beam of accelerated electrons as a source of illumination. Since the wavelength of electrons can be up to 100,000 times shorter than that of visible light photons, electron microscopes have a higher resolving power than light microscopes and can reveal the structure of smaller objects. A transmission electron microscope can achieve better than 50 pm resolution and magnifications of up to about 10,000,000x whereas most light microscopes are limited by diffraction to about 200 nm resolution and useful magnifications below 2000x (Figure 1.7.4 ).
Is Matter a Particle or a Wave?
An electron, indeed any particle, is neither a particle nor a wave . Describing the electron as a particle is a mathematical model that works well in some circumstances while describing it as a wave is a different mathematical model that works well in other circumstances. When you choose to do some calculation of the electron's behavior that treats it either as a particle or as a wave, you're not saying the electron is a particle or is a wave: you're just choosing the mathematical model that makes it easiest to do the calculation.
Neutron Diffraction (Neutrons as Waves)
Like all quantum particles, neutrons can also exhibit wave phenomena and if that wavelength is short enough, atoms or their nuclei can serve as diffraction obstacles. When a beam of neutrons emanating from a reactor is slowed down and selected properly by their speed, their wavelength lies near one angstrom (0.1 nanometer), the typical separation between atoms in a solid material. Such a beam can then be used to perform a diffraction experiment. Neutrons interact directly with the nucleus of the atom, and the contribution to the diffracted intensity depends on each isotope; for example, regular hydrogen and deuterium contribute differently. It is also often the case that light (low Z) atoms contribute strongly to the diffracted intensity even in the presence of large Z atoms.
Example 1.7.1 : Neutron Diffraction
Neutrons have no electric charge, so they do not interact with the atomic electrons. Hence, they are very penetrating (e.g., typically 10 cm in lead). Neutron diffraction was proposed in 1934, to exploit de Broglie’s hypothesis about the wave nature of matter. Calculate the momentum and kinetic energy of a neutron whose wavelength is comparable to atomic spacing (\(1.8 \times 10^{-10}\, m\)).
This is a simple use of de Broglie’s equation
\[\lambda = \dfrac{h}{p} \nonumber \]
where we recognize that the wavelength of the neutron must be comparable to atomic spacing (let's assumed equal for convenience, so \(\lambda = 1.8 \times 10^{-10}\, m\)). Rearranging the de Broglie wavelength relationship above to solve for momentum (\(p\)):
\[\begin{align} p &= \dfrac{h}{\lambda} \nonumber \\[4pt] &= \dfrac{6.6 \times 10^{-34} J s}{1.8 \times 10^{-10} m} \nonumber \\[4pt] &= 3.7 \times 10^{-24}\, kg \,\,m\, \,s^{-1} \nonumber \end{align} \nonumber \]
The relationship for kinetic energy is
\[KE = \dfrac{1}{2} mv^2 = \dfrac{p^2}{2m} \nonumber \]
where \(v\) is the velocity of the particle. From the reference table of physical constants, the mass of a neutron is \(1.6749273 \times 10^{−27}\, kg\), so
\[\begin{align*} KE &= \dfrac{(3.7 \times 10^{-24}\, kg \,\,m\, \,s^{-1} )^2}{2 (1.6749273 \times 10^{−27}\, kg)} \\[4pt] &=4.0 \times 10^{-21} J \end{align*} \nonumber \]
The neutrons released in nuclear fission are ‘fast’ neutrons, i.e. much more energetic than this. Their wavelengths be much smaller than atomic dimensions and will not be useful for neutron diffraction. We slow down these fast neutrons by introducing a "moderator", which is a material (e.g., graphite) that neutrons can penetrate, but will slow down appreciably.
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Electron diffraction chez thomson: early responses to quantum physics in britain.
Published online by Cambridge University Press: 05 February 2010
In 1927, George Paget Thomson, professor at the University of Aberdeen, obtained photographs that he interpreted as evidence for electron diffraction. These photographs were in total agreement with de Broglie's principle of wave–particle duality, a basic tenet of the new quantum wave mechanics. His experiments were an initially unforeseen spin-off from a project he had started in Cambridge with his father, Joseph John Thomson, on the study of positive rays. This paper addresses the scientific relationship between the Thomsons, father and son, as well as the influence that the institutional milieu of Cambridge had on the early work of the latter. Both Thomsons were trained in the pedagogical tradition of classical physics in the Cambridge Mathematical Tripos, and this certainly influenced their understanding of quantum physics and early quantum mechanics. In this paper, I analyse the responses of both father and son to the photographs of electron diffraction: a confirmation of the existence of the ether in the former, and a partial embrace of some ideas of the new quantum mechanics in the latter.
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1 Those writing in support of G.P. Thomson's application were E.C. Pearce, master of Corpus Christi College; William Spens, fellow, tutor and director in science, Corpus Christi; Ernest Rutherford, director of the Cavendish Laboratory; Horace Lamb, former professor in Manchester, retired in Cambridge since 1920; Alex Wood, university lecturer in experimental physics, fellow and tutor of Emmanuel College; R.A. Herman, university lecturer in mathematics, fellow of Trinity College; B. Melvill Jones, Francis Mond Professor of Aeronautics in Cambridge; C.T.R. Wilson, Solar Physics Observatory, Cambridge; and R.T. Glazebrook, who had been a demonstrator in the Cavendish before being appointed director of the National Physical Laboratory. These letters are all kept in the Special Libraries & Archives of the University of Aberdeen.
2 Letters by Alex Wood and R.T. Glazebrook, 21 July 1922, Special Libraries & Archives of the University of Aberdeen.
3 G.P. Thomson, application letter to the chair in Aberdeen, Special Libraries & Archives of the University of Aberdeen.
4 The biographical approach to an entity such as the electron has been worked in detail by T. Arabatzis in his recent ‘biography’ of the electron. However, his work does not include any reference to the dual aspect, wave and particle, of the electron. See Theodore Arabatzis, Representing Electrons: A Biographical Approach to Theoretical Entities , Chicago: University of Chicago Press, 2006. For more general considerations on the use of the biographical discourse applied to scientific entities see Lorraine Daston (ed.), Biographies of Scientific Objects , Chicago: University of Chicago Press, 2000. In this paper, however, I do not consider the electron as an active character in the story but only insofar as it binds together the scientific careers of J.J. and G.P. Thomson.
5 For recent studies on the discovery of the electron see George E. Smith, ‘J.J. Thomson and the electron, 1887–1889’, in Jed Z. Buchwald and Andrew Warwick (eds.), Histories of the Electron , Cambridge, MA: MIT Press, 2001, pp. 21–76; Isobel Falconer, ‘Corpuscles and electrons’, in Buchwald and Warwick (op. cit.), pp. 77–100; and Helge Kragh, ‘The electron, the protyle, and the unity of matter’, in Buchwald and Warwick (op. cit.), pp. 195–226; Theodore Arabatzis, ‘Rethinking the “discovery” of the electron’, Studies in the History and Philosophy of Modern Physics (1996) 27, pp. 405–435; Falconer , Isobel , ‘ Corpuscles, electrons and cathode rays: J.J. Thomson and the “Discovery of the Electron” ’, BJHS ( 1987 ) 20 , pp. 241 – 276 . CrossRef Google Scholar
6 See Isobel Falconer, ‘Theory and experiment in J.J. Thomson's work on gaseous discharge’, PhD dissertation, Cambridge, 1985; and Edward Arthur Davis and Isobel Falconer, J.J. Thomson and the Discovery of the Electron , London: Taylor & Francis, 1997. See also Heilbron , John , ‘ J.J. Thomson and the Bohr atom ’, Physics Today ( 1977 ) 30 , pp. 23 – 30 . CrossRef Google Scholar
7 See Andrew Warwick, Masters of Theory: Cambridge and the Rise of Mathematical Physics , Chicago: University of Chicago Press, 2003.
8 See Dong-Won Kim, Leadership and Creativity: A History of the Cavendish Laboratory, 1871–1919 , Dordrecht: Kluwer, 2002.
9 Robert John Strutt, The Life of Sir J.J. Thomson , Cambridge: Cambridge University Press, 1942.
10 George Paget Thomson, J.J. Thomson and the Cavendish Laboratory in His Day , London: Nelson, 1964.
11 Falconer , Isobel , ‘ J.J. Thomson's work on positive rays ’, Historical Studies in the Physical Sciences ( 1988 ) 18 , pp. 265 – 310 . CrossRef Google Scholar
12 Warwick, op. cit. (7), Epilogue.
13 The expression was used by Rutherford in a conversation with Lodge. See J. Arthur Hill (ed.), Letters from Sir Oliver Lodge: Psychical, Religious, Scientific and Personal , London: Cassell, 1932, p. 224. Quoted in Noakes , Richard , ‘ Ethers, religion and politics in late-Victorian physics: beyond the Wynne thesis ’, History of Science ( 2005 ) 63 , pp. 415 – 455 CrossRef Google Scholar , p. 445.
14 A biographical sketch of G.P. Thomson can be found in P.B. Moon, ‘George Paget Thomson’, Biographical Memoirs of the Fellows of the Royal Society (1977) 23, pp. 265–310. In this section, I partly follow this sketch and the autobiographical notes of G.P., kept in the archives of Trinity College, Cambridge, on which Moon relied to write this biographical memoir.
15 Joseph John Thomson, Recollections and Reflections , London: Bell, 1936, p. 34. The expression means that J.J. never left Cambridge for more than a few weeks and that he was in the university every single academic term since his arrival in Cambridge.
16 G.P. Thomson papers (subsequently GP). Trinity College Archive, A2, 6.
17 See Strutt, op. cit. (9), Chapter 7.
18 GP, A2, 16.
19 Moon, op. cit. (14), p. 531.
20 GP, A2, 18.
21 Warwick, op. cit. (7), pp. 260–261.
22 Oral interview with G.P. Thomson, Archive for the History of Quantum Physics, Tape T2, side 2, 1.
23 J.J. Thomson, op. cit. (15), p. 39.
24 See Joseph Larmor, Aether and Matter , Cambridge: Cambridge University Press, 1900; and Joseph John Thomson, Conduction of Electricity through Gases , Cambridge: Cambridge University Press, 1903.
25 Oral interview with G.P. Thomson, Archive for the History of Quantum Physics, Tape T2, side 2, 2.
26 Warwick, op. cit. (7). See also Andrew Warwick, ‘Cambridge mathematics and Cavendish physics: Cunningham, Campbell and Einstein's relativity, 1905–1911. Part I: the uses of theory. Part II: comparing traditions in Cambridge Physics’, Studies in the History and Philosophy of Science (1992) 23, pp. 625–656; (1993) 24, pp. 1–25.
27 Warwick, op. cit. (7), pp. 396–397, argues in the following way: ‘What I have sought to demonstrate … is that adherence to the E[lectromagnetic] T[heory of] M[atter] in Cambridge after 1900 was not just a product of dogmatic belief in the ether's existence and of hostility to an alternative theory that dismissed the ether as superfluous. As far as Larmor's students were concerned, his work stood as a comprehensive and progressive addition to a research tradition in Cambridge that stretched back to Maxwell himself. Their commitment was not simply to the notion of an ether, but to a sophisticated conceptual structure and range of practical calculating techniques that were gradually acquired through years of coaching and problem solving. As they acquired these skills, the ether became an ontological reality that lent meaning both to the idea of an ultimate reference system and to the application of dynamical concepts to electromagnetic theory.’
28 As Warwick himself points out in the Epilogue to his book, an analysis of the reception of early quantum physics in Cambridge similar to his study of relativity is still to be done. In this paper I only take J.J. Thomson as a paradigmatic case of Cambridge physics in the early 1910s, since he certainly influenced the early career of G.P. Thomson.
29 Joseph John Thomson, The Structure of Light: The Fison Memorial Lecture , Cambridge: Cambridge University Press, 1925, p. 15.
30 Bruce R. Wheaton, The Tiger and the Shark: Empirical Roots of Wave–Particle Dualism , Cambridge: Cambridge University Press, 1983.
31 See Falconer, ‘Corpuscles, electrons and cathode rays’, op. cit. (5).
32 Joseph John Thomson, ‘The relation between the atom and the charge of electricity carried by it’, Philosophical Magazine (1895) 40, pp. 511–544, p. 512.
33 Joseph John Thomson, Electricity and Matter , London: Archibald Constable, 1906.
34 Joseph John Thomson, ‘Presidential address’, in Report of the British Association for the Advancement of Science, Winnipeg, 1909 , London, 1909, pp. 21–23.
35 According to McCormmach, Joseph Larmor was the first British scientist to react, in 1902, to Planck's hypothesis. See Russell McCormmach, ‘J.J. Thomson and the structure of light’, BJHS (1967) 3, pp. 362–387, p. 375.
36 McCormmach, op. cit. (35), pp. 375–376. For these different models, see Wheaton, op. cit. (30), especially Chapters 4 and 6.
37 See the Cambridge University Reporter . In 1919 Darwin offered a course on ‘Quantum theory and origin of spectra’. This course changed to ‘Recent developments on spectrum theory’ the following year, and a joint course on isotopes with Aston in 1921. In 1922 Fowler gave his first special course on ‘The theory of quanta’.
38 G.P. Thomson, op. cit. (10), p. 70.
39 Kim, op. cit. (8), p. 129.
40 Kim, op. cit. (8), Chapter 5.
41 Falconer, op. cit. (11), develops a very fine analysis of J.J. Thomson's work on positive rays, on which much in the following paragraphs is based.
42 See Falconer, op. cit. (11). For J.J.'s interests in chemistry see Jaume Navarro, ‘Imperial incursions in late-Victorian Cambridge: J.J. Thomson and the domains of the physical sciences’, History of Science (2006) 44, pp. 469–495.
43 Kim, op. cit. (8), pp. 169–174.
44 See also Jeff Hughes, ‘Redefining the context: Oxford and the wider world of British physics, 1900–1940’, in Robert Fox and Graeme Gooday (eds.), Physics in Oxford 1839–1939: Laboratories, Learning and College Life , Oxford: Oxford University Press, 2005, pp. 267–300, p. 276: ‘From around 1910, then, the Cavendish was being partially eclipsed by the development of Rutherford's research school at Manchester and the growth of “modern” physics at Leeds, London, Oxford, and elsewhere. In some ways it was a victim of its own success … [According to Bragg] there were too many students chasing too few ideas for research and too little apparatus. Thomson's own research on positive rays was in the doldrums, and the temper of the Cavendish seemed to have changed: it had lost the cohesiveness, excitement, and tightness of direction it had possessed.’
45 George Paget Thomson, ‘Charles Galton Darwin’, Biographical Memoirs of Fellows of the Royal Society (1963) 9, pp. 69–85, p. 70.
46 Graeme K. Hunter, Light Is a Messenger: The Life and Science of William Lawrence Bragg , Oxford: Oxford University Press, 2004, p. 21.
47 George Paget Thomson, Applied Aerodynamics , London: Hodder & Stoughton, 1920.
48 Oral interview with G.P. Thomson, Archive for the History of Quantum Physics, Tape T2, side 2, 12.
49 Joseph John Thomson, Rays of Positive Electricity and their Application to Chemical Analyses , London: Longmans, Green, 1921 (1st edn. 1913).
50 G.P. Thomson, op. cit. (10), p. 137.
51 Falconer, op. cit. (11), gives a detailed account of the divergence of J.J. Thomson's and Aston's ideas on positive rays.
52 For instance, the only paper in the Proceedings of the Royal Society on positive rays in the early 1920s is one in which Lord Rayleigh uses a technique similar to the one used by J.J. Thomson to interpret a photograph from an aurora borealis: ‘A photographic spectrum of the aurora of May 13–15, 1921, and laboratory studies in connection with it’, Proceedings of the Royal Society of London (1922) 101, pp. 114–124.
53 J.J. Thomson, op. cit. (49), Preface.
54 Thomson , George Paget , ‘ A note on the nature of the carriers of anode rays ’, Proceedings of the Cambridge Philosophical Society ( 1920 ) 20 , pp. 210 – 211 Google Scholar ; idem , ‘The spectrum of hydrogen positive rays’, Philosophical Magazine (1920) 40, pp. 240–247; idem , ‘The application of anode rays to the investigation of isotopes’, Philosophical Magazine (1921) 42, pp. 857–867; idem , ‘The scattering of hydrogen positive rays, and the existence of a powerful field of force in the hydrogen molecule’, Proceedings of the Royal Society (1922) 102, pp. 197–209.
55 Warwick, op. cit. (7), pp. 325–333. It was this group, and William Niven in particular, who got J.J. Thomson interested in Maxwell's Treatise during his undergraduate years.
56 Here I want to emphasize that G.P.'s laboratory in Aberdeen eventually became an extension only of J.J. Thomson's room at the Cavendish. Historians of science have analysed the transfer of elements of what has been called the ‘Cavendish style’ by research students appointed professors in other universities, such as Rutherford in McGill, Langevin in the Collège de France, or Townsend in Oxford. In these cases, one can compare the regimes implemented in the new research groups with the Cavendish regime; but with Aberdeen this is not possible, since there was never such a thing as a research group during G.P.'s tenure. See Benoit Lelong, ‘Translating ion physics from Cambridge to Oxford: John Townsend and the electrical laboratory, 1900–24’, in Fox and Gooday, op. cit. (44), pp. 209–232; John L. Heilbron, ‘Physics at McGill in Rutherford's time’, in Mario Bunge and William R. Shea (eds.), Rutherford and Physics at the Turn of the Century , Folkestone: Dawson, 1979, pp. 42–73.
57 Thomson , George Paget , ‘ The scattering of positive rays of hydrogen ’, Philosophical Magazine ( 1926 ) 1 , pp. 961 – 977 Google Scholar ; idem , ‘The scattering of positive rays by gases’, Philosophical Magazine (1926) 2, pp. 1076–1084.
58 George Paget Thomson, ‘An optical illusion due to contrast’, Proceedings of the Cambridge Philosophical Society (1926) 23, pp. 419–421, p. 421.
59 The letters from his wife, Kathleen, are kept in a special folder in the G.P. Thomson archives at Trinity College, Cambridge. GP A14 A.
60 We find G.P. Thomson giving a presentation in the Kapitza Club on 7 February and 2 August 1927, and on 30 July 1929. He was also present on 10 March 1928. See Churchill Archives, CKFT 7/1.
61 de Broglie , Louis , ‘ A tentative theory of light quanta ’, Philosophical Magazine ( 1924 ) 47 , pp. 446 – 458 . Google Scholar This paper was communicated by Ralph Fowler.
62 De Broglie, op. cit. (61), p. 450.
63 For this process, see V.V. Raman and Paul Forman, ‘Why was it Schrödinger who developed de Broglie's ideas?’, Historical Studies in the Physical Sciences (1969) 1, pp. 291–314.
64 Topper , David R. , ‘ “To reason by means of images”: J.J. Thomson and the mechanical picture of Nature ’, Annals of Science ( 1980 ) 37 , pp. 31 – 57 . CrossRef Google Scholar
65 Thomson , Joseph John , ‘ A suggestion as to the structure of light ’, Philosophical Magazine ( 1924 ) 48 , pp. 737 – 746 Google Scholar ; and idem , op. cit. (29).
66 Thomson , George Paget , ‘ Early work in electron diffraction ’, American Journal of Physics ( 1961 ) 29 , pp. 821 – 825 CrossRef Google Scholar , p. 821.
67 Oral interview with G.P. Thomson, Archive for the History of Quantum Physics, Tape T2, side 2, 8.
68 In his reconstruction of the events, G.P. presented a slightly different version of the facts. G.P. Thomson, op. cit. (66), p. 821: ‘At that time we were all thinking of the possible ways of reconciling the apparently irreconcilable. One of these ways was supposing light to be perhaps particles after all, but particles which somehow masqueraded as waves; but no one could give any clear idea as to why this was done. The first suggestion I ever heard which did not stress most of all the behaviour of the radiation came from the younger Bragg, Sir Lawrence Bragg, who once said to me that he thought the electron was not so simple as it looked, but never followed up this idea. However, it made a considerable impression on me, and it pre-disposed me to appreciate de Broglie's first paper in the Philosophical Magazine of 1924.’
69 See Arturo Russo, ‘Fundamental research at Bell Laboratories: the discovery of electron diffraction’, Historical Studies in the Physical Sciences (1981) 12, pp. 117–160, especially pp. 141–144.
70 George Paget Thomson, ‘A physical interpretation of Bohr's stationary states’, Philosophical Magazine (1925) 1, pp. 163–164, p. 163.
71 G.P.'s article, op. cit. (70), p. 164, only studies the hydrogen atom and ‘a simple extension of the above accounts also for the stationary states of ionized helium, and gives approximately the energy of the K ring of electrons’.
72 GP, F4, 7.
73 Expression used by Sir Oliver Lodge. See Hill, op. cit. (13), p. 225. See also Jeff Hughes, ‘“Modernists with a vengeance”: changing cultures of theory in nuclear science, 1920–1930’, Studies in the History and Philosophy of Modern Physics (1998) 29, pp. 339–367.
74 GP, A6, 7.
75 GP, C24, 13.
76 The published autobiographical accounts are the following: G.P. Thomson, op. cit. (66); and an extended version of it in George Paget Thomson, ‘The early history of electron diffraction’, Contemporary Physics (1968) 9, pp. 1–15. Moon's biographical sketch of G.P. Thomson is only a transcription of some paragraphs from these accounts. See Moon, op. cit. (14). See also his autobiographical notes in Trinity College, Cambridge.
77 Born's paper had a strong impact on many of those present, but especially on the American physicist working at the Bell laboratories, Clinton J. Davisson, when he heard that the anomalous results he had been obtaining in experiments on electron dispersion with his colleague Lester H. Germer might be signs of electron diffraction. That branch of the story, which was studied in detail by historian of science Arturo Russo, ends with the confirmation of electron diffraction in the Bell laboratories and the sharing of the Nobel Prize with G.P. Thomson for their experimental proof of de Broglie's principle. At the time of his first experiments, however, Thomson was not fully aware of Davisson's project. Born also mentioned the experiments of the young German physicist Walter M. Elsasser, who had unsuccessfully tried to detect diffraction patterns in the passage of an electron beam through a metallic film. See Russo, op. cit. (69).
78 G.P. Thomson, op. cit. (76), p. 7. These results were published in Nature : E.G. Dymond, ‘Scattering of electrons in helium’, Nature (1926) 118, pp. 336–337.
79 In Cambridge, P.M.S. Blackett had also tried to obtain evidence of electron diffraction, but gave up after a few months. See Mary Jo Nye, Blackett, Physics, War, and Politics in the Twentieth Century , Cambridge, MA: Harvard University Press, 2004, p. 46.
80 G.P. Thomson, op. cit. (66), p. 823.
81 G.P. Thomson, op. cit. (76), p. 7.
82 George Paget Thomson and Alexander Reid, ‘Diffraction of cathode rays by a thin film’, Nature (1927) 119, p. 890.
83 George Paget Thomson, ‘The diffraction of cathode rays by thin films of platinum’, Nature (1927) 120, p. 802; ‘Experiments on the diffraction of cathode rays’, Proceedings of the Royal Society (1928) 117, pp. 600–609; ‘Experiments on the diffraction of cathode rays. II’, Proceedings of the Royal Society (1928) 119, pp. 651–663; ‘Experiments on the diffraction of cathode rays. III’, Proceedings of the Royal Society (1929) 125, pp. 352–370.
84 GP, A6, 10/3.
85 I do not mean to say here that there is a parallel between the story of the Braggs, father and son, and the story of the Thomsons, also father and son. I only suggest that one can easily suppose that G.P.'s friendship with Bragg was a natural channel for him to follow closely the developments on X-rays.
86 See Hunter, op. cit. (46), pp. 70 and 104. Unfortunately, I have found no evidence of conversations between G.P. Thomson and W.L. Bragg on this matter in the summer of 1926.
87 Darwin came back to Cambridge after the war and was made a fellow of Christ's College while G.P. was a fellow in Corpus Christi. On Darwin see G.P. Thomson, op. cit. (45).
88 The following anecdote helps to illustrate the importance of electromagnetic deflection. Probably around the beginning of March 1928, he also had the opportunity to discuss his experimental results with Schrödinger himself as the latter recalled in 1945: ‘After mentioning briefly the new theoretical ideas that came up in 1925/26, I wish to tell of my meeting you in Cambridge in 1927/28 (I think it was in 1928) and of the great impression the marvellous first interference photographs made on me, which you kindly brought to Mr. Birthwistle's house, where I was confined with a … cold. I remember particularly a fit of scepticism on my side (“And how do you know it is not the interference pattern of some secondary X-rays?”) which you immediately met by a magnificent plate, showing the whole pattern turned aside by a magnetic field.’ Schrödinger to G.P. Thomson, 5 February 1945, GP, J105, 4. The exact date can be traced by the minutes of the Kapitza Club, which says that Schrödinger gave a paper to the club on 10 March 1928. See Churchill Archives, CKFT, 7/1.
89 G.P. Thomson, ‘Experiments I’, op. cit. (83), p. 608.
90 G.P. Thomson, ‘Experiments I’, op. cit. (83), pp. 608–609.
91 Oral interview with G.P. Thompson, Archive for the History of Quantum Physics, Tape T2, side 2, 15.
92 G.P. Thomson, op. cit. (45), p. 81.
93 See Jaume Navarro, ‘J.J. Thomson on the nature of matter: corpuscles and the continuum’, Centaurus (2005) 47, pp. 259–282.
94 Joseph John Thomson, ‘Waves associated with moving electrons’, Philosophical Magazine (1928) 5, pp. 191–198, p. 191.
95 Joseph John Thomson, ‘Electronic waves and the electron’, Philosophical Magazine (1928) 6, pp. 1254–1281, p. 1259.
96 J.J. Thomson, op. cit. (95), p. 1254. J.J.'s model for the electron sphere would soon be expressed in terms only of what he came to call ‘granules’, particles ‘having the same mass μ, moving with the velocity of light c , and possessing the same energy μ c 2 ’. See Joseph John Thomson, ‘Atoms and electrons’, Manchester Memoirs (1930–1931) 75, pp. 77–93, p. 86.
97 Joseph John Thomson, Beyond the Electron , Cambridge: Cambridge University Press, 1928, p. 9.
98 J.J. Thomson, op. cit. (97), p. 22.
99 J.J. Thomson, op. cit. (97), p. 23.
100 J.J. Thomson, op. cit. (97), p. 31.
101 J.J. Thomson, op. cit. (97), p. 34.
102 Joseph John Thomson, Tendencies of Recent Investigations in the Field of Physics , London: British Broadcasting Corporation, 1930, pp. 26–27.
103 Oral interview with G.P. Thomson, Archive for the History of Quantum Physics, Tape T2, side 2, 9: ‘Well, I think he was very pleased [with my developments], largely because it was in the family.’
104 Joseph John Thomson, ‘Electronic waves’, Philosophical Magazine (1939) 27, pp. 1–33.
105 Thomson and Reid, op. cit. (82), and Churchill Archives, CKFT 7/1.
106 G.P. Thomson, op. cit. (83).
107 George Paget Thomson, ‘The waves of an electron’, Nature (1928) 122, pp. 279–282, p. 281.
108 George Paget Thomson, The Wave Mechanics of Free Electrons , New York: McGraw Hill, 1930, p. 11.
109 G.P. Thomson, op. cit. (108), p. 12.
110 G.P. Thomson, op. cit. (108), p. 282.
111 For a thorough analysis of the problems with beta decay and the conservation of energy see Carsten Jensen, Controversy and Consensus: Nuclear Beta Decay, 1911–1934 , Basel: Birkhäuser, 2000.
112 On Darwin's ideas on the conservation of energy see Klaus Stolzenburg (ed.), Niels Bohr, Collected Works , vol. 5, Amsterdam: North-Holland, 1984, pp. 13–19, pp. 67–69, pp. 81–83 and pp. 317–319; and Jørgen Kalckar (ed.), Niels Bohr, Collected Works , vol. 6, Amsterdam: North-Holland, 1985, pp. 91–99, pp. 305–319 and pp. 347–349.
113 George Paget Thomson, ‘On the waves associated with β-rays, and the relation between free electrons and their waves, Philosophical Magazine (1929) 7, pp. 405–417, p. 410.
114 G.P. Thomson, op. cit. (113), p. 415.
115 See George Paget Thomson, ‘The disintegration of radium E from the point of view of wave mechanics’, Nature (1928) 121, pp. 615–616: the apparent non-conservation of energy ‘is to be expected on the new wave mechanics, if the ejection of a β-particle is produced by anything like a sudden explosion. In such a case one would expect that the wave-group which accompanies, and on some views actually constitutes, the electron, would be of the nature of a single pulse, that is, the damping factor of the amplitude would be of the order of the wave-length. Such a wave-group, being very far from monochromatic, would spread rapidly lengthwise owing to the large dispersion of the phase waves, and so the distance within which the electron may occur becomes large, implying a marked “straggling” in velocity. Similarly, if the waves pass through a magnetic field, which is for them a refracting medium, the group will split into monochromatic waves going in different directions, just as white light is split up by a prism. Thus an observer who forms the magnetic spectrum of the β-rays will find electrons in places corresponding to paths of various curvatures, that is, he will find a spectrum continuous over a wide range.’
116 In Jaume Navarro, ‘“A dedicated missionary”: Charles Galton Darwin and the new quantum mechanics in Britain’, Studies in the History of Modern Physics (2009) 40, pp. 316–326, I argue that Darwin's approach to theoretical quantum mechanics can be traced back to his early training in the Cambridge Mathematical Tripos, which, following Warwick's analysis (op. cit. (7)), provided physicists and mathematical physicists with an epistemological and ontological framework that was at odds with the so-called Copenhagen interpretation of quantum mechanics, but which resonated very well with the continuous ontology of Schrödinger's approach.
117 For standard account of this episode in the history of quantum mechanics see Jagdish Mehra and Helmut Rechenberg, The Historical Development of Quantum Theory , vol. 6, part 1, New York: Springer, 2000. See also Helge Kragh, Quantum Generations , Princeton: Princeton University Press, 1999, Chapter 11. For a critical assessment of the equivalence between Heisenberg and Schrödinger's approach see F.A. Muller, ‘The equivalence myth of quantum mechanics. Part I’, Studies in History and Philosophy of Modern Physics (1997) 28, pp. 35–61.
118 Charles Galton Darwin, ‘The wave equations of the electron’, Proceedings of the Royal Society (1928) 118, pp. 654–680, 654. See also idem , The New Conceptions of Matter , London: Bell, 1931, p. 124.
119 Charles Galton Darwin, ‘Collision problem in wave mechanics’, Proceedings of the Royal Society (1929) 124, pp. 375–394, pp. 391–392.
120 Darwin, op. cit. (119), pp. 393–394: ‘The subworld of ψ expresses in its own way everything that happens; but it is a dead world, not involving definite events, but instead the potentiality for all possible events. It becomes animated by our consciousness, which so to speak cuts sections of it when it makes observations. These observations are described in a language and by means of rules which are foreign to the subworld; the quantum itself enters for the first time … whereby we can talk of atoms, electrons and light-quanta.’
121 G.P. Thomson, op. cit. (108), p. 12. My emphasis.
122 Darwin, The New Conceptions of Matter , op. cit. (118), p. 107.
123 George Paget Thomson, ‘New discoveries about electrons’, The Listener (1929) 1, pp. 219–220, p. 220.
124 One might want to ask how influential in this story was J.J.'s wife, G.P.'s mother, also trained as a physicist. We have no evidence of her playing any active role in the scientific life of the family, but even if new evidence proves otherwise, that would not invalidate the arguments in this paper, but only complement them. For a gender-based analysis of scientific families see Helena M. Pycior, Nancy G. Slack and Pnina G. Abir-Am, Creative Couples in the Sciences , New Brunswick: Rutgers University Press, 1996.
125 Jeff Hughes uses the Aberdeen example for a different purpose – to play down the overall importance of the Cavendish in the 1920s and 1930s. See Hughes, op. cit. (44), p. 283: ‘At Aberdeen, the work of J.J.'s son George Thomson on positive rays in hydrogen led to the elaboration of electron diffraction, for which he shared the 1937 Nobel Prize for physics – aptly reminding us that although we tend to associate the canonical achievements of modern British physics with the Cavendish, they often emerged elsewhere.’
126 See Falconer, ‘Corpuscles, electrons and cathode rays’, op. cit. (5).
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- Volume 43, Issue 2
- JAUME NAVARRO (a1)
- DOI: https://doi.org/10.1017/S0007087410000026
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Matter Wave Technologies
What are Matter Waves?
Matter waves were first proposed by Louis de Broglie in 1924. He suggested that particles like electrons can behave like waves. This idea challenged the traditional view of particles and had a profound impact on quantum mechanics. In this article, we will explore the properties of matter waves and how they differ from light waves. We will also look at experimental evidence and practical applications that have transformed our understanding of the quantum world.
Table of Contents
Matter waves , also known as de Broglie waves , are defined scientifically as the wave-like behavior exhibited by particles at the quantum scale. According to de Broglie’s hypothesis, any moving particle or object has an associated wave whose wavelength is inversely proportional to the momentum of the particle. This relationship is expressed by the equation:
\[\lambda = \frac{h}{p} \]
where \( \lambda \) is the wavelength, \( h \) is the Planck constant, and \( p \) is the momentum of the particle. Matter waves form a core component of quantum mechanics, illustrating the dual particle-wave nature of elementary particles, a fundamental principle that underscores the behavior of all matter at microscopic scales.
Examples of Matter Waves in Action
Matter waves play a crucial role in both scientific research and technological applications. They help demonstrate key concepts in quantum mechanics. Here are some key examples:
- Electron Diffraction : When electrons pass through a thin metal or crystal, they behave like waves. This wave-like behavior creates an interference pattern, similar to light in optical experiments. Electron diffraction is direct evidence of particles’ wave nature. It’s used in electron microscopes for detailed images of atomic structures.
- Neutron Scattering : Neutrons are neutral particles that can explore the structure of materials. Their wave properties allow them to reveal detailed internal atomic arrangements. Neutron scattering is essential in materials science, biology, and chemistry.
- Atomic Interferometry : Atoms are cooled to near absolute zero to form matter waves. These waves are manipulated with lasers and magnets, creating interference patterns. These patterns can measure forces like gravity with high precision. This technique is vital for precision measurements and navigation technologies.
- Bose-Einstein Condensates (BEC) : In BECs, cooled atoms form a single quantum entity or matter wave. This unique state lets scientists study quantum phenomena on a large scale, like superfluidity and quantum vortices.
These examples show how matter waves are fundamental in advancing our understanding of the quantum world across different scientific and technological fields.
Who Discovered the Matter Wave?
As mentioned earlier, the credit for this mind-bending concept goes to Louis de Broglie . His 1924 doctoral thesis introduced the idea of matter waves, proposing a mathematical connection between a particle’s momentum and its wavelength. This groundbreaking work laid the foundation for the further development of quantum mechanics and earned him the Nobel Prize in Physics in 1929 .
Properties of Matter Waves
Matter waves are very different from classical waves such as water waves or sound waves. They are not physical disturbances moving through space. Instead, they are mathematical descriptions of where particles might be found. Matter waves exist in the abstract world of quantum mechanics and follow its unique rules. Let’s explore some important properties of matter waves:
- Wave-Particle Duality : One of the fundamental properties of matter waves is their ability to exhibit both particle-like and wave-like characteristics. This duality is evident in phenomena like electron diffraction, where particles show interference patterns typical of waves.
- Quantization : Matter waves are quantized, meaning that certain properties such as energy and momentum take on discrete values. This quantization is a direct result of the wave-like properties and the constraints imposed by quantum mechanics.
- Superposition : Matter waves can exist in multiple states simultaneously until an observation forces them into one state. This property, known as superposition, allows particles to be in various probabilities of state until measured.
- Interference : Just like waves in classical physics, matter waves can interfere with each other, leading to constructive or destructive interference patterns. This is crucial in technologies like atomic interferometry, where the precision of measurements depends on the interference of matter waves.
- Probabilistic Nature : The wave function of a particle in quantum mechanics, which describes a matter wave, does not specify the exact location or momentum of a particle but rather the probabilities of finding the particle in various states. This probabilistic nature is central to the uncertainty principle in quantum mechanics.
- Tunneling : Matter waves can exhibit tunneling, where particles pass through potential barriers that they would not be able to overcome classically. This effect stems from the wave-like nature allowing the wave function to extend through and beyond barriers.
- Entanglement : When two particles become entangled, the state of one particle can instantaneously affect the state of the other, regardless of the distance between them. This property, which relies on the wave-like characteristics of particles, challenges classical notions of locality and causality.
These properties illustrate the complex and often non-intuitive behaviors of matter waves.
Differences Between Light and Matter Waves
Light waves and matter waves are key concepts in physics, yet they differ significantly in nature and behavior. Here are the main differences between light waves, which are electromagnetic, and matter waves, which are associated with particles:
- Nature of Waves: Light Waves – These are electromagnetic waves that travel through space without needing a medium. They consist of oscillating electric and magnetic fields. Matter Waves – Also known as de Broglie waves, these are linked to particles like electrons and atoms. They describe the probability of finding a particle in a certain position and momentum, according to quantum mechanics.
- Speed of Propagation: Light Waves – In a vacuum, light waves travel at a constant speed of about \(3 \times 10^8\) meters per second. Matter Waves – The speed of these waves depends on the mass and momentum of the particles. It varies and is generally much slower than the speed of light for particles of significant mass.
- Wave-Particle Duality: Light Waves – Light can show both wave-like behaviors (like interference and diffraction) and particle-like behaviors (comprising photons). Matter Waves – These waves also display wave-particle duality. Even though particles traditionally have specific locations and velocities, they can exhibit wave-like properties under certain conditions.
- Energy and Momentum Relationships: Light Waves – The energy and momentum of light are linked to their frequency and wavelength. The energy \(E\) of a photon is calculated by \(E = hf\), where \(h\) is Planck’s constant and \(f\) is the frequency. Matter Waves – For matter waves, the wavelength is inversely proportional to the particle’s momentum, as given by \( \lambda = \frac{h}{p} \), where \(p\) is the momentum.
- Quantum Effects: Light Waves – Quantum effects are noticeable in phenomena like the photoelectric effect, typically requiring high-frequency light. Matter Waves – Quantum effects are more pronounced in matter waves, especially at smaller scales such as electrons or atoms. Examples include quantum tunneling and entanglement.
These distinctions highlight the unique behaviors and properties of light and matter waves, showing their different roles in various physical phenomena and applications.
Experimental Evidence of Matter Waves
The existence of matter waves has been verified through numerous experiments. The most famous of these include:
- The Davisson-Germer Experiment: In 1927, Clinton Davisson and Lester Germer observed the diffraction of electrons by a nickel crystal ( Davisson and Germer, 1927 ), providing the first experimental confirmation of matter waves.
- G.P. Thomson experiment (1927) : Independent of Davisson and Germer, George Paget Thomson performed a similar experiment using thin metal foils instead of crystals ( Thomson, 1928 ). He also observed diffraction patterns, solidifying the case for the wave nature of electrons.
These and other experiments have cemented the concept of matter waves as a cornerstone of quantum mechanics, forever changing our understanding of the microscopic world.
Applications of Matter Waves
Matter waves have numerous practical applications in various fields, including:
- Electron Microscopy: By exploiting the wave properties of electrons, electron microscopes can achieve much higher resolution than traditional optical microscopes, allowing us to study structures at the atomic and subatomic levels.
- Neutron Scattering: Studying the diffraction of neutrons provides valuable information about the structure of materials, leading to advancements in fields like materials science and condensed matter physics.
- Atomic Clocks: Matter waves play a crucial role in the operation of highly accurate atomic clocks, vital for navigation, telecommunications, and scientific research.
Matter waves, also known as de Broglie waves, show that particles can behave like waves. This groundbreaking idea was introduced by Louis de Broglie in 1924. It highlights the dual nature of particles, displaying both wave and particle characteristics. Matter waves are quite different from light waves, especially in their quantum properties and behaviors. They have played a crucial role in enhancing our understanding of the quantum realm. This was proven by significant experiments, such as those conducted by Davisson-Germer and G.P. Thomson. Nowadays, matter waves are essential in various technologies, from electron microscopy to atomic clocks, underscoring their importance in both theory and practical applications.
References:
- Davisson, C. and Germer, L.H., 1927, Diffraction of electrons by a crystal of nickel, Physical Review 30 , 705.
- Thomson, G.P., 1928, Experiments on the diffraction of cathode rays, Proceedings of the Royal Society of London 117 , 600-609.
PhD Research Scholar Department of Physics, IIT Kanpur, India Research Interest: Matter Wave Optics and Plasma Physics Homepage | Gogoole Scholar
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How Two Rebel Physicists Changed Quantum Theory
David Bohm and Hugh Everett were once ostracized for challenging the dominant thinking in physics. Now, science accepts their ideas, which are said to enrich our understanding of the universe.
The field of quantum mechanics dates to 1900, the year German scientist Max Planck (1858–1947) discovered that energy could come in discrete packages called quanta. It advanced in 1913, when Danish physicist Niels Bohr (1885–1962) used quantum principles to explain what had until then been inexplicable, the exact wavelengths of light emitted or absorbed by a gas of hydrogen atoms. And since the 1920s, when Werner Heisenberg (1901–1976) and Erwin Schrödinger (1887–1961) built new quantum theories, quantum mechanics has consistently proven its value as the fundamental theory of the nanoscale and as a source of technology, from computer chips and lasers to LED bulbs and solar panels.
One question, however, still puzzles: how does the quantum world relate to the more familiar human-scale one? For a century, the Copenhagen interpretation , chiefly developed by Bohr and Heisenberg in that city, has been the standard answer taught in physics courses. It posits that the quantum scale is indeterminate; that is, operates according to the laws of probability. This world is utterly different from the deterministic and predictable “classical” human scale, yet the Copenhagen interpretation doesn’t clearly explain how reality changes between the two worlds.
Heisenberg and Bohr developed the Copenhagen interpretation amidst the blossoming of new quantum theories in the first half of the twentieth century. In 1927, Heisenberg announced his important uncertainty principle : at the quantum level, certain pairs of quantities, such as momentum and position, cannot be simultaneously measured to any desired degree of precision. The more exactly you measure one, the less well you know the other. Thus, we can never fully know the quantum world, a key feature of the Copenhagen interpretation.
Indeterminism also appears in the Schrödinger wave equation at the heart of the Copenhagen view. Einstein had shown that light waves can act like swarms of particles, later called photons; in 1924, Louis de Broglie assumed the inverse, that tiny particles are also wave-like. In 1926, Schrödinger published his equation for these “matter waves.” Its solution, the “wave function” denoted by the Greek letter Ψ (psi), contains all possible information about a quantum entity such as an electron in an atom. But the information is indeterminate: Ψ is only a list of probable values for all the different physical properties, such as position or momentum, that the electron could have in its particular surroundings. The electron is said be in a superposition , simultaneously present in all its potential states of actual being.
This superposition exists until an observer measures the properties of the electron, which makes its wave function “collapse”; the cloud of possible outcomes yields just one result, a definite value emerging into the classical world. It is as if, asked to pick a card out of a deck, the instant you select the three of hearts, the other fifty-one cards fade away. In this case, we know that the rejected cards still physically exist with definite properties, but in the Copenhagen view, subatomic particles aren’t real until they’re observed. Another problem is that the notion of a sudden wave function collapse seems an arbitrary addition to the Copenhagen interpretation; it contradicts the smooth evolution in time built into the Schrödinger equation.
These troubling features, called “the measurement problem,” were hotly debated in the 1920s. But overwhelming any objections was the fact that the Copenhagen interpretation works! Its results agree precisely with experiments, the final test of any theory, and inspire real devices. Even so, David Joseph Bohm (1917–1992) and Hugh Everett III (1930–1982) sought equally valid theories without any incongruities. In the 1950s, these two American physicists dared to challenge the conventional Copenhagen interpretation with their “pilot wave” and “many-worlds” theories, respectively. Though from different backgrounds, Bohm and Everett shared characteristics that helped them seek answers: mathematical aptitude, necessary to manipulate quantum theory; and unconventional career paths, which separated them from the orthodoxy of academic physics.
Bohm was a second-generation American, born into an immigrant family from Europe that operated a furniture store in Wilkes-Barre, Pennsylvania. In high school, where his physics instructor described him as “outstanding” and “brilliant,” Bohm developed his own alternative ideas about Bohr’s hydrogen atom. After undergraduate work at Penn State, he began earning a PhD in nuclear physics in 1941 under J. Robert Oppenheimer (1904–1967) at the University of California, Berkeley. The United States was engaged in World War II at the time and was about to build an atomic bomb. Bohm’s doctoral research was classified, and he was awarded his degree in 1943 without writing a dissertation. Though Oppenheimer wanted Bohm to work with him at Los Alamos, Bohm couldn’t get security clearance as he had briefly been, in the early 1940s, a member of the Communist Party.
In 1947, supported by theorist John Wheeler, Bohm became an assistant professor at Princeton. There he taught quantum mechanics and wrote Quantum Theory (1951), in which he presented the Copenhagen interpretation, only to disavow it the next year, when he published his alternative theory in a pair of papers in the Physical Review (in 1957, he expounded his ideas further in his book Causality and Chance in Modern Physics ).
But in 1951, his life had taken a serious turn. In that Cold War era of McCarthyism, Bohm was brought before the House Committee on Un-American Activities (HUAC). He pleaded the Fifth Amendment against self-incrimination, and he was first indicted and jailed for contempt of Congress and then acquitted when the Supreme Court decriminalized this action. Still, the damage was done. Princeton didn’t renew Bohm’s contract and banned him from campus in June 1951. Unable to obtain a new academic position in the US, he began a life-long exile, taking temporary teaching positions in Brazil and elsewhere. Finally, in 1961, he accepted the offer of a chaired professorship in physics at Birkbeck College, London. He remained in that position until he retired in 1983, continuing to develop his new approach, the “pilot wave” theory.
When de Broglie postulated that tiny particles are also wave-like, he proposed the role of the waves as guiding or piloting the motions of real physical particles. Bohm fleshed out this insight by relating the pilot wave to Schrödinger’s wave function Ψ. In Bohm’s view, Ψ doesn’t collapse, but shepherds real subatomic particles into specific trajectories. This scenario yields the same results as the Schrödinger equation and resolves a great wave-particle quantum paradox. In the famous double-slit experiment , a stream of electrons or photons sent through two slits produces a pattern that could arise only from interfering waves, not particles. Bohm’s solution is that each particle traversing one of the slits rides a wave that pilots it into a complex path and generates an interference pattern from the swarm of particles.
For his part, Everett solved the measurement problem differently, as described by biographer Peter Byrne in an article , and later, a book . Born in Washington, DC, Everett showed an early interest in logical contradictions. At age twelve, he wrote to Einstein about the paradox “irresistible force meets immovable body,” and, as Everett reports, Einstein replied that there is no such paradox, but he noted Everett’s drive in attacking the problem. Everett graduated with honors from Catholic University as an engineer with strong backgrounds in math, operations research, and physics.
In 1953, Everett went to Princeton for graduate work. There he met Bohr, whose visit at the nearby Institute for Advanced Study sparked discussions about quantum mechanics. Later Everett said that the idea for his new theory came during a sherry-fueled session with one of Bohr’s assistants, among others. Everett was soon working out the consequences of his idea in a dissertation under John Wheeler, who had mentored Bohm and also Nobel Laureate Richard Feynman (1918–1988), and who called Everett “highly original.”
In the Copenhagen view, quantum reality as determined by the Schrödinger equation is separate from classical reality. Everett boldly asserted instead that the Schrödinger equation applies to everything, small or big, object or observer. The resulting universal wave function describes a reality without a boundary between microscopic and macroscopic or any need for the wave function to collapse. In his scheme, the measurement problem doesn’t exist.
This, however, comes at the cost of accepting a highly complex universe. If large objects and their observers obey the Schrödinger equation, then the universal wave function includes all observers and objects and their links in superposition. As Byrne explains: if the object could exist at either point A or B, in one branch of the universal wave function the observer sees the measurement result as “A,” and in another branch, a nearly identical person sees the result as “B.” (Everett called different elements of the superposition “branches.”) Further, without the jarring disruption of wave function collapse, the Schrödinger equation tells us that the branches go smoothly forward in time and do not interact, so each observer separately sees a normally unfolding macroscopic world.
In layman’s terms, this means that the universe, instead of being a unity that encompasses all reality, is filled with separate multiverses or bubbles of reality, each believed to be the entire universe by its inhabitants. The observer who saw result “A” now lives in that reality, and the person who saw “B” occupies a separately evolving reality according to their different outcome. Each of these unimaginable numbers of bubbles moves ahead into its own future, forming a totality filled with what have come to be called “parallel worlds.”
Bohr and his group scorned this grandiose idea as an answer to the measurement problem, one of his circle calling it “theology,” and another deriding Everett as “ stupid .” Wheeler had Everett rewrite his dissertation so it didn’t directly criticize the Copenhagen interpretation or its proponents. His thesis was published in 1957 and, according to Byrne, “slipped into instant obscurity.” All this should have been no surprise. As Olival Freire Jr. points out , Bohm’s earlier work—which Everett cited—had also been badly received, even with hostility, in a community dominated by Bohr and champions of the Copenhagen interpretation.
That was to change for both theories. In 1964, a bombshell result from theorist John Bell showed how to experimentally confirm the exceedingly strange quantum effect of entanglement, which Einstein called “ spooky action at a distance ”: the fact that two quantum entities can affect each other over arbitrary distances. Bell, it turns out, was strongly influenced by Bohm’s work, notes Freire. This shows that rethinking the foundations of quantum mechanics, downplayed by some physicists as only a philosophical exercise, can pay off in deep theoretical insights as well as in technology; entanglement today is used in quantum computation, communication, and cryptography.
Everett’s ideas too came to be more appreciated after The Many-Worlds Interpretation of Quantum Mechanics (Bryce DeWitt and Neill Graham, editors) was published in 1973. It included Everett’s original dissertation and related papers. This and DeWitt’s evocative phrase “many-worlds interpretation” brought new interest in Everett’s work and linked it to multiverse theory , which has been developed to solve certain problems in cosmology and as an outcome of string theory. Everett won further recognition—this time in popular culture—in 1976, when his work appeared in Analog , a leading science fiction magazine. (In fact, multiverses and parallel worlds have become staples of popular culture, as the film Everything Everywhere All at Once (2022) and the streaming series Dark Matter (2024), based on the novel by Blake Crouch, make clear.)
By 2023, Bohm’s and Everett’s seminal papers had each amassed tens of thousands of citations in the scientific literature. Surveys have also asked hundreds of physicists which interpretation of quantum mechanics they consider best. Many chose the Copenhagen view, but an equal number favor either the pilot wave or many-worlds interpretation. It’s striking that what in the 1950s were outlaw ideas, met with disbelief and antagonism, today have a significant degree of acceptance and have greatly expanded our view of the quantum world and the universe.
That Bohm and Everett could produce novel theories reflects their special circumstances and their times as well as their abilities. McCarthyism interrupted Bohm’s career but also freed him from conventional views of quantum mechanics. Historian of science Christian Forstner cites a 1981 interview in which Bohm acknowledges the upside to his departure from Princeton. It “liberated me,” Bohm admitted. “I was able to think more easily and more freely…without having to talk the language of other people.” Forstner notes that in exile, the physicist had the freedom to choose like-minded colleagues so that “the US-community and its thought-style lost importance for Bohm.” Indeed, Bohm’s exile was highly productive.
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Everett’s expertise in operations research brought him the offer of a position with the Pentagon’s Weapons Systems Evaluation Group (WSEG) to analyze nuclear warfare after finishing his PhD. Wheeler wanted him to continue at Princeton but also knew, Byrne writes, that the lack of recognition for Everett’s ideas had left him “disappointed, perhaps bitter.” Nor did Everett enjoy truncating his thesis to mollify Bohr, and he must have realized that advocating an unpopular theory would cloud his academic career. In the end, he chose WSEG and never again worked in theoretical physics, but perhaps having this alternate possibility stiffened his resolve in presenting and defending his audacious idea. His talents shone at WSEG, but, according to Byrne, he was an alcoholic and died of a heart attack at age fifty-one.
The co-existing Copenhagen, Bohm, and Everett interpretations give the same results for many different tests of quantum behavior; and so we await the subtle experiment that distinguishes among them, showing which one is physically true and might give philosophers new insight into the nature of reality. Bohm’s and Everett’s sagas provide another valuable lesson. Science prides itself on being self-correcting; wrong theories are eventually made right, as in the old notion of a geocentric universe giving way to the modern view. The Copenhagen interpretation became unquestioned orthodoxy, but Bohm and Everett challenged it even at personal cost. That reflects the highest aspirations of science and deserves to be recognized in 2025, the upcoming International Year of Quantum Science and Technology.
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Quantum time travel: The experiment to 'send a particle into the past'
Time loops have long been the stuff of science fiction. Now, using the rules of quantum mechanics, we have a way to effectively transport a particle back in time – here’s how
By Miriam Frankel
29 May 2024
Ryan wills/istock/Amtitus
When Seth Lloyd first published his ideas about quantum time loops, he hadn’t considered all the consequences. For one thing, he hadn’t anticipated the countless emails he would get from would-be time travellers asking for his help. If he could have his time over again, he jokes, he “probably wouldn’t have done it”.
Sadly, Lloyd, a physicist at the Massachusetts Institute of Technology, won’t be revisiting years gone by. Spoiler alert: no one will go back in time during the course of this article. But particles? That is another matter.
Theoretical routes to the past called time loops have long been hypothesised by physicists. But because they are plagued by impracticalities and paradoxes, they have been dismissed as impossible for just as long. But now Lloyd and other physicists have begun to show that in the quantum realm, these loops to the past are not only possible, but even experimentally feasible. In other words, we will soon effectively try to send a particle back in time.
Rethinking reality: Is the entire universe a single quantum object?
If that succeeds, it raises the possibility of being able to dispatch, if not people, then at least messages in the form of quantum signals, back in time. More importantly, studying this phenomenon takes us to the heart of how cause and effect really work, what quantum theory means and perhaps even how we can create a successor theory that more fully captures the true nature of reality.
In physics, time loops are more properly known as closed time-like curves (CTCs). They first arose in Albert Einstein’s theory of general relativity…
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The Physicist Who’s Challenging the Quantum Orthodoxy
July 10, 2023
Jonathan Oppenheim, a physicist at University College London, is developing hybrid theories that could unify classical gravity and quantum mechanics.
Philipp Ammon for Quanta Magazine
Introduction
Most physicists expect that when we zoom in on the fabric of reality, the unintuitive weirdness of quantum mechanics persists down to the very smallest scales. But in those settings, quantum mechanics collides with classical gravity in a resolutely incompatible way.
So for almost a century, theorists have tried to create a unified theory by quantizing gravity, or sculpting it according to the rules of quantum mechanics. They still haven’t succeeded.
Jonathan Oppenheim , who runs a program exploring post-quantum alternatives at University College London, suspects that’s because gravity simply can’t be squeezed into a quantum box. Maybe, he argues, our presumption that it must be quantized is wrong. “That view is ingrained,” he said. “But no one knows what the truth is.”
Quantum theories are based on probabilities rather than certainties. For example, when you measure a quantum particle, you can’t predict exactly where you will find it, but you can predict the likelihood that it will be found in a particular place. What’s more, the more certain you are about a particle’s location, the less certain you are about its momentum. Over the 20th century, physicists gradually made sense of electromagnetism and other forces using this framework.
But when they tried to quantize gravity, they ran into unnatural infinities that had to be sidestepped with clumsy mathematical tricks.
The problems arise because gravity is a result of space-time itself, rather than something that acts on top of it. So if gravity is quantized, that means space-time is also quantized. But that doesn’t work, because quantum theory only makes sense against a classical space-time background — you can’t add and then evolve quantum states on top of an uncertain foundation.
Video : Oppenheim describes why he thinks gravity can’t be squeezed into the same quantum box as the other fundamental forces — and what he’s proposing as an alternative.
Christopher Webb Young/ Quanta Magazine ; Noah Hutton for Quanta Magazine
To deal with this deep conceptual conflict, most theorists turned to string theory, which imagines that matter and space-time emerge from tiny, vibrating strings. A smaller faction looked to loop quantum gravity, which replaces the smooth space-time of Einstein’s general relativity with a network of interlocked loops. In both theories, our familiar, classical world somehow emerges from these fundamentally quantum building blocks.
Oppenheim was originally a string theorist, and string theorists believe in the primacy of quantum mechanics. But he soon became uncomfortable with the elaborate mathematical acrobatics his peers performed to tackle one of the most notorious problems in modern physics: the black hole information paradox .
In 2017, Oppenheim started searching for alternatives that avoided the information paradox by taking both the quantum and the classical worlds as bedrocks. He stumbled across some overlooked research on quantum-classical hybrid theories from the 1990s, which he’s been extending and exploring ever since. By studying how the classical and quantum worlds interrelate, Oppenheim hopes to find a deeper theory that is neither quantum nor classical, but some kind of hybrid. “Often we put all our eggs in a few baskets, when there are lots of possibilities,” he said.
To make his point, Oppenheim recently made a bet with Geoff Penington and Carlo Rovelli — leaders in their respective fields of string theory and loop quantum gravity. The odds? 5,000-to-1. If Oppenheim’s hunch is correct and space-time isn’t quantized, he stands to win bucketloads of potato chips, colorful plastic bazinga balls , or shots of olive oil, according to his fancy — as long as each item costs at most 20 pence (about 25 cents).
We met in a north London café lined with books, where he calmly unpacked his concerns about the quantum gravity status quo and extolled the surprising beauty of these hybrid alternatives. “They raise all kinds of remarkably subtle questions,” he said. “I’ve really lost my feet trying to understand these systems.” But he perseveres.
“I want my 5,000 bazinga balls.”
The interview has been condensed and edited for clarity.
Why are most theorists so sure that space-time is quantized?
It’s become dogma. All the other fields in nature are quantized. There’s a sense that there’s nothing special about gravity — it’s just a field like any other — and therefore we should quantize it.
Oppenheim and his students, seen here in and around the UCL campus, are developing a new class of hybrid quantum-classical theories in which gravity stays classical. Maybe, Oppenheim argues, gravity is special and the quantum consensus is wrong.
Is gravity special in your view?
Yes. Physicists define all the other forces in terms of fields evolving in space-time. Gravity alone tells us about the geometry and curvature of space-time itself. None of the other forces describe the universal background geometry that we live in like gravity does.
At the moment, our best theory of quantum mechanics uses this background structure of space-time — which gravity defines. And if you really believe that gravity is quantized, then we lose that background structure.
What sorts of problems do you run into if gravity is classical and not quantized?
For a long time, the community believed it was logically impossible for gravity to be classical because coupling a quantum system with a classical system would lead to inconsistencies. In the 1950s, Richard Feynman imagined a situation that illuminated the problem: He began with a massive particle that is in a superposition of two different locations. These locations could be two holes in a metal sheet, as in the famous double-slit experiment. Here, the particle also behaves like a wave. It creates an interference pattern of light and dark stripes on the other side of the slits, which makes it impossible to know which slit it went through. In popular accounts, the particle is sometimes described as going through both slits at once.
But since the particle has mass, it creates a gravitational field that we can measure. And that gravitational field tells us its location. If the gravitational field is classical, we can measure it to infinite precision, infer the particle’s location, and determine which slit it went through. So we then have a paradoxical situation — the interference pattern tells us that we can’t determine which slit the particle went through, but the classical gravitational field lets us do just that.
But if the gravitational field is quantum, there is no paradox — uncertainty creeps in when measuring the gravitational field, and so we still have uncertainty in determining the particle’s location.
So if gravity behaves classically, you end up knowing too much. And that means that cherished ideas from quantum mechanics, like superposition, break down?
Yes, the gravitational field knows too much. But there’s a loophole in Feynman’s argument that could allow classical gravity to work.
What is that loophole?
As it stands, we only know which path the particle took because it produces a definite gravitational field that bends space-time and allows us to determine the particle’s location.
But if that interaction between the particle and space-time is random — or unpredictable — then the particle itself doesn’t completely dictate the gravitational field. Which means that measuring the gravitational field will not always determine which slit the particle went through because the gravitational field could be in one of many states. Randomness creeps in, and you no longer have a paradox.
So why don’t more physicists think gravity is classical?
Well, it is logically possible to have a theory in which we don’t quantize all the fields. But for a classical theory of gravity to be consistent with everything else being quantized, then gravity has to be fundamentally random. To a lot of physicists that’s unacceptable.
Oppenheim started out as a string theorist, but he eventually grew frustrated with the clumsy mathematical tricks his colleagues employed to get around one of the most notorious conundrums in physics: the black hole information paradox.
Physicists spend a lot of time trying to figure out how nature works. So the idea that there is, on a very deep level, something inherently unpredictable is troubling to many.
The outcome of measurements within quantum theory appears to be probabilistic. But many physicists prefer to think that what appears as randomness is just the quantum system and the measuring apparatus interacting with the environment. They don’t see it as some fundamental feature of reality.
What are you proposing instead?
My best guess is that the next theory of gravity will be something that is neither completely classical nor completely quantum, but something else entirely.
Physicists are only ever coming up with models that approximate nature. But as an attempt at a closer approximation, my students and I constructed a fully consistent theory in which quantum systems and classical space-time interact. We just had to modify quantum theory slightly and modify classical general relativity slightly to allow for the breakdown of predictability that is required.
Why did you start working on these hybrid theories?
I was motivated by the black hole information paradox. When you throw a quantum particle into a black hole and then let that black hole evaporate, you encounter a paradox if you believe that black holes preserve information. Standard quantum theory demands that whatever object you throw into the black hole is radiated back out in some scrambled but recognizable way. But that violates general relativity, which tells us that you can never know about objects that cross the black hole’s event horizon.
But if the black hole evaporation process is indeterministic then there’s no paradox. We never learn what was thrown into the black hole because predictability breaks down. General relativity is safe.
Recently, Oppenheim made a 5,000-to-1 bet with two colleagues that gravity can’t be quantized. If he wins, he gets to stuff his pockets with 5,000 bags of potato chips or bazinga balls or anything else that suits his fancy — as long as each item costs at most 20 pence (about 25 cents). “I feel I’ve made a pretty safe bet, even if I lose,” Oppenheim said.
So the noisiness in these quantum-classical hybrid theories allows information to be lost?
But information conservation is a key principle in quantum mechanics. losing this can’t sit easily with many theorists..
That’s true. There were huge debates about this in recent decades, and almost everybody came to believe that black hole evaporation is deterministic. I’m always puzzled by that.
Will experiments ever resolve if gravity is quantized or not?
At some point. We still know almost nothing about gravity on the smallest scales. It hasn’t even been tested to the millimeter scale, let alone to the scale of a proton. But there are some exciting experiments coming online which will do that.
One is a modern-day version of the “Cavendish experiment,” which calculates the strength of the gravitational attraction between two lead spheres. If there is randomness in the gravitational field, as in these quantum-classical hybrids, then when we try and measure its strength we won’t always get the same answer. The gravitational field will jiggle around. Any theory in which gravity is fundamentally classical has a certain level of gravitational noise.
How do you know this randomness is intrinsic to the gravitational field and not some noise from the environment?
You don’t. Gravity is such a weak force that even the best experiments already have a lot of jiggle in them. So you have to eliminate all these other sources of noise as much as possible. What’s exciting is that my students and I showed that if these hybrid theories are true, there must be some minimal amount of gravitational noise. This can be measured by studying gold atoms in a double-slit experiment. These experiments already place bounds on whether gravity is fundamentally classical. We are gradually closing in on the amount of indeterminacy allowed.
On the flip side of the bet, are there any experiments that would prove that gravity is quantized?
There are proposed experiments that look for entanglement mediated by the gravitational field. As entanglement is a quantum phenomenon, that would be a direct test of the quantum nature of gravity. These experiments are very exciting, but probably decades away.
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George Paget Thomson. The Nobel Prize in Physics 1937. Born: 3 May 1892, Cambridge, United Kingdom. Died: 10 September 1975, Cambridge, United Kingdom. Affiliation at the time of the award: London University, London, United Kingdom. Prize motivation: "for their experimental discovery of the diffraction of electrons by crystals". Prize share ...
my " silver play button unboxing " video *****https://youtu.be/uupsbh5nmsulink of " einstein's photoelectric equat...
Wave mechanics: 1927: G.P. Thomson/Davisson: Electron diffraction proved wave nature of electron: 1928: Dirac: Developed the Dirac relativistic wave equation: Table \(\PageIndex{1}\): Chronology of the development of quantum mechanics. Bohr model of the atom. The Rutherford scattering experiment, performed at Manchester in 1911, discovered that ...
the early career of his son, work that eventually led G.P. to the observation of electron diffraction and to the Nobel Prize. Furthermore, G.P.'s work in the 1920s, and J.J.'s reaction to it, may help illuminate the attitude with which Cambridge trained physicists understood and worked on quantum physics and early quantum mechanics, an aspect
Quantum mechanics is the study of matter and its interactions with energy on the scale of atomic and subatomic ... Example original electron diffraction photograph from the laboratory of G. P. Thomson, recorded 1925-1927 ... In the Stern-Gerlach experiment discussed above, the quantum model predicts two possible values of spin for the atom ...
Following the idea of Planck, Einstein assumed that the energy of a single light quantum is. ε = hν ε = h ν (1.3) where ν ν is the frequency of the light, h is Planck's constant. A frequently used notation is. ℏ = h 2π ℏ = h 2 π (1.4) and with the angular frequency ω = 2πν ω = 2 π ν we can write Einstein's relation as.
University of Aberdeen. Corpus Christi College, Cambridge. Imperial College London. Academic advisors. J. J. Thomson. Sir George Paget Thomson, FRS [1] ( / ˈtɒmsən /; 3 May 1892 - 10 September 1975) was a British physicist and Nobel laureate in physics recognized for his discovery of the wave properties of the electron by electron diffraction.
GP Thompson Experiment | Quantum Mechanics |
Note: JJ Thomson received a Nobel Prize for showing that an electron is a particle and GP Thomson received a Nobel Prize for showing that an electron is a wave . ELECTRONS HAVE BOTH WAVELIKE AND PARTICELIKE PROPERTIES. In Their Own Words: Research in the Bawendi laboratory includes the synthesis and application of quantum
George Paget Thomson was awarded the Nobel Prize for Physics in 1937 for his work in Aberdeen in discovering the wave-like properties of the electron. Whereas his father, J. J. Thomson, had been able to demonstrate the existence of the electron, the son, G. P. Thomson, demonstrated that it could be diffracted like a wave, a discovery proving ...
Thomson was one of the first to write a book for the general public G. P. Thomson "The Atom", Thornton Butterworth Ltd., London (1930 and at least 4 later editions). explaining the new developments and ideas that quantum mechanics was bringing. He also wrote one of the first academic textbooks on electron diffraction while at Aberdeen.
The theory of de Broglie in the form given to it by Schrödinger is now known as wave mechanics and is the basis of atomic physics. It has been applied to a great variety of phenomena with success, but owing largely to mathematical difficulties there are not many cases in which an accurate comparison is possible between theory and experiment.
the particles. So Thomson concluded that electrons behaved like waves. He also calculated the associated wavelength of electrons. It found that the wave length of electron depends only on the accelerating voltage and it is independent of the nature of the target material. Thomson's experiment led to the discovery of electron microscope.
The validity of de Broglie's proposal was confirmed by electron diffraction experiments of G.P. Thomson in 1926 and of C. Davisson and L. H. Germer in 1927. In these experiments it was found that electrons were scattered from atoms in a crystal and that these scattered electrons produced an interference pattern.
Electron diffraction, in fact, was observed (1927) by C.J. Davisson and L.H. Germer in New York and by G.P. Thomson in Aberdeen, Scot. The wavelike nature of electron beams was thereby experimentally established, thus supporting an underlying principle of quantum mechanics.
and worked on quantum physics and early quantum mechanics, an aspect that can be interpreted within a natural continuation of the analysis developed in Andrew Warwick's Masters of Theory.12 In this paper, I also discuss the scientific and cultural ethos that shaped the early career of G.P. Thomson.
Planck's quantum theory. Photoelectric effect. Problems on photoelectric effect . De-Broglie hypothesis. Problems on De-Broglie hypothesis. G. P. Thomson experiment . Wave function. Time independent Schrodinger equation. Particle in one dimensional box . Problems on one dimensional box . Heisenberg Uncertainty principle . Quiz 1 . Quiz 2
Two landmarks in the history of physics are the discovery of the particulate nature of cathode rays (the electron) by J. J. Thomson in 1897 and the experimental demonstration by his son G. P. Thomson in 1927 that the electron exhibits the properties of a wave. Together, the Thomsons are two of the most significant figures in modern physics, both winning Nobel prizes for their work.
76 The published autobiographical accounts are the following: G.P. Thomson, op. cit. (66); and an extended version of it in George Paget Thomson, 'The early history of electron diffraction', Contemporary Physics (1968) 9, pp. 1-15. Moon's biographical sketch of G.P. Thomson is only a transcription of some paragraphs from these accounts.
This idea challenged the traditional view of particles and had a profound impact on quantum mechanics. In this article, we will explore the properties of matter waves and how they differ from light waves. ... Thomson, G.P., 1928, Experiments on the diffraction of cathode rays, Proceedings of the Royal Society of London 117, 600-609. Sushanta ...
The field of quantum mechanics dates to 1900, the year German scientist Max Planck (1858-1947) discovered that energy could come in discrete packages called quanta. It advanced in 1913, when Danish physicist Niels Bohr (1885-1962) used quantum principles to explain what had until then been inexplicable, the exact wavelengths of light ...
Physics Quantum time travel: The experiment to 'send a particle into the past' Time loops have long been the stuff of science fiction. Now, using the rules of quantum mechanics, we have a way to ...
B.sc final Quantum mechanics G P Thomson experiment, Quantum mechanics B.sc final year , B.sc final physics quantum mechanics, Experimental verification of w...
Suggestions for you. See more. 10 Qs
Introduction. Most physicists expect that when we zoom in on the fabric of reality, the unintuitive weirdness of quantum mechanics persists down to the very smallest scales. But in those settings, quantum mechanics collides with classical gravity in a resolutely incompatible way. So for almost a century, theorists have tried to create a unified ...