Plaque at the Humboldt University of Berlin: "Max Planck, discoverer of the elementary quantum of action h, taught in this building from 1889 to 1928."

The Planck constant (denoted h, also called Planck's constant) is a physical constant reflecting the sizes of energy quanta in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory, who discovered it in 1900. Classical statistical mechanics requires the existence of h (but does not define its value).^[2]

The Planck constant was first described as the proportionality constant between the energy (E) of a photon and the frequency (ν) of its associated electromagnetic wave. This relation between the energy and frequency is called the Planck relation or the Planck–Einstein equation:

Failed to parse (Missing texvc executable; please see math/README to configure.): E = h\nu \,.

Since the frequency Failed to parse (Missing texvc executable; please see math/README to configure.): \nu , wavelength λ, and speed of light c are related by λν = c, the Planck relation can also be expressed as

Failed to parse (Missing texvc executable; please see math/README to configure.): E = \frac{hc}{\lambda}.\,

In 1923, Louis de Broglie generalized this relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but any particle. This was confirmed by experiments soon afterwards.

Planck discovered that physical action could not take on any indiscriminate value. Instead, the action must be some multiple of a very small quantity (later to be named the "quantum of action" and now called Planck's constant). This inherent granularity is counterintuitive in the everyday world, where it is possible to "make things a little bit hotter" or "move things a little bit faster". This is because the quanta of action are very, very small in comparison to everyday human experience. Thus, on the macro scale quantum mechanics and classical physics converge. Nevertheless, it is impossible, as Planck found out, to explain some phenomena without accepting that action is quantized. In many cases, such as for monochromatic light or for atoms, the quantum of action also implies that only certain energy levels are allowed, and values in between are forbidden.^[3] In applications where frequency is expressed in terms of radians per second ("angular frequency") instead of cycles per second, it is often useful to absorb a factor of 2π into the Planck constant. The resulting constant is called the reduced Planck constant or Dirac constant. It is equal to the Planck constant divided by 2π, and is denoted ħ ("h-bar"):

Failed to parse (Missing texvc executable; please see math/README to configure.): \hbar = \frac{h}{2 \pi}.

The energy of a photon with angular frequency ω, where ω = 2πν, is given by

Failed to parse (Missing texvc executable; please see math/README to configure.): E = \hbar \omega.

Value[link]

The Planck constant of action has the dimensionality of areal momentum or angular momentum's intensity. In SI units, the Planck constant is expressed in joule seconds (J·s) or (N·m·s).

The value of the Planck constant is:^[1]

Failed to parse (Missing texvc executable; please see math/README to configure.): h = 6.626\ 069\ 57(29)\times 10^{-34}\ \mathrm{J \cdot s} = 4.135\ 667\ 516(91)\times 10^{-15}\ \mathrm{eV \cdot s}.

The value of the reduced Planck constant is:

Failed to parse (Missing texvc executable; please see math/README to configure.): \hbar = {{h}\over{2\pi}} = 1.054\ 571\ 726(47)\times 10^{-34}\ \mathrm{J \cdot s} = 6.582\ 119\ 28(15)\times 10^{-16}\ \mathrm{eV \cdot s}.

The two digits between the parentheses denote the standard uncertainty in the last two digits of the value. The figures cited here are the 2010 CODATA recommended values for the constants and their uncertainties. The 2010 CODATA results were made available in June 2011^[4] and represent the best-known, internationally-accepted values for these constants, based on all data available as of 2010. New CODATA figures are scheduled to be published approximately every four years.

Significance of the value[link]

The numerical value of the Planck constant depends entirely on the system of units used to measure it. When it is expressed in SI units, it is one of the smallest constants used in physics. This reflects the fact that, on a scale adapted to humans, where energies are typically of the order of kilojoules and times are typically of the order of seconds or minutes, Planck's constant, the quantum of action, is very small.

Equivalently, the smallness of Planck's constant reflects the fact that everyday objects and systems are made of a large number of particles. To take one example, green light of a wavelength of 555 nanometres (approximately the wavelength to which human eyes are most sensitive) has a frequency of 540 THz (540×10¹² Hz). Each photon has an energy E of hν = 3.58×10⁻¹⁹ J. That is a very small energy in terms of everyday experience, but then everyday experience doesn't deal with individual photons any more than it deals with individual atoms or molecules. An amount of light that is compatible with everyday experience is the energy of one mole of photons; its energy can be calculated by multiplying the photon energy by the Avogadro constant, N_A ≈ 6.022×10²³ mol⁻¹. The result is that green light of wavelength 555 nm has an energy of 216 kJ/mol, a typical energy of everyday life.

The Planck constant is related to the quantization of light and matter. Therefore, the Planck constant can be seen as an atomic-scale constant. In a unit system adapted to atomic scales, the electronvolt is the appropriate unit of energy and the Petahertz the appropriate unit of frequency. In such an atomic units system, Planck's constant is indeed described by a number of order 1.

Origins[link]

Black-body radiation[link]

Intensity of light emitted from a black body at any given frequency. Each color is a different temperature. Planck was the first to explain the shape of these curves.

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The reason is that the electromagnetic field obeys laws of motion just like a mass on a spring, and can come to thermal equilibrium with hot atoms. When a hot object is in equilibrium with light, the amount of light it absorbs is equal to the amount of light it emits. If the object is black, meaning it absorbs all the light that hits it, then it emits the maximum amount of thermal light too.

The assumption that blackbody radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan–Boltzmann law (1879–84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength).^[5] It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

Planck hypothesized that the equations of motion for light are a set of harmonic oscillators, one for each possible frequency. He examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, and was able to derive an approximate mathematical function for black-body spectrum.^[6]

However, Planck soon realized that his solution was not unique. There were several different solutions, each of which gave a different value for the entropy of the oscillators.^[6] To save his theory, Planck had to resort to using the then controversial theory of statistical mechanics,^[6] which he described as "an act of despair … I was ready to sacrifice any of my previous convictions about physics."^[7] One of his new boundary conditions was

to interpret U_N [the vibrational energy of N oscillators] not as a continuous, infinitely divisible quantity, but as a discrete quantity composed of an integral number of finite equal parts. Let us call each such part the energy element ε;

—Planck, On the Law of Distribution of Energy in the Normal Spectrum^[6]

With this new condition, Planck had imposed the quantization of the energy of the oscillators, "a purely formal assumption … actually I did not think much about it…" in his own words,^[8] but one which would revolutionize physics. Applying this new approach to Wien's displacement law showed that the "energy element" must be proportional to the frequency of the oscillator, the first version of what is now termed "Planck's relation":

Failed to parse (Missing texvc executable; please see math/README to configure.): E = h\nu.\,

Planck was able to calculate the value of h from experimental data on black-body radiation: his result, 6.55 × 10⁻³⁴ J·s, is within 1.2% of the currently accepted value.^[6] He was also able to make the first determination of the Boltzmann constant k_B from the same data and theory.^[9]

Note that the (black) Raleigh-Jeans curve never touches the Planck curve.

Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever – that it was a continuous variable. The Rayleigh-Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh-Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

The black-body problem was revisited in 1905, when Rayleigh and Jeans (on the one hand) and Einstein (on the other hand) independently proved that classical electromagnetism could never account for the observed spectrum. These proofs are commonly known as the "ultraviolet catastrophe", a name coined by Paul Ehrenfest in 1911. They contributed greatly (along with Einstein's work on the photoelectric effect) to convincing physicists that Planck's postulate of quantized energy levels was more than a mere mathematical formalism. The very first Solvay Conference in 1911 was devoted to "the theory of radiation and quanta".^[10] Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".

Photoelectric effect[link]

The photoelectric effect is the emission of electrons (called "photoelectrons") from a surface when light is shone on it. It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz,^[11] who published the first thorough investigation in 1887. Another particularly thorough investigation was published by Philipp Lenard in 1902.^[12] Einstein's 1905 paper^[13] discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921,^[11] when his predictions had been confirmed by the experimental work of Robert Andrews Millikan.^[14] To put it another way, in 1921 at least, Einstein's theories on the photoelectric effect were considered more important than his theory of relativity (a name coined, as it happens, by Max Planck).^[11]

Prior to Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms "frequency" and "wavelength" to characterise different types of radiation. The energy transferred by a wave in a given time is called its intensity. The light from a theatre spotlight is more intense than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time (and hence consumes more electricity) than the ordinary bulb, even though the colour of the light might be very similar. Other waves, such as sound or the waves crashing against a seafront, also have their own intensity. However the energy account of the photoelectric effect didn't seem to agree with the wave description of light.

The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured. This kinetic energy (for each photoelectron) is independent of the intensity of the light,^[12] but depends linearly on the frequency;^[14] and if the frequency is too low (corresponding to a kinetic energy for the photoelectrons of zero or less), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect) ^[15] Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.^[12]

Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small "packets" or quanta. The size of these "packets" of energy, which would later be named photons, was to be the same as Planck's "energy element", giving the modern version of Planck's relation:

Failed to parse (Missing texvc executable; please see math/README to configure.): E = h\nu.\,

Einstein's postulate was later proven experimentally: the constant of proportionality between the frequency of incident light (ν) and the kinetic energy of photoelectrons (E) was shown to be equal to the Planck constant (h).^[14]

Atomic structure[link]

A schematization of the Bohr model of the hydrogen atom. The transition shown from the n=3 level to the n=2 level gives rise to visible light of wavelength 656 nm (red), as the model predicts.

Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model.^[16] In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies E_n

Failed to parse (Missing texvc executable; please see math/README to configure.): E_n = -\frac{h c_0 R_{\infty}}{n^2}

where R_∞ is an experimentally-determined constant (the Rydberg constant) and n is any integer (n = 1, 2, 3, …). Once the electron reached the lowest energy level (n = 1), it could not get any closer to the nucleus (lower energy). This approach also allowed Bohr to account for the Rydberg formula, an empirical description of the atomic spectrum of hydrogen, and to account for the value of the Rydberg constant R_∞ in terms of other fundamental constants.

Bohr also introduced the quantity h/2π, now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons – in which the energy reduces to the Bohr-model equation in the case of the hydrogen atom – were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and J_z the angular momentum measured along any given direction, these quantities can only take on the values

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{align} J^2 = j(j+1) \hbar^2,\qquad & j = 0, \tfrac{1}{2}, 1, \tfrac{3}{2}, \ldots, \\ J_z = m \hbar, \qquad\qquad\quad & m = -j, -j+1, \ldots, j. \end{align}

Uncertainty principle[link]

The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle. Given a large number of particles prepared in the same state, the uncertainty in their position, Δx, and the uncertainty in their momentum (in the same direction), Δp, obey

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta x\, \Delta p \ge \frac{\hbar}{2}

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. energy. The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis. A practical example is computational neurology trying to both measure the time effect and frequency of a neuron burst. fMRI (functional MRI), whose signal processing is based on Fourier transforms, can resolve frequency, but not time (a limit of Fourier analysis due to uncertainty). An EEG (a time series analysis measurement tool) can resolve time, but not frequency. Due to uncertainty, these are not problems with the design of the measuring instruments, but problems with the nature of quantum measurement and particle realities themselves.

In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental cornerstones to the entire theory lies in the commutator relationship between the position operator Failed to parse (Missing texvc executable; please see math/README to configure.): \hat{x}

and the momentum operator Failed to parse (Missing texvc executable; please see math/README to configure.): \hat{p}

Failed to parse (Missing texvc executable; please see math/README to configure.): [\hat{p}_i, \hat{x}_j] = -i \hbar \delta_{ij}

where δ_ij is the Kronecker delta.

Dependent physical constants[link]

The following list is based on the 2006 CODATA evaluation;^[17] for the constants listed below, more than 90% of the uncertainty is due to the uncertainty in the value of the Planck constant, as indicated by the square of the correlation coefficient (r² > 0.9, r > 0.949). The Planck constant is (with one or two exceptions)^[18] the fundamental physical constant which is known to the lowest level of precision, with a relative uncertainty u_r of 5.0×10⁻⁸.

Rest mass of the electron[link]

The normal textbook derivation of the Rydberg constant R_∞ defines it in terms of the electron mass m_e and a variety of other physical constants.

Failed to parse (Missing texvc executable; please see math/README to configure.): R_\infty = \frac{m_{\rm e} e^4}{8 \epsilon_0^2 h^3 c_0} = \frac{m_{\rm e} c_0 \alpha^2}{2 h}

However, the Rydberg constant can be determined very accurately (u_r = 6.6×10⁻¹²) from the atomic spectrum of hydrogen, whereas there is no direct method to measure the mass of a stationary electron in SI units. Hence the equation for the calculation of m_e becomes

Failed to parse (Missing texvc executable; please see math/README to configure.): m_{\rm e} = \frac{2 R_{\infty} h}{c_0 \alpha^2}

where c₀ is the speed of light and α is the fine-structure constant. The speed of light has an exactly defined value in SI units, and the fine-structure constant can be determined more accurately (u_r = 6.8×10⁻¹⁰) than the Planck constant: the uncertainty in the value of the electron rest mass is due entirely to the uncertainty in the value of the Planck constant (r² > 0.999).

Avogadro constant[link]

The Avogadro constant N_A is determined as the ratio of the mass of one mole of electrons to the mass of a single electron: The mass of one mole of electrons is the "relative atomic mass" of an electron A_r(e), which can be measured in a Penning trap (u_r = 4.2×10⁻¹⁰), multiplied by the molar mass constant M_u, which is defined as 0.001 kg/mol.

Failed to parse (Missing texvc executable; please see math/README to configure.): N_{\rm A} = \frac{M_{\rm u} A_{\rm r}({\rm e})}{m_{\rm e}} = \frac{M_{\rm u} A_{\rm r}({\rm e}) c_0 \alpha^2}{2 R_{\infty} h}

The dependence of the Avogadro constant on the Planck constant (r² > 0.999) also holds for the physical constants which are related to amount of substance, such as the atomic mass constant. The uncertainty in the value of the Planck constant limits the knowledge of the masses of atoms and subatomic particles when expressed in SI units. It is possible to measure the masses more precisely in atomic mass units, but not to convert them more precisely into kilograms.

Elementary charge[link]

Sommerfeld originally defined the fine-structure constant α as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \alpha\ =\ \frac{e^2}{\hbar c_0 \ 4 \pi \epsilon_0}\ =\ \frac{e^2 c_0 \mu_0}{2 h}

where e is the elementary charge, ε₀ is the electric constant (also called the permittivity of free space), and μ₀ is the magnetic constant (also called the permeability of free space). The latter two constants have fixed values in the International System of Units. However, α can also be determined experimentally, notably by measuring the electron spin g-factor g_e, then comparing the result with the value predicted by quantum electrodynamics.

At present, the most precise value for the elementary charge is obtained by rearranging the definition of α to obtain the following definition of e in terms of α and h:

Failed to parse (Missing texvc executable; please see math/README to configure.): e = \sqrt{\frac{2\alpha h}{\mu_0 c_0}}.

Bohr magneton and nuclear magneton[link]

The Bohr magneton and the nuclear magneton are units which are used to describe the magnetic properties of the electron and atomic nuclei respectively. The Bohr magneton is the magnetic moment which would be expected for an electron if it behaved as a spinning charge according to classical electrodynamics. It is defined in terms of the reduced Planck constant, the elementary charge and the electron mass, all of which depend on the Planck constant: the final dependence on h^½ (r² > 0.995) can be found by expanding the variables.

Failed to parse (Missing texvc executable; please see math/README to configure.): \mu_{\rm B} = \frac{e \hbar}{2 m_{\rm e}} = \sqrt{\frac{c_0 \alpha^5 h}{32 \pi^2 \mu_0 R_{\infty}^2}}

The nuclear magneton has a similar definition, but corrected for the fact that the proton is much more massive than the electron. The ratio of the electron relative atomic mass to the proton relative atomic mass can be determined experimentally to a high level of precision (u_r = 4.3×10⁻¹⁰).

Failed to parse (Missing texvc executable; please see math/README to configure.): \mu_{\rm N} = \mu_{\rm B} \frac{A_{\rm r}({\rm e})}{A_{\rm r}({\rm p})}

Determination[link]

In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. The CODATA value quoted here is based on three watt-balance measurements of K_J²R_K and one inter-laboratory determination of the molar volume of silicon,^[17] but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST).^[21] Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

There are both practical and theoretical difficulties in determining h. The practical difficulties can be illustrated by the fact that the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another. The most likely reason is that the measurement uncertainty for one (or both) of the methods has been estimated too low – it is (or they are) not as precise as is currently believed – but for the time being there is no indication which method is at fault.

The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect. If these theories are slightly inaccurate – though there is no evidence at present to suggest they are – the methods would not give accurate values for the Planck constant. More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into a circular argument. Fortunately, there are other statistical ways of testing the theories, and the theories have yet to be refuted.^[17]

Josephson constant[link]

The Josephson constant K_J relates the potential difference U generated by the Josephson effect at a "Josephson junction" with the frequency ν of the microwave radiation. The theoretical treatment of Josephson effect suggests very strongly that K_J = 2e/h.

Failed to parse (Missing texvc executable; please see math/README to configure.): K_{\rm J} = \frac{\nu}{U} = \frac{2e}{h}\,

The Josephson constant may be measured by comparing the potential difference generated by an array of Josephson junctions with a potential difference which is known in SI volts. The measurement of the potential difference in SI units is done by allowing an electrostatic force to cancel out a measurable gravitational force. Assuming the validity of the theoretical treatment of the Josephson effect, K_J is related to the Planck constant by

Failed to parse (Missing texvc executable; please see math/README to configure.): h = \frac{8\alpha}{\mu_0 c_0 K_{\rm J}^2}.

Watt balance[link]

A watt balance is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units. From the definition of the conventional watt W₉₀, this gives a measure of the product K_J²R_K in SI units, where R_K is the von Klitzing constant which appears in the quantum Hall effect. If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that R_K = h/e², the measurement of K_J²R_K is a direct determination of the Planck constant.

Failed to parse (Missing texvc executable; please see math/README to configure.): h = \frac{4}{K_{\rm J}^2 R_{\rm K}}

Magnetic resonance[link]

The gyromagnetic ratio γ is the constant of proportionality between the frequency ν of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field B: ν = γB. It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring B, but the value for protons in water at 25 °C is known to better than one part per million. The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, γ′_p. The gyromagnetic ratio is related to the shielded proton magnetic moment μ′_p, the spin number I (I = ¹⁄₂ for protons) and the reduced Planck constant.

Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma^{\prime}_{\rm p} = \frac{\mu^{\prime}_{\rm p}}{I \hbar} = \frac{2 \mu^{\prime}_{\rm p}}{\hbar}

The ratio of the shielded proton magnetic moment μ′_p to the electron magnetic moment μ_e can be measured separately and to high precision, as the imprecisely-known value of the applied magnetic field cancels itself out in taking the ratio. The value of μ_e in Bohr magnetons is also known: it is half the electron g-factor g_e. Hence

Failed to parse (Missing texvc executable; please see math/README to configure.): \mu^{\prime}_{\rm p} = \frac{\mu^{\prime}_{\rm p}}{\mu_{\rm e}} \frac{g_{\rm e} \mu_{\rm B}}{2}

Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma^{\prime}_{\rm p} = \frac{\mu^{\prime}_{\rm p}}{\mu_{\rm e}} \frac{g_{\rm e} \mu_{\rm B}}{\hbar}.

A further complication is that the measurement of γ′_p involves the measurement of an electric current: this is invariably measured in conventional amperes rather than in SI amperes, so a conversion factor is required. The symbol Γ′_p-90 is used for the measured gyromagnetic ratio using conventional electrical units. In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases. Only the high-field value Γ′_p-90(hi) is of interest in determining the Planck constant.

Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma^{\prime}_{\rm p} = \frac{K_{\rm J-90} R_{\rm K-90}}{K_{\rm J} R_{\rm K}} \Gamma^{\prime}_{\rm p-90}({\rm hi}) = \frac{K_{\rm J-90} R_{\rm K-90} e}{2} \Gamma^{\prime}_{\rm p-90}({\rm hi})

Substitution gives the expression for the Planck constant in terms of Γ′_p-90(hi):

Failed to parse (Missing texvc executable; please see math/README to configure.): h = \frac{c_0 \alpha^2 g_{\rm e}}{2 K_{\rm J-90} R_{\rm K-90} R_{\infty} \Gamma^{\prime}_{\rm p-90}({\rm hi})} \frac{\mu_{\rm p}^{\prime}}{\mu_{\rm e}}.

Faraday constant[link]

The Faraday constant F is the charge of one mole of electrons, equal to the Avogadro constant N_A multiplied by the elementary charge e. It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current. In practice, it is measured in conventional electrical units, and so given the symbol F₉₀. Substituting the definitions of N_A and e, and converting from conventional electrical units to SI units, gives the relation to the Planck constant.

Failed to parse (Missing texvc executable; please see math/README to configure.): h = \frac{c_0 M_{\rm u} A_{\rm r}({\rm e})\alpha^2}{R_{\infty}} \frac{1}{K_{\rm J-90} R_{\rm K-90} F_{90}}

X-ray crystal density[link]

The X-ray crystal density method is primarily a method for determining the Avogadro constant N_A but as the Avogadro constant is related to the Planck constant it also determines a value for h. The principle behind the method is to determine N_A as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance. Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry. The unit cell volume is calculated from the spacing between two crystal planes referred to as d₂₂₀. The molar volume V_m(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used. The Planck constant is given by

Failed to parse (Missing texvc executable; please see math/README to configure.): h = \frac{M_{\rm u} A_{\rm r}({\rm e}) c_0 \alpha^2}{R_{\infty}} \frac{\sqrt{2}d^3_{220}}{V_{\rm m}({\rm Si})}.

Particle accelerator[link]

In 2011 was the experimental measurement of the Planck constant in the Large Hadron Collider laboratory. The study called PCC using a giant particle accelerator helped to better understand the relationships between the Planck constant and measuring distances in space.

Fixation[link]

As mentioned above, the numerical value of the Planck constant depends on the system of units used to describe it. Its value in SI units is known to 50 parts per billion but its value in atomic units is known exactly, because of the way the scale of atomic units is defined. The same is true of conventional electrical units, where the Planck constant (noted h₉₀ to distinguish it from its value in SI units) is given by

Failed to parse (Missing texvc executable; please see math/README to configure.): h_{90} = \frac{4}{K_{J-90}^2 R_{K-90}}

with K_J–90 and R_K–90 being exactly defined constants. Atomic units and conventional electrical units are very useful in their respective fields, because the uncertainty in the final result doesn't depend on an uncertain conversion factor, only on the uncertainty of the measurement itself.

There are a number of proposals to redefine certain of the SI base units in terms of fundamental physical constants.^[28] This has already been done for the metre, which is defined in terms of a fixed value of the speed of light. The most urgent unit on the list for redefinition is the kilogram, whose value has been fixed for all science (since 1889) by the mass of a small cylinder of platinum–iridium alloy kept in vault just outside Paris. While nobody knows if the mass of the International Prototype Kilogram has "changed" since 1889 – the value 1 kg of its mass expressed in kilograms is by definition unchanged and therein lies one of the problems – it is known that over such a timescale the many similar Pt–Ir alloy cylinders kept in national laboratories around the world, have changed their relative mass by several tens of parts per million, however carefully they are stored, and the more so, the more they have been taken out and used as mass standards. A change of several tens of micrograms in one kilogram is equivalent to the current uncertainty in the value of the Planck constant in SI units.

The legal process to change the definition of the kilogram is already underway,^[28] but it was decided that no final decision would be made before the next meeting of the General Conference on Weights and Measures in 2011.^[29] The Planck constant is a leading contender to form the basis of the new definition, although not the only one.^[29] Possible new definitions include "the mass of a body at rest whose equivalent energy equals the energy of photons whose frequencies sum to 135,639,274×10⁴² Hz",^[30] or simply "the kilogram is defined so that the Planck constant equals 6.62606896×10⁻³⁴ J·s".

The BIPM provided Draft Resolution A in anticipation of the 24th General Conference on Weights and Measures meeting (2011-10-17 though 2011-10-21), detailing the considerations "On the possible future revision of the International System of Units, the SI".^[31]

Watt balances already measure mass in terms of the Planck constant: at present, standard mass is taken as "fixed" and the measurement is performed to determine the Planck constant but, were the Planck constant to be fixed in SI units, the same experiment would be a measurement of the mass. The relative uncertainty in the measurement would remain the same.

Mass standards could also be constructed from silicon crystals or by other "atom-counting" methods. Such methods require a knowledge of the Avogadro constant, which fixes the proportionality between atomic mass and macroscopic mass but, with a defined value of the Planck constant, N_A would be known to the same level of uncertainty (if not better) than current methods of comparing macroscopic mass.

See also[link]

• New SI definitions
• Basic concepts of quantum mechanics
• Planck units
• Stigler's law
• Wave–particle duality

Notes[link]

References[link]

• Barrow, John D. (2002), The Constants of Nature; From Alpha to Omega - The Numbers that Encode the Deepest Secrets of the Universe, Pantheon Books, ISBN 0-375-42221-8 

External links[link]

• Quantum of Action and Quantum of Spin - Numericana

Max Planck
Born	(1858-04-23)April 23, 1858 Kiel, Duchy of Holstein
Died	October 4, 1947(1947-10-04) (aged 89) Göttingen, Lower Saxony, Germany
Nationality	German
Fields	Physics
Institutions	University of Kiel University of Berlin University of Göttingen Kaiser-Wilhelm-Gesellschaft
Alma mater	Ludwig Maximilian University of Munich
Doctoral advisor	Alexander von Brill
Doctoral students	Gustav Ludwig Hertz Erich Kretschmann Walther Meissner Walter Schottky Max von Laue Max Abraham Moritz Schlick Walther Bothe Julius Edgar Lilienfeld
Known for	Planck constant Planck postulate Planck's law of black body radiation
Notable awards	Nobel Prize in Physics (1918)
Signature
Notes He is the father of Erwin Planck who was executed in 1945 by the Gestapo for his part in the July 20 plot.

Max Karl Ernst Ludwig Planck, ForMemRS,^[1] (April 23, 1858 – October 4, 1947) was a German physicist who discovered quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of quantum theory, for which he received the Nobel Prize in Physics in 1918.^[2]

Life and career[link]

Planck came from a traditional, intellectual family. His paternal great-grandfather and grandfather were both theology professors in Göttingen; his father was a law professor in Kiel and Munich; and his paternal uncle was a judge.

Max Planck's signature at ten years of age.

Planck was born in Kiel, Holstein, to Johann Julius Wilhelm Planck and his second wife, Emma Patzig. He was baptised with the name of Karl Ernst Ludwig Marx Planck; of his given names, Marx (a now obsolete variant of Markus or maybe simply an error for Max, which is actually short for Maximilian) was indicated as the primary name.^[3] However, by the age of ten he signed with the name Max and used this for the rest of his life.^[4]

He was the sixth child in the family, though two of his siblings were from his father's first marriage. Among his earliest memories was the marching of Prussian and Austrian troops into Kiel during the Danish-Prussian war of 1864. In 1867 the family moved to Munich, and Planck enrolled in the Maximilians gymnasium school, where he came under the tutelage of Hermann Müller, a mathematician who took an interest in the youth, and taught him astronomy and mechanics as well as mathematics. It was from Müller that Planck first learned the principle of conservation of energy. Planck graduated early, at age 17.^[5] This is how Planck first came in contact with the field of physics.

Planck was gifted when it came to music. He took singing lessons and played piano, organ and cello, and composed songs and operas. However, instead of music he chose to study physics.

Planck as a young man, 1878

The Munich physics professor Philipp von Jolly advised Planck against going into physics, saying, "in this field, almost everything is already discovered, and all that remains is to fill a few holes." Planck replied that he did not wish to discover new things, but only to understand the known fundamentals of the field, and so began his studies in 1874 at the University of Munich. Under Jolly's supervision, Planck performed the only experiments of his scientific career, studying the diffusion of hydrogen through heated platinum, but transferred to theoretical physics.^[when?]

In 1877 he went to Berlin for a year of study with physicists Hermann von Helmholtz and Gustav Kirchhoff and mathematician Karl Weierstrass. He wrote that Helmholtz was never quite prepared, spoke slowly, miscalculated endlessly, and bored his listeners, while Kirchhoff spoke in carefully prepared lectures which were dry and monotonous. He soon became close friends with Helmholtz. While there he undertook a program of mostly self-study of Clausius's writings, which led him to choose heat theory as his field.

In October 1878 Planck passed his qualifying exams and in February 1879 defended his dissertation, Über den zweiten Hauptsatz der mechanischen Wärmetheorie (On the second law of thermodynamics). He briefly taught mathematics and physics at his former school in Munich.

In June 1880 he presented his habilitation thesis, Gleichgewichtszustände isotroper Körper in verschiedenen Temperaturen (Equilibrium states of isotropic bodies at different temperatures).

Academic career[link]

With the completion of his habilitation thesis, Planck became an unpaid private lecturer in Munich, waiting until he was offered an academic position. Although he was initially ignored by the academic community, he furthered his work on the field of heat theory and discovered one after another the same thermodynamical formalism as Gibbs without realizing it. Clausius's ideas on entropy occupied a central role in his work.

In April 1885 the University of Kiel appointed Planck as associate professor of theoretical physics. Further work on entropy and its treatment, especially as applied in physical chemistry, followed. He proposed a thermodynamic basis for Svante Arrhenius's theory of electrolytic dissociation.

Within four years he was named the successor to Kirchhoff's position at the University of Berlin — presumably thanks to Helmholtz's intercession — and by 1892 became a full professor. In 1907 Planck was offered Boltzmann's position in Vienna, but turned it down to stay in Berlin. During 1909, as University of Berlin professor, eight of his lectures were used by the Ernest Kempton Adams Fund for Physical Research in Theoretical Physics at Columbia University in New York City for a series of lectures translated by Columbia University professor A. P. Wills.^[6] He retired from Berlin on January 10, 1926, and was succeeded by Erwin Schrödinger.

Family[link]

In March 1887 Planck married Marie Merck (1861–1909), sister of a school fellow, and moved with her into a sublet apartment in Kiel. They had four children: Karl (1888–1916), the twins Emma (1889–1919) and Grete (1889–1917), and Erwin (1893–1945).

After the apartment in Berlin, the Planck family lived in a villa in Berlin-Grunewald, Wangenheimstrasse 21. Several other professors of Berlin University lived nearby, among them theologian Adolf von Harnack, who became a close friend of Planck. Soon the Planck home became a social and cultural centre. Numerous well-known scientists, such as Albert Einstein, Otto Hahn and Lise Meitner were frequent visitors. The tradition of jointly performing music had already been established in the home of Helmholtz.

After several happy years, in July 1909 Marie Planck died, possibly from tuberculosis. In March 1911 Planck married his second wife, Marga von Hoesslin (1882–1948); in December his third son Hermann was born.

During the First World War Planck's second son Erwin was taken prisoner by the French in 1914, while his oldest son Karl was killed in action at Verdun. Grete died in 1917 while giving birth to her first child. Her sister died the same way two years later, after having married Grete's widower. Both granddaughters survived and were named after their mothers. Planck endured these losses stoically.

In January 1945, Erwin, to whom he had been particularly close, was sentenced to death by the Nazi Volksgerichtshof because of his participation in the failed attempt to assassinate Hitler in July 1944. Erwin was executed on 23 January 1945.^[7]

• Wives: Marie Merck (m. 1887), Marga von Hoesslin (m. 1910)
• Children: Karl (1888–1916), twins Emma (1889–1919) and Grete (1889–1917), Erwin (1893–1945), Hermann (1911–1954)

Professor at Berlin University[link]

In Berlin, Planck joined the local Physical Society. He later wrote about this time: "In those days I was essentially the only theoretical physicist there, whence things were not so easy for me, because I started mentioning entropy, but this was not quite fashionable, since it was regarded as a mathematical spook".^[8] Thanks to his initiative, the various local Physical Societies of Germany merged in 1898 to form the German Physical Society (Deutsche Physikalische Gesellschaft, DPG); from 1905 to 1909 Planck was the president.

Planck started a six-semester course of lectures on theoretical physics, "dry, somewhat impersonal" according to Lise Meitner, "using no notes, never making mistakes, never faltering; the best lecturer I ever heard" according to an English participant, James R. Partington, who continues: "There were always many standing around the room. As the lecture-room was well heated and rather close, some of the listeners would from time to time drop to the floor, but this did not disturb the lecture". Planck did not establish an actual "school"; the number of his graduate students was only about 20, among them:

1897 Max Abraham (1875–1922)

1904 Moritz Schlick (1882–1936)

1906 Walther Meissner (1882–1974)

1906 Max von Laue (1879–1960)

1907 Fritz Reiche (1883–1960)

1912 Walter Schottky (1886–1976)

1914 Walther Bothe (1891–1957)

Black-body radiation[link]

In 1894 Planck turned his attention to the problem of black-body radiation. He had been commissioned by electric companies to create maximum light from lightbulbs with minimum energy. The problem had been stated by Kirchhoff in 1859: "how does the intensity of the electromagnetic radiation emitted by a black body (a perfect absorber, also known as a cavity radiator) depend on the frequency of the radiation (i.e., the color of the light) and the temperature of the body?". The question had been explored experimentally, but no theoretical treatment agreed with experimental values. Wilhelm Wien proposed Wien's law, which correctly predicted the behaviour at high frequencies, but failed at low frequencies. The Rayleigh–Jeans law, another approach to the problem, created what was later known as the "ultraviolet catastrophe", but contrary to many textbooks this was not a motivation for Planck.^[9]

Planck's first proposed solution to the problem in 1899 followed from what Planck called the "principle of elementary disorder", which allowed him to derive Wien's law from a number of assumptions about the entropy of an ideal oscillator, creating what was referred-to as the Wien–Planck law. Soon it was found that experimental evidence did not confirm the new law at all, to Planck's frustration. Planck revised his approach, deriving the first version of the famous Planck black-body radiation law, which described the experimentally observed black-body spectrum well. It was first proposed in a meeting of the DPG on October 19, 1900 and published in 1901. This first derivation did not include energy quantisation, and did not use statistical mechanics, to which he held an aversion. In November 1900, Planck revised this first approach, relying on Boltzmann's statistical interpretation of the second law of thermodynamics as a way of gaining a more fundamental understanding of the principles behind his radiation law. As Planck was deeply suspicious of the philosophical and physical implications of such an interpretation of Boltzmann's approach, his recourse to them was, as he later put it, "an act of despair ... I was ready to sacrifice any of my previous convictions about physics."^[9]

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (November 2010)

The central assumption behind his new derivation, presented to the DPG on 14 December 1900, was the supposition, now known as the Planck postulate, that electromagnetic energy could be emitted only in quantized form, in other words, the energy could only be a multiple of an elementary unit Failed to parse (Missing texvc executable; please see math/README to configure.): E = h \nu , where Failed to parse (Missing texvc executable; please see math/README to configure.): h

is Planck's constant, also known as Planck's action quantum (introduced already in 1899), and Failed to parse (Missing texvc executable; please see math/README to configure.): \nu
(the Greek letter nu, not the Roman letter v) is the frequency of the radiation. Note that the elementary units of energy discussed here are represented by Failed to parse (Missing texvc executable; please see math/README to configure.): h \nu
and not simply by Failed to parse (Missing texvc executable; please see math/README to configure.): h

. Physicists now call these quanta photons, and a photon of frequency Failed to parse (Missing texvc executable; please see math/README to configure.): \nu

will have its own specific and unique energy. The amplitude of energy at that frequency is then a function of the number of photons of that frequency being produced per unit of time.

Planck in 1918, the year he received the Nobel Prize in Physics for his work on quantum theory

At first Planck considered that quantisation was only "a purely formal assumption ... actually I did not think much about it..."; nowadays this assumption, incompatible with classical physics, is regarded as the birth of quantum physics and the greatest intellectual accomplishment of Planck's career (Ludwig Boltzmann had been discussing in a theoretical paper in 1877 the possibility that the energy states of a physical system could be discrete). Further interpretation of the implications of Planck's work was advanced by Albert Einstein in 1905 in connection with his work on the photoelectric effect—for this reason, the philosopher and historian of science Thomas Kuhn argued that Einstein should be given credit for quantum theory more so than Planck, since Planck did not understand in a deep sense that he was "introducing the quantum" as a real physical entity.^[10] Be that as it may, it was in recognition of Planck's monumental accomplishment that he was awarded the Nobel Prize in Physics in 1918.

The discovery of Planck's constant enabled him to define a new universal set of physical units (such as the Planck length and the Planck mass), all based on fundamental physical constants.

Subsequently, Planck tried to grasp the meaning of energy quanta, but to no avail. "My unavailing attempts to somehow reintegrate the action quantum into classical theory extended over several years and caused me much trouble." Even several years later, other physicists like Rayleigh, Jeans, and Lorentz set Planck's constant to zero in order to align with classical physics, but Planck knew well that this constant had a precise nonzero value. "I am unable to understand Jeans' stubbornness — he is an example of a theoretician as should never be existing, the same as Hegel was for philosophy. So much the worse for the facts if they don't fit."^[11]

Max Born wrote about Planck: "He was by nature and by the tradition of his family conservative, averse to revolutionary novelties and skeptical towards speculations. But his belief in the imperative power of logical thinking based on facts was so strong that he did not hesitate to express a claim contradicting to all tradition, because he had convinced himself that no other resort was possible."^[12]

Einstein and the theory of relativity[link]

In 1905 the three epochal papers of the hitherto completely unknown Albert Einstein were published in the journal Annalen der Physik. Planck was among the few who immediately recognized the significance of the special theory of relativity. Thanks to his influence this theory was soon widely accepted in Germany. Planck also contributed considerably to extend the special theory of relativity.

Einstein's hypothesis of light quanta (photons), based on Philipp Lenard's 1902 discovery of the photoelectric effect, was initially rejected by Planck. He was unwilling to discard completely Maxwell's theory of electrodynamics. "The theory of light would be thrown back not by decades, but by centuries, into the age when Christian Huygens dared to fight against the mighty emission theory of Isaac Newton ..."

In 1910 Einstein pointed out the anomalous behavior of specific heat at low temperatures as another example of a phenomenon which defies explanation by classical physics. Planck and Nernst, seeking to clarify the increasing number of contradictions, organized the First Solvay Conference (Brussels 1911). At this meeting Einstein was able to convince Planck.

Meanwhile Planck had been appointed dean of Berlin University, whereby it was possible for him to call Einstein to Berlin and establish a new professorship for him (1914). Soon the two scientists became close friends and met frequently to play music together.

World War I[link]

At the onset of the First World War Planck endorsed the general excitement of the public, writing that, "Besides much that is horrible, there is also much that is unexpectedly great and beautiful: the smooth solution of the most difficult domestic political problems by the unification of all parties (and) ... the extolling of everything good and noble."^[13][14]

Nonetheless, Planck refrained from the extremes of nationalism. In 1915, at a time when Italy was about to join the Allied Powers, he voted successfully for a scientific paper from Italy, which received a prize from the Prussian Academy of Sciences, where Planck was one of four permanent presidents.

Planck also signed the infamous "Manifesto of the 93 intellectuals", a pamphlet of polemic war propaganda (while Einstein retained a strictly pacifistic attitude which almost led to his imprisonment, being spared by his Swiss citizenship). But in 1915 Planck, after several meetings with Dutch physicist Lorentz, revoked parts of the Manifesto. Then in 1916 he signed a declaration against German annexationism.

Post War and Weimar Republic[link]

In the turbulent post-war years, Planck, now the highest authority of German physics, issued the slogan "persevere and continue working" to his colleagues.

In October 1920 he and Fritz Haber established the Notgemeinschaft der Deutschen Wissenschaft (Emergency Organization of German Science), aimed at providing financial support for scientific research. A considerable portion of the monies the organization would distribute were raised abroad.

Planck also held leading positions at Berlin University, the Prussian Academy of Sciences, the German Physical Society and the Kaiser-Wilhelm-Gesellschaft (which in 1948 became the Max-Planck-Gesellschaft). During this time economic conditions in Germany were such that he was hardly able to conduct research.

During the interwar period, Planck became a member of the Deutsche Volks-Partei (German People's Party), the party of Nobel Peace Prize laureate Gustav Stresemann, which aspired to liberal aims for domestic policy and rather revisionistic aims for international politics.

Planck disagreed with the introduction of universal suffrage and later expressed the view that the Nazi dictatorship resulted from "the ascent of the rule of the crowds".^[15]

Quantum mechanics[link]

At the end of the 1920s Bohr, Heisenberg and Pauli had worked out the Copenhagen interpretation of quantum mechanics, but it was rejected by Planck, as well as Schrödinger, Laue, and Einstein. Planck expected that wave mechanics would soon render quantum theory—his own child—unnecessary. This was not to be the case, however. Further work only cemented quantum theory, even against his and Einstein's philosophical revulsions. Planck experienced the truth of his own earlier observation from his struggle with the older views in his younger years: "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it."^[16]

Nazi dictatorship and The Second World War[link]

When the Nazis seized power in 1933, Planck was 74. He witnessed many Jewish friends and colleagues expelled from their positions and humiliated, and hundreds of scientists emigrated from Germany. Again he tried the "persevere and continue working" slogan and asked scientists who were considering emigration to remain in Germany. He hoped the crisis would abate soon and the political situation would improve. There was also a deeper argument against emigration. Emigrating German non-Jewish scientists would need to look for academic positions abroad, but these positions better served Jewish scientists, who had no chance of continuing to work in Germany.^{[citation needed]}

Hahn asked Planck to gather well-known German professors in order to issue a public proclamation against the treatment of Jewish professors, but Planck replied, "If you are able to gather today 30 such gentlemen, then tomorrow 150 others will come and speak against it, because they are eager to take over the positions of the others."^[17] Under Planck's leadership, the Kaiser-Wilhelm-Gesellschaft (KWG) avoided open conflict with the Nazi regime, except concerning Fritz Haber. Planck tried to discuss the issue with Adolf Hitler but was unsuccessful. In the following year, 1934, Haber died in exile.

One year later, Planck, having been the president of the KWG since 1930, organized in a somewhat provocative style an official commemorative meeting for Haber. He also succeeded in secretly enabling a number of Jewish scientists to continue working in institutes of the KWG for several years. In 1936, his term as president of the KWG ended, and the Nazi government pressured him to refrain from seeking another term.

As the political climate in Germany gradually became more hostile, Johannes Stark, prominent exponent of Deutsche Physik ("German Physics", also called "Aryan Physics") attacked Planck, Sommerfeld and Heisenberg for continuing to teach the theories of Einstein, calling them "white Jews." The "Hauptamt Wissenschaft" (Nazi government office for science) started an investigation of Planck's ancestry, but all they could find out was that he was "1/16 Jewish."^[18]

In 1938 Planck celebrated his 80th birthday. The DPG held a celebration, during which the Max-Planck medal (founded as the highest medal by the DPG in 1928) was awarded to French physicist Louis de Broglie. At the end of 1938 the Prussian Academy lost its remaining independence and was taken over by Nazis (Gleichschaltung). Planck protested by resigning his presidency. He continued to travel frequently, giving numerous public talks, such as his talk on Religion and Science, and five years later he was sufficiently fit to climb 3,000-meter peaks in the Alps.

During the Second World War, the increasing number of Allied bombing campaigns against Berlin forced Planck and his wife to leave the city temporarily and live in the countryside. In 1942 he wrote: "In me an ardent desire has grown to persevere this crisis and live long enough to be able to witness the turning point, the beginning of a new rise." In February 1944 his home in Berlin was completely destroyed by an air raid, annihilating all his scientific records and correspondence. Finally, he got into a dangerous situation in his rural retreat because of the rapid advance of the Allied armies from both sides. After the end of the war he was brought to a relative in Göttingen.

Planck endured many personal tragedies after the age of 50. In 1909, his first wife died after 22 years of marriage, leaving him with two sons and twin daughters. Planck's oldest son, Karl, was killed in action in 1916. His daughter Margarete died in childbirth in 1917, and another daughter, Emma, married her late sister's husband and then also died in childbirth, in 1919. During World War II, Planck's house in Berlin was completely destroyed by bombs in 1944 and his youngest son, Erwin, was implicated in the attempt made on Hitler's life in the July 20 plot. Consequently, Erwin died at the hands of the Gestapo in 1945. Erwin's death destroyed Planck's will to live.^[19] By the end of the war, Planck, his second wife and his son by her, moved to Göttingen where he died on October 4, 1947.

Religious view[link]

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Planck was very tolerant towards alternative views and religions.^[20] In a lecture on 1937 entitled "Religion und Naturwissenschaft" he suggested the importance of these symbols and rituals related directly with a believer's ability to worship God, but that one must be mindful that the symbols provide an imperfect illustration of divinity. He criticized atheism for being focused on the derision of such symbols, while at the same time warned of the over-estimation of the importance of such symbols by believers. .^[21]

Max Planck said "All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter" in 1944, indicating that he believed in some kind of God.^[22]

Planck regarded the scientist as a man of imagination and faith, "faith" interpreted as being similar to "having a working hypothesis". For example the causality principle isn't true or false, it is an act of faith. Thereby Planck may have indicated a view that points toward Imre Lakatos' research programs process descriptions, where falsification is mostly tolerable, in faith of its future removal.^[23]

On the other hand, Planck wrote, "...'to believe' means 'to recognize as a truth,' and the knowledge of nature, continually advancing on incontestably safe tracks, has made it utterly impossible for a person possessing some training in natural science to recognize as founded on truth the many reports of extraordinary contradicting the laws of nature, of miracles which are still commonly regarded as essential supports and confirmations of religious doctrines, and which formerly used to be accepted as facts pure and simple, without doubt or criticism. The belief in miracles must retreat step by step before relentlessly and reliably progressing science and we cannot doubt that sooner or later it must vanish completely."^[24]

Six months before his death a rumour started that Planck had converted to Catholicism, but when questioned what had brought him to make this step, he declared that, although he had always been deeply religious, he did not believe "in a personal God, let alone a Christian God."^[25]

Honors and awards[link]

• "Pour le Mérite" for Science and Arts 1915 (in 1930 he became chancellor of this order)
• Nobel Prize in Physics 1918 (awarded 1919)
• Lorentz Medal 1927
• Franklin Medal (1927)
• Adlerschild des Deutschen Reiches (1928), an award from the German Reich President
• Max Planck medal (1929, together with Einstein)
• Copley Medal (1929)
• Planck received honorary doctorates from the universities of Frankfurt, Munich (TH), Rostock, Berlin (TH), Graz, Athens, Cambridge, London, and Glasgow.
• The asteroid 1069 was named "Stella Planckia" by the International Astronomical Union (1938)

Publications[link]

• Planck, Max. (1897). Vorlesungen über Thermodynamik
• Planck, Max. (1900). “Entropy and Temperature of Radiant Heat.” Annalen der Physik, vol. 1. no 4. April, pg. 719–37.
• Planck, Max. (1901). "On the Law of Distribution of Energy in the Normal Spectrum". Annalen der Physik, vol. 4, p. 553 ff.

See also[link]

• German inventors and discoverers

References[link]

Bibliography[link]

• Aczel, Amir D. Entanglement, Chapter 4. (Penguin, 2003) ISBN 978-0-452-28457-9
• Heilbron, J. L. (2000). The dilemmas of an upright man: Max Planck and the fortunes of German science. Harvard University Press. ISBN 0-674-00439-6. http://books.google.com/books?id=d5zKH2Bx2AwC. 
• Pickover, Clifford A. Archimedes to Hawking: Laws of Science and the Great Minds Behind Them, Oxford University Press, 2008, ISBN 978-0-19-533611-5
• Rosenthal-Schneider, Ilse Reality and Scientific Truth: Discussions with Einstein, von Laue, and Planck (Wayne State University, 1980) ISBN 0-8143-1650-6

External links[link]

Wikimedia Commons has media related to: Max Planck

Wikiquote has a collection of quotations related to: Max Planck

Biographies[link]

• Annotated bibliography for Max Planck from the Alsos Digital Library for Nuclear Issues
• Max Planck – Encyclopædia Britannica article
• Max Planck Biography – www.nobel-prize-winners.com
• Max Planck Institutes of Natural Science and Astrophysics
• Cinematic self portrait of Max Planck, Berlin-Brandenburgische Akademie der Wissenschaften, 1942
• Nobel Biography

Articles[link]

• Life–Work–Personality – Exhibition on the 50th anniversary of Planck's death
• Max Planck, Planck's constant, and Schrodinger's Cat

vep:Plank Maks