Incoming links: Planck constant
web.archive.org/web/20181119214326/https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf gives it in raw:The breakdown is:
- the unperturbed ground state hyperfine transition frequency of the caesium-133 atom is 9 192 631 770 Hz
- the speed of light in vacuum c is 299 792 458 m/s
- the Planck constant h is 6.626 070 15 × J s
- the elementary charge e is 1.602 176 634 × C
- the Boltzmann constant k is 1.380 649 × J/K
- the Avogadro constant NA is 6.022 140 76 × mol
- the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W,
- actually use some physical constant:
the unperturbed ground state hyperfine transition frequency of the caesium-133 atom is 9 192 631 770 Hz
Defines the second in terms of caesium-133 experiments. The beauty of this definition is that we only have to count an integer number of discrete events, which is what allows us to make things precise.the speed of light in vacuum c is 299 792 458 m/s
Defines the meter in terms of speed of light experiments. We already had the second from the previous definition.the Planck constant h is 6.626 070 15 × J s
Defines the kilogram in terms of the Planck constant.the elementary charge e is 1.602 176 634 × C
Defines the Coulomb in terms of the electron charge.
- arbitrary definitions based on the above just to match historical values as well as possible:
the Boltzmann constant k is 1.380 649 × J/K
Arbitrarily defines temperature from previously defined energy (J) to match historical values.the Avogadro constant NA is 6.022 140 76 × mol
the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W
Arbitrarily defines the Candela in terms of previous values to match historical records. The most useless unit comes last as you'd expect.
Starting in the 2019 redefinition of the SI base units, the elementary charge is assigned a fixed number, and the Ampere is based on it and on the second, which is beautiful.
This choice is not because we attempt to count individual electrons going through a wire, as it would be far too many to count!
Rather, it is because because there are two crazy quantum mechanical effects that give us macroscopic measures that are directly related to the electron charge. www.nist.gov/si-redefinition/ampere/ampere-quantum-metrology-triangle by the NIST explains that the two effects are:
- quantum Hall effect, which has discrete resistances of type:for integer values of .
- Josephson effect, used in the Josephson voltage standard. With the Inverse AC Josephson effect we are able to produce:per Josephson junction. This is about 2 microvolt / GHz, where GHz is a practical input frequency. Video "The evolution of voltage metrology to the latest generation of JVSs by Alain Rüfenacht" mentions that a typical operating frequency is 20 GHz.Therefore to attain a good 10 V, we need something in the order of a million Josephson junctions.But this is possible to implement in a single chip with existing micro fabrication techniques, and is exactly what the Josephson voltage standard does!
Those effect work because they also involve dividing by the Planck constant, the fundamental constant of quantum mechanics, which is also tiny, and thus brings values into a much more measurable order of size.
Was the first model to explain the Balmer series, notably linking atomic spectra to the Planck constant and therefore to other initial quantum mechanical observations.
This was one of the first major models that just said:
I give up, I can't tie this to classical physics in any way, let's just roll with it, OK?
It still treats electrons as little points spinning around the nucleus, but it makes the non-classical postulate that only certain angular momentums (and therefore energies) are allowed.
Bibliography:
- Inward Bound by Abraham Pais (1988) Chapter 9.e Atomic structure and spectral lines - Niels Bohr
- The Quantum Story by Jim Baggott (2011) Chapter 3 A Little Bit of Reality
This is not a truly "fundamental" constant of nature like say the speed of light or the Planck constant.
Rather, it is just a definition of our Kelvin temperature scale, linking average microscopic energy to our macroscopic temperature scale.
The way to think about that link is, at 1 Kelvin, each particle has average energy:per degree of freedom.
For an ideal monatomic gas, say helium, there are 3 degrees of freedom. so each helium atom has average energy:
If we have 2 atoms at 1 K, they will have average energy , and so on.
Another conclusion is that this defines temperature as being proportional to the total energy. E.g. if we had 1 helium atom at 2 K then we would have about energy, 3 K and so on.
This energy is of course just an average: some particles have more, and others less, following the Maxwell-Boltzmann distribution.
The discovery of the photon was one of the major initiators of quantum mechanics.
Light was very well known to be a wave through diffraction experiments. So how could it also be a particle???
This was a key development for people to eventually notice that the electron is also a wave.
This process "started" in 1900 with Planck's law which was based on discrete energy packets being exchanged as exposed at On the Theory of the Energy Distribution Law of the Normal Spectrum by Max Planck (1900).
This ideas was reinforced by Einstein's explanation of the photoelectric effect in 1905 in terms of photon.
In the next big development was the Bohr model in 1913, which supposed non-classical physics new quantization rules for the electron which explained the hydrogen emission spectrum. The quantization rule used made use of the Planck constant, and so served an initial link between the emerging quantized nature of light, and that of the electron.
The final phase started in 1923, when Louis de Broglie proposed that in analogy to photons, electrons might also be waves, a statement made more precise through the de Broglie relations.
This event opened the floodgates, and soon matrix mechanics was published in quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925), as the first coherent formulation of quantum mechanics.
It was followed by the Schrödinger equation in 1926, which proposed an equivalent partial differential equation formulation to matrix mechanics, a mathematical formulation that was more familiar to physicists than the matrix ideas of Heisenberg.
Inward Bound by Abraham Pais (1988) summarizes his views of the main developments of the subjectit:
- Planck's on the discovery of the quantum theory (1900);
- Einstein's on the light-quantum (1905);
- Bohr's on the hydrogen atom (1913);
- Bose's on what came to be called quantum statistics (1924);
- Heisenberg's on what came to be known as matrix mechanics (1925);
- and Schroedinger's on wave mechanics (1926).
Bibliography:
- physics.stackexchange.com/questions/18632/good-book-on-the-history-of-quantum-mechanics on Physics Stack Exchange
- www.youtube.com/watch?v=5hVmeOCJjOU A Brief History of Quantum Mechanics by Sean Carroll (2020) Given at the Royal Institution.
Unit of mass.
Defined in the 2019 redefinition of the SI base units via the Planck constant. This was possible due to the development of the Kibble balance.
Proportionality factor in the Planck-Einstein relation between light energy and frequency.
And analogously for matter, appears in the de Broglie relations relating momentum and frequency. Also appears in the Schrödinger equation, basically as a consequence/cause of the de Broglie relations most likely.
Intuitively, the Planck constant determines at what length scale do quantum effects start to show up for a given energy scale. It is because the Plank constant is very small that we don't perceive quantum effects on everyday energy/length/time scales. On the , quantum mechanics disappears entirely.
A very direct way of thinking about it is to think about what would happen in a double-slit experiment. TODO think more clearly what happens there.
Defined exactly in the 2019 redefinition of the SI base units to:
Used to explain the black-body radiation experiment.
Published as: On the Theory of the Energy Distribution Law of the Normal Spectrum by Max Planck (1900).
The Quantum Story by Jim Baggott (2011) page 9 mentions that Planck apparently immediately recognized that Planck constant was a new fundamental physical constant, and could have potential applications in the definition of the system of units (TODO where was that published):This was a visionary insight, and was finally realized in the 2019 redefinition of the SI base units.
Planck wrote that the constants offered: 'the possibility of establishing units of length, mass, time and temperature which are independent of specific bodies or materials and which necessarily maintain their meaning for all time and for all civilizations, even those which are extraterrestrial and nonhuman, constants which therefore can be called "fundamental physical units of measurement".'
TODO how can it be derived from theoretical principles alone? There is one derivation at; en.wikipedia.org/wiki/Planck%27s_law#Derivation but it does not seem to mention the Schrödinger equation at all.
Quantum Mechanics 2 - Photons by ViaScience (2012)
Source. Contains a good explanation of how discretization + energy increases with frequency explains the black-body radiation experiment curve: you need more and more energy for small wavelengths, each time higher above the average energy available.- 1859-1900: see Section "Black-body radiation experiment". Continuously improving culminating in Planck's law black-body radiation and Planck's law
- 1905 photoelectric effect and the photon
- TODO experiments
- 1905 Einstein's photoelectric effect paper. Planck was intially thinking that light was continuous, but the atoms vibrated in a discrete way. Einstein's explanation of the photoelectric effect throws that out of the window, and considers the photon discrete.
- 1913 atomic spectra and the Bohr model
- 1885 Balmer series, an empirical formula describes some of the lines of the hydrogen emission spectrum
- 1888 Rydberg formula generalizes the Balmer series
- 1896 Pickering series makes it look like a star has some new kind of hydrogen that produces half-integer entries in the Pickering series
- 1911 Bohr visits J. J. Thomson in the University of Cambridge for his postdoc, but they don't get along well
- Bohr visits Rutherford at the University of Manchester and decides to transfer there. During this stay he becomes interested in problems of the electronic structure of the atom.Bohr was forced into a quantization postulate because spinning electrons must radiate energy and collapse, so he postulated that electrons must somehow magically stay in orbits without classically spinning.
- 1913 february: young physics professor Hans Hansen tells Bohr about the Balmer series. This is one of the final elements Bohr needed.
- 1913 Bohr model published predicts atomic spectral lines in terms of the Planck constant and other physical constant.
- explains the Pickering series as belonging to inoized helium that has a single electron. The half term in the spectral lines of this species come from the nucleus having twice the charge of hydrogen.
- 1913 March: during review before publication, Rutherford points out that instantaneous quantum jumps don't seem to play well with causality.
- 1916 Bohr-Sommerfeld model introduces angular momentum to explain why some lines are not observed, as they would violate the conservation of angular momentum.