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
the elementary charge e is 1.602 176 634 × C
- 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
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
Most of the helium in the Earth's atmosphere comes from alpha decay, since helium is lighter than air and naturally escapes out out of the atmosphere.
Wiki mentions that alpha decay is well modelled as a quantum tunnelling event, see also Geiger-Nuttall law.
As a result of that law, alpha particles have relatively little energy variation around 5 MeV or a speed of about 5% of the speed of light for any element, because the energy is inversely exponentially proportional to half-life. This is because:
- youtu.be/_f8zeEI0oys?t=796 George Gamow and Edward Condon proposed the quantum tunnelling explanation
- youtu.be/_f8zeEI0oys?t=1725 worked out example that predicts the half-life of polonium-210 based on its emission energy
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:
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.
Lorentz transform consequence: everyone sees the same speed of light Updated 2025-04-24 +Created 1970-01-01
OK, so let's verify the main desired consequence of the Lorentz transformation: that everyone observes the same speed of light.
Observers will measure the speed of light by calculating how long it takes the light going towards cross a rod of length laid in the x axis at position .
Each observer will observe two events:
Supposing that the standing observer measures the speed of light as and that light hits the left side of the rod at time , then he observes the coordinates:
Now, if we transform for the moving observer:and so the moving observer measures the speed of light as:
Explains the propagation of light as a wave, and matches the previously known relationship between the speed of light and electromagnetic constants.
The equations are a limit case of the more complete quantum electrodynamics, and unlike that more general theory account for the quantization of photon.
The system consists of 6 unknown functions that map 4 variables: time t and the x, y and z positions in space, to a real number:and two known input functions:
- , , : directions of the electric field
- , , : directions of the magnetic field
Due to the conservation of charge however, those input functions have the following restriction:
Equation 1.
Charge conservation
. Also consider the following cases:
The goal of finding and is that those fields allow us to determine the force that gets applied to a charge via the Equation "Lorentz force", and then to find the force we just need to integrate over the entire body.
Finally, now that we have defined all terms involved in the Maxwell equations, let's see the equations:
Equation 2.
Gauss' law
. Equation 3.
Gauss's law for magnetism
. Equation 4.
Faraday's law
. Equation 5.
Ampere's circuital law
. You should also review the intuitive interpretation of divergence and curl.
Understanding Electromagnetic Radiation! by Learn Engineering (2019)
Source. Shows animations of a dipole antenna which illustrates well how radiation is emitted from moving charges and travels at the speed of light.