5 ms·

Besides the myth busted in this paper, that the actually later work of Rayleigh could have influenced Planck, there is another incorrect myth, that Planck has i

Besides the myth busted in this paper, that the actually later work of Rayleigh could have influenced Planck, there is another incorrect myth, that Planck has introduced the "constant of Planck" in his publication from 1900, where he presented the deduction of the Planck formula from the supposition that the emission and absorption of electromagnetic radiation are quantized. This frequently seen claim is also wrong. Planck has introduced the constant of Planck and he has also computed its value with excellent precision for that time (4% relative error) in an earlier work published in 1899: Max Planck, "Ueber irreversible Strahlungsvorgaenge", "Sitzungsberichte der koeniglich preussischen Akademie der Wissenschaften zu Berlin. Jahrgang 1899", pp. 440-480. There Max Planck has presented deductions of the formulae previously established by Wien for the blackbody radiation, where he replaced the empirical constants of Wien with functions of other universal constants and of the new universal constant introduced by him. Already Maxwell, a quarter of century earlier, had shown that it is possible to determine the units for all physical quantities with a single arbitrary choice (in his example, the wavelength of the yellow light emitted by sodium vapor). In 1899, Planck has shown that the law of blackbody radiation provides an additional relationship between the units of length, time and energy, which, together with the previous relationships considered by Maxwell, can determine the units of all physical quantities without any arbitrary choice. So at the end of this work from 1899, where the constant of Planck has been introduced, he has also presented the system of natural units known now as the Planck units. Nevertheless, the system of Planck units cannot be used as the base of a practical system of units, because the uncertainty of measuring the Newtonian constant of gravitation is huge. This makes useless one of the equations that connect the units of length, time and energy. Because of that, any practical system of units must contain a single arbitrary choice of a unit, which in the case of SI is the frequency of a certain hyperfine transition of the cesium-133 atom, while all the other units result from this choice by adopting conventional values for the universal constants, except for the Newtonian constant of gravitation, which must be measured experimentally (some constant determining the intensity of the electromagnetic interaction, e.g. the fine structure constant, must also be measured experimentally, but for that the uncertainty is extremely low). BTW, another extremely frequent incorrect claim about the constant of Planck is that it is a quantum of action. This is very wrong, it is a quantum of angular momentum (the ratio between energy and frequency is an angular momentum, like also the ratio between their integrals, i.e. between action and plane angle). The origin of the mistake is the fact that many follow the suggestions of the recent SI brochures (there was a resolution adopted by vote that the unit of plane angle is not a base unit, which is equivalent with establishing by vote that 2 + 2 = 5), and they omit the unit of plane angle in the dimensional formulae, in which case it appears that the unit of action is the same with the unit of angular momentum, but they are not the same, as any attempt to change the unit used for plane angles would demonstrate, e.g. between radians and degrees or cycles. The original constant of Planck corresponds to plane angles measured in cycles, while the so-called h bar is the same constant converted to correspond with plane angles measured in radians.

BlueTemplar 3y ago
> The original constant of Planck corresponds to plane angles measured in cycles My German is bad, is that from that publication ? Any closest ones in other languages ? Asking for a friend : https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto
- adrian_b 3y ago
  At that time the use of radians was still uncommon in physics. The frequency of periodic events was measured at that time in cycles per second. The unit of frequency "cycle per second" has been renamed "hertz" much later. The renaming was first proposed in 1935, but it became adopted in SI only in 1960. Because the use of cycles per second (now hertz) is entrenched, when the radian has been promoted as the preferred unit for plane angle, that has caused a split in the SI system of physical quantities, between the frequency of periodic phenomena measured in cycles per second and the angular velocity measured in radians per second. This split is a big cause of inconsistency in SI, because "frequency of periodic phenomena" and "angular velocity" are just 2 names for the same physical quantity and the "hertz"/"cycle per second" and the "radian per second" do not belong in the same consistent system of units, the former corresponds to the choice of the cycle as the unit of plane angle, while the latter corresponds to the choice of the radian as the unit of plane angle. Thus the SI system of units is a mixture of units from 2 distinct systems of consistent units. There are a number of physical quantities in SI for which 2 units are used, one derived from the cycle and one derived from the radian. In some cases distinct names are used to show the intended unit, like "frequency" and "angular velocity", while in other cases there are no distinct names. The non-SI unit of angular velocity, "rpm", i.e. "rotations per minute", is another name for "cycles per minute". All the units of physical quantities related to rotations, including the angular momentum, depend on the unit chosen for the plane angle, so they must be multiplied or divided by conversion factors (i.e. 2 times pi for conversion between cycle and radian), whenever the unit for plane angle is changed. The use of radian is a cause of confusion for those who learn about the physics of rotation, because they learn for instance that the angular momentum and the torque are proportional with the radius to the center of rotation. This is false and it appears to be true only when the radian is chosen as the unit of plane angle. In reality, the factor of conversion between the physical quantities that refer to linear motion and those that refer to rotations is not the radius, but the ratio between the arc length and the central angle corresponding to the arc. This ratio happens to be equal to the radius only when the central angle happens to be measured in radians. The correct conversion factors must be used to convert the values of a physical quantity like angular momentum between systems with different units for the plane angle. While in the system with plane angles measured in radians the angular momentum is the linear momentum multiplied by radius, in the system with plane angles measured in cycles the angular momentum is the linear momentum multiplied by perimeter. The same for torque. When you divide a kinetic energy to a frequency expressed in cycles per second, you get an angular momentum that is equal to the product of linear momentum by perimeter, corresponding to the cycle as the unit of angle. When you divide a kinetic energy to a frequency expressed in radians per second, you get an angular momentum that is equal to the product of linear momentum by radius, corresponding to the radian as the unit of angle. These 2 variants correspond to the alternative "h" and "h bar" values of the Planck constant. The same quantum of angular momentum corresponds to both choices (i.e. the double of the spin of the electron), it is just expressed in different units.

BlueTemplar 3y ago

> The original constant of Planck corresponds to plane angles measured in cycles My German is bad, is that from that publication ? Any closest ones in other languages ? Asking for a friend : https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto

adrian_b 3y ago
At that time the use of radians was still uncommon in physics. The frequency of periodic events was measured at that time in cycles per second. The unit of frequency "cycle per second" has been renamed "hertz" much later. The renaming was first proposed in 1935, but it became adopted in SI only in 1960. Because the use of cycles per second (now hertz) is entrenched, when the radian has been promoted as the preferred unit for plane angle, that has caused a split in the SI system of physical quantities, between the frequency of periodic phenomena measured in cycles per second and the angular velocity measured in radians per second. This split is a big cause of inconsistency in SI, because "frequency of periodic phenomena" and "angular velocity" are just 2 names for the same physical quantity and the "hertz"/"cycle per second" and the "radian per second" do not belong in the same consistent system of units, the former corresponds to the choice of the cycle as the unit of plane angle, while the latter corresponds to the choice of the radian as the unit of plane angle. Thus the SI system of units is a mixture of units from 2 distinct systems of consistent units. There are a number of physical quantities in SI for which 2 units are used, one derived from the cycle and one derived from the radian. In some cases distinct names are used to show the intended unit, like "frequency" and "angular velocity", while in other cases there are no distinct names. The non-SI unit of angular velocity, "rpm", i.e. "rotations per minute", is another name for "cycles per minute". All the units of physical quantities related to rotations, including the angular momentum, depend on the unit chosen for the plane angle, so they must be multiplied or divided by conversion factors (i.e. 2 times pi for conversion between cycle and radian), whenever the unit for plane angle is changed. The use of radian is a cause of confusion for those who learn about the physics of rotation, because they learn for instance that the angular momentum and the torque are proportional with the radius to the center of rotation. This is false and it appears to be true only when the radian is chosen as the unit of plane angle. In reality, the factor of conversion between the physical quantities that refer to linear motion and those that refer to rotations is not the radius, but the ratio between the arc length and the central angle corresponding to the arc. This ratio happens to be equal to the radius only when the central angle happens to be measured in radians. The correct conversion factors must be used to convert the values of a physical quantity like angular momentum between systems with different units for the plane angle. While in the system with plane angles measured in radians the angular momentum is the linear momentum multiplied by radius, in the system with plane angles measured in cycles the angular momentum is the linear momentum multiplied by perimeter. The same for torque. When you divide a kinetic energy to a frequency expressed in cycles per second, you get an angular momentum that is equal to the product of linear momentum by perimeter, corresponding to the cycle as the unit of angle. When you divide a kinetic energy to a frequency expressed in radians per second, you get an angular momentum that is equal to the product of linear momentum by radius, corresponding to the radian as the unit of angle. These 2 variants correspond to the alternative "h" and "h bar" values of the Planck constant. The same quantum of angular momentum corresponds to both choices (i.e. the double of the spin of the electron), it is just expressed in different units.