Action and Entropy: Base Physical Quantities

Introduction

According to de Broglie, action and entropy are base physical quantities .

“As a man who has devoted his whole life to the study of matter… I can tell you as a result of my research about the atoms this much: there is no matter as such.” Such were the words Planck addressed to a conference in Florence in 1944 .

In 2018, 26^th-CGPM  defined SI base units on a set of seven constants (figure [fig:si-links]) and redefined the mass unit, no longer by reference to the mass of a prototype, but by setting the value of … Planck constant.

^th-CGPM  mass defining method, together with Planck and de Broglie thoughts, suggests to consider a new system in which action and entropy would be base physical quantities .

SI Historical

*“The creation of the decimal metric system at the time of the French Revolution and the subsequent deposition of two platinum standards representing the metre and the kilogram, on 22 June 1799, in the Archives de la République in Paris, which can be seen as the first step that led to the present International System of Units.” *

In November 2018, the 26^th CGPM  redefined “the SI on a set of seven defining constants, drawn from the fundamental constants of physics and other constants of nature, from which the seven base units are deduced”.

Table [tab:si-base] displays SI base physical quantities, SI base units and their SI symbols .

SI base Physical Quantities, base units and symbols 

Within SI system, frequency, electrical charge, speed and molar entropy are derived physical quantities. Table [tab:si-derived] shows their units, as functions of SI base units . It is noticed that action is not mentioned as a derived quantity.

SI derived Physical Quantities and SI derived units . Blank boxes correspond to symbols or names that are not defined in BIPM 9th ed. 

Figure [fig:si-links] shows SI links between fundamental constants of physics ($\mathrm{\Delta }{\nu }_{\text{Cs}},c,h,e,k_B,N_A,K_{\text{cd}}$) and SI base units .

Links between fundamental constants of physics and SI base units .

New System: base quantities, units, symbols

Note: in present paper, the amount of substance and the luminous intensity are not studied. Only, action, entropy, frequency, speed and electric charge are studied here.

Proposed base physical quantities

26^th CGPM  defining method, together with Planck and de Broglie thoughts, suggests that we should consider a new system of base physical quantities. In such a system, action, entropy, frequency, speed and electric charge would be base physical quantities.

Each of these physical quantities would be directly linked to fundamental constants of physics: Planck constant $h$, Boltzmann constant $k_B$, hyperfine transition frequency of the Caesium 133 atom $\mathrm{\Delta }{\nu }_{\text{Cs}}^{133}$, speed of light in vacuum $c$ and elementary charge $e$ (figure [fig:ns-links]).

Links between fundamental constants of physics and proposed new system of base physical quantities.

Proposed quantities symbols

Table [tab:ns-base-symbols] shows the proposed base quantities names and the proposed base quantities symbols. It is proposed to use capital calligraphic fonts for base physical quantities of the new system $\mathcal{A},\mathcal{S},\mathcal{N},\mathcal{V},\mathcal{Q}$ (Table [tab:ns-base-symbols]).

Base quantities: names and symbols - New system

Proposed unit names and unit symbols

Within the new system NS, each of the fundamental constants $h,k_B,\mathrm{\Delta }{\nu }_{\text{Cs}}^{133},c$ and $e$ would be equal to one.

The proposed name of the unit of action is the planck, symbol Pk. One planck is the NS numerical value of the Planck constant, i.e., $h$ = 1 Pk.

The proposed name of the unit of entropy is the boltzmann, symbol Bz. One boltzmann is the NS numerical value of the Boltzmann constant, $k_B$ = 1 Bz.

The proposed name of the unit of frequency is the elementary frequency, symbol ${\nu }_{\text{Cs}}$. One elementary frequency is the NS numerical value of the frequency of the unperturbed ground-state hyperfine transition of the Caesium 133 atom, i.e., $\mathrm{\Delta }{\nu }_{\text{Cs}}^{133}=1{\nu }_{\text{Cs}}$.

The proposed name of the unit of speed is the light speed, symbol Ls¹. One light speed is the NS numerical value of speed of light in vacuum, $c$ = 1 Ls.

The proposed name of the unit of electric charge is the elementary electric charge, symbol Qe². One elementary electric charge is the NS numerical value of the elementary charge, i.e., $e$ = 1 Qe.

Table [tab:ns-base-units] shows the proposed names of the NS base units and the proposed symbols of the NS base units. Table [tab:ns-constants] shows the fundamental constants, their symbols and their new system numerical values.

Base units: names and symbols - New system

Fundamental Constants within NS

Table [tab:ns-to-si] converts new system units to SI units. Table [tab:si-to-ns] converts SI units to new system units (NS). Table [tab:ns-summary] summarises the NS base quantities and the related fundamental constants of physics.

Units Conversion NS $\to$ SI

Units Conversion SI $\to$ NS

Summary of proposed new system base quantities and related fundamental constants of physics

Conversion of dimensions of base quantities NS $⟷$ SI

According to the new system, time, length, mass, temperature and electric current would not be base physical quantities but NS derived physical quantities.

Table [tab:ns-dims] shows proposed symbols for the dimensions of NS base quantities. Table [tab:ns-to-si-dims] converts the new system dimensions to the SI dimensions. Table [tab:si-to-ns-dims] converts the SI dimensions to the new system dimensions.

Symbols for dimensions of NS base quantities

Dimension conversion NS $\to$ SI

Dimension conversion SI $\to$ NS

Discussion

What is studied here is not only a matter of units, but mainly a matter of physical quantities. Several points must be stressed:

Definition of base physical quantities

Figure [fig:si-links] shows how the SI base physical quantities are entangled. Here, each base quantity is defined independently of the others. Figure [fig:ns-summary] shows the proposed new system of base quantities: each base quantity would be defined by reference to only one physical constant.

Action and Entropy

Physical quantity action is not mentioned in BIPM reports as a base quantity, nor as a derived quantity. Here, following de Broglie , action and entropy would be considered as base physical quantities.

Temperature

The treatment of temperature is modified. Within the SI, temperature is a base physical quantity. Within the new system, temperature is not a base quantity, but a quantity derived from the NS base physical quantities action, frequency and entropy. Temperature is homogeneous to $\text{action}\times \text{frequency}\times (\text{entropy}{)}^{-1}$.

Mass

The treatment of mass is modified. Within the SI, mass is a base physical quantity. Within the new system, mass is not a base quantity, but a quantity derived from the NS base physical quantities action, frequency and speed. Mass is homogeneous to $\text{action}\times \text{frequency}\times (\text{speed}{)}^{-2}$.

Definition of units of action and entropy

As action is considered a base physical quantity, it is necessary to define a unit of action. The proposed name of the unit of action is the planck, symbol Pk. One planck is the NS numerical value of the Planck constant, i.e., $h$ = 1 Pk.

As entropy is considered a base physical quantity, it is necessary to define a unit of entropy. The proposed name of the unit of entropy is the boltzmann, symbol Bz. One boltzmann is the NS numerical value of the Boltzmann constant, i.e., $k_B$ = 1 Bz.

Comparison with BIPM reports

BIPM  establishes the international system of units, which is based on seven defining constants, drawn from the fundamental constants of physics.

Appendix 3 of the 26^th CGPM  defined the kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant $k$ to be $1.380649\times {10}^{-23}$ when expressed in the unit ${\text{J K}}^{-1}$, which is equal to ${\text{kg m}}^2{\text{ s}}^{-2}{\text{ K}}^{-1}$, where the kilogram, metre and second are defined in terms of $h$, $c$ and $\mathrm{\Delta }{\nu }_{\text{Cs}}$. This definition of the kelvin is based on four constants $k_B,h,c$ and $\mathrm{\Delta }{\nu }_{\text{Cs}}^{133}$.

The same remark applies to:

• the kilogram which is defined by reference to three constants $h,c$ and $\mathrm{\Delta }{\nu }_{\text{Cs}}^{133}$

• the metre, which is defined by reference to two constants $\mathrm{\Delta }{\nu }_{\text{Cs}}^{133}$ and $c$

• the ampere, which is defined by reference to two constants $e$ and $\mathrm{\Delta }{\nu }_{\text{Cs}}^{133}$.

Only the second is defined independently of the other units.

Present paper proposes a system of five base physical quantities: action, entropy, frequency, speed and electric charge. These quantities are related to fundamental physical constants: $h,k_B,\mathrm{\Delta }{\nu }_{\text{Cs}}^{133},c$ and $e$.

Each base physical quantity of the new system is defined independently of the others. Table [tab:comparison] summarises physical quantities and defining constants according to BIPM  from one part and physical quantities and defining constants according to the proposed new system from the other part.

Conclusion

Action and entropy are considered as base physical quantities. Mass and temperature are considered as derived physical quantities. Figure [fig:ns-summary] summarises the links between the proposed new system of base quantities, the fundamental constants and the proposed units. Each base quantity of the new system is defined independently of the others (Table [tab:comparison], Figure [fig:ns-summary]).

New system of base quantities, fundamental constants, units.