User:Physicsyang15/沙盒

Proposal

The numerical values given in this section are the published CODATA 2017 values.

The BIPM's Consultative Committee for Units (CCU) proposed that, in addition to the speed of light, four further constants of nature should be defined to have exact values. Using the CODATA 2017 values, these would be:

• The Planck constant h is exactly 6966662607015000000♠6.62607015×10⁻³⁴ joule-second (J⋅s).
• The elementary charge e is exactly 6981160217663400000♠1.602176634×10⁻¹⁹ coulomb (C).
• The Boltzmann constant k is exactly 6977138064900000000♠1.380649×10⁻²³ joule per kelvin (J⋅K⁻¹).
• The Avogadro constant N_A is exactly 7023602214076000000♠6.02214076×10²³ reciprocal mole (mol⁻¹).

These constants were described in the 2006 version of the SI manual, but in that version the latter three were defined as "constants to be obtained by experiment" rather than as "defining constants".

The CCU also proposed that the numerical values associated with the following constants of nature be retained unchanged:

• The speed of light c is exactly 7008299792458000000♠299792458 metres per second (m⋅s⁻¹).
• The ground state hyperfine splitting frequency of the caesium-133 atom Δν(¹³³Cs)_hfs is exactly 7009919263177000000♠9192631770 hertz (Hz).
• The luminous efficacy K_cd of monochromatic radiation of frequency 7014540000000000000♠540×10¹² Hz is exactly 7002683000000000000♠683 lumen per watt (lm⋅W⁻¹).

The seven definitions above are rewritten below after converting the derived units (joule, coulomb, hertz, lumen and watt) into the seven base units (second, metre, kilogram, ampere, kelvin, mole and candela), according to the updated draft of the 9th edition of the SI Brochure (2016). In the list that follows, the symbol sr stands for the dimensionless unit steradian.

• Δν_Cs = Δν(¹³³Cs)_hfs = 7009919263177000000♠9192631770 s⁻¹
• c = 7008299792458000000♠299792458 m⋅s⁻¹
• h = 6966662607015000000♠6.62607015×10⁻³⁴ kg⋅m²⋅s⁻¹
• e = 6981160217663400000♠1.602176634×10⁻¹⁹ A⋅s
• k = 6977138064900000000♠1.380649×10⁻²³ kg⋅m²⋅K⁻¹⋅s⁻²
• N_A = 7023602214076000000♠6.02214076×10²³ mol⁻¹
• K_cd = 7002683000000000000♠683 cd⋅sr⋅s³⋅kg⁻¹⋅m⁻²

In addition the CCU proposed that

• The international prototype kilogram be retired and that the current definition of the kilogram be abrogated,
• The current definition of the ampere be abrogated,
• The current definition of the kelvin be abrogated and
• The current definition of the mole be revised.

These changes will have the effect of redefining the SI base units, though the definitions of the derived SI units in terms of the base units will remain the same.

提案

國際度量衡局提案，除了光速 以外，下列所示的四個自然常數也應被定義為確定的數值：

• 普朗克常數 h = 6966662607015000000♠6.62607015×10⁻³⁴ (J·s)
• 基本電荷 e = 6981160217663400000♠1.602176634×10⁻¹⁹ (C)
• 波茲曼常數 k = 6977138064900000000♠1.380649×10⁻²³ (J⋅K⁻¹)
• 亞佛加厥常數 N_A = 7023602214076000000♠6.02214076×10²³ (mol⁻¹)

這些常數在2006年板的SI指南就已經出現，但在此版本中後三個常數被定義為“由實驗所得的常數”，而不是直接的“定義常數”。

國際度量衡局也提案，以下這些自然常數的數值應繼續保持不變。

• 光速 c = 7008299792458000000♠299792458 (m·s^-1)
• 銫133原子基態超精細能階分裂頻率 Δν(¹³³Cs)_hfs = 7009919263177000000♠9192631770 (Hz)
• 頻率為 7014540000000000000♠540×10¹² Hz 輻射的發光效率 K_cd = 7002683000000000000♠683 (lm·W^-1)

以上七個定義在以下改寫為以基本單位表示的形式

• Δν(¹³³Cs)_hfs = 7009919263177000000♠9192631770 (s⁻¹)
• c = 7008299792458000000♠299792458 (m⋅s⁻¹)
• h = 6966662607015000000♠6.62607015×10⁻³⁴ (kg⋅m²⋅s⁻¹)
• e = 6981160217663400000♠1.602176634×10⁻¹⁹ (A⋅s)
• k = 6977138064900000000♠1.380649×10⁻²³ (kg⋅m²⋅K⁻¹⋅s⁻²)
• N_A = 7023602214076000000♠6.02214076×10²³ (mol⁻¹)
• K_cd = 7002683000000000000♠683 (cd⋅sr⋅s³⋅kg⁻¹⋅m⁻²)

此外國際度量衡局也要求：

• 目前公斤的定義應廢除並使國際公斤原器退休
• 目前安培的定義應廢除
• 目前克耳文的定義應廢除
• 目前莫爾的定義應修改

這些改變會影響到基本單位的定義，但對於導出單位的表達形式則不會有所影響。

Impact on base unit definitions

The CCU proposal recommended that the text of the definitions of all the base units be either refined or rewritten changing the emphasis from explicit-unit to explicit-constant type definitions. Explicit-unit type definitions define a unit in terms of a specific example of that unit—for example in 1324 Edward II defined the inch as being the length of three barleycorns and since 1889 the kilogram has been defined as being the mass of the International Prototype Kilogram. In explicit-constant definitions, a constant of nature is given a specified value and the definition of the unit emerges as a consequence. For example, in 1983, the speed of light was defined to be exactly 7008299792458000000♠299792458 metres per second and, since the second had been independently defined, the length of the metre could thus be derived.

The current (2008) and proposed (2016) definitions are given below.

Second

The proposed definition of the second is effectively the same as the current definition, the only difference being that the conditions under which the measurements are made are more rigorously defined.

Current definition: The second is the duration of 7009919263177000000♠9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

Proposed definition: The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency Δν_Cs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 7009919263177000000♠9192631770 when expressed in the unit Hz, which is equal to s⁻¹.

Metre

The proposed definition of the metre is effectively the same as the current definition, the only difference being that the additional rigour in the definition of the second will propagate to the metre.

Current definition: The metre is the length of the path travelled by light in vacuum during a time interval of 1/7008299792458000000♠299792458 of a second.

Proposed definition: The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 7008299792458000000♠299792458 when expressed in the unit m⋅s⁻¹, where the second is defined in terms of the caesium frequency Δν_Cs.

Kilogram

A watt balance which is being used to measure the Planck constant in terms of the international prototype kilogram.

The definition of the kilogram is due to change fundamentally—the current definition defines the kilogram as being the mass of the international prototype kilogram, which is an artefact and not a constant of nature, whereas the new definition relates it to the equivalent energy of a photon via the Planck constant.

Current definition: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

Proposed definition: The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6966662607015000000♠6.62607015×10⁻³⁴ when expressed in the unit J⋅s, which is equal to kg⋅m²⋅s⁻¹, where the metre and the second are defined in terms of c and Δν_Cs.

A consequence of this change is that the new definition of the kilogram is dependent on the definitions of the second and the metre.

Ampere

The definition of the ampere is undergoing a major revision—the current definition, which is difficult to realise with high precision in practice, is being replaced by a definition that is more intuitive and that is easier to realise.

Current definition: The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 6993200000000000000♠2×10⁻⁷ newton per metre of length.

Proposed definition: The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 6981160217663400000♠1.602176634×10⁻¹⁹ when expressed in the unit C, which is equal to A⋅s, where the second is defined in terms of Δν_Cs.

Since the current definition contains a reference to force, which has the dimensions MLT⁻², it follows that in SI the kilogram, metre and second, the base units representing these dimensions, must be defined before the ampere can be defined. Other consequences of the current definition are that in SI the value of vacuum permeability (μ₀) is fixed at exactly 6993400000000000000♠4π×10⁻⁷ H⋅m⁻¹. Since the speed of light in vacuum (c) is also fixed, it follows from the relationship

$c^{2}={\frac {1}{\mu _{0}\varepsilon _{0}}}$

that the vacuum permittivity (ε₀) has a fixed value, and from

$Z_{0}={\sqrt {\frac {\mu _{0}}{\varepsilon _{0}}}},$

that the impedance of free space (Z₀) likewise has a fixed value.

A consequence of the proposed changes to the definition of the ampere is that the definition will no longer depend on the definitions of the kilogram and the metre, but will still depend on the definition of the second. In addition, the vacuum permeability, vacuum permittivity and impedance of free space, which, in the current definition have exact values, will be subject to experimental error.

Kelvin

The definition of the kelvin will undergo a fundamental change if the proposal is accepted. Rather than using the triple point of water to fix the temperature scale, the proposal recommends that the energy equivalent as given by Boltzmann's equation be used.

Current definition: The kelvin, unit of thermodynamic temperature, is 1/273.16 of the thermodynamic temperature of the triple point of water.

Proposed definition: 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 6977138064900000000♠1.380649×10⁻²³ when expressed in the unit J⋅K⁻¹, which is equal to kg⋅m²⋅s⁻²⋅K⁻¹, where the kilogram, metre and second are defined in terms of h, c and Δν_Cs.

One consequence of this change is that the new definition makes the definition of the kelvin depend on the definitions of the second, the metre, and the kilogram.

Mole

A near-perfect sphere of ultra-pure silicon – part of the Avogadro project, an International Avogadro Coordination project to determine Avogadro's number

The current definition of the mole links it to the kilogram. The proposed definition will break that link by making a mole a specific number of entities of the substance in question.

Current definition: The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

Proposed definition: The mole, symbol mol, is the SI unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles. It is defined by taking the fixed numerical value of the Avogadro constant N_A to be 7023602214076000000♠6.02214076×10²³ when expressed in the unit mol⁻¹.

One consequence of this change is that the current defined relationship between the mass of the ¹²C atom, the dalton, the kilogram, and Avogadro's number will no longer be valid. One of the following must change:

• The mass of a ¹²C atom is exactly 12 dalton
• The number of dalton in a gram is exactly the numerical value of the Avogadro constant

The draft SI brochure assumes the first will remain true, which would mean that the second will no longer be true. The molar mass constant, while still with great accuracy remaining equal to 1 g/mol, will no longer be exactly equal to that.

Candela

The proposed definition of the candela is effectively the same as the current definition, but has been rephrased with the only difference being the additional rigour in the definition of the second and metre will propagate to the candela.

Current definition: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 7014540000000000000♠540×10¹² Hz and that has a radiant intensity in that direction of 1/683 watt per steradian.

Proposed definition: The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 7014540000000000000♠540×10¹² Hz, K_cd, to be 683 when expressed in the unit lm⋅W⁻¹, which is equal to cd⋅sr⋅W⁻¹, or cd⋅sr⋅kg⁻¹⋅m⁻²⋅s³, where the kilogram, metre and second are defined in terms of h, c and Δν_Cs.

對於基本單位定義的建議與影響

秒

提案中關於秒的定義與目前的定義是等效的，唯一的不同點在於測量的條件被更嚴格的指定了。

目前的定義：秒，是銫133原子基態兩個超精細能階間躍遷所對應的輻射，其週期 7009919263177000000♠9192631770 倍的時長。

建議的定義：秒，記為 s，是國際單位制中的時間單位。秒是藉由指定銫133原子基態超精細能階間躍遷所對應的輻射頻率 Δν_Cs 的數值為 7009919263177000000♠9192631770 (Hz)來做為定義，其中 Hz 為 s^-1。

公尺

提案中關於公尺的定義與目前的定義是等效的，唯一的不同點在於秒被更嚴格的定義影響了公尺的定義。

目前的定義：公尺，是光在真空中走 1/ 7008299792458000000♠299792458 秒的長度。

建議的定義：公尺，記為 m，是國際單位制中的長度單位。公尺是藉由指定真空中光速 c 的數值為 7008299792458000000♠299792458 (m·s^-1)來做為定義，這裡秒是藉由 Δν_Cs 定義的。

公斤

公斤的定義將會從根本上改變。目前是定義國際公斤原器的質量為一公斤，這是人造的定義而非源於對自然的測量。然而在新的定義中是藉由光子的等效能量做為定義，之間是以普朗克常數作為聯繫。

目前的定義：公斤，是質量的單位。一公斤等於國際公斤原器的質量。

建議的定義：公斤，記為 kg，是國際單位制中的質量單位。公斤是藉由指定普朗克常數 h 的數值為 6966662607015000000♠6.62607015×10⁻³⁴ (kg⋅m²⋅s⁻¹)來做為定義，這裡秒與公尺分別藉由 Δν_Cs 與 c 定義。

這個定義的改變，使得公斤的定義與秒和公尺的定義相關聯。

安培

關於安培的定義目前正在做一個巨大的修改。目前的定義在實際上是難以達到高精度的測量，新的定義將會更易於實現。

目前的定義：若將兩平行且半徑可忽略的無限長直導線，置於真空中並使其相距一公尺。若通以1安培的定電流，他們會對彼此的導線產生作用力，大小將為 6993200000000000000♠2×10⁻⁷牛頓每公尺。

建議的定義：安培，記為 A，是國際單位制中的電流單位。安培是藉由指定基本電荷 e 的數值為 6981160217663400000♠1.602176634×10⁻¹⁹ C來做為定義，其中庫倫 C 等於 A·s。這裡秒是藉由 Δν_Cs定義。

由於目前安培的定義是與力相關的，力又與公斤、公尺和秒相關。因此公斤、公尺和秒必須在安培定義之前就預先定義。此外在國際單位制中真空中的磁導率 μ₀ = 6993400000000000000♠4π×10⁻⁷ H·m^-1 為固定的值。因為光速 c 也是固定的值，而且光速 c 滿足以下的關係式

$c^{2}={\frac {1}{\mu _{0}\varepsilon _{0}}}$

故真空電導率也會是固定的值，並且

$Z_{0}={\sqrt {\frac {\mu _{o}}{\varepsilon _{0}}}}$

因此真空中的阻抗也會是固定的值。

新的定義中關於安培的定義已經不再和公斤與公尺的定義相關，但仍和秒的定義相關。真空中的磁導率、真空中的電導率、真空中的阻抗，在目前的定義中他們都具有確定的數值，這點可能會導致實驗上的錯誤。