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Recent progress in fundamental constants and the International System of Units Third Workshop on Precision Physics and Fundamental Physical Constants 6 December 2010   Peter Mohr National Institute of Standards and Technology Gaithersburg, MD, USA

Third Workshop on Precision Physics and Fundamental Physical Constantsphysics.vniim.ru/SI50/files/mohr.pdf · and the International System of Units Third Workshop on Precision Physics

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Page 1: Third Workshop on Precision Physics and Fundamental Physical Constantsphysics.vniim.ru/SI50/files/mohr.pdf · and the International System of Units Third Workshop on Precision Physics

Recent progress in fundamental constantsand the International System of Units

Third Workshop on

Precision Physics and Fundamental Physical Constants

6 December 2010

  Peter MohrNational Institute of Standards and Technology

Gaithersburg, MD, USA

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  Related Publications

Redefinition of the kilogram: a decision whose time has come Metrologia 42, 71 (2005).  

IM Mills, PJ Mohr, T Quinn, BN Taylor, M Williams    

Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI­2005), 

Metrologia 43, 227 (2006).

IM Mills, PJ Mohr, T Quinn, BN Taylor, M Williams

Defining units in the quantum based SIMetrologia 45, 129 (2008).

PJ Mohr

Resource Letter FC-1: The physics of fundamental constants American Journal of Physics 78, 338 (2010).

PJ Mohr and DB Newell

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URL: physics.nist.gov/constants

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International System of Units (SI)SI base units and symbols

− meter m (length)− kilogram kg (mass)− second s (time)− ampere A (electric current)− kelvin K (thermodynamic temperature)− mole mol (amount of substance)− candela cd (luminous intensity)

Some SI derived units and symbols− hertz Hz (frequency)− newton N (force)− joule J (energy)− coulomb C (electric charge)− volt V (electric potential difference)

Non­SI units and symbols− electron volt eV (energy)− unified atomic mass unit u (mass)

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Kilogram

International Kilogram prototype manufactured in 1880s:

Cylinder of 90 % platinum and 10 % iridium 39 mm high and 39 mm in diameter

1st General Conference on Weights and Measures (CGPM) in 1889:

This prototype shall henceforth be considered to be the unit of mass.

3rd CGPM in 1901:

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram

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Limitations of the current kilogram prototype definition

The prototype definition is not linked to an unchanging property of nature.

The mass of the international prototype appears to be changing relative to the mass of its copies.

The drift of the kilogram prototype together with its copies (relative to an unchanging standard) could be as large as 20 ҳ 10­9 kg per year (Williams et al. 1998; Davis 2003).

The prototype and its copies appear to gain mass over time and lose mass when washed for use in comparisons.

The kilogram mass definition cannot be realized independently of the international prototype.

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Possible redefinitions of the kilogram

The limitations on stability of the definition of the kilogram in terms of the international prototype could be eliminated if the kilogram were defined in terms of a fundamental constant in analogy with the definition of the meter.

17th CGPM in 1983:

The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.

As a consequence for the velocity of light c:

An alternative statement of the definition could be:

The meter is the length scaled such that the velocity of light is  

299 792 458 m/s.

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Experimental realization of the kilogram(watt­balance experiment)

A horizontal circular coil is suspended in a radial magnetic field

The current in the coil is adjusted so that the net magnetic forces equal the force of gravity on a 1 kg mass

The coil is slowly moved with a measured velocity through the magnetic field to calibrate the field strength and the geometry factors

Electrical measurements are made in terms of the Josephson and von Klitzing constants:  KJ

2RK = 4/h

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Ed Williams

Dave Newell

Rich Steiner

NIST 1998

Ruimin Liu

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Experimental realization of the kilogram(watt­balance experiment)

Current interpretation:

− precise kilogram mass + watt­balance experiment → h  Alternative interpretation:

− unknown mass ← watt­balance experiment + h (defined value)

This suggests a possible new definition of the kilogram:

The kilogram is the unit of mass scaled such that the Planck constant is exactly 6.626 068 96 ҳ 10­34 J s.

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Experimental realization of the kilogram(X­ray­crystal­density method)

Current interpretation:

− known mass silicon sphere + volume measurement + lattice spacing measurement + silicon isotopic composition measurement → NA 

Alternative interpretation:

− known mass silicon sphere ← volume measurement + lattice spacing measurement + silicon isotopic composition measurement + NA 

This suggests a possible new definition of the kilogram:

The kilogram is the unit of mass scaled such that the Avogadro constant is exactly 6.022 141 79 ҳ 1023 mol­1.

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Relation between the Avogadro constant NA and the Planck constant h

Rydberg constant definition:

unified atomic mass unit u:

Avagadro constant:

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Limitations of the present ampere definition

9th CGPM in 1948:

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross­section, and placed one metre apart in vacuum, would produce between these conductors a force equal to 2 x 10­7 newton per metre of length.

Modern voltage measurements are based on the Josephson effect: KJ = 2e/h  [2.5 x 10­8]

Modern resistance measurements are based on the quantum Hall effect: RK = h/e2   [6.8 x 10­10]

To express measurements with better accuracy, arbitrary exact units (not SI)  are used:

KJ → KJ­90 = 483 597.9 GHz/V

RK → RK­90 = 25 812.807 Ω

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Possible ampere redefinitionto make e exact

The ampere is the electric current scaled such that the elementary charge is 1.602 176 487 ҳ 10­19 coulomb.

Consequences:

for ε0

Josephson constant (voltage measurements)

von Klitzing constant (resistance measurements)

(the latter two equalities are assumed to be exact)

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Possible kelvin redefinitionto make k exact

The kelvin, the unit of thermodynamic temperature, is scaled such that the Boltzmann constant is exactly 1.380 650 4 ҳ 10­23 joule per kelvin.

The mole, the unit of amount of substance, is scaled such that the Avogadro constant is exactly 6.022 141 79 ҳ 1023 per mole.

Possible mole redefinitionto make NA exact

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constant current SI new SI constant current SI new SI

m(K ) 0 5.0 α 0.068 0.068

h 5.0 0 KJ 2.5 0

e 2.5 0 RK 0.068 0

kB 170 0 µ0 0 0.068

NA 5.0 0 ε0 0 0.068

R 170 0 Z0 0 0.068

F 2.5 0 qP 2.5 0.034

σ 700 0 J↔kg 0 0

me 5.0 0.14 J↔m–1 5.0 0

mu 5.0 0.14 J↔Hz 5.0 0

m(12C) 5.0 0.14 J↔K 170 0

M(12C) 0 0.14 J↔eV 2.5 0

Relative standard uncertainties for a selection of fundamental constantsmultiplied by 108 (i.e. in parts per hundred million)

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Quantum SI and Unit democracy

In the Quantum SI, the fundamental constants, c, h, e, k, NA, 

νCs

, ... are given fixed numerical values.

These constants determine the scales of the base units.

The defined set of base units determines all the units in the SI.

The conclusion is:  assigning fixed values to the  fundamental constants, c, h, e, k, N

A, ν

Cs, ... determines all 

the units in the SI.

The distinction between base units and other units is unnecessary.

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Time scale for possible redefinitions

At its meeting in September 2010, the Consultative Committee on Units (CCU) prepared a draft of the form the redefined units might take.

The draft was presented to the International Committee on Weights and Measures (CIPM) at its meeting in October 2010 for consideration.

The General Conference on Weights and Measures (CGPM) next meets in 2011, and it could approve the new definitions for implementation when the results of the relevant experiments are satisfactory

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Conclusion

The SI can be improved by modernizing the way units are defined.

In particular, the current definitions of the kilogram, ampere, kelvin and mole are based on 19th century science and technology and can be replaced by ones that take into account subsequent progress in physics.

If an update of the SI is done by specifying values of the fundamental constants as discussed, many constants would become exact and others would have smaller uncertainties.

With such an update of the SI, the concepts of base units and derived units would not be not necessary.