## Posts Tagged ‘**units**’

## The Daniell Cell, Ohm’s Law and the Emergence of the International System of Units

**Joel S. Jayson**

Telegraphy originated in the 1830s and 40s and flourished in the following decades, but with a patchwork of electrical standards. Electromotive force was for the most part measured in units of the predominant Daniell cell. Each company had their own resistance standard. In 1862 the British Association for the Advancement of Science formed a committee to address this situation. By 1873 they had given definition to the electromagnetic system of units (emu) and defined the practical units of the ohm as 10^{9} emu units of resistance and the volt as 10^{8} emu units of electromotive force. These recommendations were ratified and expanded upon in a series of international congresses held between 1881 and 1904. A proposal by Giovanni Giorgi in 1901 took advantage of a coincidence between the conversion of the units of energy in the emu system (the erg) and in the practical system (the joule) in that the same conversion factor existed between the cgs based emu system and a theretofore undefined MKS system. By introducing another unit, X (where X could be any of the practical electrical units), Giorgi demonstrated that a self consistent MKSX system was tenable without the need for multiplying factors. Ultimately the ampere was selected as the fourth unit. It took nearly 60 years, but in 1960 Giorgi’s proposal was incorporated as the core of the newly inaugurated International System of Units (SI). This article surveys the physics, physicists and events that contributed to those developments.

… Read more at http://arxiv.org/pdf/1512.07306v1.pdf

## Dimensionless Units in the SI

**Peter J. Mohr** and **William D. Phillips**

The International System of Units (SI) is supposed to be coherent. That is, when a combination of units is replaced by an equivalent unit, there is no additional numerical factor.

Here we consider dimensionless units as defined in the SI, * e.g.* angular units like radians or steradians and counting units like radioactive decays or molecules.

We show that an incoherence may arise when different units of this type are replaced by a single dimensionless unit, the unit “one”, and suggest how to properly include such units into the SI in order to remove the incoherence.

In particular, we argue that the radian is the appropriate coherent unit for angles and that hertz is not a coherent unit in the SI. We also discuss how including angular and counting units affects the fundamental constants.

Read more at http://arxiv.org/pdf/1409.2794v1.pdf

## A multiple of 12 for Avogadro

Carbon, Avogadro’s Constant and the Importance of the Number 12

**Materials scientists have decided to define, rather than measure, Avogadro’s constant, triggering a lengthy debate over what number to choose. Now one physicist thinks he has the answer.**

The International System of Units (with the abbreviation of SI units) is one of the foundations of modern science. It consists of seven base units from which all others can be derived.

These are the meter for length; the kilogram for mass; the second for time; the ampere for electric current; Kelvin for thermodynamic temperature; candela for luminous intensity, and mole for the amount of substance. This is a coӧrdinated system of units that allows scientific results to be compared relatively easily, regardless of where they are made.

However, the SI system is far from perfect. One of the problems is that some of the units have values based on arbitrary objects, such as the kilogram. There is general agreement that this should be changed so that the units are based on the fundamental constants of nature and on specific numbers that are defined and therefore constant.

One of these numbers is Avogadro’s constant. This is currently defined as the number of atoms in 12 grams of carbon-12 and is known to be about 6.02214129 ×10^23. But the exact number depends on the definition of a kilogram, which for the moment is the mass of an arbitrary bar of platinum-iridium alloy hidden in a safe somewhere in Paris.

The general consensus is that it would be better to define Avogadro’s constant and let this determine the mass of the kilogram. But what number should serve? Read the rest of this entry »

## Experimental realization of an optical second …

## … with strontium lattice clocks

**R. Le Targat et al**

Progress in realizing the SI second had multiple technological impacts and enabled further constraint of theoretical models in fundamental physics.

Caesium microwave fountains, realizing best the second according to its current definition with a relative uncertainty of 2–4 × 10^{−16}, have already been overtaken by atomic clocks referenced to an optical transition, which are both more stable and more accurate. Here we present an important step in the direction of a possible new definition of the second.

Our system of five clocks connects with an unprecedented consistency the optical and the microwave worlds. For the first time, two state-of-the-art strontium optical lattice clocks are proven to agree within their accuracy budget, with a total uncertainty of 1.5 × 10^{−16}.

Their comparison with three independent caesium fountains shows a degree of accuracy now only limited by the best realizations of the microwave-defined second, at the level of 3.1 × 10^{−16}….

Read more at http://www.nature.com/ncomms/2013/130709/ncomms3109/full/ncomms3109.html

Read also: **Optical lattice atomic clock could ‘redefine the second’**

## Quantum-Hall confirmation helps define kilogram

The kilogram is currently defined by a lump of metal in Paris – but now researchers in the UK, France and Sweden have confirmed a key assumption of a new method of defining the standard based on fundamental constants. Specifically, they have shown that the quantum Hall resistances measured in a semiconductor and in graphene are identical up to a relative uncertainty of 8.6 × 10^{–11}. This resistance is given by the ratio of the Planck constant (*h*) to the square of electron charge (*e*) and can be used to define the kilogram.

The kilogram standard is made from platinum and iridium, and is housed at the International Bureau of Weights and Measures (BIPM) in Paris. Over the past 60 years, several comparisons of this kilogram with identical copies suggest that its mass is changing. As a result, scientists have been looking for a new way to define the kilogram using just fundamental constants.

The most popular way of trying to do this is with a “watt balance”, which compares the weight of an object with an electromagnetic force. Such a balance operates on the assumption that the ratio of*h*/*e*^{2} is independent of the material used to measure it. A watt balance uses this ratio along with a measurement of the quantum Hall resistance to define the kilogram in terms of *h*.

### Drifting electrons

The Hall effect is the appearance of a voltage across opposite faces of a sheet of metal when a current passes along its length. The effect requires the presence of a magnetic field that is perpendicular to the sheet. The magnetic field causes the moving electrons to drift towards one face as they cross the sheet of metal. Ordinarily, the electron’s tendency to drift depends on factors such as the density of electrons in the material and the thickness of the sheet.

The quantum Hall effect occurs in sheets that are so thin that they appear 2D to the electrons. If such a sheet is subject to very low temperatures and high magnetic fields, the Hall voltage is quantized at discreet values that appear to be independent of the material used. When the Hall voltage is compared with the current running through the conductor, the resulting Hall resistance is simply *h*/*Ne*^{2}, with *N*being an integer.

According to J T Janssen of the National Physical Laboratory (NPL) in Teddington, UK, there is no theory to explain why this should be the case; however, all experiments so far agree on this universal value for the quantum Hall resistance. If the redefinition of the kilogram is to rest on the quantum Hall effect, then the uncertainties in these experiments must be very stringent indeed.

### Direct comparison

Now Janssen and colleagues at the NPL, Chalmers University and Linköping University in Sweden, the University Lancaster in the UK and the BIPM have made a direct comparison of the quantum Hall effect of two very different materials. These are a gallium–arsenide semiconductor doped to produce a 2D sheet of electrons, and graphene – which is a single layer of carbon atoms. Previous experiments have confirmed that two semiconductors exhibit the same quantum Hall effect, but this new work is the first to directly compare two materials with very different electronic properties. While the conduction electrons in gallium arsenide behave like particles with mass, the electrons in graphene behave like massless photons.

The researchers use a standard set-up that compares the Hall resistances of two samples held at temperatures within a couple of degrees of absolute zero. Identical currents are sent through the samples to create the Hall voltages. To see whether these voltages are different, another circuit connects the sides of the two samples with an extremely sensitive current detector. No current was measured, meaning that the voltages across the samples were identical.

### Challenges remain

“This is the most precise measurement of the material independence of the quantum Hall effect,” says Janssen. However, there are still important challenges to be overcome in the design and operation of the watt balance. The most significant, according to Janssen, is the mechanical challenge of operating the balance. For example, the force produced by the magnetic coil and its velocity must be carefully aligned with gravity. And as the overall uncertainty is reduced, it gets ever harder to make these alignments.

“The redefinition of the kilogram standard now is the one of the main topics in metrology,” says Alexander Penin of the University of Alberta in Edmonton, Canada. Indeed, next week, metrologists will gather in Paris for the 24th General Conference on Weights and Measures to discuss the merits of the watt balance and other proposals for redefining the kilogram.

The work is described in *New Journal of Physics* **13** 093026.