Posts Tagged ‘Kilogram’

Physics uses new magic to define the kilogram

June 22, 2016

Some fifty years ago my Maths and Physics Professors instilled in me the concept of elegance being the hallmark of “rightness” in science. For my Maths Professor, there was nothing more admirable or elegant than being just “necessary and sufficient”. I cannot shake off the gut-feeling that unnecessary complexity of explanation is an indicator of “wrongness”. Modern Physics is no longer characterised by elegance – only by complexities which are not necessarily, necessary. Fifty-seven fundamental particles (why only 57?), magical dark energy and dark matter, even stealth dark energy are all “fudge factors”  to cover the flaws of unsatisfactory theories and which make modern physics grossly inelegant.

A new paper from the National Institute of Standards and Technology:

D. Haddad, F. Seifert, L.S Chao, S. Li, D.B. Newell, J.R. Pratt, C. Williams, and S. Schlamminger. A precise instrument to determine the Planck constant, and the future kilogram. Review of Scientific Instruments, 2016 DOI: 10.1063/1.4953825

There used to be a time when units made common sense. A day was the time from sunrise to sunrise. That one day was a little shorter or longer than the next or that it was a different length in different parts of the world, was of little practical significance. Why the earth rotates around its own axis in its orbit around the sun, even in the most advanced physics theories, remains a mystery and a consequence of fundamental magic. Nowadays, of course, modern physics cannot conceive of using something as elegant and simple as the interval from one sunrise to the next to define time. That interval was too variable, too localised to the earth-sun system to be suitable for the flights of fancy of modern physics and cosmology. The magic involved was just too unsophisticated – too crude, too simple.

So now the unit of time is no longer a day but is a second. The second used to be the 86,400th part of a “standard” day, but now the reference interval is the second, defined as the

duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom, at rest, and approaching the theoretical temperature of absolute zero, including corrections for ambient radiation.

Day-magic is now replaced by a more sophisticated atomic magic. All radiation or vibration requires energy. It follows that the radiation of any atom must eventually cease but physicists are happy enough to invoke the magical acquisition of energy by the reference atom such that its radiation remains magically “constant”.

It is a similar story with the kilogram. Once upon a more common-sensical time, it was the weight (under the force of earth’s gravity) of a mass of one litre of water at 4ºC. Since the litre needed defining and the measurement was of weight rather than mass, physics needed something more sophisticated. So was born the International Prototype Kilogram (IPK).  But that mass of platinum/iridium (90/10) alloy was found to be losing mass (about 50 μg over 120 years) and so a more “independent” and “absolute” measure was needed. Two methods were proposed

One would define the kilogram in terms of the mass of a silicon atom by counting the number of atoms in a 1 kg sphere of ultra-pure silicon-28. (See Silicon Kilogram.) 

The other …..  proposed assigning a fixed value to the Planck constant as the basis for a new definition. Mohr and Taylor reasoned that if a watt balance could use an exactly defined mass to measure the unknown value of h, then the process could be reversed: By setting an exact fixed value of h, the same system could be used to measure an unknown mass.

The idea, which came to be known as the “electric” or “electronic” kilogram, was widely discussed and finally endorsed in principle in 2011 by the international General Conference on Weights and Measures (CGPM), with a few provisions. One of them was that, prior to re-definition, at least one instrument, and preferably more, would have to measure h to a benchmark uncertainty of 2 parts in a hundred million (108). NIST’s most recent measurement has a stated relative standard uncertainty of 3.4 X 108. In addition, the values obtained by the watt balances should be in reasonable agreement with those from scientists using the atom-counting approach to defining the kilogram.

……. The measured values from different groups will have to be in very good agreement in order to set an official fixed value for h.

To get from Planck’s constant to mass is not that simple:

….. the connection between mass …  and a constant deriving from the very earliest days of quantum mechanics may not be immediately obvious. The scientific context for that connection is suggested by a deep underlying relationship between two of the most celebrated formulations in physics.

One is Einstein’s famous E =mc2, where E is energy, m is mass,and c is the speed of light. The other expression, less well known to the general public but fundamental to modern science, is E = hν, the first “quantum” expression in history, stated by Max Planck in 1900. Here E is energy, ν is frequency, and h is what is now known as the Planck constant.

Einstein’s equation reveals that mass can be understood and even quantified in terms of energy. Planck’s equation shows that energy, in turn, can be calculated in terms of the frequency (ν) of some entity such as a photon — or alternatively, with some mathematical substitutions, a significant mass — times an integer multiple of h. The integer aspect is what makes the relationship “quantized.”

Taking the two equations together yields a counterintuitive but hugely valuable insight: Mass – even on the scale of everyday objects – is inherently related to h, which Planck first used to describe the vanishingly small energy content of individual photons emitted by the atoms in hot objects. The value of h is about 0.6 trillionths of a trillionth of a billionth of 1 joule-second. The joule is the SI unit of energy.

As a practical matter, experiments linking mass to h with extraordinary precision became possible in the late 20th century as the result of two separate discoveries which led to two different physical constants related to voltage and resistance respectively.*

*These are the Josephson constant (K= 2e/h) and the von Klitzing constant (R= h/e2). …. Both constants also involve e, the fundamental charge of the electron. Because of the way the watt balance measures electrical power (albeit indirectly), e, cancels out of the equations. That leaves h as the sole quantity of interest.

The new NIST paper describes new measurements of h, with a watt-balance:

 A high-tech version of an old-fashioned balance scale at the National Institute of Standards and Technology (NIST) has just brought scientists a critical step closer toward a new and improved definition of the kilogram. The scale, called the NIST-4 watt balance, has conducted its first measurement of a fundamental physical quantity called Planck’s constant to within 34 parts per billion – demonstrating the scale is accurate enough to assist the international community with the redefinition of the kilogram, an event slated for 2018.

But the Planck constant itself is unexplained and relies on magic.

Classical statistical mechanics requires the existence of h (but does not define its value). Eventually, following upon Planck’s discovery, it was recognized that physical action cannot take on an arbitrary value. Instead, it must be some multiple of a very small quantity, the “quantum of action”, now called the Planck constant. Classical physics cannot explain this fact.

Why Planck’s constant is a constant or has to be a constant is unknown. It’s magic. Why the radiation of a caesium atom would remain constant is also counter-intuitive and just magic. Advances in physics only delve down to deeper layers of magic. Ultimately they all rely on evoking the 4 fundamental magical  forces of the universe. Giving some magic a name and a label does not explain it.

Fifty-seven fundamental particles is just inelegant and unsatisfactory. It is complication for the sake of complication. (Has CERN ever actually discovered anything? Every question it addresses is answered by two more questions – and without ever answering the first. The God of the God particle turned out to be just a deity rather than a God.)

The universe is not that messy. It is just magical.

Far simpler to take a kilogram as being the mass of a litre of water where a litre is twice the amount of beer I can drink in one gulp (when I am parched).


 

Measurement standards which can no longer be touched or seen or felt….

January 27, 2011

I have a sense of loss.

The Royal Society was home to a conference on 24th and 25th to consider how to bring the kilogram – the last of the seven base units of measurement – into line with the other six. This meeting was to discuss proposals of defining the kilogram in terms of the “fundamental” constants and to move away from using a lump of metal stored very carefully as the standard of mass.  The first General Conference on Weights and Measures was held in 1889 and meets every 4 years. The 24th Conference will be held in October this year and will table a proposal for the new definition of the kilogram. Then by the 25th Conference in 2015 the new definition may be adopted.

And when this happens there will no longer be any standard of measure left which can be seen or touched or felt. There will no longer be a King’s foot to refer to or an “Iron Ulna of our Lord the King” to signify a yard or some standard stones stored carefully to represent mass. The Mètre des Archives gave way to the International Prototype Metre.  The Imperial Standard Yard like the IPM was the distance between markings on specified bars of metal carefully stored. By 2015 all these standard definitions may be based only on the “fundamental constants” of nature (in the hope that they will truly remain constant across the reaches of space and time).

The International System of Units (SI) defines seven units of measure as a basic set from which all other SI units arederived. These SI base units and their physical quantities are:

  • metre for length
  • kilogram for mass
  • second for time
  • ampere for electric current
  • kelvin for temperature
  • candela for luminous intensity
  • mole for the amount of substance.
The seven SI base units and the interdependency of their definitions: for example

The seven SI base units and the interdependency of their definitions: for example

There used to be a time when measurements could be easily related to. Length and mass (weight) and light and temperature were all given units which were of practical and everyday use.

A candle-power was the light from one candle, a foot was a foot, an inch was either the width of your thumb or the distance from the tip of your index finger to the first knuckle, and a grain was the mass of a barley-corn. Water froze at zero °C and it boiled at one hundred divisions higher at 100 °C. Alternatively Daniel Fahrenheit set zero ° F to be the coldest stable temperature he could reach with a particular brine solution (ice, water and ammonium chloride which is a frigorific mixture) and he set 100 °F to the temperature of his wife’s armpit. Later others set the boiling point of water  to be exactly 180 divisions higher than the zero at 212 °F. This resulted in normal body temperature now becoming 98.6 °F instead of the 100. The point at which water freezes then happened to be 32 divisions higher than the zero. A comfortable temperature – inside or out – was 80 °F while 60 °F was chilly and 100 °F was on a hot day. A year was set by the seasons and the sun and the month was set by the moon. An average day was set by the sun rising and setting and this day was divided up – arbitrarily – into days and nights of 12 parts each and each part was further divided into 60 and 60 again – probably first by the Babylonians. It is only in our times that we have needed to split the second and anachronistically these further subdivisions of the second follow the metric system with milliseconds and microseconds and nanoseconds. A mile used to be 1000 paces (2 steps with a pace being a left step and a right step) of a standard Roman legionary.

But science and industry have moved on. Machines and instruments and medicine and electronics and computers and going to the moon can no longer manage with the old rules and measures of  everyday living.

From the purpose of the meeting at the  Royal Society:

From the origins of the metric system, when the metre was a fraction of the arc of the Paris meridian and the kilogram the weight of a cubic decimetre of water, the ultimate goal has been a system of measurement based on invariant quantities of nature. After more than 200 years we are now within reach of achieving this. While the kilogram is still defined as the mass of a Pt-Ir cylinder kept in a vault in Sèvres, serious plans now exist to redefine the kilogram by fixing the numerical value of the Planck constant h; and the ampere, kelvin and mole by fixed numerical values for e, k and NA. With the metre already being defined by the speed of light and the second by an atomic microwave transition, but likely soon to be redefined by an optical transition of much higher frequency, we shall have at last achieved what the savants of the 18th century had sought.

Today all the units except the kilogram are defined by natural constants:

  1. The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second with the speed of light in a vacuum being the natural constant. (And I can’t help wondering if this will remain constant under changing gravity conditions or the changing state of the expanding – or contracting – universe).
  2. The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom at rest at a temperature of 0 K.
  3. 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 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10−7newton per metre of length.
  4. The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of thetriple point of water having the isotopic composition defined exactly by the following amount of substance ratios: 0.000 155 76 mole of2H per mole of 1H, 0.000 379 9 mole of 17O per mole of 16O, and0.002 005 2 mole of 18O per mole of 16O.
  5. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12 where unbound atoms of carbon 12, at rest and in their ground state, are referred to.
  6. The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

The plan is to base the kilogram on the Planck constant .

File:CGKilogram.jpg

A computer-generated image of the International Prototype kilogram (IPK): Wikipedia

Physics World reports

In the current system, the kilogram, ampere, kelvin and the mole are all linked to exact numerical values of the mass of the international prototype kilogram in Paris, the permeability of the vacuum, the triple-point temperature of water, and to the molar-mass of carbon-12 respectively. The plan is to change all that so that these four units are linked to exact numerical values of the Planck constant, the charge of the electron, the Boltzmann constant and to the Avogadro constant respectively.

All of this is no doubt a great advance and necessary but I have difficulty to relate to the new definitions. I cannot invoke any image of 9 192 631 770 periods of a radiation or the 299 792 458th part of a second and I feel that something is being lost……


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