There is a magic rock in St. Cloud, France. It’s made not of stone, but of a metallic alloy that’s 90% platinum and 10% iridium, and it’s magic not through some supernatural force, but because scientists have declared it to have a mass of exactly 1 kilogram. Now many scientists would like to get rid of it. 

Our civilization is built upon a system of measurement standards. If two people want to trade, they have to agree on what a pound is. If you pay a contractor to build a 100 foot tall building, you have to agree on the length of a foot. Throughout history humans have had standards of measurement, often dictated by governmental decree. But since the early 1800s there has been a quest to create a truly universal standard of measurements. This became the metric system, which was further standardized to the Système international d’unités (SI) in 1960. The SI standard has become the basis for measurement across the globe. They define the physical units we use to measure things. Even in the United States, quantities like the foot and pound are defined in terms of SI units.

The most common SI units are those of the meter (length), second (time) and kilogram (mass). In the 1800s these were based upon the physical characteristics of Earth. A meter was defined by declaring the circumference of Earth to be 40,000 kilometers. A second was defined by declaring the length of an average day to be 24 hours long. A kilogram was defined as the mass of a liter (1000 cubic centimeters) of water. While these definitions initially worked well, as our measurements became more precise things became problematic. As measurement of the Earth’s circumference improved, the length of a meter would necessarily change. Since the volume of a liter is defined in terms of length, the mass of a kilogram likewise shifted. Precise measurements of Earth’s rotation showed that the length of a day varied, so even the second wasn’t entirely fixed.

There are two ways to define a set of units that don’t vary. One is by defining a particular object to be an exact standard, and the other is to define units in terms of universal physical constants. The meter and second are now defined using the later method. For example, in Einstein’s theory of relativity, the speed of light in a vacuum is always the same. No matter where you are in the universe, or how you are moving through space, the speed of light never changes. It is an absolute physical constant. This has been verified through numerous experiments, and in 1983 it was given an exact value. By definition, the speed of light is 299,792,458 meters per second. By defining this value, we also defined the length of a meter. Since the speed of light is a constant, if you know how long a second is, you know the length of a meter.

Emission spectrum of a high pressure sodium lamp. Credit: Chris Heilman

The length of a second is also defined in terms of light. By the 1960s we had developed atomic clocks based upon cesium 133. Like all elements, Cesium 133 emits light at specific frequencies. Light is emitted from an atom when an electron moves from a higher energy quantum state to a lower one, and under the right conditions they are always the same. One particular emission from cesium 133 is known as the hyperfine ground state, and it is used to regulate an atomic clock the way the swing of a pendulum regulates a grandfather clock. In 1967 the frequency of light emitted by this hyperfine transition was defined to be 9,192,631,770 Hz. By measuring the frequency, you know the length of a second.

Since the meter and second are based upon physical constants, they don’t change. They can also be measured anywhere in the universe. If an alien civilization wanted to know what units we use, we could send them a radio message with the definition for meters and seconds, and the aliens could recreate those units. But since 1889, the kilogram has been defined by a specific chunk of metal known as the International Prototype of the Kilogram (IPK). If the aliens wanted to know the mass of a kilogram, they would have to make a trip to France.

The relative mass change of kilogram copies over time. Credit: Greg L at English Wikipedia

Besides the necessary road trip for aliens, there is a big problem with using a magic rock as the standard kilogram. Since the mass of the IPK is exact by definition, it cannot change under any circumstances. If someone were to shave off a bit of metal, it would still be one kilogram by definition. Shaving the IPK down a bit wouldn’t make the kilogram lighter, it would make everything else in the world a bit heavier. Of course, that doesn’t make any sense. Shaving down a bit of metal in France doesn’t make the Statue of Liberty weigh more. The problem is with our definition of mass. And in a sense this kind of thing actually happens. In addition to the official prototype kilogram, there are official copies all over the world. By comparing the copies to the IPK, we can determine the stability of its mass. This has only been done a few times over the years, but on average the mass of the copies has increased slightly compared to the IPK. Either the official kilogram is getting lighter, or the copies are getting heavier.

The standard kilogram hasn’t been replaced by a physical constant because we haven’t been able to measure them with enough precision. The obvious physical constant for mass would be the universal constant of gravity G. But gravity is a weak force, and measuring G is difficult. So far we’ve only measured it to about one part in 10,000, which isn’t nearly accurate enough to define mass. But there is another constant we could use, and it’s known as the Planck constant.

The Planck constant lies at the heart of quantum theory. It was first introduced by Max Planck in his study of light. When objects are heated, they emit light, and the color of that light depends upon the temperature of the object. This is known as blackbody radiation. According to classical theory, most of the light emitted should have very short wavelengths, but experimentally this wasn’t the case. Planck demonstrated that light must be quantized proportional to a small constant h, which we now call Planck’s constant. As our understanding of quantum theory grew, the Planck constant played a role not just in quantization, but quantum ideas of energy and momentum. In SI units, h has units of kg∙m²/s. If the Planck constant is defined to have an exact value, then the kilogram would be defined in terms of Planck’s constant as well as the meter and second.

In principle it’s a good idea, but it can only be done if we can measure it accurately. In 2014 the Conférence Générale des Poids et Mesures  (CGPM) decided that before such a definition could occur, three independent measurements of the Planck constant would need to be made, each with an accuracy of 50 parts per billion, and one accurate to 20 parts per billion. By June of this year three experiments have been done with uncertainties smaller than 20 parts per billion. The CGPM meets again in 2018, where it is expected they will officially define the Planck constant to be exactly 6.626069934 x 10⁻³⁴ kg∙m²/s. When that happens the prototype kilogram will no longer be a magic rock, but simply a part of scientific history.

And the aliens won’t have to make that road trip after all.

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When we make measurements of things in the universe, we can express the results in some type of units. The mass of a black hole in solar masses, or the distance to Jupiter in astronomical units, for example. But to be accurate, all of these units need to be based upon well measured standards that form the basis for all other units. Defining those standards poses certain challenges. After all, how to you measure something that is used to define your measurements?

Our modern foundation of measurements is the metric system (or more formally the International System of Units). In this system, seven base units are defined by convention (meter, kilogram, second, ampere, kelvin, mole and candela), and from these all other measuring units are derived. Even most non-metric units are formally defined by metric quantities. For example, an inch is defined as 2.54 centimeters. An English pint is exactly 568.26125 cubic centimeters.

The base units and their connection to physical constants. Credit: Wikipedia

Originally, the metric base units were defined in terms of physical quantities that could be measured. A kilogram was proposed as the mass of a liter (1000 cubic centimeters) of water. The meter was proposed by declaring that the distance from the north pole to the equator along a line through Paris is 10,000 kilometers. The second was defined in terms of a standard solar day being exactly 24 hours long. While these definitions initially worked well, as our measurements became more precise things became problematic. As measurement of the Earth’s circumference improved, the length of a meter would necessarily change. Since the volume of a liter is defined in terms of length, the mass of a kilogram likewise shifted. Precise measurements of Earth’s rotation showed that the length of a day varied, so even the second wasn’t entirely fixed.

A replica of the standard kilogram. Credit: Wikipedia

To solve this problem, some of the units were redefined in terms of a specific physical object. For example, in the 1870s the meter was redefined as the distance between two marks on the prototype meter bar made of platinum and iridium. In 1889 a cylinder of platinum-iridium alloy was defined as the prototype kilogram. While these were more precise than earlier definitions, they still had problems. As physical objects they need to be handled and measured in order to calibrate units. They can also change as they interact with their environment. We know, for example, that the standard kilogram varies in mass over time relative to official copies. These are small changes, on the order of micrograms, but they limit the precision of our measurements.

As we’ve studied the physical universe, we’ve found that the universe itself seems to have a set of absolute physical standards. Some things, such as the speed of light, the universal constant of gravity, and the charge of an electron, seem to have precise values that are absolute and unchanging throughout the universe. These physical constants could thus be used as the fundamental scale from which our metric system is defined. For some units this has already been done. In 1983 the speed of light was defined as exactly 299,792,458 m/s, and the second is defined in terms of the frequency of light from a caesium 133 atom. As a result, the meter is now defined in terms of the speed of light. But other units such as the kilogram are still based upon the 1889 prototype. There is currently a proposal to redefine the kilogram and other units in terms of physical constants. If the proposal passes, the metric system would no longer depend upon prototype objects.

But if we defined our units in terms of physical constants, what if those constants change over time? While this has been expressed as a concern, it isn’t really that much of a problem. We know from observations that the physical constants appear uniform across billions of years and billions of parsecs. All evidence so far shows them to be fixed and unchanging. And fixing our definitions in terms these physical values doesn’t prevent us from detecting the relative changes of these constants over time. So if we find they are changing we can always make new definitions for our units, just as we have in the past.

It would just be a matter of holding our measurements to a higher standard.

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It is impossible to measure the speed of light, and it has been impossible since 1983.  No, the behavior of light didn’t suddenly change in 1983.  What changed was the way we define the length of a meter.

Measuring the speed of light has always been tricky because of its tremendous speed.  It wasn’t until the 1600s that astronomers such as Romer and Huygens measured its speed by observing the moons of Jupiter.   Their approach was to carefully measure the transits of Jupiter’s moon Io very carefully when the Earth was moving toward Jupiter and when it was moving away from Jupiter.  By measuring the difference in those times they were able to calculate a speed of around 200,000 kilometers per second.  Their value is about a third lower than the actual value, but it’s astoundingly accurate given the crudeness of their equipment.

By the 1900s, we were able to use the interference of light waves to get very precise measurements of light speed.  When lasers were introduced, these interferometry measurements became more precise than the definition of a standard meter.  This meant the uncertainty of the speed of light lay not in the measurement, but in the uncertainty of how long a meter was.  So in 1983, it was decided to define the meter from the speed of light.  This made the speed of light (in a vacuum) 299,792,458 m/s by definition.  As a result, if you try to measure the speed of light, you are actually measuring the length of a meter.

Of course this raises an interesting question.  If we’ve defined the speed of light in a vacuum to be a constant, doesn’t that mean that effects such as the expansion of the universe are just the same as the slowing of the speed of light?  The answer is actually no.  We can still measure changes in light regardless of how we define our units.  For example, the famous Michelson-Morley experiment (which demonstrated that the speed of light constant) was first performed in the late 1800s, before a precise speed of light was even known.

So we don’t lose anything by our new definition.  What we gain is a better way to measure distance, which is central to building better astronomical equipment.

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