A Universal Constant

Although the speed of light is a Universal Constant, fixed throughout the cosmos, the units that we use to measure it – the metre and the second – are entirely artificial.   In Napoleonic times, scientists tried to improve the accuracy and reliability of mediaeval weights and measures by finding rational,  scientific definitions of the fundamental units. This included defining the metre as one ten-millionth of the distance from the North Pole to the Equator, passing through Paris: obviously this would be pretty difficult to measure with certainty, so it was indirectly measured from the length of a platinum bar stored in a vault in Paris, that was said to be equal to that value.  Obviously, the metal bar had to be kept pretty safe from damage or contamination: furthermore metal expands with temperature so that had to be controlled too. Not very satisfactory for a fundamental international standard.

That is bad enough, but the second is arbitrary too.  Historically defined as 1⁄86400 of a day – a day being the time between noon on successive days –  the big problem is that days are not equal in length, due to the effect of the earth orbiting around the sun, and other perturbations in the earth’s rotation. With an accurate clock, you can measure the length of each day and take an average value.  Or to be more accurate, you can measure the length of a year and make the second an agreed fraction of that time.

Fundamental properties of matter

But neither of these are based on any fundamental property of matter and with a sufficiently accurate clock, we find that they are not entirely constant.

So if we say that the speed of light is, say, 299,792,458 metres per second, we presume that we know exactly and incontrovertibly the length of a metre and of a second.

The importance of the second

The measurement of time is fundamental to the measurement of most of our physical quantities – and the second has become a basis of most of our fundamental measurement units.

For example, the present standard definitions of distance (the metre), weight (the kilogram), electrical current (the ampere), temperature (the kelvin) and luminous intensity (the candela),  all depend on the second. The only base unit whose definition does not depend on the second is the mole  (the amount of a substance, derived from the word molecule). Of the 22 named derived units, only radian and steradian (measurements of angle) do not depend on the second.

So it is rather important that we know exactly, accurately and  repeatably, how long a second is.

Thus it is pretty amazing that the absolute length of a second was not internationally agreed until 1983!  And this agreement relied on Louis Essen‘s work: hence, it is astonishing that his name is almost completely unknown.

Essen’s wartime work

Louis Essen’s wartime work driven by the requirement to measure the frequency of radar and thus radio waves accurately.  After completing his degree in Physics,  he joined the NPL (the UK’s National Physical Laboratory) in 1929, and began working on measurements of frequency, leading to the development of the quartz ring clock in 1938.  A ring of quartz crystal was induced to vibrate using  an oscillating electric field and the vibrations were counted by using thermionic valves to subdivide the vibration into measurable steps which were counted to measure time.

This quartz clock was far more reliable than anything else at the time and became widely used as a time standard in observatories. It was the first device accurate enough to discover minute variations in the Earth’s speed of rotation; prior to this astronomers thought that the Earth rotated at a completely constant speed, and they divided the resulting length of day into 86,400 seconds.

Astronomers already knew that the length of a day – the time between noon on successive days (as distinct from the length of daylight) does vary throughout the year due to the tilt of the earth relative to its orbit around the sun, so International Astronomical Union decided to adopt a definition of the second as the basic unit of time, measured as a fraction of the time taken for the earth to complete one orbit of the sun (i.e. one year).

Essen ridiculed this as being even harder to measure correctly than averaging the earth’s rate of rotation, which made him rather unpopular.

Using his quartz clock to measure the frequency of his radio waves, and knowing their wavelength from the dimensions of his resonant cavity, Essen made new measurements of the speed of light which were about 15 km/s higher than the standard accepted at the time, the simple formula being c = fλ, where
c is the speed of light, f is the frequency of the wave and λ is the wavelength of the wave.

The connection between the speed of light and the second

So, how are the speed of light and the length of a second  so fundamentally connected?

We have noted that the metre was defined in Napoleonic times as the length of a platinum rod kept in a vault in Paris.  Although scientists had come up with a rationale for the length of this rod, it relied on some assumptions of dubious validity.  Likewise for the second.  But if you fix one of these values, then since the speed of light is universal, you can fix the other one, and thereby almost everything else.

The Atomic Clock

Essen designed an Atomic Clock, which used the resonance  of  Caesium atoms to further stabilise his quartz ring resonators which were already being used as a time reference in observatories.   The following describes the principle of such a clock – actually making one was at the extreme edge of physics at the time, in 1953 to 1955.

Why use Caesium?
Caesium is an ‘alkali’ metal very similar to potassium, and sets on fire when put in water, or even in air, so it is never found naturally in its metallic state.  There is only one stable isotope, Caesium 133.  [Caesium 137 is a radioactive isotope obtained from nuclear reactors and used in medical treatments,]

We are all aware of the light emitted by atoms when they change energy states – the most common example is the familiar orange glow of the sodium vapour street lamp.  In a sodium lamp, an electrical discharge through a tube containing metallic sodium causes it to heat and emit its characteristic ‘D’ lines of monochrome light.  We are also familiar with ‘neon’ tubes that emit light of various other colours.

The colour of the light depends on the atoms being used, and more correctly we should say ‘electromagnetic radiation’ or ‘photons’ because the frequency of the radiation emitted by the atom can theoretically be anywhere within the electromagnetic spectrum.

Essen chose Caesium firstly because as an alkali metal like sodium or potassium,  it only has one electron in its outer shell, so it emits a simple, single frequency rather than a range of frequencies.  When the atom is excited (energised) this electron develops a ‘spin’ (I suspect this term is a conceptualisation of a complex phenomenon) which causes it to be deflected by magnetic fields. The spin can be in the same direction as the spin of the atom’s nucleus, or in the opposite direction, and these represent two different energy states, and causing them to be deflected in opposite directions by a magnet.  When the electron changes energy state, it absorbs or emits a photon of an exact frequency that is characteristic of the particular atom.      The frequency absorbed or emitted by Caesium is  9,192,631,770 Hz, which is at the upper limit of what Essen’s wartime radar and speed-of-light apparatus could measure. So in fact it isn’t within the visible spectrum (where it was not possible to measure frequency at the time).

How the atomic clock worked
The atomic ‘clock’ worked in quite an obscure fashion.  Essen heated caesium atoms in an ‘oven’ contained within in a tube about 1.5 m long holding a total vacuum.  The atoms came out of a slit in the oven and passed down the tube between the poles of a magnet. This focussed the spinning electrons towards a narrow slit in the centre of the apparatus.  The electrons that pass through the slit then pass though another magnet which continues to deflect them away from the centre of the apparatus, where they are lost.

But when an oscillating electromagnetic (radio) field is applied to the space between the magnets at the exact resonance frequency of the electrons ( 9,192,631,770 Hz), their direction of spin reverses!

This means that when they pass through the second magnet, instead of bending further away, they bend back towards the centre of the tube and strike a detecting target made from a heated tungsten wire.  This causes charged atoms to be released from the wire and attracted to a detector, creating an electrical current.  This current is very small, but when greatly amplified, changes in the current can be detected, which increases by about 10 % when resonance occurs.

Now, the radio wave of exactly 9,192,631,770 Hz is generated from a quartz ring oscillator.  The oscillator runs at 5.00688 MHz, which when multiplied by 1836 gives the Caesium frequency.

The smallest drift of the oscillator frequency would be multiplied by almost 2000 times and detected by a change in the beam current of the clock apparatus which was used to correct the oscillator.  The oscillator could be used to run a normal quartz clock and thus to display the passage of time.  With some refinement, such a clock was accurate to 1 part in 10 million million, which is 10,000 times more accurate than astronomical time.

Ramifications
This accuracy has had many fundamental and far-reaching ramifications.  Not the least of these has been the abandonment of solar time or sidereal time as a reference for the second.  Since one of the raisons d’être for observatories has been the measurement and maintenance of time standards, it met with much resistance before being accepted and contributed further to Essen’s unpopularity.

Problems with Einstein’s Relativity

Einstein had said the since the speed of light was not affected by speed of travel, the logical consequence of this was that  passage of time must be affected by speed of travel.  This seemed illogical to Essen (perhaps because he could not believe that the rate of vibration of atoms was affected by speed of travel) argued that Einstein was wrong about the speed of travel affecting time, but in 1971 scientists sent three caesium clocks around the world in jet airliners, and found that they were showing a time slower than a clock that had been stationary in their lab.  Sadly for Essen, his own clock proved his assertion to be wrong!

The speed at which time passes does depend on how fast you are moving, after all!

But this astonishing prediction could not have been proven without Essen’s own work!

[I hope to refine this article in a while]