ee/ /e 
The present writing is concerned with how Planck quantities are perceived--especially with their perception as natural units, which is what both George Stoney and Max Planck originally called them when introducing them as a set. To experience quantities as units means above all to become acquainted with using appropriate decimal multiples of them descriptively. As was noted in the introductory chapter, the concrete reality of Planck quantities can be emphasized by the way we handle them: by identifying and using humanly scaled decimal multiples such as a penny's thickness and a mile. Other aspects which I said I would emphasize are their involvement in everyday experience and the opportunities they provide for a fresh look at physical law, but the particular business of this chapter is the identification of certain exact or approximate power-of-ten multiples.
Identifiying humanly scaled versions is intended to provide a concrete handle on the Planck quantities themselves. In what follows I will briefly indicate why I think the suggested names are justified.
| quantity | conventional value | rough equivalent | possible name |
|---|---|---|---|
| 10 | 0.539056(34) second | 0.54 second | tick |
| 10 | 1.61605(10) kilometers | statute mile | mile |
| 10 | 4220.50(81) cm | avg. US&Brit. gallons | gallon |
| 10 | 16.1605(10) centimeters | thumb to forefinger | span |
| 10 | 12.1056(15) newtons | 2.72 pounds | stone |
| 10 | 1.95633(13) joules | 2.0 joules | spanstone |
| 10e | 1.60217733(49) coulomb | 1.6 coulomb | dram |
| 10e/ | 2.97219(19) ampere | 3.0 amps | amber |
| 10 /e | 1.221044(78) metric volt | 1.2 metric volt | volt |
| 10 | 1.221044(78) metric eV | 1.2 metric eV | eevee |
| 10 | 1.41695(10) kelvin | 1.4 kelvin | degree |
For the time being, in some cases, only a rough indication of the size is
provided. The corresponding quantities will be defined more precisely later
on. Values for members of the Planck set, adapted from the 1996
Handbook of Chemistry and Physics, have here been adjusted up or
down by the appropriate powers of ten so as to make them recognizable and
suitable for direct perception at human scale. Values which the
Handbook does not explicitly give have been derived from those
it does. For instance the Planck volume
is not given in the Handbook but is readily derived by cubing
the Planck length . The
published uncertainty for and
is 64 parts per million and I
estimate the uncertainty for at
125 parts per million--standard deviations in the last two digits are given
in parenthesis.
The eevee would not ordinarily be considered as human-scale. One reason it is included in the list is that 2.0 eevee light is directly recognizable as green. The retina is sensitive to a range of photon energies and interprets energy as color--the approximate boundaries of the visible spectrum are 1.5 and 2.5 eevee, with green in the middle. So although 2 eevee is far too small to feel as mechanical work, it is associated with a recognizable sensation.
In choosing names for the humanly scaled Planck quantities, it seemed advisable to borrow those of traditional units if any the right size were available. But in the case of time there were no properly sized traditional units from which to choose. I decided that the name should be short, ideally a single syllable, should be a well established ordinary-sounding word meaning a brief interval of time.
The Planck interval of time being what it is, the appropriate humanly scaled interval is a flat 0.54 second, instead of the more elaborately precise 0.539056 second with uncertainty in the last two digits. The difference here is less than two tenths of one percent, but a flat 0.54 second is substantially easier to deal with and more simply related to the common intervals of practical time-keeping.
As was mentioned earlier, the tick interval corresponds to a tempo which can be heard and recognized. The rhythm of a metronome set at or near 111 per minute (beating at tick intervals) is intermediate between andante and allegro. It is shown as tempo moderato on some metronomes, and is easy to snap fingers in time with. One way to visualize the speed of light is to picture a flash traveling four times around the earth every time you snap your fingers. The height of a drop in paces can be estimated by counting ticks while something falls. As a crude approximation, the number of paces fallen is the square of the count. To within a percent or so, the period of a pendulum extending 16 times the earth's gravitational length is one tick. Ten thousand tick is an hour and a half: in other words
day.
Having introduced the tick as a recognizable humanly scaled decimal
relative of Planck time, I should remark the coincidence that light travels
100,000 miles in one tick. Taking this figure of 100,000 to be exact actually
defines a reasonably sized mile with a precise equivalent in meters.
Accordingly we shall define the mile as the distance light travels in
1/100,000 of a tick (at its usual speed). This has the effect of making a
mile be a certain exact but messy number of meters--to wit, 1618.8792732. Our
mile is similar in size both to the US statute mile--officially 1609.344
meters--and to the scaled-up Planck quantity
10.
There is some latitude as to what can legitimately be called a mile. Our mile is within six tenths of a percent of the ordinary US version, and thus easily qualifies. This unit, defined by the Romans as a thousand paces, has been used for millennia and has varied by a percent or so, from place to place and time to time. The Planckish mile just defined is obviously a recognizable, traditionally named, decimal cousin of the Planck length.
One millionth of a mile is roughly the thickness of a penny. One tenthousandth of a mile, likewise a decimal relative of Planck length, happens to approximate the spread between the tips of thumb and forefinger and also the width of a hand with thumb extended. A cube with that distance as side is gallon-sized, as well as being a power-of-ten scale-up of Planck volume.
Webster's traces the gallon back through the Old French
galon to the Medieval Latin word galeta, which stood for both a
liquid measure and a bucket. A range of volumes have traditionally been
called gallon. For instance the US gallon is 3785
cm and the British gallon is
4546 cm to the nearest cubic
centimeter. The average of these two is roughly
4200 cm, not far from the
humanly scaled Planck volume. We have, in effect, a Planckish gallon falling
virtually at the midpoint of a traditional gallon range--a kind of
unintentional Anglo-American compromise. This gallon clearly constitutes a
recognizable, traditionally named, humanly scaled, decimal relative of the
Planck volume.
In this connection it may be interesting to note that Roman soldiers used two alternative sorts of protective headgear, one of which, a leather helmet, was called a galea. The word Caesar would have used for "helmeted" is galeatus. There is a remote and undocumented possibility that our word for this cousin of Planck volume contains an echo of the earlier Latin, and testifies to the ancient practice of fetching water in one's hat.
The following length is intended to be slightly over 16 centimeters on your screen--and also somewhat in excess of 6 inches--the exact value being determined by the fact that light travels a billion times this interval in one tick. There have been some traditional units approximately this size, which is recognizable, humanly scaled, and decimally related to Planck length.
(thumb to forefinger span--width of both hands--width of one hand with thumb extended)
Perhaps it is worth remarking that this approximate length served as a measure for both the English (the Anglo-Saxon name for it was sceaftmund) and the ancient Greeks (the Greek term was dichas). According to Webster's, one shaftment is "the distance from the tip of the extended thumb across the breadth of the palm, about 6 inches". Among other things, the six inch shaftment length was typical of the tail section of an arrow--the part to be notched, feathered, and marked with identifying bands--which was also called the arrow's "shaftment". The name thus referred both to a unit of measure and to a definite part of a real arrow. Apparently fletchers would decide how long to make the shaftment of an arrow by comparison with the width of a hand, thumb extended.
Webster's gives the length of the ancient Greek dichas as 6.07
inches. The Greek measure was equal to 8 daktyloi or fingerwidths, and
could have been pictured as the width of both hands placed side-by-side with
all eight fingers together. The 
was half of a 
, Greek for foot,
and the name connotes division into two equal parts.
Rather than refer to the Planckish length as "shaftment" or "dichas",
which are awkward and obscure terms, I believe it is justifiable to refer to
it as a span. There was a traditional measure by that name, one which
has fallen into disuse. The traditional span was hand-related: representing
the spread between the tips of thumb and little finger, and was approximately
nine inches rather than six. Depending of course on the size of one's hands
the decimally scaled-up Planck length,
10
, is apt to match the spread
between the tips of thumb and forefinger, a kind of reduced version of the
traditional span. As a hand-referent measure our Planckish span has at least
a general similarity with the traditional measure, justifying our recycling
the name.
Light travels exactly a billion span in a tick. Ten thousand span is of course one mile. A cubic span happens to fall in the range of volumes called gallon--as was mentioned earlier, it is a kind of unintended compromise between the US and the British gallons. A pennywidth is one hundredth of a span.
The power-of-ten relative of Planck force which is most readily recognized by hefting in one hand is 2.7 pounds. A traditional name for that approximate weight is oke or oka. A recent edition of Webster's (1987) defines this as "any of three units of weight varying around 2.8 pounds (1.3 kilograms) and used respectively in Greece, Turkey, and Egypt." From a visit to the Aegean I recall food in island markets being sold by the oka. There appears to have been a similarly sized measure in the East Indies at one time as well. Here are some excerpts from a table of weights found in the second edition of Webster's New International. Webster's Ionian Island entry comes the closest to what we want.
| bedur | Singapore (two catties) | 2.67 lb. |
| chang | Thailand | 2.65 lb. |
| oka | Cyprus | 2.80 lb. |
| oka | Egypt | 2.75 lb. |
| oka | Greece, Yugoslavia | 2.82 lb. |
| oka | Ionian Islands | 2.70 lb. |
| oka | Turkey, Bulgaria etc. | 2.83 lb. |
| oka | Turkey (new or metric) | 2.2046 lb. |
The last entry suggests that Turkey, in an effort to Europeanize, tried
modifying the original measure so as to make it agree in weight with the
kilogram. Webster's traces the Turkish word back through Arabic
to a Greek word onkos meaning weight. Despite its exotic sound, oka
could serve provisionally to name a Planckish measure of force. We might
think of an oka as 12.1 newtons or 2.7 pounds of force, and consider the
Planck force to be
10
oka.
On our mantlepiece there is a collection of fist-sized riverbed stones each weighing about 2.7 pounds. Now and then I heft one of the stones to keep my hand accustomed to this human-scale cousin of Planck force. Each oka stone is a smooth rounded handful. A while ago, I immersed one of these oka stones in a bowl of water and afterwards immersed my hand for comparison, up to the wrist. The stone and my hand (whether clenched or open) displaced the same amount of water, showing that an oka stone is hand-sized. In case you want to familiarize yourself with Planck force in like manner, such stones are not difficult to find. In my case and possibly also in yours, the weight of a relaxed forearm supported level at the wrist is also about right.
The fact that hand-sized riverbed stones have this weight suggests using the word stone to name a correspondingly sized force. I will save the precise definition of this quantity for later. The word has traditionally been used to name units of weight, but at least in the US it has become obsolete and available for recycling. According to Webster's, the stone is "a varying unit of weight..." Besides the English stone of 14 pounds, "other values are or have been in use varying from 4 to 26 pounds." Stone is permissible, I think, as a familiar word which has traditionally been used for measures of weight and which can evoke an appropriate image.
Spanstone, like the traditional name footpound, needs no comment. Applied to energy in any form, it designates an amount equivalent to that delivered by pushing for the extent of a span while exerting a stone of force. To be specific, you could picture it as the effort of lifting a fist-sized stone by the width of a palm with thumb extended. The Planck energy is about one billion spanstone--the approximation is within two tenths of a percent. As a mental picture of the Planck energy, one could imagine a billion people each holding a stone who, at some agreed signal, raise all the stones by one span.
The practice of quantifying electricity is so recent that little in the way of traditional vocabulary has accumulated. Lack of alternatives to the metric measure of electric charge necessitates a minor exercise of philological taste. I judge it permissible to borrow the name of a traditional measure of some other type of charge--in this case an explosive charge of gunpowder. A dram of gunpowder was the typical charge of explosive used to load small firearms such as flintlock pistols.
The word charge derives from the Latin carrus meaning wagon and is connected with the idea of loading a container or carrier. Essentially, to charge means to load. The word dram comes from the Greek word drachma, fortuitously associated with a variety of charges. There is yet another connection in which the word dram is evocative. The once-familiar dram-shop sold spirits by the shot. Electricity has traditionally been seen as a subtle fluid metaphorically akin to fire, which can suggest the image of a volatile essence. Patrons at a dram-shop consumed drams of distillates which in other contexts have been called "fire-water" and "white lightning". A dram-shop customer was subject to becoming loaded, in the modern colloquial sense, and to being charged as well.
Judging from the specs printed on the side, each of the rechargeable
nickel cadmium D cells I see around the house can, in the course of a cycle,
supply close to 10,000 drams of charge at somewhat over one conventional
volt. When it comes to precise definition, we will make a dram correspond to
the charge on
10 electrons.
From a traditional perspective the Planckish volt is too large to be called volt. Historically there has been some variation in volts but never, as far as I know, as much as 20%. But there is no other common name for a measure of this type, and hence no acceptable alternative. Applying any other word seemed a jarring impropriety--more solecism than measure.
Voltage indicates a provision of energy per unit charge, so it would be possible to express the unit of energy as a dramvolt. The other way we have of referring to the unit of energy is spanstone--the work performed by pushing with a stone of force for the distance of one span--and the two are equivalent. The household D cells mentioned earlier are rated by the manufacturer at 1.25 conventional volts, which is close to one of our volts. Each is, in effect, a one volt cell able to deliver ten thousand drams on a single charging. Accordingly, each fully charged cell represents a store of energy which is on the order of ten thousand dramvolts.
The name is a mnemonic play on words. Amber sounds like ampere and the
Greek word elektron, which meant shining, was applied to the substance
amber. One amber of electric current consists of
10 electrons passing by in a tick--in other words one dram per
tick. By way of illustration, when the rechargeable D cell mentioned earlier
is supplying one amber of current at one volt it is delivering energy at the
rate of a voltamber (3.6 conventional watts). It can supply one amber of
current for approximately ten thousand tick, in other words for ninety minutes.
An eevee (short for electron volt) is the quantity of energy which a one
volt cell supplies to an electron circulating from it. On average, as long as
the cell sustains a one volt level, each electron is provided with that
amount of energy. During some interval of time, if the cell circulates
10
electrons then it delivers
10
eevee of energy. Light consisting of 2 eevee photons is perceived as green.
Although a small quantity, the eevee can be regarded as a practical unit for
a variety of reasons besides its connection with eyesight. A mnemonic rhyme
may be appropriate here.
With propane, diesel fuel, or wheat,
An oh-two count will tell the heat.
For every oxygen you see
The yield is three-point-four eevee.
In burning ordinary hydrocarbon fuels or metabolizing carbohydrates, there is not much variation in the energy released if it is calculated per molecule of oxygen consumed. Whether the fuel is wood, oil, ethanol, or spaghetti, the energy yield is typically 3.4 eevee per O2 molecule involved--or half that per oxygen atom.
In an earlier section on heat capacity we were somewhat hampered by not
having already introduced this unit. There is an exact identity, in humanly
scaled terms, according to which the Boltzmann constant k =
/
= 0.0001 eevee per degree.
The name eevee is commonplace and requires no discussion. Because the unit is practical, it seems advantageous to have it in clear decimal relation to the others.
In accordance with a ruling handed down in 1967 by the thirteenth General
Conference on Weights and Measures it is incorrect to say 283 degrees
kelvin or to write 283 K.
Instead, we are officially encouraged to say 283 Kelvin, and to write 283 K.
Evidently, the official body in charge of the metric system discourages using
the word "degree" with temperature: it consigns the word to retirement and
makes it available for recycling. The Planckish degree is about 1.4 Kelvin,
closely corresponding to the fraction
10
of Planck temperature
--obviously a familiar-sized
traditionally named decimal relative. Here are some sample temperatures on
this scale:
The microwave background is 1.93 degrees.
Ice melts at 193 degrees.
The average temperature on the earth's surface is 200 degrees.
A chilly outdoor temperature is 200 degrees (Fahrenheit 50).
Room temperature is commonly 207 or 208 degrees.
The conventional norm for body temperature is 218.8 degrees.
A good oven setting to bake bread is 320 degrees.
The tungsten filament of a hundredwatt bulb operates at 2000 degrees.
The sun's surface is slightly over 4000 degrees, shown by its color.
The Boltzmann k will be given an exact value of
10
spanstone per degree. The temperature scale is fundamentally an alternative
scale of energy. In the present case, the characteristic energy
k associated with the Planck
temperature is the Planck
energy . Incidentally the metric
temperature 283 Kelvin was mentioned earlier because it corresponds to the
chilly 200 degrees serving informally as a point of reference.