The Planck units are a natural system of units implicit in light and gravity, indeed in all of nature. It is convenient to scale the Planck units by powers of ten to make them less extreme, and therefore easier to visualize and assimilate. In constructing a basic set of practical units, one attractive option is to restrict the scaling to only those powers of ten which are powers of a thousand. Along the way we can truncate experimental uncertainty so as to get versions which have precise metric equivalents and equal to the natural quantities to within the accuracy of current measurement.
In the version of Practical Planck units described here the values of some basic natural constants are made powers of a thousand. The values of G, c, e, the Boltzmann k, and hbar are made 1.000E-9, E9, E-15, E-18 and E-30. Except for the first, these are exact values defining the units. The value of G is a better-than-three-place approximation of one billionth and is written 1.000E-9 instead of simply E-9 to indicate that it is not exact. The close fit to the natural constants is achieved by setting the base unit of time equal to 1/18.55 second.
Specifying these values for the fundamental physical constants essentially determines the sizes of the practical Planck units: the unit of length must be roughly a fingerwidth is size, that of force must be some 0.121 metric newtons, that of mass must be about 22 grams, and the charge unit one sixththousandth of a metric coulomb.
This much is simple. Oddly, what seems to give the most trouble is finding names for the units! Provisionally, I've chosen to call the time unit (1/18.55 second) a milliminute. This is at least moderately descriptive, since the interval is roughly a thousandth of a conventional minute. On the other hand, at four syllables the word is a mouthful, so when I get impatient I call the time unit a "trice" for short. If you do not like trice, and find it awkward to say milliminute, make up your own term. The fingerwidth unit of length is about one hundredth of a conventional pace (the sort that is one thousandth of a mile) and is provisionally called a centipace. Naming alternative units is, I said, troublesome, and this is the best I can do at present. The 22 gram mass unit just happens to correspond roughly to an ounce, and can be called by that name.
The metric system no longer uses the "dyne" force unit and the "erg" energy unit. Their use is discouraged by the governing Conference (CGPM) and different-sized force and energy units (newton and joule) have supplanted them. The same is true of "centigrade"—nowadays one is expected to say celsius.
As it happens we need a name for the roughly 1/8 of a newton force unit and the energy unit that goes with it. Nothing prevents recycling unit names discarded by the Conference, if it proves desirable.
Sizes and technical definitions of the units
A system of units for which it has been stipulated that the values of c, e, the Boltzmann k, and hbar are made exactly equal to E9, E-15, E-18 and E-30 is determined by a single additional parameter. If we choose the unit of time to be the milliminute then the sizes of all the other units are fixed. Practically speaking there is only a very limited range of choice for the time unit if we wish to make G take on a value very close to a billionth. It must be at or near 1/1113 of a minute, or as indicated earlier, 1/18.55 of a second.
The milliminute or "trice" time unit is intended only for technical contexts such as physics coursework. Outside such specialized applications, it's expected that time will be told in the usual way—in ordinary hours, minutes and seconds. The trice is essentially a power of thousand (1042) scaled-up version of the natural unit of time.
Angular format for frequency is assumed throughout.
milliminute (trice)= 1/1113 minute = 1/18.55 second
centipace = 1.616 centimeters
cubic centipace = 4.220 cubic centimeters
ounce = 21.766 gram
dyne = 0.12104 newton
erg = 1.956 millijoule
grade = 141.7 kelvin
quad = 0.1602 millicoulomb
[voltage unit] = 12.21 conventional volt
[current unit] = 2.972 conventional milliampere
The unit corresponding to an eevee in this system is equivalent to E-15
erg.
Here are some physical constants expressed in trice, centipace, ounces and
related units.
G—universal gravitational constant—1.000E-9
centipace3/trice2 per ounce
c—speed of light in vacuum—E9 centipace per trice
hbar/k—ratio of temperature to characteristic frequency of
radiation at that temperature—E-12 grade trice
hbar/e—ratio of photoelectric voltage to frequency of incident
light—E-15 [voltage unit] trice
e—elementary charge—E-15 quad.
k—Boltzmann constant—E-18 erg per grade
N—Avogadro number—E24 items per mole
hbar—E-30 erg trice
Angular format for frequency is assumed throughout.
At its average surface temperature, the reciprocal density of seawater is 5 cubic centipace per ounce. Normal pressure at sealevel is 219 dyne per square centipace. Normal human body temperature (otic thermometer) is 2.19 grade. Normal equatorial gravity is 1.76 centipace per sq.trice.
Relation to Planck and traditional units
Each new unit is equal to the corresponding Planck unit times some appropriate power of a thousand, either exactly or to the accuracy with which that Planck unit can be experimentally determined.
The number 1113 is analogous to a curve-fitting parameter. In effect we have a one-parameter family of systems and this is the value of the parameter that gives a good fit with the Planck units.
Readers familiar with the Planck units will recognize many quantities in the above list. The centipace, or 1.616 cm, is a power of ten multiple of Planck length. The ounce, or 21.766 gram, is a million times the Planck mass, and so on.
A conventional mile (1609 meters) is less than half a percent different from 1616 meters, which is a power of ten multiple of the new unit length. So the mile is at home in the new units (for practical purposes it is simply a decimal multiple of the centipace base unit.) A compromise gallon halfway between the US and Imperial gallons is also at home in the system since it is a thousand times the cubic centipace base unit. Similar observations can be made about several other traditional units. In this sense the new system aligns automatically with a representative collection of traditional units such as the mile, the gallon, the ounce, and the ton-force. It does so because these traditional or unofficial metric units are themselves approximately power-of-ten multiples of the corresponding Planck units.
There is a set of power-of-ten multiples of the natural units which happen to be similar in size to traditional units. These are the Planck mile, Planck gallon, Planck ounce (mass), Planck ton (force), and Planck minute. On the one hand, except for powers of ten, they arise naturally from light and gravity. On the other, they are close enough to traditional counterparts to have the same subjective feel. When talking about distance in miles it hardly matters whether one is thinking of US statute miles or Planck miles since the two measures differ by less than half a percent.
[Compare metric (pi2/60) k4 h-bar-3 c-2=5.6704 × 10-8 watts per meter2 per kelvin4, and metric alpha h-bar c/e2=whatever Coulomb's constant is in metric: 1/(4pi × 8.854187817...× 10-12) newton meter2 per coulomb2.]
Avogadro's number is 1024, in these contexts. Compare metric 6.022142 × 1023. The mass of 1024 carbon-12 atoms is approximately 12/13 ounce. The mass of 1024 ordinary atomic mass units, for practical purposes, is thus 1/13 ounce.
Boltzmann's k is 10-18 erg per grade and therefore the constant R in the gas law (which characterizes ideal gas behavior and equals Avogadro's number times k) is 106 erg per grade-mole. Normal temperature and pressure conditions for the context can be described by saying that the ratio of pressure to temperature, both being expressed in (grade/shot) is one hundred. If that is the case (namely that pressure in shot is a hundred times temperature expressed in grade), then the molar volume is ten gallons— 1024 molecules of an ideal gas occupy 10,000 cubic centipace.
Body temperature in grade (2.19) is numerically an hundredth of the sealevel pressure norm—219 dyne/sq.cp, so at those conditions a gallon lungful of air contains a tenth of a mole (1023) air molecules. It has been suggested to call the pressure unit dyne/sq.cp. a "shot" of pressure.
pv=219xE4=E6x2.19=RT
Referring to the NIST website
http://physics.nist.gov/cgi-bin/cuu/Value?plkt|search_for=universal_in!
1042 Planck time units is:
0 .053906 seconds
The standard uncertainty in this figure is 0.00004 second, and the standard relative uncertainty is given by NIST as 7.5 parts per tenthousand.
Therefore using the NIST data there are 1113.05 of these units in an ordinary minute, but the 0.05 is in the noise. We can define a milliminute so as to have exactly 1113 in an ordinary minute and this then agrees with the natural interval to within the accuracy with which the latter is measured.
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1. Technical definition of the basic practical Planck units:
Technically, the construction of practical Planck units imitates the 1990 metric electrical standards established by the CIPM (International Committee on Weights and Measures.) It proceeds by adopting exact values for the speed of light, the Josephson and von Klitzing constants, and the Boltzmann temperature coefficient. The fundamental constants on which the system is based are operational characteristics of the measurement devices which currently provide the most precise and reliable standards of measurement.
2. Sizes of the units:
trice — exactly 1113 to an ordinary minute
centipace — 1.616 centimeters
dyne (force) —0.12104 newtons
[erg per trice, fott?] — 36.29 milliwatts
ounce — 21.766 grams
grade —141.7 kelvin
milligrade—0.1417 kelvin (about one seventh of the metric temperature
step)
mole—E24 items
quad (charge) — 0.1602 millicoulombs
[erg per quad, wolt?] — 12.21 conventional volts, ten Planck volts
[quad per trice, vamp?] — 2.972 milliamperes
The erg of energy, about 2 metric millijoules, is the work done by pushing with dyne force for a distance of one centipace. The quad of charge is equal to the charge on a quadrillion electrons, by definition, which makes it about one sixththousandth the size of the metric unit of charge. The unit current delivers one quad per trice. The unit voltage supplies one erg per quad. Unit power could be called chi, borrowing a classical Chinese word on the fourth tone, meaning vital principle. The chi unit power delivers unit energy in unit time: one erg per trice.
4. exact conversion factors, vis a vis the 1990 CIPM metric standards
5. values of fundamental constants in practical Planck units, a comparison with metric values, and some reasons to use the units.
To keep the summary brief, values for only a few fundamental constants are listed here and links are provided to further discussion. As can be seen here what tends to happen is that the exponents are all multiples of three when fundamental constants are written out in these units.
c = 109 centipace per trice (exact)
h-bar = 10-30 erg trice (exact)
G = 1.000×10-9 dyne centipace2 per
ounce2
Coulomb's const. = alpha × 109 dyne
centipace2 per quad2
Boltzmann's k = 10-18 erg per grade (exact)
elementary charge e = 10-15 quint (exact)
Note on Coulomb's constant:
Coulomb's constant kC is determined by the definition of the fine-structure constant:
alpha = kCe2/h-bar c.
kC = alpha h-bar c/e2
= alpha×10-301091030dyne centipace 2/quad2.
= alpha×109dyne centipace2/quad2.
more possible footnote material:
The prevailing picture of the origin of the universe suggests that at large scales space is not curved and observations of the microwave background confirm this. In a flat universe without dark energy the age must be 2/3 times 1/H. If the Hubble time 1/H is 14 billion years or 8E15 minutes then the age of the universe must be 2/3 of that. And in fact the Hubble constant has recently been measured with unprecedented precision and one knows that the Hubble time is 14 billion years.
Notice that 2/3 of 14 billion is already too short---there are star clusters older than that. However it was recently discovered that about 0.7 of mass of universe is dark energy. For a flat universe there is a formula for adjusting the age. You take sqrt of 0.7, which is around 0.84 and plug that in and it gives the factor for adjusting the age. I will show you the formula in a moment but first: the factor comes out 1.45. So the age is not 2/3 of Hubble time, instead it is 1.45 x 2/3 of Hubble time. That is 0.97. Therefore the age is almost the same as the Hubble time. If one is about 14 billion years then the other is about 14 billion years. And that IS compatible with star ages and all the other handles we have on the age of the universe. The reason for the adjustment is that dark energy in the past will have tended to accelerate expansion or prevent deceleration to some extent. Since there was less deceleration, past expansion must not have been as rapid as one would otherwise suppose. So the universe has TAKEN LONGER to expand to present size and so is OLDER (in this case by 45 percent.) Here then is the formula giving that 1.45 factor [ln(1+0.84)- ln(1-0.84)]/(0.84 x 2) Because of uncertainty in the figure of 14 billion years---some people say 13-14 billion---it is not possible to be highly precise and so one just says that both the Hubble time and the age of the universe are about 14 billion years, since they are within a few percent of each other. It is amazing that the density of dark energy should turn out to very close to ONE TENTHOUSANDTH of the energy density of sunlight at earth. The sunlight in a cubic pace, at this distance, is one hundredth of an erg. The dark energy, which is now accelerating the expansion of space and which appears to be uniformly distributed throughout space--- a millionth of an erg per cubic pace.
Planck resistance is simply ONE in the centipace-ounce set.
And S-B sigma is simply what it has to be and no more: pi-squared/60.