Future Measurement
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Introduction
First off, you might want to study the various metric prefixes.
SF novels like to alter things that are taken for granted, to remind the reader that they are reading science fiction (though it is a sign of a pathetic SF story if you can change the entire background to a conventional setting without affecting the story). A different system of measurements is a quick and easy addition. Remember how the original Battlestar Galactica had the crew taking about times and distances in terms of microns, centons, and yarens.
Here are some exotic measuring systems to add that air of verisimilitude.
Measuring Time
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Time chart from Joan Vinges' The Outcasts of Heaven's Belt (1978)
A fairly standard trick is altering the "year one" of the calendar. Popular choices are 1945 (the first detonation of a nuclear weapon), 1957 (the year Sputnik went up, the first man-made object boosted into orbit), 1961 (the year Yuri Gagarin became the first man in space), and 1969 (the year Neil Armstrong became the first man to set foot on an extraterrestrial object). Extrasolar colonies tend to set year one to the year the colony was established, the year of "first landing."
So if the novel adopts the Armstrong standard, a story set in the Gregorian year 2010 would be year 41 of the Space Age.
Authors who want to strike a more secular tone will use "CE" and "BCE" instead of "AD" and "BC", especially in the academic world. Or avoid the matter entirely, say by using a 1945-based year-one with a flashy title like "Atomic Era."
An actual real live problem is the fact that measuring units such as years, days, and seasons are very closely tied to Terra. They have reduced relevance for those living on other planets, and practically no relevance to Belters and others living in deep space. In Heinlein's Podkayne of Mars the main character emphasizes the fact the novel is science fiction by mentioning that she is about eight years old and almost old enough to marry. However, she lives on Mars, which has a longer year than Terra. So while she is 8 Martian years old, she is about 15 Terran years old.
Metric Time
One solution appears in Joan Vinge's The Outcasts of Heaven's Belt. In the Heaven's Belt system, there are no habitable planets, but zillions of mineral rich asteroids. That's where the people live. The only time unit is the Second (this is sometimes called Metric Time). Three kiloseconds is about an hour, thirty megaseconds is about a year, you can read it on the chart above. It works regardless of the orbital period of the particular space habitat, you can calculate the duration between any two points in time with simple subtraction, it's great!
This system is also used in Charles Stross' novel Accelerando. The following tables are from here.
| Second-style | Conventional |
|---|---|
| 1 kilosecond | 16.7 minutes |
| 1 megasecond | 11.6 days |
| 1 gigasecond | 32 years |
| 1 terasecond | 32,000 years |
| 1 petasecond | 32,000,000 years |
| Conventional | Second-style |
|---|---|
| 1 hour | 3.6 kiloseconds |
| 1 Earth day | 86.4 kiloseconds |
| 1 week | 604.8 kiloseconds |
| 1 Earth month | 2.6 megaseconds |
| 1 Earth year | 31.6 megaseconds |
| 1 century | 3.16 gigaseconds |
Vernor Vinge used the system in A Deepness In The Sky, also known as After Epoch Astronauticum. The zero point is set to Neil Armstrong's lunar walk, though when one does that the entire system starts looking suspiciously like Unix time, or POSIX time (Armstrong was in 1969, Unix time starts in 1970).
Astronomers use a similar system that is based on days instead of seconds, the Julian Day calendar. There are no years, months or weeks, just days. Day zero is noon on January 1, 4713 BC. The date was chosen because it was the last time that three particular calendrical cycles converged.
Metric Time and Longitude
Ralph Buttigieg points out the fact that metric time does not work on the surface of a planet, due to our quaint way of measuring Longitude and celestial Right Ascension. Back in the age of sail, measuring lattitude was exceedingly easy to do with a sextant.
Longitude was hard, because measuring it requires an accurate clock, since the determination depends upon measuring how far the Earth had rotated upon its axis. Unfortunately in those days, the only accurate clocks were based upon pendulums, which won't work in a ship pitching with the ocean waves. After the British fleet was wreaked in 1707 due to an error in longitude, the British government offered the longitude prize to the first person to devise an accurate shipboard method of determining longitude. John Harrison won the prize by inventing a spring based chronometer, though the British board of longitude tried to cheat him out of the prize money.
Anyway, the point of all this is that longitude is measured in increments of the planetary day, which of course is of different lengths from planet to planet. Which puts a monkey wrench into plans of using some sort of universal metric time.
Decimal Time
There are other Decimal Time systems based on decimal Day units. 1 dekaday is about a week and a half, 1 centiday is about 14 minutes, and so on.
The Swiss watchmaking company Swatch invented Swatch Internet Time, where the 24 hour day is divided up into 1000 parts called ".beats", each .beat being 1 minute and 26.4 seconds. This is actually an advertising gimmick. It is a rehash of the French decimal time system invented right after the French Revolution in the far futuristic year 1793. You can tell that it is intended for advertising purposes since out of all the systems invented in the last two hundred years, it is the only one that moves the prime meridian from Greenwich England to Swatch Headquarters. Swatch Internet Time faded away due to lack of interest, unsurprisingly.
Of course, since all of these systems are based on the Terra-centered "Day" unit instead of the metric system "Second" unit, they are also much more parochial.
A "Decimal Time" system is one where the various units are decimal fraction or multiples of each other (e.g., A decimal hour divided into 100 decimal minutes, each minute composed of 100 decimal seconds). A "Metric Time" system is a decimal time system with only one unit, and the everything is expressed by adding a metric prefix to that unit (e.g., second, kilosecond, megasecond). In addition, a metric unit only defines units of time interval (as does a stopwatch), not time of day (as does a clock).
As an example, in Isaac Asimov's The Naked Sun, the Solarians use a decimal system. The Solarian hour as been divided into ten decads, each of which is divided into a hundred centads. This is not a metric system since the hour has not been divided into ten decihours, each of which is divided into a hundred millihours.
Star Trek
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Image from TrekCore.com
There was a flawed attempt to create a decimal time system in the TV show Star Trek, the infamous "Stardates." They were created on the spur of the moment by Gene Roddenberry to avoid the problem of tying each episode to specific dates. The writers were told to just pick four digits at random. Pedantic Star Trek fans have been trying ever since to retcon a system that would explain the dates.
Franz Joseph created his own system for Stardates: they are conventional Gregorian dates written in the form YYMM.DD (e.g., February 13, 1998 would be Stardate 9802.13). This is not considered canon. However, computer programmers have long noted the advantages of writing dates in odometer order. It simplifies sorting items by time. For example, if you have a series of files on your hard drive with names that start with a time stamp in YYMMDD form, when you examine that directory with the file names sorted alphabetically, the files will automatically be in chronological order.
The flaw with Franz Joseph's system is that is it not clear if Stardate 9802.13 refers to February 13, 1998, February 13, 2098, February 13, 2198, February 13, 2298 and so on.
Battletech
Mark Temple mentions the system used in Classic Battletech novels
In the Classic Battletech novels, particularly in the novel Tactics of Duty, a general solution to adapting to other planets was illustrated.
The length of a second remained the same, as did the number of seconds in a minute. but each planets day was divided up into twenty-four equal periods (sometimes with a twenty-fifth unequal period to make up the slack), which were the hour. So a fast rotating planet's hour would be less than Earth's, and a slow rotating planet's hour would be longer.
The number of days in a week was usually kept at seven, and the number of months left at twelve (sometimes with a few extra days tacked on at the end of the year to keep the months even). This meant a planet with a longer year would have more weeks in its months, a planet with a shorter year would have fewer (Which was the core of a supply problem used to illustrate the system. The military unit of the book used the Terran calendar, but the locals used one where the months were about two-thirds of Earth's. A supply clerk who was a local filled out forms using local months, meaning the supplies came faster, which drove up the expenses...)
Really odd worlds broke this system though, and Battletech has its share. For example, in the novel Decision at Thunder Rift, the planet of Trellwan had a year about three local days long, due to the planet orbiting a dwarf star and being almost tidally locked. That planet used Terran hours and twenty-four hour days, but divided up its year into 'light' and 'dark' months, each half a local day long.
Measuring Distance
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Station in Space by James Gunn (1958)
Strange sounding alternative metric units of length can be invented as well. In Isaac Asimov's Foundation and Empire, Toran jumps his starship through hyperspace into the star system containing the planet Haven, then has to travel "several milli-microparsecs" to the planet. Now, "milli-micro-" is not standard SI usage, but I guess the Good Doctor is trying to say "nano-" or 10-9. That would make one milli-microparsec about 31,000 kilometers, or about 1/13th the distance between Terra and Luna.
Erik Max Francis points out that the marvelously correct SI unit "megameters" makes an apperance in, of all places, the Americanized anime "Star Blazers". That anime was originally "Space Battleship Yamato", it is unclear if the term "megameters" appears in the original Japanese. One megameter is one thousand kilometers or about 620 miles.
Another metric system of measure appears in the SF show Battlestar Galactica.
| Factor | Distance | Description | |
|---|---|---|---|
| Parsecs | Other | ||
| 100 | 1 parsec (pc) | 3.26 Light Years | 74% of the distance between Sol and Proxima Centauri |
| 10-1 | 1 deciparsec (dpc) | 20,627 AU | Sol to outer boundary of Hills section of the Oort Cloud |
| 10-2 | 1 centiparsec (cpc) | 2063 AU | Sol to inner boundary of Hills section of the Oort Cloud |
| 10-3 | 1 milliparsec (mpc) | 206 AU | Approximately four times the Sol-Pluto aphelion |
| 10-6 | 1 microparsec (μpc) | 0.21 AU | A bit less than the Sol-Mercury semi-major axis |
| 10-9 | 1 nanoparsec (npc) | 30,857 Kilometers | 2.5 times the diameter of Terra |
| 10-12 | 1 picoparsec (ppc) | 31 Kilometers | Diameter of Baltimore, Maryland USA |
| 10-15 | 1 femtoparsec (fpc) | 31 Meters | Length of a Blue Whale |
| 10-18 | 1 attoparsec (apc) | 3 Centimeters | 2/3 the length of your finger |
| 10-21 | 1 zeptoparsec (zpc) | 0.031 Millimeters | 0.06 the diameter of a grain of salt |
| 10-24 | 1 yoctoparsec (ypc) | 0.000031 Millimeters | Approximately the length of 160 bacteria laid end to end. |
Measuring Everything Else
Plank Units
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Artwork by Alex Schomburg
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Gee, I wonder what system these units are from? Shuttlecraft control panel from the Star Trek episode "The Galileo Seven" (1967)
Erik Max Francis has created a powerfully compelling measurement system based on fundamental Planck units. Well, in reality he said it was not particularly revolutionary, he just did the multiplication, and actually using it would be extraordinarily silly. But for science-fictional purposes, it is far more scientifically accurate than using centons and yarens.
The system was modified by Sean Williams and Shane Dix for use in their "Orphans" novels.
In physics, there are five universal physical constants: speed of light in vacuum, Gravitational constant, Dirac's constant or "reduced Planck's constant", Coulomb force constant, and Boltzmann constant. Planck units are units that are defined in such a way that if you express any of the five universal constants in terms of Planck units, their value is "one."
Planck units are pretty much standard when doing relativity theory, and have been since at least about the 1970's (at least, Misner, Thorne, and Weaver discuss Planck units in their classic textbook "Gravitation").
A related idea is atomic units, where the electric charge, the quantum of action (Planck's constant h-bar) and the electron mass are set equal to unity, creating a system where the fundamental length scale is the Bohr radius of hydrogen and the fundamental energy scale is twice the binding energy of the hydrogen atom in its ground state (I work with these units a lot for my real job). In this system, the speed of light is equal to one over the fine structure constant (c ~ 137, alpha ~ 1/137). It is a very convenient system of units for performing calculations in solid state, condensed matter, and atomic physics.
There are five Planck units: Planck length, Planck mass, Planck time, Planck charge and Planck temperature. For his system Mr. Francis only needs the first three.
As an aside, Mr. Francis says:
Another issue that is quietly not mentioned anywhere that I'm aware of is that the Planck constant is not really known to sufficient precision to base a system of units on it.
A measurement system needs a set of fundamental units, from which all the other units can be derived. For his system Mr. Francis used the SI fundamental units: length, mass, time, electric current, thermodynamic temperature, luminous intensity, and amount of substance.
For length, mass, and time units just use the Planck units directly.
For electric current (charge divided by time), use the (unit independent) magnitude of the charge on an electron for charge, and Planck time for time.
For thermodynamic temperature, it can be derived with the Boltzmann constant. The Boltzmann constant is equal to energy divided by temperature, so simple algebra will give you the equation: temperature equals energy divided by Boltzmann constant. For the energy unit see below.
Luminous intensity is tricky, see Mr. Francis' essay for his solution.
And for amount of substance, this isn't a strictly derivable unit. Mr. Francis proposes to replace the unit with the actual number of atoms (e.g., instead of one mole, just use Avogadro's number 6.02 x 1023.)
Again, for details about the units derived from the fundamental units, refer to the essay. Any unit not defined is left as an exercise for the reader.
Erik Max Francis' Planck Unit System
| Quantity | Symbol | Value |
|---|---|---|
| Planck mass | mP | 2.177 x 10-8 kg |
| Planck length | lP | 1.616 x 10-35 m |
| Planck time | tP | 5.391 x 10-44 s |
| length | L | 1.616 x 10-35 m |
| mass | M | 2.177 x 10-8 kg |
| time | T | 5.391 x 10-44 s |
| current | C == e/T | 2.972 x 1024 A |
| temperature | E == M L2 T -2/k | 1.415 x 1032 K |
| plane angle | rad | 1 rad |
| solid angle | sr | 1 sr |
| Quantity | Symbol | Value |
|---|---|---|
| force | M L T -2 | 1.210 x 1044 N |
| energy | M L2 T -2 | 1.956 x 109 J |
| power | M L2 T -3 | 3.629 x 1052 W |
| frequency | T -1 | 1.855 x 1043 Hz |
| pressure | M L-1 T -2 | 4.635 x 10113 Pa (yikes!) |
| Quantity | Symbol | Value |
|---|---|---|
| activity | T -1 | 1.855 x 1043 Bq |
| absorbed dose | M L2 T -2 E-1 | 1.382 x 10-23 Gy |
| dose equivalent | M L2 T -2 E-1 | 1.382 x 10-23 Sv |
| Quantity | Symbol | Value |
|---|---|---|
| capacitance | M-1 L-2 T4 C2 | 1.312 x 10-47 F |
| charge | T C | 1.602 x 10-19 C |
| electric conductance | M-1 L-2 T3 C2 | 2.434 x 10-4 S |
| inductance | M L2 T -2 C-2 | 2.215 x 10-40 H |
| magnetic flux | M L2 T -2 C-1 | 6.582 x 10-16 Wb |
| magnetic flux density | M T -2 C-1 | 2.520 x 1054 T |
| resistance | M L2 T -3 C-2 | 4.108 x 103 Ω |
| voltage | M L2 T -3 C-1 | 1.221 x 1028 V |
Adjusted Planck Units
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Artwork by Chris Moore
| Quantity | Value |
|---|---|
| Mass | 2.177 kg |
| Length | 1.616 m |
| Time | 0.5391 s |
As previously mentioned, this system was adapted by Sean Williams and Shane Dix for their "Orphans" novels. The authors state that they have adapted Mr. Francis' ideas to suit their needs, and any errors introduced in the process are theirs.
Sean Williams and Shane Dix postulate the new system was adopted in the wake of even more disasters like the Mars Climate Orbiter fiasco. That was caused due to the fact that Lockheed Martin used English units while NASA (like the rest of the civilized world) uses Metric units. Everybody just assumed they were all using the same units, and didn't discover differently until the probe ricocheted off the Martian atmosphere. This sent the probe off into oblivion and $125 million dollars down the drain.
In the novels, Mr. Francis's system is modified somewhat. The Planck units are fundamental, but have exceedingly inconvenient sizes. One inch is about 157 billion quadrillion quadrillion Planck meters, an average person masses almost three trillion Planck kilograms, one hour is equal to about a trillion quadrillion quadrillion quadrillion Planck minutes.
So they scaled the Planck units, multiplying them by 1043. This makes the units more human sized.
Time
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Diagram from Echoes of Earth
The time units were fiddled with so they
- were vaguely the same as the old units
- used Adjusted Planck time units and
- were more or less decimal
Hours and minutes were divided into 100 sub-units. The day was split into two ten-hour halves: practical but not too unlike the old. And ten months of six five-day weeks gives one great flexibility when scheduling rosters and planning. From Echoes of Earth:
| Unit | Size | Conventional Equivalence |
|---|---|---|
| 1 new second | 0.54 old second | |
| 1 new minute | 100 new seconds | 0.90 old minute 54 old seconds) |
| 1 new hour | 100 new minutes | 1.5 old hours (90 old minutes) |
| 1 new day | 20 new hours | 1.2 old days (30 old hours) |
| 1 new week | 5 new days | 0.89 old week (6.2 old days) |
| 1 new month | 6 new weeks | 1.2 old months (5.3 old weeks) |
| 1 new year | 10 new months | 1.025 old years (12 old months) |
Distance
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Diagram from Echoes of Earth
The distance units were chosen to be sort of a compromise between the old Metric and the old English units, since in the novel the US was still stubbornly and idiotically sticking to English. The new centimeter was between the old centimeter and the inch. The old mile and the old gallon was very close to the new kilometer and new liter.
| Unit | Size | Conventional Equivalence |
|---|---|---|
| 1 new centimeter | 1.6 old cm, or 0.64 inches | |
| 1 new decimeter | 10 new cm | 6.5 inches |
| 1 new meter | 10 new dm | 1.6 old m, or 3.3 feet |
| 3 new meters | 10 feet | |
| 1 new kilometer | 1000 new meters | 0.97 mile |
| 1 new hectare | 2.6 old hectares | 6.4 acres |
| 1 new liter (dm3) | 4.2 old liters | 1.1 gallons |
Mass
The jingle in the US was "five old pounds equal one new kilogram".
| Unit | Size | Conventional Equivalence |
|---|---|---|
| 1 new g | 2.2 old g | |
| 1 new kg | 1000 new g | 4.8 old pounds |
| 1 new tonne | 1000 new kg | 2.1 old tons |
| 1 new ampere | 2.972 old ampere |
Temperature
| Unit | Centigrade | Fahrenheit | Kelvin |
|---|---|---|---|
| 1° | 1.415° (misprint?) | 2.563° | 1.415° |
| 0° | -273.15° | -459.67° | 0° (absolute zero) |
| 193° | 0° | 32° | 273.15° (freezing point H2O) |
| 264° | 100° | 212° | 373.15° (boiling point H2O) |
Constants
Many commonly used constants have simple values when expressed in Adjusted Planck Units.
| Quantity | Value |
|---|---|
| c (the speed of light) | 1.00 x 108 ms-1 |
| 1 light-year | 6.00 x 1015 m |
| 1 light-hour | 1.00 x 1011 m |
| 1 parsec | 2.0 x 1016 m |
| 1 g | 1.0 light-year/year2 |
| 1 solar radius | 430000 km |
| 1 Earth radius | 4000 km (equatorial) |
| geostationary orbit | 22220 km (Earth) |
Conversion Factors
The following conversion factors will convert from the old International System of Units to the new Adjusted Planck Standard International Units.
| Value | Unit | Factor |
|---|---|---|
| Velocity | m/s1 | 0.334 |
| Acceleration | m/s2 | 1.76 |
| Density | g/cm3 | 1.92 |
| Pressure | Pa | 0.216 |
| Force | N | 0.0818 |
| Energy | J | 0.0506 |
| Frequency | Hz | 1.86 |
| Resistance | Ω | 0.241 |
| Voltage | V | 0.0811 |
Alternate Metrification
Mr. Francis doesn't approve of such alternate metrification in principle. He is, however, quick to say that he is not talking about Sean Williams and Shane Dix. What he is annoyed at is some people who want to actually propose alternate second-minute-hour-type systems to replace the existing SI unit system in the real world (which of course, is not at all what Mr. Williams and Mr. Dix were doing).
It's a weird mishmash of the raw Planck units -- which are essentially so awkward as to be totally unusable -- and a reformulation of different (non-metric) multiples of "new" units like "new hours" in order to refit them into roles that are vaguely like what the old ones were, but with the values slightly different so that they're metric... but not really.
For instance, there are 100 new seconds in a new minute, 100 new minutes in a new hour, 20 new hours in a new day, 5 new days in a new week, 6 new weeks in a new month, and 10 new months in a new year. The whole point of a metric system is that the ratios are powers of ten, and especially when you're dealing with modern metric systems like SI, a primary goal is that the unit system is coherent, meaning that the conversion factors between different units are unity.
More generally, I very strongly believe that any alternative unit system should not reference old names for non-metric divisions like "hour." This will only lead to confusion, and without much use. If you're talking about time systems in other local environments where the days and years are of different lengths, then this adds a new layer of confusion because now you have to figure out whether they mean Earth hours or Epsilon Eridani IV hours.
Note that this isn't quite even academic. It has been proposed from time to time in the United States to assist with metrication that maybe we should reformulate the old units in relatively even ratios of metric units, to get people used to the switch. So for instance, 1 kg = 2.2 lb, so make 1 "new pound" = 0.5 kg. That way people can get used to the idea of using metric without the pain, right? That has to be just about the dumbest idea for metrication I've ever heard of: confusingly changing units for the supposed purpose of helping them learn a new unit system, but then making them learn the new unit system later. I guess it's a two-for-the-price-of-one type of deal. Instead, just learn the new unit system and be done with it. (Note that, as an American, I was part of the generation that was vigorously exposed to the metric system when I was young and totally bought into it. Then the rest of the country kind of got bored and forgot about it.)
Truth be told, I think the executive summary is that having a coherent, metric system of units with reasonable base units for a wide range of endeavors is the goal. And we already have that in SI. Any modifications to that system seem to be only to be done for flair and not for any good purpose. Not that (15 pieces of) flair is a bad thing, but often, it seems, when people come up with neat alternative unit systems for the sole purpose of coming up with neat alternative unit systems, they kind of miss the point and makes ones that are qualitatively worse than SI.