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| Highway Signs |
 Title text: Highway engineers like Planck units because, like the speed of light, the energy capacity of a typical car's gas tank is 1. |
Explanation
The signs on this highway apparently state things in terms of Planck units, which express things with reference to four fundamental physical constants. These may be useful in some fields of physics, but are, in most cases, impractical for everyday purposes.
In the Planck scheme, speeds are measured in terms of the speed of light, c. In this case, the speed limit of 0.000000097c is about 105 km/h or 65 mph.
The "Next Exit" sign displays the distance in terms of the Planck length, which is considered the shortest measurable length (as attempts to measure shorter lengths would require particles whose quantum wavelength was smaller than the Planck length, and short wavelengths correspond to high energy so such particles would collapse into black holes before they could be used), equal to approximately 1.616255 × 10-35 m. 1.39 × 1039 Planck lengths is about 23 km, or 14 miles.
It would likely be impractical for drivers to count the digits in that sign at highway speeds. If the highway department were to insist on this change, they would be more readable (but less funny) if the numbers were in scientific notation.
The title text claims that highway engineers like Planck units because the energy capacity of a gas tank is 1. The Planck energy is the mass-energy equivalent of 1 Planck mass. Coincidentally, this is approximately equal to the chemical energy stored in a typical gas tank, equivalent to about 57 L of fuel. Some cars' fuel gauges already use 1 to denote a tank's maximum volume: 0 means empty, then come fractions ¼, ½, and ¾, and then 1 means full. Of course, these numbers correspond to different real volume measurements between different makes of car. However, it is unclear why the units used to measure the capacity of individual gas tanks would matter to highway engineers, who are primarily concerned with things like cost, longevity and safety of the roads those vehicles drive on, not how they operate.
Systems of measurements and their advantages and disadvantages are popular discussion subjects online[actual citation needed], though most of the discussion focuses around the various Imperial systems of measurement (such as U.S. customary units) and their enduring popularity in certain (mostly anglophone) parts of the world. This comic may be exaggerating this discourse to the point of a reductio ad absurdum, introducing units more aligned with fundamental physics constants at the cost of fewer units having quantities close to quantities encountered in practice (only the Planck energy, while the other Planck units are overly large or small). The system also appears to lack any derived units capable of expressing a measurement in more convenient terms. Users of other systems can choose various distance units (commonly ranging from nanometers to kilometers or "thous" to miles) to match their needs. Similerly, a "Planck system" could be made into a somewhat usable system by borrowing SI unit prefixes, for example "quettakilolength" (1033 Planck lengths = 1.616255 cm) or the "nano-c" (10-9×c = 0.2998 m/s, 1.079 km/h, or 0.6706 MPH).
Systems of measurement are also a recurring topic on xkcd. 3092: Baker's Units demonstrates units which are arguably more ridiculous than the ones shown here. In 3065: Square Units, the issues with repeated unit conversion are demonstrated,; similarly, in this comic, unit conversions would be necessary for most people to understand the signs. 3038: Uncanceled Units and 2292: Thermometer deal with even more unusual, but valid, units. 3164: Metric Tip presents another case of switching from one system of measurements to another.
Transcript
- [Two highway signs stand along a road with mountains in the background. One wide sign reads "NEXT EXIT" above a number starting with 1,390 followed by around thirty-six zeroes (the propreantepenultimate and preantepenultimate zero are fully, the sixth-to-last is partly blocked by post of taller sign). A second, taller sign reads "Speed Limit" above the number 0.000000097.]
- [Caption below the panel:]
- Our local highway department is switching to Planck units.
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