5 ms·
It's not arbitrary at all, it's for backwards compatibility. Previously the meter was defined in terms of the emission lines of krypton-86, which was a distance
by gh02t 11y ago
It's not arbitrary at all, it's for backwards compatibility. Previously the meter was defined in terms of the emission lines of krypton-86, which was a distance that we could measure most precisely with an interferometer. Before that it was based on the size of the earth, which could be measured with a astronomical calculations. And originally it was based on the length of a pendulum that produced a period of a 1 seconds, from which the length can be calculated using a scale, a reference mass and a clock (there was another definition, but this one was more precise I believe).
Each definition gives you something pretty close to what we now define as a meter, but the precision to which they could be measured at the time differed. The length of a "meter" was more or less the same distance in everybody's mind then as now, but if a 10000 scientists would sit down and perform experiments to actually calculate the exact length in 1700 versus, the mean of the values they reported would be about the same as it is today, but the statistical uncertainty would be much much much higher.
The redefining of the meter has typically occurred when some new process was invented that was more precise than the the previous method, for instance today measuring a laser in a vacuum is something like 1/3 the uncertainty than the old method using an interferometer. So the uncertainty is smaller, but crucially the mean value is still basically the same or very close. That's the reason for the weird 1/299792458 seconds, it's because we can define seconds very very precisely (from atomic clocks) and that's the amount of time it takes light in a vacuum to travel the same distance as the previous most precise known value for the length of a meter.
If it wasn't done this way, every time we invented a more precise method to measure distance and want to improve the precision of the meter it'd be like defining a whole new unit. Defining a foot as the distance light travels in a nanosecond is fine now, but if we discover an even more precise way to measure distance than a laser in a vacuum we'd end up in the same position, where a "foot" would be some strange fraction of a reference value that makes it work out to agree with the old most precise known value.
This sort of stupidly accurate measurement doesn't matter anymore on the day-to-day life scale as the length of a meter is known to within ~(10^-9)%, which is about a ten picometers. However, that means then that if you're fabricating silicon at the nanometer scale, the actual exact length of a nanometer is only known to within about 1% of a nanometer (if I did my math right, might be off by a factor of 10). That's much more significant.
- protomyth 11y ago"It's not arbitrary at all, it's for backwards compatibility." The original definition of the meter was one ten-millionth of the distance from the equator to the North Pole. Sure, we got more precise, but its still arbitrary. The only interesting thing about metric is the relation of length, volume, mass. But, a liter is not a cubic meter, nope - its a cubic decimetre, another arbitrary decision.
- gh02t 11y agoYes, the original definition is arbitrary of course. I was talking about the random constant fraction of a second. Units are always arbitrary, by definition they're just a convention. They're a way of relating an abstract concept (a number) to some intuitively meaningful thing.
- mjevans 11y agoI'd argue that the unit liter was chosen as a nice power of 10 relation to a cubic meter (the obvious initial choice) as being the best for 'every day' common person transactions. Take a bottle of water, most commonly the sold sizes are 0.5 (about 16oz) and 1 liter bottles; a liter is also pretty close to a quart. As another example, it is common to find soda pop sold in bottles of 1, 2, and 3 liters (depending on the brand).
- jerf 11y agoThe units that have the best claim to being non-arbitrary tend to be of rather inconvenient orders of magnitude: https://en.wikipedia.org/wiki/Natural_units#Systems_of_natural_units https://en.wikipedia.org/wiki/Natural_units#Systems_of_natur... A certain amount of arbitrariness is inevitable at human scale.
- gh02t 11y agoIndeed, what units are convenient depends on context. Metric/SI is set up so that most of the un-prefixed units are a convenient size on human scale. But doing this means that some derived units will have values that are not human scale (like the Pascal, atmospheric pressure is ~100000 pascal). The nice thing about SI is that they subdivide easily in powers of ten, so even if the Pascal is inconvenient in our day-to-day lives it's easy to talk in kPa as 1000 Pa. This is contrasted with something like Imperial units, where every division of e.g. distance is supposed to be roughly based on some physical object. That's why you end up with 12 in/ft, 5280 ft/mi etc. Or alternatively you end up with metric-imperial hybrid units like the kilopound. Not to mention, what units are convenient vary depending on what you do. For instance one of the SI alternative units for energy is the electron volt (eV), the work done to move an electron through a 1 volt potential. This is a tiny amount of energy on human scale- a common analogy is that 1 MeV (10^6 eV) is enough energy to make a single grain of sand twitch a little bit. But, if you're a nuclear physicist (or maybe a chemist) then eV are typically much more convenient than say Joules.