8 ms·

> The kilometer was based on 1/10000 the distance between the poles and the equator. The definition we should have used (and almost did) was that the meter was

> The kilometer was based on 1/10000 the distance between the poles and the equator. The definition we should have used (and almost did) was that the meter was the length of a pendulum with 1 second swing (in other words, a pendulum with a 2 second period). https://maa.org/sites/default/files/images/upload_library/22/Schwartz.pdf https://maa.org/sites/default/files/images/upload_library/22... If we had done that, the gravitational constant of Earth would be exactly pi^2 m/s^2: Neat, right? https://godplaysdice.blogspot.com/2007/09/why-g-2.html https://godplaysdice.blogspot.com/2007/09/why-g-2.html

irrational 3y ago
I wish it had been defined in relation to the speed of light in a vacuum. 299,792,458 metres per second. Set it at 300,000,000 meters per second and derive the length of the meter from that.
- reaperman 3y ago
  > I wish it had been defined Wish what had been defined? the second?
  - ryanmcdonough 3y ago
    > and derive the length of the meter from that. I would assume they meant meter since they wrote that.
  - irrational 3y ago
    The meter. The distance light travels in a second in a vacuum is fixed. Divide that distance by 300,000,000. That is the length of 1 meter.
    - reaperman 3y ago
      So the current definition is: > The meter (m) is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299,792,458 when expressed in the unit m s−1, where the second is defined in terms of ∆νCs.[0] Your proposed change is keeping this the exact same but changing 299,792,458 to 300,000,000? You said: “I wish it had been defined in relation to the speed of light in a vacuum.” I believe it is already, as written above. 0: https://www.nist.gov/pml/owm/si-units-length#:~:text=The%20meter%20(m)%20is%20defined,terms%20of%20∆νCs https://www.nist.gov/pml/owm/si-units-length#:~:text=The%20m....
      - tialaramex 3y ago
        If you prefer for some universal constants to be round numbers you can choose a Natural Units systems according to your preference. For example in some of these systems c = 1, which turns Einstein's famous equation into just E = m. Convenient.
- IvyMike 3y ago
  Interesting. The meter was defined in 1791. James Bradley got the speed of light correct to about 1% in 1728, and I think that value stood in 1791. That value was less accurate than either the 10000km pole-to-equator or 1-second-pendulum, as measurable in 1791. And until special relativity, the idea of speed of light being constant wasn't really firmly established. Ultimately, I think in 1791 I think using the speed-of-light as the basis wasn't really practical. P.S. Not really necessary but in writing this comment, I read these documents, each of which taught me something new: https://interestingengineering.com/science/a-brief-history-of-the-speed-of-light https://interestingengineering.com/science/a-brief-history-o... https://spie.org/publications/tt82_25_speed_of_light https://spie.org/publications/tt82_25_speed_of_light https://en.wikipedia.org/wiki/Luminiferous_aether https://en.wikipedia.org/wiki/Luminiferous_aether
twelvechairs 3y ago
I wish we used a unit more similar to the foot as the base. Its much more useful for human-scale understanding - as seen by many civilisations (from the Japanese, Chinese, indians, ancient egyptians, romans, etc.) adopting something similar (something between about 10 and 18 inches). You can build off that as you need of course.
- 2muchcoffeeman 3y ago
  You mean, imperial?
  - twelvechairs 3y ago
    No you can still use a metric system, just use the foot (or similar) as a base and then kilofoot, megafoot, microfoot etc. rather than inches, yards, miles, links, chains, rods and perches etc.
    - 2muchcoffeeman 3y ago
      We already kind of do that. I’ve seen things like 1.5 gallons, 2.5 miles, 10.7 feet. I’ve never seen the intermediate imperial units being used.
      - tomatocracy 3y ago
        At least in the UK my experience is we don't really use decimals with Imperial units - it seems much more natural to use fractions. For example, "10 feet 8 and a half inches" not "10.7 feet" (yes I know the rounding is slightly different). For a smaller distance you might say "three sixteenths of an inch" (since thats what the imperial side of a tape measure is typically divided into) though there are some exceptions eg "0.1 inch spacing". Pints and fl oz the same (you see this quite often in recipes for example) - "1 pint 3 fl oz" or even "23 fl oz" not "1.15 pints". For gallons I think most Brits would likely use a whole number of pints rather than subdividing (ie "21 pints" not "2 gallons, 5 pints"). But I'll give you that we don't really use furlongs outside of horse racing :)
numpad0 3y ago
How is 1 second measured in that definition? Is that not going to need a Swiss watch?
- Valgrim 3y ago
  Wild guess: you don't measure a second. A second is defined as 1/86400 of a day, or 246060. Lets say a pendulum can swing for about 2 minutes. You just take a 2 minute hourglass, make a bunch of pendulums of different lengths, and assign someone to count the number of swings between the moment you turn the hourglass and the moment the sand has passed trough. The one closest to 120 is the correct length. Now this solution is mathematically elegant but comes with a lot of problems. First you must rely on a less-than-perfect time measurement device which may suffer from day to day variations due to temperature. On the contrary, to calculate the distance from the poles to the equator, all you need is a good angle measurement device, from which you can triangulate a distance.
  - defrost 3y ago
    > On the contrary, to calculate the distance from the poles to the equator, all you need is a good angle measurement device, from which you can triangulate a distance. Can you expand on how this can be done please? Particularly the bit where you measure the semi-major axis and semi-minor axis of the Earth's ellipsoid and how you settle on a particular ellipsoid out of the many that predate WGS84. https://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Earth_ellipsoids https://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Ear... "All you need" appears to bury a lot of detail in some hand waving. It's unclear to me whether you intend to measure a distance along the Geoid (gravitational equipotential surface), along the Ellipsoid (the rotated ellipse of best fit), or the actual suurface (the path that would be walked, floated, traversed from equator to pole). A complication with the Geoid path family and surface path family, of course, is that these vary by what line of longitude you might follow.
    - numpad0 3y ago
      Eratosthenes did that in his time with spherical Earth model, and it was precise enough for ~2k years. A lot that can be hand waved with that route as opposed to relying on availability of a well defined and calibrated precise time measurement device, whether it's 1 second or 2 minutes.
deleted 3y ago
[deleted]
jacquesm 3y ago
That wouldn't really work though because Earth's mass over a longer period of time isn't a constant (and hopefully it's size is).
- Eddy_Viscosity2 3y ago
  Gravity also isn't constant everywhere on the planet and it changes locally over time as well as globally. Precision measurements would be a nightmare/impossible.
fanf2 3y ago
At the time the metre was defined in the late 1700s, it was already known that g is not a constant and varies from place to place, which is why they did not choose that proposal and picked the geodetic proposal instead.

irrational 3y ago

I wish it had been defined in relation to the speed of light in a vacuum. 299,792,458 metres per second. Set it at 300,000,000 meters per second and derive the length of the meter from that.

reaperman 3y ago
> I wish it had been defined Wish what had been defined? the second?
- ryanmcdonough 3y ago
  > and derive the length of the meter from that. I would assume they meant meter since they wrote that.
- irrational 3y ago
  The meter. The distance light travels in a second in a vacuum is fixed. Divide that distance by 300,000,000. That is the length of 1 meter.
  - reaperman 3y ago
    So the current definition is: > The meter (m) is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299,792,458 when expressed in the unit m s−1, where the second is defined in terms of ∆νCs.[0] Your proposed change is keeping this the exact same but changing 299,792,458 to 300,000,000? You said: “I wish it had been defined in relation to the speed of light in a vacuum.” I believe it is already, as written above. 0: https://www.nist.gov/pml/owm/si-units-length#:~:text=The%20meter%20(m)%20is%20defined,terms%20of%20∆νCs https://www.nist.gov/pml/owm/si-units-length#:~:text=The%20m....
    - tialaramex 3y ago
      If you prefer for some universal constants to be round numbers you can choose a Natural Units systems according to your preference. For example in some of these systems c = 1, which turns Einstein's famous equation into just E = m. Convenient.
IvyMike 3y ago
Interesting. The meter was defined in 1791. James Bradley got the speed of light correct to about 1% in 1728, and I think that value stood in 1791. That value was less accurate than either the 10000km pole-to-equator or 1-second-pendulum, as measurable in 1791. And until special relativity, the idea of speed of light being constant wasn't really firmly established. Ultimately, I think in 1791 I think using the speed-of-light as the basis wasn't really practical. P.S. Not really necessary but in writing this comment, I read these documents, each of which taught me something new: https://interestingengineering.com/science/a-brief-history-of-the-speed-of-light https://interestingengineering.com/science/a-brief-history-o... https://spie.org/publications/tt82_25_speed_of_light https://spie.org/publications/tt82_25_speed_of_light https://en.wikipedia.org/wiki/Luminiferous_aether https://en.wikipedia.org/wiki/Luminiferous_aether

twelvechairs 3y ago

I wish we used a unit more similar to the foot as the base. Its much more useful for human-scale understanding - as seen by many civilisations (from the Japanese, Chinese, indians, ancient egyptians, romans, etc.) adopting something similar (something between about 10 and 18 inches). You can build off that as you need of course.

2muchcoffeeman 3y ago
You mean, imperial?
- twelvechairs 3y ago
  No you can still use a metric system, just use the foot (or similar) as a base and then kilofoot, megafoot, microfoot etc. rather than inches, yards, miles, links, chains, rods and perches etc.
  - 2muchcoffeeman 3y ago
    We already kind of do that. I’ve seen things like 1.5 gallons, 2.5 miles, 10.7 feet. I’ve never seen the intermediate imperial units being used.
    - tomatocracy 3y ago
      At least in the UK my experience is we don't really use decimals with Imperial units - it seems much more natural to use fractions. For example, "10 feet 8 and a half inches" not "10.7 feet" (yes I know the rounding is slightly different). For a smaller distance you might say "three sixteenths of an inch" (since thats what the imperial side of a tape measure is typically divided into) though there are some exceptions eg "0.1 inch spacing". Pints and fl oz the same (you see this quite often in recipes for example) - "1 pint 3 fl oz" or even "23 fl oz" not "1.15 pints". For gallons I think most Brits would likely use a whole number of pints rather than subdividing (ie "21 pints" not "2 gallons, 5 pints"). But I'll give you that we don't really use furlongs outside of horse racing :)

numpad0 3y ago

How is 1 second measured in that definition? Is that not going to need a Swiss watch?

Valgrim 3y ago
Wild guess: you don't measure a second. A second is defined as 1/86400 of a day, or 246060. Lets say a pendulum can swing for about 2 minutes. You just take a 2 minute hourglass, make a bunch of pendulums of different lengths, and assign someone to count the number of swings between the moment you turn the hourglass and the moment the sand has passed trough. The one closest to 120 is the correct length. Now this solution is mathematically elegant but comes with a lot of problems. First you must rely on a less-than-perfect time measurement device which may suffer from day to day variations due to temperature. On the contrary, to calculate the distance from the poles to the equator, all you need is a good angle measurement device, from which you can triangulate a distance.
- defrost 3y ago
  > On the contrary, to calculate the distance from the poles to the equator, all you need is a good angle measurement device, from which you can triangulate a distance. Can you expand on how this can be done please? Particularly the bit where you measure the semi-major axis and semi-minor axis of the Earth's ellipsoid and how you settle on a particular ellipsoid out of the many that predate WGS84. https://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Earth_ellipsoids https://en.wikipedia.org/wiki/Earth_ellipsoid#Historical_Ear... "All you need" appears to bury a lot of detail in some hand waving. It's unclear to me whether you intend to measure a distance along the Geoid (gravitational equipotential surface), along the Ellipsoid (the rotated ellipse of best fit), or the actual suurface (the path that would be walked, floated, traversed from equator to pole). A complication with the Geoid path family and surface path family, of course, is that these vary by what line of longitude you might follow.
  - numpad0 3y ago
    Eratosthenes did that in his time with spherical Earth model, and it was precise enough for ~2k years. A lot that can be hand waved with that route as opposed to relying on availability of a well defined and calibrated precise time measurement device, whether it's 1 second or 2 minutes.

deleted 3y ago

[deleted]

jacquesm 3y ago

That wouldn't really work though because Earth's mass over a longer period of time isn't a constant (and hopefully it's size is).

Eddy_Viscosity2 3y ago
Gravity also isn't constant everywhere on the planet and it changes locally over time as well as globally. Precision measurements would be a nightmare/impossible.

fanf2 3y ago

At the time the metre was defined in the late 1700s, it was already known that g is not a constant and varies from place to place, which is why they did not choose that proposal and picked the geodetic proposal instead.