The numerical values of the 7 defining constants now have no uncertainty
May 26, 2019 7:47 PM Subscribe
The new kilogram just debuted. It’s a massive achievement. The new definition represents a victory of humankind over chaos in the universe. Really. (Vox) Nothing changes with what a kilogram is, but rather how it is defined. The International Prototype Kilogram (a.k.a. Big K, or Le Grand K (Atlas Obscura)) had been used since 1889 (BIPM), and had copies around the world (Wikipedia), but mass of platinum-iridium alloy had been losing mass (Science Daily). It was replaced by setting exact numerical values for the Planck constant (h), along with redefinition of six other SI base units (Wikipedia).
Back on November 16, 2018, representatives from 60 countries voted to redefine the International System of Units (SI) (Science Daily). These decisions were made at the 26th meeting of the General Conference on Weights and Measures (CGPM). They included that the elementary electric charge (e) is used to redefine ampere, the Boltzmann constant (k) redefined kelvin, and the Avogadro constant (NA) redefined mole. The second, metre, and candela were already defined by physical constants and were subject to correction to their definitions. Those redefinitions came into force on May 20, 2019.
These seven definitions are new, but their sources are old.
== Kilogram ==
At the end of the nineteenth century, the kilogram was conceived as the mass of one liter of water at 4°C, the temperature at which water was densest. This was a tough standard to follow, and it was also not always consistent. For example, density may vary slightly with changes in altitude. This definition is also dependent on a stable definition of the meter, which at the time was very imprecisely defined as a particular measurement of Earth’s surface.
In 1889, in response to the impractical nature of these standards, the International Bureau of Weights and Measures in Paris built an actual reference meter and kilogram. Each was a made of platinum iridium, the most inert material available at the time (JStor Daily blog post). Now, Planck's constant (PBS, Nova), a hypothesis that was discovered in 1900 (PDF via Researchgate), is used to strictly define a kilogram.
== Ampere ==
In 1893, a scientific committee called the International Electrical Congress (IEC) met in Chicago and settled on two units to be the basis for the others: the ohm for resistance and the ampere for current. The Congress’ decision was formally accepted at the International Conference of scientists who met in London in 1908. (NIST) The new measurement is based on the discovery made by Robert A. Millikan's oil drop experiment from 1909 (Course page from the University of Alaska, Fairbanks).
== Kelvin ==
In 1848, William Thomson, who later was made Lord Kelvin, wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby "infinite cold" (absolute zero) was the scale's null point, and which used the degree Celsius for its unit increment. Kelvin calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time (Zapatopi.net copy of On an Absolute Thermometric Scale).
Since 1954, the kelvin has been defined as “equal to the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water—the point at which water, ice and water vapor co-exist in equilibrium. That is a valuable common reference because, for a precise formulation of water at a specific pressure, the triple point always occurs at exactly the same temperature: 273.16 K.
Extrapolating from the water triple-point temperature to very high or very low temperatures is problematic; so, by international agreement, 21 other defining points are specified, ranging from the freezing point of helium to the freezing point of copper.
However, the kelvin has been redefined in terms of the Boltzmann constant, which relates the amount of thermodynamic energy in a substance to its temperature (NIST). Oddly enough, Although Boltzmann first linked entropy and probability in 1877, the relation was never expressed with a specific constant until Max Planck first introduced k, and gave a precise value for it in in 1900–1901 (Wikipedia).
== Mole ==
Similarly to Boltzmann, it was in 1811 that Amedeo Avogadro first proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules regardless of the nature of the gas. But it would be almost a hundred years later, in 1909, that the French physicist Jean Perrin proposed naming the constant in honor of Avogadro. Perrin won the 1926 Nobel Prize in Physics, largely for his work in determining the Avogadro constant by several different methods. 110 years after Perrin's proposed naming, the Avogadro constant replaced previous definitions (Wikipedia x2).
Back on November 16, 2018, representatives from 60 countries voted to redefine the International System of Units (SI) (Science Daily). These decisions were made at the 26th meeting of the General Conference on Weights and Measures (CGPM). They included that the elementary electric charge (e) is used to redefine ampere, the Boltzmann constant (k) redefined kelvin, and the Avogadro constant (NA) redefined mole. The second, metre, and candela were already defined by physical constants and were subject to correction to their definitions. Those redefinitions came into force on May 20, 2019.
These seven definitions are new, but their sources are old.
== Kilogram ==
At the end of the nineteenth century, the kilogram was conceived as the mass of one liter of water at 4°C, the temperature at which water was densest. This was a tough standard to follow, and it was also not always consistent. For example, density may vary slightly with changes in altitude. This definition is also dependent on a stable definition of the meter, which at the time was very imprecisely defined as a particular measurement of Earth’s surface.
In 1889, in response to the impractical nature of these standards, the International Bureau of Weights and Measures in Paris built an actual reference meter and kilogram. Each was a made of platinum iridium, the most inert material available at the time (JStor Daily blog post). Now, Planck's constant (PBS, Nova), a hypothesis that was discovered in 1900 (PDF via Researchgate), is used to strictly define a kilogram.
== Ampere ==
In 1893, a scientific committee called the International Electrical Congress (IEC) met in Chicago and settled on two units to be the basis for the others: the ohm for resistance and the ampere for current. The Congress’ decision was formally accepted at the International Conference of scientists who met in London in 1908. (NIST) The new measurement is based on the discovery made by Robert A. Millikan's oil drop experiment from 1909 (Course page from the University of Alaska, Fairbanks).
== Kelvin ==
In 1848, William Thomson, who later was made Lord Kelvin, wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby "infinite cold" (absolute zero) was the scale's null point, and which used the degree Celsius for its unit increment. Kelvin calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time (Zapatopi.net copy of On an Absolute Thermometric Scale).
Since 1954, the kelvin has been defined as “equal to the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water—the point at which water, ice and water vapor co-exist in equilibrium. That is a valuable common reference because, for a precise formulation of water at a specific pressure, the triple point always occurs at exactly the same temperature: 273.16 K.
Extrapolating from the water triple-point temperature to very high or very low temperatures is problematic; so, by international agreement, 21 other defining points are specified, ranging from the freezing point of helium to the freezing point of copper.
However, the kelvin has been redefined in terms of the Boltzmann constant, which relates the amount of thermodynamic energy in a substance to its temperature (NIST). Oddly enough, Although Boltzmann first linked entropy and probability in 1877, the relation was never expressed with a specific constant until Max Planck first introduced k, and gave a precise value for it in in 1900–1901 (Wikipedia).
== Mole ==
Similarly to Boltzmann, it was in 1811 that Amedeo Avogadro first proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules regardless of the nature of the gas. But it would be almost a hundred years later, in 1909, that the French physicist Jean Perrin proposed naming the constant in honor of Avogadro. Perrin won the 1926 Nobel Prize in Physics, largely for his work in determining the Avogadro constant by several different methods. 110 years after Perrin's proposed naming, the Avogadro constant replaced previous definitions (Wikipedia x2).
From the first link:
"...for those thinking the kilogram doesn’t matter in the US, which uses imperial units like pounds, feet, and gallons, our measurements are derived from SI units. Officially, in the US, 1 pound is defined as 0.45359237 kilograms."posted by theory at 8:00 PM on May 26, 2019 [16 favorites]
📏
posted by Homo neanderthalensis at 8:01 PM on May 26, 2019 [1 favorite]
posted by Homo neanderthalensis at 8:01 PM on May 26, 2019 [1 favorite]
Baron Kelvin was one of the few scientists to need a special section in their Wikipedia article called, "Pronouncements later proven to be false."
posted by Chrysostom at 8:02 PM on May 26, 2019 [12 favorites]
posted by Chrysostom at 8:02 PM on May 26, 2019 [12 favorites]
How does gravitational field strength affect these new definitions?
posted by flabdablet at 8:03 PM on May 26, 2019
posted by flabdablet at 8:03 PM on May 26, 2019
It doesn't.
posted by thatwhichfalls at 8:07 PM on May 26, 2019 [1 favorite]
posted by thatwhichfalls at 8:07 PM on May 26, 2019 [1 favorite]
What an absolute unit!
posted by nikaspark at 8:20 PM on May 26, 2019 [61 favorites]
posted by nikaspark at 8:20 PM on May 26, 2019 [61 favorites]
Mass is now defined by the Planck constant, which means it's defined in meters and seconds. However, the meter is defined by the second and the value for the speed of light. So the SI definition of mass is needs only two things now: the choice of the length of a meter as defined by the speed of light and our choice of how we define a second. We don't need to refer to gravity at all.
posted by bonehead at 8:21 PM on May 26, 2019 [2 favorites]
posted by bonehead at 8:21 PM on May 26, 2019 [2 favorites]
Note that there was a major effort to use the Avogadro constant instead---effectively counting atoms to define mass. This would also have been theoretically just as satisfactory a solution, but proved to be technically harder to do.
Ultimately, the choice of which constant to use is definitional one, an anthropocentric choice. We humans had a bunch of yardsticks that all could work; we chose this one because it worked best for our level of technology right now.
posted by bonehead at 8:29 PM on May 26, 2019 [7 favorites]
Ultimately, the choice of which constant to use is definitional one, an anthropocentric choice. We humans had a bunch of yardsticks that all could work; we chose this one because it worked best for our level of technology right now.
posted by bonehead at 8:29 PM on May 26, 2019 [7 favorites]
So the constant of one Guacamole is measured in Avocado numbers?
(just kidding... this is a truly epic FPP and just makes anyone who still depends on the "English" units of pounds, Fahrenheit degrees, etc. feel just that much more stupid)
posted by oneswellfoop at 8:31 PM on May 26, 2019 [4 favorites]
(just kidding... this is a truly epic FPP and just makes anyone who still depends on the "English" units of pounds, Fahrenheit degrees, etc. feel just that much more stupid)
posted by oneswellfoop at 8:31 PM on May 26, 2019 [4 favorites]
Electrical Units in the New SI: Saying Goodbye to the 1990 Values (pdf). Standards for the Volt and the Ohm are created using the Josephson effect and quantum Hall effect, respectively (a standard meaning a physical embodiment of a unit, whether it relies on a fundamental phenomenon or not). These effects use the von Klitzing and Josephson constants RK = h/e2 and KJ = 2e/h. In 1990, the electrical community defined conventional values for these two constants; these values have been replaced by new ones based on h and e, bringing the Volt and Ohm back in the SI fold.
In practice this has little effect because the new values are so close to the old ones that the difference only matters to the extreme high end of precision standards.
posted by Monday, stony Monday at 8:37 PM on May 26, 2019 [2 favorites]
In practice this has little effect because the new values are so close to the old ones that the difference only matters to the extreme high end of precision standards.
posted by Monday, stony Monday at 8:37 PM on May 26, 2019 [2 favorites]
The new kilogram just debuted. It’s a massive achievement
I see what you've done there.
posted by The Legit Republic of Blanketsburg at 8:57 PM on May 26, 2019 [11 favorites]
I see what you've done there.
posted by The Legit Republic of Blanketsburg at 8:57 PM on May 26, 2019 [11 favorites]
Officially, in the US, 1 pound is defined as 0.45359237 kilograms."
How does gravitational field strength affect these new definitions?
Right - it's been a long time since school, but, my first thought was, isn't a pound a unit of force, not mass? Which would require you to define it as a fraction of a kilogram under some stable gravitational field. But, It looks like it's both. What a country!
posted by thelonius at 9:01 PM on May 26, 2019 [1 favorite]
How does gravitational field strength affect these new definitions?
Right - it's been a long time since school, but, my first thought was, isn't a pound a unit of force, not mass? Which would require you to define it as a fraction of a kilogram under some stable gravitational field. But, It looks like it's both. What a country!
posted by thelonius at 9:01 PM on May 26, 2019 [1 favorite]
So long as the relevant constants don't change, we're all set.
posted by They sucked his brains out! at 9:06 PM on May 26, 2019 [3 favorites]
posted by They sucked his brains out! at 9:06 PM on May 26, 2019 [3 favorites]
The candela was first stated as a particular design of candle, using sperm whale wax, and a cotton wick of a particular number of strands and a particular number of twists. The metric was the standard for the lighting industry, and accepted later into SI.
But the absolute measure has an odd fraction (1/683) to keep relating to the old candles.
So SI now and always has a whale factor in a fundamental unit.
posted by nickggully at 9:24 PM on May 26, 2019 [21 favorites]
But the absolute measure has an odd fraction (1/683) to keep relating to the old candles.
So SI now and always has a whale factor in a fundamental unit.
posted by nickggully at 9:24 PM on May 26, 2019 [21 favorites]
Fantastic post! I highly recommend the Arts et Metiers museum in Paris for any unit nerds looking to geek out over historical standards, which have their own dedicated gallery.
posted by St. Oops at 9:41 PM on May 26, 2019 [4 favorites]
posted by St. Oops at 9:41 PM on May 26, 2019 [4 favorites]
So the SI definition of mass is needs only two things now: the choice of the length of a meter as defined by the speed of light and our choice of how we define a second. We don't need to refer to gravity at all.
Aren't both of those things extremely affected by gravity? The original resounding example with regard to length being the precession of the perihelion of Mercury. And if I understand correctly, satellites need to have their clocks calibrated based on their altitude because of the relativistic effect on time.
posted by XMLicious at 9:57 PM on May 26, 2019 [2 favorites]
I still don't understand why the ampere is considered the SI base unit and the coulomb derived from it instead of the other way around. It's like if we decided to call a meter per second a velox or something and then said that a meter was equal to a velox times a second. It's especially confusing given that the new definition of an amp is derived from the elementary charge, which is expressed in coulombs to begin with.
posted by enjoymoreradio at 10:25 PM on May 26, 2019 [2 favorites]
posted by enjoymoreradio at 10:25 PM on May 26, 2019 [2 favorites]
A kilo is one thousand grams—easy to remember
posted by Jon_Evil at 10:37 PM on May 26, 2019 [1 favorite]
posted by Jon_Evil at 10:37 PM on May 26, 2019 [1 favorite]
Enjoymoreradio, I think it's because of technical limitations again. It is / was much easier to measure current than charge, since that can be directly measured via the magnetic field strength to a high precision.
That said, given the relativistic nature of our universe, the idea of having a velocity - based base unit would probably be a good idea! It is after all the one thing that truly is invariant here...
posted by Arandia at 10:50 PM on May 26, 2019 [2 favorites]
That said, given the relativistic nature of our universe, the idea of having a velocity - based base unit would probably be a good idea! It is after all the one thing that truly is invariant here...
posted by Arandia at 10:50 PM on May 26, 2019 [2 favorites]
How does gravitational field strength affect these new definitions?
Your question might or might not boil down to whether the mass 'm' in F=GMm/r2 is everywhere and for all time the same as the mass 'm' in F=ma — in other words whether gravitational mass is always identical to inertial mass — as Einstein's principle of equivalence says it is.
But in case that is the question, John Archibald Wheeler considered it interesting enough to write a book about it with Ignazio Ciufolini in 1995, Gravitation and Inertia, the first few chapters of which are available here.
I suggest reading the overview, chapter 1 – in order to witness one of the best examples of the rapture of deep questions in physics I have ever found, if nothing else!
posted by jamjam at 11:58 PM on May 26, 2019 [4 favorites]
Your question might or might not boil down to whether the mass 'm' in F=GMm/r2 is everywhere and for all time the same as the mass 'm' in F=ma — in other words whether gravitational mass is always identical to inertial mass — as Einstein's principle of equivalence says it is.
But in case that is the question, John Archibald Wheeler considered it interesting enough to write a book about it with Ignazio Ciufolini in 1995, Gravitation and Inertia, the first few chapters of which are available here.
I suggest reading the overview, chapter 1 – in order to witness one of the best examples of the rapture of deep questions in physics I have ever found, if nothing else!
posted by jamjam at 11:58 PM on May 26, 2019 [4 favorites]
I recognize some of those words.
This did remind me of the story about how the distance between railroad rails is based on the distance between wagon wheel ruts in Roman roads. Or maybe that's a myth...
posted by Brocktoon at 12:01 AM on May 27, 2019 [1 favorite]
This did remind me of the story about how the distance between railroad rails is based on the distance between wagon wheel ruts in Roman roads. Or maybe that's a myth...
posted by Brocktoon at 12:01 AM on May 27, 2019 [1 favorite]
Ultimately, the choice of which constant to use is definitional one, an anthropocentric choice.
I suppose we could have handed an infinite number of rulers to an infinite number of monkeys and see what they come up with, but Shakespeare's meter wouldn't be of much use here..
posted by zaixfeep at 12:51 AM on May 27, 2019
I suppose we could have handed an infinite number of rulers to an infinite number of monkeys and see what they come up with, but Shakespeare's meter wouldn't be of much use here..
posted by zaixfeep at 12:51 AM on May 27, 2019
Your question might or might not boil down to whether the mass 'm' in F=GMm/r2 is everywhere and for all time the same as the mass 'm' in F=ma — in other words whether gravitational mass is always identical to inertial mass — as Einstein's principle of equivalence says it is.
I was just wondering whether the metre we use to define the kilogram is one we measure normal to the prevailing gravitational field, or the stretched one parallel to it, or whether that makes any difference.
posted by flabdablet at 12:58 AM on May 27, 2019
I was just wondering whether the metre we use to define the kilogram is one we measure normal to the prevailing gravitational field, or the stretched one parallel to it, or whether that makes any difference.
posted by flabdablet at 12:58 AM on May 27, 2019
makes anyone who still depends on the "English" units of pounds, Fahrenheit degrees, etc. feel just that much more stupid
Trust me, there’s not much stupider we could feel.
posted by Tell Me No Lies at 1:03 AM on May 27, 2019 [1 favorite]
Trust me, there’s not much stupider we could feel.
posted by Tell Me No Lies at 1:03 AM on May 27, 2019 [1 favorite]
This did remind me of the story about how the distance between railroad rails is based on the distance between wagon wheel ruts in Roman roads. Or maybe that's a myth...
I’m pretty sure it is. As you can see in many films of the silent era, railroad tracks are sized to fit one standard distressed damsel.
posted by Tell Me No Lies at 1:05 AM on May 27, 2019 [7 favorites]
I’m pretty sure it is. As you can see in many films of the silent era, railroad tracks are sized to fit one standard distressed damsel.
posted by Tell Me No Lies at 1:05 AM on May 27, 2019 [7 favorites]
I was just wondering whether the metre we use to define the kilogram is one we measure normal to the prevailing gravitational field, or the stretched one parallel to it, or whether that makes any difference.
The meter is currently defined in terms of the speed of light in a vacuum, which has the nice property of being invariant in all reference frames. The path the light takes may be affected by gravity, but it's speed will be the same, so the definitional meter is not affected.
I know *why* they didn't do it, but I still wish they'd taken the opportunity to round off the speed of light to an even 300,000,000 meters per second.
posted by vibratory manner of working at 1:27 AM on May 27, 2019 [4 favorites]
The meter is currently defined in terms of the speed of light in a vacuum, which has the nice property of being invariant in all reference frames. The path the light takes may be affected by gravity, but it's speed will be the same, so the definitional meter is not affected.
I know *why* they didn't do it, but I still wish they'd taken the opportunity to round off the speed of light to an even 300,000,000 meters per second.
posted by vibratory manner of working at 1:27 AM on May 27, 2019 [4 favorites]
The candela is a jerk unit for jerks.
posted by groda at 3:14 AM on May 27, 2019 [3 favorites]
posted by groda at 3:14 AM on May 27, 2019 [3 favorites]
"Reference frames" is referring only to special relativity, though, isn't it? Like, you don't perceive length contraction of things in your own inertial reference frame.
But the effects of gravity are general relativity phenomena. So we can see the Spirograph-like behavior of Mercury's orbit, peaking in a different place each time, and diverging from what we would expect under Newtonian mechanics essentially because the length of a meter and the length of a second vary more the deeper you get into the gravity well of the Sun, even though it's in our own inertial reference frame.
That was my understanding back in school, anyways, and is the reason that like flabdablet I'm expecting that the absoluteness of the units involving space and time would require a distinction between measurements taken somewhere like flat intergalactic space versus sea-level on Earth.
posted by XMLicious at 3:29 AM on May 27, 2019 [1 favorite]
But the effects of gravity are general relativity phenomena. So we can see the Spirograph-like behavior of Mercury's orbit, peaking in a different place each time, and diverging from what we would expect under Newtonian mechanics essentially because the length of a meter and the length of a second vary more the deeper you get into the gravity well of the Sun, even though it's in our own inertial reference frame.
That was my understanding back in school, anyways, and is the reason that like flabdablet I'm expecting that the absoluteness of the units involving space and time would require a distinction between measurements taken somewhere like flat intergalactic space versus sea-level on Earth.
posted by XMLicious at 3:29 AM on May 27, 2019 [1 favorite]
The candela is a jerk unit
No, that would be metres per second cubed.
posted by flabdablet at 4:43 AM on May 27, 2019 [14 favorites]
No, that would be metres per second cubed.
posted by flabdablet at 4:43 AM on May 27, 2019 [14 favorites]
here for the posters and t-shirts with helvetica-fonted print -
Kilo
Ampere
Kelvin
& Mole
posted by entropone at 6:35 AM on May 27, 2019 [1 favorite]
Kilo
Ampere
Kelvin
& Mole
posted by entropone at 6:35 AM on May 27, 2019 [1 favorite]
Brocktoon: "This did remind me of the story about how the distance between railroad rails is based on the distance between wagon wheel ruts in Roman roads. Or maybe that's a myth..."
Snopes says mostly myth.
posted by Chrysostom at 7:28 AM on May 27, 2019
Snopes says mostly myth.
posted by Chrysostom at 7:28 AM on May 27, 2019
The candela is a jerk unit
No, that would be metres per second cubed.
While the fourth, fifth and sixth derivative of position with respect to time (m/s4,5,6) are snap, crackle, and pop.
(That's sort of unofficial but physicists and engineers do use those terms in real life.)
posted by tclark at 8:03 AM on May 27, 2019 [2 favorites]
No, that would be metres per second cubed.
While the fourth, fifth and sixth derivative of position with respect to time (m/s4,5,6) are snap, crackle, and pop.
(That's sort of unofficial but physicists and engineers do use those terms in real life.)
posted by tclark at 8:03 AM on May 27, 2019 [2 favorites]
As a complement to the fascinating adventures in attempting to objectify these standard measures, I find it useful to remember with what degree of arbitrariness they were invented in the first place.
As regards the meter, here's the story as I remember hearing it: the setting is in post-revolutionary Paris; Robespierre's recasting of standards touches on measures of lengths one day. Wanting to replace ells ("bras"), he calls in the court astronomer:
"We need a new official basic unit of measure - find me a convenient natural length, so it won't sound as though I've pulled this one out of my ass."
"Bien sûr, R, only... about how big do you want it to be? This big [holds out thumb-index span]? Or this big [holds out thumb-pinky span]?"
"Mais non, just make it... about one baguette!"
When the astronomer comes back with his demonstration that one baguette happens to be precisely one 40-millionth of the earth's circumference as he's just calculated it, although Robespierre's not quite satisfied by the four in the figure ("Pourquoi quatre!?"), after some back-and-forth, he revises the definition to "one ten-millionth of the distance from the North Pole to the equator", and decides to go with this now-scientifically-founded baguette-length as the new designated "mètre". (The astronomer actually returns a couple of times in the following weeks to refine his calculations, due to "improvements in the accuracy" of the measurements of the earth's circumference. R chooses to stick with the "one 10-millionth", thus adjusting the baguette-mètre a little bit, accordingly, each time. When the astronomer comes back a third time, Robespierre (realising that this scene would of course repeat ad infinitum) refuses to let him in. Et voilà! (Some names and actual dialogue may of course be entriely fictitious - but I've yet to hear a more convincing explanation of where that length "comes from".)
posted by progosk at 8:06 AM on May 27, 2019 [2 favorites]
As regards the meter, here's the story as I remember hearing it: the setting is in post-revolutionary Paris; Robespierre's recasting of standards touches on measures of lengths one day. Wanting to replace ells ("bras"), he calls in the court astronomer:
"We need a new official basic unit of measure - find me a convenient natural length, so it won't sound as though I've pulled this one out of my ass."
"Bien sûr, R, only... about how big do you want it to be? This big [holds out thumb-index span]? Or this big [holds out thumb-pinky span]?"
"Mais non, just make it... about one baguette!"
When the astronomer comes back with his demonstration that one baguette happens to be precisely one 40-millionth of the earth's circumference as he's just calculated it, although Robespierre's not quite satisfied by the four in the figure ("Pourquoi quatre!?"), after some back-and-forth, he revises the definition to "one ten-millionth of the distance from the North Pole to the equator", and decides to go with this now-scientifically-founded baguette-length as the new designated "mètre". (The astronomer actually returns a couple of times in the following weeks to refine his calculations, due to "improvements in the accuracy" of the measurements of the earth's circumference. R chooses to stick with the "one 10-millionth", thus adjusting the baguette-mètre a little bit, accordingly, each time. When the astronomer comes back a third time, Robespierre (realising that this scene would of course repeat ad infinitum) refuses to let him in. Et voilà! (Some names and actual dialogue may of course be entriely fictitious - but I've yet to hear a more convincing explanation of where that length "comes from".)
posted by progosk at 8:06 AM on May 27, 2019 [2 favorites]
I can't believe that no one has made reference to the Kibble balance, aka the watt balance, used to determine Planck's constant. It's kinda beautiful.
posted by Halloween Jack at 12:10 PM on May 27, 2019 [4 favorites]
posted by Halloween Jack at 12:10 PM on May 27, 2019 [4 favorites]
"Reference frames" is referring only to special relativity, though, isn't it? Like, you don't perceive length contraction of things in your own inertial reference frame.
General relativity is exactly the same as special, with the addition that there is no difference between acceleration from gravity and acceleration from other sources. So hanging out in earth's gravity is identical, as far as the physics are concerned, as being in a reference frame that's physically accelerating at 9.8 m/s^2. I think it's fair to talk about reference frames in a gravitational context because of that, but it's been a while for me too.
Terminology aside, the speed of light in a vacuum is still a constant in both special and general relativity. Wikipedia has this to say about it:
General relativity is exactly the same as special, with the addition that there is no difference between acceleration from gravity and acceleration from other sources. So hanging out in earth's gravity is identical, as far as the physics are concerned, as being in a reference frame that's physically accelerating at 9.8 m/s^2. I think it's fair to talk about reference frames in a gravitational context because of that, but it's been a while for me too.
Terminology aside, the speed of light in a vacuum is still a constant in both special and general relativity. Wikipedia has this to say about it:
In non-inertial frames of reference (gravitationally curved spacetime or accelerated reference frames), the local speed of light is constant and equal to c, but the speed of light along a trajectory of finite length can differ from c, depending on how distances and times are defined.posted by vibratory manner of working at 1:51 PM on May 27, 2019 [1 favorite]
The thing which has puzzled me for years about Einstein's equivalence principle is that I can't see how it's true except point by point in almost all circumstances.
Since, for example, if you're orbiting the Earth in a satellite with no communication with the outside, and you're observing a horizontal beam with identical pendulums at either end, with very very accurate measurements you might notice that, when completely at rest, the pendulums are not perfectly parallel because both are pointing at the center of the Earth, and that's a slightly different direction at one end of the beam than it is at the other.
But accelerating in open space with a zero gravitational field, the pendulums would hang perfectly parallel, and you could use that difference to distinguish the two situations. And if you turned your beam so that it was vertical, the two pendulums would have different periods because of the inverse square law governing gravitational force, and that would tell you the difference.
But according to Heisenberg's uncertainty principle from quantum mechanics, observations at a single point are impossible, because that would mean infinite uncertainty in momentum.
posted by jamjam at 2:30 PM on May 27, 2019
Since, for example, if you're orbiting the Earth in a satellite with no communication with the outside, and you're observing a horizontal beam with identical pendulums at either end, with very very accurate measurements you might notice that, when completely at rest, the pendulums are not perfectly parallel because both are pointing at the center of the Earth, and that's a slightly different direction at one end of the beam than it is at the other.
But accelerating in open space with a zero gravitational field, the pendulums would hang perfectly parallel, and you could use that difference to distinguish the two situations. And if you turned your beam so that it was vertical, the two pendulums would have different periods because of the inverse square law governing gravitational force, and that would tell you the difference.
But according to Heisenberg's uncertainty principle from quantum mechanics, observations at a single point are impossible, because that would mean infinite uncertainty in momentum.
posted by jamjam at 2:30 PM on May 27, 2019
Obligatory, whether you knew it or not:
1001 grams
it's a pretty good movie.
posted by hearthpig at 6:51 PM on May 27, 2019
1001 grams
it's a pretty good movie.
posted by hearthpig at 6:51 PM on May 27, 2019
I can't see how it's true except point by point
Being true point by point is exactly the point, because what that allows you to conceive of is the idea of interaction between a point test mass and a gravitational field whose magnitude and direction varies point by point: that is, a gravitational field with a shape. And once you have that idea, combining it with the idea that gravitational fields affect all matter indiscriminately yields a more general idea: that spacetime itself - i.e. the aggregate of all the spatiotemporal relationships between each of the pieces of matter you're interested in making predictions about - is most naturally described using a geometry that is not Euclidean.
When we speak of a region of spacetime being curved, what we mean is that any model of the behaviour of the observable features of that region leads to an inconsistency between (a) the observer independence of the speed of light in a vacuum according to Maxwell and (b) the properties of straight lines and triangles according to Euclid, and we'd rather dump Euclid's intuitively derived fifth postulate than Maxwell's observationally derived electrodynamics.
Which, as it turns out, is a really good idea because it yields the testable prediction that if GR is correct then all information propagation across distance via any conceivable means, not just electrodynamics, can happen no faster than the speed of light and involve a loss of energy at the information source - a prediction which has indeed been tested with respect to information about local distributions of mass, and found to be consistent with observation.
However, the only way that the geometry of spacetime according to GR becomes at all mathematically tractable, if I understand correctly, is by making use of a simplifying assumption that arbitrarily small patches of it in regions of particular interest can be modelled in a Euclidean fashion without causing significant errors, in much the same way as the curvature of the surface of the Earth doesn't stop us measuring triangles drawn on a sheet of paper and finding that their interior angles do indeed sum to 180°. To say that the "laws of physics" "break down" at "singularities" is not to say that the underlying principles are defective, merely that there are regions of interest where it's not feasible to apply them in any reasonable analytical fashion.
accelerating in open space with a zero gravitational field, the pendulums would hang perfectly parallel, and you could use that difference to distinguish the two situations
Yes you could, and per GR the least inconvenient way to model that difference is as one in the shape of the prevailing gravitational fields and, by extension, the local spacetime geometry and the actual meaning, if any, of "parallel".
posted by flabdablet at 7:55 PM on May 27, 2019 [2 favorites]
Being true point by point is exactly the point, because what that allows you to conceive of is the idea of interaction between a point test mass and a gravitational field whose magnitude and direction varies point by point: that is, a gravitational field with a shape. And once you have that idea, combining it with the idea that gravitational fields affect all matter indiscriminately yields a more general idea: that spacetime itself - i.e. the aggregate of all the spatiotemporal relationships between each of the pieces of matter you're interested in making predictions about - is most naturally described using a geometry that is not Euclidean.
When we speak of a region of spacetime being curved, what we mean is that any model of the behaviour of the observable features of that region leads to an inconsistency between (a) the observer independence of the speed of light in a vacuum according to Maxwell and (b) the properties of straight lines and triangles according to Euclid, and we'd rather dump Euclid's intuitively derived fifth postulate than Maxwell's observationally derived electrodynamics.
Which, as it turns out, is a really good idea because it yields the testable prediction that if GR is correct then all information propagation across distance via any conceivable means, not just electrodynamics, can happen no faster than the speed of light and involve a loss of energy at the information source - a prediction which has indeed been tested with respect to information about local distributions of mass, and found to be consistent with observation.
However, the only way that the geometry of spacetime according to GR becomes at all mathematically tractable, if I understand correctly, is by making use of a simplifying assumption that arbitrarily small patches of it in regions of particular interest can be modelled in a Euclidean fashion without causing significant errors, in much the same way as the curvature of the surface of the Earth doesn't stop us measuring triangles drawn on a sheet of paper and finding that their interior angles do indeed sum to 180°. To say that the "laws of physics" "break down" at "singularities" is not to say that the underlying principles are defective, merely that there are regions of interest where it's not feasible to apply them in any reasonable analytical fashion.
accelerating in open space with a zero gravitational field, the pendulums would hang perfectly parallel, and you could use that difference to distinguish the two situations
Yes you could, and per GR the least inconvenient way to model that difference is as one in the shape of the prevailing gravitational fields and, by extension, the local spacetime geometry and the actual meaning, if any, of "parallel".
posted by flabdablet at 7:55 PM on May 27, 2019 [2 favorites]
Since, for example, if you're orbiting the Earth in a satellite with no communication with the outside, and you're observing a horizontal beam with identical pendulums at either end, with very very accurate measurements you might notice that, when completely at rest, the pendulums are not perfectly parallel because both are pointing at the center of the Earth, and that's a slightly different direction at one end of the beam than it is at the other.
What you're describing is a rotating frame of reference in addition to accelerating, which also mucks things up. As I recall, rotating frames get weird, but I don't know the details. An orbiting object is not what you mean to pick for this example anyway, because they're not accelerating, but are in free-fall, which is what creates the microgravity experienced in space.
I don't know for sure, but I bet we could construct some kind of weird rotating frame that has similar effects without the gravitational source
posted by vibratory manner of working at 8:36 PM on May 27, 2019
What you're describing is a rotating frame of reference in addition to accelerating, which also mucks things up. As I recall, rotating frames get weird, but I don't know the details. An orbiting object is not what you mean to pick for this example anyway, because they're not accelerating, but are in free-fall, which is what creates the microgravity experienced in space.
I don't know for sure, but I bet we could construct some kind of weird rotating frame that has similar effects without the gravitational source
posted by vibratory manner of working at 8:36 PM on May 27, 2019
An orbiting object is not what you mean to pick for this example anyway, because they're not accelerating, but are in free-fall
...which, in the context of the specific example you gave, means that your pendulums would not hang from the ends of your beam in any particular direction at all; the only way they'd line up with the gravitational field of the Earth as measured from the surface of the Earth is if you lined them up that way to begin with and then didn't disturb them.
you're orbiting the Earth in a satellite with no communication with the outside, and you're observing a horizontal beam with identical pendulums at either end
A satellite in orbit is in free fall, and if it isn't also spinning and its own mass is small, then its local patch of spacetime is only negligibly non-Euclidean. In other words, from the viewpoint of any observer in or near that satellite who moves as if rigidly attached to it, the local gravitational field is negligibly different from zero.
The meaning of "horizontal" is not well defined under these circumstances.
posted by flabdablet at 10:50 PM on May 27, 2019
...which, in the context of the specific example you gave, means that your pendulums would not hang from the ends of your beam in any particular direction at all; the only way they'd line up with the gravitational field of the Earth as measured from the surface of the Earth is if you lined them up that way to begin with and then didn't disturb them.
you're orbiting the Earth in a satellite with no communication with the outside, and you're observing a horizontal beam with identical pendulums at either end
A satellite in orbit is in free fall, and if it isn't also spinning and its own mass is small, then its local patch of spacetime is only negligibly non-Euclidean. In other words, from the viewpoint of any observer in or near that satellite who moves as if rigidly attached to it, the local gravitational field is negligibly different from zero.
The meaning of "horizontal" is not well defined under these circumstances.
posted by flabdablet at 10:50 PM on May 27, 2019
Can't believe I made that mistake.
If you're sitting on the earth in a lab with no communication with the outside ...
posted by jamjam at 1:11 AM on May 28, 2019
If you're sitting on the earth in a lab with no communication with the outside ...
posted by jamjam at 1:11 AM on May 28, 2019
Ah, here we go, on page 141 of the new SI Brochure (PDF) of the BIPM:
I can just imagine a UFO full of ETs laughing their asses off, or ass-analogs off at least, at our provincial Terra-centrism. Small space-time domain, indeed.
posted by XMLicious at 3:57 AM on May 29, 2019 [1 favorite]
2.3.6 SI units in the framework of the general theory of relativitySo the answer is “just pretend you're on the surface of the Earth all the time and you can call them absolute.”
The practical realization of a unit and the process of comparison require a set of equations within a framework of a theoretical description. In some cases, these equations include relativistic effects.
For frequency standards it is possible to establish comparisons at a distance by means of electromagnetic signals. To interpret the results, the general theory of relativity is required, since it predicts, among other things, a relative frequency shift between standards of about 1 part in 10¹⁶ per metre of altitude difference at the surface of the earth. Effects of this magnitude must be corrected for when comparing the best frequency standards.
When practical realizations are compared locally, i.e. in a small space-time domain, effects due to the space-time curvature described by the general theory of relativity can be neglected. When realizations share the same space-time coordinates (for example the same motion and acceleration or gravitational field), relativistic effects may be neglected entirely.
I can just imagine a UFO full of ETs laughing their asses off, or ass-analogs off at least, at our provincial Terra-centrism. Small space-time domain, indeed.
posted by XMLicious at 3:57 AM on May 29, 2019 [1 favorite]
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