## 2073: "Kilogram"

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Pfhorrest
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### Re: 2073: "Kilogram"

If by pi you don't mean a specific number defined as exactly what it is defined as (which therefore couldn't drift), but the measured ratio of a circle's diameter to its circumference, then it's super easy to imagine what would make that drift across time and space, and we've seen it already: curvature of space. That ratio is only exactly 3.14159265358979... in perfectly flat space.
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rmsgrey
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### Re: 2073: "Kilogram"

Pfhorrest wrote:If by pi you don't mean a specific number defined as exactly what it is defined as (which therefore couldn't drift), but the measured ratio of a circle's diameter to its circumference, then it's super easy to imagine what would make that drift across time and space, and we've seen it already: curvature of space. That ratio is only exactly 3.14159265358979... in perfectly flat space.

How about the period of the function of x given by the sum from n=0 to infinity of (2ix)n/(n!) ?

Or any of the various other ways Pi (or e) turns up naturally once you start delving deeper into mathematics.

Pi as a mathematical entity has been happily divorced from physical reality for centuries - at best, it's the theoretical ratio of an ideal circle's diameter to its circumference in a Euclidean geometry.

If you're allowing exotic geometries, you should also distinguish between internal and external diameters - the former being the length of rope you'd need to cross from side to side; the latter the size gap the shape could fit through.

Eebster the Great
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### Re: 2073: "Kilogram"

If the physical constants are not really constant but vary with time or position, then in the new system, the definitions of the units will vary instead. That's certainly possible, but experiments have made it abundantly clear that this variation must be far less significant than the variation in the mass of the prototype and its replicas. Also, some would argue that conceptually, a variation in the definition of units makes more sense than variation in a constant with physical dimensions.

synp
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### Re: 2073: "Kilogram"

ijuin wrote:Wasn’t the original basis of the kilogram equal to the mass of one thousand cubic centimeters of pure water at one gravity under standard atmospheric conditions?

Sort of. That's the motivation for a relationship between the meter and the kilogram. But the official definition was never that. It was originally something like "The kilogram is the mass of this here chunk of platinum-iridium alloy that we're keeping in a lab in France".

In fact, it's that same chunk of platinum-iridium until next May.

Soupspoon
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### Re: 2073: "Kilogram"

rmsgrey wrote:Pi as a mathematical entity
…is what I was alluding to. Going slightly over-the-top.

Non-flat space gives effectively-altered Pi at the same point (in space and time) depending on which radii you're testing against, and as you tend to zero radius it'll tend to the theoretical perfection.

Which SF novel is it where they hack up a handheld "pimeter" to check suspicions about an alien artefact-ship when they suspect that something is odd with the entrance? Something Rama-like, but I'm also fairly sure it wasn't in the Rama series itself. I never quite knew if that was supposed to be spacial distortion or mathematical 'truth' being tested. It may be that the author never knew, of course.

synp wrote:In fact, it's that same chunk of platinum-iridium until next May.
That's Ok. Brexit is in March, so it won't matter to us!

(j/k)

reval
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### Re: 2073: "Kilogram"

Pfhorrest wrote:That ratio is only exactly 3.14159265358979... in perfectly flat space.

So when a US State Legislature declares pi equal to three, they are making a rather drastic statement about the curvature of the local space-time? Presumably due to the extreme density of local braincases. Are they, at this point, near a Schwartzschild radius? It may be a self-correcting problem. It least there will be no resulting information-loss problem.

kaloo
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### Re: 2073: "Kilogram"

I've honestly always been annoyed that kg is the SI unit for mass. Shouldn't the Gram be the unit we're defining with our arbitrary nonsense?

hetas
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### Re: 2073: "Kilogram"

rmsgrey wrote:For practical applications, it won't make a difference; for experimental physicists, it'll mean it's easier to recalibrate their equipment to keep it correct since it'll be possible by performing an experiment with a known result rather than requiring access to a specific chunk of metal (or an extremely high-quality copy).

At the moment it seems the equipment to perform that experiment is much harder to get than the metal chunk. But that will change in the future and at some point we'll be able to calibrate our smart-scales with our smart phones.

Eebster the Great
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### Re: 2073: "Kilogram"

Of course a weight standard is easier to get than a watt balance, but that weight standard will still be all you need. It's just that somewhere down the chain, that standard has been compared against either a watt balance or a prototype. The NIST claims that at first, the error in realization will actually be greater than it used to be, but that improvements in technology should bring this down, and that the error in realizing very small masses might already be less.

Cougar Allen
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### Re: 2073: "Kilogram"

reval wrote:
Pfhorrest wrote:That ratio is only exactly 3.14159265358979... in perfectly flat space.

So when a US State Legislature declares pi equal to three, they are making a rather drastic statement about the curvature of the local space-time? Presumably due to the extreme density of local braincases. Are they, at this point, near a Schwartzschild radius? It may be a self-correcting problem. It least there will be no resulting information-loss problem.

There is a little bit of truth to that story....
https://www.snopes.com/fact-check/alabamas-slice-of-pi/
https://en.wikipedia.org/wiki/Indiana_Pi_Bill

tsotate
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### Re: 2073: "Kilogram"

rmsgrey wrote:For practical applications, it won't make a difference; for experimental physicists, it'll mean it's easier to recalibrate their equipment to keep it correct since it'll be possible by performing an experiment with a known result rather than requiring access to a specific chunk of metal (or an extremely high-quality copy).

Well, yes and no. Last I checked (which was admittedly more than a year ago), there were exactly two watt balances of sufficient accuracy and precision to get the new kg definition. NIST has one, and the other is in Canada.

Vo2max
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### Re: 2073: "Kilogram"

rmsgrey wrote:...the standard kilogram is known to have changed mass over time (exactly how much is unclear)

Well no, the standard kilogram has always stayed at exactly the same mass. Everything else in the universe has slightly changed mass over time.

orthogon
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### Re: 2073: "Kilogram"

Vo2max wrote:
rmsgrey wrote:...the standard kilogram is known to have changed mass over time (exactly how much is unclear)

Well no, the standard kilogram has always stayed at exactly the same mass. Everything else in the universe has slightly changed mass over time.

Well, kind of. I mean, there's the physical concept of mass, and there's the kilogram, the particular (arbitrary) unit of mass in the SI. In terms of the former, the abstract concept, the IPK has most certainly changed mass. It's just that the definition of the kilogram simultaneously changed such that the mass of the IPK, measured in SI units, remained at 1kg.
xtifr wrote:... and orthogon merely sounds undecided.

Vo2max
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### Re: 2073: "Kilogram"

orthogon wrote:
Vo2max wrote:
rmsgrey wrote:...the standard kilogram is known to have changed mass over time (exactly how much is unclear)

Well no, the standard kilogram has always stayed at exactly the same mass. Everything else in the universe has slightly changed mass over time.

Well, kind of. I mean, there's the physical concept of mass, and there's the kilogram, the particular (arbitrary) unit of mass in the SI. In terms of the former, the abstract concept, the IPK has most certainly changed mass. It's just that the definition of the kilogram simultaneously changed such that the mass of the IPK, measured in SI units, remained at 1kg.

It does seem weird though: your mass is only your weight / your acceleration due to gravity, and weight (force) is equivalent across a whole load of other stuff - work, energy, stress/strain of things you're hanging off or sitting on, electrical charge and voltage. So none of that stuff could be precisely defined except by reference to a particular lump of metal in Paris??

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### Re: 2073: "Kilogram"

Flumble wrote:
Quizatzhaderac wrote:To understand all of the English distance units, use this handy-dandy chart.

My little cousin says 3*2*100*10 ≠ 8060, but surely an entire country knows better than someone who just learned long multiplication.
(also I hate the cubit. It has "cube" in the name but isn't a unit of volume.)
Good catch. It looks like the chart is wrong about it's definition of nautical miles. The nautical mile is actually actually one latitude minute (or 1 6^4 * 10 th of the way around the earth) or 6076.12 feet.
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ijuin
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### Re: 2073: "Kilogram"

Vo2max wrote:
orthogon wrote:
Vo2max wrote:
rmsgrey wrote:...the standard kilogram is known to have changed mass over time (exactly how much is unclear)

Well no, the standard kilogram has always stayed at exactly the same mass. Everything else in the universe has slightly changed mass over time.

Well, kind of. I mean, there's the physical concept of mass, and there's the kilogram, the particular (arbitrary) unit of mass in the SI. In terms of the former, the abstract concept, the IPK has most certainly changed mass. It's just that the definition of the kilogram simultaneously changed such that the mass of the IPK, measured in SI units, remained at 1kg.

It does seem weird though: your mass is only your weight / your acceleration due to gravity, and weight (force) is equivalent across a whole load of other stuff - work, energy, stress/strain of things you're hanging off or sitting on, electrical charge and voltage. So none of that stuff could be precisely defined except by reference to a particular lump of metal in Paris??

The tricky part is that force (Newtons or whatnot) is generally calibrated with respect to mass in the first place. How would you know the size to make a mass-independent unit of force without resorting to something as arbitrary as a standard physical object or apparatus?

DavidSh
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### Re: 2073: "Kilogram"

Quizatzhaderac wrote:Good catch. It looks like the chart is wrong about it's definition of nautical miles. The nautical mile is actually actually one latitude minute (or 1 6^4 * 10 th of the way around the earth) or 6076.12 feet.

Since the earth is somewhat oblate, the length of a latitude minute varies with latitude. For many years the official British definition of a nautical mile was 6080 feet, which is a nice round number in the range between the length of the shortest latitude minute (at the equator) and the length of the longest latitude minute (at the poles). You have to take the chart as a historical document -- most of the lengths it describes are obsolete.

I suppose you could argue that the latitude minute chosen should be a weighted average over the watery surface of the earth. (Aircraft should use an aeronautical mile instead, averaged over the entire surface of the earth.)

ijuin
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### Re: 2073: "Kilogram"

Having separate nautical and aeronautical miles would create unnecessary confusion in coordinating between surface ships and aircraft especially with regards to naval aviation.

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### Re: 2073: "Kilogram"

hmmm... GPS gives you your actual latitude, right? As in not adjusted for the Earth's oblateness? In which case it would seem to make sense to use the latitude minute definitions for both nautical and aeronautical purposes. (while also using longitude minutes so we can talk about all travel across the earth's surface.)
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Soupspoon
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### Re: 2073: "Kilogram"

https://en.wikipedia.org/wiki/World_Geodetic_System

(I mostly have to consider OSGB conversion, myself.)

SuicideJunkie
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### Re: 2073: "Kilogram"

Quizatzhaderac wrote:hmmm... GPS gives you your actual latitude, right? As in not adjusted for the Earth's oblateness? In which case it would seem to make sense to use the latitude minute definitions for both nautical and aeronautical purposes. (while also using longitude minutes so we can talk about all travel across the earth's surface.)
I'm pretty sure GPS gives you a specific location in all 4 dimensions, given the minimum number of simultaneous satellite signals. (3?) How that is actually displayed in the GUI is completely arbitrary.

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### Re: 2073: "Kilogram"

Soupspoon wrote:This assumes the fundamental constants do remain constant, of course. I know people are on the look-out for such temporal/spacial differences (assuming that they haven't been seen but been misidentified as cosmic inflation or somesuch) but we could be exactly on the verge of getting good enough to finally detect the creep.

It's not quite as hard to imagine as what might cause Pi and/or e to notably drift…

I've hypothesized that the entire universe is inside a black hole, which would mean that Planck's constant should increase slowly as the black hole deflates so that the boundary conditions between the universe and the outer "superverse" are maintained (I guess h could also drop abruptly if the black hole took in significant mass, but the superverse should also be so old that black holes finding each other should be quite unlikely)
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Soupspoon
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### Re: 2073: "Kilogram"

There's a Is The Universe A Black Hole? thread out there.

rmsgrey
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### Re: 2073: "Kilogram"

Vo2max wrote:
orthogon wrote:
Vo2max wrote:
rmsgrey wrote:...the standard kilogram is known to have changed mass over time (exactly how much is unclear)

Well no, the standard kilogram has always stayed at exactly the same mass. Everything else in the universe has slightly changed mass over time.

Well, kind of. I mean, there's the physical concept of mass, and there's the kilogram, the particular (arbitrary) unit of mass in the SI. In terms of the former, the abstract concept, the IPK has most certainly changed mass. It's just that the definition of the kilogram simultaneously changed such that the mass of the IPK, measured in SI units, remained at 1kg.

It does seem weird though: your mass is only your weight / your acceleration due to gravity, and weight (force) is equivalent across a whole load of other stuff - work, energy, stress/strain of things you're hanging off or sitting on, electrical charge and voltage. So none of that stuff could be precisely defined except by reference to a particular lump of metal in Paris??

There's two types of mass: there's gravitational mass - how strongly a body attracts other gravitational masses; and there's inertial mass - how a body responds to forces (including gravitational). The two are interchangeable (either as an intrinsic element as in general relativity, or as a specific assumption) in practice but it's still conceivable that there could be objects or circumstances where the two aren't coupled (particularly one where an object with no inertial mass has a gravitational mass or vice versa).

And, as ijuin said, the problem with using electromagnetic effects to determine mass is that they're calibrated in terms of effect on a known mass to start with. For example, a spring-balance uses the extension of a spring to measure the exerted force - the (ultimately electromagnetic) force exerted by the spring is simply related to its extension and equals the force (usually weight) being measured, but determining the force a given spring exerts from theory rather than by weighing a known mass would require a lot of precise measurements...

scarletmanuka
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### Re: 2073: "Kilogram"

Soupspoon wrote:Which SF novel is it where they hack up a handheld "pimeter" to check suspicions about an alien artefact-ship when they suspect that something is odd with the entrance? Something Rama-like, but I'm also fairly sure it wasn't in the Rama series itself. I never quite knew if that was supposed to be spacial distortion or mathematical 'truth' being tested.

Eon, by Greg Bear. And it was pretty clearly spacial distortion; there's a massive spacial distortion (the "flaw") running down the whole length of the seventh chamber. The whole, very long length of the seventh chamber...

The novel where testing the mathematical version comes into play is Contact.

kaloo wrote:I've honestly always been annoyed that kg is the SI unit for mass. Shouldn't the Gram be the unit we're defining with our arbitrary nonsense?

The cgs system was tried for a while, but that of course has the same problem with centimetre. As normal human activities go, m and kg fit a wider range of activities than cm and g, so here we are.

GlassHouses
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### Re: 2073: "Kilogram"

scarletmanuka wrote:
kaloo wrote:I've honestly always been annoyed that kg is the SI unit for mass. Shouldn't the Gram be the unit we're defining with our arbitrary nonsense?

The cgs system was tried for a while, but that of course has the same problem with centimetre. As normal human activities go, m and kg fit a wider range of activities than cm and g, so here we are.

Sure, but that doesn't answer the question of why certain units were defined with such inconvenient magnitudes in the first place.

The meter was defined as 1/10,000,000 of the distance between the North Pole and the Equator. They could have easily picked a different power of 10, but chose that specific one because it yielded a unit that was within the same order of magnitude as commonly used existing units like the foot or the ell.

So why define the unit of mass, the gram, to be something so small? Why define it as the mass of one cubic centimeter of water, and not a cubic decimeter?

It seems to me like they just screwed up on that one.

Soupspoon
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### Re: 2073: "Kilogram"

rmsgrey wrote:and there's inertial mass - how a body responds to forces (including gravitational)

You could say otherwise (than the parenthetical).

A bigger (gravitational) mass in a gravitational field (of another mass) is feeling a bigger pull because it is more mass being pulled (and, in turn, pulling back, in an equalisation of force). But, being a larger (inertial) mass its acceleration is less than if it were gravitationally attracted the same but with less inertia.

Cancelling out, this gravitationally-attracted inertial mass falls (in the absence of mass-unrelated effects) at the same speed/acceleration as all other masses. For the purposes of falling, alone, having a mass is a binary thing. Quantity does not effect your fall. The body(/ies) being fell upon are affected by your-body's mass magnitude, but their own counter-fall towards the barycentre still only relies upon the cumulation of masses that are not themself, because the counterpart tug of the gravity they provide to others is counter-counted by their inertial stubbornness in equal measure.

Under a Classical model, at least. Relativity might cause issues, but then stuff always gets weirder if it comes into play.)

((The above sat around unposted overnight, still looks right in the light of day. Meanwhile, yup: Eon sounds right, including the details I'd forgotten in the tumpty-tump years since I think I read it.))

Kit.
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### Re: 2073: "Kilogram"

GlassHouses wrote:So why define the unit of mass, the gram, to be something so small? Why define it as the mass of one cubic centimeter of water, and not a cubic decimeter?

...and not a cubic meter?

Probably because it is more convenient for cooking.

Old Bruce
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### Re: 2073: "Kilogram"

Kit. wrote:
GlassHouses wrote:So why define the unit of mass, the gram, to be something so small? Why define it as the mass of one cubic centimeter of water, and not a cubic decimeter?

...and not a cubic meter?

Probably because it is more convenient for cooking.

And stuff is cheaper by the gram than the kilogram if you are doing experiments (up until The Terror catches up with you).

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### Re: 2073: "Kilogram"

SuicideJunkie wrote:I'm pretty sure GPS gives you a specific location in all 4 dimensions
That's not really an answer to my question about which coordinate system is being used. Lots of coordinate systems use 4 dimensions.

After looking it up, GPS uses modified spherical coordinates. So a GPS latitude unit is indeed slightly longer near the equator than the poles. The modifications mostly affect altitude (so sea level is the same altitude at the equator and the poles).

So if we defined the nautical mile as a latitude or longitude minute that would work really well with GPS.

Of course we could design GPS receivers to use use a different coordinate system (without changing the satellites) to be some kind of psuedo-latitude where each unit is the same geodesic distance and slightly different angular distance.
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rmsgrey
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### Re: 2073: "Kilogram"

Soupspoon wrote:
rmsgrey wrote:and there's inertial mass - how a body responds to forces (including gravitational)

You could say otherwise (than the parenthetical).

A bigger (gravitational) mass in a gravitational field (of another mass) is feeling a bigger pull because it is more mass being pulled (and, in turn, pulling back, in an equalisation of force). But, being a larger (inertial) mass its acceleration is less than if it were gravitationally attracted the same but with less inertia.

Cancelling out, this gravitationally-attracted inertial mass falls (in the absence of mass-unrelated effects) at the same speed/acceleration as all other masses. For the purposes of falling, alone, having a mass is a binary thing. Quantity does not effect your fall. The body(/ies) being fell upon are affected by your-body's mass magnitude, but their own counter-fall towards the barycentre still only relies upon the cumulation of masses that are not themself, because the counterpart tug of the gravity they provide to others is counter-counted by their inertial stubbornness in equal measure.

Under a Classical model, at least. Relativity might cause issues, but then stuff always gets weirder if it comes into play.)

((The above sat around unposted overnight, still looks right in the light of day. Meanwhile, yup: Eon sounds right, including the details I'd forgotten in the tumpty-tump years since I think I read it.))

So far as gravity exerts a force on an object based on its (gravitational) mass, the object's acceleration under that force is determined by its (inertial) mass. Under classical mechanics, the fact the two masses are in fixed proportion (numerically equal with appropriate units chosen) is an empirical fact that could be discarded without a radical overhaul of theory - all that would be needed is to distinguish which mass is involved in any given reference, and insert the ratio of masses where they formerly cancelled.

In General Relativity, gravity is geometry rather than force, and acceleration due to gravity is an illusion caused by a misperception of the geometry - gravity warps space-time such that an object moving in a straight line in that warped space-time appears to be accelerating if space-time is assumed to be flat. Since the (apparent) acceleration is directly set, the apparent force of gravity is exactly that required to produce that acceleration of the inertial mass, making the cancellation no coincidence.

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### Re: 2073: "Kilogram"

rmsgrey wrote:So far as gravity exerts a force on an object based on its (gravitational) mass, the object's acceleration under that force is determined by its (inertial) mass. Under classical mechanics, the fact the two masses are in fixed proportion (numerically equal with appropriate units chosen) is an empirical fact that could be discarded without a radical overhaul of theory
Isn't that what the gravitational constant does?

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### Re: 2073: "Kilogram"

IIRC the gravitational constant is, like most (all?) constants of proportionality, basically just a fudge to mesh our unnatural units together with each other, and in the system of natural units is just 1.
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### Re: 2073: "Kilogram"

Quizatzhaderac wrote:That's not really an answer to my question about which coordinate system is being used. Lots of coordinate systems use 4 dimensions.
The unquoted half of what I said is what's relevant there. The raw math of satellite signal differences doesn't inherently require a specific display format.

xtifr
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### Re: 2073: "Kilogram"

Pfhorrest wrote:If by pi you don't mean a specific number defined as exactly what it is defined as (which therefore couldn't drift), but the measured ratio of a circle's diameter to its circumference, then it's super easy to imagine what would make that drift across time and space, and we've seen it already: curvature of space. That ratio is only exactly 3.14159265358979... in perfectly flat space.

The measured ratio of a [etc.] isn't that precise in any case, due to quantum. We can't accurately measure things smaller than Planck's length--we're not even sure it makes sense to talk about distances smaller than that--and it doesn't take all that many digits of pi to calculate the size of the universe to within a Planck's length. We have calculated digits of pi far beyond anything that can be considered meaningful in this universe.

Physically, pi might be considered not a transcendental number, nor even an irrational, but a simple rational number with an error bar of ±1.0e-fairlylargenumber.

And that's before you even start to consider the curvature of space.
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### Re: 2073: "Kilogram"

SuicideJunkie wrote:The unquoted half of what I said is what's relevant there. The raw math of satellite signal differences doesn't inherently require a specific display format.
I'm pretty sure GPS gives you a specific location in all 4 dimensions, given the minimum number of simultaneous satellite signals. (3?) How that is actually displayed in the GUI is completely arbitrary.
Correct, the raw satellite signal differences don't require a specific coordinate system. The raw satellite signals are also not GPS; GPS is a system for global positioning, which includes standards to systemically derive a position on the globe from those signals.

The phrase "all four dimensions" is meaningless without a coordinate system; there're not a finite number of dimensions, so the only way you can have all of them is within a specific context.
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Eebster the Great
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### Re: 2073: "Kilogram"

We refer to the base unit of mass as the kg rather than the g due to a historical accident. The original base unit of mass was called the "grave," with 1 grave = 1000 gravat and 1 bar = 1000 grave. The theory as to why in the redefinition in 1795, the "gravat" rather than the "grave" was pegged to the gram is unclear, but I remember there being political overtones.

Regardless, obviously the system we got in the end doesn't make sense.

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### Re: 2073: "Kilogram"

ucim wrote:
rmsgrey wrote:So far as gravity exerts a force on an object based on its (gravitational) mass, the object's acceleration under that force is determined by its (inertial) mass. Under classical mechanics, the fact the two masses are in fixed proportion (numerically equal with appropriate units chosen) is an empirical fact that could be discarded without a radical overhaul of theory
Isn't that what the gravitational constant does?

Jose

The gravitational constant relates (gravitational) mass to force and distance in the same way as Coulomb's constant relates (electric) charge to force and distance. In principle there could be a constant relating force, (inertial) mass and acceleration, but, because we define force in terms of (inertial) mass and acceleration, the constant disappears, and, if you take the units of force as being kg.m.s-2 it's also dimensionless.

MJPerry
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### Re: 2073: "Kilogram"

Steve the Pocket wrote:Ironically, pints are one unit of measurement us yanks don't much bother with. The standard unit of measurement for beer in America is the beer.

Yeah you guys are super-bad at drinking. I blame the high legal age.

ijuin
Posts: 1107
Joined: Fri Jan 09, 2009 6:02 pm UTC

### Re: 2073: "Kilogram"

America is a country where the normal serving size for beer is neither one glass nor one bottle, but rather the pack of bottles in which they are sold. Drinking six to twelve bottles or tins at once is quite common among enthusiasts.