Indeed. No mention of Allan deviation, and no links to references. I found this old reference https://ieeexplore.ieee.org/abstract/document/918181/
Which claims a short term Allan deviation of 5.4e-16/sqrt(tau) for 1-4s. This is pretty impressive and is comparable to Rb or Cs clocks for short time scales. The best optical clocks achieve something like 1e-18/sqrt(tau). Of course, since the sapphire oscillator is not locked to an absolute reference they drift after a few tens of seconds.
Yeah, let's throw some dBc/Hz @ 10kHz offset too for good measure, just to confound the editor :} Aren't stability units grand?
Hey, I'm just glad we heard from them before they got body snatched.
(Context: since you can drop a low-phase-noise clock into a radar and improve the performance, this area of research is one that the spooky defense types pay active attention to. Many physics departments have legends about projects like this suddenly vanishing into classified status.)
The article used simplified explanations and analogies, such as
> Tick, tick, tick. The rhythm of clocks is universal. But how exactly alike are those ticks?
> [...] Precision has to do not with delineating the perfect second but rather with creating extremely regular ticks, or oscillations. Imagine a game of darts. Atomic clocks are able to land all their darts, or oscillations, broadly around the bull's-eye so that the average position is right on target, even though any given dart might be a centimeter or two away from dead center. Luiten's device doesn't aim for the bull's-eye: instead, it is able to land all its darts at exactly the same point on the dartboard. In other words, each tick is really, really, really just like another.
But didn't even once mention the technical term for that in the entire article, making it more difficult to see what the author is talking about for people with an engineering background.
This is simply known as jitter, or phase noise.
It's especially funny given that the IEEE Spectrum's audience is engineering-minded readers.
Something kind of similar I've wondered about is whether, with sufficiently accurate time and distance measurements and a dense-enough network of satellites scattered around Earth and the solar system in general, could one detect the perturbations in the paths of the satellites caused by the transit of massive objects like large-ish asteroids? (One could think of it in science-fiction terms as a detector to counter a cloaking device.)
Perhaps we could "shotgun" a swarm of tiny cubic reflectors, literally just use a controlled explosion to scatter them through the solar system, then track their movements to spot hidden objects. Some may even be drawn in and attach to otherwise dark objects by gravity, allowing them to be more easily tracked.
I'm guessing the issue with that other than the technical challenge would be filling space with too much noise?
Space is really big. You'd need a very large number of tiny reflectors to have a decent chance of any passing close enough to unknown objects to be measurably affected by their gravity.
My intuition would be that there'd be sort of a "birthday paradox" situation at play; if you had a lot of satellites that most of the time aren't close enough to random objects to detect them, eventually as they follow their orbital paths eventually there'll be a high probability that any random asteroid will at some point get close enough to one of them to detect. Maybe you'd be able to say things like "if an asteroid has a mass of a million kilograms and spends most of its time in the inner solar system, then our odds of detecting it within a hundred years is 70%."
Initially, all the unknown, undetected massive objects would contribute background noise that would make small objects harder to find. But as you detect and classify them, they can be accounted for, and then the smaller objects get easier to detect. Then in the end I guess it's a matter of how complete of a catalog of objects can you maintain and simulate, and how precise are the time and distance measurements used to detect gravitational perturbances.
And yeah, given that space is big you'd really want to deploy a ludicrous number of these things if you really want to build a solar-system wide detection network that could spot large-ish interstellar objects as soon as they enter the system, or detect a stealth-material coated asteroid lobbed by some malefactor in a timely manner.
> But for some applications, accuracy is less important than precision. Precision has to do not with delineating the perfect second but rather with creating extremely regular ticks, or oscillations.
I don’t follow here, doesn’t accuracy follow if you have a precise oscillator? What is the difference between an accurate or a precise clock?
It implies that the "tick" intervals in atomic clocks aren't always the same length in time, they just average out very well. While the new sapphire clocks have a more consistent tick interval.
Right. Actually, from what I understand, the situation is even more dire and Cesium clocks are (would be) complete rubbish at timing consecutive ticks, so when people say cesium clock they actually mean a quartz oscillator (ultrapure, double ovenized, binned, aged, etc -- but still quartz) to create the output and then a control loop to push/pull the quartz oscillator and frequency lock it to the cesium absorption line.
A similar trick is more commonly used to lock, say, a 5.8GHz on-chip oscillator to a 10MHz quartz oscillator, except in this case the quartz oscillator plays the role of long-term reference and the on-chip VCO plays the role of short-term reference, whereas in the case of an atomic clock it's the other way around.
The overall game is that different filters/oscillators are better at different timescales, so you use control loops to synthesize the best parts of each of them into a clock that is good at all timescales.
Cesium beam atomic clocks are actually just a very selective band pass filter / detector. There is a DC output in microamperes which is proportional to how well centered the input frequency is in relationship to the resonance of the Cesium atoms in the ambient conditions as they drift across the tube. To use this filter as a clock, it is slaved to a quartz oscillator which is them multiplied and phase locked, with a small bit of FM at 137 hz prior to being fed into the tube. If the frequency is too low, the output will be in phase with the FM, if the frequency is too high, the phase will be opposite, and if it is centered, there will be a 274 hz "2x" output, which is used to indicate lock.
Thus, the cesium isn't actually sampled at ~9.192 Ghz, but rather a much slower rate. The actual loop maintaining phase is as slow as possible to keep phase noise down, which is part of why they take a while to lock on startup.
Further complicating things is the need for a small persistent magnetic field in the tube, as getting zero in all 3 dimensions is a much harder problem. This bias keeps things stable, but also changes the frequency slightly, but is offset out in the divider chain.
Well, in other electronic device, say one type of temperature sensor, let's say microchip's MCP9701A you can have accuracy of +/-2 Celcius with a precision of 0,01V per Celcius.
In this case Accuracy mean the reference as in: this device reads 10C but could actual temperature could be 8 or 12.
Because it drift according to multiple factors.
Precision means the linearity or if you prefer resolution (I think). Datasheet for the device says +/-0,5C meaning you can't have a reading more precise than 1C with that device.
I think the term linearity apply if you try to mesure below that value: the reading may become non-linear because of fluctuaction, noise or other errors in the device.
No. A precise oscillator ticks as close to the second mark as it can, but may be biased in one direction or another consistently. A precise clock can be thought of as a ruler with graduations down to millimetres, where every millimetre is 1% too short. In an accurate clock (like atomic clocks) every millimetre may be 10% too long or too short, but in a random direction.
In the precise ruler if you measure out a 1000 milimeters you will be 1 milimeter short. In the accurate ruler you will be 1/10th of a millimetre long or short.
Both are useful. If you're a carpenter measuring a space to put a cabinet in and you use the same ruler to measure the openings as to cut the cabinet you'd rather the ruler be precise than accurate. If you email those measurements to someone else you'd rather the ruler be accurate than precise.
If you try to talk yourself through how you'd actually accomplish that then you'd quickly see that it is turtles all the way down. Every time you discipline the clock for accuracy you trade some precision to do so - because that is the only way to move the needle. This isn't a big deal for most, but you'd definitely notice NTP slewing the oscillator frequency in the middle of something like a logic trace running at 10s of MHz - which is why labs generally prefer a precise local time standard that is costly (in dollars and hassle) over a cheaper GPS reliant solution offering better absolute accuracy.
The distinction between precision and accuracy in the article leaves a lot to be desired. Couldn't we just redefine the second to be X number of ticks of this clock?
There could be issues with creating accurate copies of this. You could still get very precisely spaced ticks but not get an accurate measure that could be replicated around the world. A standard doesn’t work well if there’s one extant copy you can compare against. That’s why they’re working so hard to create a new standard kilogram where it could in theory be replicated without reference to the original.
Ironically in terms of this conversation, the new definition of a Kg requires a time measurement.
>The kilogram is the mass of a body at rest whose equivalent energy equals the energy of a collection of photons whose frequencies sum to [1.356392489652×1050] hertz.
Now the units for almost all physical quantities (the few exceptions are those that are not dependent on time, length or force, e.g. angles and amount of substance) are derived from the unit of frequency.
The frequency of an atomic clock with cesium has a conventional value, and the units for the other physical quantities, e.g. length, force, voltage, electrical current, temperature and so on are derived from the unit of frequency by conversion factors that are functions of various universal constants, all of which have conventional values chosen so that the units derived in this way are approximately equal with the units that have been used in the past.
Presumably two different instances of this clock would have different tick rates due to the specific crystal used and it's very difficult to produce two identical crystals.
An atomic clock is very consistent across devices as it exploits the properties of an element which is much more repeatable (just have to have a quantity of the element).
Reminds of the Anne McCaffrey Crystal Singer series where crystals were mined for use in their space-faring technology. Each crystal was unique and would be tuned to a particular use.
What they meant by accuracy and precision was actually about which is the average value and which is the variance of the duration of a clock period.
What you want is that both the average duration of a clock period is exactly a certain fraction of a second and also its variance is very small.
However, you cannot have both in the same clock device.
For atomic clocks, you know very well which is the average value, but the duration of the clock periods has a large variance.
For sapphire clocks, the variance of the duration of the clock periods is very small but the average value is known only approximately.
According to the terminology used in the article, someone who shoots accurately spreads the shots over a large area, but the center of the area is the same as the center of the shooting target.
On the other hand, someone who shoots precisely sends all the shots through the same hole in the shooting target, but that hole is far from the center of the target.
The result of the difficulty of having both high accuracy and high precision in the same clock device is that whenever you measure short times, you must use either quartz clocks for a cheaper solution or sapphire clocks for higher precision (or also hydrogen masers in the past, before the development of sapphire clocks).
Because the average frequency of the precise clock is not known, you must either measure it periodically with an atomic clock and correct digitally the measurement results or you must use a PLL loop to adjust continuously the frequency to be in a certain ratio with the average frequency of the atomic clock.
Related side note: It has always bugged me that the defintion of 1 second, a unit of time, is defined by an atomic oscillation frequency, which is itself a unit x/t. A unit of time refers back to itself in its own definition. My lay understanding is imprecise and I'm sure there's an expert in the wings who could fix it.
Then again most belief systems have a root paradox somewhere within them. Perhaps this is ours.
It has to do with the assumed constancy of the so-called "fine structure constant." Google that for more info.
TL,DR: the only way these atomic resonant frequencies can possibly change is if the fine structure constant varies from place to place, or over time. If that turns out to be the case, the discovery will invalidate, or at least upset, the last 100 years worth of physics and cosmology. It's all but unthinkable.
You might be interested in the book Inventing Temperature by Hasok Chang which looks at similar questions but for temperature instead of time, both historically and philosophically. For example, you can define a temperature scale using the boiling point of water, but how do you know water always boils at the same temperature without a temperature scale? (And of course, it doesn't -- even at constant pressure, liquid water can exceed 100°C without boiling)
Regarding km/l or mpg, see https://what-if.xkcd.com/11/ which points out that the area term of the reciprocal - eg, liters per 100 kilometers - has a more direct physical interpretation:
> "If you took all the gas you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube [in a car which gets 20 MPG]"
WP says, "The second is defined as being equal to the time duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental unperturbed ground-state of the caesium-133 atom." I don't see an oscillation frequency in there; rather, I see a number of periods of a particular color of light.
Now, normally we do specify colors of light as frequencies in just the way you say, some number of oscillations per second (unless those frequencies are higher than about 10 GHz), but we can't do that in this case, because it would make the definition circular in just the way you say. Instead, the color of light in question is specified in terms of a quantum-physical phenomenon that produces a very precise color. The cesium-133 atom doesn't need to look at a clock to see how fast to resonate. If archaeologists from the planet Plarx land on Earth in the 37th century and are trying to figure out how our culture measured time, and this comment is all that remains from our society, well, all they need to do is build a cesium maser and hook it up to a circuit that counts to 9,192,631,770. (Actually, probably someone on Plarx has already published the spectrum of cesium, so they can just see that the oscillation period of its hyperfine transition corresponds to 0.000000038134825 of their zorps, and then they know that a "second" is 350.5594 zorps long.)
We used to do the same thing with the meter: "1650763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum." Usually we give wavelengths in terms of the meter, but in this case we're giving the meter in terms of wavelengths. That's because the wavelength is a physically existing, objective phenomenon, which can be measured by anyone. Now, instead, the meter is defined in terms of the second: a meter is defined as the distance light travels in a vacuum 299,792,458 times in a second. So the Plarxian archaeologists will have to figure out what a "second" is first, if they're working from that definition.
There is a difference between primitive physical quantities and physical quantities whose units are base units.
The primitive physical quantities are those quantities that in a theory of physics cannot be defined as functions of other previously defined quantities.
Therefore any theory of physics starts from a list of primitive physical quantities and the other quantities are defined using the primitive quantities.
Sometimes, during the evolution of physics, previously unknown relationships between quantities are discovered, which cause a previously primitive quantity to be defined now using other quantities, so in the updated theory the number of primitive quantities is reduced.
The most important examples of such cases are the discovery caused by the Oersted experiment that the magnetism is also produced by the electric charge and not by a distinct magnetic charge and the discovery as a consequence of the atomic theory and of the statistical physics that the temperature is not a primitive quantity but one that can be defined based on the distribution of the kinetic energy of an ensemble of particles.
Examples of primitive physical quantities are time, length and force.
When you establish a system of units of measurement for the physical quantities, some units are chosen arbitrary and are designated as base units. The other units are derived from them using the relationships that exist between physical quantities during various kinds of experiments.
What confuses many people, including you, is that there exists absolutely no relationship between the quantities that are primitive and the quantities whose units are chosen to be base units.
In a theory of physics, the number of primitive quantities is fixed, but the number of base units is completely arbitrary.
There might be e.g. 10 primitive quantities, but one may choose to have 0, 1, 2, 10, 20 or 50 base units.
Having too many base units makes the computations inconvenient, because in each relationship between quantities an extra base unit may introduce an extra arbitrary multiplication factor, a.k.a. "universal constant".
The systems with too few base units are disliked by many people because the units for many frequently used physical quantities become either very large or very small in comparison with the usual values, or they just become too different from the traditional units used for those quantities.
So the SI is a balance between these 2 conflicting requirements. It has much more base units than necessary but much less than the traditional systems of units that existed before SI.
The base units are chosen so that it is possible to make some devices that realize the units with high accuracy and precision.
Because of this requirement, the quantities with base units are very seldom also primitive quantities.
For a very long time, the length was both a primitive quantity and one whose unit was a base unit, because you could choose some stick or rod as the base unit for length.
Because any object has a length that is variable in time when measured with high precision, this had to be abandoned and the length does not have a base unit now (in reality it does not have a base unit, even if the SI definition attempts to preserve the illusion that the length still has a base unit).
For time, it was never possible to keep with you a certain time so the base unit has always been not for time but for the period of a periodic system or, equivalently, for its frequency. In the beginning the periodic phenomenon was the rotation of the Earth, then it was the revolution of the Earth around the Sun, then an atomic clock. The unit of time has always been derived from the unit of frequency (or of period).
The confusion for those who are not aware how the systems of units of measurement work is greatly enhanced by the definitions of the SI units, which, in an attempt to reduce the confusion (?!) define the units for the same physical quantities that were chosen to have base units at the creation of the SI, even if in fact most of them...
The thing about the AU military using this to replace a quartz frequency standard seems lacking in detail. They can get a matchbox sized rubidium standard for a couple of K$ which has to be a fraction of the cost and headache of this cryogenic thing. Maybe the new thing is even better, but is it by enough to matter?
It appears the resonance has a small, but predictable temperature dependence, you could therefor phase lock this to an atomic clock, if you have a slow enough control loop to keep the phase noise very low, and have the best of both worlds.
There’s a difference in phase locking and frequency locking. It’s hard to phase lock to an atomic reference for long periods of time. Usually atomic clocks offer correction of the frequency drift of the oscillator. So the phase of the oscillator can still wander over large time scales.
Atomic clocks have no phase to lock onto, they are narrowband RF detectors, built of a stream of atoms (or a cloud in the newer Cesium Cell clocks) unlike Quartz oscillators which are always vibrating.
54 comments
[ 4.1 ms ] story [ 102 ms ] threadImpressive accomplishment.
Hey, I'm just glad we heard from them before they got body snatched.
(Context: since you can drop a low-phase-noise clock into a radar and improve the performance, this area of research is one that the spooky defense types pay active attention to. Many physics departments have legends about projects like this suddenly vanishing into classified status.)
> Tick, tick, tick. The rhythm of clocks is universal. But how exactly alike are those ticks?
> [...] Precision has to do not with delineating the perfect second but rather with creating extremely regular ticks, or oscillations. Imagine a game of darts. Atomic clocks are able to land all their darts, or oscillations, broadly around the bull's-eye so that the average position is right on target, even though any given dart might be a centimeter or two away from dead center. Luiten's device doesn't aim for the bull's-eye: instead, it is able to land all its darts at exactly the same point on the dartboard. In other words, each tick is really, really, really just like another.
But didn't even once mention the technical term for that in the entire article, making it more difficult to see what the author is talking about for people with an engineering background.
This is simply known as jitter, or phase noise.
It's especially funny given that the IEEE Spectrum's audience is engineering-minded readers.
Those deviations must then be caused by unknown objects.
Deducing where a large enough such object is seems entirely possible.
I'm guessing the issue with that other than the technical challenge would be filling space with too much noise?
Initially, all the unknown, undetected massive objects would contribute background noise that would make small objects harder to find. But as you detect and classify them, they can be accounted for, and then the smaller objects get easier to detect. Then in the end I guess it's a matter of how complete of a catalog of objects can you maintain and simulate, and how precise are the time and distance measurements used to detect gravitational perturbances.
And yeah, given that space is big you'd really want to deploy a ludicrous number of these things if you really want to build a solar-system wide detection network that could spot large-ish interstellar objects as soon as they enter the system, or detect a stealth-material coated asteroid lobbed by some malefactor in a timely manner.
With that done, maybe you don't even need separate man made probes.
Not sure how hard making and tracking those trackers would be.
I don’t follow here, doesn’t accuracy follow if you have a precise oscillator? What is the difference between an accurate or a precise clock?
A similar trick is more commonly used to lock, say, a 5.8GHz on-chip oscillator to a 10MHz quartz oscillator, except in this case the quartz oscillator plays the role of long-term reference and the on-chip VCO plays the role of short-term reference, whereas in the case of an atomic clock it's the other way around.
The overall game is that different filters/oscillators are better at different timescales, so you use control loops to synthesize the best parts of each of them into a clock that is good at all timescales.
Thus, the cesium isn't actually sampled at ~9.192 Ghz, but rather a much slower rate. The actual loop maintaining phase is as slow as possible to keep phase noise down, which is part of why they take a while to lock on startup.
Further complicating things is the need for a small persistent magnetic field in the tube, as getting zero in all 3 dimensions is a much harder problem. This bias keeps things stable, but also changes the frequency slightly, but is offset out in the divider chain.
In this case Accuracy mean the reference as in: this device reads 10C but could actual temperature could be 8 or 12. Because it drift according to multiple factors.
Precision means the linearity or if you prefer resolution (I think). Datasheet for the device says +/-0,5C meaning you can't have a reading more precise than 1C with that device. I think the term linearity apply if you try to mesure below that value: the reading may become non-linear because of fluctuaction, noise or other errors in the device.
In the precise ruler if you measure out a 1000 milimeters you will be 1 milimeter short. In the accurate ruler you will be 1/10th of a millimetre long or short.
Both are useful. If you're a carpenter measuring a space to put a cabinet in and you use the same ruler to measure the openings as to cut the cabinet you'd rather the ruler be precise than accurate. If you email those measurements to someone else you'd rather the ruler be accurate than precise.
That's done, for now: https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_ba...
>The kilogram is the mass of a body at rest whose equivalent energy equals the energy of a collection of photons whose frequencies sum to [1.356392489652×1050] hertz.
The frequency of an atomic clock with cesium has a conventional value, and the units for the other physical quantities, e.g. length, force, voltage, electrical current, temperature and so on are derived from the unit of frequency by conversion factors that are functions of various universal constants, all of which have conventional values chosen so that the units derived in this way are approximately equal with the units that have been used in the past.
An atomic clock is very consistent across devices as it exploits the properties of an element which is much more repeatable (just have to have a quantity of the element).
https://en.wikipedia.org/wiki/Crystal_Singer
What you want is that both the average duration of a clock period is exactly a certain fraction of a second and also its variance is very small.
However, you cannot have both in the same clock device.
For atomic clocks, you know very well which is the average value, but the duration of the clock periods has a large variance.
For sapphire clocks, the variance of the duration of the clock periods is very small but the average value is known only approximately.
According to the terminology used in the article, someone who shoots accurately spreads the shots over a large area, but the center of the area is the same as the center of the shooting target.
On the other hand, someone who shoots precisely sends all the shots through the same hole in the shooting target, but that hole is far from the center of the target.
The result of the difficulty of having both high accuracy and high precision in the same clock device is that whenever you measure short times, you must use either quartz clocks for a cheaper solution or sapphire clocks for higher precision (or also hydrogen masers in the past, before the development of sapphire clocks).
Because the average frequency of the precise clock is not known, you must either measure it periodically with an atomic clock and correct digitally the measurement results or you must use a PLL loop to adjust continuously the frequency to be in a certain ratio with the average frequency of the atomic clock.
A real weird unit is km/l or miles per gallon, which cancels out to a unit of area.
TL,DR: the only way these atomic resonant frequencies can possibly change is if the fine structure constant varies from place to place, or over time. If that turns out to be the case, the discovery will invalidate, or at least upset, the last 100 years worth of physics and cosmology. It's all but unthinkable.
> "If you took all the gas you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube [in a car which gets 20 MPG]"
Ohms per square is another weird one. https://en.wikipedia.org/wiki/Sheet_resistance#Units
Now, normally we do specify colors of light as frequencies in just the way you say, some number of oscillations per second (unless those frequencies are higher than about 10 GHz), but we can't do that in this case, because it would make the definition circular in just the way you say. Instead, the color of light in question is specified in terms of a quantum-physical phenomenon that produces a very precise color. The cesium-133 atom doesn't need to look at a clock to see how fast to resonate. If archaeologists from the planet Plarx land on Earth in the 37th century and are trying to figure out how our culture measured time, and this comment is all that remains from our society, well, all they need to do is build a cesium maser and hook it up to a circuit that counts to 9,192,631,770. (Actually, probably someone on Plarx has already published the spectrum of cesium, so they can just see that the oscillation period of its hyperfine transition corresponds to 0.000000038134825 of their zorps, and then they know that a "second" is 350.5594 zorps long.)
We used to do the same thing with the meter: "1650763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum." Usually we give wavelengths in terms of the meter, but in this case we're giving the meter in terms of wavelengths. That's because the wavelength is a physically existing, objective phenomenon, which can be measured by anyone. Now, instead, the meter is defined in terms of the second: a meter is defined as the distance light travels in a vacuum 299,792,458 times in a second. So the Plarxian archaeologists will have to figure out what a "second" is first, if they're working from that definition.
The primitive physical quantities are those quantities that in a theory of physics cannot be defined as functions of other previously defined quantities.
Therefore any theory of physics starts from a list of primitive physical quantities and the other quantities are defined using the primitive quantities.
Sometimes, during the evolution of physics, previously unknown relationships between quantities are discovered, which cause a previously primitive quantity to be defined now using other quantities, so in the updated theory the number of primitive quantities is reduced.
The most important examples of such cases are the discovery caused by the Oersted experiment that the magnetism is also produced by the electric charge and not by a distinct magnetic charge and the discovery as a consequence of the atomic theory and of the statistical physics that the temperature is not a primitive quantity but one that can be defined based on the distribution of the kinetic energy of an ensemble of particles.
Examples of primitive physical quantities are time, length and force.
When you establish a system of units of measurement for the physical quantities, some units are chosen arbitrary and are designated as base units. The other units are derived from them using the relationships that exist between physical quantities during various kinds of experiments.
What confuses many people, including you, is that there exists absolutely no relationship between the quantities that are primitive and the quantities whose units are chosen to be base units.
In a theory of physics, the number of primitive quantities is fixed, but the number of base units is completely arbitrary.
There might be e.g. 10 primitive quantities, but one may choose to have 0, 1, 2, 10, 20 or 50 base units.
Having too many base units makes the computations inconvenient, because in each relationship between quantities an extra base unit may introduce an extra arbitrary multiplication factor, a.k.a. "universal constant".
The systems with too few base units are disliked by many people because the units for many frequently used physical quantities become either very large or very small in comparison with the usual values, or they just become too different from the traditional units used for those quantities.
So the SI is a balance between these 2 conflicting requirements. It has much more base units than necessary but much less than the traditional systems of units that existed before SI.
The base units are chosen so that it is possible to make some devices that realize the units with high accuracy and precision.
Because of this requirement, the quantities with base units are very seldom also primitive quantities.
For a very long time, the length was both a primitive quantity and one whose unit was a base unit, because you could choose some stick or rod as the base unit for length.
Because any object has a length that is variable in time when measured with high precision, this had to be abandoned and the length does not have a base unit now (in reality it does not have a base unit, even if the SI definition attempts to preserve the illusion that the length still has a base unit).
For time, it was never possible to keep with you a certain time so the base unit has always been not for time but for the period of a periodic system or, equivalently, for its frequency. In the beginning the periodic phenomenon was the rotation of the Earth, then it was the revolution of the Earth around the Sun, then an atomic clock. The unit of time has always been derived from the unit of frequency (or of period).
The confusion for those who are not aware how the systems of units of measurement work is greatly enhanced by the definitions of the SI units, which, in an attempt to reduce the confusion (?!) define the units for the same physical quantities that were chosen to have base units at the creation of the SI, even if in fact most of them...
Out of stock at Sparkfun, but this is the rubidium thing I'm referring to: https://www.sparkfun.com/products/14830