= System of units
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The key thing in a good system of units is to define units in a way that depends only on physical properties of nature.
Ideally (or basically necessarily?) the starting point generally has to be discrete phenomena, e.g.
* number of times some light oscillates per second
* number of steps in a or
What we don't want is to have macroscopics measurement artifacts, (or even worse, the size of body parts! Inset joke) as you can always make a bar slightly more or less wide. And even metals evaporate over time! Though the mad people of the still attempted otherwise well into the 2010s!
Standards of measure that don't depend on artifacts are known as .
= Intrinsic standards
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= Physical constant
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= Unit of measurement
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= Units of measurement
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= Dimension
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{parent=Unit of measurement}
A dimension in a is something like , or , without considering how to assign numerical values ot them, which requires such as the , or .
Talking about dimensions can be useful when explaining new derived units without worrying about the exact units involved. See e.g. this table: https://en.wikipedia.org/w/index.php?title=Lumen_(unit)&oldid=1233810964#SI_photometric_units
= List of systems of units
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= International System of Units
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{parent=List of systems of units}
{title2=SI}
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The key is to define only the minimum number of measures: if you define more definitions become over constrained and could be inconsistent.
Learning the modern SI is also a great way to learn some interesting Physics.
= Origins of Precision by Machine Thinking (2017)
{c}
{parent=International System of Units}
\Video[https://www.youtube.com/watch?v=gNRnrn5DE58]
Great overview of the earlier history of unit standardization.
Gives particular emphasis to the invention of .
= Versions of the international System of Units
{parent=International System of Units}
= 2019 redefinition of the SI base units
{parent=Versions of the international System of Units}
{wiki}
https://web.archive.org/web/20181119214326/https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf gives it in raw:
\Q[
* the unperturbed ground state hyperfine transition frequency of the atom $\Delta v_{Cs}$ is 9 192 631 770 Hz
* the speed of light in vacuum c is 299 792 458 m/s
* the h is 6.626 070 15 × $10^{-34}$ J s
* the elementary charge e is 1.602 176 634 × $10^{-19}$ C
* the k is 1.380 649 × $10^{-23}$ J/K
* the Avogadro constant NA is 6.022 140 76 × $10^{23}$ mol
* the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W,
]
The breakdown is:
* actually use some physical constant:
* \Q[the unperturbed ground state hyperfine transition frequency of the atom $\Delta v_{Cs}$ is 9 192 631 770 Hz]
Defines the in terms of experiments. The beauty of this definition is that we only have to count an integer number of discrete events, which is what allows us to make things precise.
* \Q[the speed of light in vacuum c is 299 792 458 m/s]
Defines the in terms of experiments. We already had the from the previous definition.
* \Q[the h is 6.626 070 15 × $10^{-34}$ J s]
Defines the in terms of the .
* \Q[the elementary charge e is 1.602 176 634 × $10^{-19}$ C]
Defines the in terms of the .
* arbitrary definitions based on the above just to match historical values as well as possible:
* \Q[the k is 1.380 649 × $10^{-23}$ J/K]
Arbitrarily defines temperature from previously defined energy (J) to match historical values.
* \Q[the Avogadro constant NA is 6.022 140 76 × $10^{23}$ mol]
Arbitrarily defines the mol to match historical values. In particular, the is not an exact multiple of the weight of an atom of .
* \Q[the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, is 683 lm/W]
Arbitrarily defines the Candela in terms of previous values to match historical records. The most useless unit comes last as you'd expect.
= Unit of the International System of Units
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= Ampere
{parent=Unit of the International System of Units}
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Unit of .
Affected by the .
= Ampere in the 2019 redefinition of the SI base units
{parent=Ampere}
{tag=2019 redefinition of the SI base units}
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TODO how does basing it on the help at all? Can we count individual electrons going through a wire? https://www.nist.gov/si-redefinition/ampere/ampere-quantum-metrology-triangle by the explains that is it basically due to the following two phenomena/experiments that allows for extremely precise measurements of the :
* , which has [resistances] of type:
$$
R_{xy} = \frac{V_\text{Hall}}{I_\text{channel}} = \frac{h}{e^2\nu}
$$
for integer values of $\nu$.
* , which provides the which equals:
$$
K_{J} = \frac{2e}{h}
$$
= Kilogram
{parent=Unit of the International System of Units}
{wiki}
Unit of .
Defined in the <2019 redefinition of the SI base units> via the . This was possible due to the development of the .
= Avogadro project
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{parent=Kilogram}
{{wiki=Alternative_approaches_to_redefining_the_kilogram#Avogadro_project}}
\Image[https://upload.wikimedia.org/wikipedia/commons/4/41/Silicon_sphere_for_Avogadro_project.jpg]
= Kibble balance
{parent=Kilogram}
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Measures weight from a voltage.
https://www.bipm.org/documents/20126/28432564/working-document-ID-11315/8532173e-8bae-2bdf-b74a-cb48296b4e67
TODO appears to rely on both and
= Dimension of the International System of Units
{parent=International System of Units}
{tag=Dimension (system of units)}
= Luminous intensity
{parent=Dimension of the International System of Units}
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= Candela
{parent=Luminous intensity}
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Candela is density per <#solid angle>. A sphere emitting 1 Candela uniformly in all directions produces 4π total power.
Bibliography:
* on : https://www.reddit.com/r/AskPhysics/comments/u1q7ue/what_is_a_candela_in_more_understandable_terms/
= Lumen
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{parent=Candela}
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= Lumen
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1 equals 683 Lumens of light power at 555 nm. At other wavelengths 1 Watt is less Lumens as it takes into account the sensitivity of the average human eye.
= Candela vs lumen
{parent=Lumen (unit)}
Candela is lumen density per solid angle.
Bibliography:
* on : https://www.reddit.com/r/flashlight/comments/z11gxu/comment/ld0xhaj/
= Weight
{parent=Dimension of the International System of Units}
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= Time
{parent=Dimension of the International System of Units}
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= Frequency
{parent=Time}
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= Period
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{parent=Frequency}
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= Hertz
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{parent=Frequency}
{title2=1857-1894}
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Named after pioneer .
= Hz
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= Megahertz
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= MHz
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Mega-, i.e. a million .
= Clock
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= Quartz clock
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\Video[https://www.youtube.com/watch?v=_2By2ane2I4]
{title=How a quartz watch works by (2017)}
{description=Mentions loop with the for the and an . Also mentions the choice of 32768 ($2^{15}$) as the first power of 2 that is outside of the , and then how a is used to reduce the frequency to get the counter.}
= Atomic clock
{parent=Clock}
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\Video[https://www.youtube.com/watch?v=p2BxAu6WZI8]
{title=How an atomic clock works, and its use in the global positioning system (GPS) by (2012)}
{description=Shows how conceptually an atomic clock is based on a of two states of atoms (non- as clarified by the page). Like a , it also relies on the of quartz, but unlike the , the is not shaped like a , and has a much larger resonating frequency of about 7 . The feedback is completed by producing that at the right frequency to excite the .}
\Video[https://www.youtube.com/watch?v=eOti3kKWX-c]
{title=Inside the 5061A Cesium Clock by (2020)}
{description=
A similar model was used in the to test on two planes flying in opposite directions. Miniaturization was key.
Contains a disposable tube with 6g of . You boil it, so when it runs out, you change the tube, 40k USD. Their tube is made by , so a replacement since that opened in 1999, and the original machine is from the 60s.
Detection is done with an .
https://youtu.be/eOti3kKWX-c?t=1166 They compare it with their 100 dollar disciplined oscillator, since have in them.
}
\Video[https://www.youtube.com/watch?v=Tc_tDVbjCQk]
{title=Quick presentation of the at the (2010)}
{description=Their super accurate setup first does on the atoms.}
= Caesium standard
{parent=Atomic clock}
{tag=Caesium}
{title2=1967}
{title2=3.26 cm}
{wiki}
Uses the of the of ground state, i.e spin up vs spin down of its valence electron $6s^1$, to define the .
definition of the second since 1967, because this is what use.
TODO why does this have more energy than the hyperfine split of the given that it is further from the nucleus?
Why is used:
* https://physics.stackexchange.com/questions/191871/why-do-atomic-clocks-only-use-caesium
= Unit of time
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= Decimal time
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= Second
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{title2=s}
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= Day
{parent=Unit of time}
{title2=d}
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= Calendar
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= Year
{parent=Unit of time}
{title2=y}
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= Length
{parent=Dimension of the International System of Units}
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= Meter
{parent=Length}
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= Micrometer
{parent=Meter}
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= Micron
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= Nanometer
{parent=Meter}
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= nm
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= Angstrom
{parent=Meter}
{title2=Ä}
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= Picometer
{parent=Meter}
{title2=pm}
= Gauge block
{parent=Length}
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Highlighted at the .
= Light year
{parent=Length}
{tag=Astronomical measurement unit}
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= ly
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= kly
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= Geiger counter
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{parent=International System of Units}
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= Natural units
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A series of systems usually derived from the that are more convenient for certain applications.
= Planck units
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{parent=Natural units}
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= Imperial units
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= Imperial unit
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= Imperial system
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