Replacing the Measurement standards (SI units)

[akardos]

What might be better foundational units given the knowledge we now have and disregarding legacy, human-scale units. Perhaps setting some known constants to be the base unit of 1 in that measure. For example, the second, based on the unperturbed ground-state hyperfine transition frequency of the cesium-133 atom. What if we could redefine it to some other more common universal (perhaps hydrogen), easier to measure yet with same reliable constant without the constraint of keeping the same legacy length of time? Have there been attempts to do this already?
Ditto with all of the other six foundational measures,
Length - meter (m)
Amount of substance - mole (mole)
Electric current - ampere (A)
Temperature - kelvin (K)
Luminous intensity - candela (cd)
Mass - kilogram (kg)

 

[f95toli]

In what way would a system of units that "disregard legacy, human-scale units" be better?

Also, the definition of the second (which will change in a few years) WAS chosen because Cs-133 is relatively easy to measure with high precision.
Note also that the realisation of the second DOES use hydrogen in the form of hydrogen masers. A metrology grade atomic clock consists of a a Cs-133 fountain as well as one or more hydrogen masers; the latter provide the actual signal whereas the fountain ensures long term stability

All the other SI units refer back to the second; e.g. the ampere is defined as the number of charges per second.

 

[dextercioby]

Well, fixing the irreducible fundamental constants numerically and redefining units with respect to them is/was a major step forward. It all started with the exact definition of the second which put a 10 digit (in billions/milliards) natural number suppressing all possible effects of experimental uncertainty/imprecision.

 

[Ibix]

If you weren't concerned with keeping the new SI consistent with the old you could round off all the silly numbers - so 1s could be defined as 9,000,000,000 cycles of the caesium transition, and $c$ could be defined as 300,000,000m/s, etc. It's a bad idea in the real world because it's a recipe for problems like inch-to-metric, but if you don't care about that it's a bit simpler.

Something physicists routinely do is work in units where $c=1$ (e.g. seconds and light seconds), or even $c=G=1$ or $c=\hbar=1$. That kind of thing is very convenient for physicists, but bad for everyday measures - for example, 30mph is 0.000000044 ls/s in such a system, and no-one wants to work with numbers like that. (Edit: you could call it 44 nano-lights, I suppose.)

Basically, "better" is an application dependent word. I use $c=1$ units a lot in physics, imperial for every day speeds and distances and for volumes of milk or beer (half a liter just don't satisfy) and SI for almost everything else. I could reduce that to $c=1$ and SI if there were a little less social conservatism in my country, but I'd never want to choose one for all applications.

 

[Twigg]

definition of the second (which will change in a few years)

"Sometime this decade, probably" might be a little more realistic. Still a lot to be done, especially on portable clocks.

Defining a unit system with hydrogen as a baseline is essentially what atomic units (https://en.wikipedia.org/wiki/Hartree_atomic_units) are. There's no reason to make these numbers fundamental. After all, hydrogen makes a subpar atomic clock AFAIK, so you would lose precision in the experimental realization of the second compared to cesium.

Edit: In hindsight, I realize hydrogen masers are a key ingredient in the cesium fountain clock. I meant that hydrogen doesn't have good narrow-line clock transitions like cesium does. Hydrogen makes a good gain medium, not a good clock.

 

[gmax137]

If you weren't concerned with keeping the new SI consistent with the old you could round off all the silly numbers - so 1s could be defined as 9,000,000,000 cycles of the caesium transition, and c could be defined as 300,000,000m/s,

Still anthropomorphic; 300,000,000 looks "silly" in Base 8 (2170321400) so our three-fingered two-thumbed friends from planet Zelda won't be impressed.

 

[Ibix]

Still anthropomorphic; 300,000,000 looks "silly" in Base 8 (2170321400) so our three-fingered two-thumbed friends from planet Zelda won't be impressed.

Sure, but $3\times 12^{10}$ isn't too bad. I must admit I haven't checked if the actual standard is a round number in any base...

 

[bob012345]

I have always felt we should have metric time.

 

[f95toli]

"Sometime this decade, probably" might be a little more realistic. Still a lot to be done, especially on portable clocks.

Very possible. Some of the people I know who work on optical clocks are a bit more optimistic; but it is indeed the case that they are also still working on multiple systems and no one can agree what would be best system to use for the new realization . That said, the fact that a change wouldn't fundamentally alter the SI in any way means that it should be a relatively straightforward change. One would of course also need to give the worlds NMIs the time needed to build a bunch of clocks.

 

[Twigg]

but it is indeed the case that they are also still working on multiple systems and no one can agree what would be best system to use for the new realization

It's more a matter of atomic species than of the experimental apparatus. After all, the SI units are defined by natural phenomena, not by our machines. Right now, my understanding is that the biggest hurdle is comparing the different cutting edge clocks for consistency. What's needed are more portable clock systems that can be transported from one site to the next to perform the comparisons, or some means of comparing local oscillator phases across continents.

Some of the people I know who work on optical clocks are a bit more optimistic

They might be right! Maybe the portable clocks will be up an running sooner than I expect

 

[f95toli]

They might be right! Maybe the portable clocks will be up an running sooner than I expect

I am definitely not an expert here, but my understanding that most of the focus (at least in Europe) is on better fibre links rather than portable clocks (I know of several projects working on the latter, but they are all for sensing and/ort fundamental physics) or even better satellite links (which seems very hard). I have been in various clock labs, and making a portable version of say a Sr lattice clock with the required precision (say 1 part on 10^18) seems like a daunting task...

 

[Twigg]

I only just started working on clocks last year, so I totally could be wrong about this. I hope I didn't mess that up. I'll ask my more senior coworkers about it and follow up. Sorry!

portable version of say a Sr lattice clock with the required precision (say 1 part on 10^18) seems like a daunting task...

I think it's not as bad as it sounds, because you can phase-reference the local oscillator of the portable clock to the local oscillator of the clock you're comparing it to? I'll double check and follow up.

 

[olgerm]

My idea for unitsystem:
for first I set unmultiplied units so that
$h=1$ Planck constant
$c=1$ speed of light
$k_b=1$ bolzmann constant
$k_E=\frac{1}{2*2\pi}$ Coulomb constant
$k_G=\frac{1}{2*2\pi}$ Newtons gravitational constant.
In this unitsystem many formulas have simpler form than in unitsystem, where $k_E=1$ and $k_G=1$.

conversion of unmultiplied units to SI:
$t_b=c_{SI}^{-5/2}*h_{SI}^{1/2}*k_{G\ SI}^{1/2}*(2\pi)^{1/2}*2^{1/2} \approx 4.79042770714*10^{-43}*s$ time unit
$l_b=c_{SI}^{-3/2}*h_{SI}^{1/2}*k_{G\ SI}^{1/2}*(2\pi)^{1/2}*2^{1/2}\approx 1.436134097196*10^{-34}*m$ length unit
$m_b=c_{SI}^{1/2}*h_{SI}^{1/2}*k_{G\ SI}^{-1/2}*(2\pi)^{-1/2}*2^{-1/2}\approx 1.539006070965*10^{-8}*kg$ mass unit
$q_b=c_{SI}^{1/2}*h_{SI}^{1/2}*k_{E\ SI}^{-1/2}*(2\pi)^{-1/2}*2^{-1/2}\approx 1.326211321739*10^{-18}*C$ electriccharge unit
$T_b=c_{SI}^{5/2}*h_{SI}^{1/2}*k_{G\ SI}^{-1/2}*k_{b\ SI}^{-1}*(2\pi)^{-1/2}*2^{-1/2}\approx 1.001840552719*10^{32}*K$ temperature unit

Now to make units that are more similar to values in everydaylife I multiply unmultiplied units with $2^n$ (n is arbitrarily chosen for every unit). Name of new unit will be name of unmultiplied unit, but n added to lower index of its name.

conversion of multiplied to SI:
$t_{b144}=t_b*2^{144}\approx 10.683010768898102*s$ time unit
$l_{b110}=l_b*2^{110} \approx 0.18642086403260658*m$ length unit
$m_{b28}=m_b*2^{28} \approx 4.131237964462824*kg$ mass unit
$q_{b40}=q_b*2^{40} \approx 1.4581847691398792*10^{-6}*C$ electriccharge unit
$T_{b-104}=T_b*2^{-104} \approx 4.9394552831557474*K$ temperature unit
$F_{b-150}=F_b*2^{-150} \approx 0.0067481914578038016*N$ force unit

physical constants are very easily derivable in this system:

1. take dimension of constant in units that you want to use this constant with $[k_G]=\frac{F_{b-150}*l_{b110}}{m_{b28}^2}$ (solve defining formula $F=\frac{k_G*m_1*m_2}{l^2}$ for constant $k_G=\frac{F*l^2}{m_1*m_2}$ to get it)
2. replace every unit in dimension of constant with $2^{-n}$, where n is n of unit in this unitsystem that you are using(for example n of $q_{b43}$ is 43). $\frac{2^{150}*(2^{-110})^2}{(2^{-28})^2}=2^{-14}=6.103515625*10^{-5}$
3. multiply the value with constants value in unmultiplied system. $2^{-14}*\frac{1}{2*2\pi}=\frac{2^{-15}}{2\pi}$
4. and the value of physical constant has been found $k_G=\frac{2^{-15}}{2\pi}*\frac{F_{b-150}*l_{b110}}{m_{b28}^2} \approx 4.857023409786845*10^{-6}*\frac{F_{b-150}*l_{b110}}{m_{b28}^2}$.

n of force unit or any other unit can be changed independently from n's of other units, but it might create physical constants to formulas, that do not have physical consants in SI system. For example if you used $F_{b-140}$ instead of $F_{b-150}$ , then there would be physical constant in formula $a=2^{10}*\frac{F}{m}$ (Newon's 2. law)good properties of this unitsystem:

• units are defined purely by physical constants without using quantities, that can not be mathematically expressed, but only be measured (like period of radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom is used to define second in SI unitsystem.)
• very easy to convert to natural units
• units are approximately in same size as things in everyday life are
• using this unitsystem gives people more intuition of what dimensional physical constants are
• easy to derive numerical values of physical constants in this unitsystem
• symbol of quantity, that a unit is measuring is derivable from symbol of unit - just remove subscript. for example form symbol of time-unit "$t_{b144}$" to symbol of time "$t$".
• many oftenly used formulas have simpler form in these units (less constants in them).

What do you think of this?

 

[bob012345]

My idea for unitsystem:
for first I set unmultiplied units so that
$h=1$ Planck constant
$c=1$ speed of light
$k_b=1$ bolzmann constant
$k_E=\frac{1}{2*2\pi}$ Coulomb constant
$k_G=\frac{1}{2*2\pi}$ Newtons gravitational constant.
In this unitsystem many formulas have simpler form than in unitsystem, where $k_E=1$ and $k_G=1$.

What do you think of this?

Does setting $h=1$ and $c=1$ give people more or less physical insight to the way the universe works? To me, that is the metric.

 

[olgerm]

Does setting $h=1$ and $c=1$ give people more or less physical insight to the way the universe works? To me, that is the metric.

More I think.
You could define a unitsystem, where there are physical constants in formulas like $s=t*v$ and $a=\frac{F}{m}$, but using this unitsystem would not give people more physical insight to the way the universe works. The more symmetry and less arbitrarity there is in notation, the easier it is to understand physics.

 

[bob012345]

More I think.
You could define a unitsystem, where there are physical constants in formulas like $s=t*v$ and $a=\frac{F}{m}$, but using this unitsystem would not give people more physical insight to the way the universe works. The more symmetry and less arbitrarity there is in notation, the easier it is to understand physics.

I know of a physicist who says years of using $c=1$ has obscured and shielded physicists from a more physical understanding of GR.

 

[olgerm]

I know of a physicist who says years of using $c=1$ has obscured and shielded physicists from a more physical understanding of GR.

I do not know in what context and on which reasons he said that, but generally I disagree.

 

[ohwilleke]

It's a bad idea in the real world because it's a recipe for problems like inch-to-metric, but if you don't care about that it's a bit simpler.

FWIW, the inch was indeed rounded to be a convenient metric value, when it was defined as exactly 0.0254 meters, more precise historic values of the inch be damned.

 

[ohwilleke]

My idea for unitsystem:
for first I set unmultiplied units so that
$h=1$ Planck constant
$c=1$ speed of light
$k_b=1$ bolzmann constant
$k_E=\frac{1}{2*2\pi}$ Coulomb constant
$k_G=\frac{1}{2*2\pi}$ Newtons gravitational constant.
In this unitsystem many formulas have simpler form than in unitsystem, where $k_E=1$ and $k_G=1$.

What do you think of this?

c is not very convenient unit with which to measure highway speed limits and Hurricane air speed. Physicists aren't the primary customers of units of measure.

 

[ohwilleke]

I know of a physicist who says years of using $c=1$ has obscured and shielded physicists from a more physical understanding of GR.

I'd quibble with physicists being the ones misled, but in my science education, the practice standard of always clearly showing your units was drilled into us. While PhD physicists have internalized the units of different quantities, high school students, undergraduates, and even first year graduate students have often not done so. Explicitly keeping track of units on an inline basis in your equations and formulas works a bit like double entry accounting to alert students to the fact that they have done something horribly wrong because their units aren't matching up, and nurtures and reinfoces their understanding of what different quantities represent physically.

Suppressed unit notation is really only appropriate for advanced practitioners.

 

[olgerm]

c is not very convenient unit with which to measure highway speed limits and Hurricane air speed.

Did you read whole my post? c was set to 1 to define unmultplied units. I did not explicitly write that, but (multiplied) unit of speed in his unitsystem would be $v_{b-34}=v_{b}*2^{-34}=c*2^{-34} \approx 0.01745021773967892*m/s$ if you assume n's of other units to be what they are written to be in my post #13 and do not want there to be physical constant in formula $s=v*t$.
n's of units can easily be changed. if you think unit of speed $v_{b-34}$ is to big or too small, then it can be changed.

 

[olgerm]

n of force unit or any other unit can be changed independently from n's of other units, but it might create physical constants to formulas, that do not have physical consants in SI system. For example if you used $F_{b-140}$ instead of $F_{b-150}$ , then there would be physical constant in formula $a=2^{10}*\frac{F}{m}$ (Newon's 2. law)

Actually I think it would be good idea to set n independetly for every unit. Then you have physical constant in every formula (or you can think of this as converting quatities to natural units).
For example if you use $l_{b110}$, $v_{b-32}$ and $t_{b144}$. Then to convert to natural units in formula $s=v*t$ you get $(s*2^{110})=(v*2^{-32})*(t*2^{144})$ . Or you can think of this as having constant in $k_{svt}=4*\frac{l_{b110}}{v_{b-32}*t_{b144}}$ in formula $s=k_{svt}*v*t$ .

Does setting $h=1$ and $c=1$ give people more or less physical insight to the way the universe works?

Using this unitsystem would give people more insight to what physical constants are. Many people seem have overmystified the meaning of physical constants. I think good way to think of physical constants is that a physical constant is multiplication of coefficients, that are needed to convert naturalunits to units of dimension of the physical constant.

 

[Zymurgest]

What about the calendar? I propose a 13 month calendar of 4 weeks of 7 days each, thus giving us 28 days per month. For correction, what about a midyear month called (Hexember) of 29 days, thus giving us 365 days per year, with a leap day added to Hexember to give 30 days, and a 366 day long leap year. This would make for much easier calendric notation, but would also require a correction of the New Calendar as compared to Gregorian, and Julian dates (still in use by the astronomical community) for it to be accepted at large.

 

[olgerm]

Suppressed unit notation is really only appropriate for advanced practitioners.

If by suppressed unit notation you mean not writing units, then using the unitsystem I proposed does not require using suppressed unit notation. You can write $m_{Lisa}=11.41*m_{b28}$ using this unitsystem as you would write $m_{Lisa}=47.14*kg$ using SI unitsystem.

 

[Nugatory]

What do you think of this?

What problem are we trying to solve by introducing these units?

That's a serious question, as we always choose units that are convenient to solve the problem at hand... no interesting problem, no need for any units.

Of course "convenient" can be influenced by multiple extraneous factors. For example, I work with metric length units (millimeters, specifically) when doing valve adjustments on my absurd fleet of vintage Italian rustbuckets but not because millimeters have any unique virtue here. It's because the factory specifications are written as .20-.30 mm, accurate metric micrometers and calipers are cheap and plentiful on eBay, and the shims are manufactured in thicknesses of 2.95, 3.00, 3.05, 3.10, ... 5.00 millimeters. A few centuries and billions of man-hours invested in stuff like this, and compatibility with existing metrology becomes a significant consideration.

 

[olgerm]

@Nugatory, these units are not meant for very specific application, but are good in general.

good properties of this unitsystem:

• units are defined purely by physical constants without using quantities, that can not be mathematically expressed, but only be measured (like period of radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom is used to define second in SI unitsystem.)
• very easy to convert to natural units
• units are approximately in same size as things in everyday life are
• using this unitsystem gives people more intuition of what dimensional physical constants are
• easy to derive numerical values of physical constants in this unitsystem
• symbol of quantity, that a unit is measuring is derivable from symbol of unit - just remove subscript. for example form symbol of time-unit "$t_{b144}$" to symbol of time "$t$".

The first point makes getting intuition, of what physical constants are, much easier.

 

[akardos]

My idea for unitsystem:
for first I set unmultiplied units so that
$h=1$ Planck constant
$c=1$ speed of light
$k_b=1$ bolzmann constant
$k_E=\frac{1}{2*2\pi}$ Coulomb constant
$k_G=\frac{1}{2*2\pi}$ Newtons gravitational constant.
In this unitsystem many formulas have simpler form than in unitsystem, where $k_E=1$ and $k_G=1$.

conversion of unmultiplied units to SI:
$t_b=c_{SI}^{-5/2}*h_{SI}^{1/2}*k_{G\ SI}^{1/2}*(2pi)^{1/2}*2^{1/2} \approx 4.79042770714*10^{-43}*s$ time unit
$l_b=c_{SI}^{-3/2}*h_{SI}^{1/2}*k_{G\ SI}^{1/2}*(2pi)^{1/2}*2^{1/2}\approx 1.436134097196*10^{-34}*m$ length unit
$m_b=c_{SI}^{1/2}*h_{SI}^{1/2}*k_{G\ SI}^{-1/2}*(2pi)^{-1/2}*2^{-1/2}\approx 1.539006070965*10^{-8}*kg$ mass unit
$q_b=c_{SI}^{1/2}*h_{SI}^{1/2}*k_{E\ SI}^{-1/2}*(2pi)^{-1/2}*2^{-1/2}\approx 1.326211321739*10^{-18}*C$ electriccharge unit
$T_b=c_{SI}^{5/2}*h_{SI}^{1/2}*k_{G\ SI}^{-1/2}*k_{b\ SI}^{-1}*(2pi)^{-1/2}*2^{-1/2}\approx 1.001840552719*10^{32}*K$ temperature unit

Now to make units that are more similar to values in everydaylife I multiply unmultiplied units with $2^n$ (n is arbitrarily chosen for every unit). Name of new unit will be name of unmultiplied unit, but n added to lower index of its name.

conversion of multiplied to SI:
$t_{b144}=t_b*2^{144}\approx 10.683010768898102*s$ time unit
$l_{b110}=l_b*2^{110} \approx 0.18642086403260658*m$ length unit
$m_{b28}=m_b*2^{28} \approx 4.131237964462824*kg$ mass unit
$q_{b40}=q_b*2^{40} \approx 1.4581847691398792*10^{-6}*C$ electriccharge unit
$T_{b-104}=T_b*2^{-104} \approx 4.9394552831557474*K$ temperature unit
$F_{b-150}=F_b*2^{-150} \approx 0.0067481914578038016*N$ force unit

physical constants are very easily derivable in this system:

1. take dimension of constant in units that you want to use this constant with $[k_G]=\frac{F_{b-150}*l_{b110}}{m_{b28}^2}$ (solve defining formula $F=\frac{k_G*m_1*m_2}{l^2}$ for constant $k_G=\frac{F*l^2}{m_1*m_2}$ to get it)
2. replace every unit in dimension of constant with $2^{-n}$, where n is n of unit in this unitsystem that you are using(for example n of $q_{b43}$ is 43). $\frac{2^{150}*(2^{-110})^2}{(2^{-28})^2}=2^{-14}=6.103515625*10^{-5}$
3. multiply the value with constants value in unmultiplied system. $2^{-14}*\frac{1}{2*2\pi}=\frac{2^{-15}}{2\pi}$
4. and the value of physical constant has been found $k_G=\frac{2^{-15}}{2\pi}*\frac{F_{b-150}*l_{b110}}{m_{b28}^2} \approx 4.857023409786845*10^{-6}*\frac{F_{b-150}*l_{b110}}{m_{b28}^2}$.

n of force unit or any other unit can be changed independently from n's of other units, but it might create physical constants to formulas, that do not have physical consants in SI system. For example if you used $F_{b-140}$ instead of $F_{b-150}$ , then there would be physical constant in formula $a=2^{10}*\frac{F}{m}$ (Newon's 2. law)good properties of this unitsystem:

• units are defined purely by physical constants without using quantities, that can not mathematically expressed, but only be measured (like period of radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom is used to define second in SI unitsystem.)
• very easy to convert to natural units
• units are approximately in same size as things in everyday life are
• using this unitsystem gives people more intuition of what dimensional physical constants are
• easy to derive numerical values of physical constants in this unitsystem

What do you think of this?
[

Does setting $h=1$ and $c=1$ give people more or less physical insight to the way the universe works? To me, that is the metric.

 

[akardos]

My idea for unitsystem:
for first I set unmultiplied units so that
$h=1$ Planck constant
$c=1$ speed of light
$k_b=1$ bolzmann constant
$k_E=\frac{1}{2*2\pi}$ Coulomb constant
$k_G=\frac{1}{2*2\pi}$ Newtons gravitational constant.
In this unitsystem many formulas have simpler form than in unitsystem, where $k_E=1$ and $k_G=1$.

conversion of unmultiplied units to SI:
$t_b=c_{SI}^{-5/2}*h_{SI}^{1/2}*k_{G\ SI}^{1/2}*(2pi)^{1/2}*2^{1/2} \approx 4.79042770714*10^{-43}*s$ time unit
$l_b=c_{SI}^{-3/2}*h_{SI}^{1/2}*k_{G\ SI}^{1/2}*(2pi)^{1/2}*2^{1/2}\approx 1.436134097196*10^{-34}*m$ length unit
$m_b=c_{SI}^{1/2}*h_{SI}^{1/2}*k_{G\ SI}^{-1/2}*(2pi)^{-1/2}*2^{-1/2}\approx 1.539006070965*10^{-8}*kg$ mass unit
$q_b=c_{SI}^{1/2}*h_{SI}^{1/2}*k_{E\ SI}^{-1/2}*(2pi)^{-1/2}*2^{-1/2}\approx 1.326211321739*10^{-18}*C$ electriccharge unit
$T_b=c_{SI}^{5/2}*h_{SI}^{1/2}*k_{G\ SI}^{-1/2}*k_{b\ SI}^{-1}*(2pi)^{-1/2}*2^{-1/2}\approx 1.001840552719*10^{32}*K$ temperature unit

Now to make units that are more similar to values in everydaylife I multiply unmultiplied units with $2^n$ (n is arbitrarily chosen for every unit). Name of new unit will be name of unmultiplied unit, but n added to lower index of its name.

conversion of multiplied to SI:
$t_{b144}=t_b*2^{144}\approx 10.683010768898102*s$ time unit
$l_{b110}=l_b*2^{110} \approx 0.18642086403260658*m$ length unit
$m_{b28}=m_b*2^{28} \approx 4.131237964462824*kg$ mass unit
$q_{b40}=q_b*2^{40} \approx 1.4581847691398792*10^{-6}*C$ electriccharge unit
$T_{b-104}=T_b*2^{-104} \approx 4.9394552831557474*K$ temperature unit
$F_{b-150}=F_b*2^{-150} \approx 0.0067481914578038016*N$ force unit

physical constants are very easily derivable in this system:

1. take dimension of constant in units that you want to use this constant with $[k_G]=\frac{F_{b-150}*l_{b110}}{m_{b28}^2}$ (solve defining formula $F=\frac{k_G*m_1*m_2}{l^2}$ for constant $k_G=\frac{F*l^2}{m_1*m_2}$ to get it)
2. replace every unit in dimension of constant with $2^{-n}$, where n is n of unit in this unitsystem that you are using(for example n of $q_{b43}$ is 43). $\frac{2^{150}*(2^{-110})^2}{(2^{-28})^2}=2^{-14}=6.103515625*10^{-5}$
3. multiply the value with constants value in unmultiplied system. $2^{-14}*\frac{1}{2*2\pi}=\frac{2^{-15}}{2\pi}$
4. and the value of physical constant has been found $k_G=\frac{2^{-15}}{2\pi}*\frac{F_{b-150}*l_{b110}}{m_{b28}^2} \approx 4.857023409786845*10^{-6}*\frac{F_{b-150}*l_{b110}}{m_{b28}^2}$.

n of force unit or any other unit can be changed independently from n's of other units, but it might create physical constants to formulas, that do not have physical consants in SI system. For example if you used $F_{b-140}$ instead of $F_{b-150}$ , then there would be physical constant in formula $a=2^{10}*\frac{F}{m}$ (Newon's 2. law)good properties of this unitsystem:

• units are defined purely by physical constants without using quantities, that can not mathematically expressed, but only be measured (like period of radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom is used to define second in SI unitsystem.)
• very easy to convert to natural units
• units are approximately in same size as things in everyday life are
• using this unitsystem gives people more intuition of what dimensional physical constants are
• easy to derive numerical values of physical constants in this unitsystem

What do you think of this?

As a complete amateur, i'll need time to digest how your system might work/apply. But from first glance, it looks like what I meant to ask for, a system that isn't based on how big a kings foot was or simply dividing an Earth day into specific counting frame of reference and make everything work off that.

 

[olgerm]

As a complete amateur, i'll need time to digest how your system might work/apply.

To use these units to measure things you just need to know approximate size of the units.

But from first glance, it looks like what I meant to ask for, a system that isn't based on how big a kings foot was or simply dividing an Earth day into specific counting frame of reference and make everything work off that.

I do not understand last part of your post.

 

[Melbourne Guy]

What do you think of this?

I think you're making a problem where one does not exist. Most of us will never calculate any of the numerous formula you've noted, @olgerm, and I literally mean billions of people, so it looks like angels and pins from where I'm sitting.

Not meaning to be derogatory, but how does this help me judge everyday issues, like whether bags of lollies are shrinking? I swear they were heavier before the pandemic, now the smaller Allen's Party Mix barely satisfies! And how does it help me decide whether a 34" 4K UHD curved monitor will provide better screen real estate than the two 24" HD monitors sitting side-by-side I have now?

Honestly, if there's one thing I've learned from reading PF posts, it's that the units aren't the important thing. Gleaning the underlying meaning of the universe is the key, use whatever yardstick you like, because physics doesn't care, any more than us speaking English, French, or German changes the sun coming up each day!

 

[olgerm]

I think you're making a problem where one does not exist. Most of us will never calculate any of the numerous formula you've noted, @olgerm, and I literally mean billions of people, so it looks like angels and pins from where I'm sitting.

In post#13 I noted good properties of this unitsystem. Even if most of people would not use this unitsystem in application, where they would benefit from these good properties, this unitsystem would still not be worse for them than currently popular unitsystems. Only better side of SI-system, that I notice, is that SI-system is currently more popular.

Honestly, if there's one thing I've learned from reading PF posts, it's that the units aren't the important thing. Gleaning the underlying meaning of the universe is the key, use whatever yardstick you like

Using cleaner and mathematically more beautiful notation surely helps to make thing more clear.

 

[bob012345]

Using cleaner and mathematically more beautiful notation surely helps to make thing more clear.

Since 'beauty' is subjective, what is made clear might be misleading.

 

[Melbourne Guy]

In post#13 I noted good properties of this unitsystem.

You did, @olgerm, but even then, 'good' is subjective. I appreciate that you've put thought into your idea, but I still am not seeing the benefit that a wholesale change like this provides? The effort to implement it would be costly and confusing, so does does the benefit sufficiently outweigh the effort to make it worthwhile? And if the motivation is "beautiful notation" then that is surely an insufficient reason.

 

[olgerm]

Since 'beauty' is subjective, what is made clear might be misleading.

I do not have definition of mathematical beauty on top of my head, but it is not completely subjective. Here are few points that increase mathematical beauty of a notation:

• simple rules of "grammar".
• writing simple things takes small amount of symbols or simple things are put to correspondence with small natural number.
• uses elements of traditional notations, historical notations or previous standards. (in my system symbols of units are derived from usual symbols of corresponding quantities)

Imagine if you had to use roman numberals and instead of using symbols to write mathematical formula and you had to write all mathematical operations with words ("a plus b plus VII equals to c" instead of "a+b+7=c"). It would be mathematically less beautiful and using this notation woud make understanding physics harder.

 

[bob012345]

I do not have definition of mathematical beauty on top of my head, but it is not completely subjective. Here are few points that increase mathematical beauty of a notation:

• simple rules of "grammar".
• writing simple things takes small amount of symbols or simple things are put to correspondence with small natural number.
• uses elements of traditional notations, historical notations or previous standards. (in my system symbols of units are derived from usual symbols of corresponding quantities)

Imagine if you had to use roman numbers and instead of using symbols to write mathematical formula and you had to write write all mathematical operations with words ("a plus b plus VII equals to c" instead of "a+b+7=c"). It would be mathematically less beautiful and using this notation would make understanding physics harder.

I would argue that Roman numerals are far more beautiful even while being far less useful.