I Replacing the Measurement standards (SI units)

AI Thread Summary
The discussion revolves around the potential redefinition of SI units based on fundamental constants rather than legacy human-scale measurements. Suggestions include using the hyperfine transition frequency of hydrogen as a basis for the second, which could simplify measurements and enhance precision. The conversation highlights the challenges of transitioning to a new system, particularly the need for consistency across various units and the practical difficulties in implementing portable atomic clocks for accurate timekeeping. Participants note that while a new system could offer theoretical advantages, it may complicate everyday applications. Overall, the idea of redefining measurement standards is seen as both promising and complex, requiring careful consideration of practical implications.
akardos
Messages
3
Reaction score
0
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)
 
Last edited by a moderator:
Physics news on Phys.org
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.
 
  • Like
Likes DeBangis21, jim mcnamara, ohwilleke and 4 others
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.
 
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.
 
Last edited:
f95toli said:
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.
 
Last edited:
Ibix said:
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.
 
  • Like
Likes akardos and russ_watters
gmax137 said:
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...
 
I have always felt we should have metric time.
 
Twigg said:
"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.
 
  • #10
f95toli said:
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.

f95toli said:
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
 
  • #11
Twigg said:
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...
 
  • #12
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!

f95toli said:
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.
 
  • #13
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?
 
Last edited:
  • #14
olgerm said:
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.
 
  • #15
bob012345 said:
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.
 
  • #16
olgerm said:
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.
 
  • #17
bob012345 said:
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.
 
  • #18
Ibix said:
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.
 
Last edited:
  • #19
olgerm said:
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##.
olgerm said:
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.
 
Last edited:
  • #20
bob012345 said:
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.
 
  • #21
ohwilleke said:
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.
 
Last edited:
  • #22
olgerm said:
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## .
bob012345 said:
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.
 
Last edited:
  • #23
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.
 
  • #24
ohwilleke said:
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.
 
  • #25
olgerm said:
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.
 
Last edited:
  • Like
Likes pbuk and ohwilleke
  • #26
@Nugatory, these units are not meant for very specific application, but are good in general.
olgerm said:
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.
 
Last edited:
  • #27
olgerm said:
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?
[
bob012345 said:
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.
 
  • #28
olgerm said:
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.
 
  • #29
akardos said:
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.

akardos said:
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.
 
  • #30
olgerm said:
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!
 
  • #31
Melbourne Guy said:
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.

Melbourne Guy said:
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.
 
Last edited:
  • #32
olgerm said:
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.
 
  • #33
olgerm said:
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.
 
  • #34
bob012345 said:
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.
 
Last edited:
  • #35
olgerm said:
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.
 
  • #36
  • #37
  • #38
bob012345 said:
Not necessarily. Perhaps the Pythagoreans would relish a more complex system only they understood.
You still do not understand meaning of mathematical beauty. Even if someone would enjoy mathematically less beautiful notation more, it would not make this notation mathematically more beautiful.
 
  • #39
olgerm said:
Even if someone would enjoy mathematically less beautiful notation more, it would not make this notation mathematically more beautiful.

You are a perfect example: you enjoy using ##*## instead of ##\cdot## for denoting multiplication, even though it hurts eyes of most of the people who reads that.
 
  • #40
olgerm said:
You still do not understand meaning of mathematical beauty. Even if someone would enjoy mathematically less beautiful notation more, it would not make this notation mathematically more beautiful.
You obviously have a strong opinion and perhaps most people might agree with it. I understand it but I believe mathematical beauty is in the eye of the mathematician or the physicist if we are talking about expressions of physical theories such as QED which I have heard described as the most beautiful theory . To quote Wikipedia:

Mathematical beauty is the aesthetic pleasure typically derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians often express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful. They might also describe mathematics as an art form (e.g., a position taken by G. H. Hardy[1]) or, at a minimum, as a creative activity. Comparisons are often made with music and poetry.

According to this definition, if someone enjoyed a mathematically less beautiful notation (according to some) more, it would make this notation mathematically more beautiful to them. I think the whole concept of mathematical beauty is fraught with subjective values and it is not about telling others what is or is not beautiful. This is not about a majority opinion.
 
  • #41
main-qimg-a3d27e691b5f8258d60d9fe81f76a607-lq.jpg
 
  • #42
I think you haven't thought your thought through.
Napoleon wanted a new system of measurement, and he had one created and imposed it on much of Europe and it stuck. The French Revolutionaries tried to get rid of the old calendar and systems of time. That did NOT stick. Units of measurement are USED by people--and they have habits. And old habits can be VERY hard to break. QWERTY, for example, was good for typewriters that had actuated swinging arms. Are you still using a QWERTY keyboard? You almost certainly are!

Old standards are sticky. Most of North America is gridded out in blocks measured in miles. Kilometers have made some inroads, but directions on the grid of roads laid out in miles still usually get related in miles. Ask anyone in North America for their height and weight. You will invariably get feet, inches and pounds in the reply. Land is in acres. Houses are in sq. ft. Recipes are usually still in pounds, ounces, tbsp and tsp, and NOT in grams and milliliters. Pressures are in psi and not Pa, or kg/cm2. Mechanical stuff has a mix. If it comes from abroad, you may need metric tools--or SAE tools--and you have both because you just never know. Bulk fuel in Canada get measured in litres--mainly because the imperial gallon was a unit ONLY Canadians were using, and so letting that go was easier.

Units get USED. Energy is nominally measured in joules. But your electric bill comes as kilowatt-hours and physicists like electron-volts. While physics and engineering are SUPPOSED to be in SI units, you do wind up with CGS or MKS depending on the scale of what you are doing (centimeters, grams, seconds vs metres, kilograms, seconds. If existing units are not convenient, rest assured that someone will create some SI-based one that are. You'll see some hard SF (Larry Niven and Arthur C. Clarke in particular) where a spaceship's propellant mass and energy are given as delta-v with units given as c (the ship was carrying 2.5c of delta-v, meaning it could alter its velocity a total of 2.5 times the speed of light accelerating and decelerating before running out of maneuvering ability.) We talk about fuel range in miles or km for cars -- but in minutes for aircraft. Units depend on usage. (part of why Bitcoin will never be a thing is that nothing will EVER be priced in bitcoin, it is not a convenient unit of account, nor will it ever be a stable one.) There will NEVER be one universal system of units to rule them all.

And then really, almost nothing is constant. Supposedly the distance between two stationary objects is a function of the age of the universe. The passage of time is influenced by the velocity at which you are travelling. Mass too is a function of velocity (the mass of the proton involved in a cosmic ray can be several kilograms viewed in a particular frame of reference.) Distance too is a function of velocity ( at v approaching c distances measured perpendicular to the direction of travel are not the same as those measured parallel to it.) g changes as you move away from the center of the earth. And on it goes. and on, and on.

Reality does have some constant, unitless numbers embedded in it, but they generally don't lend themselves to the construction of systems of units that are convenient to use. We do try to count where we can, rather than bulk (Avogadro's number) But nobody is purchasing bread flour in mols. So, I don't think trying to replace SI units is an exercise in anything but futility.
 
  • Informative
Likes Melbourne Guy
  • #43
N1206 said:
And then really, almost nothing is constant. Supposedly the distance between two stationary objects is a function of the age of the universe. The passage of time is influenced by the velocity at which you are travelling. Mass too is a function of velocity (the mass of the proton involved in a cosmic ray can be several kilograms viewed in a particular frame of reference.) Distance too is a function of velocity ( at v approaching c distances measured perpendicular to the direction of travel are not the same as those measured parallel to it.) g changes as you move away from the center of the earth. And on it goes. and on, and on.
Firstly your post is factually incorrect.
  • "Supposedly the distance between two stationary objects is a function of the age of the universe." It means that the distance is not constant, but word "constant" has different meaning here than in phrases "dimensional physical constant" and "mathematical constant". In this context it is an adjective, but in phrases "dimensional physical constant" and "mathematical constant" it is a noun. So this claim is misleading.
  • "The passage of time is influenced by the velocity at which you are travelling". The word that you meant is "frame-invariant", not "constant". And even if you replaced word "constant" to "frame-variant" the whole claim would still be incorrect.
  • "Mass too is a function of velocity". It is also somewhat a question of notation(terminology), but I would say it is not correct to call "relativistic mass" just "mass". "mass" should mean "restmass". If "mass" meant "restmass" here, then the whole claim is incorrect. And the word that you meant is "frame-invariant" not "constant".
  • "Distance too is a function of velocity". The word that you meant is "frame-invariant" not "constant".
  • "g changes as you move away from the center of the earth." The word that you meant is "homogeneous" not "constant".
Secondly all this has nothing to do with unitsystems. Even if some value is different in different times, different frames of reference or different locations, it is still measured in same units. For example if voltage between 2 wires is constantly 2 Volts ##U=2*V## , it is measured in volts. And if voltage between 2 wires changes in time ##U(t)=325*sin(314*t/sec)*V##, it is still measured in volts.
N1206 said:
Reality does have some constant, unitless numbers embedded in it, but they generally don't lend themselves to the construction of systems of units that are convenient to use. We do try to count where we can, rather than bulk (Avogadro's number) But nobody is purchasing bread flour in mols. So, I don't think trying to replace SI units is an exercise in anything but futility.
In my idea for unitsystem I tried to get rid of arbitrary numbers (like period of radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom). In my unitsystem all dimensional physical constants are mathematically expressable (for example ##F_G=2^{-1}*(2\pi)^{-1}##). There are still unitless contants, but these are also not related to unitsystems - these are same in every unitsystem. By the way these unitless contants might also be mathematically expressable, but it is currently unknown whether and how.
 
Last edited:
  • #44
olgerm said:
In my idea for unitsystem I tried to get rid of arbitrary numbers (like period of radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom).
I will admit freely that I don't understand your reply. Metrology is the study of measurement. One of the base requirements of a system of metrology is a system of units that all users can agree to. What is fundamentally impossible is to define a system of units that does not have some base, arbitrary assumptions to it that all the users agree and subscribe to. SI has base units that all others are derived from. Length is the distance between two points. If the inflation theory of the universe is correct, the distance between two points at rest to one another will have grown as time passes. So how then can you define an invariant unit of distance? Relativity means that all measurements of time and distance must necessarily be influenced by the conditions of the observer. A muon has a lifetime of ~ 2.2 µs at rest. Whistle the sucker up to 99.99% of c and its lifetime can be several seconds. Two atomic clocks, one left on the ground and one flown on an aircraft, will diverge in their measurement of time.

"I tried to get rid of arbitrary numbers..."
You can't. There will ALWAYS be a certain amount of arbitrariness to metrology.
SI has reduced that to seven items.
You may not like <how> the arbitrary items are defined by SI, and may want set the base value to some other arbitrary number--but it will be arbitrary.

Even our number system. We have ten fingers and have built a positional-notation system on base-10. There are good arguments that base-12 would have been better. The Mayans did base-20. The Babylonians did base-60. Computer guys do binary, octal and hexidecimal. You can do logarithms in base 10, but all logs can be reduced down to base e. Should we redefine "1 =e" as a good idea? Or what about "1=π"?

It is ALL arbitrary.
 
Last edited:
  • Like
Likes Melbourne Guy
  • #45
N1206 said:
One of the base requirements of a system of metrology is a system of units that all users can agree to.
N1206 said:
The French Revolutionaries tried to get rid of the old calendar and systems of time. That did NOT stick. Units of measurement are USED by people--and they have habits. And old habits can be VERY hard to break.
Melbourne Guy said:
The effort to implement it would be costly and confusing, so does does the benefit sufficiently outweigh the effort to make it worthwhile?
I proposed an idea for unitsystem, but I do not have power force everybody to use it. And I have not claimed to have it.
N1206 said:
There will ALWAYS be a certain amount of arbitrariness to metrology.
N1206 said:
What is fundamentally impossible is to define a system of units that does not have some base, arbitrary assumptions to it that all the users agree and subscribe to.
Maybe, but my tried to make as simple and "unarbitary" unitsytem as possible. aka make all arbitrary choices that I had to make as simple as possible.
N1206 said:
It is ALL arbitrary.
I do not have clear general mathematical method to compare which of 2 notations or unitsystems have less arbitarity in it, but despite o f that some notations have more arbritarity in them and some less. For example: Imagine a unitsystem, that which unit of length is defined as ## l_u=a_1*(sin(a_2^4*a_3^{-1}*a_4^{-3}))^{a_3/a_1} ## , where
  • ##a_1## is tallness of Julius Caesar.
  • ##a_2## is distance between Earth and Mars at time when Julius Caesar became consul for 1. time.
  • ##a_3## is distance between Venus and Pluto at time when Julius Caesar became consul for 2. time.
  • ##a_4## is length of left hand ofJulius Caesar.
It is intuitively clear, that such unitsystem would have more arbitarity in it than unitsystem, that I described in post#13.

N1206 said:
What is fundamentally impossible is to define a system of units that does not have some base, arbitrary assumptions to it that all the users agree and subscribe to. SI has base units that all others are derived from. Length is the distance between two points. If the inflation theory of the universe is correct, the distance between two points at rest to one another will have grown as time passes. So how then can you define an invariant unit of distance? Relativity means that all measurements of time and distance must necessarily be influenced by the conditions of the observer. A muon has a lifetime of ~ 2.2 µs at rest. Whistle the sucker up to 99.99% of c and its lifetime can be several seconds. Two atomic clocks, one left on the ground and one flown on an aircraft, will diverge in their measurement of time.
You have clearly very big misunderstanding here. Some quantities have different values in different frames of reference or at different times, but I do not even understand why you think that it is related to unitsystems. I already explained that in post#43:
olgerm said:
Secondly all this has nothing to do with unitsystems. Even if some value is different in different times, different frames of reference or different locations, it is still measured in same units. For example if voltage between 2 wires is constantly 2 Volts ##U=2*V## , it is measured in volts. And if voltage between 2 wires changes in time ##U(t)=325*sin(314*t/sec)*V##, it is still measured in volts.
 
Last edited:
  • #46
olgerm said:
I proposed an idea for unitsystem, but I do not have power force everybody to use it. And I have not claimed to have it.
I can't speak for others, @olgerm, but I did not intend to suggest you have that power...because if you did, I'm assuming we're all be using 'olgerms' already 🤣 Being serious, most posters on PF seem to be able to separate the idea from the person proposing it!
 
  • #47
olgerm said:
Maybe, but my tried to make as simple and "unarbitary" unitsytem as possible. aka make all arbitrary choices that I had to make as simple as possible.
The choices are ALL arbitrary, SI's, yours, the Julius Caesar example you proposed, or any other system. Two sets of arbitrary fought it out when CGS and MKS went toe-to-toe. In North America, SI and imperial duke it out on a daily basis.

"Even if some value is different in different times, different frames of reference or different locations, it is still measured in same units"

In the old days, when a foot was an actual ruler's foot, each time the king dies, the definition of the foot changed. What was 1'1'' could be come 11" the next day. Or if you crossed the border into a new king's territory. Napoleon recognized that this was an impediment to trade and that there was a vast plethora of units in use across his empire--and he put an end to most of them.

It is important that the unit NOT change.
https://en.wikipedia.org/wiki/International_Prototype_of_the_Kilogram
https://en.wikipedia.org/wiki/History_of_the_metre
https://en.wikipedia.org/wiki/Second

But given we live in a universe where inflation, relativity and Heisenberg's Uncertainty Principle reign, it has to be recognized that even the SI definitions of the seven base units are not completely static, but depend, however slightly, on the place and time in which they are situated.

Unit systems are judged on their usefulness in helping people communicate with one another. I truly don't understand how your proposed system would be more useful that what we have now.
 
  • #48
N1206 said:
Even our number system. We have ten fingers and have built a positional-notation system on base-10. There are good arguments that base-12 would have been better. The Mayans did base-20. The Babylonians did base-60. Computer guys do binary, octal and hexidecimal.
Binary would be "least arbitrary", because 2 is the smallest number that can be base.

N1206 said:
Should we redefine "1 =e" as a good idea? Or what about "1=π"?
It is different, because ##e## and ##\pi## are not physical constants with unit (dimensional physical constants).
 
Last edited:
  • #49
N1206 said:
The choices are ALL arbitrary, SI's, yours, the Julius Caesar example you proposed, or any other system.
Some unitsystems are more "simple", "mathematically beautiful", "natural" or "less arbitrary" than others.

N1206 said:
I am not proposing a new SI version, but a new unitsystem.

N1206 said:
But given we live in a universe where inflation, relativity and Heisenberg's Uncertainty Principle reign, it has to be recognized that even the SI definitions of the seven base units are not completely static, but depend, however slightly, on the place and time in which they are situated.
I am not sure, but I think these are static. Write an example, where a SI-unit and my_post#13-unitsystem unit depends of place and time.

N1206 said:
I truly don't understand how your proposed system would be more useful that what we have now.
I wrote good properties of this unitsystem to post#13:
olgerm said:
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).
 
  • #50
N1206 said:
But given we live in a universe where inflation, relativity and Heisenberg's Uncertainty Principle reign, it has to be recognized that even the SI definitions of the seven base units are not completely static, but depend, however slightly, on the place and time in which they are situated.
olgerm said:
I am not sure, but I think these are static. Write an example, where a SI-unit and my_post#13-unitsystem unit depends of place and time.
You have not written an example where SI-unitsystem unit or my_post#13-unitsystem unit depends of place and time in which they are situated. Do you still think that these units depend of place and time or you do not think that anymore?
 
Last edited:

Similar threads

Replies
13
Views
4K
Replies
18
Views
4K
Replies
6
Views
2K
Replies
6
Views
3K
Replies
1
Views
2K
Replies
5
Views
3K
Replies
9
Views
5K
Replies
95
Views
7K
Replies
1
Views
2K
Back
Top