Personal Preamble: I really thought, this community was gone somewhen in spring, but looky-loo, I found it again. Even though I made the thing and I am the admin, I still lost it... Welp now I can try to beat this dead horse further.
Introduction: What I am talking about today is how utterly terrible the standarts are in physics. Keep in mind, that I am not a professional physicist at all and am mostly talking as someone who is very disappointed.
So what I did a year ago, was to collect a bunch of important Equations and write them down, then I took the Symbols out of the equations and wrote them as a concise list of Symbols, their names, their Physical measurements and such. It was basically a project done, to prove a point. It proves it's point still, but that helps little if its just on my hard-drive.
Now I took out the project again and threw it into the LLM called Claude Sonnet 4. And after a bit of fiddling we have this:
Physical Quantities and Units
SI Base Units
Physical Quantity |
Symbol |
Unit |
Unit Symbol |
Length |
l, s, r, x, y, z |
Meter |
m |
Mass |
m |
Kilogram |
kg |
Time |
t |
Second |
s |
Electric Current |
I |
Ampere |
A |
Thermodynamic Temperature |
T |
Kelvin |
K |
Amount of Substance |
n |
Mole |
mol |
Luminous Intensity |
I_v |
Candela |
cd |
Mechanics/Dynamics
Physical Quantity |
Symbol |
Unit |
Unit Symbol |
Derivation/Equation |
Velocity |
v |
|
m/s |
v = s/t |
Acceleration |
a |
|
m/s² |
a = v/t, a = F/m |
Force |
F |
Newton |
N |
[kg⋅m/s²], F = ma |
Momentum |
p |
|
kg⋅m/s |
p = mv |
Work, Energy |
W, E |
Joule |
J |
[N⋅m = kg⋅m²/s²], W = F⋅s |
Power |
P |
Watt |
W |
[J/s = kg⋅m²/s³], P = W/t |
Angle |
α, β, φ, θ |
Radian |
rad |
|
Angular Velocity |
ω |
|
rad/s |
ω = φ/t, v = ωr |
Angular Acceleration |
α |
|
rad/s² |
α = ω/t |
Solid Angle |
Ω |
Steradian |
sr |
|
Moment of Inertia |
I, J, Θ |
|
kg⋅m² |
|
Torque |
M |
|
N⋅m |
M = F⋅r |
Angular Momentum |
L |
|
kg⋅m²/s |
L = Iω |
Spring Constant |
D, k |
|
N/m |
F = -kx |
Coefficient of Friction |
μ |
|
dimensionless |
F_R = μN |
Centripetal Force |
|
|
N |
F = mv²/r |
Gravitational Force |
|
|
N |
F = Gm₁m₂/r² |
Thermodynamics/Heat
Physical Quantity |
Symbol |
Unit |
Unit Symbol |
Derivation/Equation |
Temperature |
T |
Kelvin |
K |
(-273.15°C = 0 K) |
Internal Energy |
U |
Joule |
J |
|
Heat |
Q |
Joule |
J |
|
Entropy |
S |
|
J/K |
|
Specific Heat Capacity |
c |
|
J/(kg⋅K) |
Q = mcΔT |
Heat Capacity |
C |
|
J/K |
|
Thermal Conductivity |
λ, κ |
|
W/(m⋅K) |
|
Coefficient of Thermal Expansion |
α |
|
1/K |
Δl = αl₀ΔT |
Universal Gas Constant |
R |
|
J/(mol⋅K) |
pV = nRT |
Boltzmann Constant |
k_B |
|
J/K |
|
Stefan-Boltzmann Law |
|
|
W/m² |
j = σT⁴ |
Fluid Mechanics
Physical Quantity |
Symbol |
Unit |
Unit Symbol |
Derivation/Equation |
Density |
ρ |
|
kg/m³ |
ρ = m/V |
Pressure |
p |
Pascal |
Pa |
[N/m² = kg/(m⋅s²)], p = F/A |
Volume |
V |
|
m³ |
|
Area |
A |
|
m² |
|
Flow Velocity |
v |
|
m/s |
|
Dynamic Viscosity |
η |
|
Pa⋅s |
[N⋅s/m²] |
Kinematic Viscosity |
ν |
|
m²/s |
ν = η/ρ |
Continuity Equation |
|
|
|
ρ₁v₁A₁ = ρ₂v₂A₂ |
Bernoulli Equation |
|
|
|
p + ½ρv² + ρgh = const |
Electrostatics
Physical Quantity |
Symbol |
Unit |
Unit Symbol |
Derivation/Equation |
Electric Charge |
Q, q |
Coulomb |
C |
[A⋅s] |
Electric Voltage |
U |
Volt |
V |
[W/A = kg⋅m²/(A⋅s³)] |
Electric Potential |
φ, V |
Volt |
V |
U = φ₁ - φ₂ |
Electric Field Strength |
E |
|
V/m |
[N/C], E = F/q |
Electric Flux Density |
D |
|
C/m² |
|
Capacitance |
C |
Farad |
F |
[C/V = A⋅s/V], Q = CU |
Permittivity |
ε |
|
F/m |
|
Relative Permittivity |
ε_r |
|
dimensionless |
|
Coulomb's Law |
|
|
|
F = kq₁q₂/r² |
Electrodynamics
Physical Quantity |
Symbol |
Unit |
Unit Symbol |
Derivation/Equation |
Electric Current |
I |
Ampere |
A |
I = Q/t |
Current Density |
J, j |
|
A/m² |
J = I/A |
Electric Resistance |
R |
Ohm |
Ω |
[V/A], U = IR |
Electric Conductance |
G |
Siemens |
S |
[1/Ω], G = 1/R |
Resistivity |
ρ |
|
Ω⋅m |
R = ρl/A |
Magnetic Flux Density |
B |
Tesla |
T |
[Wb/m² = kg/(A⋅s²)] |
Magnetic Field Strength |
H |
|
A/m |
|
Magnetic Flux |
Φ |
Weber |
Wb |
[V⋅s = kg⋅m²/(A⋅s²)] |
Inductance |
L |
Henry |
H |
[Wb/A = kg⋅m²/(A²⋅s²)] |
Permeability |
μ |
|
H/m |
|
Lorentz Force |
|
|
N |
F = q(E + v×B) |
Faraday's Law |
|
|
|
U_ind = -dΦ/dt |
Oscillations and Waves
Physical Quantity |
Symbol |
Unit |
Unit Symbol |
Derivation/Equation |
Frequency |
f, ν |
Hertz |
Hz |
[1/s], f = 1/T |
Period |
T |
|
s |
T = 1/f |
Angular Frequency |
ω |
|
rad/s |
ω = 2πf |
Wavelength |
λ |
|
m |
|
Wave Velocity |
c, v |
|
m/s |
c = fλ |
Amplitude |
A |
|
m |
|
Phase Angle |
φ, Φ |
Radian |
rad |
|
Damping Coefficient |
β, γ |
|
1/s |
|
Harmonic Oscillation |
|
|
|
x(t) = A cos(ωt + φ) |
Acoustics
Physical Quantity |
Symbol |
Unit |
Unit Symbol |
Derivation/Equation |
Speed of Sound |
c |
|
m/s |
c = fλ |
Sound Pressure Level |
L_p |
Decibel |
dB |
L_p = 20 log(p/p₀) |
Sound Intensity |
I |
|
W/m² |
|
Acoustic Impedance |
Z |
|
Pa⋅s/m |
Z = ρc |
Doppler Effect |
|
|
|
f' = f(v±v_observer)/(v±v_source) |
Optics
Physical Quantity |
Symbol |
Unit |
Unit Symbol |
Derivation/Equation |
Speed of Light |
c |
|
m/s |
c = fλ |
Refractive Index |
n |
|
dimensionless |
n = c₀/c |
Focal Length |
f |
|
m |
|
Optical Power |
D |
Diopter |
dpt |
[1/m], D = 1/f |
Object Distance |
g |
|
m |
|
Image Distance |
b |
|
m |
|
Luminous Flux |
Φ_v |
Lumen |
lm |
[cd⋅sr] |
Illuminance |
E_v |
Lux |
lx |
[lm/m² = cd⋅sr/m²] |
Luminance |
L_v |
|
cd/m² |
|
Lens Equation |
|
|
|
1/f = 1/g + 1/b |
Snell's Law |
|
|
|
n₁sin(α₁) = n₂sin(α₂) |
Atomic and Nuclear Physics
Physical Quantity |
Symbol |
Unit |
Unit Symbol |
Derivation/Equation |
Energy |
E |
Joule, Electron Volt |
J, eV |
1 eV = 1.602×10⁻¹⁹ J |
Photon Energy |
E_ph |
Electron Volt |
eV |
E = hf = ħω |
De Broglie Wavelength |
λ_dB |
|
m |
λ = h/p |
Compton Wavelength |
λ_C |
|
m |
λ_C = h/(m_e c) |
Rest Energy |
E_0 |
|
eV, J |
E₀ = mc² |
Binding Energy |
B.E. |
|
eV, MeV |
|
Planck Constant |
h |
|
J⋅s |
6.626×10⁻³⁴ J⋅s |
Reduced Planck Constant |
ħ |
|
J⋅s |
h/(2π) |
Number of Particles |
N |
|
dimensionless |
|
Activity |
A |
Becquerel |
Bq |
[1/s], A = λN |
Decay Constant |
λ |
|
1/s |
N(t) = N₀e^(-λt) |
Half-life |
t_{1/2} |
|
s |
t_{1/2} = ln(2)/λ |
Cross Section |
σ |
Barn |
b |
[10⁻²⁴ cm²] |
Atomic Mass Unit |
m |
Atomic Mass Unit |
u |
1 u = 1.661×10⁻²⁷ kg |
Bohr Radius |
a₀ |
|
m |
5.292×10⁻¹¹ m |
Rydberg Energy |
Ry |
|
eV |
13.61 eV |
Photoelectric Effect |
|
|
|
E_kin = hf - W |
Important Constants
Constant |
Symbol |
Value |
Unit |
Speed of Light |
c |
2.998×10⁸ |
m/s |
Planck Constant |
h |
6.626×10⁻³⁴ |
J⋅s |
Elementary Charge |
e |
1.602×10⁻¹⁹ |
C |
Electron Mass |
m_e |
9.109×10⁻³¹ |
kg |
Proton Mass |
m_p |
1.673×10⁻²⁷ |
kg |
Avogadro Constant |
N_A |
6.022×10²³ |
1/mol |
It worked! Praised be the programming gods! One thing that is technically lacking is the Little vector-indication-arrow above F for Force, B for magnetic field... but that is a problem of the LLM.
Now that we all see the same thing in front of our peepers, I can properly begin to criticice the whole thing, but only after giving context and orientation. It always drives me nuts when someone introduces a complicated graph and doesn't give people the information or the thyme to understand it. (Like a simple explanation of what is where on a graph can already significantly help in introducing people to the thing that is being talked about but no, the thyme is apparently running out or something and we'd be much better of, with having just glanced at the best method of getting the information to the brain instead of actually analyzing it.)
Even though you probably have enough thyme to analyze it yourself, I will still give you a rundown of the system.
Context: This is all completelly settled science, this is basically "modern" Physics, in the sense that modern was the early 20th century. We have no Computers, no Quantum Mechanics, just basic physics. It actually is a list capable of solving nearly any simple engineering problem you may encounter! Well not really. If you want to disprove all of science, any of these mathematical statements are a good start, since they have been baked in deeply. Conversely it is incredibly difficult to actually disprove any of it to a rigorous degree. It's as proven as it can get in science, with the caveat that there absolutely still is more to say about any topic, but the principle is correct, just somewhere there are little details.
If you ever find yourself in a situation where you'd need quantum Physics or transistor knowledge, then you probably also have studied it for a while in uni and this place is not the place you should get your information about these topics from, yes?
This also means, that all of the confusion I will later unearth, has been happening exactly like this for 100 years and has not been fixed, so either I am seeing a problem others are ignoring, or I see a solution others haven't seen yet.
Explanation/Orientation: We have the Mathemagical representation, symbol, of the physical world, a "model" so to say, on the left side. Typically there is some Name for a Phenomena and there is a Letter ascribed to it, fairly arbitrairaly.
On the Other side we have the thing you can touch and measure. The meter for example. These are often somewhat connected to the name of the person who did some thinking about it in years yonder. Like the measurable force-unid is called Newton. Oftenthymes someone will do a calculation only with the "models", then they will introduce the measurements, shorten all the units and, if they did it right, they end up with another meausurement-unit (like m/s).
I don't quite understand, why that step of abstraction is necessary, I do however know the it creates confusion.
Here are some criticisms and rocommendations I have:
- The Symbols are ill-related to the referential Topics.
- A better approach, at least for constants, would be something like a common letter (c, for constant), then a subscript for which it concerns itself with. (c_Boltzmann, c_Lightspeed, c_EarthGravityApprox, c_Spring, etc.)
- You currently see a letter in an equation (v, q, d, k, s, t, σ, ρ, λ, ...) and you do not know where it belongs or what it is trying to say, this is inefficient and a problem.
- This could partially be alleviated by ALWAYS writing, for example all physical measurements and their direct calculations inside a [ ] like so: [N = m/s² * kg]. Here you see that the ambiguous letters, through the context of the surrounding brackets. You know its not mass/square_distance or something like that, but the SI-units or other standart units being used to express a physical thing that could happen in the real world.
- Capacitance, Symbol C, Unit F (Farad); Electric Charge, Symbol Q, Unit C (Coulomb). IF THESE APPEAR ON THE SAME PAGE I AM GOING TO CONFUSE THEM.
- Permeability is just a mess.
- Whats often written as a V? Volume, Voltage, Volt, Velocity...
- Some of the greek Letters end up being very confusing and easy to confuse with each other. What are ξ and ζ? and why do they look like someone squished a ω onto my papers when I write one of those by hand?
- WHY are there 4 different Deltas with very similar, but I am assured they are different, meanings? Δ, δ, ∂ and d! Four! and they all mean something different aparently? but they also all are just the non-capital letter Delta? Madness.
- There appears to be no trying to unify and standardize these things! Newton would use ẋ, Leibniz dx/dt, another ∂x/∂t, or even x'
- exponentials: exp(x), e^x, e², 10², 10^2...
- Bad use of an exclamation mark after a number like 80! is such a big number, i doubt you've meant what you've written but what about 10! or 5! ? how would one know whether they just wanted to emphasize the number or use the factorial?
- not knowing how exponentials work, like two data points CANNOT be exponential, you neeed at leat three of them to begin describing an exponential growth, decay... It is somewhat infuriating, but in the end not that important.
- Complex numbers. Whats the letter to use? it i, no question, yes? oh if it werent a question, then why is it on the list???
- Degrees, Radian, Gon, π, Sterradian, all are used for the "same" thing, describing how far a circle is along its circleness.
- Sinus, Cosinus, Tangens. Nobody understands them.
- π vs τ
- You could make an iceberg out of this list
- there is Redshift z, but also Redshift Δλ/λ
- The Hubble constant is not constant, which would be excusable if it werent named constant but like... something with simultanious? Simult? Simconstant? Meanst? its the same everywhere now, but changes over thyme, so we call it by one simple new name, to differentiate it from true constants, which we suspect to be unchangable.
- Positions in coordinate systems. Computers count up, when they move down similarily in a matrix or a data set, but in physical space, usually x is along, but it can also be to go vertical.
- Energy is a mess there are Joule, Kalorie, eV, kWh, BTU... Then there are the cursed units lik KW/h/Year...
- EVERYTHING JUST GETS WORSE WHEN YOU TALK TO AN AMERICAN! They have their "intuitive" units, but the more abstracted meters have the advantage of being simpler to calculate with and being more definitevely defined.
- How do you write vectors? we but an arrow above it, but others write them in bold, or underline them...
- Any standaartization in the field of phyiscs also has to adhere to standarts that are further along, like in the field of chemistry, where they have actual international agencies that do stuff and it reaches even students in normal schools.
There are some standartization agencies and commities, but obviously there has yet to be any success in merging the whole system into a coherent whole.
Ultimately what is needed is some discipline by everyone to adhere to the correct units and then we maybe could actually advance.
Here are two videos by Joseph Newton about cursed units, for those interested:
https://www.youtube.com/watch?v=kkfIXUjkYqE
https://www.youtube.com/watch?v=Zg7xe8MkJHs
Have a good day, and praise the programmers, that build upon layer and layer of magic and don't need to concern themselves with the lower levels of the simulation.
I read stumbling into it and frankly that fits alright too.