# What are the fundamental units of nature?

## Main Question or Discussion Point

So far, all i can think of is: mass, time, length & charge (maybe?). Temperature isnt even a fundamental unit, since it is a measure of kinetic energy of a particle (1/2*m*vrms^2=3/2*k*T, i think thats right...), am i missing any? If that's all of them, then thats pretty amazing to me.

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An ampere has a more natural definition than the Coloumb, or at least that's the usual one that's cited as being the more fundamental in SI. It's the current through two identical uniform parrallel bars separated at 1 metre that produces a $2\times 10^{-7}N$ force between them. A Coloumb is then just an amp second.

The Kelvin also has a physical definition, as the Gas laws are an idealisation.

All the SI definitions are pretty straight forward. There are different unit systems though.

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Astronuc
Staff Emeritus
mass, time, length & charge
mksq - that is pretty much it, and IIRC everything else can be derived from that. As for what units to use, that's pretty arbitrary, i.e. up to the user/beholder.

Nature is what is and does what is does, and we are simply participants and observers.

russ_watters
Mentor
And minor clarification: properties, not units, is what you are looking for. Units are arbitrary (mostly), as Astronuc said.

finchie_88
An electronvolt?

1 eV = 1.602 x 10E-19 (kg*m^2/s^2), mass, length, time....

You forget the amount of a substance - the mole.

nrqed
Homework Helper
Gold Member
jasc15 said:
So far, all i can think of is: mass, time, length & charge (maybe?). Temperature isnt even a fundamental unit, since it is a measure of kinetic energy of a particle (1/2*m*vrms^2=3/2*k*T, i think thats right...), am i missing any? If that's all of them, then thats pretty amazing to me.
Actually, a new unit for charge is not absolutely necessary. In SI units it comes about because there the $\epsilon_0$ but you can use a system of units (Gaussian units for example) where there is no need for a new unit of charge. After all, one could define th emagntidue of the electric force to be |q1| |q2| / r^2 in which case a charge has the units of the square root of the units of force times the units of distance.

pervect
Staff Emeritus
Base SI units are, conventionally

http://physics.nist.gov/cuu/Units/units.html

length, mass, time, thermodynamic temperature, current, amount of substance, and luminosity.

Temperature can be eliminated by realising that by making Boltzman's constant equal to 1, temperature is equivalent to energy.

Time can be eliminated by setting c=1, and using units of distance

Mass can be eliminated by setting G/c^2=1, usually done after setting c=1, and using units of distance to replace units of mass.

Current is charge/second, and charge can be eliminated by setting the permittivity of free space to 1, as in cgs units.

Amount of substance (mole) is just a constant number

Luminosity (candella) I don't use much, but with all of the above it can be eliminated as well.

This leaves one "base" unit, the scale factor of space-time, the cm. This system of units, with one base fundamental unit of distance (the cm) is commonly known as "geometric" units.

The single base unit in geometric units can be eliminated by setting the value of planck's constant equal to 1.

This leaves no fundamental units - so called "Planck" units.

I would suggest sticking with the SI units for general communications, but in working problems in GR I find geometric units very useful.

If I did more quantum mechanics, I'd make a different choice.

People doing a lot of theoretical E&M often use one of the cgs unit variants with permittivity set to 1 and a few other tweaks.

About the only people who use pure Planck units are people who need both quantum mechanics and gravity, i.e. people into quantum gravity.

In conclusion, there are a lot of different possible choices for units, the standard recommended choice for ease of communication is the SI units. These are defined and designed to be portable and easy for everyone to understand, different fields tend to have different convenient alternate choices that usually must be learned by anyone in that specific field.

rbj
jasc15 said:
So far, all i can think of is: mass, time, length & charge (maybe?). Temperature isnt even a fundamental unit, since it is a measure of kinetic energy of a particle (1/2*m*vrms^2=3/2*k*T, i think thats right...), am i missing any? If that's all of them, then thats pretty amazing to me.
i would not call these fundamental "units" but fundamental dimensions of physical quantity, and, i too, view time, length (or distance), mass, and electric charge to be the most fundamental dimensions of physical quantity that pretty much all other quantities such as momentum, force, energy, power, density, pressure, voltage, current, resistance, etc. are derived from. now this doesn't mean that a system of units like SI will do it that way (they define current and charge from that).

nrqed said:
Actually, a new unit for charge is not absolutely necessary. In SI units it comes about because there the $\epsilon_0$ but you can use a system of units (Gaussian units for example) where there is no need for a new unit of charge. After all, one could define th emagntidue of the electric force to be |q1| |q2| / r^2 in which case a charge has the units of the square root of the units of force times the units of distance.
all this is true, but while i have no problem understanding force as the time rate of change of momentum (not merely proportional to the time rate of change of momentum), i still refuse to understand electric charge as length times the square root of force or as speed times the square root of mass times length. it is proportional to such, but is not the same stuff as that.

you might want to look up Planck units, dimensional analysis, and fundamental unit at Wikipedia and see what others might think.

pervect said:
About the only people who use pure Planck units are people who need both quantum mechanics and gravity, i.e. people into quantum gravity.
and dilettantes like me who like to imagine what are the intrinsic units of Nature, and maybe what would be discrete quanta of time and length if it turned out that Nature was really discrete. i guess that really means that i don't really "use" pure Planck units.

Andrew Mason
Homework Helper
nrqed said:
Actually, a new unit for charge is not absolutely necessary. In SI units it comes about because there the $\epsilon_0$ but you can use a system of units (Gaussian units for example) where there is no need for a new unit of charge. After all, one could define th emagntidue of the electric force to be |q1| |q2| / r^2 in which case a charge has the units of the square root of the units of force times the units of distance.
That would be units of of $\sqrt{Ed}[/tex]. You could make it just as simple and have units of only energy, distance and time. Charge would be in units of [itex]\sqrt{Ed}$, mass would be in units of E/(d/t)^2.

AM

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HallsofIvy
Homework Helper
jasc15 said:
So far, all i can think of is: mass, time, length & charge (maybe?). Temperature isnt even a fundamental unit, since it is a measure of kinetic energy of a particle (1/2*m*vrms^2=3/2*k*T, i think thats right...), am i missing any? If that's all of them, then thats pretty amazing to me.
If we're going to talk about really "fundamental" units then we need to think about things that have a "natural" unit, not arbitrary. In my mind that lets out length or time.

Speed is a natural unit sense we can refer any speed to the speed of light. As rbj and russ_waters said, speed is actually a "dimension" or "property" and the speed of light is the fundamental unit.

"Action" would also be a fundamental "dimension" with Plank's constant as fundamental unit.

There would also be a fundamental unit based on the universal gravitational constant.

Of course, charge would be fundamental- the fundamental unit being the charge on a single electron.

I remember reading a paper on this many years ago. In terms of those units, the length unit (derived from Plank's constant and the speed of light) would be the diameter of an electron and the time unit would be the time for light to cross that distance.