1

I understood that from cesium that we derived the unit for second and procedurally with other universal constants we derived the other SI units. Can all other “physical” units be derived from the seven base SI units, or does it need the help of other universal constants, or are there entirely new units that is derived solely from different universal constants. Of course, I would think that it is naive to believe that no future constants will be derived entirely independent with new universal constant.

Also, upon reviewing other posts, i understand that the SI base quantities have nothing to do with its fundamentality, where it is created for its daily life impact on us. My second question would be what are the most fundamental units?

Helios
  • 49

2 Answers2

1

I am not sure what other posts you have reviewed, but the standard literature covering SI units, also make clear that the SI units of mole and candela are redundant and solely made for convenience.

Your question is thus actually down to

Are all physical constants expressible in terms of the fundamental 5 SI units?

in which case the answer is yes, for now. That is, before we had the technical precision to base SI units in terms of physical constants, we already successfully defined the units of all known physical constants in terms of SI units, and so unless we discover new physics and new physical constants, all other constants are already expressed.

I am a theorist myself, and it would have made theorists' life a lot better if everybody migrated to natural units. However, the main jobs of a unit system are

  1. to be standardised,
  2. to greatest precision,
  3. and be in widespread use.
  4. Be relatively clear and not error-prone.

Everything else pales in comparison. It is the engineering industry (and science along with it) that requires the greatest precision, and only if precise measurements of the physical constants allow us to use them as the definition of the units, are we actually industrially allowed to define units via physical constants.

You might be wondering where my theorist jab came from. It actually matters: Modern physics now understands that temperature is just a Boltzmann's constant away from energy, and so temperature should be measured in Joules (or energy in Kelvins, whichever is preferred). Similarly, either we all move to measure in lightseconds, or in lightmetres, etc. Defining things properly in the theorist's garden, then, would be that all units except one will be fixed, and while we are at it, we might as well set the last one too. And then nothing will have units. i.e. what you call "base" or "fundamental", in the context of unit systems, are all nonsense.

naturallyInconsistent
  • 14,919
-1

The short answer, to the best of my knowledge is, yes.

Let us start by listing out the base units. We have

  1. second
  2. kilogram
  3. meter
  4. Ampere
  5. kelvin
  6. mole
  7. candela

Now, run a few arbitrary checks on physical quantities, checking to see if they can be derived. For instance, the easiest example would be that of force, measured in units of Newton. 1 N of force can be derived by multiplying 1 kilogram with meter and dividing by second squared. Can you similarly do such manipulations to arrive at other SI units? The answer, like I said, is yes.

Is the help of universal constants required?

You should understand that when I say universal constants, my mind immediately jumps to constants like Planck's constant $h$, or the gravitational constant $G$. These constants aren't exactly "units" per se. Indeed, they themselves are defined in SI units, i.e., $h \approx. 6.626 \times 10^{-34} Js$, and using the exact value of Planck's constant, the unit kilogram is defined.

What I mean to say is that yes, some SI units are derived using a combination of other units and some universal constants (think mole, defined as containing exactly $N_A$ elementary entities). As for other SI units, they need the base units to be defined and some of them may also involve universal constants; there's no law saying that can't happen.

An Interesting Note

Also, an interesting thing to note is that even the base SI units themselves aren't exactly independent. A very good explanation of this is given at this link.

Disclaimer

This is what I have been able to gather from my research. If someone more knowledgeable than I has something to add, drop a comment and I'll update.

Mohammad Yasir
  • 43