I Why is length considered a fundamental (base) quantity?

[f95toli]

Note also that length is not unique in any way; ALL the base units (except the second) depends on time.
E.g. the Ampere can be realized by counting the number of charges that passes per second.

The reason for this reliance on time (=the realization of the second) is that this is by far the easiest quantity to measure; a regular atomic clock is accurate to 1 part on 10^15 or so; and the new optical clocks that are likley to replace the Cs fountains in a few years are at least 3 orders of magnitude better than that.
For the other units the realisations are typically at best accurate at a level of 1 part in 10^8. Hence,, time is much, much easier to measure than any other quantity and the fact that you need an accurate clock to measure e.g. electrical current is not going to be a significant source of errors.

Also, it is important to keep in mind that the SI is a practical system; having a "philosophically" satisfying system is useful unless you can also use it to calibrate instrumentation. The BIMP is ultimately controlled by a collection of governments and they are more interested in having a system that works in the real work than one that is "tidy".

Lastly, metrologists do NOT talk about "fundamental units"; it should be "base units" which is NOT the same thing. I don't think anyone would argue that there is anything "fundamental" about say luminous intensity, but it is a base unit

 

[Ahsan Khan]

They are seven base dimensions. They are NOT quantities.

Ok so these seven base dimensions can be inter-related (without violating the definition of base dimension)?

 

[Ahsan Khan]

Again, for the official reference on the SI see the brochure pdf here:
https://www.bipm.org/en/publications/si-brochure

or the nice html version here:
https://www.nist.gov/pml/special-publication-330

On p 129 of the .pdf they state:
So basically they indicate that the whole concept is outdated and is essentially just kept for historical consistency and usefulness.

So, for example, on p 131 the meter which is a base unit is essentially defined as $$1 \mathrm{\ m} = \frac{9192631770}{299792458} \frac{c}{\Delta \nu_{Cs}}$$
So its status as a base unit is nothing more than a convention with historical roots and has nothing whatsoever to do with the idea of some inability to define or express the meter in terms of other quantities.

In other words, the base units is simply a defined set of units that are called "base units".

They say prior to 2018 the seven(classified) base units were defined and the rest derived units were constructed using powers(combinations) of these base units. But with time we are now after 2018 are able to construct units of ANY quantity using the fundamental constants of nature and hence as of now those seven base units have remain in principle, no more different from the other derived units but we now are still giving them tag of base units for historical reason and their usefulness. I understand this. But let's say we are in year 2006. In 2006 that seven base units were not outdated rather they were of special significance. If we were to discuss this topic in 2006, how can any justify meter and second as base units(units which can't be expressed in terms of other) while also expressing meter in terms of second? The relationship : One meter is distance that light travels in 1/299792458 second!

Regards!

 

[Herman Trivilino]

But let's say we are in year 2006. In 2006 that seven base units were not outdated rather they were of special significance. If we were to discuss this topic in 2006, how can any justify meter and second as base units(units which can't be expressed in terms of other) while also expressing meter in terms of second? The relationship : One meter is distance that light travels in 1/299792458 second!

Derived units were constructed from combining the base units. In other words, the derived units depended on the base units for their definition.

The process of changing this arrangement so that the distinction between base units and derived units is a convention actually began in 1983 when they defined the meter in terms of the speed of light.

 

[Dale]

But let's say we are in year 2006. ...

I don't know, but you can look for historical versions of the SI document. They publish everything they do very publicly. You should be able to find the documents that were extant in 2006.

I don't see the point, so I will leave that as an exercise for you.

 

[anorlunda]

You are confusing the definition of quantities with the definitions of the units used to measure those quantities.

That's the best answer. Position is a physical quantity. Length is the difference in two positions. But the units used to measure position can be anything convenient, and can be defined by any valid procedure. The units are not the same as the quantity. Inches, meters, and light-seconds are all interchangeable units of length.

 

[f95toli]

Ok so these seven base dimensions can be inter-related (without violating the definition of base dimension)?

Yes, of course.
The only base unit that does not at least in principle somehow rely on any other base unit for the realization is the second.

Btw, "realization" is metrology speak for the actual experiment that is used to measure a quantity which is then used for e.g. calibrating secondary standards.
One difference between the new system and the old is that since we have now defined the fundamental constants there are multiple legitimate ways to realize most of the base units; in the past the SI prescribed one specific realization.

 

[jfmcghee]

The only base unit that does not at least in principle somehow rely on any other base unit for the realization is the second.

Is this in reference to the second being based on a cesium transition?

 

[vanhees71]

Indeed, if you think about the entire SI as it is defined today, everything starts and depends on the realization of the second as a unit of time. The reason for this is that time measurements are the most accurate measurements that can be done today. The other 5 physical base units are then fully defined by choosing the natural constants that can be realized also with sufficient accuracy ($c$, $\hbar$, $e$, $N_{\text{A}}$, $k_{\text{B}}$).

That time is still defined by referring to a specific substance (Cs-133 atoms) and not by also defining Newton's gravitational constant, $G$, is due to the impossibility to establish $G$ at satisfactory accuracy.

The 7th base unit, the candela, is more a physiological than a physical unit.