# Building a measurement system based on C

1. Aug 8, 2013

### jnorman

I always try to assume that pretty much anything I think of has been thought of before, so I am relatively sure that this is also not a new question.

we base our current measurement systems on arbitrary lengths such as the meter or foot, etc. there are certain applications where we use actual physical constants, but in general, all our measurements, since they are based on arbitrary items like the meter, are very awkward numbers with lots of decimal points - hard to remember and not reflective of the real constants of the universe.

so, my question - has someone considered, or actually developed a system of measurement that is based on a true universal constant such as the speed of light - ie, where C=1 unit, or something similar? where can I read about this topic?

thanks.

2. Aug 8, 2013

### Staff: Mentor

It's very common to use units where c = 1 in relativity and particle physics. See: Natural units

3. Aug 8, 2013

### ghwellsjr

The meter used to be defined as a physical length but now it is defined as how far light travels in 1/299,792,458 of a second, so yes, your idea has already been thought of and implemented.

4. Aug 8, 2013

### jnorman

gentlemen - thanks for your responses - the wiki article on natural units was quite helpful.

5. Aug 8, 2013

### stevendaryl

Staff Emeritus
The speed of light isn't sufficient to have a system of measurements, because you still need to choose a unit of length, and that's kind of arbitrary. You could base the unit of length on something physical, such as the Bohr radius of a hydrogen atom, or the Planck distance.

6. Aug 8, 2013

### phinds

HUH ??? The speed of light DEFINES the unit of length (did you not read the previous responses?). What is needed in addition to it is the unit of TIME to complete the definition and we have a well-defined unit of time, called the second, which is based on the cesium atom.

7. Aug 8, 2013

### stevendaryl

Staff Emeritus
Well, using the speed of light as a conversion factor, you can either have a unit of length L, and get a unit of time T by letting T = L/c, or you can have a unit of time T, and get a unit of length by letting L = cT. In either case, you need another unit.

8. Aug 9, 2013

### rbj

phinds, the speed of light only defines a unit speed. to define a unit length from c you need a unit time or to define a unit time from c you need a unit length.

the unit time based solely on the cesium atom could be (among other candidates) a period of time that is 1/9192631770th second. the 9192631770 is solely anthropometric, not a definition from nature at all. and the choice of the cesium atom might seem to be a bit more arbitrary than the choice of $c$, $G$, or $\hbar$. but for us humans, at this stage in our development, a clock based on 133Cs makes for a much more stable and reproducible and accurate clock than one based on $G$. so what is practical for humans at present is not what is ultimately a natural system of units.

i might recommend to the OP to look up Planck units and fundamental physical constants in wikipedia also. and maybe check out the Baez and two Duff articles cited. there is an older version of the Natural units article that spoke more fundamentally about building various systems of units based solely on natural and universal quantities.

9. Aug 10, 2013

### arydberg

Let time be measured in nanoseconds and length be measured in feet. Error should be less than 3%.