> John Clark wrote:
> >
> > OK, but how long is a second? Is it the time it takes light to travel
> > 299,792,458 meters? This sort of thing could give circular definitions
> > a bad name.
>
> The thing is, the definition of light is inherently circular. Once
> you've defined a "meter", you can only define the speed of light by
> reference to a "second", and you've automatically defined a "second" by
> reference to the speed of light. After all, there's really no such
> thing as separate units of "space" and "time". If you rotate a unit of
> time (a "second") by 90 degrees, it becomes a unit of space (299,792,458
meters).
Yes, but you can (and need) to define second in independent manner, or else
you'll end up not defining anything.
If you only say that x=ay and that y=x/a and give a a set value you don't
now anything about x or y. They could be any value at all. That's what you
end up with your circular definition of light.
Since the SI seems to know better than that they define a second as "the
duration of 9 192 631 770 periods of the radiation corresponding to the
transition between the two hyperfine levels of the ground state of the
cesium 133 atom".
> Trying to have a non-circular definition is like trying to have a
> non-circular way to convert units of "height" into units of "width".
> They're the same thing. You may live in some weirdo fantasy universe
> where you define height and width by entirely different measures, so
> that "height" is measured in inches by reference to the height of
> Nelson's Column, while "width" is measured in meters by reference to the
> circumference of the planet, and you use special sloping rulers to
> convert between them - but the fact is, height and width are the same
> thing, and no conversions are necessary; the debate about how to
> "define" these measurements in terms of each other is silly, you're just
> taking too many measurements.
Well, that would be all fine and dandy, except that time isn't just another dimension of space. As you might have noticed it is a dimension of time. There are some similarities but there are also many differences.
> The speed of light is equal to one. Any unit of time defines a unit of
> length, and vice versa; you just multiply by the speed of light, which
> could as easily be phrased as "one second per 299,792,458 meters".
You can define c to equal 1 (and that's what they do in that unitary units, or whatever it is called, system) which can be handy for several purposes (notably E=mc^2 turns into E=m, and some other simplifications) but that is still just as a convention as saying it to be 299,792,458 meters per second, or PI^sqrt(-35) yorts per tar.
Fábio Diales da Rocha