Re: The speed of light

=?iso-8859-1?Q?F=E1bio_Diales_da_Rocha?= (
Sun, 18 Jul 1999 23:56:11 +0100

From: Eliezer S. Yudkowsky <> To: <>
Sent: Domingo, 18 de Julho de 1999 20:49 Subject: Re: The speed of light

> 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

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