## Friday, 25 March 2011

### Direction

Interesting:
The speed of light is a dimensional quantity and so, as has been emphasized in this context by João Magueijo, it cannot be measured. Measurable quantities in physics are, without exception, dimensionless, although they are often constructed as ratios of dimensional quantities. For example, when you measure the height of a mountain you really measure the ratio of its height to the length of a meterstick. The conventional SI system of units is based on seven basic dimensional quantities, namely distance, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.
I'm missing something obvious, of course, or perhaps merely displaying my slow-wittedness; but where is orientation on this list? (I mean, for instance, the angle in a triangle's corner). Is 45⁰ the ratio between two dimensional qualities? Surely not. Another way of putting it: from the point of view of a photon, time and space are effectively dimensionless; but direction of travel still matters.

#### 1 comment:

Alexey Romanov said...

Actually, it is. To quote the Wikipedia:

In order to measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g. with a pair of compasses. The length of the arc s is then divided by the radius of the circle r...