Friday, July 3, 2009

Strange conversions

From this part of the xkcd fora:

note that if you measure distance in seconds velocity becomes dimensionless. In particular you could put c = 1. All velocities would then be measured as fractions of c.

The idea is similar to lightseconds but not the same, since lightseconds is actually a unit of length, whereas here we have introduced a system of units in which any dimensionfull quantity can be expressed as any other one (if we also have h = G = 1). That is we can express mass as a certain multiple of an inverse meter, or second. So mass is really the same as a frequency. And of course in this system all our usual units correspond to particular dimensionfull quantities: one meter, one second, etc. And thus they can be expressed in terms of each other.

I never though of this before. Basically, if you express distance in seconds, or any other unit of time, then velocity, which equals distance over time, has seconds as the unit on both the top and bottom of the equation, and is thus dimensionless. Thus, you could express velocity as a simple number, say, 0.2 (i.e, 0.2c or about 60,000 km/s), rather than including units.

A similar idea is used with transonic speeds; Mach number, a dimensionless quantity, is used rather than a unit-ed velocity.

In the above syste, there's other weird stuff: mass is in units of m-1 or s-1, and can even be expressed as a frequency.

Thank you to Certhas, whoever you are.


KenKzak said...

Nice explanation. Also the comparison of fractions of C to Mach numbers is a good point.
When flying aircraft, the airspeed in knots, nautical miles per hour, still has little or no bearing on the arrival time, since it's not the same as the groundspeed. Therefore Mach number is as good as any for a fast aircraft, say M0.5+.
In interstellar space, the same certainly applies for C.

BTW; I'm currently finishing my 3rd rocket named C/Fraction, though it's different enough from the 1st 2, to warrant a new name. All are watermelon seeds with boat tails derived from nose cones,and slick glass fins. The 2 originals had Xenon strobes for night flying though.

The EGE said...

Watermelon seed rockets? This I have to see.

Sam said...

hey its Sam from engineering camp! nice blog. i have been refining my rubik's cube skills... anyways, nothing really for me to say about your latest post. later!

The EGE said...

Ha-ha. I have now infected you with the rubix virus!

You gonna get a 5x5x5?