# Re: [curiosa] Re: Debian Centre of Mass

```On Sat, Jul 07, 2001 at 08:24:43PM +0200, Martin F. Krafft wrote:
> also sprach Steve M. Robbins (on Sat, 07 Jul 2001 01:54:25PM -0400):
> > > nonono, it is physically impossible for *anything* to go colder than
> > > 0K *because* all particles stop moving. kinetic energy (i.e.
> > > temperature) doesn't care about the sign of the velocity (i.e. the
> > > direction) since it's squared anyway.
> >
> > For a system to have negative kinetic energy,
> > the particles just need to have imaginary speed...
>
> i do admit that i am not a genious in particle physics, so could you
> please elaborate? have negative kelvin temperatures been reached?
> usually, i would say no and not believe anything else, but you never
> know with the quantum stuff going on.
>
> and imaginary speed... are you talking irrational numbers?

No, he would be talking about imaginary numbers - i.e. numbers based around
the square root of minus one ((-1)^0.5), represented in mathematics by the
letter i. For example,

sqrt(-4) = sqrt(4 * -1) = 2 * sqrt(-1) = 2i

A lot of maths is based around them, and they are useful for many things (in
maths). For example, what are the solutions to the equation

x^2 + 4x + 5 = 0 ?

You can't treat it as a normal quadratic equation, because there are no real
numbers that fit. In fact it turns out the possible solutions are

x = -2 + i or x = -2 - i

(You can confirm this by putting these answers into the original equation -
remember that i^2 = -1.)

Of course, I doubt whether anyone could imagine what an imaginary velocity
would look like, although it might be interesting to put it into some standard
mechanical/physical equations and see what happens...

But no, negative kelvin temperatures have not been reached, to the best of my
knowledge. I don't think that 0 K (how are you supposed to abbreviate Kelvin
without making it look like kilo) has been reached, but some people have
gotten close.

Dafydd Harries

```