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
