Originally posted by PBE6
As I understand it, Bose-Einstein condensates only occur at low temperatures because at low temperatures the particles can only take on a few energy states. High temperatures, even with extreme pressures, wouldn't duplicate this effect.
The underlying problem being the De Broglie wavelength has to be big enough to include several atoms. The higher the temp, the smaller the De Broglie wavelength, so it would be flat impossible no matter what the density. It is related to the momentum of particles or macroscopic masses too, but as the rest mass goes up, the wavelength goes WAY down:
W(De Broglie)=h/mv*Sqr Root(1-V^2/C^2) so the lower the rest mass and momentum, the larger the wavelength till as you get down to the NanoKelvin area, the wavelength becomes larger than individual atoms or molecules and they all start marching in step, like a laser beam, they effectively become one particle. The last part of the equation is the Lorenz equation, which also shows up as the contraction of space as you get closer to C and the contraction of time also (the twins paradox, which isn't)
h=planck's constant, m=rest mass, v=particle velocity, C= speed of light. Planck's constant is 6.62E-34 M^2*Kg/s (meter squared times Kilogram/seconds) so it helps if all the units are in Meters, Kilograms and seconds. With that you should be able to get a measure of the size of the wavelength as the particle slows down.
It is obvious on inspection the Lorenz part of the equation is just for relativistic velocities, so you can effectively ax it since it would be so close to 1 (Sqr root of (1 minus 1/C) ) Where I chose the velocity to be one meter per second, just a guess on my part but you see what I mean. So for these extremely slow velocities it would become simply h/mv, still in kg and meters/second. Just doing a quickie calc on pure protons, lets assume the buggers can become a BEC, then it would be at a velocity of 1 meter/sec, and the rest mass of a proton at about 1.6E-27 Kg, 6.62E-34/1.6E-27, De Broglie wavelength of 4E-7 meters, where the size of the proton is about 1.6E-15 meter, so the wavelength in that case is a hundred million times the size of the proton or so, way big enough to include a bunch of protons into a BEC if they could be pursuaded to do so.