# If quantum gas goes below 0K, is calling 0K absolute zero irrelevant?

Lord Kelvin defined the absolute temperature scale in the mid-1800s in such a way that nothing could be colder than absolute zero. Physicists later realized that the absolute temperature of a gas is related to the average energy of its particles. Absolute zero corresponds to the theoretical state in which particles have no energy at all, and higher temperatures correspond to higher average energies.

This and many other articles out there say that quantum gas can go below zero kelvin.They(the professors) teach that -273.15ºC is lowest temperature anything can attain and that's why it is called absolute zero.

My question is not about whether materials can or can't attain sub-0K temperatures. I'm asking, should we stop calling 0K as absolute zero?

• Possible duplicates: physics.stackexchange.com/q/21851/2451 and links therein. – Qmechanic Jan 27 '14 at 13:07
• I have posted that it(what the possible duplicate is about) is not my question.I'm asking it it is correct to call 0k as absolute zero? – user38331 Jan 27 '14 at 13:12
• For all people,If you think my question is good, up vote it.If you think it's bad,feel pride in down voting it.But please do vote.It gives a feedback to new users like me to know if I'm doing good or bad. – user38331 Jan 27 '14 at 14:16

Temperature is casually associated with hot and cold. How can something be “colder” than absolute zero? The answer lies in a more precise notion of temperature. Temperature is a single-parameter curve fit to a probability distribution. Given a large number of particles, we can say each of them has a probability to have some energy, P(E). Most will be in low-energy states and a few in higher-energy states. This probability distribution can be fit very well with an exponential falling away to zero. Of course, the actual distribution may be very noisy, but an exponential fit is still a good approximation (see the figure, panel A). Negative temperature means most particles are in a high-energy state, with a few in a low-energy state, so that the exponential rises instead of falls (see the figure, panel E).

To create negative temperature, Braun et al. had to produce an upper bound in energy, so particles could pile up in high-energy rather than low-energy states. In their experiment, there are three important kinds of energy: kinetic energy, or the energy of motion in the optical lattice; potential energy, due to magnetic fields trapping the gas; and interaction energy, due to interactions between the atoms in their gas. The lattice naturally gives an upper bound to kinetic energy via the formation of a band gap, a sort of energetic barrier to higher-energy states. The potential energy was made negative by the clever use of an anti-trap on top of the lattice, taking the shape of an upside-down parabola. Finally, the interactions were tuned to be attractive (negative). Thus, all three energies had an upper bound and, in principle, the atoms could pile up in high-energy states.

It's not a very important question that if we should stop calling absolute zero by it's current name. It's just a name, and misleading though it may be for works such as those mentioned, it is the general case. Quite like most engineering books which contain circuit diagrams with positive charges moving! That is quite obscene, but it's what they call convention.

http://www.sciencemag.org/content/339/6115/42.full

http://www.sciencemag.org/content/339/6115/52

• science is perfection?Isn't it.So why should be call something some-other-thing if it's not actually some-other-thing? – user38331 Jan 27 '14 at 13:15
• As long as you know that it's that other thing.. To this day, most engineering books contain circuit diagrams with positive charges moving! that is quite obscene, but it's what they call convention. – Hasan Jan 27 '14 at 13:17
• Nice example.I remember losing marks because I show negative charge moving.Got your point. – user38331 Jan 27 '14 at 13:19
• How can something be “colder” than absolute zero? The quote is misleading since negative temperatures are hotter than everything else. – jinawee Jan 27 '14 at 14:18
• – jinawee Jan 27 '14 at 17:49

I think saying absolute zero is correct, since temperature goes from near $0^+\mathrm{K}$ to near $0^-\mathrm{K}$, without going through $0\mathrm{K}$.

So you could say that $-100\mathrm{K}$ is higher than $\infty \mathrm{K}$. This why in some cases, temperature is not well defined and we should use coldness $\beta = \frac1 T$ (I've seen some papers which recommend other definition of entropy to avoid negative temperatures).

Physicists later realized that the absolute temperature of a gas is related to the average energy of its particles. Absolute zero corresponds to the theoretical state in which particles have no energy at all, and higher temperatures correspond to higher average energies.

This is the classical definition of temperature. In the links Qmechanic posted, you can see that the statistical definition is:

$$\frac 1 T = \frac{\partial S}{\partial E}$$

So temperature is defined by the way entropy varies wrt. energy.

And in quantum mechanics you will learn that absolute zero doesn't imply zero energy.

Still, this is more terminology and conventions than physics, since some word is correct if it's accepted by the rest of the people.

• Explain this.I isolate a particle and bring it's energy to zero.What's it's temp now? near 0<sup>+</sup>K or near 0<sup>-</sup>K? – user38331 Jan 27 '14 at 13:57
• @adityapatil I'm just an undergrad, but I think it's a tricky question because free particles don't have definite energy. But think that in almost every case you will encounter positive temperatures (negative temperatures require an energy upper bound). – jinawee Jan 27 '14 at 14:16
• What unit is GB/nJ? Is that GigaBytes per nanoJoule (so entropy / energy)? – The_Sympathizer Jul 8 '16 at 6:59