Re: Is 0K absolute zero and does absolute zero exist?

Patrick,

Temperature can get quite confusing. After a full year of undergrad study,
a quarter-long grad school class, and several years as a researcher, I like
to think I've got a handle on it. Now we'll see if all that study helps me
to clarify this particular question for you. My answer will likely be long,
because you bring up a bunch of issues - quantum mechanics, negative energy,
etc. I hope to make it readable enough that you stick with me.

Your teacher is correct when she says that "absolute" in reference to
temperature is a special term. The international standard unit for absolute
temperature is degrees Kelvin. Of course, you could make another "absolute"
scale that was 2 Widgets per Kelvin, or 0.274 Hoozits per Kelvin, but all
the absolute scales would have one thing in common: the zero point, or
origin. Other scales, like Celsius (aka centigrade) and Fahrenheit, are
relative temperature scales because the zero point is set relative to
some reference system (like the freezing point of water at 1 atmosphere of
pressure). The Kelvin scale, on the other hand, has an origin that is
based on fundamental physics, and is independent of how or where you
measure it. Good physical theories involving temperature must use absolute
units, because they should be independent of the tools used to make a
measurement.

OK, now lets address your confusion about the Kelvin scale. As you are
aware, temperature is related to the energy of the system. For warm gases,
you can get really far just relating the temperature to the average kinetic
energy of the gas particles. The faster the particles are moving, the hotter
the gas is. Pretty simple. In order to understand some of the issues you
are facing, down near absolute zero, there is another component to the
definition of temperature that matters: entropy.

Entropy is one of those wonderful words that is used in common speech, but
the vast majority of people have only a vague, qualitative sense of its
meaning. It is generally used as an intellectual-sounding synonym for
"disorder." Some people also have picked up the second law of thermodynamics,
that entropy (read: disorder, chaos) in the universe is always increasing.

A more accurate description of entropy is that it is a measure of how many
"states" a system can access. For the warm gases I mentioned, the "state"
of a particle is just its position and velocity. A large volume of gas has
more entropy because the particles can get to more possible positions. A
hotter gas has more entropy because there are more velocities they can have.
Add more particles and you've increased the entropy because there are more
combinations of positions and velocities that the gas can achieve.

Entropy is then a question of statistics and probability. Raw numbers. Count
the number of possible states. The thing that makes the Kelvin scale 
"absolute" is that it is defined in terms of entropy. Specifically, 
temperature is a measure of how the entropy increases as you add energy to 
a system. For those who've had calculus, it is defined 1/T = dS/dE (the
rate of change of entropy [S] as you add energy [E]).

Think of a gas in which none of the particles are moving. The
entropy is very low, because there is only one state: all the particles
right where they are. Now add just a teeny bit of energy, and suddenly you 
have increased the entropy immensely. Now the particles can get anywhere in
the box, however slowly. On the other hand, if you add just a little bit of
energy to a very hot gas, you haven't made a big change in the entropy. 
There is maybe a slight increase in the velocity that the particles can 
achieve, but that's it.

When you can add a miniscule amount of energy and make a huge change in
entropy, the system is cold. When adding energy makes a tiny change in
entropy, you have a hot system. In the limit that adding any energy at
all, as close to zero as you can get, will increase the entropy, then
dS/dE gets close to infinity, and T is "absolutely" zero. Note that this does
NOT mean that there is no energy in the system (like you said, there is
always some minimum energy due to the Uncertainty Principle). It does
generally mean that all particles have to be in their lowest possible
energy state. Since the lowest energy state of an electron in an atom is
stable, the electron will not fall into the nucleus, which was one of your
"concerns."

Still, it is generally considered impossible to physically achieve absolute 
zero. Any system you make will have to be in some kind of contact with the 
rest of the universe, so there will always be a source of energy and 
entropy that you can never fully shield out; however, there are 
commercially available cryostats (fancy name for refrigerator) that will 
get you well below one Kelvin, and I know 50 milliKelvin has been achieved. 
Since I'm not familiar with the forefront of technology on this subject, 
one could assume they've done better.

Now, briefly, the question of negative temperature. The discussion of
negative temperature is limited to a very special situation, namely one
in which the total number of states available is limited. The system in
which this has been seen experimentally is "spin temperature." For a
particle that has "spin," there are only two possible values -- "up" and
"down." Generally we think of "down" as the lower energy state, and "up"
as the higher energy state. At minimum energy, all the spins are down.
As you add energy, some of the particles "flip" to the spin-up state.
As the energy goes up, particles are able to be up or down, and flip back
and forth as they interact with the other particles. Eventually, you get
to the maximum entropy state, where all the particles are equally likely
to be spin up or spin down. Maximum "disorder." 

Now add more energy. Suddenly, you find that more particles tend to be 
"up." The system is actually more ordered. Eventually, as you continue 
adding energy, you find that all the particles have to be "up" in order to 
hold all that energy. Well, now you have a nice, ordered system again, with
very low entropy. All the particles are in exactly the same state... the 
high energy state. Once you got to the maximum entropy state, adding more 
energy actually reduced the amount of entropy. Since Temperature is a 
measure of the increase in entropy as you add energy, in this situation you 
have a negative spin temperature. Note the addition of the word "spin." 
These particles are also able to move, vibrate, etc., and entropy will 
continue to increase in those motions as you add energy. The negative 
temperature comes in only if you narrow your attention to the spin states 
alone. A very specialized system, and unusual because the total number of 
states available is limited, putting an upper limit on the entropy. Contrast
that with a gas, which in principle can always expand and/or gain kinetic 
energy, without limit.

I know it sounds strange, but it is true that we can "achieve" negative
absolute temperatures without ever having been at absolute zero. Because
of the way temperature is defined, you can heat up a spin system only to
some maximum value, then once you hit the maximum entropy, your temperature
immediately changes sign. You could think of it as now being "hot" in the
other direction. Add more energy, and the system becomes more orderly
again, approaching absolute zero from the negative side.

OK, I think I at least made a stab at all the components of your question.
If you aren't confused enough yet, you can try one of these physics FAQ 
sites:
What does Negative Temperature Mean?
University of Missori, St. Louis

I'm sure there are more. I found these on the first page of an Excite
netsearch of "spin temperature" (quotes included to ensure that it was
searched as one phrase). Try your favorite search engine.