Wikipedia:Reference desk/Archives/Science/2016 September 25

= September 25 =

Absolute zero
Why is it impossible to reach absolute zero? GeoffreyT2000 ( talk,  contribs ) 00:23, 25 September 2016 (UTC)
 * Our page says:The laws of thermodynamics dictate that absolute zero cannot be reached using only thermodynamic means, as the temperature of the substance being cooled approaches the temperature of the cooling agent asymptotically. A system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state at absolute zero. The kinetic energy of the ground state cannot be removed. What more do you need?--86.187.169.34 (talk) 01:00, 25 September 2016 (UTC)


 * Another way to explain this is by pointing out that to cool something you either need to have something cooler or by letting the system perform work, the former s not going to be useful to reach 0 K and the latter method will in the best case conserve the entropy of the system while at 0 K the entropy is zero. Count Iblis (talk) 02:55, 25 September 2016 (UTC)
 * Absolute zero. AllBestFaith (talk) 11:31, 25 September 2016 (UTC)


 * I think this needs a better answer - unfortunately a better answer than I am prepared to give. Bear in mind that, say, the thermal oscillation of a diatomic molecule is quantized.   In theory, a single molecule of hydrogen could possess no extractable energy of this kind, hence be at 'absolute zero' in this sense.  More surprisingly, there also seems to be a quantization of the rotation of such a molecule, imposing rotational transition, so that source of energy (relative to a bulk material) too could be depleted.  If we can truly bring two molecules of hydrogen to absolute zero, is any mode of interaction between them also quantized such that it can be brought to genuinely zero?  I'm thinking yes though I don't know.  And if two, why not three, five, a hundred?  I am not sure whether a substance can be brought to such a low temperature that its probability of being genuinely at absolute zero becomes significant, though of course, given the number of molecules, that requires a very low temperature. Wnt (talk) 16:48, 25 September 2016 (UTC)


 * To bring a system to 0K you need to evolve its quantum state to the ground state which requires a sort of Maxwell's Demon set up involving extracting the information that describes the exact quantum state and moving that to another system (e.g. the Demon's memory). There is no other way because the fundamental laws of physics are unitary, which means that two different states cannot evolve to the same final state. So, you cannot have a generic procedure that involves manipulating only a few of the many parameters of an isolated system (containing the gas that we want to cool plus and supportive systems allowing that to happen). If you can make it work for one of the possible microstates of the gas, then it cannot work for another microstate, because that other state must necessarily evolve to another final state. The pigeonhole principle thus applies, you need to move all of the information that defines the exact physical state of the gas to anpther system or else the procedure will not work for some initial states. Count Iblis (talk) 19:07, 25 September 2016 (UTC)
 * This is probably a very insightful answer, but I'm having some trouble swallowing it. The whole issue with Maxwell's demon, as I recall, is that the information requires a certain amount of energy input, but here, we kind of expect any refrigeration we set up to require power.  As for the pigeonhole principle, well, I'm not understanding it.  I would think that there is no physical law against bringing a chamber arbitrarily close to absolute zero.  So if I have a chamber full of snowflakes that are 1, 10, 100, 1000, 10000 molecules in size, I would think that as I turn down the temperature, after a while some of the 1-molecule clusters will have zero point rotation and harmonic oscillation; then as I go lower, the same will be true of 2-molecule, then 10-molecule, eventually 10000-molecule clusters.  I won't know which is at absolute zero with certainty unless I come up with some clever way to take their temperature without heating them at all, but some of them ought to be, right? Wnt (talk) 15:49, 26 September 2016 (UTC)


 * But apparently it's possible to go below 0K? See: "Quantum gas goes below absolute zero" in Nature. --Hillbillyholiday talk 19:25, 25 September 2016 (UTC)
 * See Negative temperature. It's a confusing numbering system (and I don't think Nature explained it very well) but a negative temperature is actually higher than a positive one - to reach a negative temperature, you don't have to go lower than 0 K but rather higher than infinity K. If temperature is negative, the majority of particles are in a higher energy state. Keep going, you'll reach "negative absolute zero", when all the particle are in the highest state. Smurrayinchester 20:22, 25 September 2016 (UTC)
 * When we talk about negative temperature, the definition of temperature is not "average kinetic energy of the particles." Understanding the definition is the key to understanding the situation where negative temperature is possible.
 * In most simple conditions, the definition of temperature works out such that the average kinetic energy of each particle is exactly equal to certain other statistical measurements. So, we can freely switch between definitions.  In exotic scenarios where we have extremely high energy per particle, this exact equality breaks apart - and the statistical measurement ceases to correspond to the energy-per-particle.  Now, we can call the temperature negative, if we use the statistiscal measurement; or we can call the temperature very large and positive, if we use the energy-per-particle measurement; and we can quibble endlessly over which definition is more "correct."  The best way to proceed is to recognize that each methodology for defining temperature has a different purpose; grab a good book on statistical thermodynamics; and appreciate that these "negative temperatures" are a mathematical oddity in the statistics of very high energy matter.
 * Nimur (talk) 21:12, 25 September 2016 (UTC)
 * Why is it impossible to reach absolute zero?
 * I think previous answers have been great, but today I started meditating on this question a little more, and here's what I've got for today, sort of riffing on Mach's principle. My intent is to quickly summarize the answer in an intuitive way, without getting too technical.  If you really want a better and more technical answer, a good book is Stowe's thermal physics book, which I consider to be one of the best books on pure physics at large.
 * Temperature is the ability for a particle to do work.
 * Work can be performed by colliding - especially inelastically - with another particle.
 * As long as there exists another particle, anywhere in the universe, who is not absolutely stationary with respect to your test particle, your test particle can, in principle, collide with it, and do work.
 * If you think of the temperature as the average kinetic energy, which is derived from the average velocity of the particle, then the only way to get the temperature to zero is to make the test-particle stationary - but because there is no universal reference frame, with respect what reference can we measure the velocity of the test particle? We sort of need to start expanding the volume we are considering, and compare our test-particle's velocity to the statistical average position of all other particles in an ever-expanding volume, up-to-and-including- the entire universe.
 * You can't slow a particle to zero velocity without slowing the velocity of every other particle, everywhere, also to zero, measured relative to your completely-arbitrarily-selected particle.
 * This is not a particularly precise formulation of the problem, but maybe it will give you some insights into how temperature gets defined. Ultimately, temperature is a statistical measure.  As you approach zero temperature, your statistics get less and less relevant unless your particle population becomes bigger and bigger.  This is why we can, in a laboratory, make a small clump of matter get really close to zero temperature; but we can't get it all the way to zero.
 * Nimur (talk) 21:28, 25 September 2016 (UTC)
 * The "average kinetic energy" formulation is not a bad conceptual place to start to get a mental image, but unfortunately a lot of people over-internalize it. Without special pleading and creative bookkeeping, it applies only to monatomic ideal gases.  I have to object to your claim above that it works in "most simple situations", when actually it doesn't even work in solids. --Trovatore (talk) 15:25, 26 September 2016 (UTC)
 * Trovatore makes a very fair point; if anything, it highlights the difficulty in trying to explain thermodynamics without using complicated technical language and equations. It's difficult to be correct, precise, and easy to understand.
 * For the record, I just pulled three physics books off my shelf and got three differing qualitative descriptions for which definition of temperature is "most fundamental." My plasma book, Bittencourt, insists that mean kinetic energy is the correct definition, but further insists that because kinetic energy may exist in many different modes of motion, you must therefore use multiple different temperatures to describe each separate energy-mode for the same substance... so a solid may have a crystal lattice temperature and an electron temperature and it might even also have a distinct phonon-temperature for each eigen-phonon you can decompose its vibrational modes into...
 * I actually like this approach, because it keeps the definition simple at the expense of making the application of the principle quite difficult. (Well, ...it becomes tedious, more than it becomes difficult - and it's a great example of an application where a computer method can save the day by automating tedious-but-straightforward bookkeeping!)
 * My other book, Stowe, uses the entropy definition that we all know and love - making the explanation very complicated, but the calculation of temperature becomes trivial.
 * Suffice to say that there's a little bit of domain-specificity with respect to which definition one would prefer to use.
 * Nimur (talk) 15:42, 26 September 2016 (UTC)