Cooling To Absolute Zero Mathematically Outlawed After a Century (newscientist.com)

After more than 100 years of debate -- which at one point even elicited interest from Albert Einstein and Max Planck, physicists have finally offered up mathematical proof of the third law of thermodynamics, which states that a temperature of absolute zero cannot be physically achieved because it's impossible for the entropy (or disorder) of a system to hit zero. While scientists have long suspected that there's an intrinsic 'speed limit' on the act of cooling in our Universe that prevents us from ever achieving absolute zero (0 Kelvin, -273.15 C, or -459.67 F), this is the strongest evidence yet that our current laws of physics hold true when it comes to the lowest possible temperature. From a report on NewScientist: Now Jonathan Oppenheim and Lluis Masanes at University College London have mathematically derived the unattainability principle and placed limits on how fast a system can cool, creating a general proof of the third law. "In computer science, people ask this question all the time: how long does it take to perform a computation?" says Oppenheim. "Just as a computing machine performs a computation, a cooling machine cools a system." So, he and Masanes asked how long it takes to get cold. Cooling can be thought of as a series of steps: heat is removed from the system and dumped into the surrounding environment again and again, and each time the system gets colder. How cold depends on how much work can be done to remove the heat and the size of the reservoir for dumping it. By applying mathematical techniques from quantum information theory, they proved that no real system will ever reach 0 kelvin: it would take an infinite number of steps. Getting close to absolute zero is possible, though, and Masanes and Oppenheim quantified the steps of cooling, setting speed limits for how cold a given system can get in finite time.

Comments

Re:Zeno's Paradox

[mark-t]

Actually, 0.999... *is* equal to 1.... in real life. They are simply two different ways of describing the exact same number.

I'll give you benefit of the doubt and assume that you are not somebody who thinks that they have a clear understanding of why they should be different and would ignore any proofs to the contrary, but here is one of probably a dozen proofs that should be readily understandable by anyone who knows how to compute the decimal expansion of a fraction.

Consider that the decimal expansion of 1/9 is 0.111.... repeating forever, and it is clear that if you multiply this decimal expansion of 1/9 by any one-digit number, there are no carryovers in the multiplication, so 0.111... multiplied by 9 would therefore equal 0.999... repeating forever, but we also know that 1/9 multiplied by 9 is 1, and thus 0.999... must be equal to 1... They look different, but they are actually the same. This is not simply the result of some series converging on the number 1, it literally is the exact same number. It is simply an alternative representation that arises out of the ways that we are permitted to describe numbers in mathematics.