Articles and the like. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% http://www.nature.com/nature/journal/v450/n7173/full/4501167a.html Nature 450, 1167-1168 (20 December 2007) | doi:10.1038/4501167a; Published online 19 December 2007 Physics: A quantum less quirky Seth Lloyd1 Top of page Abstract What physicists want for Christmas is a solution to the philosophical conundrums of quantum mechanics. They will be disappointed, but work that dissolves one aspect of quantum weirdness is some consolation. There is a strange quantum-mechanical phenomenon. A brilliant researcher receives a Nobel prize for work on quantum physics, but then expresses scepticism about the validity of the theory. Albert Einstein started the trend in 1921, and remains its most famous exponent. He received his Nobel for the quantum-mechanical explanation of how electric current can be generated just by shining light on a surface (the photoelectric effect), but for the rest of his life expressed a deep-seated distrust of the quantum. God, as he famously said, does not play dice. Most recently, Tony Leggett, a Nobel laureate in 2003, expressed his belief that quantum physics is at the very least incomplete, and needs to be supplemented by some new physics. Writing in Physical Review A, Wojciech Zurek1 now provides some balsam for these and other pained minds. So what makes geniuses deny the source of their inspiration, and muddy the font of their fame? The answer is the intrinsic bizarreness of quantum mechanics. Waves consist of particles; particles are shadowed by waves; electrons (or anything else, for that matter) can be in two places at once. PhysicsA quantum less quirky ILLUSTRATION BY ANDY MARTIN Tests of infant cognition show that the idea that an object cannot be in two places at once is ingrained in our psyches from the age of about three months. At the same age, babies become aware that objects exist even when they cannot be seen. Playing peek-a-boo with a child aged less than three months is intensely dissatisfying: when you cover your face, they exhibit no excitement or interest. Daddy is gone: so what? After three months, everything changes. When you cover your face, the child waits with eager anticipation for the "Boo!": he or she knows you're there behind the hands. In quantum mechanics, if you can't see an object, you mustn't assume it is there: an unmonitored electron can be, and generally is, everywhere at once. By the age of three months, children are better equipped to live in the macroscopic world, but their intuition for quantum mechanics is spoilt. Everyone finds quantum mechanics counterintuitive, Nobel laureates included (at least, Nobel laureates older than three months). I find quantum mechanics counterintuitive. I am not a Nobel laureate, but I spend my research time thinking about quantum mechanics in order to build quantum computers and quantum communication systems. But so what if I find it counterintuitive? My intuition is frequently wrong anyway. As long as I can perform the calculations and get the right answers, then I should be happy. But if ever a scientist deserved to trust his intuition, it was Einstein. For his sake, and for those like him who find quantum weirdness deeply distressing, we should delve a little further into the roots of the problem. In his paper1, Zurek does just that, providing a simple, elegant and intuitive explanation of one of the strangest and most counterintuitive features of quantum mechanics — its peculiar mathematical shape. Mathematically speaking, quantum mechanics is a strange beast. The states of particles such as electrons correspond to functions or vectors in a complex vector space. Physical transformations (an electron hopping from place to place, for example) correspond to linear operators or matrices acting on those functions and vectors. The act of measuring the properties of the system equates to applying the appropriate mathematical operator to the vector describing the system. On measurement, the system 'collapses' to an eigenvector of the measurement operator (that is, a vector that the operator, applied again, will simply transform into a multiple of itself), and an associated eigenvalue. The eigenvalue gives the outcome of the measurement. Why is this so? Why does measurement leave a system described by nothing other than an eigenvector ('in an eigenstate', in the jargon) of the measurement operator? For the past 80 years, the answer to this question has been because Erwin Schrödinger and Werner Heisenberg said so: it's just one of the 'postulates' of quantum mechanics. Zurek shows that it is in fact a consequence of an intuitively more satisfactory postulate: that if one makes a measurement twice in rapid succession, one always obtains the same result. He uses an argument based on his and William Wootters's proof2 of the celebrated 'no-cloning' theorem (essentially, that you can't create identical copies of an unknown quantum state) to show that if a measurement were to leave a system in anything other than an eigenstate of that measurement, immediate repetition of the measurement would have a chance of yielding a different result. A quirky, mathematical postulate of quantum mechanics is thus replaced by a simple derivation from an intuitive result. Einstein was celebrated for proclaiming that God is subtle, but not malicious. The proof that, despite His predilection for games of chance, God does not attempt to change the rules mid-game certainly would have delighted Einstein. Would it have convinced him of the validity of quantum mechanics? My intuition tells me not. Top of page References 1. Zurek, W. H. Phys. Rev. A 76, 052110 (2007). | Article | ChemPort | 2. Wootters, W. K. & Zurek, W. H. Nature 299, 802–803 (1982). | Article | ISI | ChemPort | http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLRAAN000076000005052110000001&idtype=cvips&gifs=yes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%