Quantum physics on the edge of chaos by Michael Berry
Quantum physics describe the world of the very small. Classical Newtonian physics describes larger scales. But in the border country between the two, rigorous mathematical descriptions are difficult to find, and chaos rears its head.
Niels Bohr, a pioneer of quantum mechanics, chose the Taoist yin-yang symbol for his coat of arms.
He saw that the polarized states of particles, for example, complement each other the way the two extremes of yin and yang create a balance in the Taoist understanding of the universe. Bohr spoke of the unity of opposites and contradictions in nature.
Many concepts in ancient Chinese science correspond to ideas physicists have only formed in the past century or so. Here’s a simple look at a few such concepts. 1. Eight Trigrams and Particle Arrangements 2. The Book of Changes and the Elusive Theory of Everything 3. Lao Tzu’s Understanding Related to Subatomic Particles
Since the world is quantum, any computer is a quantum computer. Conventional computers are just weak quantum computers, since they don’t exploit intrinsically quantum effects, such as superposition and entanglement.
A quantum computer is a computer that uses intrinsically quantum effects that cannot naturally be modeled by classical physics. Classical computers may be able to mathematically simulate instances of such computers, but they are not implementing the same kinds of quantum operations.
Definition 2, where there are strong tests or proofs of the quantum effects at play (e.g. by doing Bell tests).
A quantum computer is a computer that uses intrinsically quantum effects to gain some advantage over the best known classical algorithms for some problem.
A quantum computer is a computer that uses intrinsically quantum effects to gain an asymptotic speed-up over the best known classical algorithms for some problem. (The difference with definition 3 is that the advantage is a fundamental algorithmic one that grows for larger instances of the problem; versus advantages more closely tied to hardware or restricted to instances of some bounded size.)
A quantum computer is a computer that is able to capture the full computational power of quantum mechanics, just as conventional computers are believed to capture the full computational power of classical physics. This means, e.g. that it could implement any quantum algorithm specified in any of the standard quantum computation models. It also means that the device is in principle scalable to large sizes so that larger instances of computational problems may be tackled.
It has been suggested (arXiv) that the resolution of the information paradox for evaporating black holes is that the holes are surrounded by firewalls, bolts of outgoing radiation that would destroy any infalling observer. Such firewalls would break the CPT invariance of quantum gravity and seem to be ruled out on other grounds. A different resolution of the paradox is proposed, namely that gravitational collapse produces apparent horizons but no event horizons behind which information is lost. This proposal is supported by ADS-CFT and is the only resolution of the paradox compatible with CPT. The collapse to form a black hole will in general be chaotic and the dual CFT on the boundary of ADS will be turbulent. Thus, like weather forecasting on Earth, information will effectively be lost, although there would be no loss of unitarity.
The idea that there are no points from which you cannot escape a black hole is in some ways an even more radical and problematic suggestion than the existence of firewalls, but the fact that we’re still discussing such questions 40 years after Hawking’s first papers on black holes and information is testament to their enormous significance.
Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell’s inequalities and other conceptual obstacles. Here, it is shown how mappings can be formulated that relate quantum systems to classical systems. By generalizing these ideas, one gets quite general models in which quantum mechanics and classical mechanics can merge. It is helpful to have some good model examples such as string theory. It is suggested that notions such as ‘super determinism’ and ‘conspiracy’ should be looked at much more carefully than in the, by now, standard arguments.
First few hydrogen atom orbitals; cross section showing color-coded probability density for different n=1,2,3 and l=”s”,”p”,”d”; note: m=0
The picture shows the first few hydrogen atom orbitals (energy eigenfunctions). These are cross-sections of the probability density that are color-coded (black=zero density, white=highest density). The angular momentum quantum number l is denoted in each column, using the usual spectroscopic letter code (“s” means l=0; “p”: l=1; “d”: l=2). The main quantum number n (=1,2,3,…) is marked to the right of each row. For all pictures the magnetic quantum number m has been set to 0, and the cross-sectional plane is the x-z plane (z is the vertical axis). The probability density in three-dimensional space is obtained by rotating the one shown here around the z-axis.
Note the striking similarity of this picture to the diagrams of the normal modes of displacement of a soap film membrane oscillating on a disk bound by a wire frame. See, e.g., Vibrations and Waves, A.P. French, M.I.T. Introductory Physics Series, 1971, ISBN 0393099369, page 186, Fig. 6-13. See also Normal vibration modes of a circular membrane.
A class of fluorescent organic molecule has been designed that enables highly efficient light-emitting diodes to be made. The devices may turn out to be competitors to their conventional analogues.
Image caption: a, Energy diagram of a conventional organic molecule. b, Molecular structures of CDCBs. Me, methyl; Ph, phenyl. Image source: Uoyama H., Goushi K., Shizu K., Nomura H. & Adachi C. (2012). Highly efficient organic light-emitting diodes from delayed fluorescence, Nature, 492 (7428) 234-238. DOI: 10.1038/nature11687