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Resource Type Online
Topics Gravity
Submitted by xsama
Date Submitted Fri 03 Feb 2017

Spacetime and Spin

The Many Faces of Spin

Many of nature's deepest mysteries come in threes. Why does space have three spatial dimensions (ones that we can see, anyway)? Why are there three fundamental dimensions in physics (mass M, length L and time T)? Why three fundamental constants in nature (Newton's gravitational constant G, the speed of light c and Planck's constant h)? Why three generations of fundamental particles in the standard model (e.g. the up/down, charm/strange and top/bottom quarks)? Why do black holes have only three properties—mass, charge and spin? Nobody knows the answers to these questions, nor how or whether they may be connected. But some have sought for clues in the last-named of these properties: spin.

We are all familiar with rotation in the macroscopic world of tops, ballet dancers, planets and galaxies. Spin in the microscopic world is subtler, and obeys rules that are at once familiar (e.g. conservation of angular momentum) and bizarrely counter-intuitive (e.g. quantization and half-integer spin for fermions, which in the macroscopic world would correspond to objects that rotate through 720 rather than 360 degrees before returning to their original states). More abstract still are quantities like "isospin", which is analogous to ordinary spin in some ways but governs the behavior of the strong and weak nuclear forces (rotation through 180 degrees of isospin, for instance, converts a proton into a neutron), and torsion, a mathematical term related to the intrinsic twist of spacetime (this appears in some extensions of general relativity, but Einstein himself set it to zero in general relativity for reasons of logical economy). Are there connections between these manifestations of spin in the worlds of the large and small? Do they hint at the direction in which Einstein's theory of gravity might need to be extended in order to unify it with the other forces of nature? A generation of physicists since Einstein have thought about these questions, and they are part of the reason what makes Gravity Probe B so important, not just as another test of general relativity, but as a source of new insights about spacetime itself. Nobel laureate C.N. Yang wrote in a letter to NASA Administrator James M. Beggs in 1983 that general relativity, "though profoundly beautiful, is likely to be amended ... whatever [the] new geometrical symmetry will be, it is likely to entangle with spin and rotation, which are related to a deep geometrical concept called torsion ... The proposed Stanford experiment [Gravity Probe B] is especially interesting since it focuses on the spin. I would not be surprised at all if it gives a result in disagreement with Einstein's theory." .....

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