designed to make the locally measured mass of a particle depend on the rest of the matter in a continuously expanding universe. According to his calculations, the enormity of material in the cosmos would outweigh disparate regional influences and produce the uniform tendencies we know as inertia. Sciama never fully developed his model, however—he passed away in 1999 before completing his grand vision. Other physicists have launched similar efforts to encompass Machian notions, but none of their schemes have panned out so far. Perhaps their imaginations haven’t been properly nourished, say with cheap, wholesome cuisine.

Enter a trio of hungry cosmologists, famished for truth and a hearty meal. One of us (Paul Wesson), invited colleagues Sanjeev Seahra and Hongya Liu to a working dinner at a no-frills restaurant in Waterloo, Canada. Over heaping plates of seafood, the trio pondered ways of formulating Mach’s principle in terms of gravitational waves moving through an altered version of Einsteinian space-time. Through streams of relativistic calculations, hastily jotted down on available napkins, an intriguing picture emerged of a profoundly interconnected cosmos.

The modified theory involves expressing the space-time metric (which measures distances between space-time points) in complex numbers, instead of real (ordinary) numbers. Complex numbers, including terms such as the square root of negative one, play little role in traditional gravitational physics. However, they comprise an important part of quantum mechanics, helping to explain hidden connections between particles. In particular, they permit a complete description of particles in terms of “wave functions”: entities that can stretch out over vast regions of space.

By describing mass in terms of elongated waves rather than conventional clumps, the group found that it could express local inertia as a manifestation of the geometry of the universe as a whole. Thus, the combined effects of curvature throughout the entirety of space-time could exert a tug significant enough to affect the acceleration of

The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement