The New York Times today has Where is Physics Headed (and How Soon Do We Get There?). It’s an interview by Dennis Overbye of Maria Spiropulu and Michael Turner, the chairs of the NAS Committee on Elementary Particle Physics – Progress and Promise. This committee is tasked with advising the DOE and NSF so they can “make informed decisions about funding, workforce, and research directions.”
Turner: But it is a powerful mathematical tool. And if you look at the progress of science over the past 2,500 years, from the Milesians, who began without mathematics, to the present, mathematics has been the pacing item. Geometry, algebra, Newton and calculus, and Einstein and non-Riemannian geometry.He probably meant "Einstein and non-Euclidean geometry" or "Einstein and Riemannian geometry". Technically, general relativity metric are indefinite and not Riemannian, so he could have mean non-Riemannian. However Rimannian geometry was the math that Einstein and Hilbert used for the field equations.
Among the many features of string theory is that the equations seem to have 10⁵⁰⁰ solutions — describing 10⁵⁰⁰ different possible universes or even more. Do we live in a multiverse?If it is not testable, and not part of science, why do we have to deal with it? They are just solutions to some equations that have no known relationship to the real world.
Turner:I think we have to deal with it, even though it sounds crazy. And the multiverse gives me a headache; not being testable, at least not yet, it isn’t science. But it may be the most important idea of our time. It’s one of the things on the table. Headache or not, we have to deal with it. It needs to go up or out; either it’s part of science or it isn’t part of science.
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