Albert Einstein: A Man for the Millennium?

Abstract

ion: Abstraction by deletion ... One carefully omits parts of the data describing the mathematical concepts ... to obtain the more abstract concept (Saunders MacLane, ibid.). By dropping the assumptions of differentiability, one can extend the from theories based on differentiable manifolds to those based on topological manifolds; and by dropping the assumption of continuity the can be extended to theories based on sets of discrete elements. Even if the concepts of space, time and space-time have to be greatly modified; or are themselves explained in terms of some more fundamental entities in some future theoretical advance, it is hard to believe that one would retreat from the relational to the absolute point of view concerning the fundamental entities, whatever their nature. This suggests adoption of the of maximal permutability of the fundamental constituents as a universal formal principle in Einstein’s sense as a heuristic guide in the search for a theory of quantum gravity – and even beyond. Elementary Particles, Field Quanta The heuristic force of this is reinforced by the observation that, like the points of space-time, the particles of non-relativistic QM and the field quanta of specialrelativistic QFT also lack inherent individuality and hence obey the principle. They are only individuated (to the extent that they are) by some process (Feynman’s word) or phenomenon (Bohr’s word), in which they are involved. In any quantum system in non-relativistic QM, both the bosons and the fermions of any species can be arbitrarily permuted among themselves without changing the probability amplitude for any process; so, like the points of space-time, they are also things between relations. And in QFT, the field quanta in any Fock space state are also completely indistinguishable. A Background-Independent String Theory? As currently constituted, string theory is based on a fixed, background space time structure on a manifold of some number of dimensions higher than four. Regardless of the details of particular models, it is clear that the of maximal permutability is violated: Only diffeomorphisms that are symmetries of the fixed, background structure (usually a flat pseudo-metric) are permissible permutations of the elements of the manifold. FIGURE 23. B. Greene Many string theorists are aware of this problem. Brian Greene recently presented an appealing vision of how a background-free string theory might look, but he emphasized how far string theorists still are from realizing this vision (The Fabric of the Cosmos – Space, Time, and the Texture of Reality, 2004): Since we speak of the fabric of spacetime, maybe spacetime is stitched out of strings much as a shirt is stitched out of thread. That is, much as joining numerous threads together in an appropriate pattern produces a shirt’s fabric, maybe joining numerous strings together in an appropriate pattern produces what we commonly call spacetime’s fabric. Matter, like you and me, would then amount to additional agglomerations of vibrating strings – like sonorous music played over a muted din, or an elaborate pattern embroidered on a plain piece of material – moving within the context stitched together by the strings of spacetime. ... [A]s yet no one has turned these words into a precise mathematical statement. As far as I can tell, the obstacles to doing so are far from trifling. .... [T]o make sense of this proposal, we would need a framework for describing strings that does not assume from the get-go that they are vibrating in a preexisting spacetime. We would need a fully spaceless and timeless formulation of string theory, in which spacetime emerges from the collective behavior of strings... Many researchers consider the development of a background-independent formulation to be the single greatest unsolved problem facing string theory. Einstein’s Greatest Contribution? For reasons discussed above, I have been led to conjecture that, whatever form a future fundamental physical theory (such as some version of quantum gravity, or something even farther from our current conceptual framework) may take, there will be no absolute elements in it. Rather, its basic entities – whatever their nature – will be embedded in some discrete or continuous relational structure: The result will be a completely background-independent physics. If I am proved right, then a millennium from now (assuming humanity still exists and has not relapsed into barbarism) then Einstein’s greatest contribution to physics will be regarded as the development of the first, prototype background-independent physical theory! As I indicated earlier, it is always dangerous to try to predict the future; still, I can draw wry comfort from the fact that – right or wrong – I shall not be around when my prophecy is finally tested. But I hope some of you may.