Amelino-Camelia continues to impress me as philosophically one of the most clear-sighted people writing about quantum gravity. I've been reading "Three perspectives on the quantum gravity problem"(adsbygoogle = window.adsbygoogle || []).push({});

http://arxiv.org/gr-qc/0309054 [Broken]

based on an invited talk given in July to the tenth Marcel Grossmann meeting on GR.

On page 8 of the paper, Amelino-C has a section called "Aside on the hypothesis of a genuinely quantum spacetime" that I found enlightening. A key issue for Amelino-C is whether quantum gravity will be constructed on a classical spacetime continuum or whether the continuum properties (including symmetry) will only emerge in the appropriate limit. (He lays the issues out forcefully on page 7) Here he is expanding on this in a side comment:

"The concept of a classical spacetime is appropriate in physics (operatively meaningful) when the theory of interest allows to localize sharply a spacetime point. This statement is intended in the same sense that a classical concept of angular momentum is only appropriate when the angular-momentum vector (all of its components) can be sharply measured. In 19th century physics angular momentum was a classical concept. In our modern theories we acknowledge the experimental fact that there are limitations on the measurability of the angular-momentum vector (one cannot measure all of its components simultaneously) and therefore we describe angular momentum using a nonclassical formalism (the one of noncommuting operators) which captures this measurability limitations.

The consistency between the measurability limits established by the formalism and the in-principle measurability limits that affect measurement procedures is a key requirement for a physical theory. This important issue usually takes center stage in the physics literature only when a major “scientific revolution” challenges our understanding of the physical world. In the course of such a “revolution” it is natural to question the logical consistency of the novel theoretical frameworks which are being proposed.

Once these logical-consistency issues have been settled, and substantial experimental support for the new theory has been obtained, the focus shifts toward computational matters: one is comfortable with the logical structure of the new theory and with the

fact that the new theory has some relevance for the description of Nature, and therefore precise calculations and accurate experiments become the top priority. For example, this natural sequence of steps for the development of new theories is easily recognized in the development of the “relativity revolution” and of the “quantum-theory revolution”.

While the limited scope of these notes does not allow me to describe rigorously the issues that are to be considered in measurability analysis (and its role in establishing the logical consistency of a formalism), the interested reader can find a careful discussion in the literature, especially the literature reporting the debate (among Einstein, Pierls, Bohr, Rosenfeld and others) on the measurability of the electromagnetic fields in quantum electrodynamics..."

Part of what he is saying here is that there are times in science when philosophy actually has priority and takes center stage in determining how a theory gets developed. Just as there are moments in the history of science when it pays to know the history--there are times when rigorous thinking about fundamental concepts can actually guide the building of a successful theory---neither Einstein nor Newton were strangers to this and I guess the reader can supply other examples.

Much of the time researchers can just march along applying whatever techniques produce results, but occasionally some reflection at a foundations level is needed and Amelino-Camelia is suggesting that now is such an occasion. He sees the problem of quantum gravity as requiring a model of spacetime and insists that a spacetime model implies limits on measuring location. Further, he requires consistency between limits on measurability derived from general principles and the limits established by the formal model. I wonder how widely these ideas are shared---maybe they are obvious to a lot of people (but not to me, and I havent read quite this take on things before.)

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# On the hypothesis of a genuinely quantum spacetime

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