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PLANCK UNITS. “The value of the Planck length is around 10(-33) cm, which is truly miniscule: the diameters of an atom, nucleus, proton and quark are, respectively, about 10(-8), 10(-12), 10(-13), and 10(-16) cm. So the Planck length is as many orders of magnitude from the (upper limit for) the diameter of a quark, as that diameter is from our familiar scale of a centimetre! The same point can also be made in regard to the other so-called ‘Planck scales’: the Planck time, the Planck energy, and the Planck temperature.” https://lnkd.in/dMm_YkR View in LinkedIn

SMALLEST LENGTH. “Quantum gravity effects should be important at about a length-scale called the ‘Planck length’.” https://lnkd.in/dMm_YkR View in LinkedIn

VICTIM OF ITS OWN SUCCESS. “It should be admitted from the outset, that the subject of quantum gravity is exceptionally difficult and problematic, both in regard to mathematical and to conceptual issues. Furthermore, these problems are compounded by the almost complete lack of any unequivocal data to guide attempts to construct such a theory. In this sense, twentieth-century physics is a victim of its own success: the empirical success of general relativity and quantum theory in their present forms means that we lack data bearing on how we might reconcile them (or more generally, replace them).” https://lnkd.in/dMm_YkR View in LinkedIn

DERIVATIVES. “Physics abounds with examples of definitional extension, provided that the derived theory is conceived narrowly enough that it does not have properties, explanatory resources etc. that ‘ride free’ of the deriving theory, and so block the derivation.” https://lnkd.in/dMm_YkR View in LinkedIn

DEDUCTIVE EXTENSION. “For example: the elementary theory of equilibrium classical statistical mechanics for a strictly isolated system, which postulates the microcanonical measure on the energy hypersurface, is a definitional extension of the mechanics of the micro-constituents, once we use an underlying logic strong enough to express calculus (of many variables).” https://lnkd.in/dMm_YkR View in LinkedIn

THE KNOT. “Space and time are such crucial categories for thinking about, and describing, the empirical world, that it is bound to be ferociously difficult to understand their emerging, or even some aspects of them emerging, from ‘something else’.” https://lnkd.in/dMm_YkR View in LinkedIn

EXTENDING DEDUCTIVE REACH. “In effect all of classical pure mathematics was a definitional extension using just logical operations, of set theory. But it is equally remarkable how many examples of definitional extension there are in physics, at least once we give the reducing physical theory a suitably strong underlying logic (i.e., a rich enough set of operations) so as to ‘extend its deductive reach’.” https://lnkd.in/dMm_YkR View in LinkedIn

VALIDITY CEASES TO EXIST. “The idea that simple manifold concepts may not apply at small distances was anticipated by Riemann in his famously prophetic Habilitationschrift of 1854: “Now it seems that the empirical notions on which the metrical determinations of space are founded, the notion of a solid body and of a ray of light, cease to be valid for the infinitely small.” https://lnkd.in/dMm_YkR View in LinkedIn

BEDROCK LOGIC. “When we undertake to express such a theory in a formal language, we naturally envisage adding the theory’s distinctive physical vocabulary, and axioms governing it, to a so-called ‘underlying logic’ that is much stronger than just basic logic and set theory; i.e., to one that contains standard mathematical operations sufficient to yield the mathematical apparatus; for example, calculus, which is needed by the theory.” https://lnkd.in/dMm_YkR View in LinkedIn

THE ASSUMPTION. “Gravity is, at least prima facie, a force like the others, and these have turned out to be quantum in nature.” https://lnkd.in/dMm_YkR View in LinkedIn