Cosmic Landscape Debate: Lecture 2
“Conversely, if one believes that the geometry of space is going to have an absolute character, fixed in advance, by some a priori principles, you are going to be led to posit a homogeneous geometry. For what, other than particular states of matter, would be responsible for inhomogeneities in the geometry of space? But then spacetime will have symmetries which leave you prey to the argument just given. So from the other side also, we see that the principle of sufficientreason is hard to square with any idea that spacetime has a fixed, absolute character.
One way to formulate the argument against background spacetime is through a second principle of Leibniz, the identity of the indiscernible. This states that any two entities, which share the same properties are to be identified. Leibniz argues that were this not the case, the first principle would be violated, as there would be a distinction between two entities in nature without a rational basis. If there is no experiment that could tell the difference between the state in which the universe is here, and the state in which it is translated 10 feel to the left, they cannot be distinguished. The principle says that they must then be identified. In modern terms, this is something like saying that a cosmological theory should not have global symmetries, for they generate motions and charges that could only be measured by an observer at infinity, who is hence not part of the universe. In fact, when we impose the condition that the universe is spatially compact without boundary, general relativity tells us there are no global spacetime symmetries and no non-zero global conserved charges 4.”
Comment 5: This is an argument against conservation of total energy in cosmology. Indeed none of the generators of the Poincare group need be constants of the motion. Note that a pocket universe in the eternal chaotic inflation that populates the cosmic landscape has a Hubble horizon that is a 2D surrounding surface on expanding accelerating 3D space. I do not use “boundary” because of Higgs field singularities in 3D space. However there are boundary conditions on the horizon that may represent influences from beyond the horizon according to Susskind. We partially see the horizon as WMAP radiation from the surface of last scattering. LIGO & LISA gravity wave detectors will take us closer to the Hubble horizon that is the last frontier in our past curved light cone.
Back to Smolin:
“But it took physics a longtime to catch up to Leibniz’s thinking. Even if philosophers were convinced that Leibniz had the better argument, Newton’s view was easier to develop, and took off, whereby Leibniz’s remained philosophy. This is easy to understand: a physics where space and time are absolute can be developed one particle at a time, while a relational view requires that the properties of any one particle are determined self-consistently by the whole universe.”
Comment 6: Bohm’s super-quantum potential for the geometrodynamical field is relational because it depends on the super-pilot QUBIT wave from which the entire 3D space-geometries take their marching orders. This is qualitatively different than mechanical reductionism and there is no “problem of time” here. See below. For example, in simpler particle physics, the way in which two real particles move under each other’s influence is not only dependent on the classical IT forces, but also depends on the total nonlocal micro-quantum BIT state they swim in. The local macro-quantum Higgs-Goldstone vacuum field emerges from the micro-quantum substratum that we associate with the unstable pre-inflation false vacuum, that for our living universe is on the edge of a ledge of the cosmic landscape.
Back to Smolin:
“Leibniz’s criticisms of Newton’s physics were sharpened by several thinkers, the most important of which was Mach , who in the late 19th century gave an influential critique of Newtonian physics on the basis of its treatment of acceleration as absolute. Einstein was among those whose thinking was changed by Mach. There is a certain historical complication; because what Einstein called ”Mach’s principle” was not exactly what Mach wrote. But that need not concern us here. The key idea that Einstein got from, or read into, Mach,was that acceleration should be defined relative to a frame of reference that is dynamically determined by the configuration of the whole universe, rather than being fixed absolutely, as in Newton’s theory.”
Comment 7: The acceleration inertial g-force is only experienced in a timelike non-geodesic Local Non-Inertial Frame AKA LNIF inside the local light cone. Of course, one can write Newton’s F = ma for a test particle of mass m in a nearby “coincident” timelike geodesic weightless free-float Local Inertial Frame AKA LIF in which no inertial forces from the frame itself are needed. True gravity is locally indistinguishable from the inertial forces induced on detectors under the influence of electromagnetic forces. However, true gravity is distinguishable from real gravity nonlocally because then the effects of tidal force geodesic deviation can be measured. If L is the space resolution of the measurement, then the MEAN VALUE dimensionless effect of curvature is of the order of the invariant L^u^vL^w^lRuvwl, where L^u^v is the length-time resolution along the u-v local coordinate direction in 4D space-time and Ruvwl is the 4th rank Riemann-Christoffel curvature tensor averaged over the resolution “ball”.
Back to Smolin:
“In Newton’s mechanics, the distinction between who is accelerating and who is moving uniformly is a property of an absolute background spacetime geometry, that is fixed independently of the history or configuration of matter. Mach proposed, in essence eliminating absolute space as a cause of the distinction between accelerated and non-accelerated motion, and replacing it with a dynamically determined distinction. This resolves the problem of under-determination, by replacing an a priori background with a dynamical mechanism. By doing this Mach showed us that a physics that respects Leibniz’s principle of sufficient reason is more predictive, because it replaces an arbitrary fact with a dynamically caused and observationally falsifiable relationship between the local inertial frames and the distribution of matter in the universe. This for the first time made it possible to see how, in a theory without a fixed background, properties of local physics, thought previously to be absolute, might be genuinely explained, self-consistently, in terms of the whole universe.
There is a debate about whether general relativity is ”Machian”, which is partly due to confusion over exactly how the term is to be applied. But there is no doubt that general relativity can be characterized as a partly relational theory, in a precise sense that I will explain below.
To one schooled in the history of the relational/absolute debate 5, it is easy to understand the different choices made by different theorists as reflecting different expectations 4. That is, special solutions may have symmetries. But, as we will discuss in section 4, there are no symmetries acting on the space of physical solutions of the theory, once these have been identified with equivalence classes under diffeomorphisms  and understandings of that debate . The understanding that working physicists like myself have of the relevance of the relational/absolute debate to the physical interpretation of general relativity and contemporary efforts towards quantum gravity is due mainly to the writings and conference talks of a few physicists-primarily John Stachel  and Julian Barbour . Also important were the efforts of philosophers who, beginning in the early 90’s were kind enough to come to conferences on quantum gravity and engage us in discussion.