Some while ago I withdrew from the discussion as I had had enough of the bad tempered behaviour on this thread [posting on Dec. 22, 2008 @ 05:42 GM]. A number of technical issues relevant to my paper have however arisen in the subsequent postings, and in order to acknowledge them I will now respond to them in one global response, tackling in sequence the four main themes arising that I see as relevant. Should any respondents again attack me with new postings claiming I am either unethical or professionally incompetent [vide the previous postings], I will immediately withdraw unconditionally and permanently from this forum (the forum administrators should be protecting participants from such comments because it is a forum condition that posts may not contain language or content that is either offensive or directed at specific individuals in an inappropriate manner; but they are manifestly failing to do so).
Issue 1: The development of the metric
Dimi Chakalov wrote on Dec. 28, 2008 @ 15:02 GMT. "according to Carlo Rovelli (gr-qc/0604045 v2, p. 4): `The proper time [tau] along spacetime trajectories cannot be used as an independent variable either, as [tau] is a complicated non-local function of the gravitational field itself. Therefore, properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable.' "
For my purposes, that non locality does not matter. At any spacetime event in the EBU up to the bounding surface, the metric is already defined, and that determines proper time along all world lines in small local neighbourhoods of that event. The field equations plus conservation equations and gauge conditions then determine the metric at the next event, a small proper time further along the world line, as the EBU develops, and so it goes, as clearly stated in my essay [first full paragraph on page 5]. There does not have to be a fixed pre-existing background spacetime in order for the metric to evolve: rather the metric evolves together with the spacetime as shown by the standard existence theorems for General Relativity Theory.
Issue 2: Existence of preferred spacelike surfaces
Philip Gibbs wrote on Dec. 28, 2008 @ 09:36 GMT "In your essay you propose that time flows and spacetime evolves in an irreversible way as the wavefunction collapses. However, you say that this happens pointwise at space-time events, not on spacelike surfaces. This is an apparent contradiction because wavefunction collapse is a non-local process. Can you elaborate on how you reconcile the local vs non-local characterists of the EBU?"
My view on this has changed since I completed the essay (see my postings on Dec. 15, 2008 @ 10:02 GMT ; Dec. 17, 2008 @ 12:35 GMT). It is now my view that the coming-to-be takes place along preferred spacelike surfaces (`the present'), whose existence implies a breaking of Lorentz invariance. This is OK: it is a typical case of a broken symmetry, as happens so often in present day physics (the solution has less symmetries than the underlying equations). Thus the non-local process you refer to can preferentially take place in these preferred spacelike surfaces. Note that these surfaces are not necessarily the ones determined by an observer as simultaneous through use of radar procedures, as in special relativity.
Issue 3: Determining the preferred surfaces and associated coordinates
So then the issue arises, how can these preferred surfaces be determined? What are the preferred coordinates? [this is in essence the subject of a number of postings on this thread]. The best option, in a realistic cosmological setting, seems to be as follows:
Step 1: at each spacetime event, determine the timelike unit eigenvector u^a (u_a u^a = -1) of the Ricci tensor. This defines the preferred cosmological family of worldlines (often referred to as "fundamental observers").
Step 2: determine proper time s along these world lines by the equation dx^a/ds = 1. Set the zero of time s along each world line by the condition: s=0 is the event at the start of the universe along that world line.
Step 3: determine comoving spatial coordinates x^nu by the condition dx^nu/ds = 0 (nu = 1,2,3). Now {x^a} = {s,x^nu} (a=0,1,2,3) are normalised comoving coordinates along these preferred world lines, and the surfaces S:{s=const} are the globally preferred surfaces of time ("constant proper time since creation of the universe") on which coming into being will take place.
Comment 1: the timelike eigenvector u^a will exist and be unique because there is an effective presence of non-zero rest mass matter everywhere in the real universe. How this works out depends on the averaging scale used in the spacetime description: on large scales, cosmology is described by non-zero average density of matter and radiation; on small scales the Cosmic Microwave Background radiation is omni-present (that's right, in physical terms there are *no* spacetime regions corresponding precisely to the vacuum Schwarzschild solution in the real universe; there is for example always a non-zero presence of a radiation fluid everywhere in the solar system).
Comment 2: In effect this is a prescription for fixing the lapse function and shift vector in the ADM formalism. The lapse function is determined non-locally from the cosmological context (the start of the universe).
Comment 3: Coarse Graining will occur in relation to how these coordinates look at different scales, as discussed nicely by David Wiltshire. On a coarse scale, this procedure will give the standard coordinates in Robertson-Walker universes [for those not familiar with these spacetimes, please see section 4 of http://xxx.lanl.gov/abs/gr-qc/9812046 for a full discussion of these models, their usual coordinates, and their properties, including their conformal flatness).
Issue 4: Experimental and observational tests
Dimi Chakalov wrote on Dec. 26, 2008 @ 01:44 GMT, "I was hoping to see some written statement by George, in which he says something like 'if my conjecture [A] turns out to be wrong, then my EBU hypothesis will be indistinguishable from BU hypothesis'." A series of such tests of the EBU proposal are in essence proposed in my essay, and I thought their outcome was clear enough. But perhaps they are not made explicit enough, so I'll clarify them.
Experiment 1: Perform the usual quantum theory double-slit experiment. If you get the standard quantum theory result, see http://en.wikipedia.org/wiki/Double_slit_experiment, you will have proved that the specific outcome of the experiment in the actual world we experience is not determined until it happens [cf. section 2 of my essay]: quantum theory only predicts probabilities, not specific outcomes. This is described adequately by the EBU and not the BU. If you get a different result, you should give up physics,
Gedanken Experiment 1: Consider the gedanken experiment of the third paragraph of section 3 of my essay, illustrated there in Figure 1. A prescription is given there for the construction of an engineering device that will amplify irreducible quantum uncertainty from the micro scale to the macro scale. This will be adequately described by the EBU and not the BU. It will fail to operate as specified only if the standard quantum results on the unpredictability of outcome of decay of a quantum state do not hold. If you have shown this to be false as an experimental result in the real world in which we live, please make your method and results public, and await the call from the Nobel committee.
Observational Result 1: Consult the current cosmological literature on the observations and analysis of the Cosmic Background Radiation anisotropies observed by the WMAP satellite and the associated Baryon Acoustic Oscillations. These show the outcome, in terms of large scale structure in the universe, of quantum fluctuations in the early universe (see the quote at the bottom of page 3 of my essay). These outcomes were in principle unpredictable, and indeed were undetermined - in the universe which we actually experience - until they happened. This is again adequately described by the EBU, and not by the BU.
I could go on, but that should suffice to show there is excellent experimental and observational support for the EBU as against the BU.
