Dear Georgina:
Thank you for joining back into the discussion. I do plan to carefully read through your essay (which I've only been able to glance through up to now), and eventually rate it. I hope you do mine as well.
As to your above comment, I agree with it. I think that from what you've said you consider time and energy to be canonically conjugate variables, though, so I'm not sure I see the reason for bringing both into the discussion---unless that relates to your second comment about "why gravity can not be caused by curvature of space time[, even though you are] using a framework that allows general relativity to be seen as valid."
In that regard, I think we are in agreement. On Aug 15 at 18:53, I posted a reply to George Ellis on my topic which contained the following:
"General relativity theory describes space-time as a field that is supposed to be warped in the presence of gravitational mass. In contrast, in order to reconcile relativity with true temporal passage, I've described space-time as the emergent map of events that occur in an enduring three-dimensional universe. As such, the space-time continuum of events is not conceived as a real substantive manifold that warps and moulds due to the presence of gravitational mass; and the need to describe the flow of time associated with a uniformly enduring homogeneous present [in cosmology; this statement's given within the context of George's comment], makes the basic concept of space that truly warps under the influence of gravity seem difficult to reconcile. For instance, in cosmology we take the description of perfect fluidity to be valid on the large scale, but if space-time is a substantive manifold that's truly warped under the influence of mass, so that the local passage of time is really influenced by localised mass, is it really very consistent to say that there should be a cosmic time that passes at the same rate in our Local Group as it does in the Coma cluster? Although the description of space-time that's given by Einstein's equations seems to coincide with the idea of a substantive manifold that truly dynamically warps under the influence of mass (although, in what dimension is the warping of space-time described as dynamically changing? Dropping the assumption of a global simultaneity-relation in space-time that coincides with a uniform flow of cosmic time, while retaining the concept of dynamical change, seems to lead to Zeno's paradox of infinite regression), if an absolute cosmic time is required in order to counter the implication [from the Rietdijk-Putnam argument] that we must only imagine ourselves as existing in a block universe, it seems that some more definite background metrical structure must be required to account for that.
"And that's exactly what the RW metric provides in standard cosmology; therefore, although the local passage of time will be different in different gravitational fields and in different states of motion, the standard model still describes uniform global evolution. The same is true in the SdS cosmology I mentioned in my essay, given the description of r as the cosmic time coordinate. The difference, however, is that in FLRW cosmology the overall curvature of space and the evolution of the scale-factor are supposed to be determined by the large scale average energy content of the universe. Therefore, general relativistic dynamics are incorporated into the theory following the prior assumption of a cosmological background metric. Furthermore, this idea is supposed to be correct according to general relativity theory, so that, in taking the RW metric as background structure and passing it through Einstein's equations, we find that the overall empirical and theoretical consistency of the theory implies that the perfect fluidity of matter should be a good approximation to the large scale average; but it's really debatable whether the large scale distribution of matter really has approximated very well as a perfect fluid since structure formation, and it's anyway this aspect of the theory that really makes the horizon problem such a big problem [notwithstanding inflation].
"Now, the idea that the evolution of our Universe might really need to be described through a well-defined background metric, through which space-time emerges as the map of events that occur in the Universe, seems better suited to a metric-affine theory, whereby the metric and local connection are independent quantities and gravitation is described in terms of torsion rather than curvature. If this were the case, then regardless of what the background metric would be (i.e., regardless of the [possible] triviality [of] its stress-energy tensor), space-time would be described locally through different solutions to the Einstein field equations [that could well contain non-vanishing stress-energy].
"Therefore, if the SdS cosmological background could be used as such to describe the existence of galaxies on its fundamental worldlines, and if the distribution of galaxies would appear isotropic from every such perspective, it would be a legitimate cosmological background for a universe that *should* expand at all times, at a well-defined rate that would turn out to be modelled precisely by the flat LambdaCDM scale-factor, regardless of the actual curvature of space or its global energy content. Therefore, it would agree with empirical observations in our Universe, going a large way towards explaining why the Universe does expand, and would eliminate the flatness problem as well as the need for large amounts of dark matter and dark energy---and the horizon problem would no more be a problem than the requirement to account for that particular background metric. But then, it should be noted that this particular metric has the same form as the one that will describe the final state outside every bound cluster of galaxies in our Universe..."
Neither George, nor anyone else, has offered anything in response to this. Since we agree that there can be both "universal simultaneity as well as the observation of relativity, without contradiction"---and I have demonstrated in my essay how this can work in the case of special relativity, with the mathematical theory emerging as the appropriate description of events that occur in an emergent universe with the required inertial and causal structures---I wonder if you (or anyone else) have any thoughts on this.
Best regards,
Daryl