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The Robertson-Walker Metric

  1. Mar 10, 2008 #1
    This question is about empirical differences in certain interpretations of the Hubble expansion. Not counting integral Weyl geometry there is basically only two, the only two that I am considering here.
    1) Standard interpretation
    2) Relativistic recession of condensed mass in space-time for whatever reason. Similar to assuming some version of the Big bang was an event in space-time rather than of space-time.

    At first glance the answer might seem obvious. I mostly aware of the immense strengths of the Standard Model of Cosmology and the minor weaknesses. I am only interested in empirical differences though. The most obvious assumption is the isotropy of redshift z vs relative apparent brightness. However, consider the effects of Special Relativity. Leave the solar system in the direction of a distant galaxy at 86.6% the speed of light. The relative distance d becomes d/2, and the Hubble shift is reduced by 1. The peculiar redshift would be identifiable regardless of which interpretation is used. The relative brightness would also increase but by 86.6% rather than 50%. The opposite would obviously happen in the other direct and to varying degrees in between. This difference 86.6% vs 50% might seem to be a smoking gun until we look we actually look at a graph out to z=2. It seems that in general this is exactly what we see. It then seems that this isotropy we see would apply regardless of our peculiar motion. The anisotropy that we would see in redshift distribution would be common to both models. Note that the graph as a function of z is in comoving coordinates.

    I understand that dynamically it's not very reasonable to describe the Big Bang as an explosion in the usual sense. Again, I am only interested in empirical differences. In what way can we say the assumption that the Big Bang created space itself is more than an ontological statement lacking empirical components outside of our models. Is it in fact a purely model dependent determination?
  2. jcsd
  3. Mar 10, 2008 #2
    Can emperical differences be defined even in principle? Suppose measurements were of arbitrarily high accuracy over millions or a billion years.
  4. Mar 14, 2008 #3
    It seems that this particular section of the forum has a high incidence of related questions of mildly varying sophistication. From every angle I can think of the answer would be no, even in principle. Empirical consistency is certainly not an objection. However, even the notion of a lack of space or time seems an ill defined ontological notion. In essence saying that time doesn't exist is the same as saying there are no events at any level of nature. Kind of creates another version of wolram's nothing complaint. Space is defined by the events we measure time with. Yet fundamentally what space is is degrees of freedom, not the scale we measure it with. Then there's the issue that any measurement is by necessity a self referential process.

    Well enough cerebral diarrhea. Perhaps if empirically there is no difference in this case it makes the possibility of empirical differences with regard to other interpretations that much more clear cut. I was hoping for at least some objections on some point.
  5. Mar 15, 2008 #4


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    Observational evidence strongly suggests all possible events do not occur 'instantaneously' in our universe. That yields it a quantifiable aspect.
  6. Mar 15, 2008 #5
    Yes the Relativity of Simultaneity is fundamental to quantifying many observations. That and the lack of a preferred inertial frame produces a situation where even when our observations are well quantified it often allows seemingly mutually exclusive interpretations. I wasn't so much interested in the ontological twist of the Robertson-Walker metric as defined in the OP. It's not even a very interesting redefinition by itself. My interest is in empirical tests of possible gauge choices in Weyl geometry. To be sure that the empirical test I have imagined do what I hope I must consider what is and isn't empirically consistent, no matter how distorted the possible interpretations are. It is in no way an endorsement of or claim that the standard model uses a false ontology. It's a far more general question of what interpretations are justifiable in quantitative terms only, independent of any model. Ontology is a notoriously poor test of truth.
  7. Mar 20, 2008 #6
    In the thread "urban legends in authoritative astronomy" Ken G said;
    This was actually at the root of my question here and I was conflicted by conflating this standard analogy with the standard interpretation. The rice pudding analogy obviously sucks. This analogy avoids defining any relationship to any parameter other than proper distance. In Relativity it is tied to the stress energy tensor. This remains ripe for theoretical considerations. The question remains what covariances exist wrt other physical parameters. Given that the stress energy itself in some way must be defined as a property of matter and interactions the specific form of variances are very important. Apparently to date these variances has primarily been limited to concomitant effects of volume changes. In a very general sense the effects of these symmetries can range from variations in physical constants to a re-gauging of proper distances or simply changes in stress energy/expansion rates alone.

    My question then boils down to what empirical differences (not model specific) can be defined by possible choices of symmetries. However, my question here was limited to the improper "urban legend" version. Yet as far as I know the standard model of cosmology limits itself to concomitant measurement effects of volume change/energy density. Relativity is in fact premised on the idea that our very definition of space and time is defined as a relativistic property of matter. This is sufficient grounds to consider that there is no a priori reason to presume the evolution of stress energy is limited to effective volume/energy density and direct effects thereof.

    My initial question therefore effectively remains in the sense of what empirical differences can be defined between a change of metric defining our measurement of proper distance and a change of distance as a result of proper motion for any reason? In fact, as far as I can tell, the standard model is predicated on the notion that there are no empirical differences. I would love to be corrected on this matter.

    More general questions exceed expectations of this forums due to speculative implications. I could legitimize asking them here with published material but I'm not really interested in specific models. These stem from the notion that if the Hubble expansion is a change of metric defining our measurement why then would the effect be limited to proper distance/density and global force balancing, i.e., open, closed, flat Universe and expansion rates. Wrt to my question then it seems the answer is none. I would still appreciate any correction to my thinking wrt the standard model and/or empirical issues limited to the initial question.
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