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Newsgroups: sci.physics.research
From: carlip-nos...@physics.ucdavis.edu
Date: Sat, 19 Nov 2005 14:50:20 +0000 (UTC)
Local: Sat, Nov 19 2005 9:50 am
Subject: Re: Accuracy vs. Relevance
[...]
> They are testing a theory . If the theory truly has predictive power I think you are seriously underestimating the amount of data reduction > (which btw I believe GR has although not to the extent commonly > claimed), it should be demonstrable in real time. The point, which I > will elaborate upon later, is that there is a significant difference > between genuine prediction and data-fitting. If they are truly testing > the theory's predictions, they should be able to churn out their raw > data, check their fit immediately and be able to claim: > "see, our model works, it all fits, we predicted it right" or "oh, our > predictive model has a problem". required. Look at the article in Matters of Gravity 26 (available from http://www.phys.lsu.edu/mog/) to see what is involved. Note that the data analysis will be "blind," in the sense that all of [...] > There is another, distinct and subtler issue, which I refer to as the This is certainly a major issue in quantum gravity. But in classical GR, > semantic problem, i.e. the problem of mapping mathematical models into > measurement outcomes and viceversa, which might be relevant to discuss > here (cf. [1] ) . > Let's start with Wigner, who, contrasting the situation in QM and SR > with that in GR writes ([2]) "... the measurement of position, that is, > of the space coordinates, is certainly not a significant measurement > if the postulates of of the general theory are adopted: the > coordinates can be given any value one wants. ... Most of us have > struggled with the problem of how, under these premises, the general > theory of GR can make meaningful statements and predictions at all. ... > This is a point that which cannot be emphasised strongly enough and it > is the basis of a much deeper dilemma ... . It pervades the general > theory, and to some degrees we mislead both our students and ourselves > when we calculate , for instance, the mercury perihelon without > explaining how our coordinate system is fixed in space, what defines it > in such and such a way that it cannot be rotated, by a few seconds a > year, to follow the perihelion apparent motion. ... . There must be > some assumption on the nature of the coordinate system that keeps it > from following the perihelion. ... . A difference in the tacit > assumptions which fix the coordinate system is increasingly recognized > to be at the bottom of the many conflicting results arrived at in > calculations based on the general theory of relativity." > Wigner is talking about the problem of diffeomorphism invariance in GR. > Now, while for well studied cases, such as a.o. the mercury perihelion > and structurally similar situations, physicists know how to choose the > coordinates so as to obtain results that fit observations, I am not > sure that this holds in general. it is not, or at least need not be. The basic point to remember is that *actual observations* are diffeomorphism-invariant. We do not observe, for instance, the "coordinate value of the position of Mercury"; we observe things like "the round trip time of a radar pulse from a fixed location on Earth to Mercury and back, as measured by an atomic clock at that location," or "the angle between the light arriving from Mercury and that coming from a reference star, as measured at a particular telescope at a time determined by a clock at the location of that telescope." Such quantities do not depend on any choice of coordinates. To compare GR to observation, what you do is to compute (in, say, the post-Newtonian approximation) the predictions for such *observables*, and compare them to the the actual observations. Better, rather than just comparing GR, you look at a more general model (the *parametrized* post-Newtonian approximation, for instance), and find the best fit for your free parameters; you can then compare the result to GR, and at the same time get a good estimate for how good the fit is. For a simple example, take a look at Boddener and Will, Am. J. Phys. 71 Steve Carlip You must Sign in before you can post messages.
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