Accuracy vs. Relevance
- From: "I.Vecchi" <vecchi@xxxxxxxxxxxxx>
- Date: Sat, 26 Nov 2005 12:18:55 +0000 (UTC)
carlip-nospam@xxxxxxxxxxxxxxxxxxx ha scritto:
> I.Vecchi <vecchi@xxxxxxxxxxxxx> wrote:
>
> [...]
> > They are testing a theory . If the theory truly has predictive power
> > (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".
>
> I think you are seriously underestimating the amount of data reduction
> required. Look at the article in Matters of Gravity 26 (available from
> http://www.phys.lsu.edu/mog/) to see what is involved.
OK , no prediction.
... .
> [...]
> > There is another, distinct and subtler issue, which I refer to as the
> > 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.
>
> This is certainly a major issue in quantum gravity. But in classical GR,
> it is not, or at least need not be.
I will argue that the distinction between GR anf QG, as you introduce
it here, is arbitrary.
> The basic point to remember is that
> *actual observations* are diffeomorphism-invariant.
No. Not in any physically meaningful way. Measurement is not
diffeomorphism invariant.
Wigner points out that GR in incomplete as long as long as no
space-time measurement model is properly defined and then he actually
sets out to define such a model . Essentially you are waving the
problem away through a linguistic trick. What you refer to as "actual
observations" are measurement outcomes or "events" in Wigner's
terminology :
"In relativity theory, the state is described by a metric which
consists of a network of points in space-time, that is, a network of
events, and the distances between these events. If we wish to translate
these general statements into something concrete, we must decide what
events are, and how we measure the distance between events" ([1]).
Your statement that "actual observations" (i.e. measurement outcomes or
"events") are diffeomorphism invariant is false. There are no local
observables in GR. If you set up a space-time measurement model, as you
actually do implicitly and Wigner explicitly, it will not be
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."
Clock readings are measurement outcomes too. Essentially you are
introducing a time coordinate through your clock readings. Its values
are not diffeomorphism invariant.
> Such
> quantities do not depend on any choice of coordinates.
As I point out above, this is not true.
> 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.
Expanding around the classical limit (or any other limit for that
matter) means that you are picking a privileged coordinate system to
begin with. Such a choice of coordinates in inherently meaningless in
GR and yet it plays a crucial role in the approximation you obtain.
In reality, when you resort to the post-Newtonian approximation, you
are already taking for granted " tacit assumptions which fix the
coordinate system" .
So it seems to me that when we talk about any experiment confirming GR
we are actually referring to a quantum gravity model (GR + an implicit
space-time measurement model) , where the space-time measurement model
is taken for granted.
Now, the scope of validity of such implicit space-time measurement
model is not clear "a priori".
In my previous post I suggested that this implicitly limits GR
predictive scope.
> 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.
I doubt this has anything to do with the problem we are discussing. I
also wonder about the physical meaning of such free parameters and
their "fit", unless they are a way to fiddle the model to fit the
observed data .
>
> For a simple example, take a look at Boddener and Will, Am. J. Phys. 71
> (2003) 770, "Deflection of light to second order: A tool for illustrating
> principles of general relativity." The authors discuss the deflection of
> light by the Sun, with detailed computations in Schwarzschild, isotropic,
> and harmonic coordinates. They show that, as you say, the *coordinate*
> predictions differ, and give a careful explanation of the equivalence of
> the *physical* predictions.
>
Thank you for your suggested reading. However I believe that your
counter-argument misses the key point of Wigner's argument. Wigner
points to a deep problem of GR, i.e. its semantic incompletness and its
reliance on a tacitly assumed space-time measurement model. I do not
see how your argument addresses that issue.
Thanks you for your feedback. I think the issue we are discussing here
is important and not conceptually trivial. Discussing misconceptions
may help dispel them.
Best,
IV
[1] E. Wigner "Relativistic Invariance and Quantum Phenomena" Rev. Mod.
Phys. 29, 255 (1957)
.
- References:
- Accuracy vs. Relevance
- From: I.Vecchi
- Accuracy vs. Relevance
- Prev by Date: Re: gravity waves
- Next by Date: Covariant Volume Integration and Stokes' / Gauss' Theorem in Curved Spacetime
- Previous by thread: Re: Accuracy vs. Relevance
- Next by thread: 2005 Pioneer Anomaly Conference
- Index(es):
Relevant Pages
|
