Comments on: How Are We to Make Progress With w? http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/ Random samplings from a universe of ideas. Tue, 06 Jan 2009 21:58:25 +0000 http://wordpress.org/?v=2.3.1 By: Petabytes | Cosmic Variance http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-920 Petabytes | Cosmic Variance Tue, 06 Sep 2005 00:36:36 +0000 http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-920 [...] Science magazine has a nice article about dark energy by Adrian Cho. But you can’t read it unless you subscribe. Except that the nice folks at UC Davis have decided that the article is nice publicity for Tony Tyson and the Large Synoptic Survey Telescope, so they’ve put the article online for free. See Mark’s post for some of the theoretical background. [...] […] Science magazine has a nice article about dark energy by Adrian Cho. But you can’t read it unless you subscribe. Except that the nice folks at UC Davis have decided that the article is nice publicity for Tony Tyson and the Large Synoptic Survey Telescope, so they’ve put the article online for free. See Mark’s post for some of the theoretical background. […]

]]> By: Sean http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-919 Sean Mon, 22 Aug 2005 04:52:08 +0000 http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-919 Shantanu, it's just that the error bars were very big on that measurement. It wasn't enough to say that the universe was accelerating, only that there wasn't enough matter to provide the critical density. And there were a lot of such measurements, albeit also with substantial error bars. It was one piece of the puzzle. Nowadays, we think that supernovae or other methods are more precise. Shantanu, it’s just that the error bars were very big on that measurement. It wasn’t enough to say that the universe was accelerating, only that there wasn’t enough matter to provide the critical density. And there were a lot of such measurements, albeit also with substantial error bars. It was one piece of the puzzle. Nowadays, we think that supernovae or other methods are more precise.

]]> By: Shantanu http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-918 Shantanu Mon, 22 Aug 2005 00:59:02 +0000 http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-918 Sean and/or Mark and others, how about to my question about using radio galaxies to measure dark energy? Thanks Sean and/or Mark and others, how about to my question about using
radio galaxies to measure dark energy?
Thanks

]]> By: Gordon Chalmers http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-917 Gordon Chalmers Sun, 21 Aug 2005 22:01:09 +0000 http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-917 Perhaps the 'experts' will offer an opinion on these seeming fortuitous numbers? Perhaps the ‘experts’ will offer an opinion on these seeming fortuitous numbers?

]]> By: Gordon Chalmers http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-916 Gordon Chalmers Sun, 21 Aug 2005 21:25:57 +0000 http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-916 Recall the mass formula 10^i GeV + 2^j 5^k MeV, with almost exactly 5% of the contribution to the fermions coming from the latter. 20/21 is 95.2% and this 'number' fits almost exactly the dark matter proportions. Couldnt there be a bright explanation of this in the 'dark matter' context? The blog as a research tool; it seems reasonable with two Higgs or instantons. Recall the mass formula 10^i GeV + 2^j 5^k MeV, with almost exactly 5% of the contribution to the fermions coming from the latter. 20/21 is 95.2% and this ‘number’ fits almost exactly the dark matter proportions. Couldnt there be a bright explanation of this in the ‘dark matter’ context? The blog as a research tool; it seems reasonable with two Higgs or instantons.

]]> By: Arun http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-915 Arun Sun, 21 Aug 2005 19:56:18 +0000 http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-915 http://xxx.arxiv.org/abs/astro-ph/0508377 Authors: Mikolaj Korzynski Abstract: <blockquote>Recently a new model of galactic gravitational field, based on ordinary General Relativity, has been proposed by Cooperstock and Tieu in which no exotic dark matter is needed to fit the observed rotation curve to a reasonable ordinary matter distribution. We argue that in this model the gravitational field is generated not only by the galaxy matter, but by a thin, singular disk as well. The model should therefore be considered unphysical. </blockquote> http://xxx.arxiv.org/abs/astro-ph/0508377

Authors: Mikolaj Korzynski

Abstract:

Recently a new model of galactic gravitational field, based on ordinary General Relativity, has been proposed by Cooperstock and Tieu in which no exotic dark matter is needed to fit the observed rotation curve to a reasonable ordinary matter distribution. We argue that in this model the gravitational field is generated not only by the galaxy matter, but by a thin, singular disk as well. The model should therefore be considered unphysical.

]]> By: The Landscape - For Real This Time | Cosmic Variance http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-914 The Landscape - For Real This Time | Cosmic Variance Sun, 14 Aug 2005 07:01:37 +0000 http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-914 [...] This positivity is important. Such positive contributions to the total energy of the system will break the underlying “supersymmetry” of the string theory, and give a postitive value for the cosmological constant. (This potential energy of the system is referred to as the “vacuum energy”, being the “ground state” energy associated to universe thus constructed - this is the same as what a cosmological constant is, classically anyway.) We care about both of these because we know that the world is not supersymmetric (see the earlier post for what supersymmetry is) and because it is currently believed (and this may well turn out to be wrong (!) see Mark’s recent post) that our world does have a positive cosmological constant. [...] […] This positivity is important. Such positive contributions to the total energy of the system will break the underlying “supersymmetry” of the string theory, and give a postitive value for the cosmological constant. (This potential energy of the system is referred to as the “vacuum energy”, being the “ground state” energy associated to universe thus constructed - this is the same as what a cosmological constant is, classically anyway.) We care about both of these because we know that the world is not supersymmetric (see the earlier post for what supersymmetry is) and because it is currently believed (and this may well turn out to be wrong (!) see Mark’s recent post) that our world does have a positive cosmological constant. […]

]]> By: Doug http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-913 Doug Thu, 11 Aug 2005 22:02:44 +0000 http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-913 Arun, I think that they are arguing that what you are asserting is true in the usual analysis, but when the co-moving coordinates are used in the analysis this causes w to remain constant at 0 and consequently the field equation becomes non-linear. The justification of this approach comes from the notion of a "gravitational-bound" system, whatever that means. The upshot is that, not withstanding the weak galactic field, the galactic dynamics are non-linear: <blockquote>...insufficient attention has been paid to the fact that the stars that compose the galaxies are essentially in motion under gravity alone ("gravitationally bound"). It has been known since the time of Eddington that the gravitationally bound problem in general relativity is an intrinsically non-linear problem even when the conditions are such that the field is weak and the motions are non-relativistic, at least in the time-dependent case. Most significantly, we have found that under these conditions, the general relativistic analysis of the problem is also non-linear for the stationary (non-time-dependent) case at hand.</blockquote> I can't argue the merits of this assertion. All that I can do is ask that someone who can do so. So far, I don't think anyone has, have they? Arun,

I think that they are arguing that what you are asserting is true in the usual analysis, but when the co-moving coordinates are used in the analysis this causes w to remain constant at 0 and consequently the field equation becomes non-linear. The justification of this approach comes from the notion of a “gravitational-bound” system, whatever that means. The upshot is that, not withstanding the weak galactic field, the galactic dynamics are non-linear:

…insufficient attention has been paid to the fact that the stars that compose the galaxies are essentially in motion under gravity alone (”gravitationally bound”). It has been known since the time of Eddington that the gravitationally bound problem in general relativity is an intrinsically non-linear problem even when the conditions are such that the field is weak and the motions are non-relativistic, at least in the time-dependent case. Most significantly, we have found that under these conditions, the general relativistic analysis of the problem is also non-linear for the stationary (non-time-dependent) case at hand.

I can’t argue the merits of this assertion. All that I can do is ask that someone who can do so. So far, I don’t think anyone has, have they?

]]> By: Arun http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-912 Arun Thu, 11 Aug 2005 19:29:22 +0000 http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-912 Doug, What is the physics (as opposed to what is the math) of what the authors are arguing? It is that the rotation of the galaxy provides a contribution to the metric that is much stronger than the Newtonian contribution. Based on what we know about gravity and various weak field expansions that exist for GR, this is implausible. How do effects that die off at (1/r)^2, and or faster sum up to exceed the (1/r) contribution? Moreover the source of the (1/r)^2 effects is v/c smaller than the source of the (1/r) contribution. Absolute certitude requires redoing the calculation independently. For something very implausible, it is not worth the effort, at least, for someone like Sean. However, it may be a good exercise to give students. -Arun Doug,

What is the physics (as opposed to what is the math) of what the authors are arguing? It is that the rotation of the galaxy provides a contribution to the metric that is much stronger than the Newtonian contribution. Based on what we know about gravity and various weak field expansions that exist for GR, this is implausible. How do effects that die off at (1/r)^2, and or faster sum up to exceed the (1/r) contribution? Moreover the source of the (1/r)^2 effects is v/c smaller than the source of the (1/r) contribution.

Absolute certitude requires redoing the calculation independently. For something very implausible, it is not worth the effort, at least, for someone like Sean. However, it may be a good exercise to give students.

-Arun

]]> By: Doug http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-911 Doug Thu, 11 Aug 2005 14:43:26 +0000 http://blogs.discovermagazine.com/cosmicvariance/2005/08/02/how-are-we-to-make-progress-with-w/#comment-911 I find it hard to believe that that Cooperstock and Tieu have made such an elementary error. I don't think we are addressing the real issue here. As I read it, they are asserting that the non-linearity arises unexpectedly because, with the use of co-moving coordinates, w acts differently. In note 7, they write: <blockquote><em>7Normally, the fall-off of w with R = (r2 + z2)^-1/2 is used to derive the total mass of an isolated system. However, w is constant in this system of coordinates by (9) and we cannot do so here. The w constancy does not imply that that the mass is zero. In other (non-co-moving) coordinate systems, w would be seen to be variable. With the field being weak and the system being non-relativistic, the mass is well-approximated simply by the integral of p over coordinate volume.</em></blockquote> The constancy of w seems to be the key to their argument for non-linearity, so if non-linearity fails, as Sean asserts, is it because their argument for the constancy of w fails? They write: <blockquote><em>It is to be noted that it is the freely gravitating motion of the source material (the stars) in conjunction with the choice of co-moving coordinates (2) that leads to the constancy of w within the source. Had there been pressure, w would have been variable... the non-linearity of the galactic dynamical problem is manifest through the non-linear relation between the functions rho and N. Rotation under freely gravitating motion is the key here. By contrast, for time-independence in the non-rotating problem, there must be pressure present to maintain a static configuration, N vanishes for vanishing w and del^2w is non-zero yielding the familiar Poisson equation of Newtonian gravity. </em></blockquote> Is this a valid argument or not? If not, why not? It seems to me that we are trying to dismiss their argument rather than trying to answer it. I find it hard to believe that that Cooperstock and Tieu have made such an elementary error. I don’t think we are addressing the real issue here. As I read it, they are asserting that the non-linearity arises unexpectedly because, with the use of co-moving coordinates, w acts differently. In note 7, they write:

7Normally, the fall-off of w with R = (r2 + z2)^-1/2 is used to derive the total mass of an isolated system. However, w is constant in this system of coordinates by (9) and we cannot do so here. The w constancy does not imply that that the mass is zero. In other (non-co-moving) coordinate systems, w would be seen to be variable. With the field being weak and the system being non-relativistic, the mass is well-approximated simply by the integral of p over coordinate volume.

The constancy of w seems to be the key to their argument for non-linearity, so if non-linearity fails, as Sean asserts, is it because their argument for the constancy of w fails? They write:

It is to be noted that it is the freely gravitating motion of the source material (the stars) in conjunction with the choice of co-moving coordinates (2) that leads to the constancy of w within the source. Had there been pressure, w would have been variable… the non-linearity of the galactic dynamical problem is manifest through the non-linear relation between the functions rho and N. Rotation under freely gravitating motion is the key here. By contrast, for time-independence in the non-rotating problem, there must be pressure present to maintain a static configuration, N vanishes for vanishing w and del^2w is non-zero yielding the familiar Poisson equation of Newtonian gravity.

Is this a valid argument or not? If not, why not? It seems to me that we are trying to dismiss their argument rather than trying to answer it.

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