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Geometry of Look-Back -- lensing
Pursuant to an old thread, I wonder who can answer this:
Let's pretend for a moment that there is no dark matter, but that the gravitational lensing that we see happening out there is affected as follows: (1) The lens / target are at different distances than we suppose, and (2) There is a migrating universal "constant" such that in earlier epochs matter bent light more per kg than it does today. In other words, lensing effectiveness is proportional to 1+z, or maybe the square root of 1+z. For (1), my question is, if we alter the distances to lens and target, even if very unreasonably so, can we recover the lensing that we see? Or is the only working solution to make the lens much larger & further away? A smaller closer lens can't bend the light that much, is that right? For (2), my question is, is there broadly a redshift dependency in lens power, that is, lens mass? Are high-z lenses seen to be more powerful than low-z lenses, or is that susceptible to a Malmquist bias? A while ago I speculated that time dilation might go as the square root of 1+z instead of the standard 1+z. This is because if there is a migrating universal constant which operated on the space-time manifold, then redshift would be half time dilation and half spatial lengthening. In other words, the past would look bigger but this self-corrects via Riemannian geometry. I'm wondering how this would affect the lensing that we see, thus these questions. Appreciate any help. cheers, Eric |
#2
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Geometry of Look-Back -- lensing
In article , Eric Flesch
writes: Let's pretend for a moment that there is no dark matter, but that the gravitational lensing that we see happening out there is affected as follows: (1) The lens / target are at different distances than we suppose, and (2) There is a migrating universal "constant" such that in earlier epochs matter bent light more per kg than it does today. In other words, lensing effectiveness is proportional to 1+z, or maybe the square root of 1+z. Either you are assuming a change in the gravitational constant (which is ruled out---at interesting levels, at least) or proposing some method other than that described by GR to bend light. However, if GR is not valid, then it probably makes little sense to leave the cosmological model otherwise alone and just change the lensing effectiveness. For (1), my question is, if we alter the distances to lens and target, even if very unreasonably so, can we recover the lensing that we see? Or is the only working solution to make the lens much larger & further away? A smaller closer lens can't bend the light that much, is that right? I don't follow you here. If the lensing strength is higher at high redshift, why do you want to make the lens larger and further away? For (2), my question is, is there broadly a redshift dependency in lens power, that is, lens mass? Are high-z lenses seen to be more powerful than low-z lenses, or is that susceptible to a Malmquist bias? Check out the classic Turner, Ostriker & Gott ApJ paper for a plot of lensing effectiveness as a function of redshift or, for a non-zero cosmological constant, Fukugita, Futamase, Kasai and Turner, also in ApJ. Lensing effectiveness is roughly Gaussian when plotted against redshift, but is down to almost zero well before the redshift of the source is reached. It depends on the redshift of the source and on the cosmological model. A while ago I speculated that time dilation might go as the square root of 1+z instead of the standard 1+z. This seems rather ad-hoc. This is because if there is a migrating universal constant which operated on the space-time manifold, then redshift would be half time dilation and half spatial lengthening. Why? Unless you have an underlying theory, I don't see how you arrive at this. In other words, the past would look bigger but this self-corrects via Riemannian geometry. I'm wondering how this would affect the lensing that we see, thus these questions. Appreciate any help. You need to have a more concrete model in order to make concrete predictions. People have looked for signals of unorthodox models in lensing and found none. |
#3
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Geometry of Look-Back -- lensing
On Sat, 13 Sep 14, Phillip Helbig wrote:
writes: ... lensing effectiveness proportional to 1+z, or ... sqrt 1+z. you are ... proposing some method other than ... GR to bend light. Heavens no, all I'm saying is that just as GR generalized SR, so can GR be generalized into a larger frame where G (or some such) migrates. I don't follow you here. If the lensing strength is higher at high redshift, why do you want to make the lens larger and further away? I am looking at (1) and (2) separately. For (2), my question is, is there broadly a redshift dependency in lens power, that is, lens mass? Are high-z lenses seen to be more powerful than low-z lenses, or is that susceptible to a Malmquist bias? Check out the classic Turner, Ostriker & Gott ApJ paper for a plot of lensing effectiveness as a function of redshift or, for a non-zero cosmological constant, Fukugita, Futamase, Kasai and Turner, also in ApJ. Lensing effectiveness is roughly Gaussian when plotted against redshift, but is down to almost zero well before the redshift of the source is reached. It depends on the redshift of the source and on the cosmological model. Excellent, thanks. This is because if there is a migrating universal constant which operated on the space-time manifold, then redshift would be half time dilation and half spatial lengthening. Why? Unless you have an underlying theory, I don't see how you arrive at this. Er, that *was* the underlying theory. You need to have a more concrete model in order to make concrete predictions. People have looked for signals of unorthodox models in lensing and found none. Even concrete is wet & sloppy at the start, refer to Archimedes' "On the Method". Thanks for your answers, Phil. Eric |
#4
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Geometry of Look-Back -- lensing
Pursuant to my previous post, I'd like to answer Phil's question about
the "underlying theory" in more detail (moderator allowing): On Sat, 13 Sep 14 Phillip Helbig wrote: writes: This is because if there is a migrating universal constant which operated on the space-time manifold, then redshift would be half time dilation and half spatial lengthening. Why? Unless you have an underlying theory, I don't see how you arrive at this. Here I said "that *was* the underlying theory", but to elaborate, since you asked, Phil: As a gedankenexperiment, let's look at two mathematical spheres, one larger than the other. The larger sphere has a lower SA-to-V ratio than the other. This is an intrinsic difference. Now place each sphere into its own empty universe. The spheres haven't changed, one still has a different intrinsic nature to the other, but we have no metric to distinguish them. So I suggest we need a universal parameter of "scale" to account for this -- which would be a characteristic or dimension of the space-time manifold. "Scale" is just a reference point and so it isn't needed in our physical law model -- sort of Machian in that way. But if it migrates through the epochs, then it serves as a separator between past and future and means that our telescopes are viewing a past where the rules are different from today-- specifically, both length (xyz-axes) and the rate of timeflow are seen to change with time. So arriving photons would hail from a time which both looks bigger and is seen to run slower. The xy axes that we see with our telescopes are remapped perforce by Riemannian geometry, but the z-axis (the direction of arrival) is not remapped. The arriving photon shows a stretch in length and a slower runtime in equal measure, because of the migration of "scale". The benefit of this is that e.g., objects at z=1 are remapped to where, for us to equate them to physical law today, we need to shrink them and slow them by sqrt(2). The redshift would show that dilation already, and by spatially shrinking them, the amount of lensing that we see comes out right! Poof, dark matter! And the Riemannian remapping would make dark energy go poof because objects would be expected to be seen smaller and fainter. Mind you, my calculations are ballpark only. It needs professional work to see if the fit is exact. If the fit is exact, it's a twofer! And that's the underlying theory, Phil, wet concrete and all. Apologies to the moderator, Eric |
#5
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Geometry of Look-Back -- lensing
In article , Eric Flesch
writes: Pursuant to my previous post, I'd like to answer Phil's question about the "underlying theory" in more detail (moderator allowing): As a gedankenexperiment, let's look at two mathematical spheres, one larger than the other. The larger sphere has a lower SA-to-V ratio than the other. This is an intrinsic difference. Now place each sphere into its own empty universe. The spheres haven't changed, one still has a different intrinsic nature to the other, but we have no metric to distinguish them. So I suggest we need a universal parameter of "scale" to account for this -- which would be a characteristic or dimension of the space-time manifold. Interesting concept. Julian Barbour has also been investigating scale recently. Check up on his recent stuff. The benefit of this is that e.g., objects at z=1 are remapped to where, for us to equate them to physical law today, we need to shrink them and slow them by sqrt(2). The redshift would show that dilation already, and by spatially shrinking them, the amount of lensing that we see comes out right! The dependence of lensing strength on redshift is rather complicated, so I don't see a cancellation happening here. Poof, dark matter! Note that much evidence for dark matter comes from z essentially 0. And the Riemannian remapping would make dark energy go poof because objects would be expected to be seen smaller and fainter. Depending on the cosmological model, they might continue to become fainter with redshift, but in some, including the current "concordance model", they become brighter again at even larger redshift. Presumably, when this is observed it will disprove your theory. |
#6
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Geometry of Look-Back -- lensing
Eric Flesch wrote:
(2) There is a migrating universal "constant" such that in earlier epochs matter bent light more per kg than it does today. and later Heavens no, all I'm saying is that just as GR generalized SR, so can GR be generalized into a larger frame where G (or some such) migrates. In other words, you're effectively hypothesizing a time variation in the Newtonian gravitational constant "big G". There are quite good experimental bounds on the time variation of G. See section 4 of Jean-Philippe Uzan "Varying Constants, Gravitation and Cosmology", Living Reviews in Relativity 14 (2011), 2 http://relativity.livingreviews.org/...es/lrr-2011-2/ for a review. Notably, this quotes a very tight lunar-laser-ranging bound: J. G. Williams, S. G. Turyshev, and D. H. Boggs, "Progress in Lunar Laser Ranging Tests of Relativistic Gravity", Physical Review Letters, 93, 261101, (2004) http://journals.aps.org/prl/abstract...Lett.93.261101 preprint at arXiv:gr-qc/0411113 These researchers find (dG/dt)/G = (4 +/- 9) e-13/year i.e., (quoting from the PRL paper) "The $\dot{G}/G$ uncertainty is 83 times smaller than the inverse age of the Universe, $t_0 = 13.4$ Gyr" One can of course imagine a theory in which G varies a lot at some past time, but then the G(t) curve flattens out so that dG/dt is small at present times, but this seems somewhat ad-hoc. -- -- "Jonathan Thornburg [remove -animal to reply]" Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA "There was of course no way of knowing whether you were being watched at any given moment. How often, or on what system, the Thought Police plugged in on any individual wire was guesswork. It was even conceivable that they watched everybody all the time." -- George Orwell, "1984" |
#7
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Geometry of Look-Back -- lensing
In article ,
Eric Flesch writes: is there broadly a redshift dependency in lens power, that is, lens mass? Are high-z lenses seen to be more powerful than low-z lenses, or is that susceptible to a Malmquist bias? This seems difficult to measure, and I doubt the answer is known. You'd need a low-z and high-z lensing sample with known masses. One approach might be to use a sample of lensing galaxy clusters whose masses are derived from velocity dispersions, but I'd expect big systematic errors. I might be wrong, though; there are lots of people cleverer than I am. -- Help keep our newsgroup healthy; please don't feed the trolls. Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA |
#8
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Geometry of Look-Back -- lensing
On 9/16/14, 12:40 AM, Steve Willner wrote:
In article , Eric Flesch writes: is there broadly a redshift dependency in lens power, that is, lens mass? Are high-z lenses seen to be more powerful than low-z lenses, or is that susceptible to a Malmquist bias? This seems difficult to measure, and I doubt the answer is known. You'd need a low-z and high-z lensing sample with known masses. In as much as lensable mass varies with universe density ~H^2/G (1+z)^3 then "high-z lenses will to be more powerful than low-z lenses" |
#9
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Geometry of Look-Back -- lensing
In article ,
"Richard D. Saam" writes: In as much as lensable mass varies with universe density ~H^2/G (1+z)^3 then "high-z lenses will to be more powerful than low-z lenses" I don't understand this. Lensing depends on the contrast between high and low density regions, and all standard models have that contrast _increasing_ with time (i.e., larger at low redshift). In any case, what is needed for the test the OP proposed is not an average mass or mass density but known mass for specific lensing objects and different redshifts. -- Help keep our newsgroup healthy; please don't feed the trolls. Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA |
#10
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Geometry of Look-Back -- lensing
In article , Steve Willner
writes: In article , "Richard D. Saam" writes: In as much as lensable mass varies with universe density ~H^2/G (1+z)^3 then "high-z lenses will to be more powerful than low-z lenses" I don't understand this. Lensing depends on the contrast between high and low density regions, and all standard models have that contrast _increasing_ with time (i.e., larger at low redshift). Yes, objects tend to grow more massive with time. But for a constant mass, there is an optimal redshift. So, the "power" will be a combination of these two things. |
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