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Is general relativity incompatible with the Newtonian limit? |
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| Sep28-05, 09:15 PM | #1 |
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Is general relativity incompatible with the Newtonian limit?
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Tue, 27 Sep 2005, Ilja Schmelzer wrote:\n\n> In the extragalactic regime we need dark matter, and a lot of it. We\n> need it for galaxies, on the large scale today, on the large scale in\n> the early universe. Moreover, part of the dark matter does not have the\n> properties of usual matter (violates the strong energy condition).\n\nAre you objecting that it is unwise to try to explain galactic rotation\ncurves by keeping the EFE (indeed, by assuming that Newtonian gravitation\nis not -totally- out of whack at galactic scales) but introducing a\nconcept of dark matter, in the absence of direct evidence for such stuff?\n\nIf so, I\'d agree that at this point the "dark matter" concept is\n-speculative-. I\'d probably assess the chances that galactic rotation\ncurves will ultimately put down to a gross failure of gtr differently from\nyou, however.\n\n> Looking at the Einstein equations G_mn = T_mn it is clear that a\n> disagreement of the Einstein equations with nature may be described as\n> "dark matter"defined by\n>\n> T_mn^dark = G_mn - T_mn^obs\n\nIt might be clear to you, but not so clear to many others :-/\n\nYou\'d have to be much more specific about what alleged "disagreement with\nNature" you have in mind (are we still talking about galactic rotation\ncurves? were we -ever- talking about galactic rotation curves), and what\nconstraints if any you intend place on T_mn^dark (Segre type, for\nexample?) before I could comment except in generalities. And if this\nrefers to some prior thread or a discussion elsewhere, you should assume\nthat I missed this discussion if you want to pursue this, because I am\nlost.\n\nActually, -I- don\'t really want to pursue this, Ilja, so I hope you will\nbe willing to leave it at this:\n\nDark matter is currently a speculative concept, some would even say a\ndubious concept, but nonetheless most contemporary cosmologists seem to be\ndisinclined to abandon gtr as our Gold Standard Theory of Gravitation.\nThese are judgement calls which could be profoundly affected by new\nobservations, or possibly even by new theoretical developments, although\nat the moment many would probably agree that some independent confirmation\nof the existence of dark matter (if it does exist), new tests of the\nalleged "Pioneer effect", etc., would be more helpful than yet another\ngravitation theory, classical or otherwise. Fair enough?\n\n"T. Essel"\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Tue, 27 Sep 2005, Ilja Schmelzer wrote:
> In the extragalactic regime we need dark matter, and a lot of it. We > need it for galaxies, on the large scale today, on the large scale in > the early universe. Moreover, part of the dark matter does not have the > properties of usual matter (violates the strong energy condition). Are you objecting that it is unwise to try to explain galactic rotation curves by keeping the EFE (indeed, by assuming that Newtonian gravitation is not -totally- out of whack at galactic scales) but introducing a concept of dark matter, in the absence of direct evidence for such stuff? If so, I'd agree that at this point the "dark matter" concept is -speculative-. I'd probably assess the chances that galactic rotation curves will ultimately put down to a gross failure of gtr differently from you, however. > Looking at the Einstein equations [itex]G_{mn} = T_{mn} it[/itex] is clear that a > disagreement of the Einstein equations with nature may be described as > "dark matter"defined by > > [itex]T_{mn}^dark = G_{mn} - T_{mn}^obs[/itex] It might be clear to you, but not so clear to many others :-/ You'd have to be much more specific about what alleged "disagreement with Nature" you have in mind (are we still talking about galactic rotation curves? were we -ever- talking about galactic rotation curves), and what constraints if any you intend place on [itex]T_{mn}^dark[/itex] (Segre type, for example?) before I could comment except in generalities. And if this refers to some prior thread or a discussion elsewhere, you should assume that I missed this discussion if you want to pursue this, because I am lost. Actually, -I- don't really want to pursue this, Ilja, so I hope you will be willing to leave it at this: Dark matter is currently a speculative concept, some would even say a dubious concept, but nonetheless most contemporary cosmologists seem to be disinclined to abandon gtr as our Gold Standard Theory of Gravitation. These are judgement calls which could be profoundly affected by new observations, or possibly even by new theoretical developments, although at the moment many would probably agree that some independent confirmation of the existence of dark matter (if it does exist), new tests of the alleged "Pioneer effect", etc., would be more helpful than yet another gravitation theory, classical or otherwise. Fair enough? "T. Essel" |
| Oct1-05, 03:32 AM | #2 |
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<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Ilja Schmelzer" <Ilja.Schmelzer@FernUni-Hagen.de> schrieb im Newsbeitrag\nnews:dh89ep\\$5ba\\$1@beech.fernuni-hagen.de...\n>\n> <tessel@um.bot> schrieb\n>> > There are several obvious flaws in GR, including discrepancies with\n>> > data\n>> > especially in the extragalactic regime.\n>>\n>> GR does have flaws which are widely recognized, but discrepancies with\n>> data is emphatically -not- one of them!\n>\n> Looking at the Einstein equations G_mn = T_mn it is clear that a\n> disagreement of the Einstein equations with nature may be described as\n> "dark matter"defined by\n>\n> T_mn^dark = G_mn - T_mn^obs\n>\n> In the extragalactic regime we need dark matter, and a lot of it. We need\n> it for galaxies, on the large scale today, on the large scale in the early\n> universe. Moreover, part of the dark matter does not have the properties\n> of usual matter (violates the strong energy condition).\n>\n> In this sense, what we observe is exactly what we have to expect if there\n> are discrepancies of GR with Nature in the extragalactic regime.\n\nNot only in this general sense: There exist a great lot more very specific\narguments against GR, because its until now not possible to describe\nsatisfingly the galactic observations with exotic (or ghost) dark\nmatter-models: For this it would be necessary to explain simultaneously the\nconstant curves of rotation in galaxies, the Tully/Fisher-rule and the\nuniversality of the gravitational accelaration, at which the influence of\nexotic dark matter begins to be important. More about the astrophysical\nconstraints for a good theory of gravitation you find in (GR is by far not\nfulfilling these constraints):\n\nAstrophysical Constraints on Modifying Gravity at Large Distances by\nAguirre, Burgess, Friedland und Nolte, 25. Mai 2001,\n\nhttp://arxiv.org/abs/hep-ph/0105083\n\nHomo Lykos\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Ilja Schmelzer" <Ilja.Schmelzer@FernUni-Hagen.de> schrieb im Newsbeitrag
news:dh89ep$5ba$1@beech.fernuni-hagen.de... > > <tessel@um.bot> schrieb >> > There are several obvious flaws in GR, including discrepancies with >> > data >> > especially in the extragalactic regime. >> >> GR does have flaws which are widely recognized, but discrepancies with >> data is emphatically -not- one of them! > > Looking at the Einstein equations [itex]G_{mn} = T_{mn} it[/itex] is clear that a > disagreement of the Einstein equations with nature may be described as > "dark matter"defined by > > [itex]T_{mn}^dark = G_{mn} - T_{mn}^obs[/itex] > > In the extragalactic regime we need dark matter, and a lot of it. We need > it for galaxies, on the large scale today, on the large scale in the early > universe. Moreover, part of the dark matter does not have the properties > of usual matter (violates the strong energy condition). > > In this sense, what we observe is exactly what we have to expect if there > are discrepancies of GR with Nature in the extragalactic regime. Not only in this general sense: There exist a great lot more very specific arguments against GR, because its until now not possible to describe satisfingly the galactic observations with exotic (or ghost) dark matter-models: For this it would be necessary to explain simultaneously the constant curves of rotation in galaxies, the Tully/Fisher-rule and the universality of the gravitational accelaration, at which the influence of exotic dark matter begins to be important. More about the astrophysical constraints for a good theory of gravitation you find in (GR is by far not fulfilling these constraints): Astrophysical Constraints on Modifying Gravity at Large Distances by Aguirre, Burgess, Friedland und Nolte, 25. Mai 2001, http://arxiv.org/abs/http://www.arxi...hep-ph/0105083 Homo Lykos |
| Oct1-05, 03:33 AM | #3 |
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<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE><tessel@um.bot> schrieb\n> On Tue, 27 Sep 2005, Ilja Schmelzer wrote:\n> > In the extragalactic regime we need dark matter, and a lot of it. We\n> > need it for galaxies, on the large scale today, on the large scale in\n> > the early universe. Moreover, part of the dark matter does not have the\n> > properties of usual matter (violates the strong energy condition).\n>\n> Are you objecting that it is unwise to try to explain galactic rotation\n> curves by keeping the EFE (indeed, by assuming that Newtonian gravitation\n> is not -totally- out of whack at galactic scales) but introducing a\n> concept of dark matter, in the absence of direct evidence for such stuff?\n\nNo. We have a disagreement between theory (GR + theory of visible matter)\nwith observation. It is wise to consider different possible explanations.\nThis includes, of course, dark matter. But, as long as we have not found\nthis dark matter, the dark matter hypothesis is only an ad hoc explanation\nfor an observed discrepancy with data. And it is unwise to make claims like\nthis:\n\n>>> GR does have flaws which are widely recognized, but discrepancies with\n>>> data is emphatically -not- one of them!\n\n> If so, I\'d agree that at this point the "dark matter" concept is\n> -speculative-. I\'d probably assess the chances that galactic rotation\n> curves will ultimately put down to a gross failure of gtr differently from\n> you, however.\n\nI\'m not evaluating probabilities for the different solutions for the\nobserved discrepancy. One thing is the belief that some form of dark matter\nallows to explain the observed discrepancy, another one that there is no\ndiscrepancy.\n\n> > Looking at the Einstein equations G_mn = T_mn it is clear that a\n> > disagreement of the Einstein equations with nature may be described as\n> > "dark matter"defined by\n> >\n> > T_mn^dark = G_mn - T_mn^obs\n>\n> It might be clear to you, but not so clear to many others :-/\n>\n> You\'d have to be much more specific about what alleged "disagreement with\n> Nature" you have in mind (are we still talking about galactic rotation\n> curves? were we -ever- talking about galactic rotation curves), and what\n> constraints if any you intend place on T_mn^dark (Segre type, for\n> example?) before I could comment except in generalities.\n\nI\'m talking about a general principle. We can observe (via length and time\nmeasurements) the metric and, therefore, G_mn. We can observe T_mn of\nobservable matter, but not of dark matter - by definition of "dark" matter.\nThat means, whatever we can observe, in principle, we can always define\n\nT_mn^dark = G_mn - T_mn^obs\n\nand, as a consequence, the EFE holds. Thus, the EFE in itself cannot be\nfalsified by observation. There cannot be a discrepancy between EFE and\ndata, as long as we do not restrict the type of dark matter.\n\nJudging from your answer (where you refer to _constraints_ on T_mn^dark) you\nseem to be aware of this. I only want to emphasize the point: A dark matter\nexplanation without nontrivial constraints on T_mn^dark can explain\neverything.\n\nAnd, as an additional point, let\'s note that the GR equation of motion for\nthe dark matter nabla T^dark = 0 is not a nontrivial constraint. Instead, it\nis a consequence of nabla T^obs = 0 (which means that visible matter behaves\nlike predicted in the gravitational field) and the tautology nabla\n(T^dark+T^obs) = nabla G = 0.\n\n> Dark matter is currently a speculative concept, some would even say a\n> dubious concept, but nonetheless most contemporary cosmologists seem to be\n> disinclined to abandon gtr as our Gold Standard Theory of Gravitation.\n> These are judgement calls which could be profoundly affected by new\n> observations, or possibly even by new theoretical developments, although\n> at the moment many would probably agree that some independent confirmation\n> of the existence of dark matter (if it does exist), new tests of the\n> alleged "Pioneer effect", etc., would be more helpful than yet another\n> gravitation theory, classical or otherwise. Fair enough?\n\nAs formulated (as a judgement of most contemporary cosmologists) I see no\nreason for disagreement.\n\nBut, as observed by Kuhn, theories will be abandoned only if there is a\nreplacement which is superior. If people refuse to look at "yet another\ngravitation theory", GR will never be abandoned, independend of any\ndata.\n\nIlja\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky><tessel@um.bot> schrieb
> On Tue, 27 Sep 2005, Ilja Schmelzer wrote: > > In the extragalactic regime we need dark matter, and a lot of it. We > > need it for galaxies, on the large scale today, on the large scale in > > the early universe. Moreover, part of the dark matter does not have the > > properties of usual matter (violates the strong energy condition). > > Are you objecting that it is unwise to try to explain galactic rotation > curves by keeping the EFE (indeed, by assuming that Newtonian gravitation > is not -totally- out of whack at galactic scales) but introducing a > concept of dark matter, in the absence of direct evidence for such stuff? No. We have a disagreement between theory (GR + theory of visible matter) with observation. It is wise to consider different possible explanations. This includes, of course, dark matter. But, as long as we have not found this dark matter, the dark matter hypothesis is only an ad hoc explanation for an observed discrepancy with data. And it is unwise to make claims like this: >>> GR does have flaws which are widely recognized, but discrepancies with >>> data is emphatically -not- one of them! > If so, I'd agree that at this point the "dark matter" concept is > -speculative-. I'd probably assess the chances that galactic rotation > curves will ultimately put down to a gross failure of gtr differently from > you, however. I'm not evaluating probabilities for the different solutions for the observed discrepancy. One thing is the belief that some form of dark matter allows to explain the observed discrepancy, another one that there is no discrepancy. > > Looking at the Einstein equations [itex]G_{mn} = T_{mn} it[/itex] is clear that a > > disagreement of the Einstein equations with nature may be described as > > "dark matter"defined by > > > > [itex]T_{mn}^dark = G_{mn} - T_{mn}^obs[/itex] > > It might be clear to you, but not so clear to many others :-/ > > You'd have to be much more specific about what alleged "disagreement with > Nature" you have in mind (are we still talking about galactic rotation > curves? were we -ever- talking about galactic rotation curves), and what > constraints if any you intend place on [itex]T_{mn}^dark[/itex] (Segre type, for > example?) before I could comment except in generalities. I'm talking about a general principle. We can observe (via length and time measurements) the metric and, therefore, [itex]G_{mn}[/itex]. We can observe [itex]T_{mn}[/itex] of observable matter, but not of dark matter - by definition of "dark" matter. That means, whatever we can observe, in principle, we can always define [tex]T_{mn}^dark = G_{mn} - T_{mn}^obs[/tex] and, as a consequence, the EFE holds. Thus, the EFE in itself cannot be falsified by observation. There cannot be a discrepancy between EFE and data, as long as we do not restrict the type of dark matter. Judging from your answer (where you refer to _constraints_ [itex]on T_{mn}^dark)[/itex] you seem to be aware of this. I only want to emphasize the point: A dark matter explanation without nontrivial constraints on [itex]T_{mn}^dark[/itex] can explain everything. And, as an additional point, let's note that the GR equation of motion for the dark matter nabla [itex]T^{dark} =[/itex] is not a nontrivial constraint. Instead, it is a consequence of nabla [itex]T^{obs} =[/itex] (which means that visible matter behaves like predicted in the gravitational field) and the tautology nabla [itex](T^{dark}+T^{obs}) =[/itex] nabla G = . > Dark matter is currently a speculative concept, some would even say a > dubious concept, but nonetheless most contemporary cosmologists seem to be > disinclined to abandon gtr as our Gold Standard Theory of Gravitation. > These are judgement calls which could be profoundly affected by new > observations, or possibly even by new theoretical developments, although > at the moment many would probably agree that some independent confirmation > of the existence of dark matter (if it does exist), new tests of the > alleged "Pioneer effect", etc., would be more helpful than yet another > gravitation theory, classical or otherwise. Fair enough? As formulated (as a judgement of most contemporary cosmologists) I see no reason for disagreement. But, as observed by Kuhn, theories will be abandoned only if there is a replacement which is superior. If people refuse to look at "yet another gravitation theory", GR will never be abandoned, independend of any data. Ilja |
| Oct5-05, 04:06 PM | #4 |
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Is general relativity incompatible with the Newtonian limit?
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Sat, 1 Oct 2005, Ilja Schmelzer wrote:\n\n> It is wise to consider different possible explanations. This includes,\n> of course, dark matter. But, as long as we have not found this dark\n> matter, the dark matter hypothesis is only an ad hoc explanation for an\n> observed discrepancy with data.\n\nSo far I think I\'d agree.\n\n> And it is unwise to make claims like this:\n>\n>>>> GR does have flaws which are widely recognized, but discrepancies with\n>>>> data is emphatically -not- one of them!\n\nAs you know, gtr appears to be consistent with many, many observations at\nthe solar system scale, but rotation curves would seem to suggest neither\ngtr nor Newtonian gravitation can be even approximately accurate on\ngalactic scales, -if- you assume that what we can see is all there is.\n\nWhile this is clearly a judgement call, right now most physicists seem to\nthink the lesser of two evils is to try to work with an "ad hoc"\nhypothesis, of the form that what we see is not all there is. Don\'t\nforget, completely "ad hoc" suggestions have sometimes been right on the\nmoney, for example Planck\'s quantum hypothesis.\n\n>> If so, I\'d agree that at this point the "dark matter" concept is\n>> -speculative-. I\'d probably assess the chances that galactic rotation\n>> curves will ultimately put down to a gross failure of gtr differently from\n>> you, however.\n>\n> I\'m not evaluating probabilities for the different solutions for the\n> observed discrepancy.\n\nYou and I are making judgement calls. We happen to be calling it\ndifferent ways, but I think you are in fact trying to express here the\nsame idea which I am: neither of us really knows who made the right call\nyet.\n\n> One thing is the belief that some form of dark matter allows to explain\n> the observed discrepancy, another one that there is no discrepancy.\n\nWell, if you go that route, you have to explain why gtr works so well for\nall those other predictions, in fact you even have to explain why\nNewtonian gravity is not too bad on solar system scales and below, but\nfails grossly at larger scales. I know you think you have an explanation,\nbut my judgement is that dark matter is less implausible.\n\n> I\'m talking about a general principle. We can observe (via length and\n> time measurements) the metric and, therefore, G_mn.\n\nIndeed, we can estimate the Riemann tensor directly from sufficiently\ndetailed observations of test particle motion.\n\n> We can observe T_mn of observable matter, but not of dark matter - by\n> definition of "dark" matter. That means, whatever we can observe, in\n> principle, we can always define\n>\n> T_mn^dark = G_mn - T_mn^obs\n>\n> and, as a consequence, the EFE holds. Thus, the EFE in itself cannot be\n> falsified by observation. There cannot be a discrepancy between EFE and\n> data, as long as we do not restrict the type of dark matter.\n\nI think you are saying that if we declare it OK to toss in "completely\narbitrary" ad hoc new "stress-energy" terms whenever we like, -any-\nLorentzian manifold could become a "solution of the EFE". I agree, and in\nfact I have often stressed this very point. But I think you are\noverlooking that fact that, while the proposed dark matter term may be ad\nhoc, it is -not-, as I understand it, "completely arbitrary".\n\n> But, as observed by Kuhn, theories will be abandoned only if there is a\n> replacement which is superior. If people refuse to look at "yet another\n> gravitation theory", GR will never be abandoned, independend of any\n> data.\n\nNot sure what you are saying, since I see preprints almost every day in\nwhich physicists are looking at "yet another gravitation theory".\n\nNeither gtr nor Newtonian gravity are likely to ever be -abandoned-\nsince they are clearly useful where they are sufficiently accurate. But\nNewtonian gravity has already been -dethroned- as our gold standard\ntheory of gravitation (since not relativistic) and everyone expects gtr\nwill eventually be dethroned in turn (since not quantum).\n\nI was saying that I expect that taking this step will be avoided until\nthere is clear evidence that -gtr- specifically is failing. As in a\nclean -test- of a specific prediction which appears to be have\nessentially -no other explanation- than a failure of gtr. Taking the\nplunge will be much easier, of course, if we have a workable alternative\ntheory already at hand which explains everything which gtr does, but\ndoesn\'t fail this hypothetical future test!\n\nI would add that I happen to doubt that gtr will ever be dethroned by\nanother -classical- field theory, but agree that this -might- happen.\n\nOK, I don\'t really want to continue this conversation because apart from\na few judgement calls I think our positions are almost identical. Since\nI think we agree that either of us could be wrong about these judgement\ncalls, I don\'t see that we have anything to discuss, in the absence of\nstartling new data.\n\n"T. Essel" (hiding somewhere in cyberspace)\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Sat, 1 Oct 2005, Ilja Schmelzer wrote:
> It is wise to consider different possible explanations. This includes, > of course, dark matter. But, as long as we have not found this dark > matter, the dark matter hypothesis is only an ad hoc explanation for an > observed discrepancy with data. So far I think I'd agree. > And it is unwise to make claims like this: > >>>> GR does have flaws which are widely recognized, but discrepancies with >>>> data is emphatically -not- one of them! As you know, gtr appears to be consistent with many, many observations at the solar system scale, but rotation curves would seem to suggest neither gtr nor Newtonian gravitation can be even approximately accurate on galactic scales, -if- you assume that what we can see is all there is. While this is clearly a judgement call, right now most physicists seem to think the lesser of two evils is to try to work with an "ad hoc" hypothesis, of the form that what we see is not all there is. Don't forget, completely "ad hoc" suggestions have sometimes been right on the money, for example Planck's quantum hypothesis. >> If so, I'd agree that at this point the "dark matter" concept is >> -speculative-. I'd probably assess the chances that galactic rotation >> curves will ultimately put down to a gross failure of gtr differently from >> you, however. > > I'm not evaluating probabilities for the different solutions for the > observed discrepancy. You and I are making judgement calls. We happen to be calling it different ways, but I think you are in fact trying to express here the same idea which I am: neither of us really knows who made the right call yet. > One thing is the belief that some form of dark matter allows to explain > the observed discrepancy, another one that there is no discrepancy. Well, if you go that route, you have to explain why gtr works so well for all those other predictions, in fact you even have to explain why Newtonian gravity is not too bad on solar system scales and below, but fails grossly at larger scales. I know you think you have an explanation, but my judgement is that dark matter is less implausible. > I'm talking about a general principle. We can observe (via length and > time measurements) the metric and, therefore, [itex]G_{mn}[/itex]. Indeed, we can estimate the Riemann tensor directly from sufficiently detailed observations of test particle motion. > We can observe [itex]T_{mn}[/itex] of observable matter, but not of dark matter - by > definition of "dark" matter. That means, whatever we can observe, in > principle, we can always define > > [itex]T_{mn}^dark = G_{mn} - T_{mn}^obs[/itex] > > and, as a consequence, the EFE holds. Thus, the EFE in itself cannot be > falsified by observation. There cannot be a discrepancy between EFE and > data, as long as we do not restrict the type of dark matter. I think you are saying that if we declare it OK to toss in "completely arbitrary" ad hoc new "stress-energy" terms whenever we like, -any- Lorentzian manifold could become a "solution of the EFE". I agree, and in fact I have often stressed this very point. But I think you are overlooking that fact that, while the proposed dark matter term may be ad hoc, it is -not-, as I understand it, "completely arbitrary". > But, as observed by Kuhn, theories will be abandoned only if there is a > replacement which is superior. If people refuse to look at "yet another > gravitation theory", GR will never be abandoned, independend of any > data. Not sure what you are saying, since I see preprints almost every day in which physicists are looking at "yet another gravitation theory". Neither gtr nor Newtonian gravity are likely to ever be -abandoned- since they are clearly useful where they are sufficiently accurate. But Newtonian gravity has already been -dethroned- as our gold standard theory of gravitation (since not relativistic) and everyone expects gtr will eventually be dethroned in turn (since not quantum). I was saying that I expect that taking this step will be avoided until there is clear evidence that -gtr- specifically is failing. As in a clean -test- of a specific prediction which appears to be have essentially -no other explanation- than a failure of gtr. Taking the plunge will be much easier, of course, if we have a workable alternative theory already at hand which explains everything which gtr does, but doesn't fail this hypothetical future test! I would add that I happen to doubt that gtr will ever be dethroned by another -classical- field theory, but agree that this -might- happen. OK, I don't really want to continue this conversation because apart from a few judgement calls I think our positions are almost identical. Since I think we agree that either of us could be wrong about these judgement calls, I don't see that we have anything to discuss, in the absence of startling new data. "T. Essel" (hiding somewhere in cyberspace) |
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