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 12th April 2010, 02:39 PM #121 Thabiguy Muse   Join Date: Feb 2007 Posts: 783 Originally Posted by Perpetual Student So, that tells me that if the meter shows the forces associated with rotation, it is unambiguous that the rock/rope system is rotating and the universe is not revolving around the system. OK? In flat spacetime.
 12th April 2010, 02:43 PM #122 Uncayimmy Banned   Join Date: Oct 2008 Posts: 7,485 Originally Posted by Hellbound Nothing there contradicts me, that I can see. The ball would follow an arc, but as the person holding the string is moving at the same rate as the ball, the string would be straight and moving sideways. I've attached a photo that should explain it (please don't criticize the lack of artistic talent ). http://forums.randi.org/imagehosting...37fd6cb097.jpg The blue represents the path the ball fills over the time, the straight black lines the string. The black circles are the positions of the ball at the various time intervals. Just to make clear, it's the appearance of the string my earlier post was concerned with, not the ball path. Hope this clears up any confusion. Big thanks for taking the time to make the drawing. It's greatly appreciated. I did think you were referring to the path the ball followed rather than the string - a simple misunderstanding. Is there no reference frame where we could see the string as being curved? Part of my brain is nagging me that there is, but I haven't been able to envision it. When it comes to things like this, I am not confident enough in my knowledge to say that there isn't simply because I cannot figure it out.
 12th April 2010, 02:49 PM #123 sol invictus Philosopher     Join Date: Oct 2007 Location: Nova Roma Posts: 8,419 Originally Posted by Perpetual Student From your previous post, you said, "But you can distinguish inertial frames in which it's accelerating (including rotating around, say, the origin) from those in which it's not (Newton's bucket is a famous example)." So, that tells me that if the meter shows the forces associated with rotation, it is unambiguous that the rock/rope system is rotating and the universe is not revolving around the system. OK? I don't know, because you still haven't told us what it means to you to say that something is "really rotating". If you mean "at rest in some inertial frame" then yes - but only in flat spacetime, because in curved spacetimes (such as the one we inhabit) there are no inertial frames.
 12th April 2010, 02:52 PM #124 Tim Thompson Muse     Join Date: Dec 2008 Location: San Gabriel Valley, east of Los Angeles Posts: 963 What is Reality? Originally Posted by Perpetual Student Can I conclude that the rocks are really rotating because the meter and string shows it or not? Originally Posted by Tim Thompson I don't think it is possible under any circumstances to know what is the reality of the universe. I think the best we can do is know the relationship of consistency between our model of the universe and our observations of the universe. When we find the two in high accord we tend to treat the model as if it is reality, but we must keep in mind that is it always only a model. I think I see two things at issue here. One of them is what "really" really means, and the other is the difference between coordinate systems and reference frames (the wikipedia pages tend to make the same mistake, in my view, of equating to two improperly). I would say that "coordinate system" refers to your particular choice of orthogonal coordinates for identifying points and/or loci of points (e.g., Cartesian, spherical polar, ellipsoidal-hyperbolic, & etc.), whereas a "reference frame" refers to the fundamental properties of spacetime. So, an "inertial" reference frame is Euclidean (a geometric description) or non-accelerated (a kinematic description), and a non-inertial reference frame is either curved (a geometric description) or accelerated (a kinematic description). The geometric or kinematic descriptions are just different ways of treating the same physics. On the surface of Earth we can assume we are in an inertial reference frame, subject to non-linear Coriolis forces, or we can assume we are in a non-inertial reference frame feeling the effect of rotation. A sufficiently local experiment will not distinguish between the two. Then there is the philosophical vs the practical problem of defining real (if you want real headaches over reality, just look into quantum mechanics). You keep coming back to the concept of what is "really" happening, but I don't think there is any general agreement here over what "really" really means. I think that while you & Sol might use the same word, you are likely not saying the same thing with it. I hold to a strictly limited concept of "real". As in the quote above, I don't think you are asking a meaningful question, because I don't think it is possible to ever know what is "really" happening, or even that anything at all is "really" happening, in the philosophical sense. Only practical reality means anything to me, and practical reality is what we observe when we do an experiment. Take Newton's rocks. If those two rocks and the rope between them are alone in the universe (in which case we cannot be there to observe them), then it is of no observational consequence whether they are rotating in an inertial (non-rotating) universe, or at rest in a non-inertial (rotating) universe. The system behaves exactly the same in every sense in either case. So we pick one for convenience sake. Pick "rocks are rotating" because it makes things easier to understand, but it is not correct to say that it is "really happening" and the alternative is "really not happening", because no experiment exists that can distinguish one from the other. Therein lies the secret: You cannot pick the "real" alternative unless you can perform an experiment that will distinguish by its outcome between the two. You can pick one because it makes more sense to you, but if you call it "real", it is a subjective judgement, not a difference between objective realities. __________________ The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it. -- Bertrand Russell
 12th April 2010, 03:20 PM #125 sol invictus Philosopher     Join Date: Oct 2007 Location: Nova Roma Posts: 8,419 Originally Posted by Tim Thompson the difference between coordinate systems and reference frames (the wikipedia pages tend to make the same mistake, in my view, of equating to two improperly). I equate them. I don't think there's any distinction. Quote: I would say that "coordinate system" refers to your particular choice of orthogonal coordinates for identifying points and/or loci of points (e.g., Cartesian, spherical polar, ellipsoidal-hyperbolic, & etc.), whereas a "reference frame" refers to the fundamental properties of spacetime. That's non-standard. For example it's very common to refer to "different" inertial reference frames in special relativity (e.g. two that are in motion with respect to each other) - but the spacetime in SR is always the same (Minkowski space). Quote: Therein lies the secret: You cannot pick the "real" alternative unless you can perform an experiment that will distinguish by its outcome between the two. You can pick one because it makes more sense to you, but if you call it "real", it is a subjective judgement, not a difference between objective realities. That's my view, which is why I argue that one cannot decide whether the universe is "really" rotating - because I can always find frames in which it is and frames in which it isn't, without changing my predictions for any experiment.
 12th April 2010, 04:39 PM #126 Perpetual Student Illuminator     Join Date: Jul 2008 Location: USA Posts: 3,707 Quote: That's my view, which is why I argue that one cannot decide whether the universe is "really" rotating - because I can always find frames in which it is and frames in which it isn't, without changing my predictions for any experiment. Is it possible that you 'cannot decide whether the universe is "really" rotating' because of a deficiency of your state of knowledge and models, not a characteristic of the universe, which must be either unambiguously rotating or not? I am aware that physicists do believe that the universe is actually ambiguous (relative) in this way, but it seems to me this may be more hubris than science. There was a time in the mid to late 19th century that someone (I can't place the name) proclaimed that there are only details left to iron out, because all the fundamental laws of physics were known. Obviously, he could not have been more wrong! __________________ It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ
 12th April 2010, 06:32 PM #127 Hellbound Abiogenic Spongiform     Join Date: Sep 2002 Location: In a handbasket Posts: 8,924 Originally Posted by UncaYimmy Big thanks for taking the time to make the drawing. It's greatly appreciated. I did think you were referring to the path the ball followed rather than the string - a simple misunderstanding. Is there no reference frame where we could see the string as being curved? Part of my brain is nagging me that there is, but I haven't been able to envision it. When it comes to things like this, I am not confident enough in my knowledge to say that there isn't simply because I cannot figure it out. No, I don't think there is, but I reserve the right to be corrected by those more knowledgeable I could see a situation where, say, a black hole (or some equally dense gravitational anomoly) bent light to make it appear curved, or refraction effects, but that's a bit beyond reference frame
 12th April 2010, 07:57 PM #128 sol invictus Philosopher     Join Date: Oct 2007 Location: Nova Roma Posts: 8,419 Originally Posted by Perpetual Student Is it possible that you 'cannot decide whether the universe is "really" rotating' because of a deficiency of your state of knowledge and models, not a characteristic of the universe, which must be either unambiguously rotating or not? Of course - anything is possible (particularly since you still haven't said what "really rotating" is, so the statement is so vague as to be entirely meaningless). But as I told you, if one cannot choose coordinates in which an initially non-rotating universe rotates, then GR is not just incomplete - it's entirely and completely wrong, and in a way that I frankly cannot even imagine. Quote: I am aware that physicists do believe that the universe is actually ambiguous (relative) in this way, but it seems to me this may be more hubris than science. You don't think assertions like "it is a fundamental flaw of GR. It simply contradicts common sense, intuition and rationality to view things otherwise. And, as far as I can tell, there is no utility in viewing the universe in such an absurd manner" illustrate a certain degree of hubris? It may well be the case that there exists a good definition of angular momentum for cosmological spacetimes (as there is for asymptotically flat spacetimes), and one could then choose to call spacetimes with zero angular momentum "non-rotating", and those with it non-zero "rotating". But as I've been trying to explain, one can always choose coordinates on a non-rotating object so it rotates.... and the physics in the new coordinates will be (and must be) identical. Quote: There was a time in the mid to late 19th century that someone (I can't place the name) proclaimed that there are only details left to iron out, because all the fundamental laws of physics were known. Obviously, he could not have been more wrong! If you want to draw some lessons from the history of physics, I suggest the following: 1) "common sense" doesn't apply at all in regimes outside the human scale and the human environment, and not even always there 2) Established theories very rarely - if ever - prove to be entirely wrong. Instead they turn out to be approximations that are valid and useful in certain regimes, but must be replaced by something more general and complete in others.
 12th April 2010, 09:11 PM #129 schrodingasdawg Critical Thinker   Join Date: Jan 2010 Posts: 293 Originally Posted by UncaYimmy Is there no reference frame where we could see the string as being curved? No. The curvature of something is an invariant that doesn't depend on reference frame. Originally Posted by Perpetual Student There was a time in the mid to late 19th century that someone (I can't place the name) proclaimed that there are only details left to iron out, because all the fundamental laws of physics were known. Obviously, he could not have been more wrong! It's attributed to William Thomson (Lord Kelvin), but that's actually disputed.
 12th April 2010, 09:41 PM #130 Perpetual Student Illuminator     Join Date: Jul 2008 Location: USA Posts: 3,707 Originally Posted by sol invictus Of course - anything is possible (particularly since you still haven't said what "really rotating" is, so the statement is so vague as to be entirely meaningless). But as I told you, if one cannot choose coordinates in which an initially non-rotating universe rotates, then GR is not just incomplete - it's entirely and completely wrong, and in a way that I frankly cannot even imagine. It appears that it is my ignorance of GR that is the problem. Because GR replaces Newton's theory of gravity, I have not regarded Newton's theory as wrong, but simply limited. I have seen GR as extending not replacing Newton's gravity. There are many physical laws that break down at extreme sizes, pressure, etc. But, I have never regarded that as making those laws wrong, but only limited. Quote: You don't think assertions like "it is a fundamental flaw of GR. It simply contradicts common sense, intuition and rationality to view things otherwise. And, as far as I can tell, there is no utility in viewing the universe in such an absurd manner" illustrate a certain degree of hubris? OK, fair enough. I was trying to be provocative. I have a deep respect for physicists and their area of expertise. Unfortunately, there is much of modern physics that is not readily intuitive for a layman. If I thought my assertions here were actually correct, I would not bother people on this forum; instead, I would write a book like Terence Witt or establish a website and launch an ant-GR campaign like a certain Mr. Mozina does with his EU stuff. Quote: It may well be the case that there exists a good definition of angular momentum for cosmological spacetimes (as there is for asymptotically flat spacetimes), and one could then choose to call spacetimes with zero angular momentum "non-rotating", and those with it non-zero "rotating". But as I've been trying to explain, one can always choose coordinates on a non-rotating object so it rotates.... and the physics in the new coordinates will be (and must be) identical. Actually, I do think I am beginning to understand this. The point appears to be that the nature of GR under discussion here is so fundamental, that if there were some "outside" way of establishing some single thing as absolutely rotating, it would invalidate the whole theory. Quote: If you want to draw some lessons from the history of physics, I suggest the following: 1) "common sense" doesn't apply at all in regimes outside the human scale and the human environment, and not even always there 2) Established theories very rarely - if ever - prove to be entirely wrong. Instead they turn out to be approximations that are valid and useful in certain regimes, but must be replaced by something more general and complete in others. Two excellent and relevant points. I really hope this exchange has not been too tedious for you. If it has, perhaps you can gain some small satisfaction in knowing that it has been very helpful for me. BUT: I still do hate it that I can't view the earth as really rotating. __________________ It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ Last edited by Perpetual Student; 12th April 2010 at 09:44 PM.
 12th April 2010, 10:40 PM #131 ynot Illuminator     Join Date: Jan 2006 Location: New Zealand Posts: 4,652 Originally Posted by Perpetual Student BUT: I still do hate it that I can't view the earth as really rotating. Why do you think water spins down the plughole one way in the northern hemisphere and the opposite way in the southern? I have as much if not more trouble accepting Relativity as you do by the way. __________________ Rumours of a god’s existence have been greatly exaggerated. My post are all (IMO) unless stated otherwise. Last edited by ynot; 12th April 2010 at 10:45 PM.
 12th April 2010, 11:14 PM #132 Uncayimmy Banned   Join Date: Oct 2008 Posts: 7,485 Originally Posted by schrodingasdawg No. The curvature of something is an invariant that doesn't depend on reference frame. Groovy. Then I shall trouble myself no more with it.
 12th April 2010, 11:47 PM #133 Sideroxylon Gavagai!     Join Date: Aug 2008 Location: Turkey Posts: 10,628 Originally Posted by ynot Why do you think water spins down the plughole one way in the northern hemisphere and the opposite way in the southern? I have as much if not more trouble accepting Relativity as you do by the way. That the coriolis effect acts on water going down drains is apparently bunk: http://www.snopes.com/science/coriolis.asp __________________ 'The first principle is that you must not fool yourself - and you are the easiest person to fool.' - Richard Feynman
 13th April 2010, 05:25 AM #134 sol invictus Philosopher     Join Date: Oct 2007 Location: Nova Roma Posts: 8,419 Originally Posted by ynot Why do you think water spins down the plughole one way in the northern hemisphere and the opposite way in the southern? It doesn't (and yes, I've actually checked myself). Coriolis force is too weak to matter much on the scale of a bathtub or sink. A better question is why large storms curl opposite ways in the two hemispheres. If you want to explain Corliois force without rotation, it's simple - you must simply introduce a force field that acts on all mass uniformly with a force exactly proportional to the mass. Kind of like gravity, huh?
 13th April 2010, 06:28 AM #135 DeiRenDopa Master Poster   Join Date: Feb 2008 Posts: 2,378 Maybe tangential, or even OT, but perhaps not tooo much ... How does the core of the discussion in this (excellent, many thanks PS! ) thread relate to equivalence principle(s)? IIRC, both SR and GR involve some kind of reference to 'laws of physics'; what is meant (in the theory) by this phrase? Lastly, if it's any help PS, the relationship between a well-established theory in contemporary physics and 'reality' is a topic not for the faint of heart. Among other things, IM(NSH)O, those who tackle this from a philosophical background all too often make serious mistakes (albeit rather subtle ones; these folk tend to be, after all, really really smart), and those from a strong physics background all too often show they have not bothered to absorb some painfully learned core lessons in philosophy. In any case, here's something you might like to start with: how can you, PS, determine what's real (part of reality), and what's not? In principle, of course
 13th April 2010, 09:24 AM #136 Perpetual Student Illuminator     Join Date: Jul 2008 Location: USA Posts: 3,707 Originally Posted by DeiRenDopa Maybe tangential, or even OT, but perhaps not tooo much ... How does the core of the discussion in this (excellent, many thanks PS! ) thread relate to equivalence principle(s)? Do you mean, for example, the equivalence of gravitational and inertial mass? I guess the relationship is fundamental, since, as I understand things, under GR, going from one reference frame to another inevitably involves the interchangeability of these two aspects of mass. Quote: IIRC, both SR and GR involve some kind of reference to 'laws of physics'; what is meant (in the theory) by this phrase? As a layman, I have come to the (provisional) conclusion that the term "laws of physics" is a bit of a stretch. All we really have are models, that tell us (approximately) how nature behaves. If there are any real fundamental descriptions of reality, that we could label as absolute laws, these remain to be discovered. Quote: Lastly, if it's any help PS, the relationship between a well-established theory in contemporary physics and 'reality' is a topic not for the faint of heart. Among other things, IM(NSH)O, those who tackle this from a philosophical background all too often make serious mistakes (albeit rather subtle ones; these folk tend to be, after all, really really smart), and those from a strong physics background all too often show they have not bothered to absorb some painfully learned core lessons in philosophy. In any case, here's something you might like to start with: how can you, PS, determine what's real (part of reality), and what's not? In principle, of course Based on my latter comment, I would guess there is no way to make such a determination. __________________ It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ
 13th April 2010, 10:59 AM #137 schrodingasdawg Critical Thinker   Join Date: Jan 2010 Posts: 293 Originally Posted by DeiRenDopa How does the core of the discussion in this (excellent, many thanks PS! ) thread relate to equivalence principle(s)? The equivalence principle states that a being held at a constant position in a uniform gravitational field is indistinguishable from being at a constant position in a uniformly accelerated (relative to an inertial frame) reference frame. A change-of-coordinates to an inertial frame would get rid of the gravitational field, i.e. a frame of reference where an object in freefall is at rest is indistinguishable from an inertial frame of reference. If we're really naive, we can assume this suggests that gravitational forces are fictitious. But real gravitational fields aren't uniform, so they can't be completely gotten rid of by a change-of-coordinates. The equivalence principle still suggests an equivalence between 'fictitious' and gravitational forces, however, so the other conclusion---that what we call 'fictitious' forces in Newton's formulation of mechanics should be described as gravitational forces in the coordinate systems in which they appear---is taken. After all, there's no fundamental reason that any particular perceived gravitational force should be taken as either real or fictitious, as all of them are indistinguishable from a fictitious force, and it's impossible to get rid of all of them at once: and there's no way to determine the coordinate system that correctly determines which are real and which aren't. Of course, that's fairly sloppy reasoning, but it's the best way I can think to relate the equivalence principle to the discussion. (I'm open to corrections to my sloppy reasoning. I'm here to learn as much as anything.) The better reason for taking the coordinate system dependent forces as being legitimate gravitational forces in the coordinate system in which they appear, as opposed to some mathematical artifact as in Newton's mechanics, is that we can formulate the laws of physics so that they're the same in all coordinate systems, suggesting that none of the coordinate systems is in any way special and we cannot determine a special coordinate system which tells us which forces are real and which are fictitious. Originally Posted by DeiRenDopa IIRC, both SR and GR involve some kind of reference to 'laws of physics'; what is meant (in the theory) by this phrase? The laws of physics are fairly generalized formulas from which the motion and behavior of matter can be derived. The Einstein Field Equations, for instance, are a law of physics: they, together with a few initial conditions (they are differential equations), can be used to figure out the behavior of the gravitational field. The geodesic equation, when given a spacetime geometry and some initial conditions, can be used to calculate the path that it will take. Both of these are formulated in a way that's the same in all coordinate systems. Maxwell's equations, in their common form, only apply to inertial frames of reference. They have been reformulated so that they are true in all coordinate systems (and all spacetime geometries, including curved ones). http://en.wikipedia.org/wiki/Maxwell...rved_spacetime (If I'm not mistaken, even in a flat Minkowski spacetime, a change to curvilinear coordinates will still require that covariant differentiation be done, so the Maxwell laws need their form changed a bit even though the curvature tensors will be zero.)
 27th March 2012, 05:26 PM #139 Vorpal Extrapolate!     Join Date: Jan 2005 Posts: 1,009 We discard (√-1)\$100 and keep, say, \$44 because they have different implications for our financial situation and one of them does not match how money works. Other times, we discard solutions if they don't satisfy constraints/boundary conditions on our problem. If different coordinate systems had different implications for our physical situation, that's indeed a lot of incentive to keep one and discard another. But they don't. And given that they don't, making a criteria to sort them in the first place is more than a little ad hoc and of no practical value. And that, by the way, doesn't inherently have to do with GTR per se. It is just one example of physical theory that doesn't care about coordinates. A universe that comes with its own coordinates seems to me to be quite bizarre, but YMMV. __________________ For every philosopher, there exists an equal and opposite philosopher. They're both wrong.
 27th March 2012, 05:32 PM #140 Mehdimentio Thinker     Join Date: Jun 2011 Location: Sweden Posts: 161 Originally Posted by Perpetual Student It simply contradicts common sense, intuition and rationality to view things otherwise.? Since when does science have to be in accordance with all of the above?
 27th March 2012, 06:34 PM #141 Roboramma Philosopher     Join Date: Feb 2005 Location: Shanghai Posts: 7,095 It seems to me that the solutions to quadratic equations are simply ways in which the equation can work out to equality. If you are looking for a solution to a specific equation because the equation models some particular system that you're looking at, you know that at least one of those ways must match your actual system. In that case, it makes sense to look at the other properties of the system, that are not modeled by the equation, to see if they are consistent or not with each of the possible solutions. If they aren't consistent with a particular solution, then that solution can be discarded. I don't see how this applies to coordinate transforms in GR. __________________ "... when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together." Isaac Asimov
 27th March 2012, 08:01 PM #142 Perpetual Student Illuminator     Join Date: Jul 2008 Location: USA Posts: 3,707 Originally Posted by Roboramma It seems to me that the solutions to quadratic equations are simply ways in which the equation can work out to equality. If you are looking for a solution to a specific equation because the equation models some particular system that you're looking at, you know that at least one of those ways must match your actual system. In that case, it makes sense to look at the other properties of the system, that are not modeled by the equation, to see if they are consistent or not with each of the possible solutions. If they aren't consistent with a particular solution, then that solution can be discarded. I don't see how this applies to coordinate transforms in GR. It was intended as an analogy. Because quadratics can give us useless answers, we do not abandon quadratics and we do not accept all the useless answers. __________________ It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ
 27th March 2012, 09:38 PM #143 sol invictus Philosopher     Join Date: Oct 2007 Location: Nova Roma Posts: 8,419 Originally Posted by Perpetual Student It was intended as an analogy. Because quadratics can give us useless answers, we do not abandon quadratics and we do not accept all the useless answers. But the coordinate system you mention is far from useless, especially if you happen to be in Princeton, NJ. When was the last time you took the velocity of the solar system in its orbit around the center of the Milky Way into account in calculating the time it will take you to drive to the grocery store?
 27th March 2012, 10:09 PM #144 corbin Critical Thinker     Join Date: Jul 2010 Posts: 396 I think the short answer to your conundrum, PS, is that you've run into a place where science ends and philosophy begins. There really IS no scientific reason to believe that one explanation for motion is better than any other. I've recently become very interested in this subject myself... still need to digest the Wiki articles on it. Last edited by corbin; 27th March 2012 at 10:10 PM.
 27th March 2012, 11:22 PM #145 Perpetual Student Illuminator     Join Date: Jul 2008 Location: USA Posts: 3,707 Originally Posted by sol invictus But the coordinate system you mention is far from useless, especially if you happen to be in Princeton, NJ. When was the last time you took the velocity of the solar system in its orbit around the center of the Milky Way into account in calculating the time it will take you to drive to the grocery store? Consider this: Just as √-1 is very meaningful in many contexts but useless in others, the Princeton, NJ coordinate system is useful in the context you mention but meaningless when doing cosmology. It's when we do cosmology and ask questions about the nature of the universe that we reject Princeton, NJ as being a meaningful basis for a coordinate system. So, does it not seem that the Princeton, NJ system in the context of the whole universe is analogous to an "imaginary" answer -- as √-1 would be when we get \$i100.00 as an answer for a financial question? __________________ It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ
 27th March 2012, 11:25 PM #146 Perpetual Student Illuminator     Join Date: Jul 2008 Location: USA Posts: 3,707 Originally Posted by Vorpal ... A universe that comes with its own coordinates seems to me to be quite bizarre, but YMMV. Why? __________________ It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ
 27th March 2012, 11:30 PM #147 Roboramma Philosopher     Join Date: Feb 2005 Location: Shanghai Posts: 7,095 Originally Posted by Perpetual Student Consider this: Just as √-1 is very meaningful in many contexts but useless in others, the Princeton, NJ coordinate system is useful in the context you mention but meaningless when doing cosmology. It's when we do cosmology and ask questions about the nature of the universe that we reject Princeton, NJ as being a meaningful basis for a coordinate system. So, does it not seem that the Princeton, NJ system in the context of the whole universe is analogous to an "imaginary" answer -- as √-1 would be when we get \$i100.00 as an answer for a financial question? The issue that I have with your analogy is that when we discard √-1 as an answer to a financial question there are valid reasons to do so. What reason do you have to discard a coordinate system in which Princeton, NJ is put at rest? __________________ "... when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together." Isaac Asimov
 27th March 2012, 11:52 PM #148 theprestige Philosopher   Join Date: Aug 2007 Posts: 8,605 Originally Posted by Perpetual Student It's when we do cosmology and ask questions about the nature of the universe that we reject Princeton, NJ as being a meaningful basis for a coordinate system. Isn't it rather the whole point that all coordinate systems are equally meaningful? I think the real reason cosmologists don't use PNJ Coordinates is that they're not particularly convenient. But "convenient" and "meaningful" are two entirely different things.
 28th March 2012, 07:38 AM #149 W.D.Clinger Master Poster     Join Date: Oct 2009 Posts: 2,442 Originally Posted by Perpetual Student So, my question is, could it not be that even though GR renders all coordinate systems valid, the one where everything revolves around Princeton NJ, for example, would be rejected as a real description of the entire universe even though it might have some specific utility? Yes, but you may not have expected me to highlight the critical word in your question. See below. Originally Posted by Perpetual Student I am anticipating the response that there can be no preferred frame under GR -- end of discussion. Although that response is correct, it should be the beginning of discussion. In this context, "coordinate system" is synonymous with a coordinate patch or chart in the sense of differential geometry. Any such chart is just one of many possible homeomorphisms between an open subset of the spacetime manifold (or manifold with boundary) and an open subset of 4-dimensional Euclidean space (or space with boundary), regarded as Minkowski space. The entire spacetime manifold is covered by a full atlas, which is a collection of such charts subject to a condition that says they play nicely together. (Their compositions of the form f(g-1(x)) are diffeomorphisms, and the higher order derivatives exist also.) In general, it takes more than one chart to cover a manifold. The 2-sphere, for example, cannot be covered by a single chart. So far as we know, a chart that's approximately at rest with respect to the cosmic microwave background radiation covers as much of the known universe as any other chart can cover. For all I know, a chart that says the residents of Princeton are being accelerated directly upward at 9.8 m/s2 may not be able to cover so much of the universe. Locally preferred charts may run into coordinate singularities or other pathologies when you try to extend them to cover large sections of the universe. That's why, for all I know, a chart "where everything revolves around Princeton NJ" might have to "be rejected as a real description of the entire universe". We've seen an example of that in both the Black holes and mathematics of black hole denialism threads. Schwarzschild coordinates work just fine as a static description of spacetime around an isolated star or black hole, but they run into a coordinate singularity at the event horizon of a black hole. To obtain a chart that includes the event horizon, you have to give up the illusion of staticity and use different coordinates, such as Painlevé-Gullstrand or Lemaître or Eddington-Finkelstein or Kruskal-Szekeres coordinates. Of the coordinate systems just mentioned, it is my understanding that Kruskal-Szekeres coordinates are the only ones that can describe the largest possible spacetime manifold that contains an isolated black hole and satisfies Einstein's field equations. That gives you an example of why some coordinate systems must be "rejected as a real description of the entire universe", even though those coordinate systems make perfect sense (and may even be preferred!) when describing some small piece of the universe. Last edited by W.D.Clinger; 28th March 2012 at 08:39 AM. Reason: per second squared
 28th March 2012, 08:24 AM #150 Perpetual Student Illuminator     Join Date: Jul 2008 Location: USA Posts: 3,707 Thanks for all the thoughtful responses. Here's another angle: Earlier in this thread there was a lot of discussion about using the rest frame of the CMB as a basis for establishing the "real" reference frame of the universe. That idea was roundly rejected because it would violate GR. Now that's an interesting expression: "violating" GR. Would we say that because we reject \$i100 as an answer to a financial question that we are "violating" quadratic equations? Why is the one example a "violation" and the other simply an obvious and practical decision? The CMB is the largest and most pervasive thing we know of in the universe. The CMB has a crucial historical significance for the universe. Why would we be "violating" some equation if we make the practical and obvious decision that the CMB tells us what the actual frame of reference of the whole universe really is, while Princeton, NJ has some value only in some very local and very specific analysis? __________________ It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ
 28th March 2012, 03:47 PM #152 Perpetual Student Illuminator     Join Date: Jul 2008 Location: USA Posts: 3,707 Quote: ... coordinate systems ... are related to each other by continuous transformations... That is, perhaps, the most persuasive point of all. However, for this layman, just as we have a grounding for time (with the universe some 13.75 years old), I would like to think of space as also having some grounding. So looking at the infinity of coordinate systems that are related by continuous transformations, I can argue that the one with the simplest description of the universe is the preferred one. It is likely that it would be one, or close to one, with the CMB at rest. It may not currently have much of a scientific basis, but it makes good common sense. Here's another consideration: I'm not sure what this means, but I have seen the universe described as either infinite and bounded or finite. In either case, there should be no difficulty in concluding it has a center, unless some geometric rationale prohibits it -- like being on the surface of the analog of a sphere in four dimensions. Does GR necessarily give us such a geometry? __________________ It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ
 28th March 2012, 04:06 PM #153 theprestige Philosopher   Join Date: Aug 2007 Posts: 8,605 Originally Posted by Perpetual Student That is, perhaps, the most persuasive point of all. But you remain unpersuaded, right? Quote: However, for this layman, just as we have a grounding for time (with the universe some 13.75 years old), I would like to think of space as also having some grounding. As a layman looking for spatial grounding, you could do a lot worse than a coordinate system centered on your town square (i.e., a localized version of your PNJ coordinates). For this layman, I'm having a hard time understanding why cosmic space needs "some grounding", or why it would matter to me from a layman's perspective if it didn't have it. Quote: So looking at the infinity of coordinate systems that are related by continuous transformations, I can argue that the one with the simplest description of the universe is the preferred one. And if there isn't a single coordinate system that gives a complete "description of the universe" (whatever that means)? What if the idea of "simplest description" depends on what part of the universe you're looking at, and which questions you're trying to answer? If the whole point is that cosmologists can freely switch from one coordinate system to another, whenever it is convenient to do so, why would they bother trying to define one as "preferred"? Wouldn't it make more sense to simply develop an appreciation for the capabilities of each one, and simply prefer whichever one is most convenient for the question at hand? Quote: It is likely that it would be one, or close to one, with the CMB at rest. Even if a coordinate system at rest with regard to the CMB were somehow "preferred", what would that actually mean to cosmologists? We already know that GR provides a description of the universe that is independent of any particular coordinate system. So "preferring" CMB coordinates wouldn't really be helpful. Indeed, such a preference would end up being an unnecessary entity that would have to promptly be discarded as soon as it was acknowledged. And cosmologists would be discarding it anyway, whenever some other system was more convenient to their inquiries. So from the perspective of GR it can't truly be "preferred", and from the perspective of practical applications it pretty much won't be preferred. Quote: It may not currently have much of a scientific basis, but it makes good common sense. It's been this layman's experience that appeals to "good common sense" is counter-productive to establishing a good scientific basis for anything. Besides, to the extent that "common sense" is relevant, it suggests that cosmologists have no need of a preferred coordinate system, and would ignore one half the time anyway. Last edited by theprestige; 28th March 2012 at 04:07 PM.
 28th March 2012, 09:35 PM #155 sol invictus Philosopher     Join Date: Oct 2007 Location: Nova Roma Posts: 8,419 Originally Posted by Perpetual Student Here's another consideration: I'm not sure what this means, but I have seen the universe described as either infinite and bounded or finite. In either case, there should be no difficulty in concluding it has a center, unless some geometric rationale prohibits it -- like being on the surface of the analog of a sphere in four dimensions. Does GR necessarily give us such a geometry? All the evidence we have is consistent with the universe not having a center. None of the standard cosmologies have either a boundary or a center; instead, they are homogeneous (every point is identical to every other point, which precludes both centers and boundaries) and isotropic (all directions are equivalent).
 28th March 2012, 10:01 PM #156 Perpetual Student Illuminator     Join Date: Jul 2008 Location: USA Posts: 3,707 Originally Posted by drgsrinivas If you believe in commonsense and logic, you will immediately throw away your Relativity. If you believe in Relativity, then don't bother about logic and rationality. When you don't have to bother about logic, then you don't have to bother about the experimental evidence also- You can (mis)interpret any data/ observation as strongly supportive of your belief system because you don't have to be logical while interpreting. For example, if someone believes that ants are the biggest enemies to mankind, then every movement of every ant may be interpreted as part of an organised coup against the humans. What is important is your belief- Do you believe in Logic or Relativity? Identify your belief and stick to the same. Two opposite religions can't go together. You can't expect things to be logical at one time and ignore the same logic at another time as per your convenience. www.debunkingrelativity.wordpress.com Nonsense! All science is based on logic and logic is what resulted in the discovery of relativity and continues to drive its development. Many aspects of relativity and quantum theory are counter-intuitive but that does not mean that they defy logic. __________________ It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ
29th March 2012, 03:16 AM   #157
Ziggurat
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Join Date: Jun 2003
Posts: 26,199
Originally Posted by drgsrinivas
If you believe in commonsense and logic, you will immediately throw away your Relativity.

If you believe in Relativity, then don't bother about logic and rationality.
 Edited by kmortis: removed personal comment
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"As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law

Last edited by kmortis; 31st March 2012 at 07:55 AM. Reason: Removed to comply with Rule 12 & Rule 0

 29th March 2012, 03:23 AM #158 edd Graduate Poster     Join Date: Nov 2007 Posts: 1,556 __________________ When I look up at the night sky and think about the billions of stars out there, I think to myself: I'm amazing. - Peter Serafinowicz
 29th March 2012, 09:03 PM #159 Perpetual Student Illuminator     Join Date: Jul 2008 Location: USA Posts: 3,707 So, it seems, based on the physicists who have respond here (thanks to all), that I've traveled on a road leading to another dead end. We spend all our lives (at least, I have) with an encompassing feeling that we are in some "place." This "place" leads me to think in terms of my day-to-day coordinate system. I am here and stationary; my wife is in the office; my grandchildren are 120 miles to the west, etc. But I know that is a narrow and unrealistic perspective. I am also rotating, revolving and spiraling in some complex dance, when compared to the CMB. Nevertheless, my "intellectual" big picture perspective would like the universe to be a well defined "place" in the same way. The vast structures we see shaping the observable universe give me a sense of place in the universe, but GR and the impossibility of a preferred coordinate system seems to take some of that away -- and I find that disturbing. If I did not have such a strong dedication to science and the scientific method, it would be tempting for me to give in to the dark side and take up some crackpot anti-relativity belief system. __________________ It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong. - Richard P. Feynman ξ Last edited by Perpetual Student; 29th March 2012 at 09:05 PM.
 29th March 2012, 10:59 PM #160 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 26,199 Originally Posted by Perpetual Student Nevertheless, my "intellectual" big picture perspective would like the universe to be a well defined "place" in the same way. The vast structures we see shaping the observable universe give me a sense of place in the universe, but GR and the impossibility of a preferred coordinate system seems to take some of that away -- and I find that disturbing. If I did not have such a strong dedication to science and the scientific method, it would be tempting for me to give in to the dark side and take up some crackpot anti-relativity belief system. If you relax what you mean by "preferred", then GR actually does provide something that may suit your purposes, and you actually alluded to it. And that's the co-moving reference frame of the universe, which we can observe by watching the CMB. This reference frame isn't preferred in the sense that the laws of physics are any different in this frame from any other frame. But it is still a unique reference frame in terms of a number of observable details of the universe, such as the CMB being essentially isotropic. In more tangible terms than the CMB, the co-moving reference frame is the reference frame in which mater is (on average) stationary within the universe. Local measurements can't distinguish this reference frame from any other reference frame (so again, the laws of physics are no different), but we're not confined to local measurements, and large-scale measurements (like the CMB) are sensitive to it. So if you want a reference frame on which you can hang a sense of place without everything becoming seemingly completely arbitrary, well, the co-moving reference frame can serve that purpose perfectly well. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law

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