| Subject: The positive mass conjecture at null infinity Date: Mon, 25 Sep 2006 03:48:55 +0300 From: Dimi Chakalov <dimi@chakalov.net> To: Xiao Zhang <xzhang@amss.ac.cn> Dear Dr. Zhang, Regarding your math.DG/0604154 v2, I wonder if you plan to elaborate on http://www.god-does-not-play-dice.net/Kirchner.html#2 As he stated, "... the famous positive mass theorems [64] should also be My efforts are at Please convey my kindest regards to Dr. Wen-ling Huang and Dr. Shing Tung Yau. Best regards, Dimi Chakalov ========= From: Dimi Chakalov <dimi@chakalov.net> Dear Dr. Zhang, Regarding G.F.R. Ellis' finite infinity proposal: did you click on the first link from my preceding email? You can read it at http://www.god-does-not-play-dice.net/Xiao.html The first link in it will bring you to a recent paper by G.F.R. Ellis, gr-qc/0102017 v1, in which he explains his proposal and provides extensive references. See George F R Ellis, gr-qc/0102017 v1, Sec. 5, "Finite Infinity and Local Physics", p. 10: "So the obvious proposal [54] is that we should put boundary conditions on all fields at that distance, rather than at infinity itself, leading to the concept of a 'finite infinity' F ... " See also ref. [57] therein, Best regards, Dimi Chakalov ================= From: "Dimi Chakalov" <dimi@chakalov.net> Dear Xiao, I believe the questions in my first email about the positive mass conjecture were raised in the context of G.F.R Ellis' proposal, http://www.god-does-not-play-dice.net/Xiao.html His proposal is an effort to set the proper framework for the whole bundle of issues related to the positive mass conjecture. Instead of *postulating* time-orientability and showing that, in certain cases and under certain additional assumptions, the quasi-local mass is indeed positive, George Ellis tried to formulate the very foundations for addressing the puzzle of 'positive mass'. In other words, if you were doing analytical chemistry and were trying to prove that there is NaCl in your sample, you must not contaminate it with NaCl from the outset. Having said that, I am by no means trying to underestimate your research and those by your colleagues. Some brief comments follow. 1) Y.G. Shi, L.F. Tam, math.DG/0301047 Title: Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature, math.DG/0301047 v1: "Conversely, under the assumption that the theorem is true, then one can prove the ADM mass of an asymptotically flat manifold is nonnegative, which is part of the Positive Mass Theorem. Comment: In the context of Ellis' proposal, it is mandatory to ask what we can say about the mechanism producing some "boundary", in the first place. 2) C.Liu, S.T.Yau, gr-qc/0303019 Title: Positivity of Quasilocal Mass, gr-qc/0303019 v2. "We show that the quasilocal energy of the boundary of a compact spacelike hypersurface which satisfies the local energy condition is strictly positive unless the spacetime is flat along the spacelike hypersurface. Comment: It is not clear to me how you impose a local control of energy to see how the space changes, and how you sustain such local control of energy, since you're 'part of the picture'. 3) M.T.Wang, S.T.Yau, math.DG/0602321 Title: A generalization of Liu-Yau¡¯s quasi-local mass, math.DG/0602321 v1. "... a future-directed time-like quasi-local energy-momentum is obtained." Question: Did you drop some NaCl from the outset? 4) Xiao Zhang, gr-qc/0603004 Title: A New Quasi-local Mass and Positivity, gr-qc/0603004 v2. "The definition of Kijowski, Liu and Yau belongs to the class of definitions Comment: But please don't start with "time orientable spacetime" (NaCl). This is the underlying PUZZLE that needs resolving in the first place. Please see the link from my preceding email. Of course, if you prefer to explore Geroch-Kronheimer-Penrose "ideal points" instead of Ellis' finite infinity proposal, that's perfectly fine with me. Best regards, Dimi ----- Original Message ----- Dear Dr. Chakalov, I wonder whether the following papers relate to the positive mass conj you asked? 1) Y.G. Shi, L.F. Tam, math.DG/0301047 2) C.Liu, S.T.Yau, gr-qc/0303019 3) M.T.Wang, S.T.Yau, math.DG/0602321 4) Xiao Zhang, gr-qc/0603004 Best, Xiao Zhang > P.S. More at ================= Note 1: I mentioned earlier my not-so-humble opinion that contemporary physicists come in two varieties. Type 1 physicists are bothered by the Hamiltonian formulation of GR. Type 2 (the majority) are not, but one has to distinguish two subvarieties. Type 2a physicists explain why they are not bothered. Their explanations tend either to miss the point entirely or to contain physical assertions that can be shown to be false. Type 2b are not bothered and refuse to explain why. I don't know in which category belongs Xiao Zhang, but if he explains to me the meaning of the phrase 'an isolated gravitational system' [Ref. 2], I'll probably understand his viewpoint. However, I was never able to comprehend the notion of 'maximal spacelike hypersurface' [Ref. 3], which is why I was curious to learn whether Xiao Zhang would wish to elaborate on George Ellis' finite infinity proposal. That's the only way I could try to think of some kind of 'isolated gravitational system'. The physical reality is relational, and so is the human knowledge. In order to think of some system, call it A , we must place it in some context, and define its relation to 'something that it is not', or 'not-A'. In this sense it is "isolated" from 'not-A'. The only entity that does not have any boundaries is the omnipresent reference fluid in GR, as well as the Aristotelian First Cause. It is ONE entity, hence is truly background-free, since there is nothing left to serve as 'not-A' and 'background'. In the case under consideration, the gravitational system must also have some sort of "boundaries", otherwise we cannot define its dynamics. If you agree, I can think of two ways to approach the task of describing these "boundaries" -- minimalist and proper. As a minimalist approach within ADM "dynamics" of GR, you may wish to try some custom-made "patches" in terms of off-shell fiducial boundary conditions. Effectively, you may be able to produce a "patch" of a finite, causally regularized domain from the spacelike hypersurface. Think of this domain as one in which you've eliminated all Cauchy problems, by collecting the additional canonical data from a null surface, as mentioned here. Metaphorically speaking, all "points" from the spacelike hypersurface of the domain communicate with 'the rest of points' by the rule 'think globally act locally' (notice the relational ontology). Can you "attach" a global null surface to all points (try elliptic PDEs)? Perhaps it is possible with some fibre bundle formulation of GR. I just don't know, and personally wouldn't try it, because I don't believe in the Hamiltonian formulation of GR in the first place. It brings all sorts of pathologies and catastrophes, from CTCs to time-like naked singularities, which, just like the ultraviolet catastrophe, have never happened. Which brings us to the second possibility, dubbed 'proper approach'. Start from first principles, such as a generalized form of Mach's Principle, which assumes that all the local properties of matter are governed and determined by the global distribution of the matter and energy content in the whole universe. Thus, the relational properties of matter (cf. Jeeva Anandan), and particularly the "non-tangible" nature of gravitational energy [Ref. 4], must not be well-defined locally, to allow for great flexibility in choosing/fixing the relationally localized properties of matter by the global distribution of the matter and energy content in the whole universe. If you don't include this additional fixing of the local properties of matter by 'the whole universe', you will have to live with the Cauchy problem in GR forever [Ref. 5]. But to allow 'the whole universe' to do its job, you should leave a generic "ambiguity" (non-tensorial quantities) in the local properties of matter, which will then be exploited as flexibility by 'the whole universe'. The Christoffel symbols, for example, are not tensorial, and "even if we start with genuine tensorial variables, then certain important physical quantities turn out to be non-tensorial" (Laszlo Szabados, private communication). Contrary to Sir Hermann [Ref. 4], I believe a non-localizable form of energy is utterly needed in GR. (It is indeed inadmissible in STR, but GR, being a background-free theory, is entirely different.) Locally, the effect from the transition of the non-tangible, non-localizable form of energy into "tangible forms of energy" [Ref. 4] will look like "self-acting", because the gravitational field "is not only nonlinear in its own coupling, but also makes all matter fields self-interacting" (T. Padmanabhan). This is as it should be, since -- locally -- the action of 'the whole universe' on its constituents is nothing but 'self-action', "and so its location can in principle be found" [Ref. 4]. (Recall that there are no "non-local" interactions in the human brain either, yet the brain is acting on itself, as we think about the brain, with the brain.) To cut the long story short, the first off hurdle in the so-called 'proper approach' is the emergence of inertia in the cosmos (James F. Woodward). Look at the phase space of GR and try to unravel some degrees of freedom, which are not observed (cf. Steve Carlip). Then please forget about GWs "travelling" in 3-D space, and think of two virtual GWs, whose cancellation produces 'positive mass' and 'inertia', as hinted here. As Chen Ning Yang put it, "all fundamental forces are phase fields". See an insight from Kevin S. Brown here; general considerations here. Hopefully, you may be able to explain why mass comes with one "sign" only, and why Mother Nature has supplied the universe with a "dark" counterpart. More from the LSST Collaboration. Good luck. D. Chakalov [Ref. 1] Xiao Zhang, The Positive Mass Theorem near null infinity, math.DG/0604154 v2. [Ref. 2] Wen-ling Huang, Shing Tung Yau, Xiao Zhang, Positivity of the Bondi mass in Bondi's radiating spacetimes, math.DG/0604155 v2. "A fundamental conjecture is that gravitational waves can not carry away more energy than they have initially in an isolated gravitational system. It is usually referred as the positive mass conjecture at null infinity." [Ref. 3] R. Schoen and S-T Yau, On the proof of the positive mass conjecture in general relativity, Commun. math. Phys. 65, 45-76 (1979). From the abstract: "So far we are making the reasonable assumption of the existence of a maximal spacelike hypersurface. We will treat this topic separately." p. 45: "An isolated gravitating system having non-negative local mass density must have non-negative total mass, measured gravitationally at spatial infinity." [Ref. 4] Sir Hermann Bondi, Conservation and Non-Conservation in General Relativity, Proc. R. Soc. London A427, 249-258 (February 1990). From the abstract: "The difficulties of conservation laws in general relativity are discussed, with special reference to the non-tangible nature of gravitational energy and its transformation into tangible forms of energy." p. 249: "In relativity a non-localizable form of energy is inadmissible, because any form of energy contributes to gravitation and so its location can in principle be found." [Ref. 5] John Stachel, Prolegomena to any future Quantum Gravity, gr-qc/0609108 v1. p. 16: "The Cauchy problem for the Einstein equations has a major drawback: The initial data on a space-like hypersurface are subject to four constraint equations (see Section 5), which must be solved in order to find a pair of ”true observables,” freely specifiable as ”positions” and ”velocities” initially, the evolution of which off the initial hypersurface should be uniquely determined by a pair of coupled, nonlinear field equations. Only in certain highly idealized cases, such as cylindrical waves (see Section 7) can this program be carried out with locally-defined variables. In general, quantities expressing the degrees of freedom and the equations governing their evolution are highly non-local and can only be specified implicitly (...)." ================ Note 2: I just received a somewhat emotional question, which boils down to the following: But how do you get localizable "fixing" from 'the whole universe' onto non-tensorial quantities in GR? Is this "fixing" reversible, making non-tensorial quantities observable/tensorial, and then reverting them to non-tensorial? Okay, let's start with an example, bearing in mind that we model the universe as a human brain. Look at your arm, and think of it as matter coupled to gravitational field: your arm will then become 'self-acting'. Question: Is your arm pre-determined to ANY particular movement? Nope. Which is why your self-acting brain (not mind) can perform ANY movement with your self-acting arm. If you wish to examine the dynamics of your arm in the context of a static, time-reversible block universe (as you do in GR, regrettably), you will face insurmountable "initial value" and "geodesic incompleteness" problems, due to "diffeomorphism freedom" (Bob Geroch), because the dynamics of your arm is being determined with non-tensorial/non-tangible [Ref. 4] quantities, which enable its genuine flexibility. Yet at any instant from its dynamically build geodesic (cf. Graham Nierlich's affine structure), your arm takes a perfectly local and well-defined position. It isn't smeared into some cloud of alleged "virtual paths", as in the path-integral approach to QFT. It isn't "semi-classical" either. Only if you were a robot and your arm were made from iron rods, you wouldn't have any Cauchy problems whatsoever [Ref. 5]. This is a brand new (at least to the theoretical physicists, it seems) dynamical determinism, which explores the generic flexibility of both gravitational and quantum systems, and restores the notion of quantum reality 'out there'. The old-fashioned classical determinism [Ref. 6] can no longer support the foundation of the exact sciences. NB: The crucial difference between the classical determinism and the newly proposed dynamical determinism is not in the way we treat the "atom" of spacetime: in both cases we shrink the variables in line with the rules of diff calculus, as known since Leibnitz. What makes the dynamical determinism different from the classical one is that we allow the Aristotelian final cause to cast its influence on that same infinitesimal "atom" of spacetime, hence the interactions become quasi-local. Capiche? As to the second part from your question, the "fixing" is indeed reversible, due to the dynamical determinism. Try the four sayings at the link here. I'll be happy to switch from the brain to GR, but first please read the text here. Then show me just one example of spacetime -- any spacetime, your choice -- that is time-orientable (see a non-technical and incomplete introduction below). A simple operational definition of 'time-orientable spacetime' can be derived from the following example. Examine the trajectory of a rocket that is launched at particular time and particular location. Say, a Katyusha launched from Lebanon to Israel. Once itis in the air (say, 3 sec after launch), you don't know where it will land. Let's denote the instant '3 sec after launch' with tn . Can you calculate with certainty the location of the launch from the instantaneous state of the rocket at tn ? You can only use probabilities, for both the initial time and location and the time and location at which the rocket will inevitably hit Israel. However, the real spacetime you use is time-orientable, such that at tn you know that (i) there was a fixed event and location in the past, from which the rocket was launched, and (ii) there is only a probability distribution for the future event of the rocket hitting Israel. Try to implement this knowledge at tn with math, and you'll produce a time-orientable spacetime (instead of some "block world" from GR textbooks). If you can't, your math will be just an exotic intellectual exercise, at best. The purpose of this exercise is to elucidate the mechanism by which the time-orientable spacetime (cf. (i) vs (ii) above) is being completely obliterated in the "block universe" model (please don't miss the link here), leaving just "knowledge" about it. The same mechanism hides the dynamical determinism as well, since you can't observe its action "online" in the block universe model, but just a snapshot from its action in the past. Instead of contaminating QM and GR with "knowledge", use the dynamical determinism of the cosmological time arrow. Perhaps you don't want to be bothered, since you'd prefer to explore the minimalist approach, not the proper one. But you need some kind of boundaries introduced from the outset, which is why the 'time-orientable spacetime', produced by the cosmological time arrow, is conditio sine qua non for your minimalist approach as well. This is the real world from the cosmological time arrow, and nobody should bypass it. So, let's compare the idea of off-shell fiducial boundary conditions to the well-known 'constraint projection' technique, as explained by David Brown and Lisa Lowe here. In the latter, you modify the constraint hypersurface by "periodically (perhaps every time step)" solving the constraints to project the regularization solutions back onto the constraint hypersurface, while in the former you design a custom-made constraint hypersurface from the outset, with the requirement that all "points" from it will be already correlated with each other, by executing the rule 'think globally act locally' (details above). This is a generic formula for designing a 'spacetime', but it will be specific to, and dependent on, the physical situation under consideration. Just a "patch", which will stay always "asymptotically flat". Bottom line is this: if all "point" are pre-correlated with the rule 'think globally act locally' (details above), they will inevitably display a frozen snapshot from a time-oriented spacetime, in which all quantities related to gravity have fixed local values -- relationally, with respect to 'all the rest from the domain'. I don't know of any other way to "invoke" time, since GR has a generic 'problem of time' since its inception in 1915. Go ahead, you have plenty of diffeomorphism freedom and "non-tangible" stuff to play with (off-shell, of course). If you don't know how to proceed, there could be an easy solution. Find a way to contact Professor Chris Isham, and ask him to shed some light on the task of constructing a spacetime. I could be all wrong, since he claims that I "do not know enough theoretical physics to help with any research in that area." D.C. [Ref. 6] Quantum Mechanics, by Messrs Max Born and Werner Heisenberg (Fifth Solvay Conference, 1927). Published in: W. Heisenberg, Gesammelte Werke, eds. W. Blum et al., Springer, Berlin, 1984, Ser. B, vol. 2, pp. 58-99. (English translation from G. Bacciagaluppi and A. Valentini, quant-ph/0609184 v1, pp. 421-422.) "If one asks the question when a quantum jump occur, the theory provides no answer. (...) One sees that quantum mechanics yields mean values correctly, but cannot predict the occurrence of an individual event. Thus determinism, held so far to the foundation of the exact sciences, appears here to go no longer unchallenged."
A brief and biased note on the time-orientability of spacetime The spacetime should be both orientable and time-orientable, since there is no evidence of a lack of orientability. For example, if the 3-D space were non-orientable, you could take a round trip along some path through spacetime, and when you arrived back (well, that may take some time, depending on the topology of space), the rest of the universe (or you, depending on what you wish to choose) would have become left-right reversed, like a mirror image of itself. Also, if time orientability were absent, a Lorentzian manifold would admit a 2-fold time-orientable covering, resembling Cramer's TI of QM. However, is there a rigorous proof that the spacetime is indeed orientable and time-orientable, given the fact that the alternative assumption is not supported by any factual evidence? I'm not aware of any such proof, and very much doubt that it can be delivered, because the global structure of the universe (the topology and "orientability" of spacetime) is defined by the cosmological time arrow, which in turn depends on those 96 per cent from the universe, which are "dark". For example, if you choose a particular region of spacetime in which the mass of most particles have the same sign, you can unambiguously define a time orientation such that their mass is positive (Hunter Monroe, private communication). Once you choose an already-oriented spacetime, you can even elaborate on the positive mass "theorems" (e.g., Xiao Zhang, The Positive Mass Theorem near null infinity, math.DG/0604154 v1). That's what mathematical physicists enjoy doing for living. But here's a classical Catch 22 paradox: How would matter make its spacetime "time-orientable", unless it has already been made "time-orientable"? So, before you postulate that "mass of most particles have the same sign", ask yourself what agent has already created some 'law and order', such that you may enjoy some physical stuff that can allow for some "time-orientability" (e.g., because the mass of most particles have the same sign, cf. H. Monroe above). The crux of the puzzle is this: you cannot reach some fundamental property of matter, which will unambiguously define a time orientation and topology of space. Nor is it possible to reach some fundamental property of geometry, such that it will unambiguously define the "proper" physical stuff. So, we need a new kind of determinism, such that it will allow for introducing 'law and order' from the Holon of the universe via the geometry of the universe onto the physical stuff of the universe. The origin of this "agent" will inevitably look "dark", because it can never be fully derived from the dynamics of the physical stuff on which it is acting upon. You simply look at your math, and say -- 'hey, I should have all sorts of nasty things here, from Closed Time Curves to naked time-like singularities, but something has obviously taken care of them.' Similar puzzle occurs in neuroscience. So, all we can do at this moment is to start from something that we can trust, such as the overwhelming evidence that we currently live in some "asymptotically flat" spacetime, and then try to explain the dynamical mechanism by which it is being kept "asymptotically flat" by the two opposite presentations of gravity: the one known from GR textbooks, and its perfectly smooth "dark brother". The main idea, again, is here, since the bottom line is the elusive notion of 'boundaries of spacetime', which in turn brings us to the 'finite infinity' proposal by G.F.R. Ellis. Let me stress again that the proposal for dynamical determinism (borrowed from neuroscience) is based on "dark" energy, since the action of 'the whole universe' on its relationally-localized constituents is being "smuggled" via the 'self-acting' faculty of matter, as acquired due to its coupling to gravity. If you try to do reverse-engineering and trace back the ultimate agent which delivers 'law and order', you will only notice that matter and geometry have been behaving in some pre-established fashion, as if they were directed by the Aristotelian First Cause, which is a bona fide "dark" agent: you cannot reach it in principle. If you could, you would reveal a new level of some physical stuff, which would in turn require another one for its existence (for a modern version of this argument, recall Gödel's theorems), as noticed by Aristotle. Thus, the First Cause should exist, but its action will be inevitably "dark". I'm just scratching the tip of the iceberg here, and from my perspective only. To get the grip on the whole bundle of issue, I suggest reading Mario Castagnino et al. (notice footnote 5 therein) and Steven Harris. Also, instead of starting with phrases like "let M be a causally continuous space-time", try to suggest a mathematical presentation of "dark action", and then use it in your new theory of gravity to actually derive a causally continuous spacetime. I cannot suggest such new math, but if you like the task, it is explained here. It is indeed a very simple task. I explained it to my 13-year old daughter in the following way: you know that, if the weather is cold and you open the window of your room, the room will get colder, not warmer. So, there are physical laws which explain why these, and many other things, happen in one particular direction only. But guess what: theoretical physicists can't imagine that at the very level of geometry there could be some "remnants" from the physical things, which will define 'one particular direction only', and push all the things in the physical world to follow 'this particular direction only'. These guys use some highly sophisticated math language, only haven't read Aristotle and aren't aware that the First Cause, as an Unmoved Mover, cannot be found in their math. There is indeed an invisible force from the First Cause (they call it "dark energy"), which links the "points" of spacetime at the very last, and truly fundamental level of 'pure geometry' [Ref. 7, No. 72]. These guys have tacitly included it in their initial mathematical assumptions, but haven't explained the origin of this invisible binding force. Confucius has said about such efforts the following: The hardest thing of all is to find a black cat in a dark room, especially if there is no cat. The "cat" is not in the "dark room", because the very engine of the time arrow cannot originate from any physical stuff whatsoever. It is being "smuggled" via the 'self-acting' faculty of matter, but if we try to trace back its origin, we will hit 'pure geometry' only [Ref. 7, No. 72]. That's how the Aristotelian First Cause shows up in GR, despite the fact that such 'prior-geometry plenum' and 'unmoved mover' were excluded from GR from the outset. In philosophical language, the old-fashioned classical determinism [Ref. 6] operates exclusively with the efficient cause, totally ignoring the final cause operating at the geometrical realm [Ref. 7, No. 87]. The fusion of these two fundamental forms of causality is presented with the dynamical determinism. See Wolfgang Pauli here. As explained by Karel Kuchar: "The profound message of general relativity is that spacetime does not have any fixed structure which is not dynamical but governs dynamics from outside as an unmoved mover." But I don't see any reason why we should trust this "profound message" of GR, given the facts that (i) it can explain only 4 per cent from the world, and (ii) cannot derive the energy conditions that tell us what constitute "physically reasonable" distributions of mass-energy, which in turn tell us what are the "physically reasonable" spacetime geometries (T. Roman). It seems to me that we should approach (i) and (ii) en bloc, as suggested here. Besides, why should the Unmoved Mover have some "fixed structure"? It can 'remain unaffected while affecting', and could be a dynamical non-Archimedean reality: check out 'the quantum state' here. In the context of GR, Karel Kuchar calls it Perennials, and has suggested the following: "Perennials in canonical gravity may have the same ontological status as unicorns -- a priori, these are possible animals, but a posteriori, they are not roaming on the Earth. According to bestiaries, the unicorn is a beast of fabulous swiftness, strength, and beauty, but, alas, it can be captured only by a virgin [38]. Corrupt as we are, we better stop hunting mythical beasts." I disagree Regrettably, Karel Kuchar is not interested. His last feedback was from Tue, 28 Jan 2003 13:09:32 -0700 (MST), and I'm afraid he won't be willing to help you, so you may wish to seek advice from the other expert in quantum gravity, Chris Isham. I am very lucky that I don't need advanced differential geometry to do my job -- I'm just a psychologist, and am interested in the physical mechanism of Leibniz' pre-established harmony [Ref. 7]. With human volition, we only alter the propensities for our future states, but do not act on matter directly, by means of some "psi field", psychons, or whatever. For that reason, there are no "gravitons", no generic "gravitational energy", no "k-essence" or any "dark energy" scalar field whatsoever (cf. T. Padmanabhan). Just an effect from 'the whole universe' (cf. above); hence the Ansatz for 'dynamical determinism'. Bottom line here is not the human mind, but the very mechanism by which 'matter acts on matter' in quantum gravity. If you picture this mechanism as a car, the human mind is just the driver, which directs its car by exploring the flexibility of the car, just like you move your arm. (One obvious corollary is that there might exist a "driver" at the level of 'the whole universe' [John 1:1-4], but let's confine ourselves to His "brain" only.) Put it differently, the final layer of reality, occupied by the First Cause of Aristotle, is the "spirit" of geometry: Mens agitat molem (Vergil, The Aeneid, Ch. 6, 727). It may look "dark" only to those obstinately opinionated people who endorse the Hamiltonian formulation of GR. That's PHI, plain and simple. Why would I need the exotic math of quantum gravity? Would it help me learn how to move my arm? Would a fish need a bicycle? D. Chakalov [Ref. 7] G.W. Leibniz, The Monadology.
"72. God alone is without body. "78. These principles have given me a way of explaining naturally the union or rather the mutual agreement [conformite] of the soul and the organic body. The soul follows its own laws, and the body likewise follows its own laws; and they agree with each other in virtue of the pre-established harmony between all substances, since they are all representations of one and the same universe. "87. As we have shown above that there is a perfect harmony between the two realms in nature, one of efficient, and the other of final causes, ... "
Subject: The dynamical behavior of "dark" energy What we will learn, we cannot possibly imagine Dear Dr. Tyson, I like your statement, and wish you best of luck with 'the unknown unknown'. As to the dynamical behavior of "dark" energy [Ref. 1], perhaps we should examine whether its roots can be revealed in GR, http://www.god-does-not-play-dice.net/download.html#GR http://www.god-does-not-play-dice.net/Chrusciel.html#comment http://www.god-does-not-play-dice.net/Chrusciel.html#Papadopoulos_note Kindest regards, Dimi Chakalov [Ref. 1] J. Anthony Tyson, for the LSST Collaboration, Precision Studies "Our universe appears to be composed mainly of unknown forms of non-luminous mass-energy: 96 percent of the mass-energy is "dark". Over the last decade multiple measurements have led to a "standard model" of cosmology containing two mysterious new components: non-baryonic dark matter and dark energy. Non-baryonic dark matter implies the existence of a totally new sector of particle physics, which dominates the matter inventory of the universe. "Dark Energy "Two independent lines of evidence point to accelerated expansion of our universe at late times. Within Einstein's theory, the underlying cause is a component of energy with large negative pressure referred to as dark energy. Dark energy accounts for 2/3 of the mass-energy in the universe, and is outside the current standard model. Indeed, a direct vacuum energy calculation yields an estimate 120 orders of magnitude larger than the value observed. "Current data merely constrain the existence of the effect but little else. Of particular interest is the dynamical behavior of dark energy, i.e. how it behaves with cosmic time or with redshift." ================ Subject: Quantum gravity vs Hermann Minkowski Dear Max, In your latest gr-qc/0610018 v1, you wrote: "First, the gravitational field itself is taken seriously as the prime carrier of the relevant classical and quantum degrees of freedom." If you're really serious about the gravitational field, I think your first off task is to resolve the generic problem with its dynamics; please see the abstract at http://www.god-does-not-play-dice.net/download.html If you or any of your colleagues believe that I got it wrong, please don't hesitate to write me back. Regards, Dimi ================
Dear Professor Bombelli, I like your web site very much. RE Mermin's remark that "mathematical physics is done by mathematicians who lack the necessary skills to do real mathematics", please see the famous song in the subject line at http://www.god-does-not-play-dice.net/download.html The new math concept (called [phi]) is perhaps relevant to your research interests, particularly "where the continuum picture that we are used to from our experience at large scales probably breaks down". It may never break down with [phi]. As to GR, please see http://www.god-does-not-play-dice.net/Straumann.html#hobby http://www.god-does-not-play-dice.net/Straumann.html#non_linear Best regards, Dimi Chakalov Note: The above-mentioned remark by N. David Mermin can be read here. See the zoo of causality violations here. Let's consider just one of these catastrophic and pathological events, which have never happened (just like the ultraviolet catastrophe): Closed Timelike Curves (CTCs) in GR (e.g., William B. Bonnor, gr-qc/0211051 v1). These so-called CTCs are unavoidable in present-day interpretation of GR, because, mathematically, you can "move" in time just like you "move" in space, so because you can make loops in space, you cannot avoid loops in "time": you have not, as of yet, captured the true dynamics of GR. Now, it has been proven that any locally reflecting spacetime with a CTC is 'totally vicious', i.e. one with a CTC through every point (Jong-Chul Kim and Jin-Hwan Kim, Totally vicious space-times, J Math Phys 34 (1993) 2435-2439). A CTC is worse than the Ebola virus, as it is interwoven in the possible structures of spacetimes, permitted in GR. So, there should be at least one such catastrophic event in the past 13.7 billion years, after which you shouldn't be reading these lines. If you got curious, you may be heading toward a breakthrough, resembling the one of Max Planck. Perhaps all you need is new mathematical ideas to elucidate the crucial assumption that the Hausdorff topological space is indeed connected. Amazingly, people just mention this crucial presumption (most often in footnotes), but do not cast it in math. Thus, they start with a Hausdorff topological space that is already equipped -- by hand! -- with the same mysterious feature which they try to explain much later, after introducing affine structure and Lorentzian signature. And of course they can't explain the nature of continuum, and fail miserably on both accounts: the dynamics of GR and the nature of spacetime continuum. No CTC should be possible with the true dynamics of GR. No Cosmic Censorship Conjecture (R. Penrose) or Chronological Protection Conjecture (S. Hawking) are admissible either. We do not accept "miracles" in theoretical physics.
I'm very curious to learn if Luca Bombelli agrees. If you prefer something more prosaic and practical, look no further than the Gravitational Wave Astronomy (as they call it). Four-hundred and ninety (490) distinguished scholars from USA, UK, Germany, Australia, Canada, India, and Spain have joined their professional efforts in what they call LIGO Scientific Collaboration (LSC); a multi-billion research project, which is expected to collect "interesting data in 2014". The task seems pretty straightforward: firstly, these 490 distinguished scholars (490, as of September 2007) believe that, if they look at their wrist watch, they will record some time variable that is pertinent to GR. Secondly, they believe that might have developed a "linearized approximation" of GR, in which the Gravitational Waves (GWs) would display their "amplitude" and (of course) "phase", so they are trying to detect these GWs, which supposedly "travel" in 3-D space just like photons, from one place to another, like all waves with phase and amplitude do in Minkowski spacetime. And thirdly, these 490 distinguished scholars deeply believe that the time variable from GR, which they (according to their first assumption) can "obviously" record with their wrist watch, is the same "time parameter" t (cf. the horizontal line in [Ref. 2], Fig. 22.1), which pertains to the (slow) temporal evolution of the dimensionless number h . The latter denotes the amplitude of GWs (ibid.) and pertains to the "strain" of GWs -- the real physical "push" of GW energy, spanned along a trajectory of already-localized manifestations of GW energy and momentum, the duration of which can be read by a wristwatch, in line with the first assumption (more here). Can you 'divide Tuesday by 11'? If you can, join LSC. D. Chakalov ======================= Subject: Re: Aleph-null bottles of beer on the wall, ... Dear Professor Bombelli, It is a pleasure to hear from you. > I have taken a look at your website, ad I have seen a number of Let's help each other, okay? Please give me one example of such statements, and the reason why you don't agree with it. I promise to do the same for you. From now on, every email exchange with you will be kept strictly private and confidential, as far as I'm concerned. Best regards, Dimi Chakalov =========== Note: I regret that cannot post here the reply from Prof. Bombelli. I haven't yet heard from him, but very much hope to learn his objections some day this calendar year. I suppose he will pick up the most drastic statement of mine, call it [X], which he does not agree with. Then I anticipate a number of possible developments: 1. He has properly understood my statement [X], and has proven it wrong. I will be delighted! That will be really fantastic, since I'll correct it and move further. I will, of course, mention his name and contribution to the theory of PHI in my book and DVD. 2. Prof. Bombelli has misunderstood [X]. This happens very often. Look at arXiv.org and will find many such cases: people post a paper, then someone post a comment on it, claiming (politely) that it is crap, and then the author(s) of the paper explain how their statements have been totally misunderstood by their colleague. 3. Prof. Bombelli will apply what I call 'the Bulgarian/Russian logic': the statement [X] is wrong, because it contradicts what was initially rejected by it. Having worked in three research institutes at the BG Academy of Sciences, and collecting a huge mail correspondence with eminent Russian physicists from August 1981 to March 1988, I believe have solid experience with such logical error. 4. None of the above. Well, that's 'the unknown unknown', isn't it? To understand this fundamental notion from the non-unitary evolution of the universe along the universal time arrow, consider 'the set of all sets that have never been considered' (David Batchelor). Relative to the history of the universe up to the instant 'now', it's an empty set, but you just never know what might come out from the 'the unknown unknown'. As John Wheeler put it, "Time is Nature's way to keep everything from happening all at once". I'm so sorry I cannot post here the reply from Prof. Luca Bombelli (if I got one some day). Will try to persuade him to write a brief paper and post it at arXiv.org, then perhaps I'll try case (2) above. D. Chakalov ================= Subject: The Hamiltonian formulation of GR: physics/0701299 v2? Dear Dr. Salisbury, I very much appreciated your historical account of the Hamiltonian formulation of GR [Ref. 1]. In case you wish to supply your paper with some concrete examples of current interest, may I suggest you to elucidate the crucial issue of observability of Gravitational Waves (GWs). Surely GWs exist, but can you or any of your colleagues solve the puzzle of the "direction" of GW propagation? All you need to do is to cancel the phase of GWs. Please try to suggest some Gedankenexperiment. With EM waves, the solution is simple. If you consider a light beam coming from the Sun, you can BOTH identify its direction of propagation AND prove that EM waves are indeed transverse waves [Ref. 2]. You need two Polaroid filters to cancel the phase of the light beam, by positioning the filters in a plane perpendicular to the direction of the beam: all you have to do is to orient/twist one of the Polaroid filters on 90 degrees with respect to the other one. Thus, you use two spatial directions from the plane, X and Y, and the third spatial direction, Z, which has been defined by the light beam coming to Earth from the Sun. Obviously, Z is perpendicular (transverse) to the plane defined by X and Y, and you have consumed all three axes of the 3-D space. In the case of GWs, however, you can't do anything of the above. The kind of geometrical object that is turned into itself by an 360o rotation is a line [Ref. 2]. But the geometrical object presenting the "phase" of GWs must be mapped onto itself by an _180 degree_ rotation.
There is no such animal. Sorry. http://www.god-does-not-play-dice.net/gw.pdf Hence the "phase" of GWs is an artifact of the linearized approximation Thus, it is impossible *in principle* to disentangle the two cases of GWs, longitudinal quadrupolar mode and transverse quadrupolar mode, and LIGO will fail to detect any GW effect whatsoever. LIGO will inevitably "measure" the initial dipole mode, and of course it will get nothing, zero, zilch. And this is exactly what LIGO has produced so far. There is no sense of "increasing sensitivity" with the Advanced LIGO, because it will, again and again, "measure" the dipole mode of GWs. LISA will fail miserably, too. More from Prof. Angelo Loinger, http://www.god-does-not-play-dice.net/Heinzel.html#3 I believe one can learn a lot about the dynamics of GR from the "dynamics" of GWs. More at http://www.god-does-not-play-dice.net/Straumann.html#hobby I wonder if you or any of your colleagues has something to say on these issues, which are undoubtedly rooted on the misfortunate Hamiltonian formulation of GR [Ref. 1]. Sincerely, Dimi Chakalov References [Ref. 1] Donald Salisbury, Rosenfeld, Bergmann, Dirac and the Invention [Ref. 2] Bernard Schutz, GRAVITY from the Ground Up: An Introductory "You can prove that light is a transverse wave by using Polaroid, the semi-transparent material that is used in some sunglasses. If you take two pieces of Polaroid and place them over one another, then if they are oriented correctly they will pass about half the light through that falls on them. But if you rotate one piece by 90o, then the two pieces together will completely block all the light. (...) A further rotation by 90o restores transmission. The kind of geometrical object that is turned into itself by an 180o rotation is a line."
--------- Note: See also Kip Thorne, Overview of GW Science - part 1 and 2 and slides 4 and 5 below.
If GWs had genuine "phase", there should be a way to cancel it, like with the EM transverse waves: see my email above and [Ref. 2, p. 311]. Hence you would determine the "direction" z in slide 5 above, and proceed with the Gedankenexperiment based on mock data: see Marie-Anne Bizouard et al., gr-qc/0701026 v1 below. Can you cancel the phase of GWs in 3-D space, without leaving the "rubber band" [Ref. 2, Fig. 24.3, p. 349]? Notice that "each polarization has its own gravitational-wave field", as stressed by Kip Thorne. Notice also that you got into this whole mess only by trusting the so-called quadrupole approximation. In the exact dipole mode there are no observable GWs whatsoever, as confirmed by all five LIGO runs so far. In my humble opinion, the two "polarizations", which have their own gravitational wave fields, as stressed by Kip Thorne in slide 5 above, are completely "outside" the 3-D space of positive mass. These imaginary, or rather atemporal "gravitational wave fields" should completely overlap and cancel each other on each and every "point" from 3-D space, in a manner resembling the atemporal, "handshaking" mechanism in John Cramer's Transactional Interpretation of QM. In other words, if we "unpack" a point from 3-D space in the global mode of spacetime, we would see just one standing Gravitational Wave as a combination of "forward-backward" and "inside-outside" nodes, going simultaneously "inwards" and "outwards" from that point. In the local mode of spacetime, the 3-D space will exhibit spherical symmetry, because the "center" of rotation is that same point. The residual effects from the cancellation of the two atemporal GWs are (i) spin -- from galaxies to the whole universe (see below), and (ii) two opposite "dark" effects, cold dark matter and dynamic dark energy. NB: These are effects of the very 3-D space; we simply need a large domain to observe them.
Look at the note on the phase space of GR above, and follow the link from Steve Carlip. Do I pass Caltech's Physics 237-2002? If neither you nor Kip Thorne can cancel the "phase" of GWs resulting from the "quadrupole approximation", read John Stachel below. D. Chakalov --------- Note: My efforts to post a paper on ArXiv.org server two years ago were rejected in a purely communist fashion: read the story here. It is a very serious issue. Let me quote from John Stachel's gr-qc/0507078 v2, Footnote 46, pp. 21-22: "There is one big difference between the Maxwell field and the gravitational field: the non-universality of the electromagnetic charge-current vector versus the universality of gravitational stress-energy tensor. Because charges occur with two signs that can neutralize each other, a charge-current distribution acting as a source of an electromagnetic field can be manipulated by matter that is electrically neutral and so not acting as a source of a further electromagnetic field; and one can shield against the effects of a charge-current distribution. "Because mass comes with only one sign, all matter (including non-gravitational fields) has a stress-energy tensor, no shielding is possible, and any manipulation of matter acting as a source of gravitational field will introduce an additional stress-energy tensor as a source of gravitational field. A glance at Bohr and Rosenfeld 1933 shows how important the possibility of neutralizing the charges on test bodies is for measurement of the (averaged) components of the electric field with arbitrary accuracy, for example. This difference may well have important implications for the measurement of gravitational field quantities." On Monday, July 25, 2005, I wrote to 377 physicists, requesting their endorsement of my paper, so that I can re-post it on ArXiv.org server. Nobody agreed to endorse the submission of my paper to the gr-qc section of ArXiv.org e-print archive. I only got a dark and somber silence. I expect that nobody will replied to this email either. Perhaps it is much easier to take the stand of an eminent theoretical physicist, who has his pay check secured and is too busy to reply to unsolicited email from some unknown guy from Borneo, Bulgaria, Botswana, or whatever. How would you separate the “additional, non-radiative degrees of freedom” (reference here) from the genuine metric perturbations (if any) caused by GWs? How can you describe the propagation of GWs within themselves? With respect to what? Going back to the comparison of GWs to EM waves (see above), recall that light propagates in 3-D space, thanks to which we can cancel the EM phase and uniquely define the direction of light propagation in 3-D space, while GWs propagate 'within themselves', just as the 3-D space is expanding 'within itself': there is no "extra dimension" [Ref. 2, Fig. 24.3, p. 349] to help you define the propagation of GWs, their phase, and amplitude. Yes, they exist, but cannot be observed (sorry, Dr. Faraoni). The difference between EM waves and GWs is crucial: since a photon propagates in spacetime, there is always a finite domain of space 'ahead of it', in which the photon is 'not yet', while GWs are spacetime themselves (Kip Thorne) -- there is no "place" ahead of them, in which they are 'not yet', because the spacetime itself does not "move". Notice that the picture below, from GWDAW-9, is highly delusory!
To understand the dynamics of GWs, we need to determine the "boundary" of the lake (cf. G.F.R. Ellis' proposal above) in the first place. You can't just take the stand of some meta-observer, who has dropped his fishing rod in the lake and is patiently waiting for GWs: the 3-D component of the GW "push" on a fishing rod float (LIGO's arms) will be undetectable. Can you measure intrinsically the impact from the Dynamic Dark Energy? Yes, it exists, but cannot be observed (sorry, Dr. Faraoni). Moreover, you will also have to separate the curvature of time from the curvature of space. And this is not a joke. B. Schutz argues that "the force of the Moon comes from the curvature of time" [Ref. 2, p. 310], and "the deformation produced by the Moon is partly directed towards the Moon (the longitudinal direction), whereas gravitational waves are transverse" [Ref. 2, p. 311]. Thus, you have to separate two crucially distinct cases: curvature of time, as in the example with the tidal effect on Earth caused by the Moon (no GWs in principle), from curvature of space, as in the case of time-dependent spatial curvature (lots of GWs waiting for LSC), depicted with the center (horizontal) line of Fig. 22.1 [Ref. 2]. To elucidate the situation, let me quote again from B. Schutz: "The fact that gravitational waves are transverse and do not act like the Moon does on Earth implies that they are not part of the curvature of time, since that is where the Newtonian forces originate. They are purely (emphasis added - D.C.) a part of the curvature of space." [Ref. 2, p. 312]. Thus, in addition to the task of identifying the "direction" of GW propagation by demonstrating that GWs are indeed transverse waves (see above), which is needed to pinpoint the "direction" of that mysterious "dimensionless number" h [Ref. 2, Fig. 22.1] and its even more puzzling "time parameter" t (ibid.), B. Schutz and his LSC colleagues will have to disentangle the curvature of time from the curvature of space (see the paragraph above), and finally map the "time parameter" t (ibid.) to the one read by their wristwatch. Failing to do so will result in measurements of the initial dipole mode, in which there are no observable GW effects whatsoever, as confirmed by all five LIGO runs so far: see the latest Gravitational Wave Data Analysis Workshop (December 18-21, 2006) below. Or think about it this way: give GW astronomy the benefit of the doubt, and suppose, just for the sake of the argument, that some day LSC could measure the GW strain effect (cf. footnote 1). The duration of the measurement of this strain effect must be finite, as LSC would measure a trajectory of already-localized GW energy spread along a GW trajectory in 3-D space, which links the object of GW emission (e.g., at the center of the Galaxy) to its GW detector on Earth (e.g., Virgo, LIGO or Advanced LIGO). Question: are the parameters of such GW evolution (i) invariant under all differentiable diffeomorphisms (the group Diff(M)), or are they (ii) just a gauge? If LSC observe 'GWs on a trajectory', they will confirm the first answer (i), and then will discover, by a simple reverse-engineering, some brand new non-linear GR from such confirmation of its "linearized approximation". Put it differently, the case (i) is a bona fide reductio ad absurdum. Why? Because an observation of 'GWs on a trajectory' requires case (i), which amounts to "discovering" a genuine Hamiltonian of GW evolution, which will have to explicitly include the time variable of the amplitude and phase of GWs (the "time parameter" t , cf. [Ref. 2], Fig. 22.1), which is absurd, plain and simple. As it is well-known since November 1915, in generally covariant systems there is no possibility for Hamiltonian; there are only Hamiltonian constraints. Read Karel Kuchar and Angelo Loinger -- carefully. The evidence for existence of GWs are indeed overwhelming, but GWs cannot, not even in principle, be detected with ADM 'spherical cow' approximation: they got to be unobservable. In the second case, LSC will never observe any GW effect whatsoever. Q.E.D. D. Chakalov
The underlying puzzle, again, is how can GWs exist but be unobservable: see the crux of GR (H. Weyl) and QM in the context of 'potential reality' here. In order to detect the quasi-local GW propagation in 3-D space, we need some brand new detector, which has access to the global mode of time, just as in the case of detecting "online" the ongoing EPR-like correlation of entangled particles, explained here. Thus, all ground- and space-based GW detectors are manifestly blind and deaf to the quasi-local propagation of GW waves -- the ripples of spacetime metric itself. The proper GW detector will have to implement the faculty of "self-acting", resembling the human brain: we think about our brain, with our brain. And surely gravity makes all matter fields "self-acting", much like the context of a sentence defines the meaning of all words in it (=matter fields), and all words are "self-coupled" by their common context (=gravity). Put it differently, what makes energy in GR 'quasi-local' is that it is localized only in regions(=the whole sentence), hence the GW detector will have to distribute the GW strain to all particles in that region instantaneously, just like in the correlation of entangled particles. To make the GW detector fully relativistic system, it has to be build on the basis of Reichenbach's Common Cause Principle: see again the 'forest' metaphor here. Thus, if you wish to detect GWs, you have to build their proper detector in full compliance with STR (recall Cramer's atemporal hand-shaking medium), but then the instantaneous correlation of all "trees" by their common atemporal "forest" (Reichenbach's Common Cause Principle) will require that the "forest" itself be a non-tensorial quantity: "measurements across the band are unphysical" [Ref. 2, Fig. 24.3, p. 349]. Can't win. Only the human brain can do it. Or try to imagine the EPR-like correlation, due to the atemporal "forest", like the collective movement of a shoal of fish along a coral reef. Capiche? BTW Max Born was awarded a Nobel Prize for one small footnote, which he added to the final revised version of his celebrated paper, just before mailing it for publication. I wonder if this footnote will attract the attention of LIGO Scientific Collaboration (email here). Marie-Anne Bizouard et al., A comparison of methods for gravitational wave burst searches from LIGO and Virgo, gr-qc/0701026 v1. "As an elementary building block of an all-time, all-sky search we decided to look for a source that emits from a fixed location in the sky. The burst “repeater” source was placed at the center of the Galaxy and the performance modulation due to Earth’s rotation has been studied with 24 hours of simulated data." A. S. Eddington, The propagation of gravitational waves, Proc. R. Soc. London, Series A, 102, 268 (1922). "Einstein had also become suspicious of these waves (in so far as they occur in his special co-ordinate system) for another reason, because he found that they convey no energy. They are not objective, and (like absolute velocity) are not detectable by any conceivable experiment. They are merely sinuosities in the co-ordinate system, and the only speed of propagation relevant to them is "the speed of thought." ============== Subject: Quasi-local Energy of Gravitational Waves (request for paper) Dear Professor Yoon, If possible, please send me a copy from your poster paper at GWDAW-8 (The 8th Gravitational Wave Data Analysis Workshop, December 17th to 20th, 2003, Milwaukee, Wisconsin, USA), entitled: "Quasi-local Energy of Gravitational Waves". It seems to me that the fundamental issue of "localization" of GW energy is On the other hand, I personally cannot comprehend the *dynamics* of GWs, resulting from your (2,2) fibre bundle description of Einstein's GR [Ref. 1], and will be very grateful to receive your poster paper. Kindest regards, Dimi Chakalov "The key ingredient of the (2,2) fibre bundle formalism discussed so far is "But one should notice that, in the standard ADM formalism, it is also possible to obtain another non-vanishing Hamiltonian if one chooses a time function such as the Gauss normal time coordinate[29]." Note: Regarding G.F.R. Ellis' finite infinity proposal (see the initial email above), there is a very simple, and perhaps terribly "counterintuitive", idea mentioned by Jong Hyuk Yoon, in the context of the so-called event horizon [Ref. 2]. What if the cosmological horizon is "bounded" by a pool of quasi-local negative energy of the Holon (global mode of spacetime), such that the horizon can be (i) not too far and not too close (G.F.R. Ellis) to any observer inside the universe, and (ii) expanding due to the Dynamic Dark Energy? More here. As to the fundamental issue of "localization" of GW energy (the localizability of gravitational energy), recall that the problem is known since the inception of GR, and is not solved up to this day: the gravitational energy and momentum densities are nonmeasurable quantities, simply because the gravitational field can and should always be locally transformed away according to the Strong Equivalence Principle. If you are professional, do not invoke miracles in your theory of GW astronomy, like all those LSC guys do. Just look at their GWDAW-11 (11th Gravitational Wave Data Analysis Workshop, AEI, December 18-21, 2006, http://gwdaw11.aei.mpg.de/program.html The "All-Sky Search for Gravitational Wave Bursts during the fifth LIGO Science Run" (Brian O'Reilly for the LSC) came out again empty-handed, as expected. In case you wonder why, look at Lee Samuel Finn's presentation, "Astrophysical Interpretation of Gravitational Wave Burst Searches", slide 3: Wave "strength" at detector depends on the "intrinsic energy radiated in each polarization", says Lee Samuel Finn. But in order to be detected, this "intrinsic energy radiated in each polarization" must be already localized along a trajectory. LSC don't have a theory, since their primitive model is based on a "miracle", which nobody from LSC can explain: the apparent localization of the gravitational energy and momentum densities. And what do LSC do? They ask for money: see their dreams below.
Billions of U.S. dollars and Euro -- all taxpayers' money -- are scheduled to be wasted, because all these guys from LSC are too lazy to think and do their homework on a sheet of paper. See Karsten Danzmann, The Status of LISA, slides 6, 63, 64, and 69.
For example, they use a linearized approximation to answer the tantalizing question of “why there is a net effect if the wavelength of light and the Bottom line is the "approximation" that reduces the non-linear GR to some "effects" cast on the flat metric of special relativity [Refs. 3 and 4]. Why? Because GWs that arrive at LIGO's arms are "quite weak"? Aren't you throwing the baby with the bath water? These LSC guys must be kidding. There are quantum effects that are quite week too, but nobody would treat them classically. Most importantly, nobody would search for some "weak" quantum effects with some classical mechanics approximation, given the indisputable fact that such "weak" quantum effects cannot exist in quantum theory in principle. Now, replace 'quantum theory' with 'full non-linear GR', and 'classical mechanics approximation' with 'linearized approximation', and you will get the full coverage of "GW astronomy". You will also understand the recent wishful thinking about some "net effect", because the wavelength of GW is "so much larger than the wavelength of light" [Ref. 3]. All these are artifacts from a 'dead cow' approximation (see below). As a rule, scientists are very cautious and open-minded when they deal with approximations, and in this case we only have an indirect confirmation of the "quadrupole approximation": the calculations of Russell Hulse and Joseph Taylor (cf. gw.pdf, p. 2). To be specific, recall that in 1995 Kip Thorne (cf. gr-qc/9506086 v1, gw.pdf, p. 11) predicted that "if the source estimates described in this review article are approximately correct, then the planned interferometers should detect the first waves in 2001 or several years thereafter, thereby opening up this rich new window onto the Universe." But this didn't happen. Why? Let's read again Kip Thorne's gr-qc/9506086 v1: "There is an enormous difference between gravitational waves, and the electromagnetic waves on which our present knowledge of the Universe is based: Electromagnetic waves are oscillations of the electromagnetic field that propagate through spacetime; gravitational waves are oscillations of the "fabric" of spacetime itself." However, this "enormous difference" is completely blurred in the so-called quadrupole approximation (explanation here), because if you employ a second approximation -- the linearized approximation of GR -- you can treat the propagation of GWs just like photons: "Gravity can propagate in waves and carry information from one place in the Universe to another, just like photons." (Louis J. Rubbo et al., Gravitational Waves: new observatories for new astronomy, physics/0509201 v1.) And from ESA website (emphasis added): "A gravitational wave passing through the Solar System creates a time-varying strain in space that periodically changes the distances between all bodies in the Solar System in a direction that is perpendicular to the direction of wave propagation." Only you cannot define "the direction of wave propagation", because "there is an enormous difference between gravitational waves, and the electromagnetic waves on which our present knowledge of the Universe is based" (Kip Thorne): see my email to D. Salisbury above. Thus, LSC (490 professional physicists) work on the premise that the combination of two approximations will produce "GW astronomy". NB: If any of these 490 professional physicists believe that GWs are detectable in principle, I would appreciate to learn about the opposite possibility, which would make GWs undetectable in principle, but leads to contradiction with theory or experiment, hence LSC have chosen the first possibility. Just a hint: what if the "time parameter t " [Ref. 2, Fig. 22.1], which is supposed to create a "time-varying strain in space", is undetectable in principle? What contradiction with theory or experiment will be reached if we consider such possibility? Answer: none. Actually, you'd need a preferred reference frame to observe this "time parameter t ", as it is known since 1922 -- read Arthur Eddington above. None of LSC has explored this, and many other, possibilities resulting from the combination of two approximations. They can only hope and pray that GWs are detectable in principle. That's the wishful thinking of LSC, to say the least. Instead of doing their job professionally, they ask for taxpayers' money. Lots of money. Just like in parapsychology, the "predictions" of LSC hold only and exclusively only within the framework of their two approximations. But let's ponder for a moment on the meaning of 'approximation'. You may, for example, talk about a 'spherical cow' as a first-order approximation to a real Swiss cow, and then try to measure some observable quantity that belongs to the real Swiss cow 'out there' in the Alps, as it walks graciously, munching hay and herbs. As an example of 'spherical cow' approximation, recall the model of spacetime used by A. Einstein to test his GR (the perihelium shift of the planet Mercury). Although it was highly unrealistic model, it had captured some essential features of the 'real Swiss cow', and the result led, as we know, to confirmation of Einstein's GR. Notice, however, that Einstein's model of spacetime, no matter how rough it was, did not contradict any known physical theory, in the sense that it didn't have other "predictions" which were ridiculous, as in the case of GW astronomy. In other words, if your approximation leads to a decapitated cow, you can never measure anything related to the real Swiss cow. You would, metaphorically speaking, kill the real cow with such "approximation", by "predicting" some feature of the 'spherical cow', which is absolutely incompatible with the real Swiss cow. In the case of GW astronomy, the 'decapitated cow' is exposed with the well-known, and completely unresolved, problem of untangling the two modes of GWs, longitudinal quadrupolar mode and transverse quadrupolar mode: see my email to D. Salisbury above and the discussion of the so-called quadrupole approximation by Clifford Will (gw.pdf, p. 2). It's a dead-cow approximation. Not only it is incompatible with the real, non-linear theory, but also leads to absurdities: in Cartesian coordinates, the geometrical object presenting the "phase" of GWs must be mapped onto itself by an 90 degree rotation. Moreover, you attach some "time parameter" to a "dimensionless number", h , so that it can vary in time, but always remain dimensionless [Ref. 2, Fig. 22.1]. There is no such animal, even in a Gedankenexperiment. More from the "GW lake" above. Hence you will -- in fact -- measure the initial dipole mode, and of course will get nothing. Zilch. To paraphrase Thomas Huxley, the great success of Science -- the slaying of an ugly hypothesis by a beautiful fact. Forget about GW astronomy. The sooner, the better. Some twenty-five years ago, people like Franco Selleri were envisaging the detection of empty waves, that is, de Broglie waves propagating in Minkowski spacetime (cf. F. Selleri, On the direct observability of quantum waves, Found. Phys., 12 (1982) 1087-1112). However, both GWs and quantum waves are bona fine empty waves "traveling" in the global mode of spacetime. These empty waves contact the local mode of spacetime only through the apex of Minkowski cone, hence the duration of their interaction with the physical stuff in the local mode -- as recorded with an inanimate clock that has no access to the global mode of spacetime -- will be infinitesimal. If we model the universe as a human brain, there is no problem for these "empty waves" to correlate all the physical stuff in the local mode of the "brain", in line with the ontology of 'relational reality'. Which of course brings us to the dynamics of GR, since only in STR and classical mechanics we can infer the dynamics of physical bodies from one instantaneous state (K. Kuchar) of infinitesimal duration: read about the dualistic conception of time here. Again, the true dynamics of GR is not "frozen": there is an 'absolute past' in the universal/master time arrow, which keeps the pattern of GWs, as well as 'potential future' of the same arrow, and this 'potential future' is being converted into an already-linearized absolute past. If you wish to detect these empty waves "online", as they enrich/expand the absolute past of the universe, you need a brain that has access to the global mode of spacetime. The so-called block universe does not permit any clock that can "read" more than one instant, because the "block universe" itself contains just one single instant of time. It cannot accommodate the next instant -- the "block universe" cannot possibly "self-stretch", from "within" or "intrinsically" (recall Baron Munchausen). Your wristwatch, however, is reading the already-linearized local mode of time, only you can't find its dynamics in present-day GR textbooks: just ponder for a minute on the meaning of the word "until" here, then read the text highlighted in red here, and finally read about the whole mess in loop quantum gravity (LQG) here. To sum up, there is indeed overwhelming evidence from the history of the universe that GWs exist, but they cannot be observed with LIGO, tarot cards, Advanced LIGO, crystal balls, LISA, or The Big Bang Observer, whichever comes first. We can, of course, convert those long, air-conditioned tunnels from LIGO detectors to wine cellars, but what can we do with the LISA satellites? Another junk in space? D. Chakalov [Ref. 2] Jong Hyuk Yoon, Quasi-Local Conservation Equations in General Relativity, gr-qc/0004074 v2. "This counter-intuitive aspect is a manifestation of the well-known teleological nature of the event horizon. That is, when the event horizon H evolves, its quasi-local energy must be negative so as to cancel out the positive in-flux of energy carried by subsequently in-falling matter or gravitational radiation, leaving UH = 0 when the black hole reaches the final stationary state. Details of this derivation and discussions of the remaining quasi-local conservation equations on the event horizon will be presented elsewhere [16]. [Ref. 3] Valerio Faraoni, A common misconception about LIGO detectors of gravitational waves, gr-qc/0702079 v1. "The objection is: “Given that the gravitational field stretches both the "The immediate answer to this objection is that the calculation of the phase shift [delta][psi] between the laser beams of a laser interferometer produces a result that is gauge-independent, while the interpretation in terms of stretching of an interferometer’s arm and of the wavelength of light depends on the gauge adopted, and only gauge-independent results are acceptable in physics. However, this is truly an indirect answer and it may be preferable to provide a direct argument in the same gauge (TT gauge) used for the above-mentioned interpretation of the workings of LIGO." pp. 3-4: "the question of “why there is a net effect if the wavelength of light and the interferometer’s arm are both stretched?” "The gravitational wave is described as a small perturbation of the Minkowski metric ?? . "The only nonzero components of h? in this gauge are hxx = ?hyy and hxy = hyx, corresponding to two independent polarizations of the gravitational wave. "Only first order quantities in the metric perturbations h? and their derivatives are considered because of the smallness of these quantities in any physical situation of interest. "For simplicity we consider a gravitational wave with a single polarization traveling along the z-axis perpendicular to the interferometer’s arms, perfectly reflecting mirrors, and a single reflection of each laser beam. "Therefore the objection that “all lengths are stretched at the same rate by the gravitational wave” and based on the analogy with the expanding three-space of cosmology, is incorrect. The gravitational wave “treats in a different way” the wavelength of light and the length of the interferometer’s arm. "Physically, the interferometer works by measuring the differential stretching of the x and y arms while the high frequency light wave essentially experiences no inhomogeneities in the “medium” in which it propagates — the gravitational wave — because the wavelength ?gw of the gravitational wave is so much larger than the wavelength of light." [Ref. 4] David Garfinkle, Gauge invariance and the detection of gravitational radiation, gr-qc/0511083 v1; Am. J. Phys. 74 (2006) 196-199. p. 8: "General relativity is the theory of the metric g?? of curved spacetime. In a strong gravitational field, including those where the gravitational waves of interest are produced, the field equations of general relativity are highly nonlinear and somewhat (notice the poetry - D.C.) complicated. "However, once the gravitational waves get to the detector, they are quite weak. The metric can then be expressed as g?? = ??? + h?? (8) "Here h?? is small and ??? is the flat metric of special relativity." ============== Subject: The Hamiltonian mess Dear Dr. Salisbury, In case my preceding email has gone astray, you can read it at http://www.god-does-not-play-dice.net/Xiao.html#Salisbury Sincerely, Dimi Chakalov Note: Let me briefly comment on a very intriguing paper by J. M. Pons and D. C. Salisbury, The issue of time in generally covariant theories and the Komar-Bergmann approach to observables in general relativity, gr-qc/0503013 v1. Regarding the problem of time in classical GR, Pons & Salisbury wrote (emphasis mine - D.C.): "Time evolution is of course (I think Pons & Salisbury haven't solved the puzzle; see Lee Smolin here - D.C.) the mapping of initial data to produce solution trajectories. Diffeomorphism gauge transformations map entire solution trajectories into solution trajectories. "The misidentification of evolution and gauge has led to the often repeated assertion that gauge invariants in generally covariant theories must be constants of the motion. It is true that the Poisson brackets of invariants with all of the first class constraints in a generally covariant theory must vanish (since these constraints all appear multipying arbitrary functions in the generator G(t)). "But this assertion fails to take into account any explicit time dependence (as opposed to implicit time dependence, that is, time dependence appearing in canonical variables) in the invariants of the theory. We have shown that such an explicit time dependence arises in any acceptable gauge fixing. It is compulsory in order to uniquely fix a solution on the gauge orbit (just one gauge orbit - D.C.). We have shown in detail how the Hamiltonian dynamics in generally covariant theories accommodates time-dependent gauge fixing. In particular, the dynamics is not frozen; time evolution is non-trivial after the imposition of time-dependent gauge conditions." Okay, suppose the dynamics is not frozen. How is your wristwatch reading such non-trivial but explicit "time", in which the time-dependent gauge conditions evolve as well? Sounds like a miracle. If it isn't, how come we haven't heard about Pons & Salisbury's discovery on CNN Breaking News? To get you started, read Josep M. Pons' physics/0409076 v2, pp. 27-28. D. Chakalov ============ Subject: hep-th/0612215 v2, Existence of eternal geodesics, Theorem 2 Dear Dr. Vanchurin, May I ask a question. You wrote: "The first class of measures is obtained from a single geodesic, which is analyzed in the third section. The second class of measures is defined from an ensemble of geodesics, which is discussed in the forth section." "An eternal geodesic that passes through an infinite number of bubbles would undergo L-tunneling with probability one, regardless of how unlikely the event is." What is the difference (if any) between your eternal geodesic and a transcendental tachyon? It seems to me that the latter can "smell" all bubbles on the whole Landscape, in no time, as measured by your wristwatch. Regards, Dimi Chakalov ============ Subject: Re: Forget about GW astronomy. The sooner, the better. P.S. Here's your chance to revive GW astronomy: http://www.god-does-not-play-dice.net/Xiao.html#trajectory Make your best shot (if any). D.C. On Wed, 31 Jan 2007 23:15:54 +0200, Dimi Chakalov wrote: ============== Subject: Are the physical effects from the First Cause "dark"? Dear colleagues, Back in 1933, I think Fritz Zwicky made an error by calling it "dark matter", http://www.god-does-not-play-dice.net/Minchin.html Perhaps we can suggest another interpretation: all these "dark" effects [refs.] are the physical manifestation of Aristotelian First Cause, http://www.god-does-not-play-dice.net/Xiao.html#First_Cause These holistic effects, produced by 'the universe as ONE' (=The FirstCause), may look "dark" only to those obstinately opinionated people whoendorse the Hamiltonian formulation of GR, http://www.god-does-not-play-dice.net/Straumann.html#hobby http://www.God-does-not-play-dice.net/download.html I wonder if you agree. Kindest regards, Dimi Chakalov Alexander Unzicker, Why do we Still Believe in Newton's Law? Facts, Claus Lämmerzahl, Oliver Preuss, and Hansjörg Dittus, Is the physics within the Solar system really understood? gr-qc/0604052 v1. Eric Linder, Universe's Skeleton Sketched, News & Views, Nature 445, 273 Eric Linder, Theory Challenges of the Accelerating Universe, astro-ph/0610173 v1. Eric Linder, Seeing Darkness: the New Cosmology, astro-ph/0511197 v1. E |
. You need not be a virgin to derive a causally continuous spacetime and reveal its orientability and time-orientability. Perhaps all you need is sound 
