|Subject: The positive mass conjecture at null infinity|
Date: Mon, 25 Sep 2006 03:48:55 +0300
From: Dimi Chakalov <firstname.lastname@example.org>
To: Xiao Zhang <email@example.com>
Dear Dr. Zhang,
Regarding your math.DG/0604154 v2, I wonder if you plan to elaborate on
As he stated, "... the famous positive mass theorems  should also be
My efforts are at
Please convey my kindest regards to Dr. Wen-ling Huang and Dr. Shing Tung Yau.
From: Dimi Chakalov <firstname.lastname@example.org>
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
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  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.  therein,
From: "Dimi Chakalov" <email@example.com>
I believe the questions in my first email about the positive mass conjecture were raised in the context of G.F.R Ellis' proposal,
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.
----- 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
> 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 (e.g., Mukherjee & Saha, arXiv:0705.4358; Kiriushcheva et al., arXiv:0808.2623 and arXiv:0809.0097v1). 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.
[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.
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."
[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 . Corrupt as we are, we better stop hunting mythical beasts."
I disagree. 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 mathematical ideas.
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.
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?
[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,
[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.
"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
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
If you or any of your colleagues believe that I got it wrong, please don't hesitate to write me back.
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
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
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).
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.
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.
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.
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.
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,
I believe one can learn a lot about the dynamics of GR from the "dynamics" of GWs. More at
"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.
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.
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."
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.
"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."
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,
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.
[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 .
[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."
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
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.
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.
Subject: Re: Forget about GW astronomy. The sooner, the better.
P.S. Here's your chance to revive GW astronomy:
Make your best shot (if any).
On Wed, 31 Jan 2007 23:15:54 +0200, Dimi Chakalov wrote:
Subject: Are the physical effects from the First Cause "dark"?
Back in 1933, I think Fritz Zwicky made an error by calling it "dark matter",
Perhaps we can suggest another interpretation: all these "dark" effects [refs.] are the physical manifestation of Aristotelian 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,
I wonder if you agree.
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.
Eric Linder, Curved Space or Curved Vacuum? Astropart. Phys. 24 (2005)
Eric V. Linder, Ramon Miquel, Is Dark Energy Dynamical? Prospects for an
Map reveals strange cosmos, by Dr David Whitehouse, Monday, 3 March,
"And he (Max Tegmark) added: "We found something very bizarre; there is
"We had expected that the microwave background would be truly isotropic, with no preferred direction in space but that may not be the case."
Looking at the symmetry of the CMB - measures technically called its
They had expected to see no pattern at all but what they saw was
"We don't think this is due to foreground contamination," Dr Tegmark
"The large-angle (low-ell) correlations of the Cosmic Microwave Background (CMB) as reported by the Wilkinson Microwave Anisotropy Probe (WMAP) after their first year of observations exhibited statistically significant anomalies compared to the predictions of the standard inflationary big-bang model.
"Suppose you accelerate a car, but the gauge fuel shows that you're actually gaining more fuel by accelerating the car. That's the ultimate 'free lunch' provided by DDE, only physicists cannot explain it."
I merely translated an explanation offered by Eric Linder (link here), replacing "you store extra energy" with "gaining more fuel":
Such springiness, whether of matter, energy, or space itself, is described mathematically by a term called the equation-of-state parameter (w). For lambda, the value of this parameter is minus one, corresponding to a component of the universe that has "negative pressure" — unlike matter or radiation, which have zero or positive pressure. True to its name, the cosmological constant doesn't change over time: the energy stored by lambda scales uniformly, increasing exactly as the volume of the universe increases.
The problem is that the most obvious source for lambda's stored energy is what quantum theory calls the energy of the vacuum — so much more powerful (10 to the 120th power!) than what's been observed for lambda, Linder says, that if this were the dark energy "it would overwhelm the expansion of the universe. It would have brought the universe to a swift end a miniscule fraction of a second after it was created in the big bang."
To understand Linder's metaphor of 'springiness of space', read his brief article in CERN Courier [Ref. 1], the Cosmology Teach-In article from 26 June 2003 [Ref. 2], and finally Linder's astro-ph/0501057 v1 [Ref. 3]. I emailed Dr. E. Linder on April 5, 2004, but the eminent cosmologist at Berkeley Lab and director of the Center for Cosmology and Spacetime Physics at Florida Atlantic University hasn't yet found some spare time to reply.
Notice that "negative" pressure can produce "negative" mass [Ref. 2], which is exactly what is needed for fixing a sliding (due to the expansion of space from DDE) "boundary" of spacetime -- please see G.F.R. Ellis' proposal above and follow the links. The DDE engine is mentioned here; think of it as a reversed negative matter-positive matter nullification (cf. Bob Forward), which creates the combined system of positive-negative mass from the Absolute Vacuum, with constant rate.
Hence we obtain an irreversible "direction" of the universal/master cosmological time arrow, following the ultimate non-unitary creatio ex nihilo from the Absolute Vacuum, as one would expect to see the blueprint from [John 1:1] in the context of quantum gravity. Being confined "inside" our material world, we can only notice that "any non-constancy in [lambda] would have to be accompanied by a compensating non-conservation of the mass-energy of the matter" (R. Penrose), such that it does not produce any catastrophes (M. Visser).
Notice also that if we envisage the non-unitary, creatio ex nihilo evolution of the universe backward in time (the deflation time), we would "witness" a non-unitary process (cf. John Wheeler above) opposite to creatio ex nihilo (cf. Edward Tryon), such that the material content of the universe would be "dissolved" back into the potential reality in the global mode of spacetime. Thus, by following the deflation time, the universe would gradually decrease/lose its concrete physical content (resembling the so-called information loss), and will asymptotically approach The Beginning -- the initial state of the Absolute Vacuum -- in which it has had "absolute zero" entropy (known also as [John 1:1]). Also, because we follow the local mode of time, we will be confronted with the puzzle of the Aristotelian First Cause: the cosmological time, as "measured" in the local mode of time, can only approach asymptotically The Beginning/The First Cause, but can never actually reach it. With such cosmological scenario, we can both eliminate the so-called inflation and explain the homogeneity/isotropy and spatial flatness of our universe (cf. the summary of Hollands & Wald), as well as answer Bob Wald's question of "why the very early universe was in a very low entropy state" (reference here). Put it differently, the "inflation" (cf. the 'cosmic hen' story here) is an artifact from a wrong cosmological model, based exclusively on the teleological local mode of time: you inevitably have to "hook" the cosmological time on the so-called big bang/whatever, hence you will always run into insurmountable metaphysical problems (eternal inflation, multiverse, you-name-it), firstly because the whole idea of "inflation" is ridiculous, to say the least. Just recall the calculation of the chance (or rather "miracle") to wind up in a universe like ours, as performed by R. Penrose: one part in 101230. With a dual age of the universe, we can eliminate such "miracles" of inflationary cosmology from the outset, and perhaps be able some day to understand Quantum Mechanics as well. As a bonus, we could discover the blueprint from [John 1:1] cast on the landscape of quantum gravity, and when the time comes to drop off our old "jackets", we'll be fully prepared for our next, and hopefully more exciting, incarnation.
Life is really beautiful in such universe, isn't it? In the first place, there is no room for actual "miracles" in it. Only non-unitary transformations, new math, and advanced PHI technology: any sufficiently advanced technology is indistinguishable from magic (Arthur C. Clarke's Third Law). Also, the future is completely open and undecidable à la Gödel: "Traveler, there are no paths, paths are made by walking." Of course, the ultimate puzzle of The Beginning may never be fully comprehend and resolved mathematically, hence theology can never be reduced to science. I personally am quite comfortable with such generic "ambiguity" in cosmology, but if you don't like it, feel free to denounce it. It's your free will choice, a gift from God (compared it with the Koran, sura 51:56).
If you don't like these ideas, perhaps you can find comfort in the latest review article by A. Ashtekar [Ref. 4]. There are 19 (nineteen) questions in the first three pages, after which we read at the bottom of p. 3 (italics by Abby Ashtekar):
"The goal of this article is show that such questions can be answered satisfactorily within LQC."
[Ref. 1]. Eric Linder, On the trail of dark energy, The CERN Courier,
"The nature of dark energy
"While gravitation due to matter or radiation is attractive, a sufficiently negative pressure p would offset a positive energy density ? to give repulsive gravity under Einstein's equations (the gravitating density depends on ?+3p), pulling on space to accelerate the expansion of the universe. Researchers often discuss this in terms of the equation of state ratio of the pressure to energy density: w = p/?.
"Negative pressures are not a wholly exotic phenomenon. After all, one of the equations of expansion of the universe, the Friedmann equation, looks remarkably similar to the first law of thermodynamics: d(?V) = -pdV, where V is the volume considered. Negative pressure leads to an overall plus sign, turning this equation into something that looks like the tension in a spring or rubber band. Such a "springiness" of space was postulated soon after Einstein developed the general theory of relativity in his cosmological constant term, and Hermann Weyl attempted to link such a background energy to the quantum vacuum.
"If the vacuum is a true ground state then all observers must agree on its form. But the only Lorentz invariant energy-momentum tensor is the diagonal Minkowski tensor that has negative pressure equal and opposite to its energy density, that is, the cosmological constant has equation of state ratio w = -1. This would cause an accelerating universe."
[Ref. 3] Eric V. Linder, Dealing with Dark Energy, astro-ph/0501057 v1.
p. 4: "What is the physical meaning of a negative pressure? It is not as unusual as it might appear. Consider the first law of thermodynamics:
dU = -p dV, (4)
where dU is the change in internal energy of a system upon expansion of the volume by dV . Expansion then decreases the energy (for positive p) as (adiabatically) opening an oven door cools down the air inside, or breathing out through pursed lips gives a stream of cooler air than your internal temperature (contrast the feeling on your hand in front of your mouth when breathing with lips pursed vs. with mouth open).
"Systems with negative pressure would have an overall positive sign for dU, increasing energy upon expansion. Everyday examples include springs, dU = +kx dx, and rubber bands, dU = +T dl, where dx, dl are displacements, k the spring constant, and T the tension. So what we need for the acceleration of the expansion of the universe is a sort of springiness of spacetime.
"Dark energy dominates the energy of the universe, governing the expansion, accelerating it like inflation did in the first fraction of a second of cosmic history, and determining the fate of the universe. But what is it? We do not even know whether it belongs to the right hand side or left hand side of the Einstein equations, ... "
p. 9: "By studying the growth of massive structure over cosmic history, one can infer properties of the dark energy. While mass aggregates in an expanding universe, with gravitational attraction causing overdense regions to become more and more so, this growth shuts down in an accelerating universe. As an analogy, consider a person trying to join a group of friends standing at the bottom of a uprunning escalator. Due to the “stretching” of space between the groups, the attraction is overcome and clustering does not increase."
[Ref. 4] A. Ashtekar, An Introduction to Loop Quantum Gravity Through Cosmology, 20 pages, 4 figures. Introductory Review, Monday, 5 February 2007, gr-qc/0702030 v1.
p. 2: "Next, the dual role of the space-time metric also implies that space-time itself ends when the gravitational field becomes infinite. This is in striking contrast with Minkowskian physics, where singularity of one specific field has no bearing at all on the space-time structure or on the rest of physics. In general relativity singularities of the gravitational field represent an absolute boundary of space-time where all of physics comes to a halt."
Footnote 5: "Thus, in contrast to the Schrodinger Hilbert space [XXX], the kinematical LQC Hilbert space [XXX] is non-separable. However, as we will see, quantum dynamics is governed by a discrete evolution equation. This leads to superselection sectors so that the final physical Hilbert spaces are all separable. (...)"
p. 12: "In particular, as we will now see, it makes the gravitational part C_grav of the constraint a difference operator, rather than a differential operator as in the Wheeler-DeWitt theory. As one might expect, the ‘step size’ is governed by the area gap [X]."
p. 17: "These advances are encouraging because they deal with the long standing questions I discussed in section I.
"Furthermore, one resolves space-like singularities that are of greatest interest rather than ones that are sometimes chosen in other approaches specifically because they are mathematically manageable in spite being physically rather uninteresting. (...) I think we are still at a preliminary stage largely because we do not have a clear candidate for full LQG."
Note: It is not at all surprising that Abby Ashtekar does not have a clear candidate for full LQG, but since he and his colleagues are "still at a preliminary stage" of understanding the nature of so-called singularities, perhaps it will be a good idea if they study the lessons from Lanczos and Lemaître (reference here), and recall that Albert Einstein has been struggling with the implications from the principle of general covariance for three years, until he finally decided to formulate his General Relativity in 1915: read the history of the early years of GR in C. Rovelli's book on quantum gravity here. Bottom line is that "the requirement of general covariance takes away from space and time the last remnant of physical objectivity", as stressed by Einstein. Recall also the Hole Argument and everything written on it by John Stachel (surely Ashtekar knows Stachel: see ref.  in [Ref. 4]).
Unless LQG solves this fundamental problem of classical GR, it will inevitably fail. If Ashtekar keeps this fundamental problem unresolved -- "the points occurring in the base sets of diffrerentiable manifolds with which general relativity models spacetime should not be reified as physically real" (Butterfield & Isham) -- his LQG can never make contact with the world of tables and chairs, and will remain a purely philosophical exercise cast in a very complicated math language, involving some exotic "superselection sectors so that the final physical Hilbert spaces are all separable" (footnote 5 in [Ref. 2]). Just read how LQG envisages the cosmological "singularity" here.
I don't think Ashtekar and his colleagues are joking, because they use tons of math, and sound really serious about their "difference operator, rather than a differential operator as in the Wheeler-DeWitt theory" [Ref. 2]. Only the puzzle of cosmological "singularity" is known since Aristotle. How do you model the First Cause with a difference operator, Abby?
I hope A. Ashtekar will never read these lines, because he might be seriously upset. And that will be really bad for Loop Quantum Gravity.
As to the rest of people, they still wonder "what has really been gained in LQG in comparison with the old geometrodynamics approach".
Subject: Re: Netiquette
P.S. My comments follow the excerpts from your latest paper at
Three years ago, I advised Martin Bojowald to drop that LQG, but he didn't listen. See John Coleman below.
On Wed, 07 Feb 2007 05:31:49 +0200, Dimi Chakalov wrote:
Subject: gr-qc/0702079 v1: Is "GW astronomy" parapsychology?
Dear Dr. Faraoni,
RE your recent gr-qc/0702079 v1, perhaps you may wish to see
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".
It is indeed parapsychology. Am I wrong?
I will appreciate the opinion from your colleagues as well.
Time is running out.
Note: On 25 February 2003, Steven Weinberg expressed his concerns that GW strain cannot be observed (reference here). The essence of Valerio Faraoni's gr-qc/0702079 v1 is to refute this claim, by showing that the "net effect" of GW strain can be measured (see the "GW lake" above), which, in turn, amounts to the following hypothetical observations:
1. The measuring device (LIGO's arms) would read a chain of events, t0, t1, t2, corresponding to 'zero perturbations of spacetime metric' at t0 , then 'start of perturbations of spacetime metric' at t1, and finally 'end of perturbations of spacetime metric' at t2 . Thus, the periodic wobbling of LIGO's arms will result in distinctive interference pattern, and GW astronomy may have a chance to survive.
2. This finite timelike interval, (t1, t2), as calculated with the cutoff at t0, corresponds to a temporal embedding of the non-tensorial energy of the gravitational field into the Cauchy surface of the measuring device. Notice that all values of t are point-like, the duration of the measurement is well-defined, and the localization of GW energy can be read by your wristwatch, as a cyclical expansion/contraction of spacetime metric.
3. The cutoff at t0 belongs to the open interval (0, t1), where by 0 we denote The Beginning of time and space (or "big bang", if you prefer), hence it can fix the "boundary" of spacetime (cf. G.F.R. Ellis' 'finite infinity' proposal above), by "sliding" asymptotically close to The Beginning. It has to have a point-like value though, or else we cannot have any fixed finite interval, (t1, t2), as calculated with the "sliding" cutoff at t0.
Question: What kind of spacetime can produce such luxury? The trick of cooking a conservation equation for GW energy, as explained by Roger Penrose, applies (i) "where it may be assumed that the spacetime is asymptotically flat", and (ii) "in an exact way in the limit (Sic! - D.C.) when the system becomes completely spatially isolated from everything else". Surely Penrose's recipe sounds better than GW parapsychology, but is still astrology. To be specific, see Eanna Flanagan and Scott Hughes, The basics of gravitational wave theory, gr-qc/0501041 v1 (emphasis added):
"Assuming that hab --> 0 as r --> [inf], we define the quantities (...) together with the constraints (...) and boundary conditions (...) as r --> [inf]."
I don't expect any professional reaction from Valerio Faraoni or from his colleagues (cf. above), nor from the rest of LSC people (email here). Let me just stress that what they "gain" from the so-called linearized approximation is the fake ability to treat the preferred reference frame of GW "propagation" (cf. the 1922 paper by Arthur Eddington above) as a fully legitimate reference frame, which serves as a fixed "background" of GW dynamics, as explained here. Which is why all these LSC people are desperately trying to "define" the "direction" of GW propagation in Minkowski spacetime, and ask for money to detect these, in fact, empty waves. So much about GW parapsychology.
Subject: In Defense of Leslie
"At the end of Bernie’s talk, a member of the audience asked whether Cliff had ever been known to be wrong on a serious issue. Bernie answered that to his knowledge, this had never happened. At this moment Leslie, Cliff’s wife, raised an eager hand and offered to present many examples of Cliff being in error."
B. Schutz, "Will and Testament", MATTERS OF GRAVITY, Number 29, Winter2007
Here's another error,
If you wish to reply, please do it professionally.
Twenty-five years ago, I read your beautiful book, and of course I still have no idea why the space is 3-dimensional.
Let me put it this way: my guess is that the space got to be 3-dimensional, or else LIGO Scientific Collaboration may detect those GWs,
In other words, the impossibility *in principle* to detect GWs should be derived from the very nature of 3-D space.
What do you think? I am indeed interested in your professional opinion, and not in what Matvei Bronstein (God bless his soul) might have said, had he been alive and well in Boston University, say.
I hope your salary at Boston U. does not depend on "GW astronomy".
Final note on GW parapsychologyEver since May 31, 2004, I've lost any hope to receive any professional reaction from LIGO Scientific Collaboration (currently 490 distinguished scholars). The sole feedback so far came from Prof. Dr. Dick Gustafson, who wrote (email from Tue, 07 Jun 2005 00:13:17 -0400) the following:
"I don't know you and wish you out of my face, my computer."
It goes without saying that no physicist has replied to my request (July 25, 2005) for endorsement of my manuscript, so that I can re-post it on arXiv.org server: see GW_log.zip here. Many people know me, but wish me out of their faces and their computers.
Fine. I will wait patiently until the end of 2008, when LIGO will again fail miserably. By that time many more people will know me, however. Especially those who give away taxpayers' money for GW parapsychology:
"The authors gratefully acknowledge the support of the United States National Science Foundation for the construction and operation of the LIGO Laboratory and the Particle Physics and Astronomy Research Council of the United Kingdom, the Max-Planck-Society and the State of Niedersachsen/Germany for support of the construction and operation of the GEO600 detector. The authors also gratefully acknowledge the support of the research by these agencies and by the Australian Research Council, the Natural Sciences and Engineering Research Council of Canada, the Council of Scientific and Industrial Research of India, the Department of Science and Technology of India, the Spanish Ministerio de Ciencia e Tecnologia, the John Simon Guggenheim Foundation, the David and Lucile Packard Foundation, the Research Corporation, and the Alfred P. Sloan Foundation."
Then the whole society of people working on these issues will become meta-stable. What I expect to happen by the end of 2008 is the so-called 'butterfly effect', from René Thom's theory of catastrophes: a small perturbation of the "landscape" of GW parapsychology will trigger a massive reaction with unimaginable magnitude. I mean, some of those LSC people will read carefully the arguments starting from above, and will finally decide to take a stand on the observability of GWs. As of today, they all prefer to keep quiet. I don't blame them. There is too much money and politics involved with "GW astronomy", and nobody wants to be the first to expose this scandalous situation. It takes time for the butterfly effect, but it will inevitably happen.
But because every story has two sides, I suggest you read and study the opinions of 'the other side'. Fortunately, Prof. Dr. Kip S. Thorne has produced a very clear presentation of "GW astronomy": see his course on Gravitational Waves (Caltech, July 2002) at
I suggest you download "Overview of GW Science", part 1 and 2,
WEEK 4: GRAVITATIONAL WAVES IN FLAT SPACETIME
and Dr. Marc Scheel's "Numerical Relativity as a Tool for Computing GW Generation", Week 10, Lecture 18,
"I've learned perhaps more physics, as I tried to understand gravitational wave detectors, I've learned in most anything else I've done in my career."
"In essence, the system employed by LIGO consists of suspended weights that are free to move horizontally. A passing gravitational wave would change the distance between the weights, first in one arm, then in the other arm, which is arranged at a right angle to the first."
Kip Thorne wasn't joking: watch the movie, Lecture1_web.mov, from 29:15 to 29:30. This is Quantum Gravity from 1960s, ladies and gentlemen from LIGO Scientific Collaboration. I call it GW parapsychology. Well, Kip Thorne calls it "something that is dimensionless": watch again Lecture1_web.mov, from 32:55 - 33:08. We obviously use different terminology.
The most important thing in GW astronomy is the amplitude of GWs, which is of course "dimensionless", just like QW's amplitude, yet LSC deeply believe that this "dimensionless" entity will act on LIGO's arms. The bold reality is totally different (reference here).
As a comparison example, recall that there are quantum effects which are also quite week, 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".
It is indeed parapsychology.
As to the "invariance angle" and the "phase" of GWs (see Kip Thorne above), which require gravitons and their alleged "spin", see (i) Tony Rothman and Stephen Boughn, Can Gravitons Be Detected? gr-qc/0601043 v3; Found. Phys. 36 (2006) 1801-1825, (ii) Mário Everaldo de Souza, Gravity cannot be quantized, gr-qc/0208085 v1, p. 6, and (iii) Stephen Boughn and Tony Rothman, Aspects of Graviton Detection: Graviton Emission and Absorption by Atomic Hydrogen, gr-qc/0605052 v2; Class. Quant. Grav. 23 (2006) 5839-5852 (cf. Sec. 5, regarding the gauge properties of the interaction Hamiltonian). From my perspective, if some boson (cf., e.g., Peter R. Phillips) were mediating the gravitational force, it would have to "spread around" the gravitational force "instantaneously", like in EPR-correlation of entangled particles (see above), but then it wouldn't have the kind of "spin" predicted by Kip Thorne, and of course wouldn't be a boson in the first place. The last statement is trivial for another reason: if the hypothetical gravitons were indeed mediating the gravitational force, they'd have to "act on themselves" like Baron Munchausen, since gravitons are, by definition, "particles" of spacetime itself, propagating "within themselves". No boson or fermion can perform this "self-acting" miracle. Only the human brain is capable of 'acting on itself', as stressed above.
On May 31, 2004, I asked Clifford Will: "If the graviton cannot exist in principle, what would you need to fix in your theory of detecting GR waves?" No answer so far. Maybe Clifford Will has also read that 1960s article by E. Wigner.
I am only trying to elaborate on facts that are widely known since 1922. Why did Prof. Dr. Kip S. Thorne decide to skip them? Why was R. Penrose's proof that "the total energy-momentum of a system must, therefore, involve nonlocal contributions" ignored? It isn't enough just to say that GW energy is localizable "only in regions"; you need to develop the proper detectors of this very special "nonlocal" GW energy.
Kip Thorne made it agonizingly clear that there is nothing non-local in the theory of GW detectors: watch his lecture "Weak GW's in Flat Spacetime", Lect6_tape1_web.mov, normal resolution (217,285,174 bytes), where he mentioned Einstein at 39:19 - 40:02: "the waves are absolutely transverse ... no force along the transverse z axis ... if you take the point of view of Einstein, both particles are falling freely, and neither one is to perform over the other one ... only if you take A's point of view, it seems that particle B is having a gravitational wave force on it ... but if you look from the point of view of the local Lorentzian frame of B, A seems to have the gravitational force on it ... ." Don't miss the prerequisites of these "local Lorentzian frames" of "test particle A" and "test particle B", and watch carefully the video from 5:58 to 16:04, particularly at 5:58 - 8:22 - 10:03 - 11:50 - 12:27 - 13:32 ("coordinate time") - 15:01 - 16:04.
Thus, all you have to do is to take the point of view of Einstein (watch 39:19 - 40:02), and imagine two test particles in the state of 'fee fall': neither one is to perform over the other, but if you take the stand of 'test particle A', you will notice that 'test particle B' is being acted upon by some gravitational force, -- not your 'test particle A', but 'test particle B'. Same story if you take the viewpoint of the other test particle, so if LIGO has taken the place of any of these test particles, you'd detect GWs, says Kip Thorne. Just make sure that LIGO has not taken "the point of view of Einstein", because you'll detect nothing.
So, after you've been in the local Lorentzian frame of 'test particle A', take now the local Lorentzian frame of 'test particle B' and look back at 'test particle A': you will notice the same GW strain acting on test particle A, which you were unable to notice previously, but now you won't notice the same GW strain on your current test particle B, which you had already noticed previously, by taking the viewpoint from test particle A.
Got a headache? If yes, feel free to take the stand of Einstein, and you won't notice anything, because "neither one is to perform over the other one", says Kip Thorne.
NB: This is the only possible scenario for detecting GWs -- they are dead weak, as stressed by David Garfinkle (gr-qc/0511083 v1) and Valerio Faraoni (gr-qc/0702079 v1), so you can "effectively" use flat metric and treat them as "GRAVITATIONAL WAVES IN FLAT SPACETIME".
It is like building an antennae that can only detect very weak TV signal, because the "theory" itself cannot cope with any strong TV signal at all. That would be "TV parapsychology", correspondingly.
Click on the picture below for possible solution, by a new global degree of freedom interwoven in the Christoffel connection.
Well, somebody from LSC got to "see" some GW "force" along the free fall trajectories of either "test particle A" or "test particle B", in their local Lorentzian frames, or else the alleged GW "force" will be just a gauge, which will render it unobservable in principle, as noticed by Arthur Eddington (see above). See also Hans-Jürgen Schmidt (gr-qc/0407095, p. 35): if no system of reference is preferred, "then it is not a priori clear whether one can constructively distinguish flat spacetime from a gravitational wave."
Just make sure you can jump freely from the global point of view of Einstein to the local view of test particles A and/or B, in their local Lorentzian frames. Then shave quickly, pack your luggage, and leave for Stockholm to collect your Nobel Prize, awarded for discovering a genuine Hamiltonian of GW evolution, with an explicit time variable (the "time parameter" t , cf. [Ref. 2], Fig. 22.1) of the amplitude and phase of GWs. More on this tantalizing exercise below.
To understand Kip Thorne and eventually pass Caltech's Physics 237-2002, I'm afraid you will need a theory of "localization" of GW energy in the first place. See my question to Hans-Jürgen Schmidt from Thursday, 20 February 2003. Nobody has replied so far (Easter 2007).
The answer provided by Kip Thorne in his Lect6_tape1_web.mov, from 41:48 to 43:27, was that "this force [X] is divergence-free ... like an electrical force, which is divergence-free ... so it is very nice to use field lines that point in to the direction ... so they are just like the field lines ... stretch along the x-direction and squeeze along the y-direction ... like magnetic field lines in quadropolar magnets used in particle accelerators." And that was the answer from Kip Thorne: the tape finished at 43:27.
Surely the remote analogy with magnetic field lines is "very nice", to the extent to which these field lines are a mathematical description of the magnetic field, and are no more tangible than the lines of latitude and longitude which describe the surface of the Earth.
But how do you define two separate, distinguishable gravitational-wave fields corresponding to those two separate, distinguishable polarizations? With a "very nice" analogy, courtesy from Prof. Dr. Kip S. Thorne, and with a couple of billion U.S. dollars and Euro, courtesy from the taxpayers.
It goes without saying that Kip Thorne's claim "this force [X] is divergence-free" is wrong. It cannot be "divergence-free" in principle. Unless of course you live in absolutely flat spacetime, and use a lot of imagination and wishful thinking.
To quote from Andrzej Trautman, "the underlying Minkowski space-time admits, as its group of automorphisms, the full Poincaré group, consisting of translations and Lorentz transformations. It follows from the first Noether theorem that classical, special-relativistic field equations, derived from a variational principle, give rise to conservation laws of energy-momentum and angular momentum."
If you choose to use such "linearized approximation", you will certainly "discover" some "axis of polarization" and some "divergence-free force" acting along some "very nice", albeit imaginary, field lines, cast on the fictional geometry of those "axes of polarization" and the "phase" of GWs. The latter refers to some mysterious object which can be mapped onto itself by an 1800 rotation, in 3-D space.
With just a few "very nice" analogies from Minkowski spacetime, you will ultimately discover that "each polarization has its own gravitational-wave field" (see Slide 5 above) as well.
Don't miss the Kip Thorne show! It's worth watching every second. Besides, you have already paid for it.
Let's go back to the non-localizable GW energy. Unlike in quantum theory, where you can speculate about "non-local" interactions by referring to 'local interactions' in your model of spacetime at the length scale of your measurement devices, in GR you don't have any reference object of the type 'local gravitational interactions on classical spacetime', to elucidate the meaning of 'quasi-local gravitational interactions on that same classical spacetime'. You have just one classical spacetime. No example whatsoever of genuine "local" gravitational interactions is available, simply because you can always eliminate the gravitational energy by hand: recall Hermann Weyl. Thus, you need a unified approach to all "non-local" and "quasi-local" interactions (Sir Roger Penrose should be fully aware of this problem, but he never replied to my review of his book and is still keeping quiet, since 19 April 2002). Which in turn requires new ideas about 'local interactions': the "back bone" of the whole physical world, at all scales (local mode of spacetime). This "back bone" can be revealed in the smooth, Lorentz-invariant, reversible, and bi-directional transition between the classical and quantum realms, as exposed with a Gedankenexperiment here, regarding the classical limit of QM, derived from STR.
We shall learn the answers to these and many more questions by the end of 2008, after the 8th consecutive failure of LIGO. No need to wait until 2014, when LSC will begin to collect "interesting data". See again the 1922 paper by Sir Arthur Eddington above.
The way I understand GR, its amazing effectiveness as a calculation tool originates from all the cases in which we can ignore, by way of a 'spherical cow' approximation, the genuine dynamics of GR. Namely, in all cases in which we can neglect the "dark" holistic effects of the Holon, GR works quite satisfactory, FAPP. In the rest of cases in which the effect of the Holon is significant, the rules are as follows: the global mode of spacetime is unobservable in the already-linearized local mode. We can only observe its additional, "dark" effects cast on the local mode post factum: the Gravitational Wave, for example.
"... the change of the mass distribution (...) has to somehow be communicated throughout the whole universe. And in Newton's picture there is a problems with that, because there isn't any way for that information to take some finite amount of time. Somehow the whole universe must know about everything instantaneously. It's called the
Just like in the human brain, the Holon from the global mode of spacetime will produce these "waves", by enabling all bodies to 'think globally and act locally'. The "propagation" of these EPR-like correlations "takes place" in the Holon, and the resulting wave will propagate in the local mode of spacetime with speed not greater than that of light. All biological systems, not just the human brain, exhibit wave-like behavior; just recall the wave-like movement of centipede's legs. In Einstein's GR, however, we don't have the luxury of some reference frame "outside" spacetime, hence we cannot detect the ongoing correlation through ripples in spacetime, as explained eloquently by Mike Zucker above. Bottom line here is the unresolved issue of the dynamics of GR.
Yes, Gravitational Waves exist (read Rainer Weiss here), but they cannot be observed "online", as they pass through LIGO's arms. Steven Weinberg was right. Only the reason is quite different: all measurements across the "rubber band" are unphysical ([Ref. 2], Fig. 24.3, p. 349). Surely GWs exist, but they cannot be observed with LIGO, tarot cards, Advanced LIGO, crystal balls, LISA, or The Big Bang Observer, whichever comes first. You need a brain.
Can you detect "online" the expansion of spacetime due to the Dynamic Dark Energy (DDE)? See the "GW lake" above. If that were possible, you would identify the "direction" from which the DDE "push" comes from: it is orthogonal to the 3-D wine bottle mesh discovered by Ray Weiss. As a typical example of people treating the 'global properties of spacetime' with flat Minkowski metric, see David Garfinkle and Valerio Faraoni.
In summary, the present-day GW detectors are based on, and depend upon, flat spacetime metric and "linearized gravity", hence they might, at least in principle, detect only one instant from the self-acting, hence genuinely non-linear, talk of matter and space: "Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve" (John Wheeler). As is well known, GWs are fictitious entities in the full, non-linear GR: cf. A. Eddington and A. Loinger. Moreover, a brief, and certainly incomplete, investigation of the alleged quadrupole approximation reveals many pitfalls which completely ruin the whole enterprise: see, for example, the recent discussion of the "axes of polarization" above, and a brief list of unresolved problems below.
Do I pass Caltech's Physics 237-2002? Russell Hulse and Joseph Taylor were awarded a Nobel Prize (details in gw.pdf), and now someone has to demonstrate that there is a fundamental time asymmetry interwoven in the structure of spacetime from the outset, such that there is a crucial difference between observing GW phenomena in the past (cf. the calculations of Hulse and Taylor) and observing them "online", as they evolve in our local inertial frame. Notice that the Dynamic Dark Energy (DDE) could be a bona fide "transverse" phenomenon, such that its "stretching" force imposed on the metric will inevitably overlap "online" with (i) the "curvature of spacetime" (see NB below) and (ii) the wobbling of that same metric due to GWs: see the GW "lake" above and some simple considerations below. Only a human brain might eventually detect such complex force "online".
Since in present-day GR textbooks the spacetime itself does not move (cf. Bob Geroch and G.F.R. Ellis), there is no room for some 'DDE transverse to 3-D space' in these textbooks. Thus, we should either update our textbooks to include a new dynamics of GR for DDE & GWs, or ask Mother Nature to take Caltech's Physics 237-2002.
Last but not least, I am grateful to the proponents of GW astronomy for their insights regarding the possible origin of 'inertial mass', as an emerging property of physical bodies due to the action of the Gravitational Wave: there could be only one Gravitational Wave in the Machain theory of quantum gravity. The study of these preliminary ideas is still in a state of flux.
To be completely frank, I must stress that there is light in the tunnel for LSC: I could be all wrong. Or perhaps 'not even wrong'. Read the opinion of Britain's leading expert in quantum gravity here.
Subject: Re: Within themselves, and with respect to themselves
Dear Professor Thorne,
I haven't yet received your reply to my email from Sun, 16 May 2004 02:02:03 +0300 (printed below), so I decided to take your web course "Gravitational Waves" (July, 2002). Please see what I made from your
Do I pass Caltech's Physics 237-2002?
Subject: Within themselves, and with respect to themselves
RE: Prof. Kip Thorne - "Probing the Universe and Black Holes with
Dear Professor Thorne,
I wonder how would those gravitational waves propagate within
Your insights and those from your colleagues will be highly appreciated,
What object can be mapped onto itself by an 180 degree rotation, in 3-D space and using Cartesian coordinates?
Hint: Watch the explanation of the "imprint" from the graviton (a special spin-2 "particle" of the geometry of space), left on the classical spacetime of GR, in Kip Thorne's video lecture above. This "imprint" is utterly mysterious, since no one has managed so far to include that hypothetical "spin-2 particle" into 'QFT on curved spacetime'. Recall that in the linearized approximation of GR, the total ADM energy has a unique status: "In no other theories of physics is energy effectively a charge and the same holds for momentum" (Leszek Sokolowski and Andrzej Staruszkiewicz, On the issue of gravitons, gr-qc/0606111 v2, pp. 12-13).
Should you encounter any difficulties, simply call Kip Thorne or David Garfinkle, who also use the linearized approximation of GR to study global properties of spacetime, such as the "waves" of the metric itself, as propagating within themselves. The proponents of GW parapsychology see no difference between GWs propagating "within themselves", and EM wave propagating on the grid of the flat metric of STR.
As to Prof. Warren Johnson, he believes that the classical behavior of gravitational fields "do not encounter any (of the hypothetical) quantum
Surely "radio wave detectors are completely describable by the classical linear theory of Maxwell, and do not encounter any of the real quantum behavior of the EM field", but only because we can explain EM wave propagation on the fixed grid of the flat metric of STR. Drawing analogies between these two drastically different cases is like the old joke from Radio Erevan: What is the difference between the crocodile? It is longer than green!
Can you use the linearized approximation of GR to study the global properties of spacetime? If you can, join LIGO Scientific Collaboration.
The only way we could avoid the hypothetical "particle" of geometry -- be it "graviton" or any other hypothetical physical object building the very geometry of space -- would be with new ideas about the spacetime continuum. Any other approach will inevitably face the insoluble challenge of explaining a 'force from geometry', with either (i) GW parapsychology (direct action of space geometry on matter) or (ii) some alternative theory of gravity, be it string-based misunderstanding that includes "gravitons", or some field theory of gravity, say, [Ref. 1]. Everything we know from textbooks leads to dead-end, for different reasons, chief among which is the Dynamic Dark Energy (DDE).
If the excerpt from Babak & Grishchuk's article [Ref. 1] is not quite clear to the readers of these lines, notice that the main reference there is the landmark monograph by Landau & Lifshits "The Classical Theory of Field", which perhaps can explain their attitude towards Einstein's GR (called 'geometrical formulation of the general relativity') and subsequently their efforts to derive some alternative "energy-momentum tensor" that would be "somehow related" to Landau-Lifshitz pseudotensor [ibid., p. 24].
To understand the issue of “looking for the right answer to the wrong question” [Ref. 1] -- the 'force from geometry' encoded in the gravitational energy-momentum tensor and in the nonlinearity of Einstein equations due to the dual role of certain components of the metric tensor [ibid.] -- may I suggest an analogy with the mind-body problem: direct interactions between the two sides of Einstein equations, along the lines of John Wheeler's "talk" metaphor, are forbidden. We need a third "intermediate" entity (cf. the elephant trunk metaphor here), which acts on both sides of Einstein equation -- the Dynamic Dark Energy of the Holon.
The correct answer to the question of 'how can something totally immaterial affect something totally material?' is not provided by 'interactive dualism' (mind/geometry of space interacts directly with its brain/matter), nor by Marxist-Leninist philosophy which denies any influence of mind on its brain (correspondingly, by the efforts of many Russian physicists to produce some "field theory of gravity", in line with their anti-theistic religion postulating that only matter cat act on matter). As to string-based efforts to mimic the nature of gravity, their status is not clear enough even to elucidate their internal consistency (if any), which is why I consider them misunderstandings, in plain English (follow the links in this sentence).
On the one hand, Einstein's GR does not leave any possibility for direct interaction between 'geometry of space' and 'matter', in the sense that there is no answer to the obviously wrong question of 'the gravitational energy-momentum tensor' [Ref. 1]; more from Angelo Loinger, Carl Hoefer, and Michael Weiss and John Baez here. It it were a tensor, it would have been (i) directly observable and (ii) localizable in points along a trajectory [Ref. 2], hence the Hamilton's Principle would have been applicable (see below). More from Adrian Scheidegger.
On the other hand, we certainly assume conversion of gravitational energy into physical energy (just recall Gamma-Ray Bursts), which implies some kind of indirect interactions between the parties in the two sides of Einstein equation. For example, we are fairly confident to talk about the energy balance of 'the whole universe', and if we wish to assume closed topology of space and zero cosmological constant, we inevitably come to the suggestion that its total energy is, and should be, zero (cf. Ed Tryon): the positive mass-energy of matter is being exactly canceled by the negative gravitational energy. But once the (negative) gravitational energy has been converted into physical energy and becomes "localized", we are deeply puzzled by this apparent localization: it is not, and cannot be a 'simple localisation of energy', as stressed by Tullio Levi-Civita back in 1917 (reference here). And the debate on the nature of this not-at-all-simple localization of gravitational energy is far from being settled, even in the relatively simple case of zero cosmological "constant" [Ref. 2].
Let's not waste more time and money for the Advanced LIGO and LISA. LSC needs blank notebooks and sharp pencils -- nothing more, nothing else.
I personally need a large gin tonic now, since I'm just a psychologist. Seriously, I believe every non-linear correlation of the type 'relational reality' in the putative global mode of spacetime will produce a wave-like pattern in the local mode of spacetime, but these "waves" could only be empty waves with dimensionless amplitudes, as we know from Quantum Mechanics. Actually, there could be only ONE quantum-gravitational wave 'out there'. It is 'potential reality', and is both 'physical entity' and 'pure geometry' (cf. the "trunk" metaphor here). Why is this necessary?
Recall Albert Einstein: "The right side (the matter part) is a formal condensation of all things whose comprehension in the sense of a field theory is still problematic. Not for a moment, of course, did I doubt that this formulation was merely a makeshift in order to give the general principle of relativity a preliminary closed expression. For it was essentially not anything more than a theory of the gravitational field, which was somewhat artificially isolated from a total field of as yet unknown structure."
Let's make a brief 'reality check' for this "total field of as yet unknown structure". I believe it is an UNspeakable 'context' (called Holon, in the global mode of spacetime): feel free to try it with your own brain here; general considerations here. Notice that if we model the universe as a human brain, the brain correlates of what we call 'context' -- not their subjective presentation in our mind -- should be sought in our current Weltbild. There are no 'tiny little minds' in the quantum realm, contrary to the speculations by many physicists (say, Bernard d'Espagnat). Let's go back to Einstein's GR now.
A planet follows a "curved" path not because it is being acted upon by some physical force from the left hand side of Einstein equation, but because the "curved" spacetime leaves it with no other choice. Same with the so-called inflation and its current remnant, Dynamic Dark Energy: all these are "dark" effect from the geometry of 3-D space.
Put it differently, the two primitive options, dubbed now "GR scientific communism" and "GR psychokinesis" (see above), are wrong: we are indeed dealing with "a total field of as yet unknown structure", which alters (or "curves", if you prefer) the potential paths of physical bodies, leaving no other choice to the physical stuff in the right hand side but to follow these modified paths, like a train following its railroad. In some cases the modification is enormous, as with the inflation and DDE, and the energy needed to complete such path modifications comes from the Holon, hence it is again "dark". All you need is a generic flexibility of both sides from Einstein equation: see the concept of 'dynamical determinism' above.
This is the beauty of Einstein's GR: both sides of his equation are flexible and can negotiate their next state by following the non-linear "talk" of the relational reality, in their common Holon ("UNspeakable context").
If you switch to Minkowski spacetime, you have no flexibility whatsoever. To quote from Andrzej Trautman, "the underlying Minkowski space-time admits, as its group of automorphisms, the full Poincaré group, consisting of translations and Lorentz transformations. It follows from the first Noether theorem that classical, special-relativistic field equations, derived from a variational principle, give rise to conservation laws of energy-momentum and angular momentum." (And if you use that same "linearized approximation", you may decide to join LSC and go hunting for GWs.)
Needless to say, you have in Minkowski spacetime geometrical "points" with fixed physical content -- contrary to Einstein's GR, as we know after the Hole Argument.
Einstein was fully aware of the inevitable consequences from the principle of general covariance -- it takes away from space and time "the last remnant of physical objectivity". Up to his last days in the local mode of spacetime, he was struggling to find his "total field of as yet unknown structure" and restore the notion of reality, in both GR and QM:
"I should not want to be forced into abandoning strict causality without defending it more strongly than I have so far. I find the idea quite intolerable that an electron exposed to radiation should choose of its own free will, not only its moment to jump off, but also its direction. In that case I would rather be a cobbler, or even an employee in a gaming-house, than a physicist" (A. Einstein, Born-Einstein Letters, 29 April 1924).
Not surprisingly perhaps, no "cobbler" is interested in my efforts. Read the reply from a prominent LSC member above.
[Ref. 1] Stanislav Babak and Leonid Grishchuk, gr-qc/9907027 v2.
p. 28: "One then finds that, just as charge conservation implies that there is no monopole type electro-magnetic radiation, but only dipole or higher orders of polarity, the conservation of energy-momentum implies the absence of monopole and dipole gravitational radiation.
Note: My email above was also prompted by a question posed by Cooperstock & Tieu, The Energy of a Dynamical Wave-Emitting System in General Relativity, gr-qc/0302020 v1:
I believe it could be sensible, but only if we upgrade Einstein GR. As it is now, it isn't sensible to speak of a localized energy. We only know that it is not a 'simple localization', as stressed in 1917 by Tullio Levi-Civita.
As to the ideas mentioned in my email above, notice the favicon.ico of this web site:
It is a symbolic presentation of the Kruskal-Szekeres diagram for the extended Schwarzschild spacetime, which might resemble the conditions, yet unknown, for the cancellation of two GWs in the global mode of spacetime, as mentioned in my email to Fred Cooperstock above. John Cramer doesn't offer such four-part diagram for his atemporal handshaking waves.
Notice a very important consideration regarding the two virtual GWs, running on a "positive mass" and "negative mass" universes in the global mode of spacetime: their imprint on the local mode will not display any negative mass pool/boundary/universe whatsoever -- we can only see an "inverted" or tachyonic universe, as presented by Max Tegmark here.
Briefly, I suppose the cancellation of the two virtual GWs should "enter" the local mode of spacetime from null hypersurfaces (in the case of Minkowski spacetime, the "entry point" is the apex of the cone: recall the classical limit of QM, derived from STR, here). Notice that the "time" in the global mode of spacetime matches that of a luxonic world -- it is standstill in the local mode of spacetime, so you can "walk around" the whole physical universe in the local mode (comprised exclusively from positive mass) for zero "time", as measured with your good old wristwatch. Hence my speculations about Virtual Geodesic Path (VGP) formulation of GR, resembling Feynman's path integral approach to QM.
As to Yakov Terletsky's book [Ref. 2], the notorious KGB agent was manifestly silent about possible implications of the three kinds of masses (positive, imaginary, and negative) for Einstein's GR, so the whole bundle of issues is still in the realm of 'things we know that we don't know'.
It will be nice if somebody sort out the puzzle of "localized energy" by November 2015, before the celebration of the 100th anniversary of Einstein's GR. I personally was never able to understand the physical mechanism behind the affine and Levi-Civita "connections", since it seems to me that they presuppose "localized energy" from the outset, while we can only speculate about some "quasi-local" localization of energy, correct? Notice László Szabados' "Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article" (reference here), in which he explained the crux of the issue as follows (emphasis added):
But in Einstein's GR, the so-called non-local (or quasi-local, if you prefer) gravitational energy-momentum or angular momentum requires an additional degree of freedom, which can be unraveled even in textbooks. It may produce a straightforward solution to the Hamiltonian constraint problem in canonical quantum gravity ("the problem of time"), provided the coordinate-independent part of the metric, known as the "3-geometry", is being created anew at each and every instant. Think of such re-created instants as an emergence of time & space (cf. C. Isham and J. Butterfield), which is rooted on the diffeomorphism freedom: "the connection coefficients at a given point can be taken zero by an appropriate coordinate/gauge transformation" (cf. L. Szabados above).
The fact that we can make 'by hand' these connection coefficients zero at a given point, as well as make the energy-components of the gravitational field "at one point vanish" (Hermann Weyl), is perhaps related to another "quasi-local" puzzle: the von Neumann's Process I or "collapse". But if we keep all non-tensorial stuff in the Holon (see above), there will be no "collapse" but re-creation of points/event on a perfectly continuous and dynamical spacetime (local mode): the global mode of spacetime would be compactified to succession of "points" in the local mode (cf. vanishing flux, tµv = 0), one-at-a-time, matching the Heraclitian master/cosmological time arrow.
This could bring us to the ultimate goal of describing the universe as ONE: an unbroken ring with no circumference, for the circumference is nowhere (hence no absolute reference frame) and the center (in the local time) is everywhere. There's nowhere where [John 1:1] is not.
I don't know if such hypothetical additional degree of freedom can be shown with Ted Neuman's H-space (cf. ref.  in gw.pdf), but I believe it is worth trying it, or else you will have to live with the Cauchy problems forever.
Hope the readers of these lines will shed light on the whole bundle of issues by November 2015 (I'm just a psychologist). For if we don't leave for India, how can we discover America?
Subject: enc2.pdf, p. 47, footnote 38
Note: Let me quote from
On Hilbert's tombstone at Göttingen, one can read his famous epitaph:
Wir müssen wissen, wir werden wissen, right. As my grandma used to say, watch out what you pray for, because you might get it!
Well, let's see what shall unfold by November 2015. Apart from a few insults (some polite, some not), the reaction so far from the established theoretical physics community has been a dark and somber silence. Even my private Easter greetings (not posted on my web site, of course) have been ignored. I'm not trying to imply that these great theoretical physicists are impolite or uneducated, but that their attitude toward the unfinished GR and quantum gravity is that of a singer who performs only his kind of songs and follows strictly his style. Can you imagine what would happen if you ask 50 Cents to sing some of the songs of Luciano Pavarotti? You'll most likely get only a dark and somber silence, too.
Subject: Hamilton's principle for LIGO Scientific Collaboration
It is customary for the proponents of "GW astronomy" to mention the famous PSR 1913+16 and the calculations by Russell Hulse and Joseph Taylor, since this is the sole indirect evidence in favor of their two approximations (the linearized approximation of GR and the quadrupole approximation), which they use to convince the rest of the world to finance their enterprise (or rather hobby).
If LIGO Scientific Collaboration (LSC) are indeed serious about their "GW astronomy", their first off task will be to answer two simple questions: How do you detect a physical force originating from spacetime geometry? How is the Dynamic Dark Energy treated in your theory, if any?
Let's try a Gedankenexperiment. Surely Mother Nature is not constrained to the situations for which LIGO and LISA were supposed to detect GWs. The simple wisdom is this: if LSC claims that GW effects can be detected with LIGO-type devices and/or with LISA, they should prove that their theory can trace back the source of GW emission, in all physically conceivable situations. The burden of proof is with LSC. Our idea is to suggest a Gedankenexperiment which combines strong effects predicted in both Einstein's theory and LSC speculations, in such a way that the rigorous proof delivered by Hermann Weyl and Angelo Loinger can no longer be ignored.
In other words, if you claim that can measure the room temperature in your house, but your "theory of thermometers" cannot be applied to the surface of the Sun even with a Gedankenexperiment, then your "theory of thermometers" (LIGO 'n LISA), as well as your initial "theory of temperature" (the quadrupole approximation), are for the birds. Then it shouldn't be surprising that you will fail to measure any "temperature" at all (you will in fact measure the dipole mode, and no "increasing of sensitivity" will help), as confirmed by all failures of LSC to detect 'the force from geometry'.
Objections? Let me suppose that you say 'none'.
Let's try to find out what would happen to those "test particles", in their local Lorentzian frames (watch the video lecture by Kip Thorne above, Lect6_tape1_web.mov), if we place them in the vicinity of the pulsar PSR 1913+16 that was (supposedly) losing energy by emitting GWs. It wasn't losing some 'pure genuine gravitational energy', because there is no such animal. There was a conversion of gravitational energy into some real, physical form of energy, and the latter were (supposedly) carried away by GWs. Kip Thorne says that if you place an observer in, say, test particle A, she will gather the impression that test Particle B is being acted upon by GWs, but won't feel any GW push on her Particle A. Same if you place a curious observer at Particle B. But if you take the global view of Einstein, you will "know" that both particles are in the well-known state of 'free fall', wobbling like hell due to the near-by PSR 1913+16. Of course, neither you nor Einstein would notice any periodic wobbling of the two test particles, but if you've already passed Caltech's Physics 237-2002 (Einstein would fail, I'm afraid), you will be deeply convinced that their free fall trajectories were influenced by GW strain, so you will join LSC and go hunting for GWs.
All you have to do is to write down the Hamiltonian for the trajectory of Particle B, as seen from the viewpoint of Particle A, and then repeat the same exercise for Particle A w.r.t. Particle B. Then take the stand of Einstein, and report what he would "see". Notice that both test particles are immersed into a vicious GW lake in which the intensity of GWs is immense, and are also attracted by PSR 1913+16, by means of the ordinary gravity we know from Albert Einstein.
Thus, you can't refer to some Minkowski background spacetime, like David Garfinkle or his Russian colleagues do (if you believe you can -- be my guest), and also have to consider the trajectories of the test particles, comprised of well-defined -- hence observable -- energy states. If you succeed, you will turn Hermann Weyl upside-down, because you will "discover" a perfectly localized GW energy, converted into some physical form of energy along the trajectory of these test particles, as well as in their free-fall state 'from the viewpoint of Einstein' (see above).
Simply write down the Hamiltonian of the dynamics of the test particles, using that physical form of energy originating from GWs, and add the ordinary gravitational effect from the pulsar PSR 1913+16.
If you wish, feel free to design your own version of Gedankenexperiment with two test particles orbiting around the pulsar (or binary system of two neutron stars, if you prefer). Use all your imagination and creativity, provided you include strong effects predicted by both Einstein's GR and the hypotheses generated by LSC.
Notice also a very specific challenge for LSC: you have to somehow separate two crucially "different" cases, namely, 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 from PSR 1913+16 waiting patiently for your two test particles), depicted with the horizontal line in Fig. 22.1, from B. Schutz [Ref. 2]. To be specific, let me quote from the book by Prof. Dr. Bernard F. 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]
In other words, the horizontal line in Fig. 22.1, from B. Schutz [Ref. 2], which refers to the dynamics (hence denoted by t ) of GWs, pertains exclusively to "the curvature of space", yet it must be somehow related to the usual time parameter from "curvature of time", since the two "test particles" are dreadfully close to PSR 1913+16, hence the latter will inevitably act on them along the longitudinal direction ("like the Moon does on Earth") as well.
Thus, your Hamiltonian may be a bit complicated, since it will have to incorporate both the "curvature of time" (cf. the beautiful article by J. L. Brun above) and "the curvature of space", but because we accept, after Hermann Minkowski, that we're dealing with 'spacetime', there shouldn't be any problem for the members of LIGO Scientific Collaboration to construct this Hamiltonian. Please consult Sec. 5, "Linearized theory of gravitational waves in a curved background", from the leading article by Eanna Flanagan and Scott Hughes, entitled: "The basics of gravitational wave theory", gr-qc/0501041 v1 (their main reference  is again from 1960s). Notice also that in the linearized approximation of GR, the metric perturbation hab "encapsulates GWs, but contains additional, non-radiative degrees of freedom as well" (ibid.), so the task becomes more than obvious even in this highly unrealistic case of "linearized gravity".
If you fail to write down the Hamiltonian for the two "test particles", you will produce an indirect proof that LIGO Scientific Collaboration are indeed doing parapsychology. Read Hermann Weyl's article in Amer. J. Math. 66 (1944) 591, mentioned below. For an outline of the whole bundle of issues included in this task, see K.S. Thorne and C.M. Will, Astrophysical Journal, 163 (1971) 595-610, Eq. 6 and footnotes 15 and 16; K. Grabowska and J. Kijowski, Canonical gravity and gravitational energy; and my efforts here.
Please write down your report and post it on ArXiv.org server. It shouldn't be difficult: we're talking Hamilton's principle for beginners, so there should be at least one scholar from these 490 members of LSC to defend their "GW astronomy", by examining strong gravitational effects along both the transverse axis z of GW propagation -- absolutely no GW effect (Kip Thorne) but strong effect from "the curvature of time" (Bernard Schutz) -- and the remaining " x/y plane ".
NB: Notice that all gravitational effects (DDE included) are inevitably fused, because you have just one temporal degree of freedom, and the Lorentzian signature won't help you disentangle them and sieve only the GW strain, hence you will, again, measure the dipole mode (see the thermometer analogy above). In this context, may I offer my opinion that the magnitude of GW strain should be in the range of DDE "stretching" the spacetime metric, so the detection of GW strain by LIGO-like detectors and/or LISA is pure fantasy. Yes, the GW strain exists, but you need brand new detectors to harness the additional or "dark" degree of freedom of the metric field in Einstein's GR. But if you try to modify the latter, you just don't know how and where to insert the dynamical [lambda]: "We do not even know whether it belongs to the right hand side or left hand side of the Einstein equations", says Eric Linder, an eminent cosmologist at Berkeley Lab and Director of the Center for Cosmology and Spacetime Physics at Florida Atlantic University. Thibault Damour, Permanent Professor (since 1989) at the Institute of Advanced Scientific Studies (I.H.É.S.), is also deeply confused: read pp. 9-10 from his current report "General Relativity Today" (5 Apr 2007) here. You may choose to add [lambda] to the left-hand side, as did Einstein in February 1917, but there are equally compelling evidence in favor of adding [lambda] to the right-hand side, argues Thibault Damour. To make his innocent readers completely befuddled (notice that the kind of [lambda] added to the r.h.s is related to the stress-energy "tensor" of the quantum vacuum, which is just as mysterious as the unknown kind of [lambda] added to the purely geometrical l.h.s.), Thibault Damour never mentions explicitly the so-called Dynamic Dark Energy (DDE), but declares (p. 28) that "the conservation of energy-momentum implies the absence of monopole and dipole gravitational radiation." As if one could enjoy conservation of energy-momentum in a universe dominated by DDE (cf. R. Penrose, p. 777).
It's a whole new ball game with DDE, mon cher ami. Why not have a dipole gravitational "radiation"? All five runs of LIGO have beautifully confirmed it.
Approximately 40 physicists have received their PhD at Caltech under Kip Thorne's personal mentorship, most notably the current proponents of "GW astronomy" Clifford Will, Richard H. Price, Bernard Schutz, Saul Teukolsky,
All these physicists, Kip Thorne included, explain their five consecutive failures with "need for increasing sensitivity" of LIGO and Advanced LIGO, and plan to waste humungous resources for LISA: it will cost billions.
Make this Hamiltonian exercise instead, as a Gedankenexperiment with your PSR 1913+16, and pass it on to the people who finance your enterprise. All you need is plain sheets of paper and sharp pencils, to explain how you plan to detect a physical force originating from geometry.
Please do not procrastinate. The sooner, the better.
If you fail again with the Enhanced LIGO S6, notice that this time you won't be able to say that you knew nothing about your fundamental problems and inconsistencies. All you managed to do was to delete my first report from ArXiv.org server, and now ignore my efforts to post a second report on "GW astronomy" at ArXiv.org server.
I wonder how long will these LSC people keep quiet. The countdown to their forthcoming S6 failure has begun on 3/24/2007 01:21:18 GMT +0200: read my email "Don't miss the Kip Thorne show!" sent to 198 recipients here.
Day 23, 16 April 2007: Dead silence. Maybe Prof. J. Goldberg will say something?
[To be continued]
On Mon, 19 Feb 2007 12:35:47 -0500 (EST), David Garfinkle wrote:
You just don't want to make the effort to click on the links from my email from Thu, 15 Feb 2007 15:57:29 +0200, Subject: gr-qc/0702079 v1: Is "GW astronomy" parapsychology?
The issue is not that "certain terms in the equations are very small and can be neglected." You are neglecting Hermann Weyl's article, entitled: How far can one get with a linear field theory of gravitation in flat space-time? Amer. J. Math. 66 (1944) 591; cf. physics/0407134.
What makes "GW astronomy" parapsychology is the complete obliteration of the fundamental difference between GWs and EM waves.
What you "gain" from the so-called linearized approximation is the fake ability to treat the preferred reference frame of GW "propagation" (recall the 1922 paper by Arthur Eddington) as a fully legitimate reference frame, which serves as a fixed "background" of GW dynamics,
Read Kip Thorne at the link above. He stressed the fundamental difference between GWs and EM waves in 1995.
Where is the "direction" of the expansion of 3-D space due to the Dynamic Dark Energy (DDE)? That's what you need to clarify in the first place, to detect the passage of GWs, as they proceed from point A to point B in 3-D space.
May I offer you and your colleagues the following tasks:
1. Prove that the "direction" of GW propagation does NOT overlap with the "direction" of the global expansion of space due to DDE, hence you may ignore the latter and keep your "linearized approximation" of GR.
2. Discover the genuine "direction" of GW propagation in 3-D space, as
3. Restore the dimensionality of the GW "amplitude", h , and discover the "time parameter" pertaining to the "waveforms" that "carry detailed information about the source" (cf. Kip's slide 5 above).
5. Finally, check out if your result from #4 confirms your solution offered
If you fail, you will confirm the status of "GW astronomy" as parapsychology.
It isn't easy to be in Jorge's shoes, as the Editor of MATTERS OF GRAVITY, but I'm sure you can handle the tasks above. You are so good in math!
Please reply by writing a paper and posting it at arXiv.org server, so that all people can read it. If you wish, you may mention my name and web site, as 'private communication'. More at
Note: The first obvious problem in task #2 above is the "direction" of GW propagation: see the spatial coordinate, z , in Kip Thorne's slide 5, from Caltech's Physics 237-2002. Geometrically, there is no difference between propagation of EM waves and GWs, since they both travel in 3-D space. That's trivial, since both waves have no other choice. (I believe the difference is that GWs are bona fide "dark" effect of the Holon, but let's put my hypothesis aside.)
Try to imagine, just as a Gedankenexperiment, some device that can eliminate the phase of GW, similarly to the Polaroid filters used to cancel the phase of the light beam, by positioning them in the x-y plane perpendicular to the direction of the beam along the z axis (see the initial email to Donald Salisbury above). What matters here is not the unknown physics of the device that would cancel the phase of GWs, but the very geometry of its operation: the amplitude , h , of GWs will inevitably be projected on the x-y plane. Then, just as with EM transverse waves, this GW amplitude will inevitably acquire dimensionality.
But what could be the "dimensionality" of GW amplitude, ladies and gentlemen from LIGO Scientific Collaboration? Meters? Or maybe bananas? It can't have any dimensionality whatsoever.
The purpose of this Gedankenexperiment is to demonstrate that, if we obliterate the difference between EM waves and GWs by providing some fixed background of flat metric -- the flat metric of special relativity -- we inevitably reach contradiction of the kind reductio ad absurdum.
LSC bravely acknowledge that their most important "parameter" of GWs is dimensionless, yet they claim that h can evolve in time, as read by their wristwatch. That's parapsychology, plain and simple. If they really insist on their "linearized approximation", like D. Garfinkle and V. Rafaoni do, they should simply "resurrect" the dimensionality of GW amplitude (cf. task #3 above). I don't know how this can be done, but David Garfinkle is definitely very good in math, so maybe he can come up with some trick that is still in the realm of the 'unknown unknown', to me at least.
To sum up on task #2 above, recall that the only dimensionless amplitude that we know is that of Quantum Waves (QWs), and the only way we can deal with it is with the famous 'shut-up-and-calculate' interpretation of QM. Surely QW amplitudes evolve in "time", but only when no one is looking at them, much like T. S. Eliot's cat Macavity. Hence I suggest that QWs "propagate" in the global mode of time, and are effect of the Holon: a new kind of luxonic reality, which I call 'potential reality'. If you "look" at the global mode of time from the local mode, you will only "see" that the proper "time" of the Holon, as measured with your wristwatch in all inertial reference frames, is frozen, just like the proper time of the photon in the famous Gedankenexperiment of Albert Einstein: see a beautiful video at this http URL.
In the local mode of time, however, both QWs and GWs are empty waves. This is as it should be, because if GWs were real waves, the manifold on which they "propagate" would have to be composed from real bare points, in blatant contradiction with Einstein's GR and the Hole Argument.
Regarding the "direction" of the global expansion of space due to DDE (cf. task #1 above), notice that we can detect observationally only the motions of the particles of some cosmic substratum/domain (cf. the abstract of Michal Chodorowski's astro-ph/0610590 v2), but not the global expansion of space, as inferred from the observed redshift of some astrophysical "candles".
The "dark" puzzle is this: on the one hand, we cannot detect any physical stuff operating within a finite domain of 3-D space (the radius being the distance between Earth and Type I Supernovae), which would explain the anomalous redshift effect, and eliminate the adjective "dark" in DDE. Which shouldn't be surprising, given that DDE can very well spring out of "empty space". On the other hand, there is nothing that can ban the extrapolation of these finite domain effects to 'the whole 3-D space'. Hence the DDE effect can only come from "stretching" the 3-D space itself, and this DDE effect is both physical and "dark".
The "direction" of global 3-D space expansion will inevitably overlap with the "direction" of local GW propagation in that same 3-D space. Because the "direction" of the GLOBAL expansion of 3-D space due to DDE does not point to some extra-spacelike dimension (see again Ned Wright), the "direction" of this global expansion will inevitably and completely "overlap" with the local, physical direction of receding of distant bodies from Earth (as inferred from their anomalous redshift effect): the "dark direction" and the physical one -- GWs included -- are indistinguishable. They don't have any choice but to overlap. See again task #1 above.
The effect of the Holon (global mode of spacetime), which is being "added" to the dynamics of the physical stuff in terms of some 'additional "dark" features', can again be demonstrated with the biochemistry and neurophysiology of the human brain: no matter how you study them, you will only find ordinary chemistry and physics, although their quality denoted with the prefix "life" or "bio" are irreducible to chemistry and physics. It's a pity that Fritz Zwicky called the effects of the Holon "dark". It is very difficult to be "more wrong" than calling the essence of life sciences and quantum gravity "dark". Anyway.
In our current epoch, the impact of the "dark" effect is such that 96 % from the stuff in the universe has become "dark". Compared to the situation in neuroscience, such statement will be translated as '96 % from the stuff of the human brain is some invisible, "dark" computer (known as homunculus) residing inside the brain'. Nobody is searching for such "dark" homunculus, of course. More here.
Notice also that the Ansatz for 'dynamical determinism' explores these "dark" holistic effects and the "non tangible" nature of gravitational energy (Hermann Bondi) to restore the reality in GR and QM, as sought by Einstein. All this "dark" and "non tangible" stuff resides in the Holon, and the mechanism by which it can be superimposed onto the "normal" physical stuff is provided by the mechanism for creation of "points": see the Hole Argument and its discussion here. If these "points" were like 'classical reality out there', there would be no room for the "dark" and "non tangible" stuff to get actualized and enter the local mode of time, as read by your wristwatch.
Going back to the origin of the global expansion of 3-D space due to DDE, perhaps it cannot be 100% 'classical physics' nor 100% "dark" (=quantum-gravitational). Even your good old inanimate table has some quantum wave associated with it, so it is not 100% 'classical physics'. If you're a carpenter, you definitely can and should ignore the quantum nature of your inanimate table. But once you leave the boring classical world of tables and chairs and focus on the quantum-gravitational realm, please be very careful what kind of approximation you're using, or else you may also be doing GW parapsychology. And wasting billions of dollars and Euro, too.
See again task #1 above, and recall that DDE has been "stretching" the spacetime metric in some totally anti-relativistic, faster-than-light way during the inflation, and is now spanned everywhere, in no time. It "covers" the whole spacetime en bloc, hence it cannot be directly observed due to bans from STR; more here. Same holds for the observation of GWs: see again the GW lake above. Yes, DDE and GWs exist, but their proper detector will have to be entirely different, as explained above. Pity that nobody cares.
To finish this long story, let me go back to the initial subject, and try to be a bit more technical. Pankaj Joshi has just posted (22 February 2007) a brilliant paper on the causality structure and general global properties of a spacetime manifold [Ref. 1]. I will quote from it and will outline my understanding of the basic challenge of quantum gravity.
With Dynamic Dark Energy (DDE), we have a vast global violation of the energy conditions [Ref. 1, p. 5], which is very likely to affect the occurrence of "singularities" (if any). Nobody knows how to modify Einstein's GR to allow such directly unobservable, dynamical, and perfectly smooth stuff to interact -- safely -- with the type I matter fields [Ref. 1, p. 16].
Hence the question put forward at this web site is whether we can actually employ the global violation of the energy conditions (cf. M. Visser) to design a model of a universe that is geodesically complete and preserves causality at every event of spacetime. But how?
I've been trying, since December 1999, to suggest a new kind of quasi-local interactions and a new kind of retarded causality (called biocausality): see the Ansatz for 'dynamical determinism'. The latter assumes a brand new, luxonic-type form of reality, called 'potential reality'. All the "dark" and "non tangible" stuff in GR is placed in the Holon state of the whole universe, in the form of potential reality. The consequences are likely to be highly intriguing, since quantum gravity effects may be accessible with a human brain. If you have one, just follow the links.
Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae. The rset can be a total mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae the huamn biran deos not raed ervey lteter by istlef, but the wrod as a wlohe. Pritie amzanig huh?
To paraphrase Stephen Reucroft [Ref. 2], because the qiasi-local 'context' spanned over the whole sentence would be responsible for the localized 'meaning' of the words, the very fact that the words acquire concrete meaning is regarded as an indication of the existence of the Holon. Just as a song played with two entirely different instruments would sound differently but will preserve its pattern, the effects of the Holon will be displayed through different "instruments" in the Large (GWs and dark galaxies) and in the Small (quarks and Higgs field), yet be unmistakably identifiable as generic "dark" (after Fritz Zwicky) holistic effects.
If you wish to spend your life in searching for GWs or some "God particle" [Ref. 3], beware of the Holon. In the context of gravitational physics, perhaps you may wish to explore it with Ted Newman’s H-space (cf. p. 16 in gw.pdf) or with the 'minimalist approach' above.
A propos this web site, perhaps it is worth noting that the famous statement by Einstein about "playing dice" has to be understood in the context of his deep conviction that the reality in physics must be restored (reference here). We should not leave the 'reality' dependent on pure chance. But because we don't have a 'chooser' in QM (Phil Pearle), the only possible 'chooser', in my opinion, can be 'the whole universe' in its ONE state -- the Holon. Which in turn leads to the task of suggesting a replacement for von Neumann's Process I or "collapse", based on gravitational field: see Jeeva Anandan and Roger Penrose. But with the current understanding of the gravitational field, this task seems impossible, hence we need quantum gravity to understand the "ordinary" non-relativistic QM, as well as the 'chooser' in the Very Early Universe (the earliest possible universe). As stressed by M. Gell-Mann and J. B. Hartle, "quantum mechanics is best and most fundamentally understood in the framework of quantum cosmology" (reference here). All this leads, in my opinion, to the task of "embedding" the 'chooser' in the spacetime manifold from the outset, in such a way that we can always have the 'global mode of time' of potential reality kept in the Holon.
If we don't make an effort to understand the nature of time (recall Bill Unruh's 'explicit but unmeasureable time'), we shall never understand quantum cosmology and the textbook version of QM, and will be haunted forever by the old joke of Yakov Zel'dovich: "Long time ago, there was a brief period of time during which there was still no time at all" (private communication, April 1986). See a beautiful expose (no math) of the current state of affairs by Bob Wald in gr-qc/0507094 v1.
I plan to present my efforts at understanding the nature of space and time on Sunday, 21 September 2008, commemorating 100th anniversary of the celebrated talk by Hermann Minkowski in Cologne. I shall outline a Virtual Geodesic Path (VGP) formulating of GR, after which will demonstrate reversible BCCP (Brain-Controlled Cold Plasma) and levitation. (There will be nothing particularly new in these demonstrations, since many Chinese researchers have demonstrated these and other similar abilities of the human brain, under strictly controlled laboratory conditions.) Perhaps the VGP formulating of GR contains some new ideas: the local and the global modes of spacetime will be modeled with Archimedean and non-Archimedean spaces, respectively. The task is to avoid "the limitations of a one world Archimedean world view" [Ref. 4], by placing the "many worlds" of potential reality in a non-Archimedean space (global mode of spacetime), while the actualized, already-linearized, local mode of spacetime "is like R" [ibid., p. 8]. Thus, the Einstein-Hilbert action will have to be substantially modified à la R. Feynman's path integral taken over two virtual worlds (as hinted above, and exposed here and here), so that the action can be re-calculated for each and every "instantaneous state" (cf. the minimalist approach above), by taking into consideration all 'virtual paths', which reside in the "next" potential state in the non-Archimedean partition of space (global mode). For this purpose, I will first introduce a new "number", called [phi]. It is a big headache, however, and I haven't figured out the corresponding [phi] algebra and calculus, if any.
Briefly, the VGP formulating of GR is based on the conjecture that quantum-gravitational interactions propagate "instantaneously" in the non-Archimedean [Ref. 4], or 'global mode', partitions of 3-D space, being a function of both the position and momentum of a given particle and of positions and momenta of all other particles in the whole universe at the same time instant: a purely relational, Machian viewpoint on quantum gravity. Hence we can, locally and reversibly, modify the emerging quality of physical bodies, called 'inertia', since all physical entities 'think globally and act locally'. All you need is a brain that can 'act on itself' [Ref. 5]. If you have one and happen to be in Munich in September 2008, call me. Tickets are still available.
But of course I could be all wrong: read the opinion of Britain's leading expect in quantum gravity here.
[Ref. 1] Pankaj S. Joshi, On the genericity of spacetime singularities, gr-qc/0702116 v1.
p. 5: "However, both from causal structure analysis and from the global properties of a spacetime manifold M (which is assumed to satisfy the generic condition as well as a specific energy condition), ... "
"Because the Higgs field would be responsible for mass, the very fact that the fundamental particles do have mass is regarded by many physicists as an indication of the existence of the Higgs field."
p. 6: "... the intuitive essence of the Archimedean property is that, in a finite number of steps, one can walk past every point in the respective space, no matter where one started to walk. In this way, an Archimedean space, like for instance the real line R, is but one single world.
Subject: Gravitational dynamics within the "boundaries" of spacetime
Subject: Re: Paper you might like
Subject: The correlated universe
Note: The cosmic equator, as a snapshot from 'the universe as ONE', must show up from each and every point/reference frame on the balloon surface, because we have the "center of the balloon" multiplied as infinitely many (actual infinity) points/reference frames on the balloon surface -- read the text at the link above. My teenage daughter grasped it, hope you will too.
Note: In case there are people interested in new energy sources, check out the definition of a bath (reservoir), in E.P. Gyftopoulos and G.P. Beretta, Thermodynamics: Foundations and Applications, Macmillan, New York, 1991, p. 87, and Elias P. Gyftopoulos, Maxwell's demon. (I) A thermodynamic exorcism, Physica A, 307 (2002) 405-420.