Subject: The One-Eyed Green Underground Stone Eating Monster
Date: Thu, 10 Mar 2005 18:43:16 +0200
From: Dimi Chakalov <>
To: Neil Turok <>
CC: Steven Gratton <>,
     Jaume Garriga <>,
     Alexander Vilenkin <>,
     Sean Carroll <>,
     Claus Kiefer <>,
     Emilio Elizalde <>,
     Gordon McCabe <>,
     Alan Guth <>,
     Norbert Straumann <>,
     Jim Hartle <>,
     Karel Kuchar <>,
     Julian Barbour <>,
     William G Unruh <>,
     Jorge Pullin <>,
     Don N Page <>
BCC: [snip]

Dear Dr. Turok,

I was reading your recent "Langevin Analysis of Eternal Inflation",
hep-th/0503063 v1 [Ref. 1], and recalled a quiz from my daughter:

Q: What is green, lives underground, has one eye, and eats stones?
A: The One-Eyed Green Underground Stone Eating Monster!

It seems to me that you and many of your colleagues have neglected
the Occam's razor and have adopted a similar line of reasoning in
inflationary cosmology,

I agree that it isn't easy to handle some totally unknown dark matter & dark energy and try to model the universe with some hypothetical

Yet I believe we can avoid the 'One-Eyed Green Underground Stone Eating Monster' in inflationary cosmology. We currently have R^2, new, chaotic, extended, power-law, hybrid, natural, supernatural, extranatural, eternal, D-term, F-term, brane, oscillating, and trace-anomaly driven inflation, and if we add some "anthropic considerations" a la Steve Weinberg, the whole story looks like a joke, much like the quiz from my 11-year old daughter.

There are some very old and widely known ideas, which I've been trying to present 'en bloc' with the so-called global mode of spacetime,

Regarding your recent paper [Ref. 1], I think the idea of "back-reaction of quantum fluctuations on the process of inflation itself", in real (Hubble) time, is quite a rough guess, to say the least. It presumes that a physical clock, as defined in GR, can survive the UNphysical "inflationary stage". Hence the notion of "ideal" eternal observer, or rather "an indestructible test particle", introduced by Jaume Garriga and Alexander Vilenkin (ibid., ref. [22]).

I believe all this belongs to the global mode of spacetime. It can handle any kinds of cat states and "quantum fluctuations", included those in canonical quantum gravity at Planck scale. Please see the links in this email, and I will be happy to elaborate.

Perhaps the most important aspect of the global mode of spacetime is the non-Archimedean nature of this atemporal and spaceless medium: it provides for a genuine *non-unitary* evolution of the universe. To explain this non-unitary evolution, we model the universe as a human brain,

At any given instant from the cosmological time arrow, the set of 'things that we still don't know that we don't know' is an *empty set* in the global mode of spacetime. Hence brand new things can literally emerge from the global mode of spacetime, and we can enjoy a genuine cosmological time *arrow*. It does look like 'creatio ex nihilo', yes. The idea is not new at all, I believe Edward P. Tryon has suggested that the universe can be created from 'nothing' [Ref. 2].

But if we run this cosmological time arrow backwards, we should "dissolve" the content of the universe back to the global mode of spacetime. There will be no need to postulate some scalar (inflaton) field, since all this will be brought back to the global mode of spacetime. Instead of some "big bang", we can have a perfectly smooth Beginning from [John 1:1], and a dual age of the universe: finite in the local mode of spacetime, and infinite (or rather indecisive) in the global mode,

I cannot accept the idea that 73 per cent of the stuff in the universe could be in some "dark energy" form, some ubiquitous and *perfectly smooth* stuff [Ref. 3]. This is not metaphysics anymore. The fact that we're alive and well indicates that all "dark" stuff should be dropped in the global mode of spacetime. It's just a virtual reality, much like the Platonic ideas we keep in our brains,

Again, I believe all this is very old and well-known.

I will appreciate your comments, as well as those from your colleagues.


Dimi Chakalov


[Ref. 1] Steven Gratton and Neil Turok, Langevin Analysis of Eternal Inflation, hep-th/0503063 v1, 7 March 2005,

"In any case, it seems important to try and develop calculations of
conditional probabilities within inflationary models, taking into
account the back-reaction of quantum fluctuations on the process of
inflation itself. At first glance, one might think of a slow rolling inflaton field as being similar to an overdamped harmonic oscillator in the presence of weak stationary noise. After a short time such an oscillator ends up at the bottom of its potential and it only rarely fluctuates appreciably upwards.

"As we shall discuss, with a change of variable we see that the system is actually an upside-down, over-damped harmonic oscillator, for which there is no stationary state."

"It would also be interesting to extend the model to allow the inflaton
field to jump back up from its minimum into an inflating regime, a
situation referred to by Garriga and Vilenkin as a "recycling universe"
[22] (see also [23])."
[22] Jaume Garriga and Alexander Vilenkin, Recycling universe,
astro-ph/9707292 v1, Phys. Rev. D57 (1998) 2230-2244,

[Ref. 2] Edward P. Tryon, Cosmic inflation. In: The Encyclopedia of Physical Science and Technology, 2nd Edition, Volume 3, Academic Press, New York, 1992, p. 570.
Edward Tryon, Is the Universe a Vacuum Fluctuation? Nature 246, 396-397 (1973).

[Ref. 3] Matt Visser, Jerk, snap, and the cosmological equation of state, gr-qc/0309109 v3,

"Exotic matter is powerful stuff: Apart from possibly destroying the universe in a future "big rip" singularity [7], if the exotic matter clumps to any extent there is real risk of even more seriously bizarre behaviour -- everything from violations of the positive mass condition (that is, objects with negative asymptotic mass), through traversable wormholes, to time warps [4, 14, 15, 16, 17]."

Note: The cosmological time arrow should be driven by some fundamental time asymmetry, correct? If true, I claim that the entropy increase in not, and cannot be the engine of the fundamental time asymmetry. Entropy is merely a "reading device", like a thermometer. It can only show us that there is some global feature of the universe, which is being affected by the fundamental time asymmetry.

Hence I suggest that there are "dark" effects of the Holon in the global mode of spacetime, which produce the cosmological time arrow (called here 'universal time arrow'), but these effects cannot be completely reduced to the observable machinery of our universe. This is, again, the old story of a holistic "forest" in which every individual tree is affected by [the rest of the trees] via their common "context" placed in the Holon. The input from 'the forest' produces a totally "dark" effect on each and every tree. The effect is "dark", because we cannot pinpoint or trace back its origin by "looking at the tree" alone. Examples: we look at the neurons in the human brain, and see nothing but normal standard chemistry and classical physics, but we cannot, even in principle, reproduce the holistic organization of the brain by using that same chemistry and physics. If the brain is too complicated, think of a centipede and try to build a machine exactly as a centipede, and you'll see that it won't walk.

Another example: we look at galaxy clusters, and see nothing but normal physical stuff, which is, however, affected severely by some "dark matter". The puzzle is from 1933, but what do we do? We invent new particles and "black holes". See the subject of the email above.

But what is the meaning of fundamental time asymmetry? What makes it fundamental? Recall that every physical phenomenon can only be explained by including it into some wider theory; all this is well-known since Aristotle and Gödel's theorems. The fundamental time asymmetry can be produced only by the Aristotelian First Cause, the Unmoved Mover. Then all observable physical phenomena will be affected by it, and all of them will point to some "thermometers" which read their totally "dark" Unmoved Mover.

More on the Aristotelian Unmoved Mover from Karel Kuchar; he uses math, I don't. Why not? Because I believe the fundamental time asymmetry comes from the evolution of the state space of the universe, that is, from its enrichments with totally new events. That's creatio ex nihilo, as mentioned above. If I could describe this non-unitary evolution with math, I would have rushed my manuscript to PRL or Nature. That's what my colleagues can do, if they are interested. They are damn good in math. I'm just a psychologist, from the BBB world.

D. Chakalov
March 11, 2005

Addendum 1

The very idea of inflation is a blatant sci-fiction, but in order to suggest a credible explanation of the whole bundle of data which seem to support the inflationary cosmology, we need new physics. I've chalked out some basic ideas about this new physics, and now will briefly argue that these efforts were indeed necessary, because the whole idea of inflation is a blatant sci-fiction. It may look "scientific" only because people use math, as does, for example, Max Tegmark [Ref. 4]. Let's look at the basic ideas in inflationary cosmology, as illustrated with the picture below, and then will comment on the ideas of Max Tegmark.

Much like forensic science, cosmologists try to reproduce the history of the universe, and the first thing they do is to introduce a scalar field, called inflanton field, because the machinery of GR alone cannot "produce" the observed evolution of the universe. Hence the inflaton field is being introduced post hoc, because matter cannot be created by gravity alone (violation of conservation laws). But any dynamical evolution of the mysterious dark energy "would have to be accompanied by a compensating non-conservation of the mass-energy of the matter", says R. Penrose.

Thus, we have violation of mass-energy conservation law anyway. Not only is the exotic "dark energy" perfectly smooth, but it has an intrinsic dynamics as well. In what reference frame do we describe its dynamics? We need some global reference frame for the ubiquitous dark energy, correct? But note that this isn't some innocuous preferred frame such as the one associated with the Cosmic Background Radiation, as George Smoot argues. No. This is the preferred frame of some totally mysterious entity that covers the whole universe, and evolves in time  ... as you read these lines. It takes 73 per cent of the content of the universe, and is pushing uniformly its metric with constant acceleration.

And here we enter that huge can of worms called 'coincidence problem', which is part and parcel of the cosmological constant problem, and people just give up and switch to religion and parapsychology (read: anthropic principles), like Steve Weinberg. Perhaps we -- not Mother Nature -- have missed something right from the outset, you may wonder. Or maybe we've done the opposite. Maybe we have introduced yet another superfluous 'One-Eyed Green Underground Stone Eating Monster'. Or both.

If you are a 'rigorously inclined reader' and read M. Tegmark's paper [Ref. 4], you will notice that he hasn't even mentioned the fundamental problems of inflationary cosmology, which produce this whole mess above.

To begin with, look again at the picture above, and notice a very peculiar phrase: "tiny fraction of a second". We can try to suggest some ideas about the evolution of the universe only and exclusively only after the completion of this "tiny fraction of a second".

Let's zoom on it. We will denote The Beginning with {?}, and the onset of inflation with {I}.

{?} ---[tiny fraction of a second]----> {I}
Isn't this totally ridiculous? It is 'not even wrong', as W. Pauli might have said. You can't insert a time interval such as "tiny fraction of a second" before some totally unphysical "inflation stage", because the latter cannot be reconciled with Special Relativity.

All we know about the universe is after the completion of inflation, some 380,00 years after  {I}  . But in order to talk about these 380,000 years, first we must explain how a physical clock ("an indestructible test particle", in Garriga-Vilenkin's terminology) can read the duration of a superluminal metric expansion, what could be its proper time, and in what reference frame it could be measured. Once we get this job done, we can safely move backwards along the deflation time, and speculate about the actual duration of "tiny fraction of a second"  before  {X} . More in the 'cosmic hen' story here.

Max Tegmark [Ref. 4] hasn't explained any of these puzzles, but one can find tons of calculations in his paper, some of them employing very sophisticated math. Pay attention to the way he tries to unscramble the 'global orderings' from 'pocket-based orderings', it is really amazing.

I have tried to suggest a conceptual solution to this ultimate puzzle with the two modes of spacetime, and have suggested the idea of dual age of the universe here. It is very important to stress that the same kind of paradoxical situation arises with the so-called relativistic "collapse". In both cases, we have the case of being in "short circuit" with the Holon of the universe, in the global mode of spacetime.

If we ignore the latter, we must explain the evolution of the universe and the link between the quantum and classical worlds with the 'time read by a clock', as suggested by John Baez. This is the established paradigm, and it inevitably requires new 'One-Eyed Green Underground Stone Eating Monsters'.

 Anyway, I tried to raise my voice four years ago, on May 8, 2001, by writing to fifty-two prominent theoretical physicists, Max Tegmark included. Nobody replied, ever. I can try to understand their attitude, maybe they are treating theoretical physics as a hobby, as if they were collecting bottle labels while I was suggesting to switch to matches. Of course they will keep collecting their favorite bottle labels, and will keep quiet.

After all, it's a free world. Besides, they are not taking any significant amount of taxpayers' money, and are free to do anything they want. Fair enough. For example, read M. Tegmark's "Parallel Universes" (Sci American, May 2003): "The simplest and most popular cosmological model today predicts that you have a twin in a galaxy about 10 to the 1028 meters from here. This distance is so large that it is beyond astronomical, but that does not make your doppelgänger any less real." Then take a deep breath and try to imagine how are the infinite number of doppelgängers related, Max Tegmark included -- by global orderings or pocket-based orderings [Ref. 4]. That's what inflation predicts, really. Fascinating, and doesn't cost much at all.

However, there are cases in which that same kind of people are wasting billions of dollars and euro for chasing 'One-Eyed Green Underground Stone Eating Monsters'. Read about them here.

I wish I could keep my mouth shut. But I can't. I couldn't make a career in communist Bulgaria only because I was "talking too much". Now I'm too old to change.

D. Chakalov
March 17, 2005

[Ref. 4] Max Tegmark, What does inflation really predict? astro-ph/0410281 v2, 11 March 2005


"Above we saw that to make inflation a testable physical theory, the ordering problem must be solved. This is a wide open problem in dire need of further work -- the purpose of this section is not to give a solution, merely to describe some possible approaches to solving it.

"A variety of solutions to the ordering problem have been discussed in the literature, albeit using different terminology. We will consider two broad classes of orderings: 

1. Global orderings based on some time variable (say t or a).

2. Pocket-based orderings (ordering separately within each thermalized region (pocket), then averaging the pocket results with some weighting (say equally, by [psi]-volume or by r-volume).

A. Global time-based orderings

The first class of orderings foliates spacetime into a sequence of three-dimensional spatial hypersurfaces, each corresponding to a fixed “time”, and computes the parameter probability distribution fp(p) separately on each hypersurface. We will see that this is in many cases equivalent to simply ordering the reference objects by increasing formation “time”.

p. 26: "In Section IV, we saw that a global ordering is uniquely defined by specifying a "time" variable to order the reference objects by. We found that all observable quantities (e.g., p, T or H) are inadequate as such global time variables, leading instead to pocket-based orderings, so let us now explore time variables that are not observable (except in differences or ratios, like t and a). We will focus most of our discussion on the case of ordering by time  t  [footnote 13], then discuss how these conclusions can be generalized to other global orderings.
Footnote 13:
"Specifically, we define t as the time variable in synchronous coordinates
where the metric is

ds2 = dt2 - a(x, t)2dx2 .                (84)

"The lines of constant  x  in this metric are timelike geodesics corresponding to the worldlines of Gedanken co-moving observers, and  t  is the proper time of these observers. This coordinate system remains well-defined until these geodesics start to cross, which happens only long after thermalization when fluctuations go non-linear -- the coolness problem discussed below becomes severe long before then, so it cannot be circumvented by a creative choice of gauge at late times. When we discuss  t  for a particle in the present epoch, the rigorously inclined reader can simply take this to mean its proper time, since this provides a well-defined ordering even after geodesic crossing."

p. 29: "Physical questions must be expressible in terms of observables. This implies that it is a big no-no to condition on quantities that are not physically observable, like t or a. t-ordering violates this principle since, as described above, it corresponds to defining reference objects such as, say, "protons at time t". The global time  t  is a completely unobservable quantity, because all we can measure in our thermalized region is time intervals, e.g., the time interval (t - ttherm) since inflation ended here. Moreover, there are infinitely many alternative choices of time variable, and between causally disconnected regions of spacetime (such as two different thermalized pockets), gauge ambiguities imply that there is no objective way of defining simultaneity.

"A standard definition of eternal inflation (e.g., [57]) is that "at any given time, part of space is inflating, and the inflating volume increases over time", yet this definition uses precisely the infamous time foliation by considering the situation "at any given time"."

Addendum 2

What if the Snark was a Boojum? As we know from Lewis Carroll's "The Hunting of the Snark", Snark is a fictional animal, while Boojum is a very dangerous form of Snark.

This tantalizing question is presented in Sec. 7 of a recent review by T. Padmanabhan [Ref. 5, p. 20]. Here, he elaborates on the idea that the cosmological constant (the Snark) could be a dangerous form of Snark, known as "dark energy" (a Boojum). That's scary, really.

Regarding the so-called dark energy or Boojum, T. Padmanabhan wrote [Ref. 5, p. 25]:

"In fact, the acid test for any viable quantum gravity model is whether it has something nontrivial to say about [omega]DE; all the current candidates have nothing to offer on this issue and thus fail the test.

"The second question is: How (and why!) was the universe created and
what happened before the big bang ? The cosmologist giving the public lecture usually mumbles something about requiring a quantum gravity model to circumvent the classical singularity -- but we really have no idea! String theory offers no insight; the implications of loop quantum gravity for quantum cosmology have attracted fair mount of attention recently [Martin Bojowald, this volume] but it is fair to say we still do not know how (and why) the universe came into being."

I regret that Paddy (T. Padmanabhan) has ignored all my email sent in the past three years, but he certainly deserves credit for trying to avoid new creatures, such as The One-Eyed Green Underground Stone Eating Monster (see above).

It will be very interesting to see if another mathematical physicist, Alan Rendall [Ref. 6], has read Lewis Carroll's "The Hunting of the Snark".

Watch this space! The zoo of amazing creatures is clearly expanding, perhaps with constant acceleration too!

To be serious, many people have explored, and continue to explore, a large variety of mind-boggling possibilities, but none of them -- to the best of my knowledge -- has tried to modify the underlying theories, QM and GR, by offering the simplest possible solution, as outlined here. They just keep quiet, and don't reply to my email. Then they submit their contributions to "100 Years of Relativity. Space-time structure: Einstein and beyond", as T. Padmanabhan did [Ref. 5].

Who cares about Einstein's heritage?

D. Chakalov
March 28, 2005

[Ref. 5] T. Padmanabhan, Understanding Our Universe: Current Status and Open Issues, March 28, 2005, gr-qc/0503107 v1. To appear in "100 Years of Relativity - Space-time Structure: Einstein and Beyond", A. Ashtekar (Editor), World Scientific, Singapore, 2005; 30 pages; 4 figures.

Excerpts from pp. 15-20, Sec 6:
"6. The Dark Energy

"It is rather frustrating that we have no direct laboratory evidence for nearly 96% of matter in the universe. (Actually, since we do not quite understand the process of baryogenesis, we do not understand X_B either; all we can theoretically understand now is a universe filled entirely with radiation!).

"Assuming that particle physics models will eventually (i) explain X_B and X_DM (probably arising from the lightest supersymmetric partner) as well as (ii) provide a viable model for inflation predicting correct value for A, one is left with the problem of understanding X_DE. While the issues (i) and (ii) are by no means trivial or satisfactorily addressed, the issue of dark energy is lot more perplexing, thereby justifying the attention it has received recently.

"In other words, dark energy with sufficiently negative pressure will accelerate the expansion of the universe, once it starts dominating over the normal matter. This is precisely what is established from the study of high redshift supernova, which can be used to determine the expansion rate of the universe in the past.

"Figure 2 presents the supernova data as a phase portrait of the universe. It is clear that the universe was decelerating at high redshifts and started accelerating when it was about two-third of the present size.

"Observations demand (XXXX)< 10-120 requiring enormous fine tuning.

"What is more, the energy density of normal matter and radiation would have been higher in the past while the energy density contributed by the cosmological constant does not change. Hence we need to adjust the energy densities of normal matter and cosmological constant in the early epoch very carefully so that (XXX) around the current epoch. Because of these conceptual problems associated with the cosmological constant, people have explored a large variety of alternative possibilities. Though none of them does any better than the cosmological constant, we will briefly describe them in view of the popularity these models enjoy.
"Given this situation, we shall take a closer look at the cosmological constant as the source of dark energy in the universe.

p. 20, Sec 7: "7. ...For the Snark was a Boojum, you see

"If we assume that the dark energy in the universe is due to a cosmological constant, (...)."

[Ref. 6] Alan D. Rendall, The nature of spacetime singularities, AEI-2005-046, submitted to "100 Years of Relativity. Space-time structure: Einstein and beyond", (Eds.) A. Ashtekar, World Scientific, Singapore, 2005.


Addendum 3

Subject: Dynamical "dark" stuff
Date: Tue, 17 May 2005 18:36:53 +0300
From: Dimi Chakalov <>
To: Philip D Mannheim <>
CC: Norbert Straumann <>,
     Petr Hajicek <>

Dear Professor Mannheim,

I've been trying to understand the *dynamics of the cancellation process*, as suggested in your recent "Alternatives to Dark Matter and Dark Energy", astro-ph/0505266 v1. It is incomprehensible to me. Surely I haven't been able to understand your ideas. Please correct me if I got them wrong.

Statement of the problem: The task is to find a dynamical mechanism such that (p. 25) "these two types of cosmological constant to cancel each other to unbelievable precision".

The main idea in to explore the generic ambiguities in introducing cosmological constants to either side of Einstein equations: "It is this lack of a principle which renders the choice of gravitational action non-unique, with there then being no principle with which to control the contribution of the cosmological constant." (ibid.)

You then introduce (p. 42) a fundamental cosmological constant on the left-hand side, "one which will then almost, but not quite cancel the dynamical one so that the current era observer then sees a net [omega_lambda](t0) = 0.7. Such a proposal requires that a fundamental cosmological constant exist as part and parcel of the fundamental gravitational equations, that it be included in gravitational theory in all epochs, and that it be preset with just the value needed to lead to a net [omega_lambda](t0) = 0.7 today. It is not clear how one might test such an idea, with such a cancellation having to be regarded as being a cosmic coincidence itself."

But it isn't a "cosmic coincidence". It's a fine-tuning problem, as seen in Eq. 143 (p. 39). Thus, we drop all "anthropic" bullshit (footnote 46), and wind up with the *dynamics* of this fine-tuning puzzle.

So far so good, but here's my problem: we don't have any background whatsoever, anything that can possibly define the dynamics of this fine-tuning process: with respect to what?

Both sides of Einstein equation are affected by this fine-tuning process, with "unbelievable precision".

Thus, the fine-tuning process has nothing to 'hold onto'.

Recap: Not only is the dynamics of the dark energy extremely precise, but is "self-acting" as well, à la Baron von Münchausen.

Conclusion: There is no "coincidence" problem but a dynamical fine-tuning process which surpasses Einstein's equations. We need to go "beyond" the bi-directional talk of matter and geometry,

Am I wrong?

Please don't take this as criticism to your work; I'm only trying to understand the crux of the puzzle.

BTW I'm not a big fan of "D dimensional bulk and a D-space brane"; see an alternative idea at

More at

All my efforts, however, are at the stage of 'pure ideas', and if you can suggest a rigorous solution, I will gladly accept it.

Kindest regards,

Dimi Chakalov

Note: Philip Mannheim has compared the two "dark" components in the following manner:

"As regards dark matter, there is nothing in principle wrong with the existence of nonluminous material per se (indeed objects such as dead stars, brown dwarfs and massive neutrinos are well-established in nature).

"Rather, what is disturbing is the ad hoc, after the fact, way in which dark matter is actually introduced, with its presence only being inferred after known luminous astrophysical sources are found to fail to account for any given astrophysical observation.

"Dark matter thus seems to know where, and in what amount, it is to be needed, and to know when it is not in fact needed (dark matter has to avoid being abundant in the solar system in order to not impair the success of standard gravity in accounting for solar system observations using visible sources alone); and moreover, in the cases where it is needed, what it is actually made of (astrophysical sources (Machos) or new elementary particles (Wimps)) is as yet totally unknown and elusive.

"Disturbing as the dark matter problem is, the dark energy problem is even more severe, and not simply because its composition and nature is as mysterious as that of dark matter. Rather, for dark energy there actually is a very good, quite clear-cut candidate, viz. a cosmological constant, and the problem here is that the value for the cosmological constant as anticipated from fundamental theory is orders of magnitude larger than the data can possibly permit. With dark matter then, we see that luminous sources alone underaccount for the data, while for dark energy, a cosmological constant overaccounts for the data."

I believe have suggested here that these two "dark" effects of the Holon should be interpreted as two "opposite" blueprints on the local mode of spacetime cast from the time-symmetric Holon in the global mode: the smart dark matter, with all its irregularities resembling the neural structure of the brain, is a "dark" effect pointing to the past (implosion), while the smooth dark energy comes from "empty space" and is expanding the metric (explosion). Similar ideas hold for the so-called BH/NS. We certainly need new physics. The deadline is November 2015.

If you don't like these ideas, consider the options suggested by Neil Turok's colleague Stephen Hawking [Ref. 7]. He writes about black holes as if they were confirmed by observations. S. Hawking is certainly good in math, but math alone isn't enough. It is the necessary condition to be a good physicist, while the sufficient condition is to discriminate between facts and wishful thinking. Such as living with black holes and ghosts.

D. Chakalov
May 17, 2005


[Ref. 7] S.W. Hawking, The Nature of Space and Time, hep-th/9409195, 30 September 1994.

"So Einstein was wrong when he said "God does not play dice". Consideration of black holes suggests, not only that God does play dice, but that He sometimes confuses us by throwing them where they can't be seen."

S.W. Hawking, Virtual Black Holes, hep-th/9510029, 6 October 1995.

"Unless quantum gravity can make contact with observation, it will become as academic as arguments about how many angels can dance on the head of a pin."

S.W. Hawking and Thomas Hertog, Living with Ghosts, hep-th/0107088 v2, 27 July 2001. Phys. Rev. D65 (2002) 103515.

"Perturbation theory for gravity in dimensions greater than two requires higher derivatives in the free action. Higher derivatives seem to lead to ghosts, states with negative norm."