Primordial basis: How many angels can dance on the head of a pin?
First about the hypothetical information loss due to the hypothetical black holes absorbing "negative amounts of energy, allowing positive energy to escape to infinity". Well, that's quite a challenge. Since Gerard 't Hooft has clearlty declared his intention to develop some fundamental theory, I think the first and foremost task should be to resolve the basic problems with the socalled black holes  they might not exist at all [Loinger 2000a; Loinger 2000b; Mashkevich 2000; Singh 1998; Singh 2000]. A second and parallel task should be to cure the string theory from some builtin inconsistencies [Woit 2001]. I have no idea whether his theory would survive after completing these first off tasks, but it will be certainly very useful if Gerard 't Hooft could suggest a solution to the cosmological constant problem, which requires new physics. I believe new physics will be needed to explain why we don't observe naked singularities [Joshi et al., 2001]. There must be at least one testable prediction from his new theory, otherwise it will be as academic as arguments about how many angels can dance on the head of a pin [Hawking 1995]. Let's wish him best of luck in his
endeavors.
Dimiter G. Chakalov April 6, 2001 References and notes 1.
Gerard 't Hooft. Quantum Gravity as a Dissipative Deterministic System.
Thu, 1 Apr 1999 15:52:56 GMT,
"We have learned to live with the curious phenomenon that our wave functions can be eigenstates of operators which at different spacetime points usually do not commute. A "physical state" can be an eigenstate of an arbitrary set of mutually commuting operators, but then other operators are not diagonalized, and so, these observables tend to be smeared, becoming "uncertain". The idea that such uncertainties may be due to nothing other than our limited understanding of what really is going on, has become unpopular, for very good reasons. Attempts at lifting these uncertainties by constructing theories with 'hidden variables', have failed. "It is the author's
suspicion, however, that these hidden variable theories failed because
they were based far too much upon notions from everyday life and 'ordinary'
physics, and in particular because general relativistic effects have not
been taken into account properly. The interpretation adhered to by most
investigators at present is still not quite correct, and a correct interpretation
is crucial for making further progress at very technical levels in quantum
gravity.
"It is of interest
to observe that, in constructing models with a deterministic interpretation
for quantum states, the restriction to 1+1 dimensions is usually
quite helpful. This is a reason to suspect that a deterministic interpretation
of string theory is possible. In Appendix A, a construction is shown. Here,
we succeeded in producing a model in 3+1 dimensions, but its
ultraviolet cutoff is fairly artificial. In 1+1 dimensions,
the cutoff is straightforward."
2.
Gerard 't Hooft. Determinism and Dissipation in Quantum Gravity, Erice
lecture. Tue, 16 May 2000 13:40:51 GMT,
"(iii) Even at a local scale (i.e. not cosmological), there are problems that we could attribute to a clash with Quantum Mechanics. Apart from the question of the cosmological principle, these are:  the nonrenormalizability of gravity;  the fact that the gravitational action (the EinsteinHilbert action) is not properly bounded in Euclidean space, while the Maxwell and YangMills actions are. This is related to the fundamental instability of the gravitational force.  topologically nontrivial quantum fluctuations. They could destroy the causal coherence of any theory. Perhaps most such fluctuations may have to be outlawed, as they would also require the boundary conditions to fluctuate into topologically nontrivial ones.  black holes cause the most compelling conflicts with local quantum mechanics.  there still
is the mystery of the cosmological constant. It appears to require a reconsideration
not only of physical principles at the Planck scale, but also at cosmological
scales, since we are dealing here with an infrared divergence that appears
to be cancelled out in a way that requires new physics.
Fig. 3, traj.ps. Stable orbits, a)
for the harmonic oscillator, b) an anhormonic oscillator. After switching
on a dissipative term, the regions in between these trajectories will have
only nonperiodic solutions, tending towards the stable attractors.
"The next step, yet to be taken,
is to couple infinite numbers of dissipating oscillators to form models
of quantum field theories. This may appear to be a very difficult task,
but we do notice that in classical general relativity black hole formation
is inevitable, and black holes indeed absorb information. This would imply
that the distance scale at which dissipation plays a role must be the Planck
scale.
3. Gerard 't Hooft. In Search of the Ultimate Building Blocks. Cambridge: Cambridge UP, 1996. Frank
Wilczek (review for Nature): "One finds on every page of this
book sharp statements and novel formulations that show the workings of
a firstrate, confident and original mind. It deserves attention."
4.
Gerard 't Hooft. Distinguishing causal time from Minkowski time and a model
for the black hole quantum eigenstates. Tue, 18 Nov 1997 09:54:57 GMT,
"Of even more importance, however,
appears to be the fact that assuming the preservation of quantum
information leads to interesting new insights in the forces of nature.
Conservation of quantum informationis likely to demand a new kind of conspiracy,
and the resolution of the paradox may well lead to important new physics.
"In Fig. 3, this is further illustrated.
The collapse is observed at the point S . The ingoing observer
follows the path B towards the Schwarzschild singularity.
The outside observer continues along the path A . After the
collapse, Hilbert space is not described by the products of the
states along path A and the ones along path B
, but it is spanned either by the states at A alone,
or by the states at B alone. The Hamiltonian H
is defined along A and along B ,
and it dictates the evolution everywhere along the curve. Thus, we see
that time has become a manifold more complicated than just a single line."
5.
Angelo Loinger. On continued gravitational collapse. Wed, 26 Jan 2000 12:50:43
GMT,
Abstract: "According to a widespread idee fixe, the sphericallysymmetric collapse of a sufficiently massive celestial body of spherical shape should generate a black hole. I prove that this process generates simply an ordinary point mass. My argument is modelindependent." Angelo Loinger: "The conclusion is
obvious. Vain is the chase of the black holes."
6.
Angelo Loinger. On the concept of mass point in general relativity. Sat,
10 Jun 2000 04:55:42 GMT,
(To see the list of all papers by
A. Loinger posted at Los Alamos Eprint archive, click here.)
7.
Vladimir S. Mashkevich. Unboundable Spacetimes with Metric Singularities
and Matching Metrics and Geodesics: A BlackWhite Hole and a Big CrunchBang.
Sat, 25 Nov 2000 04:02:00 GMT,
"Spacetime singularities are inherent in general relativity, or more specifically in gravitational collapse and cosmology. The analysis of spacetimes with singularities is one of the most principal and difficult problems in general relativity. Singularity theorems of general relativity utilize the notion of causal geodesic incompleteness as a criterion for the presence of a singularity. (A comprehensive presentation and discussion is given in [1].) The incompleteness of a causal, i.e., timelike or null curve implies physically the end and/or beginning of the existence of a particle, which are undeniably events. In the commonly accepted approach, singularities are not incorporated into a spacetime manifold. Thus spacetime turns out to be eventincomplete, i.e., does not include all events. "Furthermore, the beginning and end
of the existence of a free particle means that there is creation from nothing
and extinction into nothing. Those phenomena are in conflict with conservation
laws and appear physically pathological. Maybe it is possible to put up
with extinction into nothing, arguing that nature is so structured. At
least extinction follows a clearcut law: Arriving at a singularity results
in extinction. With creation from nothing, the situation is much worse.
In this role, (naked) singularities are sources of lawlessness. All sorts
of nasty things  green slime, Japanese horror movie monsters, etc. 
may emerge helterskelter from a singularity [1]. To get rid of that
nightmare, Penrose proposed the cosmic censorship hypothesis. But cosmic
censorship may be legislated only by a fiat, it does not follow from known
physical laws."
8.
T.P. Singh. Gravitational Collapse, Black Holes and Naked Singularities.
Mon, 18 May 1998 13:04:53 GMT,
9.
T.P. Singh. Comparing quantum black holes and naked singularities. Thu,
21 Dec 2000 11:55:48 GMT,
10. Peter
Woit. String Theory: An Evaluation. Fri, 16 Feb 2001 18:03:42 GMT,
11. Pankaj
S. Joshi, Naresh Dadhich, Roy Maartens. Why do naked singularities form
in gravitational collapse? Fri, 14 Sep 2001 16:04:06 GMT,
12.
Stephen W. Hawking. Virtual Black Holes. Fri, 6 Oct 1995 16:09:21 +0100
(BST), Stephen W. Hawking: "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."
