Quantum Black Holes, the Holographic Principle and Pathological Science
Yvan Leblanc (eFieldTheory.COM)
Friday, 21 June 2013 - [no. 1]
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Hawking's quantum black holes

A CLASSICAL black hole is a massive object of high density which warps the spacetime of Einstein's General Relativity so dramatically that all matter and radiation crossing its horizon (a causal surface englobing its center) become trapped forever. Classically, nothing can escape from it and since light itself does not escape, the hole is black for external observers.

But what happens when the black hole horizon becomes so small that its size approaches the so-called Compton wavelength at which Quantum Mechanics takes over Classical Mechanics? There is no definitive answer to this question at the present time.

In the seventies, Hawking, Bekenstein and Unruh approached this question at the intermediate scale called "semiclassical". Two methods of approach exist at such a scale: (1) the so-called WKB approach and (2) the Mean-field approach.

In the WKB approach, Bekenstein and Hawking arrived at a description of a QUANTUM black hole as a black body (heat reservoir) in thermal equilibrium at the Bekenstein-Hawking temperature. The quantum black hole is then hot and emits heat in the form of particles also in equilibrium at the same temperature, a result apparently confirmed by Hawking in the Mean-field approach. This new theory of quantum black holes is called Bekenstein-Hawking Black Hole Thermodynamics.

So, contrary to classical black holes, quantum black holes of the Bekenstein-Hawking type allow particles to escape, albeit with a thermal signature. The thermal radiation from the black hole is called the Hawking effect, wich is similar to the so-called Unruh effect predicting thermal particle emission from the flat spacetime vacuum as seen by accelerating observers. This is sometimes viewed as a quantum equivalence principle.

The quantum black hole being a thermal object in the Hawking theory, its equilibrium state is characterized by a quantity called the Bekenstein-Hawking entropy and which is calculated from the so-called Area law as one quarter of the horizon surface. Before Hawking's theory, entropy was a quantity characterizing the macroscopic states of matter such as gases, solids and liquids. Entropy is a measure of the number of macrostates and related to the information about the system.

Today, the Bekenstein-Hawking entropy (the Area law) constitutes the fundamental basis for the so-called Holographic Principle of 't Hooft-Susskind-Bousso and which limits the amount of information (in bits per square meters) contained in a theory of Quantum Gravity. This principle constitutes a universal link between geometry (horizon) and information (entropy).

A critical analysis

In 1992, I was an associate researcher at the physics department of the University of Alabama in Tuscaloosa. At that time, one of my collaborators, Prof. Benjamin Harms was interested by Hawking's theory. I was not! But to help our theory group move forward, I suggested a project of studying the physics of a gas of Hawking's black holes. I had acquired a certain expertise in fields and strings at finite temperature in previous jobs at M.I.T. and Paris-Sud at Orsay.

To our surprise, our calculations rigorously showed the mathematical and physical impossibility for a thermal description of quantum black holes as put forward by Bekenstein-Hawking Black Hole Thermodynamics. A crucial quantity called the heat capacity is really negative in Hawking's theory. Every well educated physicist knows that the fundamental requirement for the existence of thermal equilibrium in normal systems is a positive heat capacity. Consequently black holes did not form normal systems and could not reach thermal equilibrium, ever! This meant the collapse of Black Hole Thermodynamics.

An alternative consistent and traditional interpretation of the WKB calculation led us instead to an entirely new description. Quantum black holes were identified as unstable Gamow resonances at the Planck scale, very much similar to the known resonances of nuclear physics. The latter however cannot be black holes as their Compton radii are larger than the size of their would-be horizon. Quantum black holes were in fact massive resonant excitations of so-called p-branes and strings, quantum objects that are believed to play a part in the unification of all the forces of nature, including gravity.

In the Leblanc-Harms WKB theory, quantum black holes were no longer thermal objects but pure state quantum resonances at the Planck scale, with no classical horizon and no longer characterized by temperature or entropy.

The concept of black hole entropy being evacuated in the new theory, the Area law as well as the related Holographic Principle are consequently no longer valid. Those laws cannot and do not form the fundamental building blocks of a theory of quantum gravity.

Since the mid-nineties, important complementary mathematical and physical studies from the Moscow and Rome theory group of Prof. Vladimir Belinski further confirmed the non-validity of the Unruh and Hawking effects within the Mean-field approach. While the Alabama group fully demonstrated the inconsistency of Bekenstein-Hawking Black Hole Thermodynamics, the Russian team formulated a rigorous proof of the non-existence of the Unruh and Hawking effects in Mean-Field theory.

The Leblanc-Harms theory combined with the results of the Belinski group therefore give the final blow to the thermal description of quantum black holes, as envisioned by Hawking and co-workers since the seventies.

Pathological science and Scholasticism

Although our results were accepted for publication in prestigious refereed Journals such as Physical Review D and presented at various international conferences in Boston, San Francisco, New York, Jerusalem, Banff and more recently in Paris (12th Marcel Grossmann Meetings, July 2009), there was very little feedback from the physics community. Back in 1992-93, I had hoped for our results to generate reactions and healthy discussions. That never was to be. No significant reaction.

Although these same results lead to the total collapse of Hawking's thermal black hole theory, many still today remain reluctant to abandon such a theory. The concept of black hole entropy in particular is a die hard, although there is absolutely no mathematical nor physical basis for it. The so-called Cambridge school of thoughts, which is composed of the club members of the Hawking thermal black hole theory, has cut itself off from sound physical principles to promote a new kind of theory, disconnected from the successful laws of Quantum Theory and Statistical Mechanics. Black Hole Thermodynamics research, not unlike String Theory research, arrogantly ignores the most serious criticisms. Black Hole Thermodynamics lies in the face of sound physics and forms the basis for a club that acts like a cult.

Black Hole Thermodynamics has often been viewed as a field with great potential for high rewards. So it is naturally targeted by select groups and prominent individuals who work hard to preserve their personal interests. This is an understandable competitional attitude, but one that is severely lacking in collegiality and science ethics. This is the beginning of pathological science.

Following his convincing proof about the impossibility of quantum tunneling through a black hole horizon, Prof. Belinski has himself attracted unfriendly responses. One response in particular is revealing: «Sadly there are a tiny but vociferous minority who do not believe in such tunneling at all, and instead believe that they have disproved it already.» (arXiv:0911.4417v1 [gr-qc])

D. L. Rousseau (Bell Laboratories, translated from a text in pensee-unique.fr) warns us: «Pathological science is created by the self-delusion of scientists who believe to be acting in a disciplined and scientific way while in fact they have lost their objectivity. Practitioners of pathological sciences cannot believe their findings to be wrong and are ready to ignore prevalent theories and critics from experts».

Critical analysis is fundamental to real scientific progress. In science, one should not be sad about the fact that other researchers can hold different views, when honest and thoughtful. In his historical perspective on the creation of the Landau Institute entitled "Our History", Isaak M. Khalatnikov (1996), Honorable Director of the Landau Institute of Theoretical Physics, wrote the following: «The role of criticism in theoretical physics can hardly be overestimated because its absence means a speedy and unavoidable lapse into scholasticism and other sins. ... If there is no contact with practical physics, then theoretical physics is just scholasticism, having nothing to do with life» (Khalatnikov, I. M., 1996. Our History. In: Thirty years of the Landau Institute. Selected Papers. World Scientific, Singapore.).

Unfortunately, this is the disease that strucked quantum black hole and string theory research since the mid-seventies.