Author: Leonard Susskind & James Lindesay

Published in: World Scientific Publishing

ISBN: 981-256-083-1

File Type: pdf

File Size:  2 MB

Language: English


It is now almost a century since the year 1905, in which the principle of relativity and the hypothesis of the quantum of radiation were introduced. It has taken most of that time to synthesize the two into the modern quantum theory of fields and the standard model of particle phenomena. Although there is undoubtedly more to be learned both theoretically and experimentally, it seems likely that we know most of the basic principles which follow from combining the special theory of relativity with quantum mechanics.It is unlikely that a major revolution will spring from this soil. By contrast, in the 80 years that we have had the general theory of relativity, nothing comparable has been learned about the quantum theory of gravitation.The methods that were invented to antiquate electrodynamics, which were so successfully generalized to build the standard model, prove wholly inadequate when applied to gravitation.The subject is riddled with paradox and contradiction.One has the distinct impression that we are thinking about the things in the wrong way.The paradigm of relativistic quantum field theory almost certainly has to be replaced. How then are we to go about finding the right replacement? It seems very unlikely that the usual incremental increase of knowledge from a combination of theory and experiment will ever get us where we want to go, that is, to the Planck scale.

Under this circumstance our best hope is an examination of fundamental principles, paradoxes and contradictions, and the study of gedanken experiments.Such strategy has worked in the past. The earliest origins of quantum mechanics were not experimental atomic physics, radioactivity, or spectral lines.The puzzle which started the whole thing was a contradiction between the principles of statistical thermodynamics and the field concept of Faraday and Maxwell.How was it possible, Planck asked, for the infinite collection of radiation oscillators to have a finite specific heat? In the case of special relativity it was again a conceptual contradiction and a gedanken experiment which opened the way.According to Einstein, at the age of 15 he formulated the following paradox: suppose an observer moved along with a light beam and observed it.The electromagnetic field would be seen as a static, spatially varying field.But no such solution to Maxwell’s equations exists.By this simple means a contradiction was exposed between the symmetries of Newton’s and Galileo’s mechanics and those of Maxwell’s electrodynamics.

The development of the general theory from the principle of equivalence and the man-in-the-elevator gedanken experiment is also a matter of historical fact.In each of these cases the consistency of readily observed properties of nature which had been known for many years required revolutionary paradigm shifts. What known properties of nature should we look to, and which paradox is best suited to our present purposes? Certainly the most important facts are the success of the general theory in describing gravity and of quantum mechanics in describing the microscopic world.Furthermore, the two theories appear to lead to a serious clash that once again involves statistical thermodynamics in an essential way.The paradox was discovered by Jacob Bekenstein and turned into a serious crisis by Stephen Hawking.By an analysis of gedanken experiments, Bekenstein realized that if the second law of thermodynamics was not to be violated in the presence of a black hole, the black hole must possess an intrinsic entropy.This in itself is a source of paradox.How and why a classical solution of field equations should be endowed with thermodynamic attributes has remained obscure since Bekenstein’s discovery in 1972.
Hawking added to the puzzle when he discovered that a black hole will radiate away its energy in the form of Planckian black body radiation. Eventually the black hole must completely evaporate.Hawking then raised the question of what becomes of the quantum correlations between matter outside the black hole and matter that disappears behind the horizon.As long as the black hole is present, one can do the bookkeeping so that it is the black hole itself which is correlated to the matter outside.But eventually the black hole will evaporate.Hawking then made arguments that there is no way, consistent with causality, for the correlations to be carried by the outgoing evaporation products.Thus, according to Hawking, the existence of black holes inevitably causes a loss of quantum coherence and breakdown of one of the basic principles of quantum mechanics – the evolution of pure states to pure states.For two decades this contradiction between the principles of general relativity and quantum mechanics has so puzzled
theorists that many now see it as a serious crisis. Hawking and much of the traditional relativity community have been of  the opinion that the correct resolution of the paradox is simply that quantum coherence is lost during black hole evaporation.From an operational viewpoint this would mean that the standard rules of quantum mechanics  would not apply to processes involving black holes.Hawking further argued that once the loss of quantum coherence is permitted in black hole  evaporation, it becomes compulsory in all processes involving the Planck scale.The world would behave as if it were in a noisy environment which continuously leads to a loss of coherence.The trouble with this is that there is no known way to destroy coherence without, at the same time violating energy conservation by heating the world.The theory is out of control as argued by Banks, Peskin and Susskind, and ’t Hooft. Throughout this period, a few theorists, including’t Hooft and Susskind, have felt that the basic principles of quantum mechanics and statistical mechanics have to be made to co-exist with black hole evaporation. ’t Hooft has argued that by resolving the paradox and removing the contradiction, the way to the new paradigm will be opened.The main purpose of this book is to lay out this case.  A second purpose involves development of string theory as a unified description of elementary particles, including their gravitational interactions.

Although still very incomplete, string theory appears to be a far more consistent mathematical framework for quantum gravity than ordinary field  theory.It is therefore worth exploring the differences between string theory and field theory in the context of black hole paradoxes.Quite apart from the question of the ultimate correctness and consistency of string theory, there are important lessons to be drawn from the differences between  these two theories.As we shall see, although string theory is usually well approximated by local quantum field theory, in the neighborhood of a black  hole horizon the differences become extreme.The analysis of these differences suggests a resolution of the black hole dilemma and a completely new view of the relations between space, time, matter, and information.
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