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More-skeptical reviews can be found in my physics parodies. A more technical analysis can be found at "Warren Siegel's research". Predictability The main problem in high energy theoretical physics today is predictions, especially for quantum gravity and confinement. An important part of predictability is calculability. It is easy to write down the most general theory consistent with special and for gravity, general relativity, quantum mechanics, and field theory, but it is too general: The spectrum of particles must be specified, and more coupling constants and varieties of interaction become available as energy increases.

The solutions to this problem go by various names -- "unification", "renormalizability", "finiteness", "universality", etc.

Solving the Impossible in Quantum Field Theory - Space Time

Unfortunately, most solutions to these problems simply sweep them under the rug, solving one form of the problem and replacing it with another: For example, "renormalization", a systematic way of eliminating infinities in certain calculations, eliminates ambiguities at one stage only to have them reappear later. Other approaches look only at "low" energies, and thus effectively ignore most of the problem altogether.

Quantum Field Theory of Point Particles and Strings

But "low" might be ridiculously high by current standards for very weak forces, such as electromagnetism or gravity. If the observable dimensions are constrained to 4, predictive power is lost. However, useful particle models can be accomodated. When the infinite number of terms is summed to find an exact answer, predictive power is lost in the absence of supersymmetry. Thus, particle theory predicts supersymmetry. Known string theories have serious difficulties already at low orders of perturbation in the absence of supersymmetry, so string theory predicts supersymmetry. However, treating the graviton as a fundamental particle leads to a loss of predictability, even at low orders of perturbation.

A possible alternative is to treat the graviton as a composite state of other particles: Such theories have been constructed, but have not yet been shown to be predictive. The existence of the graviton is required by known string theories, and thus predicted: This is true for the superstring, which has maximal supersymmetry although it may be hidden in some formulations.

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It is also true for the bosonic string; however, that string has some consistency problems. Known string theories retain their predictive power in their critical dimension at all orders of perturbation; however, summation leads to the kind of effects hidden dimensions that are expected to destroy predictability. Thus the very existence of black holes in a theory of gravity indicates its inadequacy.

However, black hole singularities might be avoided by formulations in "Euclidean space", with imaginary time. Black hole solutions are not expected in a composite-state theory of gravity. Some advantages are found in the description of black holes, but the situation is unclear. Observed matter quarks and leptons can be unified, resulting in a unification of forces less gravity, plus yet unseen forces , but requiring many yet unseen and un-unified "Higgs scalars" to break the symmetry.

Supersymmetry introduces unseen particles as least as numerous as the known ones, and thus is not truly unifying. String theories are essentially unique in their critical dimension, and unify all forces and particles, including gravity. Strings can describe properties of hadrons of all mass, and agree with qualitative properties of hadron scattering.

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But known string theories don't fit well to experiment, since they include massless hadrons. Both particle and string theory have difficulty with unification. Both theories predict supersymmetry. Unfortunately, it hasn't been observed yet. Such strings would not contain gravity, since hadrons have no corresponding massless "strong graviton". They would be based on the particle theory of quarks and gluons. Perhaps some generalization would include both hadrons and gravitons.

Possible solution: A composite graviton might be necessary to solve the gravity problem in particle theory. Thus particle theory and string theory would be unified, and this unification would be a requirement to solve the problems of both theories.

Quantum Field Theory

In fact, at least one of the known strings can be expressed as a composite of particles, but this particle theory has serious problems, probably related to those of the string theory. Is string theory a waste of time? Considering that string theory has close to a monopoly on high energy theoretical physics nowadays, yet in over 40 years has failed to reach its promised goal, panic can easily set in about the future of this area of research.

In response to the above question, I can think of at least 4 answers: Don't blame the product for the advertisement. String theory has been grossly over-sold.

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It isn't even a "theory" yet, just a "model". It hasn't solved anything, much less everything. Part II emphasizes the quantization of the bosonic string. The treatment is most detailed in the path integral representation where the object of interest, the partition function, is a sum over random surfaces.

The relevant mathematics of Riemann surfaces is covered. Superstrings are briefly introduced, and the sum over genus 0 supersurfaces is computed. The emphasis of the book is calculational, and most computations are presented in step-by-step detail. In many cases, identical results are worked out in each representation to emphasize the representation-independent structures of quantum field theory.