This in an excerpt from this book
Modern science and physics in particular, primarily consists of two basic theories, namely the general relativity or particle physics and the theory of gravity. There had been great heights scaled by these two theories taken together in the past, since the very beginning. Hence, it’s highly surprising to accept the fact that the overall picture given by these two theories taken together reflects a higher degree of inconsistency. This inconsistency arises mainly after taking into consideration a part of the theory, the standard model, as a quantum theory while the other, gravity, as a classical theory. At a first glance, it may appear that quantizing general relativity may remove the inconsistencies. If one performs an expansion in terms of Feynman diagrams, the technique used in the standard model, then one finds infinities that cannot be absorbed in a renormalization of the Cosmological constant also known as Newton constant.
In fact as one goes to higher and higher orders in perturbation theory one would have to include more and more counter terms. In other words, the theory is not renormalizable. Hence, the most crucial principle in constructing the so called Standard model is not capable to hold firm. What is more surprising to an observer is the fact that an inconsistent theory could fit in so well with the experiments, apparently explaining it flawlessly. What happens is that quantum gravity effects are usually very small due to the weakness of gravity relative to other forces. The effects of gravity are proportional to the energy or mass, so they see a rise in high energies.
At energies of the order of E ÿ 1019 Gev the strength of gravity would be comparable enough with that other Standard Model interactions. It should never be forgotten that the way we understand Physics today, still cannot account for the most important “experiment” that ever happened in the past: the Big Bang. One of the most startling outcome of this study is that, the Big-Bang theory gets linked with high energy physics and cosmology and in order to understand what happened in the very beginning, the necessity to understand quantum gravity is highlighted.
It interests me to explain the origin of the gauge group, the relations between the three couplings, the remaining parameters of the standard model including what is the reason behind getting three generations, etc. Renormalizability, or mathematical consistency, was a crucial clue for the discovery of the Standard Model. The major challenges faced can be separated, according to in degree of difficulty, in the following hierarchy:
1. Formulate and develop an internally consistent theory of quantum gravity. This actually points to the formation of a theory which reduces at low energies, E ÿ 10^19 Gev, to general relativity but which is capable of allowing one to perform quantum calculations to any order without any hindrance. And in doing that, this theory should be potent enough to be able to deal with problems involving quantum gravity explaining things such as the origin of black hole entropy, etc. These dilemmas involve the idea of gravity but not of the one that directly deals with particle physics as is observable in nature.
2. Capability to incorporate the Standard Model so much so that the theory must hold good at lower energy levels and should be able to make space for fermions, chiral gauge fields
3. Explaining the basic parameters of standard theory or the the theory which is famously known as big bang. The initial singularity in cosmology and its resolution must be understood as well as the reason behind having the standard model. Moreover, the arising of the parameter of Standard model has to be understood along with, which parameters are related, and which parameters (if any)arise as a “historical” accident.
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