### 物理代写|宇宙学代写cosmology代考|Black Holes, Cosmology and Extra Dimensions

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|宇宙学代写cosmology代考|Einstein after Einstein

But let us again avoid “running ahead of the engine” and return to the 20 s and 30 s of last century. It was the time of physics’ active penetration into the micro-world and formation of a language adequate to its properties – quantum mechanics, later quantum electrodynamics and, wider, quantum field theory. The quantum theory was first built in the framework of the old, Newtonian concepts of absolute time and absolute space (nonrelativistic quantum mechanics), and it required substantial effort to extend it to the world of large velocities and high energies and to formulate its content in Minkowski’s four-dimensional space-time.

The understanding of gravity as space-time curvature endowed GR with an exclusive character as compared to all the rest of physics, and this was in conflict with the feeling of unity of the material world, important for both philosophers and physicists. On the other hand, in GR itself there emerge quite a number of important problems, one of which is known as the problem of energy. The notions of energy and other conserved quantities play a very significant part in the structure of quantum theory. In flat space, one easily formulates the energy, momentum and angular moment conservation laws due to the symmetry of Minkowski space with respect to temporal and spatial translations and rotations, forming the 10 -parameter Poincaré group. In curved space-time there are no such symmetries at all, and it is therefore quite difficult to define the energy and momentum of the gravitational field in GR in a consistent way.

For this and some other reasons, not all physicists have agreed with GR, and even now there are repeated attempts to build a theory of gravity in Minkowski space. Unlike the first attempts of this kind, the new authors have learned to explain the classical observed effects of GR, and gravitation in such theories is represented by a field with normal conservation laws and hopes to be quantized on equal grounds with other physical fields. According to Will’s book [563], as early as in 1960 the number of such theories exceeded 25. But neither then nor afterwards did such theories give rise to really substantial interest (though certainly their followers would not agree with such a conclusion).

## 物理代写|宇宙学代写cosmology代考|The technological breakthrough

By the end of the 1950 s, physics already knew four rather than two basic interactions: the gravitational, electromagnetic, strong nuclear (due to which protons and neutrons join to form atomic nuclei) and weak nuclear (which is responsible for many particle transmutations and nuclear reactions of which the most well-known is beta decay). Among them, the gravitational interaction appeared to be something of minor importance: for particles, being much weaker than even the weak interaction, it seemed absolutely insignificant in micro-world physics. The accelerators supplied more and more new experimental data about the other three interactions, and quantum field theory in flat Minkowski space experienced rapid progress, formulating and solving various problems of particle physics. Against such a background, gravitational studies seemed to be something of extravagance. Yes, GR was recognized as a fundamental, almost philosophical theory, important for the world outlook, but its experimental basis was too poor: one effect, Mercury’s perihelion advance, was checked up to $1 \%$, and another, light bending near the Sun, up to roughly $30 \%$. The cosmological observations could only testify to a nontrivial geometry of the Universe but could tell us nothing about the validity of particular gravitational equations… Kip Thorne, at that time a student and now one of the most famous gravitational physicists, was advised by his professors not to deal with GR, which, in their opinion, was a theory very weakly connected with the rest of physics and astronomy. He did not obey such an advice and, as far as we can guess, hardly regrets now.

## 物理代写|宇宙学代写cosmology代考|To quantize or not

As already pointed out, the experiment entirely supports GR. However, the picture is not so unclouded in theory. We have previously mentioned the gravitational energy problem. Another well-known difficulty of GR is the existence of singularities which emerge in the majority of exact solutions to the Einstein equations and, in particular, they are hidden beyond black hole horizons and occur at the beginning and, in some models, at the end of the cosmological evolution as well as in modeling isolated bodies. These are, to put it simply, the points, lines or surfaces where the space-time loses smoothness and the quantities characterizing the curvature become either indefinite or infinite. Singularities may be connected with infinite matter densities or pressures, but there also exist purely geometric singularities, such as those in solutions to the Einstein equations in vacuum, in the absence of any matter. The inevitability of singularities in GR solutions has been proved under very general and reasonable conditions in a number of theorems, and this clearly indicates that GR is apparently not very precise in its description of extremely strong gravitational fields.

Unlike event horizons, i.e., black hole boundaries (distinguished but quite regular surfaces that work according to the remarkable principle “everybody can come in, nobody can go out”), singularities represent a real problem for the theory since they indicate, on the

basis of the theory itself, the places where it does not work any more. Thus GR itself prompts to the necessity of going out of its own framework. How to do that? It is a question of great importance, the subject of many studies and discussion, maybe a question outside the framework of not only gravitation theory but physics as a whole.
It seems natural, for example, to try to account for quantum phenomena.

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## MATLAB代写

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