Mathematical Principles of Theoretical Physics

(Rick Simeone) #1

Chapter 1


General Introduction


1.1 Challenges of Physics and Guiding Principle


2.1 Essence of Physics


Physics is an important part of science of Nature, and is one of the oldest science disci-
plines. It intersects with many other disciplines of science such as mathematics and chemistry.
Great progresses have been made in physics since the second half of the 19th century.
The Maxwell equation, the Einstein special and general relativity and quantum mechanics
have become cornerstones of modern physics. Nowadays physics faces new challenges. A
partial list of most important and challenging ones is givenas follows.



  1. What is dark matter?

  2. What is dark energy?


Dark matter and dark energy are two great mysteries in physics. They gravitational effects
are observed and are not accounted for in the Einstein gravitational field equations, and in the
Newtonian gravitational laws.



  1. Is there a Big-Bang? What is the origin of our Universe? Is ourUniverse
    static? What is the geometric shape of our Universe?


These are certainly most fundamental questions about our Universe. The current dom-
inant thinking is that the Universe was originated from the Big-Bang. However, there are
many unsolved mysteries associated with the Big-Bang theory, such as the horizon problem,
the cosmic microwave radiation problem, and the flatness problem.



  1. What is the main characteristic of a black hole?


Black holes are fascinating objects in our Universe. However, there are a lot of confusions
about black holes, even its very definition.



  1. Quark Confinement: Why has there never been observed free quarks?


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