Theoretical Physics for the Masses

The following sections are included:

• Preface
• Acknowledgements
• Contents

The following sections are included:

• History of Modern Theoretical Physics
  • Discovery of subatomic particles
  • Unified field theories
• Organization of Book

The theory of relativity considers the special theory developed in 1905. This theory, as described in Section 2.1, applies to physical phenomena without gravity. The general theory proposed in 1915, as detailed in Section 2.2, further explains the laws of gravity. Relativity helped to transform the basis of theoretical physics. It superseded Sir Isaac Newton’s theory of mechanics detailing the laws of motion of macroscopic and astronomical objects as well as classical gravitational theory.

“Quantum mechanics” in Section 3.1 describes the behaviour of particles. On the other hand, “quantum field theory”, in Section 3.2, treats particles instead as excited states of their underlying quantum fields. Quantum field theory provides a seamless way to integrate quantum mechanics with special relativity. A coupling of quantum mechanics with general relativity is further described in Section 3.3 based on the use of a loop quantum gravity approach…

The Standard Model is based on quantum field theory and predicts almost all known particles and forces in nature other than gravity with high accuracy. It provides a model of particle physics with a theoretical framework for describing three of the four forces of nature (Section 4.1) along with a classification of elementary particles (Section 4.2). The model was developed in the latter half of the 20th century. Its current formulation was presented in the mid 1970s with experimental confirmation of quarks. This confirmation included the most recent and important discoveries of the top quark (1995), the tau neutrino (2000) and the Higgs boson (2012).

Currently a single “unified field theory” that encompasses gravity does not exist despite the fact that quantum physics and general relativity were significant theoretical developments in the twentieth century. Quantum calculations are particularly plagued by the occurrence of infinities. This result happens because particle interactions take place at a single mathematical point of zero distance. On the other hand, string theory may offer greater possibilities where interactions do not occur among point particles. Hence, this more generalized theory may possibly offer a unified theory of both particle physics and quantum gravity…

Cosmology involves the investigation of the large-scale structure, dynamics and fate of the universe. It depends on the disciplines of astronomy and particle physics. This field of study accounts for the presence of dark matter and energy, which is parametrized in the model of “Big Bang theory” known as the “Lambda (i.e., for inclusion of the cosmological constant)-cold dark matter (CDM) model”. The universe is thought to have begun with the Big Bang about 13.8 billion years ago. It underwent an immediate expansion of space as a result of cosmic “inflation”…

A black hole is a region of space–time where particles and/or electromagnetic radiation are unable to escape the strong gravitational forces generated by a sufficiently compact mass that can deform space–time. There is no escape from the boundary of a black hole, which is called the “event horizon”. In accordance with the general theory of relativity, when an object crosses this boundary, the fate of an in-falling object is sealed as the space–time interval for the spatial position switches with the temporal one so that one cannot escape the black hole. Locally, however, there are no detectable features for an observer that crosses the event horizon…

There still remain important questions in theoretical physics yet to be resolved or new theories to be advanced and developed. Such phenomena still not understood include the following:

• (i) A rigorous quantum field theory, with interactions as constructed in four-dimensional space–time, does not exist to replace the current theory that must resort to perturbative methods of solution.
• (ii) A complete theory of fundamental interactions does not exist. For instance, general relativity is a classical theory. A quantum theory of gravity would require a fully-consistent and unified theory of quantum mechanics and general relativity that is supported by experimental and observational evidence. In addition, a full unification of the electroweak force with the strong force (i.e., quantum chromodynamics theory) is needed for all particle energies. Currently, an ad hoc theory has been developed where the electroweak and strong forces act separately in the standard model and are therefore not truly unified. Gravity remains a separate stand-alone classical theory as one of the four fundamental forces of nature. As a hierarchical problem, it is not clear why gravity is such a weak force compared to the other fundamental forces of nature.
• (iii) The standard model does not account for neutrino oscillations and their non-zero masses. In particle physics, an explanation for the discrepancy between the measured and theoretical value of the anomalous magnetic dipole moment is needed. It is also not understood why there are three generations of quarks and leptons in particle physics.
• (iv) The standard model does not contain any viable particle candidates for dark matter that possess the required properties as deduced from observational cosmology. In addition, there is no specific theory accounting for the accelerating nature of the expansion of the universe, as purposed with the concept of “dark energy” in cosmology. It is not clear why the mass of the quantum vacuum does not directly affect the expansion of the universe.
• (v) There is an observed matter-antimatter asymmetry in nature. This asymmetry includes an imbalance in the baryonic matter as experienced in everyday life as well as antibaryonic matter existing in the observable universe. Neither the standard model of particle physics nor the general theory of relativity can explain this asymmetry. The Big Bang, in reality, should have produced equal amounts of matter and antimatter. Thus, some physical laws must have acted differently during the evolution of the universe to explain this imbalance of matter and antimatter in the baryogenesis process.
• (vi) In the current formulation of chromodynamics theory, a violation of charge-parity(CP)-symmetry in strong interactions can occur. Nevertheless, no violation has ever been observed in any experiments involving this type of interaction. Thus, the observed conservation of CP in particle physics suggest a “CP-problem” in the present standard model. Also, it is not understood why magnetic monopoles do not exist in nature, which are important for understanding the dynamics of strongly coupled gauge fields such as in quantum chromodynamics.
• (vii) The physical nature of the hypothetical inflaton scalar field, which gave rise to cosmic inflation in the early universe, is not known.
• (viii) There is no physical evidence to show that black holes irradiate thermal energy, which has only been suggested on theoretical grounds. With black hole evaporation, there is a loss of information that occurs giving rise to an information paradox for evaporating black holes. Black hole evaporation is specifically predicted in accordance with classical theories suggesting again the need for a quantum gravity theory. A quantum gravity theory is needed to explain phenomena near the singularity of a black hole with extreme densities where gravity is so strong that space–time itself breaks down catastrophically.

The following sections are included:

• Classical Theory
  • Classical Mechanics
    • Lagrangian
    • Hamiltonian
  • Maxwell’s Equations
• Theory of Relativity
  • Special Relativity
    • Lorentz transformation
    • Time dilation
    • Length contraction
    • Relativistic energy
  • General Relativity
    • General field equations
    • Newtonian limit
    • Gravitational waves
    • Unification of gravity and electromagnetism
  • Experimental Tests of General Relativity Theory
    • Advance of the perihelion of mercury
    • Bending of light
    • Gravitational red-shift
• Quantum Theory
  • Quantum Mechanics
    • Uncertainty principle
  • Quantum Field Theory
    • Quantization
    • Feynman’s path integrals
  • Loop Quantum Gravity
• The Standard Model
  • Spontaneous Symmetry Breaking
  • The Higgs Mechanism
  • Langrangian Functions of the Standard Model
    • Quantum field theory fundamentals
• String Theory
  • Extended Dimensions for an Open Boson String
  • Compactification in a Closed Boson String
• Cosmology
  • Friedmann Model
  • Fluid Equation
  • Acceleration Equation
  • Geometry and Evolution of the Universe
    • Hubble’s law
    • Evolution of the universe
    • Astronomical observations
    • The inflationary universe
    • The cosmological constant problem
  • Black Holes
    • Black Hole Mechanics
    • Field Equations
    • Event Horizon
  • Glossary

The following sections are included:

• Bibliography
• Index