The history is full of misconceptions that opposed the progress of physics. The book starts with reviewing some historical cases, such as the arguments against the Earth rotation, or the famous problem of ¾ in the theory of electromagnetic mass of electron. After having pointed out that misconceptions have been common in the history of physics, it is argued that they must be present today as well. In fact, it is now commonly being realized that in the last forty years there has been no significant progress in the fundamental theoretical physics. A reason certainly lies in certain stumbling blocks on our way towards the unification of interaction and of gravity with quantum mechanics. The author discusses what he perceives as some persisting misconceptions that have not yet been recognized as such by physics community in general.
Author(s): Matej Pavsic
Publisher: World Scientific Publishing
Year: 2020
Language: English
Pages: 256
City: Singapore
Contents
Preface
Acknowledgement
1. About Historical Misconceptions in Physics
2. Higher Derivative Theories and Negative Energies
2.1 Negative energies and stability
2.2 Unequal masses, unequal tension: Special cases of generic metric
2.3 Collision or scattering of two particles
2.4 Positive and negative masses
2.5 Discussion
3. Upon Quantization — Ghosts or Negatives Energies?
3.1 Illustrative example: The system of two equal frequency oscillators
3.2 Interacting quantum oscillator
3.3 On the stability of higher derivative field theories
3.4 Conclusion
4. Transformations of Spinors
4.1 Transformations of Clifford numbers
4.2 Clifford algebra and spinors in Minkowski space
4.3 Four independent spinors
4.4 Behavior of spinors under Lorentz transformations
4.4.1 Rotation
4.4.2 Space inversion
4.5 Generalized Dirac equation (Dirac-K¨ahler equation)
5. Quantum Fields as Basis Vectors
5.1 Introduction
5.2 Clifford space as an extension of spacetime
5.3 Generators of Clifford algebras as quantum mechanical operators
5.3.1 Orthogonal and symplectic Clifford algebras
5.3.2 Equations of motion for a particle’s coordinates and the corresponding basis vectors
5.3.3 Supersymmetrization of the action
5.4 Basis vectors, Clifford algebras, spinors and quantized fields
5.4.1 Spinors as particular Clifford numbers
5.4.2 Quantized fields as generalized Clifford numbers
5.4.3 The action and field equations
5.5 Towards quantum gravity
5.5.1 Gravitational field from Clifford algebra
5.5.2 Fermion creation operators, branes as vacuums, branes with holes, and induced gravity
5.6 Quantized fields and Clifford space
5.7 Conclusion
6. Brane Space and Branes as Conglomerates of Quantum Fields
6.1 Introduction
6.2 Brane as a point in the brane space M
6.3 Special case: Flat brane space M
6.4 An interacting bunch of scalar fields
6.5 Generalization to arbitrary configurations
6.5.1 Non interacting case
6.5.2 Bunch of Stuckelberg fields interacting in a particular way
6.5.3 Self interacting Stueckelberg field in configuration space
6.6 Conclusion
7. Particle Position in Quantum Field Theories
7.1 Manifestly covariant formulation of a scalar field quantum theory
7.2 States with indefinite position or momentum
7.2.1 Wave packet profiles for a Hermitian and non Hermitian scalar field
7.2.2 The action principle for the wave packet profiles and conserved currents
7.2.3 Working with field operators
7.2.4 The action principle for creation operators and conserved currents
7.2.5 The action principle for states
7.2.6 The scalar product between states at different times: The propagator
7.3 Motion of wave packets
7.4 What about causality violation?
8. Misconceptions and Confusion About Tachyons
8.1 Introduction
8.2 The superluminal transformations of extended relativity
8.3 Formulating extended relativity in real spacetime M4,4
8.4 Klein-Gordon equation in Clifford space
8.5 Tachyons and causality
8.6 Conclusion
9. Ordering Ambiguity of Quantum Operators
9.1 Introduction
9.2 Geometric definition of momentum
9.3 The equations of motion for the expectation value of momentum
9.4 On the integration of vectors in curved space
9.5 Conclusion
10. What Have We Learned?
Bibliography
Index
