Lindgren, J. et al. (2025) Electromagnetism as a purely geometric theory
Lindgren, Jussi and Kovacs, Andras and Liukkonen, Jukka (2025) Electromagnetism as a purely geometric theory [1].
Содержание
1 Резюме
- В статье фактически проводится геометризация Вейля электромагнитного поля.
- Геометризация только полевой части уравнений Максвелла, без среды.
- Статья крайне поверхностная.
- Не стоит никакого внимания.
2 Notes
2.1 Highlight on page 2
2.1.1 Contents
The history of physics may be viewed as a slow progression from particle-oriented concepts towards wave-oriented concepts.
2.1.2 Comment
- Весьма смелое утверждение.
- Кроме того, это не имеет никакого отношения к геометризации.
2.2 Highlight on page 2
2.2.1 Contents
A key milestone in the development of wave oriented concepts was the recognition during the early 20th century that gravity is essentially not a force, but a manifestation of spacetime curvature, due to Albert Einstein in 1915.
2.2.2 Comment
- Странные у них впечатления о парадигмах физики.
2.3 Highlight on page 3
2.3.1 Contents
quantum mechanics is an instrumental theory in the sense that it describes correctly the universe at small scales.
2.3.2 Comment
- Возможно, под термином инструментальная они понимают конструктивная.
2.4 Highlight on page 3
2.4.1 Contents
If electrodynamic force, i.e. the Lorentz force could be related directly to metrics, it directly leads to the explanation of the Zitterbewegung phenomenon and quantum mechanical waves as well.
2.4.2 Comment
- Предполагают соответствие между полем и геометрией.
2.5 Highlight on page 3
2.5.1 Contents
For the above assumptions to work, we would need to be able to establish electrodynamics as a purely geometrical theory.
2.5.2 Comment
- Целью статьи является геометризация электродинамики.
2.6 Highlight on page 3
2.6.1 Contents
It has been the tradition in general relativity that the spacetime is modeled using pseudo-Riemannian geometry.
2.6.2 Comment
- Кажется, им не нравится риманова геометрия.
2.7 Highlight on page 3
2.7.1 Contents
∇σ of the metric tensor gµν
2.7.2 Comment
- Да, им нравится геометризация Вейля.
2.8 Highlight on page 4
2.8.1 Contents
g µν , which make stationary the following functional over the spacetime Ω:
2.9 Highlight on page 4
2.9.1 Contents
g is in the Lagrangian to keep the functional volume form coordinate invariant.
2.10 Highlight on page 4
2.10.1 Contents
where ηνµ is the Minkowski metric, and Aν
2.10.2 Comment
- Строят метрику из плоского Минковского и электромагнитного потенциала.
2.11 Highlight on page 4
2.11.1 Contents
An almost similar construction is also used in the Kaluza-Klein theory, where the four-dimensional part of the five-dimensional metric is having the same structure,
2.11.2 Comment
- Упоминание Калуцы-Клейна.
- Впрочем, далее это не используется.
2.12 Highlight on page 5
2.12.1 Contents
The nonlinear system of partial differential equations depends on the electromagnetic four-potential and of its first and second order covariant derivatives.
2.13 Highlight on page 5
2.13.1 Contents
The nonlinear system of partial differential equations depends on the electromagnetic four-potential and of its first and second order covariant derivatives.
2.14 Highlight on page 5
2.14.1 Contents
we consider a special Weyl geometry
2.14.2 Comment
- Да, используют вейлевскую модель.
2.15 Highlight on page 7
2.15.1 Contents
As in the Weyl space the symmetry properties of the Riemann curvature tensor hold, the rest of the Maxwell’s equations are given by the algebraic Bianchi identity
2.16 Highlight on page 9
2.16.1 Contents
In this section we derive the mathematically simplest formulation of Maxwell’s equation, and shall com- pare it against the above obtained linear Maxwell’s equation.
2.17 Highlight on page 9
2.17.1 Contents
In this section we derive the mathematically simplest formulation of Maxwell’s equation, and shall com- pare it against the above obtained linear Maxwell’s equation.
2.18 Highlight on page 9
2.18.1 Contents
In the early 20th century, it was discovered that the four Maxwell’s equations can be written as a single differential equation of the electromagnetic four-potential field Aν .
2.18.2 Comment
- Они оставляют из уравнений Максвелла только полевую часть.
- Среду даже не рассматривают.
2.19 Highlight on page 9
2.19.1 Contents
In the early 20th century, it was discovered that the four Maxwell’s equations can be written as a single differential equation of the electromagnetic four-potential field Aν .
2.20 Highlight on page 11
2.20.1 Contents
The light-speed circulating v ∥
2.20.2 Comment
- Весьма дискутабельно.
2.21 Highlight on page 13
2.21.1 Contents
The present study shows that first of all electrodynamics and electromagnetism can be made into a pure geometric theory in the spirit of John Wheeler’s geometrodynamics,
2.21.2 Comment
- Ещё раз напоминается, что используется формализм Вейля.
2.22 Highlight on page 14
2.22.1 Contents
Clifford algebra is defined by the multiplication rule of its basis elements.
2.22.2 Comment
- Тут вообще очень плохо написано.
