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New perspectives in electrodynamics and geometry of space-time
Dear fellow Mechanicians,This paper demonstrates the geometrical and kinematical character of electrodynamics theory and its relation with space and time. It is seen that the theory of electrodynamics essentially is a non-Euclidean geometrical theory with interesting results. The essential meaning of space and time and its relation with matter is also discussed. Based on these observations some difficulties in theory of electrodynamics and modern physics are examined. One can see that continuum mechanics has played an essential role in developing the present theory of motion and interaction.
The most important conclusions are:
Every massive particle specifies a space-time body frame in a universal entity, here referred to as ether.
Particle is a four-dimensional object.
Geometry of uniform and accelerating motion is non-Euclidean.
Space-time is relative and created by matter.
This is the origin of non-Euclidean geometry governing the three vectors and three tensors.
Theory of relative motion is a model for hyperbolic geometry.
Relative motion of particles is the result of relative rotation among their body frames.
Particles interact with each other through four-vorticity and four-stress that they create in the ether.
Fully symmetric Maxwell's equations is not allowed.
Electromagnetic field is a four-dimensional vortex field.
Magnetic field is a circular vorticity field.
Electric field is a hyperbolic vorticity field.
Magnetic monopole is an inconsistent concept.
Geometry governing electrodynamics is non-Euclidean.
A Maxwellian theory of gravity is inevitable.
| Attachment | Size |
|---|---|
 Geom_Electrodynamics.pdf | 1.17 MB |
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Comments
Hyperbolic rotation
Reading your pdf I see extra minus signs in the matrices for several equations including 2.36, 2.37, 2.53, and others. Circular rotations have opposite signs in the counter-diagonal, but hyperbolic rotation requires the same sign. You may be interested in my new entry on "corner flow" on iMechanica.
Hyperbolic rotation
Thank you very much for you interest in my article. As you know the equations 2.36, 2.37 and 2.53 are expressions for Lorentz transformations. The form of Lorentz transformation depends on the choice of representing Minkowskian space-time. I have considered the space-time x1x2x3x4 such that x1x2x3 is the usual space and x4 the axis measuring time with imaginary values x4=ict (see page 3). Therefore, the metric tensor is the unit tensor gmn=diag(1,1,1,1). As a result, we have the correct complex form for Lorentz transformations in equations 2.36, 2.37 and 2.53. You can check this in textbook such as:
Classical Mechanics, Herbert Goldstein, 1980.
Classical Theory of Electromagnetism, Baldassare Di Bartolo, 1991.
If we choose to represent x4 by a real number x4=ct, then we have to consider the metric tensor in the forms gmn=diag(1,1,1,-1) or gmn=diag(-1,-1,-1,1). In these notations the transformations are real and can become similar to the one you have mentioned. We can also realize that the circular rotations and hyperbolic rotations have the correct signs based on the convention I have used.
In the future, please email me directly regarding these kinds of matters, instead of putting comments on iMechanica. Thank you.