Note 409(3): Equivalence of Lorentz boost and Thomas Rotation
Many thanks, agreed with your insight below, the boost and Thomas rotation (more accurately the generally covariant ECE2 rotation) produce the same gamma factor when the rotation takes place at the Newtonian velocity. These important insights can go into your new textbook. Your Eq. (1) is an elegant result which can be used in the final paper. In Eq. (41) only the spacelike part is transformed so the timelike part is the same, so there is no prime. The prime in Eq. (43) was a typo, only the spacelike part is rotated. On the other hand the Lorentz boost as you know is a four rotation in which both timelike and spacelike parts change.
Note 409(3): Equivalence of Lorentz boost and Thomas Rotation
This note makes finally clear that the gamma factor for rotations is the same as for translations. In particular linearly moving and rotating systems can be handled by the same covariant frame formalism without principal approximations. This is a remarkable progress over Einstein’s special relativity.
According to the previous note, eq.(47) can be written (the ordering has been messed up by Maxima):
with
.
A question: Why is no primed "t" in eq.(41)? In eq.(43) it has been primed as expected.
Horst
Am 17.06.2018 um 12:17 schrieb Myron Evans:
Note 409(3): Equivalence of Lorentz boost and Thomas Rotation
This note shows that the Thomas rotation at the Newtonian velocity is a type of four rotation, Eq. (43) taht immediatly produces the relativistic kinetic energy , hamiltonian, lagrangian, total energy and Thomas half . The Thomas rotation produces all the fundamental concepts of ECE2 covariant physics in a simpler way than the four rotation (8) that defines the Lorentz factor and Lorentz boost. In order to define concepts from Eq. (8), additional considerations are needed, such as the work done, Eq. (17). The static ECE2 line element Eq. (13) produces the same relativistic kinetic energy as the Thomas rotated line element. However the latter method also produces an observable precession, while the Lorentz boost does not. The Thomas rotation is the origin of all precessions, such as planetary precession and pendulum precession. UFT406 shows that the planetary precession theory of EGR is completely wrong because it omits de Sitter and Lense Thirring precessions.