The Mechanics of Lorentz Transformations by Taha Sochi

Author:Taha Sochi [Sochi, Taha]
Language: eng
Format: azw3
Publisher: UNKNOWN
Published: 2018-10-24T16:00:00+00:00

γ[tB − (vxB ⁄ c2)] − γ[tA − (vxA ⁄ c2)] =

γ[(tB − tA) − (v ⁄ c2)(xB − xA)]

where the subscripts A and B correspond to VA and VB respectively. In fact, Eq. 149↑ may be seen as a special case for the last equation that corresponds to t’A = tA = xA = 0 which is inline with the state of standard setting where VA occurred at the common origin of space and time. This fact may also be demonstrated by writing the last equation as: (156) Δt’ = γ[Δt − (v ⁄ c2)Δx]

where the similarity between the last equation and Eq. 149↑ is more obvious since the two equations are identical apart from the Δ symbol which is just a notational artifact.

An important feature of Lorentz transformations is that when there is a relative motion between two inertial frames then both space (in the x dimension which is the dimension of motion according to the state of standard setting) and time coordinates are defined in each frame in terms of both space and time coordinates in the other frame, as seen in Eqs. 146↑ and 149↑ and in Eqs. 151↑ and 154↑. Hence, space and time are entangled in the formalism of Lorentz mechanics to form a single spacetime manifold. Another important feature of Lorentz transformations is the Lorentz γ factor which makes the spacetime coordinates dependent on the speed of the relative motion between the frames. Both these features are Lorentzian and hence they do not exist in the classical Galilean transformations (although there is a temporal factor in the spatial x transformation).

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.