Lorentz Transformation and time dilatation

• Main Author: Miodrag Mateljević (Author)
• Format: Book
• Published: Annals of Mathematics and Physics - Peertechz Publications, 2024-01-10.
• Subjects: Research Article
• Online Access: Connect to this object online.

<p>We consider two inertial frames S and and suppose that frame moves, for simplicity, in a single direction: the X -direction of frame S with a constant velocity v as measured in frame S.</p><p>Using homogeneity of space and time we derive a modified Lorentz Transformation (LT) between two inertial reference frames without using the second postulate of Einstein, i.e., we do not assume the invariant speed of light (in vacuum) under LT.</p><p>Roughly speaking we suppose: (H) Any clock which is at rest in its frame measures a small increment of time by some factor s=s(v). As a corollary of relativity theory (H) holds with Lorentz factor 1/γ. For s=1 we get the Galilean transformation of Newtonian physics, which assumes an absolute space and time. We also consider the relation between absolute space and Special Relativity Theory, thereafter STR.</p><p>It seems here that we need a physical explanation for (H). </p><p>We introduce Postulate 3. The two-way speed of light in and -directions are c and outline derivation of (LT) in this setting. Note that Postulate 3 is a weaker assumption than Einstein's second postulate. </p>