The discussion centers on the understanding of Lorentz transformations in special relativity, specifically whether they accurately represent events in the primed reference frame (O') or merely reflect the perspective of the non-primed reference frame (O). Participants express confusion about the algebraic application of these transformations, particularly in relation to time dilation and length contraction. Key points include the necessity of considering the relativity of simultaneity and the importance of transforming both spatial and temporal coordinates to avoid contradictions. The conversation highlights that Lorentz transformations must yield consistent results when applied in both directions between frames.
PREREQUISITESStudents and educators in physics, particularly those studying special relativity, as well as anyone seeking to clarify concepts related to Lorentz transformations and their applications in understanding relativistic effects.
davidbenari said:I don't see how relativity of simultaneity is important
In the case of time dilation, both observers will consider the other one's clock slow. This sounds like a contradiction until you realize that statements about an observer's point of view are really statements about numbers assigned by a coordinate system that we associate with his motion. Since the two observers move in different ways, we associate different coordinate systems with their motions. So there's nothing inherently contradictory about a disagreement between two observers describing the same thing in different ways. Look at an object that's now on your right. An observer at your location facing the opposite direction would say that the object is to the left. This is clearly not a contradiction.davidbenari said:But equation with t'a=t'b yields something of the form x'<x. While equation with ta=tb yields something of the form x<x'. Why isn't this contradictory?