On Tue, Jan 14, 2025 at 12:02 AM Alan Grayson <[email protected]> wrote:
> Using the LT, we have the following transformations of Length, Time, and > Mass, that is, > x --->x', t ---> t', m ---> m' > The length contraction equation is not part of the Lorentz transformation equations, the x --> x' equation in the LT is just about the position coordinate assigned to a *single* event in each frame. The length contraction equation can be derived from the LT but only by considering worldlines of the front and back of an object, and looking at *pairs* of events (one on each of the two worldlines) which are simultaneous in each frame--length in a given frame is just defined as the difference in position coordinate between the front and back of an object at a single time-coordinate in that frame, so it requires looking at a pair of events that are simultaneous in that frame. The result is that for any inertial object, it has its maximum length L in the frame where the object is at rest (the object's own 'rest frame'), and a shorter length L*sqrt(1 - v^2/c^2) in a different frame where the object has nonzero velocity v. The t ---> t' equation is likewise not the same as the time dilation equation, it's just about the time coordinate assigned to a single event in each frame, although it has a simpler relation to time dilation since you can consider an event on the worldline that passes through the origin where both t and t' are equal to 0, and then the time coordinates t and t' assigned to some other event E on this worldline tell you the time elapsed in each frame between the origin and E. And the LT don't include any mass transformation equation. Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/CAPCWU3Leb0WzoLCuvnjEdMbE5C4dHJvZEaodng_gsnGx58bdOQ%40mail.gmail.com.
