On Thursday, January 16, 2025 at 11:36:48 AM UTC-7 Jesse Mazer wrote:
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're right of course. TY. I see the LT as giving appearances because, say for length contraction, the reduced length is not measured in the primed frame, but that is the length measurement from the pov of the unprimed or stationary frame. About mass, since the measured mass grows exponentially to infinity as v --> c, isn't this derivable from the LT, but in which frame? AG -- 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/80c630e5-a88d-4461-85af-959651c06342n%40googlegroups.com.
