The speed of light c in a vacuum , is constant relative to its point of origin.
It should be emphasized that the time dilation is a result of the frame moving with respect to light,
not motion relative to another frame.
The equations verify this fact.
Wallace said:Hmmm, that doesn't seem any simpler than typical textbook explanations and I'm not sure that it's correct in any case.
Is not true. The speed is constant relative to all observers!?
I should hope not!
phyti said:Where in the expression for time dilation do you see a factor for another frame of reference? It's only v and c!
G01 said:t = \frac{t_p}{\sqrt{1-\frac{v^2}{c^2}}}
What about t and t_p? One is a factor from one reference frame, the other from a different reference frame, so, no, it isn't only v & c there are the times. Plus v is the speed of a reference frame, so that is another factor relating to reference frames. Sorry, but you can't really get rid of the concept of reference frames moving relative to each other here.
Huh? You refer to "the speed v of Al's frame", but don't talk about the other frame. "v" is certainly not the speed of the frame with respect to the light signals, whatever that might mean. (Why v and not 2v or 3.5v? Where does the v come from?)phyti said:The t and v are for the observer moving
with the clock relative to the light signals.
An "event" is not a reference frame. The space-time coordinates of an event can be measured from any reference frame.The only other reference frame besides the observer is the event (the emission of light).