Understanding Lorentz Factor & Proper Time Invariance

[Dale]

I'm always somewhat in doubt, whether Minkowski diagrams really help.

They really helped me. It was Minkowski diagrams and the concept of four-vectors that made relativity click for me.

I think different students are going to “get it” with different mental tools. So educators need to know and use all of them. Of course, it is ok to have a favorite one and it is ok for that favorite to be different from person to person

 

[nitsuj]

...in a frame where the clock is moving it is measured to be time dilated.

Note that it's not correct to say that the proper time is dilated, because proper time is the length of the spacetime interval, which is frame invariant.

That is, perhaps, a subtle point.

imo is crucial for better understanding.
I find the part I underlined to be VERY well worded. Textbook quality imo. (only thing I can think of is including the spatial separation between measurement taken and the thing being measured. for example "is measured at a distance to be time dilated.")

I get that is very implicit as was mentioned there is relative motion. but feel it may help separate the concepts [proper / dilated time] a bit quicker for those new to them.

 

[nitsuj]

They really helped me. It was Minkowski diagrams and the concept of four-vectors that made relativity click for me.

I think different students are going to “get it” with different mental tools. So educators need to know and use all of them. Of course, it is ok to have a favorite one and it is ok for that favorite to be different from person to person

me too, though of course to a MUCH lesser understanding than you have. (you've explained lots to me years ago)
I found the simple light clock to be very helpful too, for me helped visualize / see it play out.

The Minkowski modeling gets into comparatively more abstracted presentation than the idealized clock imo, but of course is a math tool of sorts, the idealized light clock is just an imaginary thing that helps my simple mind figuratively see the "mechanics" of this "tiny bit" of spacetime physics.