Recent content by Mike_bb

Hello! When I was proving that coefficient ##a## ##(s'=as)## is equal to ##1##, I noticed that ##(t_1' - t_2')^2## should be constant then the proof works but otherwise it doesn't. ##c^2(t_1'-t_2')^2 - (x_1'-x_2')^2 - (y_1'-y_2')^2 - (z_1'-z_2')^2=a(c^2(t_1-t_2)^2 - (x_1-x_2)^2 - (y_1-y_2)^2 -...

At first, I consider two frames: Frame 1: 1m/s Frame 2: 5m/s; (1-5)m/s and (5-1)m/s => absolute value of relative velocity is 4m/s Then, I consider another two frames: Frame 3: 2m/s Frame 4: 6m/s; (2-6)m/s and (6-2)m/s =>absolute value of relative velocity is 4m/s What's wrong?

martinbn wrote: I wrote in more details as martinbn said above:

##ds_1^2## - interval between two events in frame 1. ##ds_2^2## - interval between the same two events in frame 2. ##ds_3^2## - interval between another two events in frame 3. ##ds_4^2## - interval between the same two events in frame 4.

No. Different pair of events. For two events in the frame 1 and the frame 2: ##ds_1^2## - interval in the frame 1 ##ds_2^2## - interval in the frame 2 For another two events in the frame 3 and the frame 4: ##ds_3^2## - interval in the frame 3 ##ds_4^2## - interval in the frame 4

##ds_1^2## - interval in the frame 1 ##ds_2^2## - interval in the frame 2 ##ds_3^2## - interval in the frame 3 ##ds_4^2## - interval in the frame 4

Hello! Consider two pairs of frames and their velocities (absolute value of relative velocities are the same): 1) Frame 1: 1m/s Frame 2: 5m/s 2) Frame 3: 2m/s Frame 4: 6m/s Absolute value of relative velocities is 4m/s. ##K=4##. Let ##ds_2^2=4ds_1^2## and ##ds_4^2=4ds_3^2##. Now, I want to...

Could you explain how to derive this formula?

fresh_42 martinbn Big thanks!! :smile:

I'm not sure if it's so but the book uses such terms as "very small element f" = "infinitesimal element f" in context of vector ##V## circulation on element f. Perhaps it's the reason why we say about tangent vector as approximation of vector ##V## in infinitesimal scale of element f (or...

You missed one thing that I wrote in post #1. I mentioned about Taylor series as it was written in the book.

The book doesn't use such terms as "tangent space" and "manifold" quite. The book contains a chapter that is devoted to an introduction to vectors and that's all.

Russian book "Theory of electricity". https://scask.ru/k_book_tel.php?id=19 page 38

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected...

It's interpreted as ##(\partial v_x/\partial y)\vec{\hat{x'}}##