nswer. Beleve me this is not hard task to switch in 4 dim. You did this but in your space time is independent. I am not sure for my english _expression_ but you think sharp and this means that you can go this way. Why t'c=t(c-v). If you want to synchronize their clocks you need create loop: send and receive signals. Then you will see that clocks go with different speed.    My belief is tha Aleks,     The way I visualize this is from a set of equations that I use to represent the light. Starting with Einstein's explanation of coordinates, we see that he concludes that distance and time are contracted in the direction of the motion.  I have a different idea about this.     Einstein starts out with the idea of motion in the x direction with a beam of light in the same direction for which he gets x'=(x-vt)/(1-v^2/c^2) instead of x'=x-vt. The difference I have with Einstein is that he also uses the equations y'y,z'=z, which do not make sense to me.  How does the light get a distance of y or z in a time of t'?  t' is less time than t.     Now on pages 33 and 34 of Einstein's book there are two more little equations which do make sense.  x=ct, x'=ct'.  The distance light travels in a _frame_ of reference is equal to time in that _frame_ of reference times the speed of light.     Consequently, I took these two little equations and substituted in for x and x' to obtain ct'=ct-vt.   From this we get t'=t(c-v)/c.   This shows a time dilation, but no distance contraction.     Then to show a true representation of what light does in each _frame_ of reference, we say ct=sqrt(x^2+y^2+z^2) and ct'=sqrt(x'^2+y'^2 +z'^2), which shows light expanding in each _frame_ of reference in a sphere with a radius of c times time in that _frame_ of reference.  This is how I visualize light. Robert B. Winn

times time in that _frame_ of reference.  This is how I visualize light. Robert B. Winn You work on light cone. And realy, if you picture how light distributes in your reference _frame_, you will see sphera. Lihgt does not know that his source moves. He left it and spoke good bye. The last paragragh that you wrote does not have relation for all another. This is what was postulated before. Time dilation that follows from special relativity was proved in nature a lot of time. In particular, physics have it in mind when work with accelerator. For instance synchrophasatron. Another case cosmic rays. There are a lot of particles there that cannot reac earth according Newton mechanics. Physics were surprised by this fact but then they remind what speed cosmic rays have. Aleks Kleyn

lot of time. In particular, physics have it in mind when work with accelerator. For instance synchrophasatron. Another case cosmic rays. There are a lot of particles there that cannot reac earth according These equations I use have a time dilation. t'=t(c-v)/c At about 400 km per second, the time dilation agrees with the Lorentz equation time dilation to about six or seven decimal places.  However, the equation is saying something different about time than the Lorentz equations. Robert B. Winn

saying something different about time than the Lorentz equations. Robert B. Winn You use time dilation that is good approximation for small speed. More exactly it looks like t'=t (1-1/2 v^2/c^2)=t (1-1/sqrt(2) v/c) (1+1/sqrt(2) v/c) When v is small we can ignore second (). sqrt(2)=1.41... . So we can receive your approximation. May be there is another way how you received it. But here you have to be careful. Aleks Kleyn.