Why Does t' Include vx/c² in Lorentz Transformations?

[Pochen Liu]

Homework Statement

I don't understand how they were derived

Relevant Equations

*as attached

I understand x' = λ(x - vt) but why does t' = λ(t - vx/c^2)? where does the vx/c^2 come from?
and honestly I don't understand what t' is.

because from what I understand is that t' is the length of time t as observed from the reference frame S'. which means t' = t*λ?

 

[phyzguy]

This Wikipedia page gives a number of different derivations. The easiest (for me) to understand is the one called "Spherical wavefronts of light", which basically follows from the assumption that the speed of light is the same in all reference frames.

 

[PeroK]

Problem Statement: I don't understand how they were derived
Relevant Equations: *as attached

I understand x' = λ(x - vt) but why does t' = λ(t - vx/c^2)? where does the vx/c^2 come from?
and honestly I don't understand what t' is.

because from what I understand is that t' is the length of time t as observed from the reference frame S'. which means t' = t*λ?

It's better to say that $t'$ is the time coordinate of an event in frame S'.

In classical physics we have always $t' =t$. So, no one bothered ever to write $t'$, because $t'$ is always the same as $t$. In SR, of course, the time coordinate is not the same in different frames and, indeed, the Lorentz Transformation transforms the time coordinate from one frame to another.