# Einstein's relativity of simultaneity - train

Einstein's thought experiment has two lightning flashes at either end of a moving train as seen by an observer on the train, and a platform observer. They disagree on the simultaneity of the flashes.. But if we alter the experiment as follows they will agree on simultaneity. Have the flashes located in front of the train on the rails, front left and front right, with the on train observer equidistant from the flashes. He will see them as simultaneous whether the train is moving or stationary.

The platform observer is positioned on a footbridge in front of the train also equidistant from the flashes, so he also sees the flashes as simultaneous.

Both observers agree on simultaneity. How is this possible ? DAC

• Note: The Lorentz boost in the $x$-direction (where $w=ct,$ $\beta = v/c,$ and $\gamma=1/\sqrt{1-\beta^2}$) says that $w' = \gamma~(w - \beta x)$ and $x' = \gamma~(x - \beta w)$ while $y' = y$ and $z'=z.$ You have given the two events the same $x$-coordinate and $w$-coordinate (albeit different $y$ coordinates) and are surprised that they have the same $w'$-coordinate, but in fact that is the only possibility allowed by the Lorentz boost. Jan 2, 2017 at 15:55