# Equivalence in all inertial frames

Suppose there is a train moving to the right. and inside the train there is an observer, A. Outside the track, there is another observer B. When the train passes in front of B, right at the instant when both the ends of the train are equidistant from B, two lightnings strike the two ends. Now, to A it would appear that one of the lightning hit before the other. Now suppose, that there are devices at the ends of the two trains, which either let a current flow through a particular circuit or it doesn't depending on whether the lightnings hit its ends simultaneously. And the mechanism (on how this device works) is out there for both observers A and B to see. So will A observe a current and B will not, or will both A and B observe a current flowing through them? Assume that current flows if lightning does not hit both ends simultaneously. Since the mechanism is out there for any observer to see, it would appear that if both ends are hit simultaneously to one observer, there shouldn't be any current observed by that observer, right? Or else the laws of physics will seem to be not working properly for that observer or so I think.

• How do you propose this device works? When you work that out you will discover that if the device is at rest in the frame of the train (ie in $A$'s frame), then no current will flow, while if it is at rest in the frame of the station (ie in $B$'s frame), then current will flow. Both observers will agree on this. – tfb Jan 21 at 14:51
• maybe the two ends are connected by some sort of wire with a capacitor in between? when lightning seems to hit one end first, it leaves one end highly charged, causing there to be a flow of current and the capacitor charges and discharges several times before lightning hits the other end? While lightning hitting both ends simultaneously would leave both plates of the capacitor equally charged and hence no flow of current. Maybe. It may be faulty and maybe I'm missing something. I'm not really good at electronics. – Achilles' Advisor Jan 21 at 14:59
• Something like that: some kind of signal gets sent from the points where the lightning strikes and something compares the arrival times of the two signals. Now work out where the centre of the device will end up being when the two signals reach it (a) if it's on the train and (b) if it's in the station. And you can immediately see that if it's in the station, the two signals get there at the same time, while if it's on the train, they don't. – tfb Jan 21 at 15:02