We have two sets: set No.1 and set No.2 as in this picture: 
The observer is fixed to set No.1 . He sees set No.1 motionless and observes set No. 2 approaching with velocity 100,000 m/s.
Each set has one lamp and two, so called, touchers. Each set is designed so that if both touchers are touched simultaneously the lamp is turned on otherwise it remains off.
Set No. 2 is approaching set No. 1 so that each toucher in each set will be touched twice by the touchers of the other set.
The observer on set No. 1 observes the distance between touchers in each set 10 meters. He thinks the lamps on set No. 1 will be turned on because touchers in it will be touched simultaneously.
My question: Will the lamp on set No. 2 be turned on? How if an electrical current flowing from one toucher in a set to the other proves simultaneous touching?
Answer
If all the lengths in this diagram are as measured by the observer on set 1 then only lamp 1 will light up, but not lamp 2. When the left "touchers" on each set align in frame 1 then the right touchers will too, because they are both 10 meters separated from the left ones. However, the touchers on set 2 are further than 10 meters apart according to observer 2 while the touchers on set 1 are less than 10 meters apart, so they can never simultaneously align in that moving frame.
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