Lightbulb Paradox: Solving John Wheeler's Problem in SpaceTime Physics

[daniel_i_l]

I'm reading SpaceTime Physics by John Wheeler (not for school) and came across a problem that doesn't have answer in the back so i want to see if i understood it properly. the problem goes like this:
You have two parallel wires with a battery and lighbulb connecting one end. on top of the two wires there are two metal bars perpendicular to the wires which are conneceted by nonconducting material. these bars complete the circuit so the lightbulb is on.
Somewere along the wires there is a gap in the top wire which has the length of 2 in the wire's frame. the two bars are moving with a constant velocity relative to the wires so that in the wires frame the distance between them is 1. because of this, when the bars get to the gap the light will turn off when both bars are in the gap and then turn back on.
But in the bars frame the gap has the length of 1 and the distance between the bars is 2 so in this frame the light will not go off since the gap is smaller than the distance between the bars. how can they both be right?

Well, i think that the answer is that in the bar frame the light does turn off and on but these two events happen at the same time. in the wire frame they happen at the same place at different timesand in the the bars frame the happen at different places at the same time. Is this the right solution?
Thanks.

 

[JesseM]

I'm reading SpaceTime Physics by John Wheeler (not for school) and came across a problem that doesn't have answer in the back so i want to see if i understood it properly. the problem goes like this:
You have two parallel wires with a battery and lighbulb connecting one end. on top of the two wires there are two metal bars perpendicular to the wires which are conneceted by nonconducting material. these bars complete the circuit so the lightbulb is on.
Somewere along the wires there is a gap in the top wire which has the length of 2 in the wire's frame. the two bars are moving with a constant velocity relative to the wires so that in the wires frame the distance between them is 1. because of this, when the bars get to the gap the light will turn off when both bars are in the gap and then turn back on.
But in the bars frame the gap has the length of 1 and the distance between the bars is 2 so in this frame the light will not go off since the gap is smaller than the distance between the bars. how can they both be right?

Your description was a little confusing to me, but for those who have access to the book, it's on pp. 186-187.

I would say that the light bulb does turn off and on, and the answer has to do with the fact that the electricity travels at a finite speed through the wire, and no matter which frame you analyze it in, there will be a delay beteen the electricity that was supplied by the bar in the rear (C in the diagram) continuously until it passes the beginning of the gap (A in the diagram), and the electricity that was supplied by the bar in the front (D in the diagram) continuously after the moment it passes the end of the gap (B in the diagram). It might help to imagine the two bars as hoses which are pouring water into a channel representing the wire, with the water flowing at a constant rate through the channel, and with each hose having its nozzle covered during the period it is crossing the gap. Because there is a spacelike separation between the event of C beginning to cross the gap and stopping pouring and the event of D coming to the end of the gap and resuming pouring (you know the separation is spacelike because there's a frame where the two events happen simultaneously, namely the frame where the size of the gap and the distance between the bars are equal), there is no way the water from D's resuming pouring could have reached the point in space and time where C stops pouring, even if the water was flowing at the speed of light.

Well, i think that the answer is that in the bar frame the light does turn off and on but these two events happen at the same time. in the wire frame they happen at the same place at different timesand in the the bars frame the happen at different places at the same time. Is this the right solution?
Thanks.

What are the two events you're referring to? Is one of them the event of the light turning on or off, or are they both the events of the bars passing one end or another of the gap? Either way I don't think there could be any frame where the events happen at the same time, but I would need to understand your proposed solution better to critique it.

 

[daniel_i_l]

The two events are:
1-light turning off
2-light turning on
but after thinking it over a little i see that even though that the rocket sees those two events happening at different places since he's moving relative to the light bulb, he can't see them happening at the same time since they're coming from the same source. your answer sounds better:)
And also, is it true that the answer to most of the paradoxs of this type involving length contraction (like the rod and the barn question in the same book, i think around chapter 3 and the question with the TNT in this chapter) involve physical constraints such as the fact that there's no such thing as completely rigid body together with the relativity of simultanity?
Thanks.