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

• daniel_i_l
In summary, the problem described in the conversation involves two frames of reference, one in which the light turns off and on due to the bars passing through a gap in the wire, and another in which the light does not turn off because the gap is smaller than the distance between the bars. The explanation for this paradox lies in the fact that the electricity traveling through the wire has a finite speed, causing a delay between the bars crossing the gap and the light turning off and on. This is due to the fact that there is a spacelike separation between the events, and no frame can exist where the events occur simultaneously. The solution also involves understanding the concept of length contraction and the relativity of simultaneity.
daniel_i_l
Gold Member
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.

daniel_i_l said:
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.
daniel_i_l said:
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.

Last edited:
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.

## 1. What is the Lightbulb Paradox?

The Lightbulb Paradox, also known as Wheeler's Problem, is a thought experiment proposed by physicist John Wheeler to illustrate the concept of time dilation in special relativity. It involves a lightbulb that is placed in a moving train and the question of whether an observer on the train would perceive the lightbulb to be on for a longer or shorter amount of time compared to an observer outside the train.

## 2. Why is the Lightbulb Paradox considered a paradox?

The Lightbulb Paradox is considered a paradox because it challenges our intuitive understanding of time. According to special relativity, time is relative and can appear to move at different rates for observers in different frames of reference. In the case of the lightbulb paradox, both observers may have different perceptions of the amount of time the lightbulb is on, but both perceptions are equally valid.

## 3. How is the Lightbulb Paradox resolved?

The Lightbulb Paradox is resolved by understanding that time is relative and depends on the observer's frame of reference. In the scenario of the lightbulb, the observer on the moving train is in a different frame of reference than the observer outside the train. This means that they will perceive time differently and there is no absolute answer to the question of how long the lightbulb is on.

## 4. What is the significance of the Lightbulb Paradox?

The Lightbulb Paradox is significant because it highlights the counterintuitive nature of time in special relativity and the concept of time dilation. It also demonstrates the importance of considering frames of reference when making observations and calculations in physics.

## 5. Are there any real-world applications of the Lightbulb Paradox?

While the Lightbulb Paradox is a thought experiment, the concept of time dilation has real-world applications in modern technology. For example, GPS systems have to take into account the difference in time dilation between satellites in orbit and receivers on Earth in order to accurately determine location. This is due to the satellites moving at high speeds and experiencing time at a different rate compared to Earth's surface.

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