Question about Einstein's train and lightning

[robert Ihnot]

Einstein wrote about a long train that experienced bolts of lighting hitting on both ends. Einstein tells us that a midway observer on the ground would see both bolts at the same time, but the midway observer on the train would have moved off from the same ground point because of the time it takes the flash to travel.

Now if you look at this problem using the Lorentz transform, it is not true that momentum of the train is important to the Galilean observer aboard the train, writing for the transform C+V and C-V?

This problem would not occur for the ground observer, but there is still the question if the bolts came straight down on both ends of the train, how does the bolt now instantly travel at right angles to the ground to meet at the midpoint of the tracks?

 

[Doc Al]

Einstein wrote about a long train that experienced bolts of lighting hitting on both ends. Einstein tells us that a midway observer on the ground would see both bolts at the same time, but the midway observer on the train would have moved off from the same ground point because of the time it takes the flash to travel.

The lightning bolts strike the ends of the train simultaneously according to the ground observers. And since, again according to the ground observers, the train moves during the time it takes light to travel to the midpoint observer, the light from each lightning bolt cannot reach the midway observer at the same time. From this one can deduce (by appealing to the principle that the speed of light is the same for all observers) that according to the train observers the light flashes were not simultaneous.

Now if you look at this problem using the Lorentz transform, it is not true that momentum of the train is important to the Galilean observer aboard the train, writing for the transform C+V and C-V?

I'm not sure what you are talking about here, since you mention Lorentz transforms and Galilean observers in the same breath. According to ground observers, the speed of the train is V and the speed of light is C. Thus according to ground observers the rate at which the light reaches the midpoint is C+V for one flash and C-V for the other.

This problem would not occur for the ground observer, but there is still the question if the bolts came straight down on both ends of the train, how does the bolt now instantly travel at right angles to the ground to meet at the midpoint of the tracks?

Think of the lightning bolts as flashes of light that occur at the ends of the train. The light emanates outward from each flash. (Just like turning on a light bulb.) The bolt doesn't travel to the midpoint, just the light from the bolt. (You can see a lightning bolt strike someplace miles away because the light travels from the bolt to your eyes. That doesn't mean the lightning bolt strikes you!)

 

[Entropia]

First of all, it is important to note that Einstein's thought experiment using the train and lightning bolts is a simplified scenario used to explain the concepts of relativity. It is not meant to be taken as a literal representation of real-life events.

That being said, the Lorentz transform does play a role in understanding this scenario. According to the Lorentz transform, the time and distance measurements of events are relative to the observer's frame of reference. In the case of the train and lightning bolts, the midway observer on the train would see both bolts at the same time because they are in the same frame of reference. However, the ground observer would see the events happening at different times because they are in a different frame of reference.

As for the question about the bolts coming straight down on both ends of the train and then traveling at right angles to meet at the midpoint of the tracks, this can be explained by the concept of time dilation. As the train is moving at a high speed, time is passing slower for the observer on the train compared to the observer on the ground. This means that the bolts of lightning would appear to take longer to reach the midpoint of the tracks for the observer on the train, while for the ground observer, the bolts would appear to reach the midpoint at the same time. This can be seen as the bolts "bending" in order to meet at the midpoint from the perspective of the observer on the train.

In conclusion, while the Lorentz transform and time dilation play a role in understanding this scenario, it is important to remember that it is a simplified thought experiment and not a literal representation of events. The main takeaway is that the perception of time and distance is relative to the observer's frame of reference.