Relativistic Lightning on Train Problem

In summary, the conversation discusses a question about the simultaneity of two lightning bolts to an observer on a train and on the ground. The answer suggests using the constancy of the speed of light to explain how the perception of simultaneity differs between the two observers. The question is related to the principles of special relativity.
  • #1
TFM
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0

Homework Statement



Suppose the two lightning bolts shown in the figure 37.5a in the txtbook are simultaneous to an observer on the train.

Show that they are not simultaneous to an observer on the ground.

(Relevant Diagram Attached)

Homework Equations





The Attempt at a Solution



Thios is a long written Answer of Mastering Physics, but I am not quite sure what soirt of answer they are looking for, any ideas would be greatly appreciated,

TFM
 

Attachments

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  • #2
Hi TFM! :smile:

Assuming they don't want you to use the Lorentz transformations …

… my guess is that they want you to draw in rays of light going between Mavis and A´ or B´,

and then describe how Stanley sees those rays. :smile:
 
  • #3
Assuming that the train is moving, then surely the lightning bolts will travel equal distances to Mavis in the middle as they have to travel equal distances, but to Stanley, they rays have to travel different distances. But this doesn't seem to be related to relativity?

TFM
 
  • #4
TFM said:
… But this doesn't seem to be related to relativity?

Hi TFM! :smile:

It's related to the constancy of the speed of light.

The question is designed to make you see that once we assume that everyone regards the speed of light as c, then the whole of special relativity follows! :smile:
 
  • #5
That makes Sense!

Thanks for the Advice, Tiny-Tim :smile:

The Ferry Man
 

What is the "Relativistic Lightning on Train Problem"?

The Relativistic Lightning on Train Problem is a thought experiment that explores the concept of relativity in physics. It involves a train moving at a high speed and two lightning strikes that occur simultaneously on either end of the train, as observed by a person on the train and a person outside of the train.

What is the significance of this thought experiment?

The Relativistic Lightning on Train Problem helps to illustrate the principles of special relativity, which states that the laws of physics are the same for all observers in uniform motion. It also highlights the concept of time dilation, where time appears to pass slower for objects moving at high speeds.

How does the problem challenge our understanding of time and space?

The problem challenges our understanding of time and space by demonstrating that they are relative concepts and can be perceived differently by different observers depending on their relative velocities. It also shows that the speed of light is constant for all observers, regardless of their frame of reference.

What are the different perspectives in the problem?

The problem involves two different perspectives - one from the person on the train and one from the person outside of the train. The person on the train sees the lightning strikes occurring at the same time, while the person outside of the train sees a time difference between the two strikes due to the speed of the train.

How does the problem relate to real-world phenomena?

The Relativistic Lightning on Train Problem has real-world applications in understanding and predicting the behavior of particles at high speeds, such as in particle accelerators. It also helps to explain the phenomena of time dilation, which has been observed in experiments with atomic clocks on airplanes and satellites.

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