Suppose the two lightning bolts shown in Fig. 37.5a are simultaneous to an observer on the train. Show that they are not simultaneous to an observer on the ground. Which lightning strike does the ground observer measure to come first?

Verified step by step guidance

1. First, understand the concept of simultaneity in the context of special relativity. Simultaneity is relative and depends on the observer's frame of reference. Events that are simultaneous in one frame may not be simultaneous in another.
2. Consider the scenario: there are two lightning strikes, one at the front and one at the back of a train. An observer on the train sees these strikes as simultaneous because the light from both strikes reaches them at the same time.
3. Now, analyze the situation from the perspective of an observer on the ground. The train is moving relative to the ground observer. According to the principles of relativity, the speed of light is constant in all inertial frames, but the train's motion affects the timing of when the light from each strike reaches the ground observer.
4. For the ground observer, the light from the strike at the front of the train has to travel a longer distance because the train is moving forward. Conversely, the light from the strike at the back of the train travels a shorter distance because the train is moving towards the point where the light was emitted.
5. Therefore, the ground observer will see the light from the strike at the back of the train first, followed by the light from the strike at the front. This demonstrates that the events are not simultaneous for the ground observer, and the strike at the back is measured to come first.

Key Concepts

Relativity of Simultaneity

The relativity of simultaneity is a concept from Einstein's theory of special relativity, which states that two events that are simultaneous in one frame of reference may not be simultaneous in another frame moving relative to the first. This occurs because the speed of light is constant in all inertial frames, leading to differences in the perception of time between observers in relative motion.

Inertial Reference Frames

An inertial reference frame is a frame of reference in which an object either remains at rest or moves at a constant velocity unless acted upon by a force. In the context of the question, the train and the ground represent two different inertial frames, each with its own perspective on the timing of the lightning strikes due to their relative motion.

Speed of Light Constancy

The constancy of the speed of light is a fundamental postulate of special relativity, asserting that the speed of light in a vacuum is the same for all observers, regardless of their relative motion. This principle leads to time dilation and the relativity of simultaneity, as observers moving relative to each other will measure the timing of light-based events differently.