Two events occur simultaneously at separated points on the y axis of reference frame S. According to an observer moving in the positive x direction

Options

A. The event with the greater y coordinate occurs first
B. The event with the greater y coordinate occurs last
C. Either event might occur first, depending on the observer's speed
D. The events are simultaneous

Answer

To solve the problem, we need to analyze the situation of two events occurring simultaneously in a reference frame S and how they are perceived by an observer moving in the positive x-direction.

### Step-by-Step Solution:

1. **Identify the Events**:
Let's denote the two events as Event A and Event B. Assume Event A occurs at coordinates (0, y1) and Event B occurs at (0, y2) on the y-axis, where y1 and y2 are the y-coordinates of the events.

2. **Simultaneity in Frame S**:
In the reference frame S, both events occur simultaneously. This means that the time coordinate for both events is the same, i.e., t_A = t_B.

3. **Observer's Motion**:
Now consider an observer moving in the positive x-direction. This observer is not at rest in frame S and will perceive the timing of the events differently due to the effects of relativity.

4. **Lorentz Transformation**:
To analyze how the observer perceives the events, we can use the Lorentz transformation equations. The time coordinate in the moving frame (let’s call it S') is given by:
\[ t' = \gamma \left( t - \frac{vx}{c^2} \right) \]
where \( \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} \), v is the velocity of the observer, and c is the speed of light.

5. **Calculate the Time for Each Event**:
- For Event A (at (0, y1)):
\[ t'_A = \gamma \left( t - \frac{v \cdot 0}{c^2} \right) = \gamma t \]
- For Event B (at (0, y2)):
\[ t'_B = \gamma \left( t - \frac{v \cdot 0}{c^2} \right) = \gamma t \]

6. **Conclusion on Simultaneity**:
Since both events occur at the same time in frame S, the observer moving in the positive x-direction will also see them as simultaneous. Therefore, the observer will perceive both events happening at the same time, despite their separation in space.

### Final Answer:
The observer moving in the positive x-direction will see both events occurring simultaneously.