Einstein's train (simultaneity)

In summary, we have an observer on a moving train car who sees two light signals emitted from each end of the car simultaneously. From the observer's point of view, he must be passing the middle of the train when he sees the lights. As for which signal was sent first, it is possible that neither was sent first and they were both sent at the same time.
  • #1
sunrah
199
22

Homework Statement



We have an observer moving along a moving train car with speed v (assumed to be relative velocity between observer and car). Two light signals are emitted from each end of the car.

a)Where is the observer if he sees both signals simultaneously?
b)From his point of view, which signal was sent first?

Homework Equations


None

The Attempt at a Solution



I simply took the frame in which the observer is at rest and said the train is moving past with speed v. This is the typical Einstein's train scenario with the observer on the platform (except the train is pretty slow). So our observer must be passing the middle of the train when he sees the lights.

But why the second part of the question? So I must be wrong.
 
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  • #2
sunrah said:

Homework Statement



We have an observer moving along a moving train car with speed v (assumed to be relative velocity between observer and car). Two light signals are emitted from each end of the car.

a)Where is the observer if he sees both signals simultaneously?
b)From his point of view, which signal was sent first?


Homework Equations


None


The Attempt at a Solution



I simply took the frame in which the observer is at rest and said the train is moving past with speed v. This is the typical Einstein's train scenario with the observer on the platform (except the train is pretty slow). So our observer must be passing the middle of the train when he sees the lights.

But why the second part of the question? So I must be wrong.

Have you considered the possibility "neither, they were sent at the same time"
 

1. What is Einstein's train experiment?

Einstein's train experiment is a thought experiment proposed by Albert Einstein to illustrate his theory of relativity. In this experiment, there are two observers, one on a moving train and one on the platform. The observers have a synchronized clock and a light at the center of the train and at the center of the platform. The experiment explores the concept of simultaneity, or whether two events happening in different locations can be considered simultaneous.

2. What does the train experiment prove?

The train experiment shows that simultaneity is relative and depends on the observer's frame of reference. In the experiment, the observer on the train sees the light from the center of the train hit the front and back of the train at the same time, while the observer on the platform sees the light hit the back of the train first. This means that what is considered simultaneous in one frame of reference may not be simultaneous in another.

3. How does the train experiment relate to Einstein's theory of relativity?

The train experiment is used to illustrate the concepts of time dilation and length contraction, which are central to Einstein's theory of relativity. The experiment shows that time and space are not absolute, but rather depend on the observer's frame of reference and their relative motion.

4. Can the train experiment be applied to real-life situations?

While the train experiment is a thought experiment, it has real-world applications. Einstein's theory of relativity has been confirmed through numerous experiments and is used in many modern technologies, such as GPS systems. Understanding the concept of simultaneity is also important in fields like astrophysics, where the relative motion of objects can affect the perception of time and space.

5. Are there any limitations to the train experiment?

Like all thought experiments, the train experiment has its limitations. It simplifies the complex concepts of relativity and does not take into account factors such as acceleration and gravity. It also assumes perfect synchronization of the clocks and lights, which may not be possible in real-life situations. However, the experiment remains a useful tool in understanding the fundamental principles of relativity.

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