# Observers A & B: Rest & Simultaneity

• I
In summary, the discussion is about two observers, A and B, who are at rest with respect to each other. A observes two objects falling from a height and wonders if B will measure different times for the duration of their fall due to their different locations. However, according to the principles of relativity, A and B will actually measure the same time for the objects' fall. This difference only arises when the observers are in relative motion. This concept is also demonstrated in Einstein's train thought experiment. This discussion shows that there cannot be an absolute time, as it is inconsistent with the principle of relativity and the constant speed of light.
Suppose we have two observers A and B and they are at rest. Observer A observes two objects falling from height H (A has same distance between the two objects). Does observer B will measure different times for the duration of falling of the two objects ? (because the two object are not in the same location therefore a finite time interval must exist for the information of their position to reach B).

You mean that A and B are at rest with respect to one another? In that case no, if the impacts are simultaneous for one then they are simultaneous for both (although strictly the presence of gravity makes this more complicated, we can easily arrange things so we can neglect that). B will certainly receive light from the impacts at different times, but relativity is about what happens after you correct for the travel time of light. Observers in relative motion turn out to get different results if they use the same procedure to correct for the travel time, but observers at relative rest (like your A and B) get the same result.

I assume you've heard of Einstein's train thought experiment? The point is not that the observers receive the light at different times, but that they put different interpretations on what they see.

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Ibix said:
You mean that A and B are at rest with respect to one another? In that case no, if the impacts are simultaneous for one then they are simultaneous for both (although strictly the presence of gravity makes this more complicated, we can easily arrange things so we can neglect that). B will certainly receive light from the impacts at different times, but relativity is about what happens after you correct for the travel time of light. Observers in relative motion turn out to get different results if they use the same procedure to correct for the travel time, but observers at relative rest (like your A and B) get the same result.

I assume you've heard of Einstein's train thought experiment? The point is not that the observers receive the light at different times, but that they put different interpretations on what they see.
I think i get it. The difference come when they move relative to each other. This is why we can't have an absolute time ? Thanks for the response.

This is why we can't have an absolute time ?
Strictly, it's one way to show that a global notion of time is inconsistent with an invariant speed of light and the principle of relativity. You then need to go out and do an actual experiment to see if it's consistent with reality. Which we've done, and so far it is consistent.

## 1. What is the concept of "Observers A & B: Rest & Simultaneity"?

"Observers A & B: Rest & Simultaneity" is a thought experiment that explores the concept of relative motion and the relativity of time. It involves two observers, A and B, who are moving at different speeds and how they perceive the concept of simultaneity.

## 2. How does the speed of an observer affect their perception of time?

According to the theory of relativity, the speed of an observer affects their perception of time. The faster an observer moves, the slower time appears to pass for them. This is known as time dilation and is a fundamental principle of the theory of relativity.

## 3. Can two events be considered simultaneous for one observer but not for another?

Yes, two events can be considered simultaneous for one observer but not for another. This is because the perception of time is relative and can be affected by the speed of the observer. What may appear to happen at the same time for one observer may not be simultaneous for another.

## 4. How does the concept of simultaneity challenge our understanding of time?

The concept of simultaneity challenges our understanding of time by showing that it is not an absolute concept, but rather a relative one. The perception of time can be different for different observers, depending on their relative motion. This challenges the traditional notion of time as a universal constant.

## 5. What are some real-world applications of the concept of "Observers A & B: Rest & Simultaneity"?

The concept of "Observers A & B: Rest & Simultaneity" has many real-world applications, particularly in the fields of physics and engineering. It has been used to explain phenomena such as time dilation in space travel and the synchronization of clocks in GPS systems. It has also been applied in the development of technologies such as atomic clocks and satellite communication systems.

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