Simple Question regarding spacetime interval

• jimmypoopins
In summary, two events occurring 9000 km apart in one inertial system are observed to be 11000 km apart in another inertial system. By using the spacetime interval equation, we can find the time difference between the two events in the second inertial system by dividing the difference in spacetime intervals by c squared and taking the square root. The correct answer is 2.108*10^-8 seconds, but an algebra mistake may have caused an incorrect answer at first.

Homework Statement

Two events occur in an inertial system at the same time, but 9000 km apart. However in another inertial system these two events are observed to be 11000 km apart.

What is the time difference between the two events in this second inertial system?

Homework Equations

s^2=x^2+y^2+z^2-(ct)^2

The Attempt at a Solution

since the spacetime interval is invariant in any inertial frame, s^2 can equal s'^2
for the first inertial system i got s^2=9m^2
putting it into the second equation i got
9m^2=11m^2-(ct)^2
subtracting 11m^2, dividing by -c, and taking the square root, i am left with 2.108*10^-8sec, which seems like it could be a reasonable answer, but it is not correct.

can anyone tell me what i am doing wrong and lead me in the right direction please?

jimmypoopins said:

Homework Statement

Two events occur in an inertial system at the same time, but 9000 km apart. However in another inertial system these two events are observed to be 11000 km apart.

What is the time difference between the two events in this second inertial system?

Homework Equations

s^2=x^2+y^2+z^2-(ct)^2

The Attempt at a Solution

since the spacetime interval is invariant in any inertial frame, s^2 can equal s'^2
for the first inertial system i got s^2=9m^2
putting it into the second equation i got
9m^2=11m^2-(ct)^2
subtracting 11m^2, dividing by -c, and taking the square root, i am left with 2.108*10^-8sec, which seems like it could be a reasonable answer, but it is not correct.

can anyone tell me what i am doing wrong and lead me in the right direction please?

You have the right idea, it just seems that you are making some algebra mistake. First, it is 9000 km apart so $9 \times 10^6 m$. Second, when solving for the time interval in the other frame, you must divide by the square of c before taking the square root.

ah you are right, thank you. for some reason when i saw 4000km i assumed that i had to divide by 1000 to get it in meters. i don't know why, a stupid mistake on my part.

1. What is the spacetime interval?

The spacetime interval is a measure of the distance between two events in the fabric of spacetime. It takes into account both the spatial and temporal components of the events.

2. How is the spacetime interval calculated?

The spacetime interval is calculated using the equation Δs² = Δx² + Δy² + Δz² - (cΔt)², where Δs is the spacetime interval, Δx, Δy, and Δz are the spatial distances between the events, c is the speed of light, and Δt is the time difference between the events.

3. What does a negative spacetime interval mean?

A negative spacetime interval indicates that the two events are not causally connected, meaning that there is no way for one event to have influenced the other. This is in contrast to a positive spacetime interval, which indicates a causal relationship between the events.

4. How does the spacetime interval relate to the theory of relativity?

The concept of the spacetime interval is a fundamental part of Einstein's theory of relativity. It is used to describe the geometry of spacetime and how it is affected by the presence of mass and energy. The theory of relativity also predicts that the spacetime interval is the same for all observers, regardless of their relative motion.

5. Can the spacetime interval be measured?

Yes, the spacetime interval can be measured using precise instruments and techniques. However, due to the extremely small values involved, it is not something that can be directly observed by humans. Instead, it is often used in theoretical calculations and models to better understand the nature of spacetime.

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