Calculating Spacetime Interval: Alpha & Beta Supernovae

In summary, using the spacetime interval equation, the time between the explosions is found to be 67.1 years. The use of light years as a unit of distance already accounts for the speed of light, making it unnecessary to include the c^2 term in the equation.
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Homework Statement
The star Alpha goes supernova. Ten years later and 100 ly away, as measured by astronomers in the galaxy, star Beta explodes.

An alien spacecraft passing through the galaxy finds that the distance between the two explosions is 120 ly. According to the aliens, what is the time between the explosions?

Relevant equations
c^2*t^2 - x^2 = c^2(t')^2 - (x')^2 The attempt at a solution
I tried using the spacetime interval equation but the distances are too small to see a difference and gives me a wrong answer. Then i did not include c^2 with the equation and i got the correct answer. Which is 67.1 years. I also tried to multiply x^2 and (x')^2 with c^2 and got the same answer. Is it under specific units, like light years, where we can neglect the c^2 or did I just used the wrong equation in the first place?
 
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  • #2
Lightyear is the dist light travels in 1 year, so it's equal to c*1 year, and already the c is inside it, if you measure time in years. That's why you didn't have to multiply by c^2.
 
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As a scientist, it is important to consider the context and units when using equations to solve problems. In this case, since we are dealing with distances in light years, it is appropriate to neglect the c^2 term in the spacetime interval equation. This is because the speed of light, c, is already accounted for in the conversion from time to distance in light years. Therefore, your approach of neglecting the c^2 term in the equation was correct and led to the correct answer of 67.1 years. It is important to always check the units and context when using equations to ensure accurate solutions.
 

FAQ: Calculating Spacetime Interval: Alpha & Beta Supernovae

1. What is the spacetime interval?

The spacetime interval is a measure of the distance between two events in the four-dimensional spacetime. It takes into account both space and time, and is represented as a mathematical quantity in the special theory of relativity.

2. How is the spacetime interval calculated?

The spacetime interval is calculated using the equation: ∆s² = ∆t² - ∆x² - ∆y² - ∆z². This equation takes into account the differences in time and space between two events, and results in a value that is invariant for all observers.

3. What is the significance of Alpha and Beta supernovae in calculating the spacetime interval?

Alpha and Beta supernovae are used as standard candles in cosmology, meaning that their luminosity can be accurately measured. This allows scientists to calculate the distance between the supernova and Earth, which is a necessary component in calculating the spacetime interval.

4. How does the spacetime interval change for different observers?

The spacetime interval is an invariant quantity, meaning that it is the same for all observers regardless of their frame of reference. However, the perception of space and time may vary for different observers due to the effects of relativity.

5. What are the implications of calculating the spacetime interval in understanding the universe?

Calculating the spacetime interval is crucial in understanding the fundamental nature of the universe, as it allows scientists to accurately measure the distances and times involved in cosmic events. It also plays a key role in the special theory of relativity and helps us understand the relationship between space and time in our universe.

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