Simple Special relativity question

[theneedtoknow]

Homework Statement

The star alpha goes nova, 10 years later (in the ref frame of an astornomer observingthe stars), the star beta also explodes. The distance between them according to the same observer is 100LY. An alien spacecraft passing through the galaxy finds that the distance b/w the explosions is 120ly. According to the aliens, what is the time difference between the explotions?

The Attempt at a Solution

I don't really get the question...the 2 explosions are 100ly away in a reference frame in which they're at rest wrt each other. Shouldn't the distance be contracted for a spaceship passin through the galaxy? how can a spaceship moving measure the distance between them as greater than the astronomer's reference frame?

 

[tiny-tim]

Hi theneedtoknow!

You're reading too much into this question …

the question doesn't give you any information about what the stars are doing, only the position and time coordinates of two specific events

 

[nlightner]

I can provide a response by explaining the concept of time dilation in special relativity. According to the theory of special relativity, time is not absolute and can be affected by the relative motion between two observers. This means that different observers can measure different times for the same event depending on their relative motion.

In this scenario, the alien spacecraft is moving relative to the astronomer's reference frame. This means that the alien's measurement of the distance between the two explosions will be affected by the phenomenon of length contraction, where objects in motion appear shorter in the direction of motion.

As a result, the alien's measurement of the distance between the two explosions will be greater than the astronomer's measurement. This also means that the time difference between the explosions, as measured by the alien, will be shorter than the time difference measured by the astronomer. This is known as time dilation, where time appears to pass slower for objects in motion compared to objects at rest.

Therefore, the time difference between the explosions as measured by the alien spacecraft will be less than 10 years, as measured by the astronomer. This phenomenon of time dilation is a fundamental concept in special relativity and has been observed and confirmed through various experiments.