How Does Relativity Affect the Perception of Time Between Supernovae?

[doublemint]

1. The star Alpha goes supernova. Then ten years later and 100 light years away, star beta goes supernova. Aliens passing by observes that the explosions occur 120 light years away. According to them, what is the time between the explosions?


2. So I think I am supposed to used the Lorentz Transformations.
x'=$$\gamma$$(x-vt) and x=$$\gamma$$(x'+vt')
Then I solved for v in both equations since we do not know the speed at which the aliens are traveling at. I equate them together to get t'
$$\gamma$$t'=[$$\gamma$$t(x-$$\gamma$$x')]/($$\gamma$$x-x')
I solved for it and got -24 years..
So does it mean that it took 24 years inbetween explosions according to the aliens reference frame?

Thank You

DoubleMint

 

[doublemint]

Nvm I've got it! I had to use the spacetime interval..obviously XD

 

[kerimek]

I would like to first clarify that the concept of relativity is a complex and intricate theory that requires a deep understanding of mathematics and physics to fully comprehend and apply. With that being said, I will provide a simplified explanation to the question at hand.

The key concept in relativity is that the laws of physics are the same for all observers, regardless of their relative motion. This means that the passage of time and the measurement of distances can vary for different observers depending on their relative motion.

In this scenario, the aliens are observing the supernova explosions from a distance of 120 light years away. However, due to their relative motion, the time and distance measurements will be different for them compared to an observer who is stationary relative to the two stars.

Using the Lorentz transformations, you have correctly calculated the time between the explosions in the aliens' reference frame to be -24 years. This negative value simply means that the explosions were observed in reverse order due to the aliens' relative motion. In other words, the explosion of star beta was observed first, followed by the explosion of star alpha.

It is important to note that this calculation is based on the assumption that the aliens are traveling at a constant speed relative to the two stars. In reality, their speed may have varied during the 10 years between the two explosions, which would affect the time measurement.

In conclusion, the time between the explosions according to the aliens' reference frame is -24 years. However, this value may vary depending on their actual speed and other factors. It is also important to keep in mind that this is just one perspective and the actual time between the explosions may be different for other observers in different reference frames.