When exactly light started its journey away from a supernova?

1. Aug 11, 2013

Romulo Binuya

When media reports a supernova it sounds like it happened just a while ago despite the photon stream came from say 10 million light-years away. Is it approximately correct to tell the layman that actually that supernova happened 10 million years ago because it took that time for its light to reach us? I like to include time dilation and length contraction in the calculation of when exactly light started its journey away from a supernova. Unfortunately, I don't know yet how to calculate that :-D

2. Aug 11, 2013

Staff: Mentor

yes.

You don't need to consider either - they aren't involved in this problem.

3. Aug 11, 2013

Staff: Mentor

At least for nearby ones, which aren't moving fast wrt us.

4. Aug 11, 2013

Staff: Mentor

Well, presumably a reporter on Earth would report on events wrt Earth's frame, so even for a relativistically moving star you wouldn't need to worry about length contraction and time dilation. After all, reporters rarely bother to report both sides of a story.

5. Aug 13, 2013

Romulo Binuya

Someone in the web explained time dilation and length contraction, and he said "A journey to the 4.3 light-years distant Alpha Centauri C, the closest star to our Sun, would take only 7.4 months in a space ship moving at 0.99c". Since he didn't show the calculation and I don't know yet how to do it myself, my judgement is deferred.

6. Aug 13, 2013

phinds

7. Aug 13, 2013

Romulo Binuya

I agree with Nugatory, that's what I've been telling the kids, that if the photon stream of a supernova came from 10 million light-years away then that supernova happened 10 million years ago. But that guy who thrown in time dilation and length contraction in the equation made me worried that I might misleading the kids.

8. Aug 13, 2013

ghwellsjr

The calculations are based on the Lorentz Transformation. I have drawn a couple spacetime diagrams to show you the results. First a diagram showing earth as the thick blue line with dots spaced one year apart, Alpha Centauri C as the thick red line 4.3 light years away from earth and a space ship as the thick black line traveling for one year of its own Proper Time. I have also shown a light signal as the thin blue line just below the space ship sent to the star:

As you can see, in the earth-star rest frame, it takes just over 4.3 years for the space ship to get to the star at 99%c.

Now if we use the Lorentz Transformation process to convert to the rest frame of the space ship we get:

Now the distance between the earth and the star is contracted and so the spaceship can get there in just over 7 months.

Attached Files:

File size:
12.2 KB
Views:
110
• AlphaCentauriSS6.PNG
File size:
15.7 KB
Views:
112
Last edited: Aug 13, 2013
9. Aug 14, 2013

Romulo Binuya

You made it look simple ghwellsjr! I have an illusion I'm starting to understand the not intuitive warped spacetime. So in one perspective i.e. diagram no.1 I'm not misleading the kids. Btw, this article had it too in the same way, but then they have reason to emphasize it... about a supernova that happened 7 billion light-years away and the three little photons that travelled for 7 billion years...
http://www.space.com/17399-gamma-ray-photons-quantum-spacetime.html