Light Leaving Earth-Observer's View of Events in Time

[happyhacker]

TL;DR Summary

Light traveling from Earth

Would an observer many light years from Earth (and approaching say) see events leading onwards through time (to what level of detail i am not proposing but say weather and maybe Humans on the ground?) in the light received?

 

[Ibix]

I don't know what you are trying to ask.

An observer ten light years away will see the Earth as it was in 2011. If they then set off to Earth at 0.8c the journey will take them 12.5 years by Earth clocks, which time dilation reduces to 7.5 years by shipboard clocks. So they will arrive in late 2033, having seen the history of the Earth from 2011 to 2033 in ×3 fast-forward in the 7.5 years they experience, if that's what you are asking.

Edit: building a sufficiently powerful telescope to image the Earth in any detail from 10ly, and getting it moving at 0.8c, are left as exercises for the reader.

 

[PeroK]

Summary:: Light traveling from Earth.

Would an observer many light years from Earth (and approaching say) see events leading onwards through time (to what level of detail i am not proposing but say weather and maybe Humans on the ground?) in the light received?

There's a short video here that might interest you:

 

[FactChecker]

If you are asking if a fast-approaching traveler will see things in reverse, the answer is no. The light nearest Earth always shows the more recent events. So a traveler will see everything in the correct order, whether the light comes to him, or he speeds toward the Earth, or both. He will just see it in a compressed time.

 

[Ibix]

So they will arrive in late 2033, having seen the history of the Earth from 2011 to 2033 in ×3 fast-forward in the 7.5 years they experience, if that's what you are asking.

If they don't stop and just carry on, by the way, it shifts to ×3 slow-motion as they pass Earth and start moving away, assuming they just keep going at the same speed.

 

[happyhacker]

Thanks, great answers even though I was not entirely clear with my question. What is the maths for the time dilation?

 

[Ibix]

Thanks, great answers even though I was not entirely clear with my question. What is the maths for the time dilation?

The time dilation factor is usually written $\gamma$ and is $\gamma=\frac 1{\sqrt{1-v^2/ ^2}}$. If you plug in $v=0.8c$ and multiply $\gamma$ by the 12.5 year travel time you'll get the 7.5 years the travellers experience.

Note that time dilation is not enough to explain relativistic effects in general, although it works here. If you try to apply it to different scenarios you may well find yourself confused - you should look up the Lorentz transforms if you want more general tools.

 

[hutchphd]

If you are interested in the rate at which you will "see" events happen, the frequency of any series of events encoded in the light will simply be Doppler shifted according to the usual relativistic equations.

 

[PeroK]

Thanks, great answers even though I was not entirely clear with my question. What is the maths for the time dilation?

The relevant equation here would be the relativistic Doppler effect:

https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

Which also gives you the apparent change in time between events when moving towards or away from something.