Earliest time of light emission after Big Bang

[sir_manning]

Good evening ladies and gents

I'm in the process of wrapping my brain around Special Relativity, and I've come across an interesting application having to do with Cosmological Horizons. Basically, the question goes like this:

"Assume a time T has passed since the Big Bang and that we are receiving light from a galaxy receding from us at velocity v (assume v remains constant since the big bang). What is the earliest time T' that the light could have been emitted if it is arriving at Earth now."

Does anybody know of any resources that goes into greater depths regarding this question? By the way, this example is from "Relativity: An introduction to Space-Time physics" by Steve Adams.

Thanks,
-Alan

 

[vanesch]

This is a question that pertains to general relativity, not special relativity. I will move your post to the relativity forum...

 

[Heathera152]

An interesting question. Would not the earliest time that you could know be the number of years that it would take light to travel from the edge of the expanding universe to earth. How fast is the universe expanding compared to the speed of light?

 

[Chronos]

See Ned Wright's page.

 

[hellfire]

The question is misleading because if you make use of the usual cosmological solutions to general relativity to solve it, then the assumption that v remains constant since the big-bang makes no sense. Moreover, leaving this aside, the answer to the question for a generic cosmological model cannot be obtained analitically.

It seems to me that you are asked to solve the problem within the framework of special relativity, i.e. assume that the recession speed is not due to expansion of space but due to the motion of objects in a flat spacetime background. In that case I suggest to draw a space-time diagram for the motion of the galaxy (vertical axis t, horizontal axis x) and try to depict the scenario. You will see that the geometry of the diagram will provide you an answer.