Where are the future background microwaves now

[YummyFur]

In this thought experiment the sun does not run out of fuel and the Earth is still here.

So in 14 billion years we will still be detecting the CMB radiation which I presume will be a bit cooler.

My question is where are these microwaves that will reach us then, now.

 

[Chalnoth]

In this thought experiment the sun does not run out of fuel and the Earth is still here.

So in 14 billion years we will still be detecting the CMB radiation which I presume will be a bit cooler.

My question is where are these microwaves that will reach us then, now.

Well, they are currently at a distance such that it will take 14 billion years for them to reach us. It would take a fair amount of calculation to determine exactly where those photons now are, so I'm not sure I want to go into that. But because the expansion will slow somewhat over the intervening time, we can expect that they are a little closer than 14 billion light years away, perhaps 12 billion light years as a rough guestimate?

 

[YummyFur]

What I'm trying to get at is probably a misconception due to the 4 dimensional nature of the universe which I don't understand. However this is the picture I'm trying to understand...

I see a sphere that has been expanding for 380,000 years whose inside surface is covered with the CMB radiation which has just been released. There's a spot somewhere on the inside of this ever expanding sphere of universe, which is reserved for the formation of the Solar system 10 billion years hence.

What's going on. Wouldn't this sphere of expanding CMBr be traveling at greater than the speed of light at a certain point during the intervening 14 billion years and now?

In 42 billion years will CMB still be reaching us?

 

[Chalnoth]

First, a better picture for the CMB is not as a sphere, but instead as a nearly-uniform gas of photons that is continually expanding.

What's going on. Wouldn't this sphere of expanding CMBr be traveling at greater than the speed of light at a certain point during the intervening 14 billion years and now?

Sure, in some coordinate systems it travels faster than light relative to us. But that is arbitrary, because the velocity of far-away objects is not well-defined. The light always travels at the speed of light relative to the material it is passing.

In 42 billion years will CMB still be reaching us?

Yes. It's just a uniform gas of photons that is continuously being redshifted. It will always exist, it will just get lower and lower in temperature as time passes.

 

[Imax]

My question is where are these microwaves that will reach us then, now.

CMB radiation permeated space from the last scattering surface, so 14 billion years from now we should still be detecting CMB radiation, possibly a bit cooler. We are embedded within spacetime from the big bang and CMB radiation should still come from the last scattering surface.

 

[chrisbaird]

Think of it this way. A friend stands 5 meters away from you, another one 10 meters away, another one 15 meters away, etc. They all throw balls at you at the same instant. The ball from the friend at 5 m reaches you first, then the ball from the 10 m friend arrives next. If the number of friends participating in this is very large, you will continually receive balls at later an later times. If a ball arrives every second, then the ball I will catch in 6 seconds was thrown by the friend 6 people farther away than the friend connected to the ball I just caught. So even though all my friends throw their balls at the same instant (the big bang), they don't arrive at me the same time. To be a more realistic analogy, I would have to put friends all over the field, not just in one direction, and they would throw the balls in all directions at the same instant.