# Relativity and the Cosmic Microwave Background

Q:
Reading about the Cosmic Microwave Background (CMB) radiation I understand that we consider that this radiation originates from the early stages of the universe evolution. In particular we consider that it corresponds to photons whose wavelength has increased to become microwaves that have been emitted from what is called the "the surface of last scattering" some billions of years ago. I understand the meaning of future and past light cone which explains how an event that has actually taken place in the past can be observed in earth at a later time. What I cannot understand in the particular case of CBM is the following: At the time that the photons today we observe as CMB in earth, started their trip a few billions of years ago travelling at the speed of light. At that time the matter that today has formulated earth (and ourselves) was actually inside the same sphere that emitted these photons (the universe at that time). Apparently the matter that later created earth was moving since then at a speed lower than light. So to put my question in a simplistic way: we have at a signle point in time in the past and a concentrated location (the sphere of the universe at that time) photons travelling at the speed of light and matter travelling at a speed lower than the speed of light that at a later stage has formulated earth. How is it possible to observe the CMB today as the time it took our mass to reach our current location is obviously much longer than the time it took the photons to reach the same location?
- Yannis (age 40)
Athens, Greece
A:
You refer at many points to our "speed". What does that mean? With respect to what? The basic finding of relativity is that there is no special reference frame to measure speeds in. So you can take a whole batch of stuff, say everything in the vicinity of what later became our galaxy, and pick a reference frame where its average velocity is zero. Let's do that, for simplicity.

So now the question becomes simpler: was any of the universe far enough away at the time of last scattering for it to take until now for the light to just be reaching us? The answer is yes. There are a few reasons for this.
1. We have no compelling reason to think the universe is finite. If it's infinite, there's nothing more to explain.
2. If it were finite and small, then the light would still get here, just wrapping around the curved universe a few times on the way. That's not the situation in our particular universe.
3. If the universe were finite but big then the light from distant parts would get here without wrapping around. This is probably what puzzles you, since it would seem that so much more time has elapsed since the last scattering than before that nothing could have gotten far enough away.  It turns out that things don't work out that way due to relativistic effects.  Even ignoring general relativity (a bad idea for this problem) one can see why.

Say we pretend we can use a special relativistic reference frame. Look at some region that's young by its own local time, just reaching last scattering. If it's moving away from us at speed of almost c, then the relativistic time dilation says it's much older in our reference frame. It will have had time to get far enough away from us, according to us. The math is different in general relativity but that conclusion remains.

Mike W.

(published on 01/02/2013)

## Follow-Up #1: where does CMB come from?

Q:
Thank you Mike for your answer. I have already made some attempt to use special relativity to understand this phenomenon without success. So I need to make some further study on that. Another question related to CMB is the following one: CMB was emitted ~13bn years ago from the universe of that time which occupied a much lower space volume (for simplicity let's assume a "sphere") vs. the unitverse we have today. As the universe has expanded significantly since then we may assume that the earth is topologically outside the "sphere" that emitted the photons of CMB. In this context it would be expected to detect CMB from a specific region in the sky and not to receive CMB from the entire sky.
- Yannis (age 40)
Athens, Greece
A:
It seems like you're working with a picture of a ball of stuff expanding in some 3-D space. If the universe happens to be finite it's more like the 3-D analog of the 2-D surface of a balloon. There are no edges. Each point has a neighborhood (in the relevant dimension) extending out symmetrically in each direction. So the CMB should come in equally from all directions to anybody traveling along with the average of stuff in their vicinity.

We find a slight asymmetry in the CMB intensity we see, indicating that, compared to the average of everything within sight, we're moving a bit. That Doppler shifts the CMB in one direction up a bit, and down a bit in the opposite direction. For further discussion, see .

Mike W.

(published on 01/03/2013)

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