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if the Cosmic microwave background radiation is coming towards us in the speed of light and all matter and energy was singular at the big bang, doesn't that mean we somehow moved faster than the speed of light (otherwise the CMBR would have already passed us not be coming toward us?)

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  • $\begingroup$ If the universe was small enough then, yes, or, perhaps, maybe. I get confused thinking about this sometimes too. The thing is, the Universe is very very very large and expanding too. The things that we see that look 13 billion light years away are closer to 42 billion light years away now. $\endgroup$ – userLTK Jun 30 '16 at 4:21
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    $\begingroup$ Not sure why this question was downvoted. It could be clearer, but the question overall is a good one and worth answering. $\endgroup$ – zephyr Jun 30 '16 at 17:11
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You seem to struggle with a very common thing; the understanding that The Big Bang is not something that happened in space, but rather to space. It could be good for you to read some answers to misconceptions about The Big Bang here, or the answer to a question about it on Physics Stack Exchange. The Big Bang caused everything in the universe to move away from each other; there is no central point from which everything is receding.

For the first few hundred thousand years of our Universe, photons and matter particles were coupled in a photon-particle soup. They were all so close together, that they constantly bumped into each other, not being able to travel far at all before changing directions. As the universe expanded and the temperature of the soup became colder, the photons and matter particles were able to travel further before interacting with each other. When the temperature became low enough for protons and electrons to form hydrogen, the number of matter particles the photons had to interact with became even lower, allowing the photons to travel even further before having to interact with matter particles. It was approximately at this point in time that the CMB originated; the CMB is simply the light of the photons which interacted a very last time around the time photons and matter particles stopped being a photon-particle soup (we call this time the recombination epoch).

The universe was expanding everywhere both at the very start of its existence and during the recombination epoch, as well as now. The release of the CMB photons thus happened everywhere, and the photons of the CMB travelled in all directions. As the universe expands, the photons travel new distances, and we are constantly observing the CMB photons, which simply are reaching us from different places of origin in the universe -- which, for all we know, may be infinitely large, so we may just be seeing these kind of photons until the end of time.

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The CMBR is coming at us at the speed of light -- but not from a distinct point. It comes from everywhere. It is distributed evenly throughout the universe because the universe used to be a lot closer together before the period of inflation. Inflation was the epoch from 10^-36 seconds after the big bang to 10^-33 after where the universe increased in volume by a factor of about 10^78.

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Going back to the beginning, we used to have CMBR right here in our vicinity. It, indeed, has been moving away from us for the last 13.7 billion years. The CMBR we do see now is reaching us from space that emitted it 13.7 billion years ago. Observers over THERE can now see our own radiation that departed our vicinity 13.7 billion years ago as their CMBR, ie, this is a symmetric situation.

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