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This radiation (CMBR) is said to have its origin at the surface of last scattering that exposed itself when the big bang universe had expanded for less than a million years.

In order to see radiation from a source, one has to be on its future light cone. In a universe that is flat and open, which our Universe is asserted to be at the large scale, we are not on the future light cone of this radiation, but almost maximally remote from it. One can also say that the surface of last scattering is not on our own past light cone.

How is this visibility to be understood within standard big bang cosmology? (This question is different from an earlier one with the same wording.)

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  • $\begingroup$ I believe this is the referenced "earlier one with the same wording": Why can we see the cosmic microwave background (CMB)? $\endgroup$ – David Hammen Sep 24 '18 at 14:34
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    $\begingroup$ I am confused, but part of that may just be that I come from cond-mat and so my context for cosmology stinks. However as far as I understood, CMBR comes from "the universe was opaque, then later it was not" which seems like a timelike separation to me, so assuming continuity there should be a universe-spanning "normal" hypersurface, it would be 3D and everywhere locally spacelike. Presumably this is the true 4D shape of your "surface of last scattering." But if that surface crosses the entire universe, why wouldn't it intersect with every light cone? $\endgroup$ – CR Drost Sep 24 '18 at 14:48
  • $\begingroup$ Light has moved at c from the surface at which the universe became transparent, while our galaxy and all the baryonic content of the universe has only moved a much smaller distance since then. $\endgroup$ – Hartmut Sep 24 '18 at 14:59
  • $\begingroup$ @Harmut Why is that relevant? As CR Drost said, the CMBR was emitted by the whole universe, a 3D hypersurface. Yes, at any given moment of an observer's time they are receiving CMBR from a 2D surface of last scattering, but that surface is dynamic. One second later, you get radiation from 1 light-second further distant (ignoring the various complications in cosmological distance measurement). $\endgroup$ – PM 2Ring Sep 24 '18 at 15:50
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    $\begingroup$ @Hartmut: In the simplest case of a Minkowski space with $w = ct$ we have a burst of light at all $(0,x,y,z)$ in all directions. You look back from time $w=W$ at position $(x, y, z) = (0, 0, 0).$ You see the light from those points $w=0$ such that $x^2 + y^2 + z^2 = W^2,$ no? Now I can understand that in GR your light paths might not be straight lines and might complicate this picture by getting all screwy, but I struggle to see the cosmological reason that they would spread out to infinity before reaching this surface, which is the only reason they wouldn't intersect that surface. $\endgroup$ – CR Drost Sep 24 '18 at 16:28
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One has to keep remembering that in the Big Bang model, the (0,0,0,0) is located in all points of the present day universe. Each of us is sitting at the center of the universe.

As the universe expanded all points expanded away from each other.

history of universe

Light that decoupled from matter at 380.000 years after the Big bang, decoupled and left with velocity c from our points to wherever they were pointing when they decoupled. In our instruments we measure photons from the other parts of the universe that were pointing at us and which have undergone the doppler effect of the expansion. This is not radiation from a surface.

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I get the feeling you think the CMBR is the flash from the explosion that was the Big Bang - like when Ripley blows up the Nostromo at the end of Alien.

If so, that's not really it. Rather, the universe was full of this radiation (heading in all directions) as it expanded. At our random position, we are now seeing photons that have been travelling for 13.7 billion years from a distant point in the universe. When they set out from that point, we were much closer (and they had a shorter wavelength), but as space expanded they had further to go to get to us.

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  • $\begingroup$ My question concerns the visibility of the surface of last scattering. (Unfortunately, I am not familiar with your analogies.) $\endgroup$ – Hartmut Sep 24 '18 at 14:36
  • $\begingroup$ @Hartmut You never saw Alien? - Ok. Imagine any explosion you did see. It's not like we are outside and the blast washes over us, rather, it's like we are inside the explosion fireball and it is still exploding. $\endgroup$ – Oscar Bravo Sep 25 '18 at 6:53
  • $\begingroup$ To my memory, I never saw Alien and I agree with you in the rest you say. $\endgroup$ – Hartmut Sep 25 '18 at 8:41
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The answer by anna v is in line with what I have seen previously, but is it clear enough?

The "light cones" I mentioned can be shown in a graph in which one axis represents time and the other any spatial dimension. The scaling of the axes can be chosen so that a light cone is represented by a pair of lines inclined at +/- 45 degrees from the time axis. The future light cone of the radiation starts close to the zero-point of the time axis and is directed forwards. Our past light cone starts at the time axis much later and is directed backwards. I see no way of connecting two widely separated points close to the time axis by a 45 degree line without introducing closure or reflection.

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  • $\begingroup$ Is this supposed to be an answer? It seems more like additional information belonging to your question. $\endgroup$ – PM 2Ring Sep 25 '18 at 3:55
  • $\begingroup$ @PM 2Ring Right. In this orientation it is a horizontal line, but a very short one, as compared with the vertical. (As to your first point: my "answer" was too long to be added as a comment.) $\endgroup$ – Hartmut Sep 25 '18 at 8:30
  • $\begingroup$ @PM 2Ring I understand your reasoning, which presupposes the universe to be infinite (or at least 98 GLY), but to my understanding, this is not so in standard big bang cosmology, which presumes the universe to have emerged only 13.8 GY ago. When it became transparent, it cannot have been larger than 1 MLY in diameter. $\endgroup$ – Hartmut Sep 25 '18 at 10:32
  • $\begingroup$ I should perhaps clarify that by ”a universe that is flat and open” in my question, I meant a universe that is flat and not surrounded by a wall. Such a wall would provide for the reflection mentioned at the end of my ”answer” and turn the universe into a classical black body. $\endgroup$ – Hartmut Sep 25 '18 at 14:02
  • $\begingroup$ @PM 2Ring Thanks for this information, which answeres my question, but coud you please give me a reference to a text that describes this more in detail? (42 MLY is larger than my guess of 1MLY, but still very much smaller than the present size of the universe.) $\endgroup$ – Hartmut Sep 25 '18 at 16:20

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