<p>The universe isn't space. It's spacetime. We are 13.8 billion years away from the big bang in the time direction. We aren't 13.8 billion light years away from it in any spatial direction, nor any other spatial distance from it. It happened in the past, and there's no correspondence between spatial points then and spatial points now. They're different points in spacetime.</p>
<p>&quot;The rate of expansion was once up to six times the speed of light&quot; isn't true, and I've never heard anyone claim such a thing, although they often claim the expansion is &quot;faster than light&quot; which is also not true. The rate of expansion is given by the Hubble parameter or by the time derivative of the scale factor. Neither of those has units of speed, so they can't be compared to the speed of light.</p>
<p>It's also not true that the CMB is 13.8 billion light years away (from comments). The CMB is everywhere; it fills the universe uniformly.</p>

CC BY-SA 4.0
2023-12-08T20:14:54.007Z
So when the JWST sees a galaxy that it reports as being 13.3 billion light years away I know that the light has taken 13.3 billion years to get here so I know that it is showing the galaxy as it was 13.3 billion years ago but you are saying that is not a spatial distance.
Michael Mcgarry
CC BY-SA 4.0
2023-12-08T20:21:31.187Z
@MichaelMcgarry If an article says a galaxy is 13.3 Gly away and we're seeing it as it was 13.3 Gyr ago, then it's wrong. The lookback time and comoving distance should be different. If the article only mentions a distance, then it's a tossup whether it's a correct comoving distance or they incorrectly multiplied the lookback time by $c$.
benrg
CC BY-SA 4.0
2023-12-08T20:45:01.000Z
I am still not sure I get it. An earlier comment said that a photon from the CMB has taken 13.8 billion years to get here. That photon has been travelling at the speed of light. When that photon left the CMB the atoms that make up the milky way would have also have been commingled with the atoms that that photon left from. So they must have been travelling at the speed of light to be here to receive that photon.
Michael Mcgarry
CC BY-SA 4.0
2023-12-08T20:58:04.320Z
@MichaelMcgarry The early universe was filled with an opaque plasma, and when it became transparent, it became transparent everywhere. The relic light was everywhere, and at later times it's still everywhere since there's no reason for there to be more of it in one place than another. The matter we're made of came from one location in the plasma, and the CMB light we see came from a different location, and has taken the intervening time to reach our location.
benrg
CC BY-SA 4.0
2023-12-08T22:48:50.900Z
If the CMB and the matter we are made of left the plasma from very different locations it is very unlikely we would both have ended up at the same location 13.8 Gly later
Michael Mcgarry
CC BY-SA 4.0
2023-12-08T23:52:54.840Z
@MichaelMcgarry That's like saying it's very unlikely the air molecules you're breathing happened to be in the right place for you to breathe them. The CMBR is everywhere. We see only a tiny portion of it, the portion that happens to be right here right now.
benrg
CC BY-SA 4.0
2023-12-09T00:01:55.117Z
Sorry I thought the CMBR was microwave radiation that traveled in straight lines from a source at the speed of light.
Michael Mcgarry
CC BY-SA 4.0
2023-12-09T06:34:51.513Z
@MichaelMcgarry You can think of it as a bunch of particles traveling in straight lines at the speed of light, in all directions from all starting points. Some had the right starting point and direction to reach us now.
benrg
CC BY-SA 4.0
2023-12-08T19:39:25.437Z
2023-12-08T19:39:25.437Z
benrg
<p>Scientists tell us that the rate of expansion was once up to six times the speed of light. It then slowed down, by how much I am not sure. Now it is increasing again. The big bang happened 13.8 billion years ago and we are now 13.8 billion light years from it ergo the average expansion rate must be the speed of light. Are we just living in an incredibly lucky era or have I got something totally wrong again.</p>

CC BY-SA 4.0
2023-12-08T15:44:05.090Z
the big bang is not any point in space. there is no distance to the big bang
Topcode
CC BY-SA 4.0
2023-12-08T15:47:46.517Z
So we are not 13.8 billion light years form the cosmic background radiation. I thought the whole point of the big bang was that it started from a single point in space.
Michael Mcgarry
CC BY-SA 4.0
2023-12-08T15:54:20.537Z
no, the big bang did not start from a point in space, it started from space being a point, and then all space expanding from that. Every point in space was in that point, at least as far as we can tell. The CMB is about 13.8 billion light years away, but the CMB is not the big bang.
Topcode
CC BY-SA 4.0
2023-12-08T15:55:40.280Z
The cosmic background is not the big bang, it's the surface of last scattering, the plasma that filled the universe at the time when it cooled enough to become transparent.
Christopher James Huff
CC BY-SA 4.0
2023-12-08T16:02:29.713Z
If the CMB is 13.8 billion light years away and the universe is 13.8 billion years old. Surely that means that the average rate of expansion has been the speed of light. Am I right in assuming the time between the big bang and the CMB was very short.
Michael Mcgarry
CC BY-SA 4.0
2023-12-08T16:35:39.097Z
@MichaelMcgarry Yes, you're right: The CMB was emitted only 380,000 yr after BB. However, the CMB is _not_ 13.8 Glyr away. The CMB was emitted from everywhere, in every direction. A CMB photon that you see _today_ has indeed traveled for (almost) 13.8 Gyr, and if space didn't expand, the atom that emitted that particular photon would indeed be 13.8 Glyr away. However, expansion carried it farther away so that, today, it is 45.3 Glyr away. A CMB photon that you saw yesterday was emitted from an atom slightly closer, and a CMB photon that you see tomorrow was emitted from a more distant atom.
pela
CC BY-SA 4.0
2023-12-08T16:58:44.900Z
I see so the average expansion rate is about three and a half times the speed of light. The fact that we are 13.8 billion light years from something that happened 13.8 billion years ago is totally coincidental. Thank you for that.
Michael Mcgarry
CC BY-SA 4.0
2023-12-08T19:20:47.217Z
Where did you hear "Scientists tell us that the rate of expansion was once up to six times the speed of light"? That's not true at all.
benrg
CC BY-SA 4.0
2023-12-08T20:21:09.827Z
If the big bang theory was a sentient being, I'd strike its face for being so ludicrous.
White Prime
CC BY-SA 4.0
2023-12-08T22:04:50.663Z
@MichaelMcgarry No, my point was that you must be quoting a wrong source (or perhaps misunderstood it): the CMB is _not_ 13.8 Glyr away. Because space expands, anything that is seen $x$ Glyr in the past is _more_ than $x$ Gyr away.
pela
CC BY-SA 4.0
2023-12-08T22:26:08.650Z
Surely the point is that it was 13.8 Glyr away from this point when the microwave photon started its journey. Where it is now is irrelevant.
Michael Mcgarry
CC BY-SA 4.0
2023-12-08T23:25:22.267Z
@MichaelMcgarry Well no, it was alot less than 13.8 glyr away when the photon was emitted, the universe expanded in the mean time. The light itself travelled 13.8 glyr, but that’s not exactly its distance depending on how you measure distance, it would specifically be 13.8 in light travel distance.
Topcode
CC BY-SA 4.0
2023-12-09T04:02:06.107Z
There are various cosmological [distance measures](https://en.wikipedia.org/wiki/Distance_measure) for different purposes. The CMB radiation we currently receive is from a spherical shell with a comoving radius of ~46 billion LY, but that sphere had a radius of ~42 million LY at the time the radiation was emitted. See https://physics.stackexchange.com/a/659681/123208 & https://physics.stackexchange.com/a/621281/123208
PM 2Ring
CC BY-SA 4.0
2023-12-10T07:13:24.803Z
Technically the big bang happened everywhere.
Arcturus
CC BY-SA 4.0
2023-12-10T11:57:10.683Z
Technically the big bang may have happened everywhere but it happened 13.8 Gl years ago and thats what created the CMB. The photons of the CMB started their journey 13.8 Gl years ago. The atoms that make up the milky way also started their journey 13.8 Gl years ago. So both have covered the same distance, arrived at the same point in space at the same time. So they must have travelled at the same approx speed. We know the speed the photons travel at.
Michael Mcgarry
CC BY-SA 4.0
2023-12-10T23:52:33.183Z
*"So both have covered the same distance"* How does that follow?
PM 2Ring
CC BY-SA 4.0
2023-12-11T14:39:35.593Z
@MichaelMcgarry Because the Universe has expanded by a factor of 1100 since the CMB was emitted, that atom (the current distance of which you refer to as being irrelevant, but I disagree on that) was a factor 1100 closer to us when it emitted the photon you see today. Since it is 45.3 Glyr today, it was 41.2 Mlyr away at that time. The distance "13.8 Glyr" has no significant in the context of the CMB, except "This is the distance that a photon _would_ travel, in the hypothetical case that the Universe did not expand."
pela
CC BY-SA 4.0
2023-12-27T21:51:59.560Z
You can do the problem in the frame of the MW.  In that frame the MW has not moved at all.  The entire universe expanded from this point.   Inflation expanded the universe to tremendous size in less than a second.  Recombination happened across the entire universe at some early time.  As time goes by, Earthlings can see the recombination event from a more and more distant sphere.  Now we see it from the sphere that was 13.8 Gly in radius 13.8 Gly ago. The beings in each galaxy in the universe see the same thing at the same time (ignoring perturbations).
eshaya
<big-bang-theory>
Are we really 13.8 billion light years from the big bang
Michael Mcgarry
# Are we really 13.8 billion light years from the big bang

(Asked by: username_0 on 2023-12-08)

Scientists tell us that the rate of expansion was once up to six times the speed of light. It then slowed down, by how much I am not sure. Now it is increasing again. The big bang happened 13.8 billion years ago and we are now 13.8 billion light years from it ergo the average expansion rate must be the speed of light. Are we just living in an incredibly lucky era or have I got something totally wrong again.

**Tags:** big-bang-theory
> **Comments:**
> **username_1**: the big bang is not any point in space. there is no distance to the big bang  
> **username_0**: So we are not 13.8 billion light years form the cosmic background radiation. I thought the whole point of the big bang was that it started from a single point in space.  
> **username_1**: no, the big bang did not start from a point in space, it started from space being a point, and then all space expanding from that. Every point in space was in that point, at least as far as we can tell. The CMB is about 13.8 billion light years away, but the CMB is not the big bang.  
> **username_2**: The cosmic background is not the big bang, it's the surface of last scattering, the plasma that filled the universe at the time when it cooled enough to become transparent.  
> **username_0**: If the CMB is 13.8 billion light years away and the universe is 13.8 billion years old. Surely that means that the average rate of expansion has been the speed of light. Am I right in assuming the time between the big bang and the CMB was very short.  
> **username_3**: @MichaelMcgarry Yes, you're right: The CMB was emitted only 380,000 yr after BB. However, the CMB is _not_ 13.8 Glyr away. The CMB was emitted from everywhere, in every direction. A CMB photon that you see _today_ has indeed traveled for (almost) 13.8 Gyr, and if space didn't expand, the atom that emitted that particular photon would indeed be 13.8 Glyr away. However, expansion carried it farther away so that, today, it is 45.3 Glyr away. A CMB photon that you saw yesterday was emitted from an atom slightly closer, and a CMB photon that you see tomorrow was emitted from a more distant atom.  
> **username_0**: I see so the average expansion rate is about three and a half times the speed of light. The fact that we are 13.8 billion light years from something that happened 13.8 billion years ago is totally coincidental. Thank you for that.  
> **username_4**: Where did you hear "Scientists tell us that the rate of expansion was once up to six times the speed of light"? That's not true at all.  
> **username_5**: If the big bang theory was a sentient being, I'd strike its face for being so ludicrous.  
> **username_3**: @MichaelMcgarry No, my point was that you must be quoting a wrong source (or perhaps misunderstood it): the CMB is _not_ 13.8 Glyr away. Because space expands, anything that is seen $x$ Glyr in the past is _more_ than $x$ Gyr away.  
> **username_0**: Surely the point is that it was 13.8 Glyr away from this point when the microwave photon started its journey. Where it is now is irrelevant.  
> **username_1**: @MichaelMcgarry Well no, it was alot less than 13.8 glyr away when the photon was emitted, the universe expanded in the mean time. The light itself travelled 13.8 glyr, but that’s not exactly its distance depending on how you measure distance, it would specifically be 13.8 in light travel distance.  
> **username_6**: There are various cosmological [distance measures](https://en.wikipedia.org/wiki/Distance_measure) for different purposes. The CMB radiation we currently receive is from a spherical shell with a comoving radius of ~46 billion LY, but that sphere had a radius of ~42 million LY at the time the radiation was emitted. See https://physics.stackexchange.com/a/659681/123208 & https://physics.stackexchange.com/a/621281/123208  
> **username_7**: Technically the big bang happened everywhere.  
> **username_0**: Technically the big bang may have happened everywhere but it happened 13.8 Gl years ago and thats what created the CMB. The photons of the CMB started their journey 13.8 Gl years ago. The atoms that make up the milky way also started their journey 13.8 Gl years ago. So both have covered the same distance, arrived at the same point in space at the same time. So they must have travelled at the same approx speed. We know the speed the photons travel at.  
> **username_6**: *"So both have covered the same distance"* How does that follow?  
> **username_3**: @MichaelMcgarry Because the Universe has expanded by a factor of 1100 since the CMB was emitted, that atom (the current distance of which you refer to as being irrelevant, but I disagree on that) was a factor 1100 closer to us when it emitted the photon you see today. Since it is 45.3 Glyr today, it was 41.2 Mlyr away at that time. The distance "13.8 Glyr" has no significant in the context of the CMB, except "This is the distance that a photon _would_ travel, in the hypothetical case that the Universe did not expand."  
> **username_8**: You can do the problem in the frame of the MW.  In that frame the MW has not moved at all.  The entire universe expanded from this point.   Inflation expanded the universe to tremendous size in less than a second.  Recombination happened across the entire universe at some early time.  As time goes by, Earthlings can see the recombination event from a more and more distant sphere.  Now we see it from the sphere that was 13.8 Gly in radius 13.8 Gly ago. The beings in each galaxy in the universe see the same thing at the same time (ignoring perturbations).  

---

## 1 answers

### Answer by username_4 on 2023-12-08. Score: 3

The universe isn't space. It's spacetime. We are 13.8 billion years away from the big bang in the time direction. We aren't 13.8 billion light years away from it in any spatial direction, nor any other spatial distance from it. It happened in the past, and there's no correspondence between spatial points then and spatial points now. They're different points in spacetime.

"The rate of expansion was once up to six times the speed of light" isn't true, and I've never heard anyone claim such a thing, although they often claim the expansion is "faster than light" which is also not true. The rate of expansion is given by the Hubble parameter or by the time derivative of the scale factor. Neither of those has units of speed, so they can't be compared to the speed of light.

It's also not true that the CMB is 13.8 billion light years away (from comments). The CMB is everywhere; it fills the universe uniformly.

> **Comments:**
> **username_0**: So when the JWST sees a galaxy that it reports as being 13.3 billion light years away I know that the light has taken 13.3 billion years to get here so I know that it is showing the galaxy as it was 13.3 billion years ago but you are saying that is not a spatial distance.  
> **username_4**: @MichaelMcgarry If an article says a galaxy is 13.3 Gly away and we're seeing it as it was 13.3 Gyr ago, then it's wrong. The lookback time and comoving distance should be different. If the article only mentions a distance, then it's a tossup whether it's a correct comoving distance or they incorrectly multiplied the lookback time by $c$.  
> **username_0**: I am still not sure I get it. An earlier comment said that a photon from the CMB has taken 13.8 billion years to get here. That photon has been travelling at the speed of light. When that photon left the CMB the atoms that make up the milky way would have also have been commingled with the atoms that that photon left from. So they must have been travelling at the speed of light to be here to receive that photon.  
> **username_4**: @MichaelMcgarry The early universe was filled with an opaque plasma, and when it became transparent, it became transparent everywhere. The relic light was everywhere, and at later times it's still everywhere since there's no reason for there to be more of it in one place than another. The matter we're made of came from one location in the plasma, and the CMB light we see came from a different location, and has taken the intervening time to reach our location.  
> **username_0**: If the CMB and the matter we are made of left the plasma from very different locations it is very unlikely we would both have ended up at the same location 13.8 Gly later  
> **username_4**: @MichaelMcgarry That's like saying it's very unlikely the air molecules you're breathing happened to be in the right place for you to breathe them. The CMBR is everywhere. We see only a tiny portion of it, the portion that happens to be right here right now.  
> **username_0**: Sorry I thought the CMBR was microwave radiation that traveled in straight lines from a source at the speed of light.  
> **username_4**: @MichaelMcgarry You can think of it as a bunch of particles traveling in straight lines at the speed of light, in all directions from all starting points. Some had the right starting point and direction to reach us now.  

---

