You are the center of the universe

People have been asking me: “If the Big Bang began at a some point in space, then what–”

Hold it!  The Big Bang did not begin at any point in space.  The Big Bang is everywhere, it has no center.  The standard analogy is that space is like the surface of an expanding balloon, and as you can see a balloon has no center on its surface.

big bang balloonImage from “Misconceptions About the Big Bang“, which incidentally is a really good article.

People find this confusing though, since balloons do have centers (not on their surface).  Scientists also say that the universe as we know it used to be the size of a grapefruit.  Doesn’t a grapefruit have a center?  Well you got me there.  So where’s the center of the universe?

The answer is that you are the center of the universe.  I’m not referring to “you” in the abstract, I mean the literal person that is currently reading this.  You are the center of the universe.

I will drop the balloon analogy and just draw some diagrams.  Let’s say that each colored square is a galaxy.  Your galaxy is the grapefruit-colored square, the one with a circle around it.  The circle represents the universe as you know it.  Successive diagrams show how the universe looks as time moves forward.

expansion 2Please credit me if you use my images.

At first, the universe is small, and galaxies are closely packed.  Then galaxies start to move away from you, and the universe gets bigger.  At all points in time, you are at the center of the universe.

I know what you’re about to say.  You’re about to say, “But you’re assuming I’m human!  I’m actually a space alien in a galaxy far away, and I’m reading this from radio signals transmitted from planet Earth a long time ago.  I don’t live on the grapefruit-colored galaxy in the center of the universe, I live on the avocado-colored galaxy at the edge of it!”

To that I say, you’re right.  I’m going to have to change my story.  Here it is.

You are the center of the universe.  I’m not referring to “you” in the abstract, I mean the literal space alien that is currently reading this.  You are the center of the universe.

Let’s say that each colored square is a galaxy.  Your galaxy is the avocado-colored square, the one with a circle around it.  The circle represents the universe as you know it.  Successive diagrams show how the universe looks as time moves forward.

The next question you might ask is, how come I drew so many squares outside the universe?  Ah, the circle doesn’t represent the entire universe, it just represents the universe as you know it.*  The universe as you know it is limited by the speed of light and finite age of the universe.  It could be that the galaxies we see are the only ones that exist.  But probably the galaxies go on and on beyond our vision.  Possibly they go on forever.  We don’t really know.

*I’m referring to the universe as you currently know it.  The universe as you will know it in the future will be bigger, not just because the universe is expanding, but also because light will have had more time to travel.

Given that the universe as we know it is limited by our own vision, it is not surprising that we are at the center.  All that really says is that we can see equally far in all directions.

Based on what we can see, all far away galaxies are receding away from us.  But the motion is such that everyone, even space aliens, will see the same.  The space aliens on the avocado-colored galaxy will also find that they are the center of the universe as they know it, and will also find that all far away galaxies are receding away from them.  They will conclude that at one time, their universe was as small as an avocado, and they were at the center.

The Big Bang has no special center point.  If you define the center as the point from which every galaxy is receding, then every point in the known universe is a center of the Big Bang.

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7 thoughts on “You are the center of the universe

  1. The Barefoot Bum January 12, 2016 / 2:13 am

    I’ve noted in many descriptions of GR, including the one you mention here, that the curvature of space does not require any extra dimensions to be curved in. IIRC, Kip Thorne mentions the same sort of thing when talking about wormholes.

    Would it be possible for you to explain in more detail (with math if necessary)?

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  2. Siggy January 12, 2016 / 9:10 am

    @Barefoot Bum,

    In differential geometry and GR, any curved space can be described with a few flat maps, some information about how the maps are connected, and some parameters describing the curvature at every point in the maps. It’s possible that the curved space can be realized with as a surface “embedded” within a higher-dimensional space, but embedding is a separate process. In general, embedding is very difficult, and does not lead to a unique solution. I’m not even sure if it’s proven that an embedding always exists.

    GR equations do not describe the motion of a surface embedded in a higher-dimensional space; instead they describe the motion of the parameters describing curvature. There is no particular reason to think the universe is embedded within a higher dimensional space, so we skip that step.

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  3. The Barefoot Bum January 12, 2016 / 9:26 am

    Thanks. Would it be possible to go into more detail on the math?

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  4. Siggy January 12, 2016 / 11:06 am

    I can comment on some of the parameters that are important to a curved space.

    There’s the metric tensor, which describes the sense of “distance” within the space. And there are the Christoffel symbols, which describe the sense of “parallel”. If you have a vector, say the velocity of some object, that vector is attached to a particular point in space (the location of that object). As the object moves, we need to transport that velocity vector while keeping it “parallel” to what it was originally (this procedure is called “parallel transport”). But the concept of parallel is not well defined in a curved space, and we need Christoffel symbols to describe it. In general, the result of parallel transport depends on the path of transportation.

    When you describe a general curved space, you simply define one or more maps, and define the Christoffel symbols and metric tensor at every point on those maps. There are some constraints on these parameters, but for the most part they can be chosen freely. But when you embed the curved space within a higher-dimensional space, the Christoffel symbols and metric tensor are determined by the shape of the embedding, rather than being defined freely. Given an embedded surface, it’s easy to calculate the metric tensor and Christoffel symbols, but given a set of metric tensors and Christoffel symbols, it’s difficult to find an embedded surface that reproduces them exactly.

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  5. The Barefoot Bum January 12, 2016 / 12:17 pm

    Interesting. This makes a little bit of sense. Does this apply to wormholes too?

    In general, the result of parallel transport depends on the path of transportation.

    Greg Egan talks about this concept in Schild’s Ladder.

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  6. Siggy January 12, 2016 / 1:34 pm

    I am not very familiar with wormholes. There’s a major difference between wormholes and curvature–curvature is a local property of space, while wormholes are nonlocal properties. As I said, a space can be described by one or more maps, as well as information about how the maps connect. A wormhole will never appear in any single map, but instead is a property of how the maps connect.

    I think GR places some constraints on the nonlocal properties of space, but I have a poor understanding of what those constraints are. When physicists talk about the possibility of wormholes, I strongly suspect that they’re saying wormholes are allowed, not that they’re required.

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